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-
+
-
-
+
+
-
+
<h2 class="titleHead">Vorbis I specification</h2>
<div class="author" ><span
-class="cmr-12x-x-120">Xiph.org Foundation</span></div>
+class="cmr-17">Xiph.org Foundation</span></div>
<br />
<div class="date" ><span
-class="cmr-12x-x-120">April 7, 2009</span></div>
+class="cmr-17">June 2, 2009</span></div>
</div>
<h3 class="likesectionHead"><a
id="x1-1000"></a>Contents</h3>
href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
<br />   <span class="subsubsectionToc" >1.2.2 <a
href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
+
+
+
<br />   <span class="subsubsectionToc" >1.2.3 <a
href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
<br />   <span class="subsubsectionToc" >1.2.4 <a
href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
<br />   <span class="subsubsectionToc" >1.2.6 <a
href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
-
-
-
<br />  <span class="subsectionToc" >1.3 <a
href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
<br />   <span class="subsubsectionToc" >1.3.1 <a
href="#x1-610004.2.1" id="QQ2-1-66">Common header decode</a></span>
<br />   <span class="subsubsectionToc" >4.2.2 <a
href="#x1-620004.2.2" id="QQ2-1-67">Identification header</a></span>
+
+
+
<br />   <span class="subsubsectionToc" >4.2.3 <a
href="#x1-630004.2.3" id="QQ2-1-68">Comment header</a></span>
<br />   <span class="subsubsectionToc" >4.2.4 <a
href="#x1-730004.3.2" id="QQ2-1-79">floor curve decode</a></span>
<br />   <span class="subsubsectionToc" >4.3.3 <a
href="#x1-740004.3.3" id="QQ2-1-80">nonzero vector propagate</a></span>
-
-
-
<br />   <span class="subsubsectionToc" >4.3.4 <a
href="#x1-750004.3.4" id="QQ2-1-81">residue decode</a></span>
<br />   <span class="subsubsectionToc" >4.3.5 <a
href="#x1-980007.2.1" id="QQ2-1-104">model</a></span>
<br />   <span class="subsubsectionToc" >7.2.2 <a
href="#x1-990007.2.2" id="QQ2-1-109">header decode</a></span>
+
+
+
<br /> <span class="sectionToc" >8 <a
href="#x1-1020008" id="QQ2-1-112">Residue setup and decode</a></span>
<br />  <span class="subsectionToc" >8.1 <a
href="#x1-1080008.6" id="QQ2-1-120">Residue decode</a></span>
<br />   <span class="subsubsectionToc" >8.6.1 <a
href="#x1-1090008.6.1" id="QQ2-1-121">header decode</a></span>
-
-
-
<br />   <span class="subsubsectionToc" >8.6.2 <a
href="#x1-1100008.6.2" id="QQ2-1-122">packet decode</a></span>
<br />   <span class="subsubsectionToc" >8.6.3 <a
href="#x1-129000A.1.2" id="QQ2-1-141">MIME type</a></span>
<br />  <span class="subsectionToc" >A.2 <a
href="#x1-130000A.2" id="QQ2-1-142">Encapsulation</a></span>
+
+
+
<br /> <span class="sectionToc" >B <a
href="#x1-132000B" id="QQ2-1-144">Vorbis encapsulation in RTP</a></span>
</div>
-
+
-
-<h3 class="sectionHead"><span class="titlemark">1 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">1
</span> <a
id="x1-20001"></a>Introduction and Description</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">1.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">1.1
</span> <a
id="x1-30001.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
specification appears beginning in <a
sections assume a high-level understanding of the Vorbis decode process, which is provided
here.
<!--l. 15--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.1
</span> <a
id="x1-40001.1.1"></a>Application</h5>
<!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
-flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At the
-high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same league as
-MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT rate stereo at
-below 48kbps without resampling to a lower rate. Vorbis is also intended for lower and higher
-sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
-representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255 discrete
-channels).
+flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At
+the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same
+league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT
+rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower
+and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
+representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
+discrete channels).
<!--l. 29--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.2
</span> <a
id="x1-50001.1.2"></a>Classification</h5>
-<!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete Cosine
-Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in Vorbis II to
-offer better transient response and reproduction using a transform better suited to localized time
-events.
+<!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete
+Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in
+Vorbis II to offer better transient response and reproduction using a transform better suited to
+localized time events.
+
+
+
<!--l. 37--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.3
</span> <a
id="x1-60001.1.3"></a>Assumptions</h5>
-
-
-
<!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
-require more working memory as Vorbis has no static probability model; the vector codebooks used
-in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
-bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent
-to which they are pre-decoded into a cache is the dominant factor in decoder memory
+require more working memory as Vorbis has no static probability model; the vector codebooks
+used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
+bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to
+which they are pre-decoded into a cache is the dominant factor in decoder memory
usage.
-<!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it is solely a
-method of accepting input audio, dividing it into individual frames and compressing these frames
-into raw, unformatted ’packets’. The decoder then accepts these raw packets in sequence, decodes
-them, synthesizes audio frames from them, and reassembles the frames into a facsimile of the
-original audio stream. Vorbis is a free-form variable bit rate (VBR) codec and packets have no
-minimum size, maximum size, or fixed/expected size. Packets are designed that they may be
-truncated (or padded) and remain decodable; this is not to be considered an error condition and is
-used extensively in bitrate management in peeling. Both the transport mechanism and
+<!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it
+is solely a method of accepting input audio, dividing it into individual frames and
+compressing these frames into raw, unformatted ’packets’. The decoder then accepts
+these raw packets in sequence, decodes them, synthesizes audio frames from them, and
+reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form
+variable bit rate (VBR) codec and packets have no minimum size, maximum size, or
+fixed/expected size. Packets are designed that they may be truncated (or padded)
+and remain decodable; this is not to be considered an error condition and is used
+extensively in bitrate management in peeling. Both the transport mechanism and
decoder must allow that a packet may be any size, or end before or after packet decode
expects.
<!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
-framing, sync, positioning and error correction in accordance with these design assumptions, such as
-Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
+framing, sync, positioning and error correction in accordance with these design assumptions, such
+as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
although this is by no means a requirement or fundamental assumption in the Vorbis
design.
<!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
-href="#x1-126000A">Section A<!--tex4ht:ref: vorbis:over:ogg --></a>, “<a
-href="#x1-126000A">Embedding
-Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
+href="#x1-126000A">Section A<!--tex4ht:ref: vorbis:over:ogg --></a>,
+“<a
+href="#x1-126000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
<!--l. 77--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.4
</span> <a
id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
<!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
decades of continuous encoder improvement before running out of room within the codec
specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
extreme of forward adaptive.
-<!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis developer
-to keep in mind) is that the entire probability model of the codec, the Huffman and
+
+
+
+<!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis
+developer to keep in mind) is that the entire probability model of the codec, the Huffman and
VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
parameters (often several hundred fields). This makes it impossible, as it would be with
MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
decode at any frame in the stream without having previously fetched the codec setup
header.
-
-
-
<!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a
id="x1-80001.1.4"></a><span
-class="cmbx-10x-x-109">Note:</span></span> Vorbis <span
-class="cmti-10x-x-109">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
+class="cmbx-12">Note:</span></span> Vorbis <span
+class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
has been initialized/setup with the setup headers.
-<!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream headers
-go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less is
-recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
-<!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is an
-unusual design and thus causes some amount of complaint among engineers as this runs against
-current design trends (and also points out limitations in some existing software/interface designs,
-such as Windows’ ACM codec framework). However, we find that it does not fundamentally limit
-Vorbis’ suitable application space.
+<!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream
+headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less
+is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
+<!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is
+an unusual design and thus causes some amount of complaint among engineers as this runs
+against current design trends (and also points out limitations in some existing software/interface
+designs, such as Windows’ ACM codec framework). However, we find that it does not
+fundamentally limit Vorbis’ suitable application space.
<!--l. 115--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.5
</span> <a
id="x1-90001.1.5"></a>Format Specification</h5>
-<!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces
-packets that are correctly decoded by the reference Vorbis decoder described below may be
-considered a proper Vorbis encoder. A decoder must faithfully and completely implement
-the specification defined below (except where noted) to be considered a proper Vorbis
+<!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets
+that are correctly decoded by the reference Vorbis decoder described below may be considered
+a proper Vorbis encoder. A decoder must faithfully and completely implement the
+specification defined below (except where noted) to be considered a proper Vorbis
decoder.
<!--l. 123--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.1.6 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.1.6
</span> <a
id="x1-100001.1.6"></a>Hardware Profile</h5>
+
+
+
<!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
-embedded design. For this reason, embedded designs are allowed to deviate in limited ways from the
-‘full’ decode specification yet still be certified compliant. These optional omissions are labelled in
-the spec where relevant.
+embedded design. For this reason, embedded designs are allowed to deviate in limited ways from
+the ‘full’ decode specification yet still be certified compliant. These optional omissions are
+labelled in the spec where relevant.
<!--l. 131--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">1.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">1.2
</span> <a
id="x1-110001.2"></a>Decoder Configuration</h4>
<!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
perform specific functions in the decode pipeline. Each different component instance of a specific
type is semantically interchangeable; decoder configuration consists both of internal component
configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
-
-
-
arrangement is roughly as follows:
<div class="center"
>
class="content">decoder pipeline configuration</td></tr></table><!--tex4ht:label?: x1-110011 -->
</div>
<!--l. 146--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.1
</span> <a
id="x1-120001.2.1"></a>Global Config</h5>
<!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
configuration is in the context of specific components.
<!--l. 152--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.2
</span> <a
id="x1-130001.2.2"></a>Mode</h5>
+
+
+
<!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
modes.
<!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
modes are, e.g. how frame size is changed from frame to frame. The mode number of a
frame serves as a top level configuration switch for all other specific aspects of frame
decode.
-<!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis window,
-in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping number. The
-mapping number specifies which mapping configuration instance to use for low-level packet decode
-and synthesis.
+<!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis
+window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping
+number. The mapping number specifies which mapping configuration instance to use for low-level
+packet decode and synthesis.
<!--l. 171--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.3
</span> <a
id="x1-140001.2.3"></a>Mapping</h5>
-
-
-
-<!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle
-sets of channel vectors together for grouped encoding and decoding. These submaps
-are not references to external components; the submap list is internal and specific to a
+<!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets
+of channel vectors together for grouped encoding and decoding. These submaps are
+not references to external components; the submap list is internal and specific to a
mapping.
-<!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors within a
-mapping. The submap functions as a last layer of indirection such that specific special floor or
-residue settings can be applied not only to all the vectors in a given mode, but also
+<!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors
+within a mapping. The submap functions as a last layer of indirection such that specific special
+floor or residue settings can be applied not only to all the vectors in a given mode, but also
specific vectors in a specific mode. Each submap specifies the proper floor and residue
instance number to use for decoding that submap’s spectral floor and spectral residue
vectors.
<!--l. 186--><p class="noindent" >As an example:
-<!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth channel, as
-is normal in 5.1, is bass only. Therefore it would be wasteful to encode a full-spectrum version of it
-as with the other channels. The submapping mechanism can be used to apply a full range floor and
-residue encoding to channels 0 through 4, and a bass-only representation to the bass channel,
-thus saving space. In this example, channels 0-4 belong to submap 0 (which indicates
-use of a full-range floor) and channel 5 belongs to submap 1, which uses a bass-only
-representation.
+<!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth
+channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a
+full-spectrum version of it as with the other channels. The submapping mechanism can be used
+to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only
+representation to the bass channel, thus saving space. In this example, channels 0-4 belong to
+submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which
+uses a bass-only representation.
+
+
+
<!--l. 199--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.4
</span> <a
id="x1-150001.2.4"></a>Floor</h5>
<!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
-representation of the audio spectrum for the given channel in the current frame, generally used akin
-to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has historically
-used it as a unit-baseline for spectral resolution.
+representation of the audio spectrum for the given channel in the current frame, generally used
+akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has
+historically used it as a unit-baseline for spectral resolution.
<!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
-are semantically interchangeable in encoding/decoding. However, floor type 1 provides
-more stable inter-frame behavior, and so is the preferred choice in all coupled-stereo
-and high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
+are semantically interchangeable in encoding/decoding. However, floor type 1 provides more
+stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and
+high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
0.
<!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
encoder past Xiph.org’s own beta 4 makes use of floor 0.
-<!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of
-entropy coding to save space. For this reason, a floor configuration generally refers to
-multiple codebooks in the codebook component list. Entropy coding is thus provided as an
+<!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy
+coding to save space. For this reason, a floor configuration generally refers to multiple
+codebooks in the codebook component list. Entropy coding is thus provided as an
abstraction, and each floor instance may choose from any and all available codebooks when
coding/decoding.
-
-
-
<!--l. 230--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.5
</span> <a
id="x1-160001.2.5"></a>Residue</h5>
-<!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve
-has been subtracted out. In simplest terms, it is coded in the bitstream using cascaded
-(multi-pass) vector quantization according to one of three specific packing/coding algorithms
-numbered 0 through 2. The packing algorithm details are configured by residue instance.
-As with the floor components, the final VQ/entropy encoding is provided by external
+<!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been
+subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector
+quantization according to one of three specific packing/coding algorithms numbered
+0 through 2. The packing algorithm details are configured by residue instance. As
+with the floor components, the final VQ/entropy encoding is provided by external
codebook instances and each residue instance may choose from any and all available
codebooks.
<!--l. 241--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.2.6 </span> <a
+
+
+
+<h5 class="subsubsectionHead"><span class="titlemark">1.2.6 </span> <a
id="x1-170001.2.6"></a>Codebooks</h5>
-<!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use the
-entropy-decoded integer value as an offset into an index of output value vectors, returning the
-indicated vector of values.
+<!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use
+the entropy-decoded integer value as an offset into an index of output value vectors, returning
+the indicated vector of values.
<!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
representation. This tree is tightly packed using one of several methods, depending on whether
codeword lengths are ordered or unordered, or the tree is sparse.
<!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
-the vector index is encoded as a single list of values of possible values that are then permuted into a
-list of n-dimensional rows (lattice VQ).
+the vector index is encoded as a single list of values of possible values that are then permuted
+into a list of n-dimensional rows (lattice VQ).
<!--l. 260--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">1.3 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">1.3
</span> <a
id="x1-180001.3"></a>High-level Decode Process</h4>
<!--l. 262--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.3.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.3.1
</span> <a
id="x1-190001.3.1"></a>Decode Setup</h5>
<!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
-stream to be decoded. Vorbis uses three header packets; all are required, in-order, by this
-
-
-
-specification. Once set up, decode may begin at any audio packet belonging to the Vorbis stream. In
-Vorbis I, all packets after the three initial headers are audio packets.
+stream to be decoded. Vorbis uses three header packets; all are required, in-order, by
+this specification. Once set up, decode may begin at any audio packet belonging to
+the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio
+packets.
<!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
header.
<!--l. 274--><p class="noindent" ><span class="paragraphHead"><a
id="x1-200001.3.1"></a><span
-class="cmbx-10x-x-109">Identification Header</span></span>
+class="cmbx-12">Identification Header</span></span>
The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
characteristics of the stream such as sample rate and number of channels.
+
+
+
<!--l. 279--><p class="noindent" ><span class="paragraphHead"><a
id="x1-210001.3.1"></a><span
-class="cmbx-10x-x-109">Comment Header</span></span>
+class="cmbx-12">Comment Header</span></span>
The comment header includes user text comments (“tags”) and a vendor string for the
application/library that produced the bitstream. The encoding and proper use of the comment
header is described in <a
href="#x1-810005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
<!--l. 284--><p class="noindent" ><span class="paragraphHead"><a
id="x1-220001.3.1"></a><span
-class="cmbx-10x-x-109">Setup Header</span></span>
+class="cmbx-12">Setup Header</span></span>
The setup header includes extensive CODEC setup information as well as the complete VQ and
Huffman codebooks needed for decode.
<!--l. 289--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">1.3.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">1.3.2
</span> <a
id="x1-230001.3.2"></a>Decode Procedure</h5>
<!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
- <ol class="enumerate1" >
- <li
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-23002x1">decode packet type flag
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23004x2">decode mode number
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23006x3">decode window shape (long windows only)
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23008x4">decode floor
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23010x5">decode residue into residue vectors
-
-
-
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23012x6">inverse channel coupling of residue vectors
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23014x7">generate floor curve from decoded floor data
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23016x8">compute dot product of floor and residue, producing audio spectrum vector
- </li>
- <li
- class="enumerate" id="x1-23018x9">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis I
- </li>
- <li
+ </li>
+ <li
+ class="enumerate" id="x1-23018x9">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis
+ I
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-23020x10">overlap/add left-hand output of transform with right-hand output of previous frame
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23022x11">store right hand-data from transform of current frame for future lapping
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-23024x12">if not first frame, return results of overlap/add as audio result of current frame</li></ol>
-<!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can take
-advantage of symmetries in the MDCT to store the right-hand transform data of a partial MDCT
-for a 50% inter-frame buffer space savings, and then complete the transform later before
+<!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can
+take advantage of symmetries in the MDCT to store the right-hand transform data of a partial
+MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before
overlap/add with the next frame. This optimization produces entirely equivalent output and is
naturally perfectly legal. The decoder must be <span
-class="cmti-10x-x-109">entirely mathematically equivalent </span>to the
+class="cmti-12">entirely mathematically equivalent </span>to the
specification, it need not be a literal semantic implementation.
<!--l. 317--><p class="noindent" ><span class="paragraphHead"><a
id="x1-240001.3.2"></a><span
-class="cmbx-10x-x-109">Packet type decode</span></span>
-Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis headers
-described above. The fourth packet type marks an audio packet. All other packet types are reserved;
-packets marked with a reserved type should be ignored.
+class="cmbx-12">Packet type decode</span></span>
+Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis
+headers described above. The fourth packet type marks an audio packet. All other packet types
+are reserved; packets marked with a reserved type should be ignored.
<!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
audio packet decode is to read and verify the packet type; <span
-class="cmti-10x-x-109">a non-audio packet when audio is</span>
+class="cmti-12">a non-audio packet when audio is</span>
<span
-class="cmti-10x-x-109">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the packet</span>
+class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
<span
-class="cmti-10x-x-109">and not attempt decoding it to audio</span>.
+class="cmti-12">packet and not attempt decoding it to audio</span>.
<!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
id="x1-250001.3.2"></a><span
-class="cmbx-10x-x-109">Mode decode</span></span>
+class="cmbx-12">Mode decode</span></span>
Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
offset into the mode instance index.
-
-
-
<!--l. 341--><p class="noindent" ><span class="paragraphHead"><a
id="x1-260001.3.2"></a><span
-class="cmbx-10x-x-109">Window shape decode (long windows only)</span></span>
-Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis
-I, legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling,
-Vorbis handles channels as independent vectors and these frame sizes are in samples per
+class="cmbx-12">Window shape decode (long windows only)</span></span>
+Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I,
+legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis
+handles channels as independent vectors and these frame sizes are in samples per
channel.
+
+
+
<!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
according to MDCT requirements, overlapped 50% with the output of the previous frame and
class="content">overlap of a long and a short window</td></tr></table><!--tex4ht:label?: x1-260023 -->
</div>
<!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
-seamless lapping as above. It is possible to correctly infer window shape to be applied to the current
-window from knowing the sizes of the current, previous and next window. It is legal for a decoder to
-use this method. However, in the case of a long window (short windows require no modification),
-Vorbis also codes two flag bits to specify pre- and post- window shape. Although not strictly
-necessary for function, this minor redundancy allows a packet to be fully decoded to the
-point of lapping entirely independently of any other packet, allowing easier abstraction
-of decode layers as well as allowing a greater level of easy parallelism in encode and
+seamless lapping as above. It is possible to correctly infer window shape to be applied to the
+current window from knowing the sizes of the current, previous and next window. It is legal for a
+decoder to use this method. However, in the case of a long window (short windows require no
+modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although
+not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to
+the point of lapping entirely independently of any other packet, allowing easier abstraction of
+decode layers as well as allowing a greater level of easy parallelism in encode and
decode.
<!--l. 382--><p class="noindent" >A description of valid window functions for use with an inverse MDCT can be found in <span class="cite">[<a
-href="#XSporer/Brandenburg/Edler">1</a>]</span>. Vorbis
-windows all use the slope function
+href="#XSporer/Brandenburg/Edler">1</a>]</span>.
+Vorbis windows all use the slope function
<center class="math-display" >
<img
-src="Vorbis_I_spec0x.png" alt="y = sin (.5* π sin2((x + .5)∕n *π )).
+src="Vorbis_I_spec0x.png" alt="y = sin (.5 * π sin2((x + .5)∕n * π)).
+
+
+
" class="math-display" ></center>
<!--l. 385--><p class="nopar" >
<!--l. 389--><p class="noindent" ><span class="paragraphHead"><a
id="x1-270001.3.2"></a><span
-class="cmbx-10x-x-109">floor decode</span></span>
+class="cmbx-12">floor decode</span></span>
Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
specifies which floor configuration to use. All floors are decoded before residue decode
begins.
<!--l. 395--><p class="noindent" ><span class="paragraphHead"><a
id="x1-280001.3.2"></a><span
-class="cmbx-10x-x-109">residue decode</span></span>
-Although the number of residue vectors equals the number of channels, channel coupling may mean
-that the raw residue vectors extracted during decode do not map directly to specific channels. When
-channel coupling is in use, some vectors will correspond to coupled magnitude or angle. The
-coupling relationships are described in the codec setup and may differ from frame to frame, due to
-different mode numbers.
-<!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from submap
-0 through n-1. This differs from floors which are coded using a configuration provided by submap
-number, but are coded individually in channel order.
+class="cmbx-12">residue decode</span></span>
+Although the number of residue vectors equals the number of channels, channel coupling may
+mean that the raw residue vectors extracted during decode do not map directly to specific
+channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or
+angle. The coupling relationships are described in the codec setup and may differ from frame to
+frame, due to different mode numbers.
+<!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from
+submap 0 through n-1. This differs from floors which are coded using a configuration provided by
+submap number, but are coded individually in channel order.
<!--l. 411--><p class="noindent" ><span class="paragraphHead"><a
id="x1-290001.3.2"></a><span
-class="cmbx-10x-x-109">inverse channel coupling</span></span>
-A detailed discussion of stereo in the Vorbis codec can be found in the document <a
-href="stereo.html" >Stereo Channel
-Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo coupling, but the stereo
-document also gives a good overview of the generic coupling mechanism.
-<!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place
-a pair at a time in the order and using the vectors specified in the current mapping
+class="cmbx-12">inverse channel coupling</span></span>
+A detailed discussion of stereo in the Vorbis codec can be found in the document
+<a
+href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo
+coupling, but the stereo document also gives a good overview of the generic coupling
+mechanism.
+<!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a
+pair at a time in the order and using the vectors specified in the current mapping
configuration. The decoupling operation is the same for all pairs, converting square polar
representation (where one vector is magnitude and the second angle) back to Cartesian
representation.
<!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
represent the fine spectral detail of each output channel.
+
+
+
<!--l. 432--><p class="noindent" ><span class="paragraphHead"><a
id="x1-300001.3.2"></a><span
-class="cmbx-10x-x-109">generate floor curve</span></span>
-
-
-
-The decoder may choose to generate the floor curve at any appropriate time. It is reasonable
-to generate the output curve when the floor data is decoded from the raw packet, or
-it can be generated after inverse coupling and applied to the spectral residue directly,
+class="cmbx-12">generate floor curve</span></span>
+The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to
+generate the output curve when the floor data is decoded from the raw packet, or it
+can be generated after inverse coupling and applied to the spectral residue directly,
combining generation and the dot product into one step and eliminating some working
space.
-<!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied (dot
-product) by the linear-range, linear-domain spectral residue.
+<!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied
+(dot product) by the linear-range, linear-domain spectral residue.
<!--l. 447--><p class="noindent" ><span class="paragraphHead"><a
id="x1-310001.3.2"></a><span
-class="cmbx-10x-x-109">compute floor/residue dot product</span></span>
-This step is straightforward; for each output channel, the decoder multiplies the floor curve
-and residue vectors element by element, producing the finished audio spectrum of each
+class="cmbx-12">compute floor/residue dot product</span></span>
+This step is straightforward; for each output channel, the decoder multiplies the floor curve and
+residue vectors element by element, producing the finished audio spectrum of each
channel.
<!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
-implementation might be to assume that a 32 bit fixed-point representation for floor
-and residue and direct multiplication of the vectors is sufficient for acceptable spectral
-depth in all cases because it happens to mostly work with the current Xiph.Org reference
+implementation might be to assume that a 32 bit fixed-point representation for floor and
+residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
+in all cases because it happens to mostly work with the current Xiph.Org reference
encoder.
<!--l. 462--><p class="noindent" >However, floor vector values can span <span
-class="cmsy-10x-x-109">~</span>140dB (<span
-class="cmsy-10x-x-109">~</span>24 bits unsigned), and the audio spectrum vector
-should represent a minimum of 120dB (<span
-class="cmsy-10x-x-109">~</span>21 bits with sign), even when output is to a 16 bit PCM
-device. For the residue vector to represent full scale if the floor is nailed to <span
-class="cmsy-10x-x-109">-</span>140dB, it must be able
-to span 0 to +140dB. For the residue vector to reach full scale if the floor is nailed at 0dB, it must
-be able to represent <span
-class="cmsy-10x-x-109">-</span>140dB to +0dB. Thus, in order to handle full range dynamics, a residue
-vector may span <span
-class="cmsy-10x-x-109">-</span>140dB to +140dB entirely within spec. A 280dB range is approximately 48 bits
-with sign; thus the residue vector must be able to represent a 48 bit range and the dot product
-must be able to handle an effective 48 bit times 24 bit multiplication. This range may be
+class="cmsy-10x-x-120">~</span>140dB (<span
+class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum
+vector should represent a minimum of 120dB (<span
+class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16
+bit PCM device. For the residue vector to represent full scale if the floor is nailed
+to <span
+class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
+full scale if the floor is nailed at 0dB, it must be able to represent <span
+class="cmsy-10x-x-120">-</span>140dB to +0dB.
+Thus, in order to handle full range dynamics, a residue vector may span <span
+class="cmsy-10x-x-120">-</span>140dB to
++140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
+residue vector must be able to represent a 48 bit range and the dot product must
+be able to handle an effective 48 bit times 24 bit multiplication. This range may be
achieved using large (64 bit or larger) integers, or implementing a movable binary point
representation.
<!--l. 479--><p class="noindent" ><span class="paragraphHead"><a
id="x1-320001.3.2"></a><span
-class="cmbx-10x-x-109">inverse monolithic transform (MDCT)</span></span>
+class="cmbx-12">inverse monolithic transform (MDCT)</span></span>
The audio spectrum is converted back into time domain PCM audio via an inverse Modified
Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
<span class="cite">[<a
href="#XSporer/Brandenburg/Edler">1</a>]</span>.
-<!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be lapped
-with surrounding frames using an appropriate window (such as the Vorbis window) before the
-MDCT can be considered orthogonal.
-
+<!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be
+
-
+
+lapped with surrounding frames using an appropriate window (such as the Vorbis window) before
+the MDCT can be considered orthogonal.
<!--l. 492--><p class="noindent" ><span class="paragraphHead"><a
id="x1-330001.3.2"></a><span
-class="cmbx-10x-x-109">overlap/add data</span></span>
-Windowed MDCT output is overlapped and added with the right hand data of the previous window
-such that the 3/4 point of the previous window is aligned with the 1/4 point of the current window
-(as illustrated in the window overlap diagram). At this point, the audio data between the center of
-the previous frame and the center of the current frame is now finished and ready to be
-returned.
+class="cmbx-12">overlap/add data</span></span>
+Windowed MDCT output is overlapped and added with the right hand data of the previous
+window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
+current window (as illustrated in the window overlap diagram). At this point, the audio data
+between the center of the previous frame and the center of the current frame is now finished and
+ready to be returned.
<!--l. 501--><p class="noindent" ><span class="paragraphHead"><a
id="x1-340001.3.2"></a><span
-class="cmbx-10x-x-109">cache right hand data</span></span>
-The decoder must cache the right hand portion of the current frame to be lapped with the left hand
-portion of the next frame.
+class="cmbx-12">cache right hand data</span></span>
+The decoder must cache the right hand portion of the current frame to be lapped with the left
+hand portion of the next frame.
<!--l. 507--><p class="noindent" ><span class="paragraphHead"><a
id="x1-350001.3.2"></a><span
-class="cmbx-10x-x-109">return finished audio data</span></span>
-The overlapped portion produced from overlapping the previous and current frame data is finished
-data to be returned by the decoder. This data spans from the center of the previous window to the
-center of the current window. In the case of same-sized windows, the amount of data to return is
-one-half block consisting of and only of the overlapped portions. When overlapping a short and long
-window, much of the returned range is not actually overlap. This does not damage transform
-orthogonality. Pay attention however to returning the correct data range; the amount of data to be
-returned is:
+class="cmbx-12">return finished audio data</span></span>
+The overlapped portion produced from overlapping the previous and current frame data
+is finished data to be returned by the decoder. This data spans from the center of
+the previous window to the center of the current window. In the case of same-sized
+windows, the amount of data to return is one-half block consisting of and only of the
+overlapped portions. When overlapping a short and long window, much of the returned
+range is not actually overlap. This does not damage transform orthogonality. Pay
+attention however to returning the correct data range; the amount of data to be returned
+is:
<!--l. 519--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb1">
<a
id="x1-35002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
</div>
<!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
-<!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The encoder
-accounts for this priming when calculating PCM offsets; after the first frame, the proper PCM
-output offset is ’0’ (as no data has been returned yet).
-
+<!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
+encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
+PCM output offset is ’0’ (as no data has been returned yet).
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">2 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">2
</span> <a
id="x1-360002"></a>Bitpacking Convention</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">2.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">2.1
</span> <a
id="x1-370002.1"></a>Overview</h4>
-<!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary integer
-fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the encoder
-and then read one-by-one in the same monotonically increasing order by the decoder. Most current
-binary storage arrangements group bits into a native word size of eight bits (octets), sixteen bits,
-thirty-two bits or, less commonly other fixed word sizes. The Vorbis bitpacking convention specifies
-the correct mapping of the logical packet bitstream into an actual representation in fixed-width
-words.
+<!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
+integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
+encoder and then read one-by-one in the same monotonically increasing order by the decoder.
+Most current binary storage arrangements group bits into a native word size of eight bits
+(octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
+bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
+representation in fixed-width words.
<!--l. 19--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.1
</span> <a
id="x1-380002.1.1"></a>octets, bytes and words</h5>
-<!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits. This
-has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
+<!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
+This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
For purposes of the bitpacking convention, a byte implies the native, smallest integer
storage representation offered by a platform. On modern platforms, this is generally
assumed to be eight bits (not necessarily because of the processor but because of the
filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
size.
-<!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word to
-be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis bitpacking
-convention is still well defined for any native byte size; Vorbis uses the native bit-width of a
-given storage system. This document assumes that a byte is one octet for purposes of
-example.
+<!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
+to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
+bitpacking convention is still well defined for any native byte size; Vorbis uses the native
+bit-width of a given storage system. This document assumes that a byte is one octet for purposes
+of example.
<!--l. 39--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.2 </span> <a
+
+
+
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.2 </span> <a
id="x1-390002.1.2"></a>bit order</h5>
<!--l. 41--><p class="noindent" >A byte has a well-defined ’least significant’ bit (LSb), which is the only bit set when the byte is
storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
-
-
-
opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
-class="cmmi-10x-x-109">n </span>(<span
-class="cmmi-10x-x-109">n </span>= 7 in an octet)
-for the MSb.
+class="cmmi-12">n </span>(<span
+class="cmmi-12">n </span>= 7 in an
+octet) for the MSb.
<!--l. 50--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.3
</span> <a
id="x1-400002.1.3"></a>byte order</h5>
-<!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word;
-the common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
+<!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
+common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
endian’).
performance code that operates on a word of storage at a time rather than by byte.
Logically, bytes are always coded and decoded in order from byte zero through byte
<span
-class="cmmi-10x-x-109">n</span>.
+class="cmmi-12">n</span>.
<!--l. 68--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.4
</span> <a
id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
<!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
wide, into packets. These integer fields are not aligned to the boundaries of the byte
representation; the next field is written at the bit position at which the previous field
ends.
-<!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical bitstream
-first, followed by next least significant bit, etc, until the requested number of bits have been coded.
-When packing the bits into bytes, the encoder begins by placing the LSb of the integer to be written
-into the least significant unused bit position of the destination byte, followed by the next-least
-significant bit of the source integer and so on up to the requested number of bits. When all bits of
-the destination byte have been filled, encoding continues by zeroing all bits of the next byte
-and writing the next bit into the bit position 0 of that byte. Decoding follows the same
-process as encoding, but by reading bits from the byte stream and reassembling them into
+<!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
+bitstream first, followed by next least significant bit, etc, until the requested number of bits
+have been coded. When packing the bits into bytes, the encoder begins by placing
+the LSb of the integer to be written into the least significant unused bit position of
+the destination byte, followed by the next-least significant bit of the source integer
+and so on up to the requested number of bits. When all bits of the destination byte
+have been filled, encoding continues by zeroing all bits of the next byte and writing
+the next bit into the bit position 0 of that byte. Decoding follows the same process
+
+
+
+as encoding, but by reading bits from the byte stream and reassembling them into
integers.
<!--l. 90--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.5
</span> <a
id="x1-420002.1.5"></a>signedness</h5>
-
-
-
-<!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder given
-decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
+<!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
+given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
encoder and decoder are responsible for knowing if fields are to be treated as signed or
unsigned.
<!--l. 101--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.6 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.6
</span> <a
id="x1-430002.1.6"></a>coding example</h5>
<!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
<!--l. 106--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb2">
<a
id="x1-43002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> |</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> |</span>
<br class="fancyvrb" /><a
id="x1-43004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> V</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> V</span>
<br class="fancyvrb" /><a
id="x1-43006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-43008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-43010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> <-</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> <-</span>
<br class="fancyvrb" /><a
id="x1-43012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ...</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ...</span>
<br class="fancyvrb" /><a
id="x1-43020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> n</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bytestream</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> byte</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> n</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bytestream</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> byte</span>
<br class="fancyvrb" /><a
id="x1-43022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
<!--l. 123--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb3">
<a
id="x1-43024r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> |</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> |</span>
<br class="fancyvrb" /><a
id="x1-43026r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> V</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> V</span>
<br class="fancyvrb" /><a
id="x1-43028r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-43030r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
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+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> 6</span><span
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+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-43032r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> <-</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> <-</span>
<br class="fancyvrb" /><a
id="x1-43034r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
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-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
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+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-43036r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43038r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43040r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ...</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ...</span>
<br class="fancyvrb" /><a
id="x1-43042r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> n</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bytestream</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> byte</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> n</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bytestream</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> byte</span>
</div>
<!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
<!--l. 139--><p class="noindent" >
-
-
-
<div class="fancyvrb" id="fancyvrb4">
<a
id="x1-43044r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> |</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> |</span>
<br class="fancyvrb" /><a
id="x1-43046r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> V</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> V</span>
<br class="fancyvrb" /><a
id="x1-43048r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-43050r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-43052r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> [1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> [1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-43054r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> <-</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> <-</span>
<br class="fancyvrb" /><a
id="x1-43056r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43058r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-43060r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ...</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ...</span>
<br class="fancyvrb" /><a
id="x1-43062r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> n</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bytestream</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> bytes</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> n</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bytestream</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> bytes</span>
<br class="fancyvrb" /><a
id="x1-43064r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> cursor</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 6</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> cursor</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 6</span>
</div>
<!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
<!--l. 156--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb5">
<a
id="x1-43066r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> |</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> |</span>
<br class="fancyvrb" /><a
id="x1-43068r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> V</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> V</span>
<br class="fancyvrb" /><a
id="x1-43070r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-43072r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-43074r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> [1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> [1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-43076r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-43078r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> [1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> [1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-43080r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> <-</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> <-</span>
<br class="fancyvrb" /><a
id="x1-43082r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ...</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ...</span>
<br class="fancyvrb" /><a
id="x1-43084r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> n</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bytestream</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bytes</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> n</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bytestream</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bytes</span>
<br class="fancyvrb" /><a
id="x1-43086r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 173--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.7 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.7
</span> <a
id="x1-440002.1.7"></a>decoding example</h5>
<!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
<!--l. 177--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb6">
+
+
+
<a
id="x1-44002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> |</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> |</span>
<br class="fancyvrb" /><a
id="x1-44004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> V</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> V</span>
<br class="fancyvrb" /><a
id="x1-44006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-44008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-44010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> [1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> <-</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> [1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> <-</span>
<br class="fancyvrb" /><a
id="x1-44012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-44014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> [1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> [1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0]</span>
<br class="fancyvrb" /><a
id="x1-44016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> [0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> bytestream</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> ==</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bytes</span>
-
-
-
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> [0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> bytestream</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> ==</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bytes</span>
<br class="fancyvrb" /><a
id="x1-44018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
are worth noting here:
- <ul class="itemize1">
- <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
- some other combination of bit-widths from the bitstream is well defined. There are no
- artificial alignment boundaries maintained in the bitstream.
- </li>
- <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted either
- as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on decode
- context.</li></ul>
+ <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
+ some other combination of bit-widths from the bitstream is well defined. There are
+ no artificial alignment boundaries maintained in the bitstream.
+ </li>
+ <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
+ either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
+ decode context.</li></ul>
<!--l. 208--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.8 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.8
</span> <a
id="x1-450002.1.8"></a>end-of-packet alignment</h5>
<!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
-the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space in
-the last byte of a packet.
+the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
+in the last byte of a packet.
<!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
should this unused space be read, it will return binary zeroes.
<!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
End-of-packet is not to be considered an error; it is merely a state indicating that there is
-insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a normal
-mode of operation, and as such, decoders must handle reading past the end of a packet as a typical
-mode of operation. Any further read operations after an ’end-of-packet’ condition shall also return
-’end-of-packet’.
+insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
+normal mode of operation, and as such, decoders must handle reading past the end of a packet as
+a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
+also return ’end-of-packet’.
+
+
+
<!--l. 233--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">2.1.9 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">2.1.9
</span> <a
id="x1-460002.1.9"></a>reading zero bits</h5>
<!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
-
-
-
end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
shall also fail with ’end-of-packet’.
-
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">3 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">3
</span> <a
id="x1-470003"></a>Probability Model and Codebooks</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">3.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">3.1
</span> <a
id="x1-480003.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
bitstream itself in the third header, the codec setup header. This packed configuration consists of
multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
compressed codewords as well as an optional lookup table of output vector values to which a
-decoded Huffman value is applied as an offset, generating the final decoded output corresponding to
-a given compressed codeword.
+decoded Huffman value is applied as an offset, generating the final decoded output corresponding
+to a given compressed codeword.
<!--l. 18--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">3.1.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">3.1.1
</span> <a
id="x1-490003.1.1"></a>Bitwise operation</h5>
<!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
-and the codewords they decode are unrolled from a packet as a series of arbitrary-width values read
-from the stream according to <a
+and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
+
read from the stream according to <a
href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
<!--l. 27--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">3.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">3.2
</span> <a
id="x1-500003.2"></a>Packed codebook format</h4>
-<!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is eight
-bits. This is not universally true; see <a
+<!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
+
eight bits. This is not universally true; see <a
href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
-href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion relating to
-non-eight-bit bytes.
+href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
+relating to non-eight-bit bytes.
+
+
+
<!--l. 34--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">3.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">3.2.1
</span> <a
id="x1-510003.2.1"></a>codebook decode</h5>
<!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
<!--l. 38--><p class="noindent" >
-
-
-
<div class="fancyvrb" id="fancyvrb7">
<a
id="x1-51002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 0:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> (0x42)</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 0:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> (0x42)</span>
<br class="fancyvrb" /><a
id="x1-51004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 1:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> (0x43)</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 1:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> (0x43)</span>
<br class="fancyvrb" /><a
id="x1-51006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 2:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> (0x56)</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 2:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> (0x56)</span>
</div>
<!--l. 44--><p class="noindent" >16 bit <span
-class="cmtt-10x-x-109">[codebook_dimensions] </span>and 24 bit <span
-class="cmtt-10x-x-109">[codebook_entries] </span>fields:
+class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span
+class="cmtt-12">[codebook_entries] </span>fields:
<!--l. 46--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb8">
<a
id="x1-51008r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51010r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 3:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 3:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-51012r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 4:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> [codebook_dimensions]</span><span
-class="cmtt-10"> (16</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> unsigned)</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 4:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> [codebook_dimensions]</span><span
+class="cmtt-8"> (16</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> unsigned)</span>
<br class="fancyvrb" /><a
id="x1-51014r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51016r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 5:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 5:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-51018r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 6:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 6:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-51020r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 7:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> [codebook_entries]</span><span
-class="cmtt-10"> (24</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> unsigned)</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 7:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> [codebook_entries]</span><span
+class="cmtt-8"> (24</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> unsigned)</span>
<br class="fancyvrb" /><a
id="x1-51022r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 57--><p class="noindent" >Next is the <span
-class="cmtt-10x-x-109">[ordered] </span>bit flag:
+class="cmtt-12">[ordered] </span>bit flag:
<!--l. 59--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb9">
<a
id="x1-51024r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51026r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 8:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> [ordered]</span><span
-class="cmtt-10"> (1</span><span
-class="cmtt-10"> bit)</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 8:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> [ordered]</span><span
+class="cmtt-8"> (1</span><span
+class="cmtt-8"> bit)</span>
<br class="fancyvrb" /><a
id="x1-51028r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
-class="cmtt-10x-x-109">[codebook_entries]</span>, is assigned a codeword length. We now read
-the list of codeword lengths and store these lengths in the array <span
-class="cmtt-10x-x-109">[codebook_codeword_lengths]</span>.
-Decode of lengths is according to whether the <span
-class="cmtt-10x-x-109">[ordered] </span>flag is set or unset.
- <ul class="itemize1">
- <li class="itemize">If the <span
-class="cmtt-10x-x-109">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
- needs to read each codeword length one-by-one.
- <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
-class="cmtt-10x-x-109">[sparse] </span>flag. This flag determines
- whether or not the codebook contains unused entries that are not to be included in the
- codeword decode tree:
- <!--l. 82--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb10">
+class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length.
+We now read the list of codeword lengths and store these lengths in the array
+<span
+class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span
+class="cmtt-12">[ordered] </span>flag
+is set or unset.
+ <ul class="itemize1">
+ <li class="itemize">If the <span
+class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
+ needs to read each codeword length one-by-one.
+ <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
+class="cmtt-12">[sparse] </span>flag. This flag determines
+ whether or not the codebook contains unused entries that are not to be included in
+
+
+
+ the codeword decode tree:
+ <!--l. 82--><p class="noindent" >
+ <div class="fancyvrb" id="fancyvrb10">
<a
id="x1-51030r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> byte</span><span
-class="cmtt-10"> 8:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> X</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ]</span><span
-class="cmtt-10"> [sparse]</span><span
-class="cmtt-10"> flag</span><span
-class="cmtt-10"> (1</span><span
-class="cmtt-10"> bit)</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> byte</span><span
+class="cmtt-8"> 8:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> X</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ]</span><span
+class="cmtt-8"> [sparse]</span><span
+class="cmtt-8"> flag</span><span
+class="cmtt-8"> (1</span><span
+class="cmtt-8"> bit)</span>
</div>
-
-
-
- <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
-class="cmtt-10x-x-109">[codebook_entries] </span>codebook entries:
- <!--l. 89--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb11">
+ <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
+class="cmtt-12">[codebook_entries] </span>codebook entries:
+ <!--l. 89--><p class="noindent" >
+ <div class="fancyvrb" id="fancyvrb11">
<a
id="x1-51032r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51034r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> if([sparse]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set)</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> if([sparse]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set)</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51036r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51038r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [flag]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> one</span><span
-class="cmtt-10"> bit;</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [flag]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> one</span><span
+class="cmtt-8"> bit;</span>
<br class="fancyvrb" /><a
id="x1-51040r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> if([flag]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set)</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> if([flag]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set)</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51042r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51044r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> five</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer;</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> five</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer;</span>
<br class="fancyvrb" /><a
id="x1-51046r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> for</span><span
-class="cmtt-10"> this</span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> [length]+1;</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> for</span><span
+class="cmtt-8"> this</span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> [length]+1;</span>
<br class="fancyvrb" /><a
id="x1-51048r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51050r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51052r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51054r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> this</span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> unused.</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> mark</span><span
-class="cmtt-10"> it</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> such.</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> this</span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> unused.</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> mark</span><span
+class="cmtt-8"> it</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> such.</span>
<br class="fancyvrb" /><a
id="x1-51056r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51058r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-51060r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51062r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> sparse</span><span
-class="cmtt-10"> flag</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> sparse</span><span
+class="cmtt-8"> flag</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51064r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51066r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> five</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer;</span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> five</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer;</span>
<br class="fancyvrb" /><a
id="x1-51068r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> for</span><span
-class="cmtt-10"> this</span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> [length]+1;</span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> for</span><span
+class="cmtt-8"> this</span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> [length]+1;</span>
<br class="fancyvrb" /><a
id="x1-51070r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51072r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-51074r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
- </li>
- <li class="itemize">If the <span
-class="cmtt-10x-x-109">[ordered] </span>flag is set, the codeword list for this codebook is encoded in ascending length
- order. Rather than reading a length for every codeword, the encoder reads the number of
- codewords per length. That is, beginning at entry zero:
- <!--l. 120--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb12">
+ </li>
+ <li class="itemize">If the <span
+class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
+ ascending length order. Rather than reading a length for every codeword, the
+ encoder reads the number of codewords per length. That is, beginning at entry
+ zero:
+ <!--l. 120--><p class="noindent" >
+ <div class="fancyvrb" id="fancyvrb12">
<a
id="x1-51076r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [current_entry]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0;</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [current_entry]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0;</span>
<br class="fancyvrb" /><a
id="x1-51078r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [current_length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> five</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> 1;</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [current_length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> five</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> 1;</span>
<br class="fancyvrb" /><a
id="x1-51080r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [number]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [number]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> </span><a
href="#x1-1170009.2.1"><span
-class="cmtt-10">ilog</span></a><span
-class="cmtt-10">([codebook_entries]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [current_entry])</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmtt-8">ilog</span></a><span
+class="cmtt-8">([codebook_entries]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [current_entry])</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-51082r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> entries</span><span
-class="cmtt-10"> [current_entry]</span><span
-class="cmtt-10"> through</span><span
-class="cmtt-10"> [current_entry]+[number]-1,</span><span
-class="cmtt-10"> inclusive,</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> entries</span><span
+class="cmtt-8"> [current_entry]</span><span
+class="cmtt-8"> through</span><span
+class="cmtt-8"> [current_entry]+[number]-1,</span><span
+class="cmtt-8"> inclusive,</span>
<br class="fancyvrb" /><a
id="x1-51084r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> [codebook_codeword_lengths]</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> [current_length]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> [codebook_codeword_lengths]</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> [current_length]</span>
<br class="fancyvrb" /><a
id="x1-51086r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> [current_entry]</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> [number]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [current_entry]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> [current_entry]</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> [number]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [current_entry]</span>
<br class="fancyvrb" /><a
id="x1-51088r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [current_length]</span><span
-class="cmtt-10"> by</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [current_length]</span><span
+class="cmtt-8"> by</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-51090r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> [current_entry]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [codebook_entries]</span><span
-class="cmtt-10"> ERROR</span><span
-class="cmtt-10"> CONDITION;</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> [current_entry]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [codebook_entries]</span><span
+class="cmtt-8"> ERROR</span><span
+class="cmtt-8"> CONDITION;</span>
<br class="fancyvrb" /><a
id="x1-51092r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> decoder</span><span
-class="cmtt-10"> will</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> be</span><span
-class="cmtt-10"> able</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> this</span><span
-class="cmtt-10"> stream.</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> decoder</span><span
+class="cmtt-8"> will</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> be</span><span
+class="cmtt-8"> able</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> this</span><span
+class="cmtt-8"> stream.</span>
<br class="fancyvrb" /><a
id="x1-51094r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> [current_entry]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [codebook_entries],</span><span
-class="cmtt-10"> repeat</span><span
-class="cmtt-10"> process</span><span
-class="cmtt-10"> starting</span><span
-class="cmtt-10"> at</span><span
-class="cmtt-10"> 3)</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> [current_entry]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [codebook_entries],</span><span
+class="cmtt-8"> repeat</span><span
+class="cmtt-8"> process</span><span
+class="cmtt-8"> starting</span><span
+class="cmtt-8"> at</span><span
+class="cmtt-8"> 3)</span>
<br class="fancyvrb" /><a
id="x1-51096r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> done.</span>
-</div>
- </li></ul>
-
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> done.</span>
+
-
-<!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis I
-supports three lookup types:
- <ol class="enumerate1" >
- <li
+
+</div>
+ </li></ul>
+<!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
+I supports three lookup types:
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-51098x1">No lookup
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-51100x2">Implicitly populated value mapping (lattice VQ)
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-51102x3">Explicitly populated value mapping (tessellated or ’foam’ VQ)</li></ol>
<!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
<div class="fancyvrb" id="fancyvrb13">
<a
id="x1-51104r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [codebook_lookup_type]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> four</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [codebook_lookup_type]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> four</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
</div>
<!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
-class="cmtt-10x-x-109">[codebook_lookup_type]</span>:
- <ul class="itemize1">
- <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
- </li>
- <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values
- to be read. Lookup type one reads a list of values that are permuted in a set pattern
- to build a list of vectors, each vector of order <span
-class="cmtt-10x-x-109">[codebook_dimensions] </span>scalars. Lookup
- type two builds the same vector list, but reads each scalar for each vector explicitly,
- rather than building vectors from a smaller list of possible scalar values. Lookup decode
- proceeds as follows:
- <!--l. 168--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb14">
+class="cmtt-12">[codebook_lookup_type]</span>:
+ <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
+ </li>
+ <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
+ be read. Lookup type one reads a list of values that are permuted in a set pattern to
+ build a list of vectors, each vector of order <span
+class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup
+ type two builds the same vector list, but reads each scalar for each vector explicitly,
+ rather than building vectors from a smaller list of possible scalar values. Lookup
+ decode proceeds as follows:
+
<!--l. 168--><p class="noindent" >
+
<div class="fancyvrb" id="fancyvrb14">
<a
id="x1-51106r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [codebook_minimum_value]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [codebook_minimum_value]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1180009.2.2"><span
-class="cmtt-10">float32_unpack</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer)</span>
+class="cmtt-8">float32_unpack</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer)</span>
<br class="fancyvrb" /><a
id="x1-51108r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [codebook_delta_value]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [codebook_delta_value]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1180009.2.2"><span
-class="cmtt-10">float32_unpack</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer)</span>
+class="cmtt-8">float32_unpack</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer)</span>
<br class="fancyvrb" /><a
id="x1-51110r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [codebook_value_bits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [codebook_value_bits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-51112r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [codebook_sequence_p]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> boolean</span><span
-class="cmtt-10"> flag</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [codebook_sequence_p]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> boolean</span><span
+class="cmtt-8"> flag</span>
<br class="fancyvrb" /><a
id="x1-51114r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51116r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [codebook_lookup_type]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [codebook_lookup_type]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51118r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51120r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [codebook_lookup_values]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [codebook_lookup_values]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1190009.2.3"><span
-class="cmtt-10">lookup1_values</span></a><span
-class="cmtt-10">([codebook_entries],</span><span
-class="cmtt-10"> [codebook_dimensions]</span><span
-class="cmtt-10"> )</span>
+class="cmtt-8">lookup1_values</span></a><span
+class="cmtt-8">([codebook_entries],</span><span
+class="cmtt-8"> [codebook_dimensions]</span><span
+class="cmtt-8"> )</span>
<br class="fancyvrb" /><a
id="x1-51122r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51124r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-51126r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51128r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [codebook_lookup_values]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [codebook_entries]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [codebook_dimensions]</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [codebook_lookup_values]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [codebook_entries]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [codebook_dimensions]</span>
<br class="fancyvrb" /><a
id="x1-51130r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51132r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-51134r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-51136r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> total</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [codebook_lookup_values]</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integers</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [codebook_value_bits]</span><span
-class="cmtt-10"> each;</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> total</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [codebook_lookup_values]</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integers</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [codebook_value_bits]</span><span
+class="cmtt-8"> each;</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-51138r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> store</span><span
-class="cmtt-10"> these</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> order</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [codebook_multiplicands]</span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> store</span><span
+class="cmtt-8"> these</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> order</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [codebook_multiplicands]</span>
</div>
-
-
-
- </li>
- <li class="itemize">A <span
-class="cmtt-10x-x-109">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is not
- decodable by the specification in this document.
- </li></ul>
+ </li>
+ <li class="itemize">A <span
+class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is
+ not decodable by the specification in this document.
+ </li></ul>
<!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
rendering the stream undecodable.
<!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
id="x1-520003.2.1"></a><span
-class="cmbx-10x-x-109">Huffman decision tree representation</span></span>
+class="cmbx-12">Huffman decision tree representation</span></span>
The <span
-class="cmtt-10x-x-109">[codebook_codeword_lengths] </span>array and <span
-class="cmtt-10x-x-109">[codebook_entries] </span>value uniquely define the
+class="cmtt-12">[codebook_codeword_lengths] </span>array and <span
+class="cmtt-12">[codebook_entries] </span>value uniquely define the
Huffman decision tree used for entropy decoding.
-<!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused codeword
-entries) is assigned, in order, the lowest valued unused binary Huffman codeword possible. Assume
-the following codeword length list:
+<!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
+codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
+possible. Assume the following codeword length list:
<!--l. 209--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb15">
<a
id="x1-52002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 0:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 0:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-52004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 1:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 1:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span>
<br class="fancyvrb" /><a
id="x1-52006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 2:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 2:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span>
<br class="fancyvrb" /><a
id="x1-52008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 3:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 3:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span>
<br class="fancyvrb" /><a
id="x1-52010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 4:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 4:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span>
<br class="fancyvrb" /><a
id="x1-52012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 5:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 5:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-52014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 6:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 3</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 6:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 3</span>
<br class="fancyvrb" /><a
id="x1-52016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 7:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 3</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 7:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 3</span>
</div>
-<!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results in
-the following codeword list:
+<!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
+in the following codeword list:
<!--l. 223--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb16">
<a
id="x1-52018r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 0:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 00</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 0:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 00</span>
<br class="fancyvrb" /><a
id="x1-52020r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 1:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 0100</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 1:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 0100</span>
<br class="fancyvrb" /><a
id="x1-52022r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 2:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 0101</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 2:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 0101</span>
<br class="fancyvrb" /><a
id="x1-52024r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 3:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 0110</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 3:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 0110</span>
<br class="fancyvrb" /><a
id="x1-52026r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 4:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 0111</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 4:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 0111</span>
<br class="fancyvrb" /><a
id="x1-52028r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 5:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 10</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 5:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 10</span>
<br class="fancyvrb" /><a
id="x1-52030r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 6:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 110</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 6:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 110</span>
<br class="fancyvrb" /><a
id="x1-52032r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> entry</span><span
-class="cmtt-10"> 7:</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> codeword</span><span
-class="cmtt-10"> 111</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> entry</span><span
+class="cmtt-8"> 7:</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> codeword</span><span
+class="cmtt-8"> 111</span>
</div>
-
+
-
+
<!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
id="x1-530003.2.1"></a><span
-class="cmbx-10x-x-109">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to be
-read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero, one’.
-When determining ’lowest possible value’ in the assignment definition above, the leftmost bit is the
-MSb.
-<!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry numbers
-equivalent to the leaves numbered left-to-right:
+class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
+be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
+one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
+bit is the MSb.
+<!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
+numbers equivalent to the leaves numbered left-to-right:
<div class="center"
>
<!--l. 247--><p class="noindent" >
</div>
<!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
possible position.
-<!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list. In the above
-example, if codeword seven were eliminated, it’s clear that the tree is unfinished:
+<!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
+In the above example, if codeword seven were eliminated, it’s clear that the tree is
+unfinished:
<div class="center"
>
<!--l. 260--><p class="noindent" >
><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 5: </td><td
class="content">underspecified huffman tree illustration</td></tr></table><!--tex4ht:label?: x1-530025 -->
</div>
-<!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth codeword is
-impossible. Both underspecified and overspecified trees are an error condition rendering the stream
-undecodable.
-<!--l. 271--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
-codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read from
-the stream to decode to that entry number.
-<!--l. 278--><p class="noindent" ><span class="paragraphHead"><a
+<!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
+codeword is impossible. Both underspecified and overspecified trees are an error condition
+rendering the stream undecodable. Take special care that a codebook with a single used
+entry is handled properly; it consists of a single codework of zero bits and ’reading’
+a value out of such a codebook always returns the single used value and sinks zero
+bits.
+<!--l. 274--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
+codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
+from the stream to decode to that entry number.
+
+
+
+<!--l. 281--><p class="noindent" ><span class="paragraphHead"><a
id="x1-540003.2.1"></a><span
-class="cmbx-10x-x-109">VQ lookup table vector representation</span></span>
+class="cmbx-12">VQ lookup table vector representation</span></span>
Unpacking the VQ lookup table vectors relies on the following values:
<div class="fancyvrb" id="fancyvrb17">
-
-
-
<a
id="x1-54002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> [codebook_multiplicands]</span><span
-class="cmtt-10"> array</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> [codebook_multiplicands]</span><span
+class="cmtt-8"> array</span>
<br class="fancyvrb" /><a
id="x1-54004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_minimum_value]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_minimum_value]</span>
<br class="fancyvrb" /><a
id="x1-54006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_delta_value]</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_delta_value]</span>
<br class="fancyvrb" /><a
id="x1-54008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_sequence_p]</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_sequence_p]</span>
<br class="fancyvrb" /><a
id="x1-54010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_lookup_type]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_lookup_type]</span>
<br class="fancyvrb" /><a
id="x1-54012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_entries]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_entries]</span>
<br class="fancyvrb" /><a
id="x1-54014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_dimensions]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_dimensions]</span>
<br class="fancyvrb" /><a
id="x1-54016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_lookup_values]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_lookup_values]</span>
</div>
-<!--l. 29
4--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
+<!--l. 29
7--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
<span
-class="cmtt-10x-x-109">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return during
-audio packet decode in a VQ context.
-<!--l.
299--><p class="noindent" ><span class="paragraphHead"><a
+class="cmtt-12">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return
+during audio packet decode in a VQ context.
+<!--l.
302--><p class="noindent" ><span class="paragraphHead"><a
id="x1-550003.2.1"></a><span
-class="cmbx-10x-x-109">Vector value decode: Lookup type 1</span></span>
-Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of scalar
-values. Calculate (unpack) the final values of a codebook entry vector from the entries in
-<span
-class="cmtt-10x-x-109">[codebook_multiplicands] </span>as follows (<span
-class="cmtt-10x-x-109">[value_vector] </span>is the output vector representing the
-vector of values for entry number <span
-class="cmtt-10x-x-109">[lookup_offset] </span>in this codebook):
-<!--l. 308--><p class="noindent" >
+class="cmbx-12">Vector value decode: Lookup type 1</span></span>
+Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of
+scalar values. Calculate (unpack) the final values of a codebook entry vector from
+the entries in <span
+class="cmtt-12">[codebook_multiplicands] </span>as follows (<span
+class="cmtt-12">[value_vector] </span>is the output
+vector representing the vector of values for entry number <span
+class="cmtt-12">[lookup_offset] </span>in this
+codebook):
+<!--l. 311--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb18">
<a
id="x1-55002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0;</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0;</span>
<br class="fancyvrb" /><a
id="x1-55004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [index_divisor]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 1;</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [index_divisor]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 1;</span>
<br class="fancyvrb" /><a
id="x1-55006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [codebook_dimensions]-1</span><span
-class="cmtt-10"> (once</span><span
-class="cmtt-10"> for</span><span
-class="cmtt-10"> each</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> vector)</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [codebook_dimensions]-1</span><span
+class="cmtt-8"> (once</span><span
+class="cmtt-8"> for</span><span
+class="cmtt-8"> each</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> vector)</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-55008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [multiplicand_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [lookup_offset]</span><span
-class="cmtt-10"> divided</span><span
-class="cmtt-10"> by</span><span
-class="cmtt-10"> [index_divisor]</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [multiplicand_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [lookup_offset]</span><span
+class="cmtt-8"> divided</span><span
+class="cmtt-8"> by</span><span
+class="cmtt-8"> [index_divisor]</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-55012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> division</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> modulo</span><span
-class="cmtt-10"> [codebook_lookup_values]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> division</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> modulo</span><span
+class="cmtt-8"> [codebook_lookup_values]</span>
<br class="fancyvrb" /><a
id="x1-55014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [value_vector]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [value_vector]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-55018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [codebook_multiplicands]</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [multiplicand_offset]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> *</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [codebook_multiplicands]</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [multiplicand_offset]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> *</span>
<br class="fancyvrb" /><a
id="x1-55020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_delta_value]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [codebook_minimum_value]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [last];</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_delta_value]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [codebook_minimum_value]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [last];</span>
<br class="fancyvrb" /><a
id="x1-55022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [codebook_sequence_p]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [value_vector]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [codebook_sequence_p]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [value_vector]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-55026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [index_divisor]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [index_divisor]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [codebook_lookup_values]</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [index_divisor]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [index_divisor]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [codebook_lookup_values]</span>
<br class="fancyvrb" /><a
id="x1-55030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-55034r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-55036r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> calculation</span><span
-class="cmtt-10"> completed.</span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> calculation</span><span
+class="cmtt-8"> completed.</span>
</div>
-<!--l. 331--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-560003.2.1"></a><span
-class="cmbx-10x-x-109">Vector value decode: Lookup type 2</span></span>
-
+
-
-Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set by
-the <span
-class="cmtt-10x-x-109">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final values
-of a codebook entry vector from the entries in <span
-class="cmtt-10x-x-109">[codebook_multiplicands] </span>as follows
+
+<!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
+ id="x1-560003.2.1"></a><span
+class="cmbx-12">Vector value decode: Lookup type 2</span></span>
+Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set
+by the <span
+class="cmtt-12">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final
+values of a codebook entry vector from the entries in <span
+class="cmtt-12">[codebook_multiplicands] </span>as follows
(<span
-class="cmtt-10x-x-109">[value_vector] </span>is the output vector representing the vector of values for entry number
+class="cmtt-12">[value_vector] </span>is the output vector representing the vector of values for entry number
<span
-class="cmtt-10x-x-109">[lookup_offset] </span>in this codebook):
-<!--l. 34
1--><p class="noindent" >
+class="cmtt-12">[lookup_offset] </span>in this codebook):
+<!--l. 34
4--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb19">
<a
id="x1-56002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0;</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0;</span>
<br class="fancyvrb" /><a
id="x1-56004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [multiplicand_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [lookup_offset]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [codebook_dimensions]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [multiplicand_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [lookup_offset]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [codebook_dimensions]</span>
<br class="fancyvrb" /><a
id="x1-56006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [codebook_dimensions]-1</span><span
-class="cmtt-10"> (once</span><span
-class="cmtt-10"> for</span><span
-class="cmtt-10"> each</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> vector)</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [codebook_dimensions]-1</span><span
+class="cmtt-8"> (once</span><span
+class="cmtt-8"> for</span><span
+class="cmtt-8"> each</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> vector)</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-56008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-56010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [value_vector]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [value_vector]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-56012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [codebook_multiplicands]</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [multiplicand_offset]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> *</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [codebook_multiplicands]</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [multiplicand_offset]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> *</span>
<br class="fancyvrb" /><a
id="x1-56014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [codebook_delta_value]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [codebook_minimum_value]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [last];</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [codebook_delta_value]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [codebook_minimum_value]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [last];</span>
<br class="fancyvrb" /><a
id="x1-56016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-56018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [codebook_sequence_p]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [value_vector]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [codebook_sequence_p]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [value_vector]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-56020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-56022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [multiplicand_offset]</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [multiplicand_offset]</span>
<br class="fancyvrb" /><a
id="x1-56024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-56026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-56028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-56030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> calculation</span><span
-class="cmtt-10"> completed.</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> calculation</span><span
+class="cmtt-8"> completed.</span>
</div>
-<!--l. 3
67--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">3.3 </span> <a
+<!--l. 3
70--><p class="noindent" >
+<h4 class="subsectionHead"><span class="titlemark">3.3
</span> <a
id="x1-570003.3"></a>Use of the codebook abstraction</h4>
-<!--l. 369--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a specific
-codebook reads a codeword from the bitstream, decoding it into an entry number, and then returns
-that entry number to the decoder (when used in a scalar entropy coding context), or uses
-that entry number as an offset into the VQ lookup table, returning a vector of values
-(when used in a context desiring a VQ value). Scalar or VQ context is always explicit;
-any call to the codebook mechanism requests either a scalar entry number or a lookup
+<!--l. 372--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a
+specific codebook reads a codeword from the bitstream, decoding it into an entry number, and
+then returns that entry number to the decoder (when used in a scalar entropy coding context), or
+uses that entry number as an offset into the VQ lookup table, returning a vector of values (when
+used in a context desiring a VQ value). Scalar or VQ context is always explicit; any
+call to the codebook mechanism requests either a scalar entry number or a lookup
vector.
-<!--l. 379--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting decode using a
-codebook of lookup type 0 in any context expecting a vector return value (even in a case where a
-vector of dimension one) is forbidden. If decoder setup or decode requests such an action, that is an
-error condition rendering the packet undecodable.
-<!--l. 386--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding
-the next codeword in the bitstream. The decoder reads bits until the accumulated bits
-match a codeword in the codebook. This process can be though of as logically walking
-the Huffman decode tree by reading one bit at a time from the bitstream, and using
-
+<!--l. 382--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting
+decode using a codebook of lookup type 0 in any context expecting a vector return
+value (even in a case where a vector of dimension one) is forbidden. If decoder setup
+or decode requests such an action, that is an error condition rendering the packet
+
-
-the bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
+
+undecodable.
+<!--l. 389--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
+next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
+codeword in the codebook. This process can be though of as logically walking the
+Huffman decode tree by reading one bit at a time from the bitstream, and using the
+bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
branch (right in the above examples). Walking the tree finishes when the decode process
hits a leaf in the decision tree; the result is the entry number corresponding to that
leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
decoder.
-<!--l. 398--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return value.
-<!--l. 401--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
+<!--l. 401--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
+value.
+<!--l. 404--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
table. The value returned to the decoder is the vector of scalars corresponding to this
offset.
-
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">4 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">4
</span> <a
id="x1-580004"></a>Codec Setup and Packet Decode</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">4.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">4.1
</span> <a
id="x1-590004.1"></a>Overview</h4>
-<!--l. 8--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification of
-Vorbis I. This document assumes a high-level understanding of the Vorbis decode process, which is
-provided in <a
+<!--l. 8--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
+of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
+pro
cess, which is provided in <a
href="#x1-20001">Section 1<!--tex4ht:ref: vorbis:spec:intro --></a>, “<a
href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
-href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
-href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers
-reading and writing bit fields from and to bitstream packets.
+href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>,
+“<a
+href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
+packets.
<!--l. 16--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">4.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">4.2
</span> <a
id="x1-600004.2"></a>Header decode and decode setup</h4>
<!--l. 18--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
identification header, the comments header, and the setup header. All are required for decode
-compliance. An end-of-packet condition during decoding the first or third header packet renders the
-stream undecodable. End-of-packet decoding the comment header is a non-fatal error
+compliance. An end-of-packet condition during decoding the first or third header packet renders
+the stream undecodable. End-of-packet decoding the comment header is a non-fatal error
condition.
<!--l. 25--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.2.1
</span> <a
id="x1-610004.2.1"></a>Common header decode</h5>
<!--l. 27--><p class="noindent" >Each header packet begins with the same header fields.
<!--l. 30--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb20">
<a
id="x1-61002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [packet_type]</span><span
-class="cmtt-10"> :</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> value</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [packet_type]</span><span
+class="cmtt-8"> :</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> value</span>
<br class="fancyvrb" /><a
id="x1-61004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> 0x76,</span><span
-class="cmtt-10"> 0x6f,</span><span
-class="cmtt-10"> 0x72,</span><span
-class="cmtt-10"> 0x62,</span><span
-class="cmtt-10"> 0x69,</span><span
-class="cmtt-10"> 0x73:</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> characters</span><span
-class="cmtt-10"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> six</span><span
-class="cmtt-10"> octets</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> 0x76,</span><span
+class="cmtt-8"> 0x6f,</span><span
+class="cmtt-8"> 0x72,</span><span
+class="cmtt-8"> 0x62,</span><span
+class="cmtt-8"> 0x69,</span><span
+class="cmtt-8"> 0x73:</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> characters</span><span
+class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> six</span><span
+class="cmtt-8"> octets</span>
</div>
-<!--l. 35--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment header
-type 3 and the setup header type 5 (these types are all odd as a packet with a leading single bit of
-’0’ is an audio packet). The packets must occur in the order of identification, comment,
-setup.
-
+
-
+
+<!--l. 35--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
+header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
+single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
+comment, setup.
<!--l. 43--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.2.2
</span> <a
id="x1-620004.2.2"></a>Identification header</h5>
-<!--l. 45--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream definitively
-as Vorbis, and provide a few externally relevant pieces of information about the audio stream. The
-identification header is coded as follows:
+<!--l. 45--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream
+definitively as Vorbis, and provide a few externally relevant pieces of information about the audio
+stream. The identification header is coded as follows:
<!--l. 50--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb21">
<a
id="x1-62002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [vorbis_version]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [vorbis_version]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-62004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [audio_channels]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [audio_channels]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span>
<br class="fancyvrb" /><a
id="x1-62006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [audio_sample_rate]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [audio_sample_rate]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-62008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [bitrate_maximum]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> signed</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [bitrate_maximum]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> signed</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-62010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [bitrate_nominal]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> signed</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [bitrate_nominal]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> signed</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-62012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [bitrate_minimum]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> signed</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [bitrate_minimum]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> signed</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-62014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [blocksize_0]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> exponent</span><span
-class="cmtt-10"> (read</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer)</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [blocksize_0]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> exponent</span><span
+class="cmtt-8"> (read</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer)</span>
<br class="fancyvrb" /><a
id="x1-62016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> [blocksize_1]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> exponent</span><span
-class="cmtt-10"> (read</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer)</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> [blocksize_1]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> exponent</span><span
+class="cmtt-8"> (read</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer)</span>
<br class="fancyvrb" /><a
id="x1-62018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [framing_flag]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> one</span><span
-class="cmtt-10"> bit</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [framing_flag]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> one</span><span
+class="cmtt-8"> bit</span>
</div>
<!--l. 62--><p class="noindent" ><span
-class="cmtt-10x-x-109">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
+class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
<span
-class="cmtt-10x-x-109">[audio_channels] </span>and <span
-class="cmtt-10x-x-109">[audio_sample_rate] </span>must read greater than zero. Allowed final blocksize
-values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
-class="cmtt-10x-x-109">[blocksize_0] </span>must be less
-than or equal to <span
-class="cmtt-10x-x-109">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet any of these
-conditions renders a stream undecodable.
+class="cmtt-12">[audio_channels] </span>and <span
+class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final
+blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
+class="cmtt-12">[blocksize_0]</span>
+must be less than or equal to <span
+class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet
+any of these conditions renders a stream undecodable.
<!--l. 70--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
considerably off in purely VBR streams. The fields are meaningful only when greater than
zero.
- <ul class="itemize1">
- <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
- fixed-rate bitstream
- </li>
- <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
- </li>
- <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
- </li>
- <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
-<!--l. 84--><p class="noindent" >
-
+ <ul class="itemize1">
+ <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
+ fixed-rate bitstream
+ </li>
+ <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
+
-
-<h5 class="subsubsectionHead"><span class="titlemark">4.2.3 </span> <a
+
+ </li>
+ <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
+ </li>
+ <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
+<!--l. 84--><p class="noindent" >
+<h5 class="subsubsectionHead"><span class="titlemark">4.2.3 </span> <a
id="x1-630004.2.3"></a>Comment header</h5>
<!--l. 85--><p class="noindent" >Comment header decode and data specification is covered in <a
href="#x1-810005">Section 5<!--tex4ht:ref: vorbis:spec:comment --></a>, “<a
-href="#x1-810005">comment field and header
-specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
+href="#x1-810005">comment field and
+header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
<!--l. 89--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.2.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.2.4
</span> <a
id="x1-640004.2.4"></a>Setup header</h5>
<!--l. 91--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
<div class="center"
<!--l. 99--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
header contains, in order, the lists of codebook configurations, time-domain transform
configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
-mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header decode
-proceeds in the following order:
+mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
+decode proceeds in the following order:
<!--l. 107--><p class="noindent" ><span class="paragraphHead"><a
id="x1-650004.2.4"></a><span
-class="cmbx-10x-x-109">Codebooks</span></span>
- <ol class="enumerate1" >
- <li
+class="cmbx-12">Codebooks</span></span>
+
+
+
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-65002x1"><span
-class="cmtt-10x-x-109">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-65004x2">Decode <span
-class="cmtt-1
0x-x-109">[vorbis_codebook_count] </span>codebooks in order as defined in <a
+class="cmtt-1
2">[vorbis_codebook_count] </span>codebooks in order as defined in <a
href="#x1-470003">Section 3<!--tex4ht:ref: vorbis:spec:codebook --></a>,
- “<a
-href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array of
- codebook configurations <span
-class="cmtt-10x-x-109">[vorbis_codebook_configurations]</span>.</li></ol>
+href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
+ of codebook configurations <span
+class="cmtt-12">[vorbis_codebook_configurations]</span>.</li></ol>
<!--l. 119--><p class="noindent" ><span class="paragraphHead"><a
id="x1-660004.2.4"></a><span
-class="cmbx-10x-x-109">Time domain transforms</span></span>
-These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must be
-read to maintain bitstream sync.
-
-
-
-<!--l. 126--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+class="cmbx-12">Time domain transforms</span></span>
+These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must
+be read to maintain bitstream sync.
+<!--l. 125--><p class="noindent" >
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-66002x1"><span
-class="cmtt-10x-x-109">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-66004x2">read <span
-class="cmtt-10x-x-109">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
- nonzero, this is an error condition and the stream is undecodable.</li></ol>
+class="cmtt-12">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
+ nonzero, this is an error condition and the stream is undecodable.</li></ol>
<!--l. 132--><p class="noindent" ><span class="paragraphHead"><a
id="x1-670004.2.4"></a><span
-class="cmbx-10x-x-109">Floors</span></span>
+class="cmbx-12">Floors</span></span>
Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
type.
-<!--l. 13
8--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+<!--l. 13
7--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-67002x1"><span
-class="cmtt-10x-x-109">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-67004x2">For each <span
-class="cmtt-10x-x-109">[i] </span>of <span
-class="cmtt-10x-x-109">[vorbis_floor_count] </span>floor numbers:
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[i] </span>of <span
+class="cmtt-12">[vorbis_floor_count] </span>floor numbers:
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-67006x1">read the floor type: vector <span
-class="cmtt-10x-x-109">[vorbis_floor_types] </span>element <span
-class="cmtt-10x-x-109">[i] </span>= read 16 bits as
- unsigned integer
- </li>
- <li
+class="cmtt-12">[vorbis_floor_types] </span>element <span
+class="cmtt-12">[i] </span>= read 16 bits
+ as unsigned integer
+ </li>
+ <li
class="enumerate" id="x1-67008x2">If the floor type is zero, decode the floor configuration as defined in <a
href="#x1-890006">Section 6<!--tex4ht:ref: vorbis:spec:floor0 --></a>,
- “<a
href="#x1-890006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
-class="cmtt-10x-x-109">[i] </span>of the floor
- configuration array <span
-class="cmtt-10x-x-109">[vorbis_floor_configurations]</span>.
- </li>
- <li
+class="cmtt-12">[i] </span>of the floor
+ configuration array <span
+class="cmtt-12">[vorbis_floor_configurations]</span>.
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-67010x3">If the floor type is one, decode the floor configuration as defined in <a
href="#x1-950007">Section 7<!--tex4ht:ref: vorbis:spec:floor1 --></a>,
- “<a
href="#x1-950007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
-class="cmtt-10x-x-109">[i] </span>of the floor
- configuration array <span
-class="cmtt-10x-x-109">[vorbis_floor_configurations]</span>.
- </li>
- <li
+class="cmtt-12">[i] </span>of the floor
+ configuration array <span
+class="cmtt-12">[vorbis_floor_configurations]</span>.
+ </li>
+ <li
class="enumerate" id="x1-67012x4">If the the floor type is greater than one, this stream is undecodable; ERROR
- CONDITION</li></ol>
- </li></ol>
+ CONDITION</li></ol>
+ </li></ol>
<!--l. 156--><p class="noindent" ><span class="paragraphHead"><a
id="x1-680004.2.4"></a><span
-class="cmbx-10x-x-109">Residues</span></span>
+class="cmbx-12">Residues</span></span>
Vorbis uses three residue types; header decode of each type is identical.
-<!--l. 162--><p class="noindent" >
-
-
-
- <ol class="enumerate1" >
- <li
+<!--l. 161--><p class="noindent" >
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-68002x1"><span
-class="cmtt-10x-x-109">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-68004x2">For each of <span
-class="cmtt-10x-x-109">[vorbis_residue_count] </span>residue numbers:
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[vorbis_residue_count] </span>residue numbers:
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-68006x1">read the residue type; vector <span
-class="cmtt-10x-x-109">[vorbis_residue_types] </span>element <span
-class="cmtt-10x-x-109">[i] </span>= read 16
- bits as unsigned integer
- </li>
- <li
+class="cmtt-12">[vorbis_residue_types] </span>element <span
+class="cmtt-12">[i] </span>= read 16
+ bits as unsigned integer
+ </li>
+ <li
class="enumerate" id="x1-68008x2">If the residue type is zero, one or two, decode the residue configuration as defined
- in <a
href="#x1-1020008">Section 8<!--tex4ht:ref: vorbis:spec:residue --></a>, “<a
href="#x1-1020008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
-class="cmtt-10x-x-109">[i] </span>of
- the residue configuration array <span
-class="cmtt-10x-x-109">[vorbis_residue_configurations]</span>.
- </li>
- <li
+class="cmtt-12">[i] </span>of
+ the residue configuration array <span
+class="cmtt-12">[vorbis_residue_configurations]</span>.
+ </li>
+ <li
class="enumerate" id="x1-68010x3">If the the residue type is greater than two, this stream is undecodable; ERROR
- CONDITION</li></ol>
- </li></ol>
+ CONDITION</li></ol>
+ </li></ol>
<!--l. 176--><p class="noindent" ><span class="paragraphHead"><a
id="x1-690004.2.4"></a><span
-class="cmbx-10x-x-109">Mappings</span></span>
-Mappings are used to set up specific pipelines for encoding multichannel audio with varying channel
-mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM channel
-mappings.
-<!--l. 187--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+class="cmbx-12">Mappings</span></span>
+Mappings are used to set up specific pipelines for encoding multichannel audio with varying
+channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
+channel mappings.
+
+
+
+<!--l. 186--><p class="noindent" >
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-69002x1"><span
-class="cmtt-10x-x-109">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-69004x2">For each <span
-class="cmtt-10x-x-109">[i] </span>of <span
-class="cmtt-10x-x-109">[vorbis_mapping_count] </span>mapping numbers:
- <ol class="enumerate2" >
- <li
- class="enumerate" id="x1-69006x1">read the mapping type: 16 bits as unsigned integer. There’s no reason to save the
- mapping type in Vorbis I.
- </li>
- <li
+class="cmtt-12">[i] </span>of <span
+class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers:
+
<ol class="enumerate2" >
+ <li
+ class="enumerate" id="x1-69006x1">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
+ the mapping type in Vorbis I.
+ </li>
+ <li
class="enumerate" id="x1-69008x2">If the mapping type is nonzero, the stream is undecodable
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-69010x3">If the mapping type is zero:
- <ol class="enumerate3" >
- <li
+
<ol class="enumerate3" >
+ <li
class="enumerate" id="x1-69012x1">read 1 bit as a boolean flag
- <ol class="enumerate4" >
- <li
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-69014x1">if set, <span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer and
- add one
-
-
-
- </li>
- <li
+class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer
+ and add one
+ </li>
+ <li
class="enumerate" id="x1-69016x2">if unset, <span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>= 1</li></ol>
- </li>
- <li
+class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-69018x2">read 1 bit as a boolean flag
- <ol class="enumerate4" >
- <li
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-69020x1">if set, square polar channel mapping is in use:
- <ul class="itemize1">
- <li class="itemize"><span
-class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned integer
- and add one
- </li>
- <li class="itemize">for <span
-class="cmtt-10x-x-109">[j] </span>each of <span
-class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>steps:
- <ul class="itemize2">
- <li class="itemize">vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
-class="cmtt-10x-x-109">[j]</span>= read
- <a
-href="#x1-1170009.2.1">ilog</a>(<span
-class="cmtt-10x-x-109">[audio_channels] </span>- 1) bits as unsigned integer
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned
+ integer and add one
</li>
- <li class="itemize">vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_angle] </span>element <span
-class="cmtt-10x-x-109">[j]</span>= read
- <a
+ <li class="itemize">for <span
+class="cmtt-12">[j] </span>each of <span
+class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps:
+ <ul class="itemize2">
+ <li class="itemize">vector <span
+class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
+class="cmtt-12">[j]</span>= read
+ <a
href="#x1-1170009.2.1">ilog</a>(<span
-class="cmtt-10x-x-109">[audio_channels] </span>- 1) bits as unsigned integer
- </li>
- <li class="itemize">the numbers read in the above two steps are channel numbers
- representing the channel to treat as magnitude and the channel to
- treat as angle, respectively. If for any coupling step the angle channel
- number equals the magnitude channel number, the magnitude channel
- number is greater than <span
-class="cmtt-10x-x-109">[audio_channels]</span>-1, or the angle channel is
- greater than <span
-class="cmtt-10x-x-109">[audio_channels]</span>-1, the stream is undecodable.</li></ul>
- </li></ul>
- </li>
- <li
+class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
+ </li>
+ <li class="itemize">vector <span
+class="cmtt-12">[vorbis_mapping_angle] </span>element <span
+class="cmtt-12">[j]</span>= read
+ <a
+href="#x1-1170009.2.1">ilog</a>(<span
+class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
+ </li>
+
+
+
+ <li class="itemize">the numbers read in the above two steps are channel numbers
+ representing the channel to treat as magnitude and the channel
+ to treat as angle, respectively. If for any coupling step the
+ angle channel number equals the magnitude channel number, the
+ magnitude channel number is greater than <span
+class="cmtt-12">[audio_channels]</span>-1, or
+ the angle channel is greater than <span
+class="cmtt-12">[audio_channels]</span>-1, the stream
+ is undecodable.</li></ul>
+ </li></ul>
+ </li>
+ <li
class="enumerate" id="x1-69022x2">if unset, <span
-class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>= 0</li></ol>
- </li>
- <li
+class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= 0</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-69024x3">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-69026x4">if <span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
- settings. For each <span
-class="cmtt-10x-x-109">[j] </span>of <span
-class="cmtt-10x-x-109">[audio_channels] </span>channels:
- <ol class="enumerate4" >
- <li
- class="enumerate" id="x1-69028x1">vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
-class="cmtt-10x-x-109">[j] </span>= read 4 bits as unsigned
- integer
- </li>
- <li
- class="enumerate" id="x1-69030x2">if the value is
- greater than the highest numbered submap (<span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps]</span>
- - 1), this in an error condition rendering the stream undecodable</li></ol>
-
-
-
- </li>
- <li
+class="cmtt-12">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
+ settings. For each <span
+class="cmtt-12">[j] </span>of <span
+class="cmtt-12">[audio_channels] </span>channels:
+ <ol class="enumerate4" >
+ <li
+ class="enumerate" id="x1-69028x1">vector <span
+class="cmtt-12">[vorbis_mapping_mux] </span>element <span
+class="cmtt-12">[j] </span>= read 4 bits as unsigned
+ integer
+ </li>
+ <li
+ class="enumerate" id="x1-69030x2">if the value is greater than the highest numbered submap
+ (<span
+class="cmtt-12">[vorbis_mapping_submaps] </span>- 1), this in an error condition rendering
+ the stream undecodable</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-69032x5">for each submap <span
-class="cmtt-10x-x-109">[j] </span>of <span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>submaps, read the floor and
- residue numbers for use in decoding that submap:
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[j] </span>of <span
+class="cmtt-12">[vorbis_mapping_submaps] </span>submaps, read the floor and
+ residue numbers for use in decoding that submap:
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-69034x1">read and discard 8 bits (the unused time configuration placeholder)
- </li>
- <li
- class="enumerate" id="x1-69036x2">read 8 bits as unsigned integer for the floor number; save in vector
- <span
-class="cmtt-10x-x-109">[vorbis_mapping_submap_floor] </span>element <span
-class="cmtt-10x-x-109">[j]</span>
- </li>
- <li
- class="enumerate" id="x1-69038x3">verify the floor number is not greater than the highest number floor
- configured for the bitstream. If it is, the bitstream is undecodable
- </li>
- <li
+ </li>
+ <li
+ class="enumerate" id="x1-69036x2">read 8 bits as unsigned integer for the floor number; save in vector
+ <span
+class="cmtt-12">[vorbis_mapping_submap_floor] </span>element <span
+class="cmtt-12">[j]</span>
+ </li>
+ <li
+ class="enumerate" id="x1-69038x3">verify the floor number is not greater than the highest number floor
+ configured for the bitstream. If it is, the bitstream is undecodable
+ </li>
+ <li
class="enumerate" id="x1-69040x4">read 8 bits as unsigned integer for the residue number; save in vector
- <span
-class="cmtt-10x-x-109">[vorbis_mapping_submap_residue] </span>element <span
-class="cmtt-10x-x-109">[j]</span>
- </li>
- <li
+ <span
+class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
+class="cmtt-12">[j]</span>
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-69042x5">verify the residue number is not greater than the highest number residue
- configured for the bitstream. If it is, the bitstream is undecodable</li></ol>
- </li>
- <li
+ configured for the bitstream. If it is, the bitstream is undecodable</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-69044x6">save this mapping configuration in slot <span
-class="cmtt-10x-x-109">[i] </span>of the mapping configuration array
- <span
-class="cmtt-10x-x-109">[vorbis_mapping_configurations]</span>.</li></ol>
- </li></ol>
- </li></ol>
+class="cmtt-12">[i] </span>of the mapping configuration array
+ <span
+class="cmtt-12">[vorbis_mapping_configurations]</span>.</li></ol>
+ </li></ol>
+ </li></ol>
<!--l. 246--><p class="noindent" ><span class="paragraphHead"><a
id="x1-700004.2.4"></a><span
-class="cmbx-10x-x-109">Modes</span></span>
- <ol class="enumerate1" >
- <li
+class="cmbx-12">Modes</span></span>
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-70002x1"><span
-class="cmtt-10x-x-109">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
- </li>
- <li
+class="cmtt-12">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
+ </li>
+ <li
class="enumerate" id="x1-70004x2">For each of <span
-class="cmtt-10x-x-109">[vorbis_mode_count] </span>mode numbers:
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[vorbis_mode_count] </span>mode numbers:
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-70006x1"><span
-class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>= read 1 bit
- </li>
- <li
+class="cmtt-12">[vorbis_mode_blockflag] </span>= read 1 bit
+ </li>
+ <li
class="enumerate" id="x1-70008x2"><span
-class="cmtt-10x-x-109">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
- </li>
- <li
+class="cmtt-12">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
+ </li>
+ <li
class="enumerate" id="x1-70010x3"><span
-class="cmtt-10x-x-109">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
- </li>
- <li
+class="cmtt-12">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
+ </li>
+ <li
class="enumerate" id="x1-70012x4"><span
-class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
-
-
-
- </li>
- <li
- class="enumerate" id="x1-70014x5">verify ranges; zero is the only legal value
- in Vorbis I for <span
-class="cmtt-10x-x-109">[vorbis_mode_windowtype] </span>and <span
-class="cmtt-10x-x-109">[vorbis_mode_transformtype]</span>.
- <span
-class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
- in use. Any illegal values render the stream undecodable.
- </li>
- <li
+class="cmtt-12">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
+ </li>
+ <li
+ class="enumerate" id="x1-70014x5">verify ranges; zero is the only legal value in
+ Vorbis I for <span
+class="cmtt-12">[vorbis_mode_windowtype] </span>and <span
+class="cmtt-12">[vorbis_mode_transformtype]</span>.
+ <span
+class="cmtt-12">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
+ in use. Any illegal values render the stream undecodable.
+ </li>
+ <li
class="enumerate" id="x1-70016x6">save this mode configuration in slot <span
-class="cmtt-10x-x-109">[i] </span>of the mode configuration array
- <span
-class="cmtt-10x-x-109">[vorbis_mode_configurations]</span>.</li></ol>
- </li>
- <li
+class="cmtt-12">[i] </span>of the mode configuration array
+ <span
+class="cmtt-12">[vorbis_mode_configurations]</span>.</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-70018x3">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
- decodable.</li></ol>
+ decodable.</li></ol>
+
+
+
<!--l. 267--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
<!--l. 276--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">4.3 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">4.3
</span> <a
id="x1-710004.3"></a>Audio packet decode and synthesis</h4>
<!--l. 278--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
audio packet decode is to read and verify the packet type. <span
-class="cmti-10x-x-109">A non-audio packet when audio is</span>
+class="cmti-12">A non-audio packet when audio is</span>
<span
-class="cmti-10x-x-109">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the packet</span>
+class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
<span
-class="cmti-10x-x-109">and not attempt decoding it to audio</span>.
+class="cmti-12">packet and not attempt decoding it to audio</span>.
<!--l. 285--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.1
</span> <a
id="x1-720004.3.1"></a>packet type, mode and window decode</h5>
-<!--l. 28
8--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+<!--l. 28
7--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-72002x1">read 1 bit <span
-class="cmtt-10x-x-109">[packet_type]</span>; check that packet type is 0 (audio)
- </li>
- <li
+class="cmtt-12">[packet_type]</span>; check that packet type is 0 (audio)
+ </li>
+ <li
class="enumerate" id="x1-72004x2">read <a
href="#x1-1170009.2.1">ilog</a>([vorbis˙mode˙count]-1) bits <span
-class="cmtt-10x-x-109">[mode_number]</span>
- </li>
- <li
+class="cmtt-12">[mode_number]</span>
+ </li>
+ <li
class="enumerate" id="x1-72006x3">decode blocksize <span
-class="cmtt-10x-x-109">[n] </span>is equal to <span
-class="cmtt-10x-x-109">[blocksize_0] </span>if <span
-class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is 0, else
- <span
-class="cmtt-10x-x-109">[n] </span>is equal to <span
-class="cmtt-10x-x-109">[blocksize_1]</span>.
- </li>
- <li
- class="enumerate" id="x1-72008x4">perform window selection and setup; this window is used later by the inverse MDCT:
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[n] </span>is equal to <span
+class="cmtt-12">[blocksize_0] </span>if <span
+class="cmtt-12">[vorbis_mode_blockflag] </span>is 0,
+ else <span
+class="cmtt-12">[n] </span>is equal to <span
+class="cmtt-12">[blocksize_1]</span>.
+ </li>
+ <li
+ class="enumerate" id="x1-72008x4">perform window selection and setup; this window is used later by the inverse
+ MDCT:
+ <ol class="enumerate2" >
+ <li
class="enumerate" id="x1-72010x1">if this is a long window (the <span
-class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>flag of this mode is
-
-
-
- set):
- <ol class="enumerate3" >
- <li
+class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is
+ set):
+ <ol class="enumerate3" >
+ <li
class="enumerate" id="x1-72012x1">read 1 bit for <span
-class="cmtt-10x-x-109">[previous_window_flag]</span>
- </li>
- <li
+class="cmtt-12">[previous_window_flag]</span>
+ </li>
+ <li
class="enumerate" id="x1-72014x2">read 1 bit for <span
-class="cmtt-10x-x-109">[next_window_flag]</span>
- </li>
- <li
- class="enumerate" id="x1-72016x3">if <span
-class="cmtt-10x-x-109">[previous_window_flag] </span>is not set, the left half of the window will be a
- hybrid window for lapping with a short block. See <a
-href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
-href="#x1-260001.3.2">Window
- shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of overlapping dissimilar
- windows. Else, the left half window will have normal long shape.
- </li>
- <li
+class="cmtt-12">[next_window_flag]</span>
+
+
+
+ </li>
+ <li
+ class="enumerate" id="x1-72016x3">if <span
+class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will
+ be a hybrid window for lapping with a short block. See <a
+href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>,
+ “<a
+href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
+ overlapping dissimilar windows. Else, the left half window will have normal
+ long shape.
+ </li>
+ <li
class="enumerate" id="x1-72018x4">if <span
-class="cmtt-10x-x-109">[next_window_flag] </span>is not set, the right half of the window will be a
- hybrid window for lapping with a short block. See <a
-href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
-href="#x1-260001.3.2">Window
- shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of overlapping dissimilar
- windows. Else, the left right window will have normal long shape.</li></ol>
- </li>
- <li
- class="enumerate" id="x1-72020x2">if this is a short window, the window is always the same short-window shape.</li></ol>
- </li></ol>
+class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be
+ a hybrid window for lapping with a short block. See <a
+href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>,
+ “<a
+href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
+ overlapping dissimilar windows. Else, the left right window will have normal
+ long shape.</li></ol>
+ </li>
+ <li
+ class="enumerate" id="x1-72020x2">if this is a short window, the window is always the same short-window
+ shape.</li></ol>
+ </li></ol>
<!--l. 320--><p class="noindent" >Vorbis windows all use the slope function <span
-class="cmmi-10x-x-109">y </span>= sin(<img
-src="Vorbis_I_spec1x.png" alt="π
-2" class="frac" align="middle"> <span
-class="cmsy-10x-x-109">*</span> sin<sup><span
+class="cmmi-12">y </span>= sin(<img
+src="Vorbis_I_spec1x.png" alt="π2" class="frac" align="middle"> <span
+class="cmsy-10x-x-120">*</span> sin <sup><span
class="cmr-8">2</span></sup>((<span
-class="cmmi-10x-x-109">x </span>+ 0<span
-class="cmmi-10x-x-109">.</span>5)<span
-class="cmmi-10x-x-109">∕n</span><span
-class="cmsy-10x-x-109">*</span><span
-class="cmmi-10x-x-109">π</span>)), where <span
-class="cmmi-10x-x-109">n </span>is window size
-and <span
-class="cmmi-10x-x-109">x </span>ranges 0<span
-class="cmmi-10x-x-109">…</span><span
-class="cmmi-10x-x-109">n </span><span
-class="cmsy-10x-x-109">- </span>1, but dissimilar lapping requirements can affect overall shape. Window
+class="cmmi-12">x </span>+ 0<span
+class="cmmi-12">.</span>5)<span
+class="cmmi-12">∕n </span><span
+class="cmsy-10x-x-120">* </span><span
+class="cmmi-12">π</span>)), where <span
+class="cmmi-12">n </span>is window
+size and <span
+class="cmmi-12">x </span>ranges 0<span
+class="cmmi-12">…</span><span
+class="cmmi-12">n</span><span
+class="cmsy-10x-x-120">- </span>1, but dissimilar lapping requirements can affect overall shape. Window
generation proceeds as follows:
-<!--l. 32
6--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+<!--l. 32
5--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-72022x1"><span
-class="cmtt-10x-x-109">[window_center] </span>= <span
-class="cmtt-10x-x-109">[n] </span>/ 2
- </li>
- <li
+class="cmtt-12">[window_center] </span>= <span
+class="cmtt-12">[n] </span>/ 2
+ </li>
+ <li
class="enumerate" id="x1-72024x2">if (<span
-class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is set and <span
-class="cmtt-10x-x-109">[previous_window_flag] </span>is not set)
- then
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
+class="cmtt-12">[previous_window_flag] </span>is not set)
+ then
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-72026x1"><span
-class="cmtt-10x-x-109">[left_window_start] </span>= <span
-class="cmtt-10x-x-109">[n]</span>/4 - <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/4
- </li>
- <li
+class="cmtt-12">[left_window_start] </span>= <span
+class="cmtt-12">[n]</span>/4 - <span
+class="cmtt-12">[blocksize_0]</span>/4
+ </li>
+ <li
class="enumerate" id="x1-72028x2"><span
-class="cmtt-10x-x-109">[left_window_end] </span>= <span
-class="cmtt-10x-x-109">[n]</span>/4 + <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/4
- </li>
- <li
+class="cmtt-12">[left_window_end] </span>= <span
+class="cmtt-12">[n]</span>/4 + <span
+class="cmtt-12">[blocksize_0]</span>/4
+ </li>
+ <li
class="enumerate" id="x1-72030x3"><span
-class="cmtt-10x-x-109">[left_n] </span>= <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/2</li></ol>
- <!--l. 335--><p class="noindent" >else
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[left_n] </span>= <span
+class="cmtt-12">[blocksize_0]</span>/2</li></ol>
+
<!--l. 335--><p class="noindent" >else
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-72032x1"><span
-class="cmtt-10x-x-109">[left_window_start] </span>= 0
- </li>
- <li
+class="cmtt-12">[left_window_start] </span>= 0
+ </li>
+ <li
class="enumerate" id="x1-72034x2"><span
-class="cmtt-10x-x-109">[left_window_end] </span>= <span
-class="cmtt-10x-x-109">[window_center]</span>
-
+class="cmtt-12">[left_window_end] </span>= <span
+class="cmtt-12">[window_center]</span>
+
-
- </li>
- <li
+
+ </li>
+ <li
class="enumerate" id="x1-72036x3"><span
-class="cmtt-10x-x-109">[left_n] </span>= <span
-class="cmtt-10x-x-109">[n]</span>/2</li></ol>
- </li>
- <li
+class="cmtt-12">[left_n] </span>= <span
+class="cmtt-12">[n]</span>/2</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-72038x3">if (<span
-class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is set and <span
-class="cmtt-10x-x-109">[next_window_flag] </span>is not set) then
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
+class="cmtt-12">[next_window_flag] </span>is not set) then
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-72040x1"><span
-class="cmtt-10x-x-109">[right_window_start] </span>= <span
-class="cmtt-10x-x-109">[n]*3</span>/4 - <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/4
- </li>
- <li
+class="cmtt-12">[right_window_start] </span>= <span
+class="cmtt-12">[n]*3</span>/4 - <span
+class="cmtt-12">[blocksize_0]</span>/4
+ </li>
+ <li
class="enumerate" id="x1-72042x2"><span
-class="cmtt-10x-x-109">[right_window_end] </span>= <span
-class="cmtt-10x-x-109">[n]*3</span>/4 + <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/4
- </li>
- <li
+class="cmtt-12">[right_window_end] </span>= <span
+class="cmtt-12">[n]*3</span>/4 + <span
+class="cmtt-12">[blocksize_0]</span>/4
+ </li>
+ <li
class="enumerate" id="x1-72044x3"><span
-class="cmtt-10x-x-109">[right_n] </span>= <span
-class="cmtt-10x-x-109">[blocksize_0]</span>/2</li></ol>
- <!--l. 351--><p class="noindent" >else
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[right_n] </span>= <span
+class="cmtt-12">[blocksize_0]</span>/2</li></ol>
+
<!--l. 351--><p class="noindent" >else
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-72046x1"><span
-class="cmtt-10x-x-109">[right_window_start] </span>= <span
-class="cmtt-10x-x-109">[window_center]</span>
- </li>
- <li
+class="cmtt-12">[right_window_start] </span>= <span
+class="cmtt-12">[window_center]</span>
+ </li>
+ <li
class="enumerate" id="x1-72048x2"><span
-class="cmtt-10x-x-109">[right_window_end] </span>= <span
-class="cmtt-10x-x-109">[n]</span>
- </li>
- <li
+class="cmtt-12">[right_window_end] </span>= <span
+class="cmtt-12">[n]</span>
+ </li>
+ <li
class="enumerate" id="x1-72050x3"><span
-class="cmtt-10x-x-109">[right_n] </span>= <span
-class="cmtt-10x-x-109">[n]</span>/2</li></ol>
- </li>
- <li
+class="cmtt-12">[right_n] </span>= <span
+class="cmtt-12">[n]</span>/2</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-72052x4">window from range 0 ... <span
-class="cmtt-10x-x-109">[left_window_start]</span>-1 inclusive is zero
- </li>
- <li
+class="cmtt-12">[left_window_start]</span>-1 inclusive is zero
+ </li>
+ <li
class="enumerate" id="x1-72054x5">for <span
-class="cmtt-10x-x-109">[i] </span>in range <span
-class="cmtt-10x-x-109">[left_window_start] </span>... <span
-class="cmtt-10x-x-109">[left_window_end]</span>-1, window(<span
-class="cmtt-10x-x-109">[i]</span>) =
- sin(<img
+class="cmtt-12">[i] </span>in range <span
+class="cmtt-12">[left_window_start] </span>... <span
+class="cmtt-12">[left_window_end]</span>-1, window(<span
+class="cmtt-12">[i]</span>) =
src="Vorbis_I_spec2x.png" alt="π
2" class="frac" align="middle"> <span
-class="cmsy-10x-x-109">*</span> sin<sup><span
+class="cmsy-10x-x-120">*</span> sin <sup><span
class="cmr-8">2</span></sup>( (<span
-class="cmtt-10x-x-109">[i]</span>-<span
-class="cmtt-10x-x-109">[left_window_start]</span>+0.5) / <span
-class="cmtt-10x-x-109">[left_n] </span><span
-class="cmsy-10x-x-1
09">*</span><img
+class="cmtt-12">[i]</span>-<span
+class="cmtt-12">[left_window_start]</span>+0.5) / <span
+class="cmtt-12">[left_n] </span><span
+class="cmsy-10x-x-1
20">*</span><img
src="Vorbis_I_spec3x.png" alt="π
- 2" class="frac" align="middle">) )
- </li>
- <li
+2" class="frac" align="middle">) )
+ </li>
+ <li
class="enumerate" id="x1-72056x6">window from range <span
-class="cmtt-10x-x-109">[left_window_end] </span>... <span
-class="cmtt-10x-x-109">[right_window_start]</span>-1 inclusive is
- one
- </li>
- <li
+class="cmtt-12">[left_window_end] </span>... <span
+class="cmtt-12">[right_window_start]</span>-1 inclusive is
+ one
+ </li>
+ <li
class="enumerate" id="x1-72058x7">for <span
-class="cmtt-10x-x-109">[i] </span>in range <span
-class="cmtt-10x-x-109">[right_window_start] </span>... <span
-class="cmtt-10x-x-109">[right_window_end]</span>-1, window(<span
-class="cmtt-10x-x-109">[i]</span>) =
- sin(<img
+class="cmtt-12">[i] </span>in range <span
+class="cmtt-12">[right_window_start] </span>... <span
+class="cmtt-12">[right_window_end]</span>-1, window(<span
+class="cmtt-12">[i]</span>) =
src="Vorbis_I_spec4x.png" alt="π
2" class="frac" align="middle"> <span
-class="cmsy-10x-x-109">*</span> sin<sup><span
+class="cmsy-10x-x-120">*</span> sin <sup><span
class="cmr-8">2</span></sup>( (<span
-class="cmtt-10x-x-109">[i]</span>-<span
-class="cmtt-10x-x-109">[right_window_start]</span>+0.5) / <span
-class="cmtt-10x-x-109">[right_n] </span><span
-class="cmsy-10x-x-1
09">*</span><img
+class="cmtt-12">[i]</span>-<span
+class="cmtt-12">[right_window_start]</span>+0.5) / <span
+class="cmtt-12">[right_n] </span><span
+class="cmsy-10x-x-1
20">*</span><img
src="Vorbis_I_spec5x.png" alt="π
2" class="frac" align="middle"> + <img
src="Vorbis_I_spec6x.png" alt="π
2" class="frac" align="middle">) )
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-72060x8">window from range <span
-class="cmtt-10x-x-109">[right_window_start] </span>... <span
-class="cmtt-10x-x-109">[n]</span>-1 is zero</li></ol>
-<!--l. 367--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this packet
-from the stream. An end of packet condition past this point is to be considered a possible nominal
-occurrence.
+class="cmtt-12">[right_window_start] </span>... <span
+class="cmtt-12">[n]</span>-1 is zero</li></ol>
+<!--l. 367--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this
+packet from the stream. An end of packet condition past this point is to be considered a possible
+nominal occurrence.
+
+
+
<!--l. 374--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.2
</span> <a
id="x1-730004.3.2"></a>floor curve decode</h5>
-
-
-
<!--l. 376--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
-class="cmtt-10x-x-109">[mode_number]</span>
+class="cmtt-12">[mode_number]</span>
from configuration array <span
-class="cmtt-10x-x-109">[vorbis_mode_configurations] </span>and the map number
+class="cmtt-12">[vorbis_mode_configurations] </span>and the map number
<span
-class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
+class="cmtt-12">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
array <span
-class="cmtt-10x-x-109">[vorbis_mapping_configurations]</span>.
+class="cmtt-12">[vorbis_mapping_configurations]</span>.
<!--l. 383--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
<!--l. 385--><p class="noindent" >For each floor <span
-class="cmtt-10x-x-109">[i] </span>of <span
-class="cmtt-10x-x-109">[audio_channels]</span>
- <ol class="enumerate1" >
- <li
+class="cmtt-12">[i] </span>of <span
+class="cmtt-12">[audio_channels]</span>
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-73002x1"><span
-class="cmtt-10x-x-109">[submap_number] </span>= element <span
-class="cmtt-10x-x-109">[i] </span>of vector [vorbis˙mapping˙mux]
- </li>
- <li
+class="cmtt-12">[submap_number] </span>= element <span
+class="cmtt-12">[i] </span>of vector [vorbis˙mapping˙mux]
+ </li>
+ <li
class="enumerate" id="x1-73004x2"><span
-class="cmtt-10x-x-109">[floor_number] </span>= element <span
-class="cmtt-10x-x-109">[submap_number] </span>of vector [vorbis˙submap˙floor]
- </li>
- <li
- class="enumerate" id="x1-73006x3">if the floor type of this floor (vector <span
-class="cmtt-10x-x-109">[vorbis_floor_types] </span>element <span
-class="cmtt-10x-x-109">[floor_number]</span>)
- is zero then decode the floor for channel <span
-class="cmtt-10x-x-109">[i] </span>according to the <a
-href="#x1-930006.2.2">subsubsection 6.2.2<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>,
+class="cmtt-12">[floor_number] </span>= element <span
+class="cmtt-12">[submap_number] </span>of vector [vorbis˙submap˙floor]
+ </li>
+ <li
+ class="enumerate" id="x1-73006x3">if the floor type of this floor (vector
+ <span
+class="cmtt-12">[vorbis_floor_types] </span>element <span
+class="cmtt-12">[floor_number]</span>) is zero then decode the floor for
+ channel <span
+class="cmtt-12">[i] </span>according to the <a
+
href="#x1-930006.2.2">subsubsection 6.2.2<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>, “<a
href="#x1-930006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-73008x4">if the type of this floor is one then decode the floor for channel <span
-class="cmtt-10x-x-109">[i] </span>according to the
- <a
+class="cmtt-12">[i] </span>according to the
href="#x1-1000007.2.2">paragraph 7.2.2<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>, “<a
href="#x1-1000007.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-73010x5">save the needed decoded floor information for channel for later synthesis
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-73012x6">if the decoded floor returned ’unused’, set vector <span
-class="cmtt-10x-x-109">[no_residue] </span>element <span
-class="cmtt-10x-x-109">[i] </span>to true,
- else set vector <span
-class="cmtt-10x-x-109">[no_residue] </span>element <span
-class="cmtt-10x-x-109">[i] </span>to false</li></ol>
+class="cmtt-12">[no_residue] </span>element <span
+class="cmtt-12">[i] </span>to true,
+ else set vector <span
+class="cmtt-12">[no_residue] </span>element <span
+class="cmtt-12">[i] </span>to false</li></ol>
<!--l. 405--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
output vectors and skipping to the add/overlap output stage.
<!--l. 411--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.3
</span> <a
id="x1-740004.3.3"></a>nonzero vector propagate</h5>
<!--l. 413--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
-coded in the stream, save for one complication. If some vectors are used and some are not, channel
-coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
+coded in the stream, save for one complication. If some vectors are used and some are not,
+
+
+
+channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
vectors.
<!--l. 420--><p class="noindent" >for each <span
-class="cmtt-10x-x-109">[i] </span>from 0 ... <span
-class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps]</span>-1
-<!--l. 42
3--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+class="cmtt-12">[i] </span>from 0 ... <span
+class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1
+<!--l. 42
2--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-74002x1">if either <span
-class="cmtt-10x-x-109">[no_residue] </span>entry for channel (<span
-class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
-class="cmtt-10x-x-109">[i]</span>)
-
-
-
- or channel (<span
-class="cmtt-10x-x-109">[vorbis_mapping_angle] </span>element <span
-class="cmtt-10x-x-109">[i]</span>) are set to false, then both must be
- set to false. Note that an ’unused’ floor has no decoded floor information; it is important
- that this is remembered at floor curve synthesis time.</li></ol>
+class="cmtt-12">[no_residue] </span>entry for channel (<span
+class="cmtt-12">[vorbis_mapping_magnitude] </span>element
+ <span
+class="cmtt-12">[i]</span>) or channel (<span
+class="cmtt-12">[vorbis_mapping_angle] </span>element <span
+class="cmtt-12">[i]</span>) are set to false, then both
+ must be set to false. Note that an ’unused’ floor has no decoded floor information; it
+ is important that this is remembered at floor curve synthesis time.</li></ol>
<!--l. 435--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.4
</span> <a
id="x1-750004.3.4"></a>residue decode</h5>
<!--l. 437--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
order.
<!--l. 440--><p class="noindent" >for each submap <span
-class="cmtt-10x-x-109">[i] </span>in order from 0 ... <span
-class="cmtt-10x-x-109">[vorbis_mapping_submaps]</span>-1
-<!--l. 44
3--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+class="cmtt-12">[i] </span>in order from 0 ... <span
+class="cmtt-12">[vorbis_mapping_submaps]</span>-1
+<!--l. 44
2--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-75002x1"><span
-class="cmtt-10x-x-109">[ch] </span>= 0
- </li>
- <li
+class="cmtt-12">[ch] </span>= 0
+ </li>
+ <li
class="enumerate" id="x1-75004x2">for each channel <span
-class="cmtt-10x-x-109">[j] </span>in order from 0 ... <span
-class="cmtt-10x-x-109">[audio_channels] </span>- 1
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[j] </span>in order from 0 ... <span
+class="cmtt-12">[audio_channels] </span>- 1
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-75006x1">if channel <span
-class="cmtt-10x-x-109">[j] </span>in submap <span
-class="cmtt-10x-x-109">[i] </span>(vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
-class="cmtt-10x-x-109">[j] </span>is equal to
- <span
-class="cmtt-10x-x-109">[i]</span>)
- <ol class="enumerate3" >
- <li
+class="cmtt-12">[j] </span>in submap <span
+class="cmtt-12">[i] </span>(vector <span
+class="cmtt-12">[vorbis_mapping_mux] </span>element <span
+class="cmtt-12">[j] </span>is equal to
+ <span
+class="cmtt-12">[i]</span>)
+
<ol class="enumerate3" >
+ <li
class="enumerate" id="x1-75008x1">if vector <span
-class="cmtt-10x-x-109">[no_residue] </span>element <span
-class="cmtt-10x-x-109">[j] </span>is true
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[no_residue] </span>element <span
+class="cmtt-12">[j] </span>is true
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-75010x1">vector <span
-class="cmtt-10x-x-109">[do_not_decode_flag] </span>element <span
-class="cmtt-10x-x-109">[ch] </span>is set</li></ol>
- <!--l. 452--><p class="noindent" >else
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[do_not_decode_flag] </span>element <span
+class="cmtt-12">[ch] </span>is set</li></ol>
+
<!--l. 452--><p class="noindent" >else
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-75012x1">vector <span
-class="cmtt-10x-x-109">[do_not_decode_flag] </span>element <span
-class="cmtt-10x-x-109">[ch] </span>is unset</li></ol>
- </li>
- <li
+class="cmtt-12">[do_not_decode_flag] </span>element <span
+class="cmtt-12">[ch] </span>is unset</li></ol>
+ </li>
+ <li
class="enumerate" id="x1-75014x2">increment <span
-class="cmtt-10x-x-109">[ch]</span></li></ol>
- </li></ol>
- </li>
- <li
+class="cmtt-12">[ch]</span></li></ol>
+
+
+
+ </li></ol>
+ </li>
+ <li
class="enumerate" id="x1-75016x3"><span
-class="cmtt-10x-x-109">[residue_number] </span>= vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_submap_residue] </span>element <span
-class="cmtt-10x-x-109">[i]</span>
- </li>
- <li
+class="cmtt-12">[residue_number] </span>= vector <span
+class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
+class="cmtt-12">[i]</span>
+ </li>
+ <li
class="enumerate" id="x1-75018x4"><span
-class="cmtt-10x-x-109">[residue_type] </span>= vector <span
-class="cmtt-10x-x-109">[vorbis_residue_types] </span>element <span
-class="cmtt-10x-x-109">[residue_number]</span>
- </li>
- <li
+class="cmtt-12">[residue_type] </span>= vector <span
+class="cmtt-12">[vorbis_residue_types] </span>element <span
+class="cmtt-12">[residue_number]</span>
+ </li>
+ <li
class="enumerate" id="x1-75020x5">decode <span
-class="cmtt-10x-x-109">[ch] </span>vectors using residue <span
-class="cmtt-10x-x-109">[residue_number]</span>, according to type <span
-class="cmtt-10x-x-109">[residue_type]</span>,
- also passing vector <span
-class="cmtt-10x-x-109">[do_not_decode_flag] </span>to indicate which vectors in the bundle should not
- be decoded. Correct per-vector decode length is <span
-class="cmtt-10x-x-109">[n]</span>/2.
-
-
-
- </li>
- <li
+class="cmtt-12">[ch] </span>vectors using residue <span
+class="cmtt-12">[residue_number]</span>, according to type <span
+class="cmtt-12">[residue_type]</span>,
+ also passing vector <span
+class="cmtt-12">[do_not_decode_flag] </span>to indicate which vectors in the bundle should
+ not be decoded. Correct per-vector decode length is <span
+class="cmtt-12">[n]</span>/2.
+ </li>
+ <li
class="enumerate" id="x1-75022x6"><span
-class="cmtt-10x-x-109">[ch] </span>= 0
- </li>
- <li
+class="cmtt-12">[ch] </span>= 0
+ </li>
+ <li
class="enumerate" id="x1-75024x7">for each channel <span
-class="cmtt-10x-x-109">[j] </span>in order from 0 ... <span
-class="cmtt-10x-x-109">[audio_channels]</span>
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[j] </span>in order from 0 ... <span
+class="cmtt-12">[audio_channels]</span>
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-75026x1">if channel <span
-class="cmtt-10x-x-109">[j] </span>is in submap <span
-class="cmtt-10x-x-109">[i] </span>(vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
-class="cmtt-10x-x-109">[j] </span>is equal to
- <span
-class="cmtt-10x-x-109">[i]</span>)
- <ol class="enumerate3" >
- <li
+class="cmtt-12">[j] </span>is in submap <span
+class="cmtt-12">[i] </span>(vector <span
+class="cmtt-12">[vorbis_mapping_mux] </span>element <span
+class="cmtt-12">[j] </span>is equal
+ to <span
+class="cmtt-12">[i]</span>)
+
<ol class="enumerate3" >
+ <li
class="enumerate" id="x1-75028x1">residue vector for channel <span
-class="cmtt-10x-x-109">[j] </span>is set to decoded residue vector <span
-class="cmtt-10x-x-109">[ch]</span>
- </li>
- <li
+class="cmtt-12">[j] </span>is set to decoded residue vector <span
+class="cmtt-12">[ch]</span>
+ </li>
+ <li
class="enumerate" id="x1-75030x2">increment <span
-class="cmtt-10x-x-109">[ch]</span></li></ol>
- </li></ol>
- </li></ol>
+class="cmtt-12">[ch]</span></li></ol>
+ </li></ol>
+ </li></ol>
<!--l. 479--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.5
</span> <a
id="x1-760004.3.5"></a>inverse coupling</h5>
<!--l. 481--><p class="noindent" >for each <span
-class="cmtt-10x-x-109">[i] </span>from <span
-class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
-<!--l. 48
4--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+class="cmtt-12">[i] </span>from <span
+class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
+<!--l. 48
3--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-76002x1"><span
-class="cmtt-10x-x-109">[magnitude_vector] </span>= the residue vector for channel (vector
- <span
-class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
-class="cmtt-10x-x-109">[i]</span>)
- </li>
- <li
+class="cmtt-12">[magnitude_vector] </span>= the residue vector for channel (vector
+ <span
+class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
+class="cmtt-12">[i]</span>)
+ </li>
+ <li
class="enumerate" id="x1-76004x2"><span
-class="cmtt-10x-x-109">[angle_vector] </span>= the residue vector for channel (vector <span
-class="cmtt-10x-x-109">[vorbis_mapping_angle]</span>
- element <span
-class="cmtt-10x-x-109">[i]</span>)
- </li>
- <li
+class="cmtt-12">[angle_vector] </span>= the residue vector for channel (vector <span
+class="cmtt-12">[vorbis_mapping_angle]</span>
+
+
+
+ element <span
+class="cmtt-12">[i]</span>)
+ </li>
+ <li
class="enumerate" id="x1-76006x3">for each scalar value <span
-class="cmtt-10x-x-109">[M] </span>in vector <span
-class="cmtt-10x-x-109">[magnitude_vector] </span>and the corresponding scalar value
- <span
-class="cmtt-10x-x-109">[A] </span>in vector <span
-class="cmtt-10x-x-109">[angle_vector]</span>:
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[M] </span>in vector <span
+class="cmtt-12">[magnitude_vector] </span>and the corresponding scalar value
+ <span
+class="cmtt-12">[A] </span>in vector <span
+class="cmtt-12">[angle_vector]</span>:
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-76008x1">if (<span
-class="cmtt-10x-x-109">[M] </span>is greater than zero)
- <ol class="enumerate3" >
- <li
+class="cmtt-12">[M] </span>is greater than zero)
+
<ol class="enumerate3" >
+ <li
class="enumerate" id="x1-76010x1">if (<span
-class="cmtt-10x-x-109">[A] </span>is greater than zero)
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[A] </span>is greater than zero)
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-76012x1"><span
-class="cmtt-10x-x-109">[new_M] </span>= <span
-class="cmtt-10x-x-109">[M]</span>
- </li>
- <li
+class="cmtt-12">[new_M] </span>= <span
+class="cmtt-12">[M]</span>
+ </li>
+ <li
class="enumerate" id="x1-76014x2"><span
-class="cmtt-10x-x-109">[new_A] </span>= <span
-class="cmtt-10x-x-109">[M]</span>-<span
-class="cmtt-10x-x-109">[A]</span></li></ol>
-
-
-
- <!--l. 497--><p class="noindent" >else
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[new_A] </span>= <span
+class="cmtt-12">[M]</span>-<span
+class="cmtt-12">[A]</span></li></ol>
+ <!--l. 497--><p class="noindent" >else
+ <ol class="enumerate4" >
+ <li
class="enumerate" id="x1-76016x1"><span
-class="cmtt-10x-x-109">[new_A] </span>= <span
-class="cmtt-10x-x-109">[M]</span>
- </li>
- <li
+class="cmtt-12">[new_A] </span>= <span
+class="cmtt-12">[M]</span>
+ </li>
+ <li
class="enumerate" id="x1-76018x2"><span
-class="cmtt-10x-x-109">[new_M] </span>= <span
-class="cmtt-10x-x-109">[M]</span>+<span
-class="cmtt-10x-x-109">[A]</span></li></ol>
- </li></ol>
- <!--l. 504--><p class="noindent" >else
- <ol class="enumerate3" >
- <li
+class="cmtt-12">[new_M] </span>= <span
+class="cmtt-12">[M]</span>+<span
+class="cmtt-12">[A]</span></li></ol>
+ </li></ol>
+
<!--l. 504--><p class="noindent" >else
+
<ol class="enumerate3" >
+ <li
class="enumerate" id="x1-76020x1">if (<span
-class="cmtt-10x-x-109">[A] </span>is greater than zero)
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[A] </span>is greater than zero)
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-76022x1"><span
-class="cmtt-10x-x-109">[new_M] </span>= <span
-class="cmtt-10x-x-109">[M]</span>
- </li>
- <li
+class="cmtt-12">[new_M] </span>= <span
+class="cmtt-12">[M]</span>
+ </li>
+ <li
class="enumerate" id="x1-76024x2"><span
-class="cmtt-10x-x-109">[new_A] </span>= <span
-class="cmtt-10x-x-109">[M]</span>+<span
-class="cmtt-10x-x-109">[A]</span></li></ol>
- <!--l. 511--><p class="noindent" >else
- <ol class="enumerate4" >
- <li
+class="cmtt-12">[new_A] </span>= <span
+class="cmtt-12">[M]</span>+<span
+class="cmtt-12">[A]</span></li></ol>
+
<!--l. 511--><p class="noindent" >else
+
<ol class="enumerate4" >
+ <li
class="enumerate" id="x1-76026x1"><span
-class="cmtt-10x-x-109">[new_A] </span>= <span
-class="cmtt-10x-x-109">[M]</span>
- </li>
- <li
+class="cmtt-12">[new_A] </span>= <span
+class="cmtt-12">[M]</span>
+ </li>
+ <li
class="enumerate" id="x1-76028x2"><span
-class="cmtt-10x-x-109">[new_M] </span>= <span
-class="cmtt-10x-x-109">[M]</span>-<span
-class="cmtt-10x-x-109">[A]</span></li></ol>
- </li></ol>
- </li>
- <li
+class="cmtt-12">[new_M] </span>= <span
+class="cmtt-12">[M]</span>-<span
+class="cmtt-12">[A]</span></li></ol>
+ </li></ol>
+ </li>
+ <li
class="enumerate" id="x1-76030x2">set scalar value <span
-class="cmtt-10x-x-109">[M] </span>in vector <span
-class="cmtt-10x-x-109">[magnitude_vector] </span>to <span
-class="cmtt-10x-x-109">[new_M]</span>
- </li>
- <li
+class="cmtt-12">[M] </span>in vector <span
+class="cmtt-12">[magnitude_vector] </span>to <span
+class="cmtt-12">[new_M]</span>
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-76032x3">set scalar value <span
-class="cmtt-10x-x-109">[A] </span>in vector <span
-class="cmtt-10x-x-109">[angle_vector] </span>to <span
-class="cmtt-10x-x-109">[new_A]</span></li></ol>
- </li></ol>
+class="cmtt-12">[A] </span>in vector <span
+class="cmtt-12">[angle_vector] </span>to <span
+class="cmtt-12">[new_A]</span></li></ol>
+ </li></ol>
<!--l. 528--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.6 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.6
</span> <a
id="x1-770004.3.6"></a>dot product</h5>
-<!--l. 530--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to packet
-type. Note that the vector synthesis length for floor computation is <span
-class="cmtt-10x-x-109">[n]</span>/2.
-<!--l. 534--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that channel’s residue
-vector. The result is the dot product of the floor and residue vectors for each channel; the produced
-vectors are the length <span
-class="cmtt-10x-x-109">[n]</span>/2 audio spectrum for each channel.
+<!--l. 530--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
+packet type. Note that the vector synthesis length for floor computation is <span
+class="cmtt-12">[n]</span>/2.
+<!--l. 534--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
+channel’s residue vector. The result is the dot product of the floor and residue vectors for
+each channel; the produced vectors are the length <span
+class="cmtt-12">[n]</span>/2 audio spectrum for each
+channel.
<!--l. 542--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
-implementation might be to assume that a 32 bit fixed-point representation for floor
-
-
-
-and residue and direct multiplication of the vectors is sufficient for acceptable spectral
-depth in all cases because it happens to mostly work with the current Xiph.Org reference
+implementation might be to assume that a 32 bit fixed-point representation for floor and
+residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
+in all cases because it happens to mostly work with the current Xiph.Org reference
encoder.
<!--l. 549--><p class="noindent" >However, floor vector values can span <span
-class="cmsy-10x-x-109">~</span>140dB (<span
-class="cmsy-10x-x-109">~</span>24 bits unsigned), and the audio spectrum vector
-should represent a minimum of 120dB (<span
-class="cmsy-10x-x-109">~</span>21 bits with sign), even when output is to a 16 bit PCM
-device. For the residue vector to represent full scale if the floor is nailed to <span
-class="cmsy-10x-x-109">-</span>140dB, it must be able
-to span 0 to +140dB. For the residue vector to reach full scale if the floor is nailed at 0dB, it must
-be able to represent <span
-class="cmsy-10x-x-109">-</span>140dB to +0dB. Thus, in order to handle full range dynamics, a residue
-vector may span <span
-class="cmsy-10x-x-109">-</span>140dB to +140dB entirely within spec. A 280dB range is approximately 48 bits
-with sign; thus the residue vector must be able to represent a 48 bit range and the dot product
-must be able to handle an effective 48 bit times 24 bit multiplication. This range may be
+class="cmsy-10x-x-120">~</span>140dB (<span
+class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum
+vector should represent a minimum of 120dB (<span
+class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16
+bit PCM device. For the residue vector to represent full scale if the floor is nailed
+to <span
+class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
+full scale if the floor is nailed at 0dB, it must be able to represent <span
+class="cmsy-10x-x-120">-</span>140dB to +0dB.
+Thus, in order to handle full range dynamics, a residue vector may span <span
+class="cmsy-10x-x-120">-</span>140dB to
++140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
+residue vector must be able to represent a 48 bit range and the dot product must
+be able to handle an effective 48 bit times 24 bit multiplication. This range may be
achieved using large (64 bit or larger) integers, or implementing a movable binary point
representation.
<!--l. 566--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.7 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.7
</span> <a
id="x1-780004.3.7"></a>inverse MDCT</h5>
<!--l. 568--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
-inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT
-is available in <span class="cite">[<a
+
+
+
+inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is
+available in <span class="cite">[<a
href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
earlier.
<!--l. 575--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.8 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.8
</span> <a
id="x1-790004.3.8"></a>overlap˙add</h5>
<!--l. 577--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
current window (as illustrated in <a
href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
href="#x1-260001.3.2">Window shape decode (long windows
-only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame
-data is finished data to be returned by the decoder. This data spans from the center
-of the previous window to the center of the current window. In the case of same-sized
+only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
+is finished data to be returned by the decoder. This data spans from the center of
+the previous window to the center of the current window. In the case of same-sized
windows, the amount of data to return is one-half block consisting of and only of the
overlapped portions. When overlapping a short and long window, much of the returned
range does not actually overlap. This does not damage transform orthogonality. Pay
<div class="fancyvrb" id="fancyvrb22">
<a
id="x1-79002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
-
-
-
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
</div>
<!--l. 595--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
windowsize/2-1, inclusive) of the current window.
-<!--l. 598--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The encoder
-accounts for this priming when calculating PCM offsets; after the first frame, the proper PCM
-output offset is ’0’ (as no data has been returned yet).
+<!--l. 598--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
+encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
+PCM output offset is ’0’ (as no data has been returned yet).
<!--l. 605--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">4.3.9 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">4.3.9
</span> <a
id="x1-800004.3.9"></a>output channel order</h5>
-<!--l. 607--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is implicitly
-defined as follows for standard audio applications:
-<!--l. 612--><p class="noindent" >
- <dl class="description"><dt class="description">
+<!--l. 607--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
+implicitly defined as follows for standard audio applications:
+<!--l. 611--><p class="noindent" >
+
+
+
+ <dl class="description"><dt class="description">
<span
-class="cmssbx-10x-x-109">three channels</span> </dt><dd
+class="cmssbx-10x-x-120">three channels</span> </dt><dd
class="description">the stream is monophonic
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">two channels</span> </dt><dd
+class="cmssbx-10x-x-120">two channels</span> </dt><dd
class="description">the stream is stereo. channel order: left, right
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">three channels</span> </dt><dd
+class="cmssbx-10x-x-120">three channels</span> </dt><dd
class="description">the stream is a 1d-surround encoding. channel order: left, center, right
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">four channels</span> </dt><dd
-class="description">the stream is quadraphonic surround. channel order: front left, front right, rear
- left, rear right
- </dd><dt class="description">
+class="cmssbx-10x-x-120">four channels</span> </dt><dd
+class="description">the stream is quadraphonic surround. channel order: front left, front right,
+ rear left, rear right
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">five channels</span> </dt><dd
-class="description">the stream is five-channel surround. channel order: front left, front center, front
- right, rear left, rear right
- </dd><dt class="description">
+class="cmssbx-10x-x-120">five channels</span> </dt><dd
+class="description">the stream is five-channel surround. channel order: front left, front center,
+ front right, rear left, rear right
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">six channels</span> </dt><dd
+class="cmssbx-10x-x-120">six channels</span> </dt><dd
class="description">the stream is 5.1 surround. channel order: front left, front center, front right,
- rear left, rear right, LFE
- </dd><dt class="description">
+ rear left, rear right, LFE
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">greater than six channels</span> </dt><dd
+class="cmssbx-10x-x-120">greater than six channels</span> </dt><dd
class="description">channel use and order is defined by the application
- </dd></dl>
+ </dd></dl>
<!--l. 639--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
channel mappings (such as three and four channel <a
-href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel mappings
-other than mapping 0.
-
+href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
+mappings other than mapping 0.
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">5 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">5
</span> <a
id="x1-810005"></a>comment field and header specification</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">5.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">5.1
</span> <a
id="x1-820005.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
-bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata belongs
-in a separate logical bitstream (usually an XML stream type) that provides greater structure and
-machine parseability.
-<!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of a
-CDR. It should be a little information to remember the disc by and explain it to others; a short,
-to-the-point text note that need not only be a couple words, but isn’t going to be more
+bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
+belongs in a separate logical bitstream (usually an XML stream type) that provides greater
+structure and machine parseability.
+<!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
+a CDR. It should be a little information to remember the disc by and explain it to others; a
+short, to-the-point text note that need not only be a couple words, but isn’t going to be more
than a short paragraph. The essentials, in other words, whatever they turn out to be,
eg:
<!--l. 21--><p class="noindent" >
- <div class="quote">
- <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
-class="cmti-10x-x-109">“I’m Still Around”</span>, opening for
- Moxy Früvous, 1997.</div>
+
<!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
+class="cmti-12">“I’m Still Around”</span>, opening
+ for Moxy Früvous, 1997.</div>
<!--l. 29--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">5.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">5.2
</span> <a
id="x1-830005.2"></a>Comment encoding</h4>
<!--l. 31--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">5.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">5.2.1
</span> <a
id="x1-840005.2.1"></a>Structure</h5>
-<!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is bounded
-to 2<sup><span
+<!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
+bounded to 2<sup><span
class="cmr-8">32</span></sup> <span
-class="cmsy-10x-x-109">- </span>1 and the length of each vector is limited to 2<sup><span
+class="cmsy-10x-x-120">- </span>1 and the length of each vector is limited to 2<sup><span
class="cmr-8">32</span></sup> <span
-class="cmsy-10x-x-109">- </span>1 bytes. The vector length is encoded;
-the vector contents themselves are not null terminated. In addition to the vector list,
-there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits).
-For example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
-20020717”.
-
+class="cmsy-10x-x-120">- </span>1 bytes. The vector length is
+
-
-<!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit packing
-conventions of the vorbis codec. However, since data in the comment header is octet-aligned, they
-can simply be read as unaligned 32 bit little endian unsigned integers.
+
+encoded; the vector contents themselves are not null terminated. In addition to the vector list,
+there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
+example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
+20020717”.
+<!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
+packing conventions of the vorbis codec. However, since data in the comment header
+is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
+integers.
<!--l. 46--><p class="noindent" >The comment header is decoded as follows:
<!--l. 48--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb23">
<a
id="x1-84002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [vendor_length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [vendor_length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-84004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [vendor_string]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> UTF-8</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> [vendor_length]</span><span
-class="cmtt-10"> octets</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [vendor_string]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> UTF-8</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> [vendor_length]</span><span
+class="cmtt-8"> octets</span>
<br class="fancyvrb" /><a
id="x1-84006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [user_comment_list_length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [user_comment_list_length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-84008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [user_comment_list_length]</span><span
-class="cmtt-10"> times</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [user_comment_list_length]</span><span
+class="cmtt-8"> times</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-84010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [length]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 32</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [length]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 32</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-84012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> this</span><span
-class="cmtt-10"> iteration’s</span><span
-class="cmtt-10"> user</span><span
-class="cmtt-10"> comment</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> UTF-8</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> [length]</span><span
-class="cmtt-10"> octets</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> this</span><span
+class="cmtt-8"> iteration’s</span><span
+class="cmtt-8"> user</span><span
+class="cmtt-8"> comment</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> UTF-8</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> [length]</span><span
+class="cmtt-8"> octets</span>
<br class="fancyvrb" /><a
id="x1-84014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-84016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [framing_bit]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> single</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> boolean</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [framing_bit]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> single</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> boolean</span>
<br class="fancyvrb" /><a
id="x1-84018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [framing_bit]</span><span
-class="cmtt-10"> unset</span><span
-class="cmtt-10"> or</span><span
-class="cmtt-10"> end-of-packet</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> ERROR</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [framing_bit]</span><span
+class="cmtt-8"> unset</span><span
+class="cmtt-8"> or</span><span
+class="cmtt-8"> end-of-packet</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> ERROR</span>
<br class="fancyvrb" /><a
id="x1-84020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> done.</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> done.</span>
</div>
<!--l. 64--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">5.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">5.2.2
</span> <a
id="x1-850005.2.2"></a>Content vector format</h5>
-<!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is, comment
-fields consist of a field name and a corresponding value and look like:
+<!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is,
+comment fields consist of a field name and a corresponding value and look like:
<!--l. 70--><p class="noindent" >
- <div class="quote">
- <!--l. 71--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb24">
+
<!--l. 71--><p class="noindent" >
+
<div class="fancyvrb" id="fancyvrb24">
<a
id="x1-85002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> comment[0]="ARTIST=me";</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> comment[0]="ARTIST=me";</span>
<br class="fancyvrb" /><a
id="x1-85004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> comment[1]="TITLE=the</span><span
-class="cmtt-10"> sound</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> Vorbis";</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> comment[1]="TITLE=the</span><span
+class="cmtt-8"> sound</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> Vorbis";</span>
</div>
- </div>
+ </div>
+
+
+
<!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
ASCII 0x61 through 0x7A inclusive (characters a-z).
-<!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to terminate
-the field name.
-
-
-
+<!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
+terminate the field name.
<!--l. 87--><p class="noindent" >0x3D is followed by 8 bit clean UTF-8 encoded value of the field contents to the end of the
field.
<!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
id="x1-860005.2.2"></a><span
-class="cmbx-10x-x-109">Field names</span></span>
+class="cmbx-12">Field names</span></span>
Below is a proposed, minimal list of standard field names with a description of intended use. No
-single or group of field names is mandatory; a comment header may contain one, all or none of the
-names in this list.
-<!--l. 9
9--><p class="noindent" >
- <dl class="description"><dt class="description">
+single or group of field names is mandatory; a comment header may contain one, all or none of
+the names in this list.
+<!--l. 9
8--><p class="noindent" >
+
<dl class="description"><dt class="description">
<span
-class="cmssbx-10x-x-109">TITLE</span> </dt><dd
+class="cmssbx-10x-x-120">TITLE</span> </dt><dd
class="description">Track/Work name
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">VERSION</span> </dt><dd
-class="description">The version field may be used to differentiate multiple versions of the same track
- title in a single collection. (e.g. remix info)
- </dd><dt class="description">
+class="cmssbx-10x-x-120">VERSION</span> </dt><dd
+class="description">The version field may be used to differentiate multiple versions of the same
+ track title in a single collection. (e.g. remix info)
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">ALBUM</span> </dt><dd
+class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
class="description">The collection name to which this track belongs
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">TRACKNUMBER</span> </dt><dd
+class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
class="description">The track number of this piece if part of a specific larger collection or
- album
- </dd><dt class="description">
+ album
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">ARTIST</span> </dt><dd
+class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
class="description">The artist generally considered responsible for the work. In popular music this is
- usually the performing band or singer. For classical music it would be the composer.
- For an audio book it would be the author of the original text.
- </dd><dt class="description">
+ usually the performing band or singer. For classical music it would be the composer.
+ For an audio book it would be the author of the original text.
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">PERFORMER</span> </dt><dd
+class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
class="description">The artist(s) who performed the work. In classical music this would be the
- conductor, orchestra, soloists. In an audio book it would be the actor who did the
- reading. In popular music this is typically the same as the ARTIST and is omitted.
- </dd><dt class="description">
+ conductor, orchestra, soloists. In an audio book it would be the actor who did the
+ reading. In popular music this is typically the same as the ARTIST and is omitted.
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">COPYRIGHT</span> </dt><dd
+class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
- </dd><dt class="description">
+ </dd><dt class="description">
+
+
+
<span
-class="cmssbx-10x-x-109">LICENSE</span> </dt><dd
-class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to a
- license such as a
- Creative Commons license (”www.creativecommons.org/blahblah/license.html”) or the
- EFF Open Audio License (’distributed under the terms of the Open Audio License. see
- http://www.eff.org/IP/Open˙licenses/eff˙oal.html for details’), etc.
- </dd><dt class="description">
+class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
+class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to
+ a license such as a Creative
+ Commons license (”www.creativecommons.org/blahblah/license.html”) or the EFF
+ Open Audio License (’distributed under the terms of the Open Audio License. see
+ http://www.eff.org/IP/Open˙licenses/eff˙oal.html for details’), etc.
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">ORGANIZATION</span> </dt><dd
+class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
class="description">Name of the organization producing the track (i.e. the ’record label’)
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">DESCRIPTION</span> </dt><dd
+class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
class="description">A short text description of the contents
-
-
-
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">GENRE</span> </dt><dd
+class="cmssbx-10x-x-120">GENRE</span> </dt><dd
class="description">A short text indication of music genre
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">DATE</span> </dt><dd
+class="cmssbx-10x-x-120">DATE</span> </dt><dd
class="description">Date the track was recorded
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">LOCATION</span> </dt><dd
+class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
class="description">Location where track was recorded
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">CONTACT</span> </dt><dd
-class="description">Contact information for the creators or distributors of the track. This could be
- a URL, an email address, the physical address of the producing label.
- </dd><dt class="description">
+class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
+class="description">Contact information for the creators or distributors of the track. This could
+ be a URL, an email address, the physical address of the producing label.
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">ISRC</span> </dt><dd
+class="cmssbx-10x-x-120">ISRC</span> </dt><dd
class="description">International Standard Recording Code for the track; see <a
-href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for more
- information on ISRC numbers.
- </dd></dl>
+href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for
+ more information on ISRC numbers.
+ </dd></dl>
<!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
id="x1-870005.2.2"></a><span
-class="cmbx-10x-x-109">Implications</span></span>
-Field names should not be ’internationalized’; this is a concession to simplicity not an attempt to
-exclude the majority of the world that doesn’t speak English. Field <span
-class="cmti-10x-x-109">contents</span>, however, use the
-UTF-8 character encoding to allow easy representation of any language.
+class="cmbx-12">Implications</span></span>
+Field names should not be ’internationalized’; this is a concession to simplicity not
+an attempt to exclude the majority of the world that doesn’t speak English. Field
+<span
+class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
+language.
<!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
the field name is bounded in a known way. Thus we also have the length of the field
contents.
-<!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper use of comment
-fields should be clear through context at this point. Abuse will be discouraged.
-<!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort to
-avoid arbitrarily polluting the common namespace. We will generally collect the more useful tags
-here to help with standardization.
-<!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an example,
-assume a track was recorded by three well know artists; the following is permissible, and
-encouraged:
+<!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
+use of comment fields should be clear through context at this point. Abuse will be
+discouraged.
+
+
+
+<!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
+to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
+tags here to help with standardization.
+<!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
+example, assume a track was recorded by three well know artists; the following is permissible,
+and encouraged:
<!--l. 183--><p class="noindent" >
- <div class="quote">
- <!--l. 184--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb25">
+
<!--l. 184--><p class="noindent" >
+
<div class="fancyvrb" id="fancyvrb25">
<a
id="x1-87002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ARTIST=Dizzy</span><span
-class="cmtt-10"> Gillespie</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ARTIST=Dizzy</span><span
+class="cmtt-8"> Gillespie</span>
<br class="fancyvrb" /><a
id="x1-87004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ARTIST=Sonny</span><span
-class="cmtt-10"> Rollins</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ARTIST=Sonny</span><span
+class="cmtt-8"> Rollins</span>
<br class="fancyvrb" /><a
id="x1-87006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> ARTIST=Sonny</span><span
-class="cmtt-10"> Stitt</span>
-
-
-
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> ARTIST=Sonny</span><span
+class="cmtt-8"> Stitt</span>
</div>
- </div>
+ </div>
<!--l. 197--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">5.2.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">5.2.3
</span> <a
id="x1-880005.2.3"></a>Encoding</h5>
-<!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the first
-bitstream header packet, it is not generally the only packet on the second page and may not be
-restricted to within the second bitstream page. The length of the comment header packet is
+<!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
+first bitstream header packet, it is not generally the only packet on the second page and may not
+be restricted to within the second bitstream page. The length of the comment header packet is
(practically) unbounded. The comment header packet is not optional; it must be present in the
bitstream even if it is effectively empty.
-<!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which renders
-least-significant-bit of the word to be coded into the least significant available bit of the current
-bitstream octet first):
-<!--l. 21
3--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+<!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
+renders least-significant-bit of the word to be coded into the least significant available bit of the
+current bitstream octet first):
+<!--l. 21
2--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-88002x1">Vendor string length (32 bit unsigned quantity specifying number of octets)
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-88004x2">Vendor string ([vendor string length] octets coded from beginning of string to end of
- string, not null terminated)
- </li>
- <li
+ string, not null terminated)
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-88006x3">Number of comment fields (32 bit unsigned quantity specifying number of fields)
- </li>
- <li
+ </li>
+ <li
class="enumerate" id="x1-88008x4">Comment field 0 length (if [Number of comment fields] <span
-class="cmmi-10x-x-109">> </span>0; 32 bit unsigned quantity
- specifying number of octets)
- </li>
- <li
- class="enumerate" id="x1-88010x5">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to end
- of string, not null terminated)
- </li>
- <li
+class="cmmi-12">> </span>0; 32 bit unsigned quantity
+ specifying number of octets)
+ </li>
+ <li
+ class="enumerate" id="x1-88010x5">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
+ end of string, not null terminated)
+ </li>
+ <li
class="enumerate" id="x1-88012x6">Comment field 1 length (if [Number of comment fields] <span
-class="cmmi-10x-x-109">> </span>1...)...
- </li></ol>
-<!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found in
-<span
-class="cmtt-10x-x-109">vorbis/lib/info.c</span>, <span
-class="cmtt-10x-x-109">_vorbis_pack_comment() </span>and <span
-class="cmtt-10x-x-109">_vorbis_unpack_comment()</span>.
-
+class="cmmi-12">> </span>1...)...
+ </li></ol>
+<!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
+in <span
+class="cmtt-12">vorbis/lib/info.c</span>, <span
+class="cmtt-12">_vorbis_pack_comment() </span>and <span
+class="cmtt-12">_vorbis_unpack_comment()</span>.
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">6 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">6
</span> <a
id="x1-890006"></a>Floor type 0 setup and decode</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">6.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">6.1
</span> <a
id="x1-900006.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
-response of the LSP filter. This representation is equivalent to a traditional all-pole infinite impulse
-response filter as would be used in linear predictive coding; LSP representation may be converted to
-LPC representation and vice-versa.
+response of the LSP filter. This representation is equivalent to a traditional all-pole infinite
+impulse response filter as would be used in linear predictive coding; LSP representation may be
+converted to LPC representation and vice-versa.
<!--l. 18--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">6.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">6.2
</span> <a
id="x1-910006.2"></a>Floor 0 format</h4>
<!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
coding/decoding the LSP filter coefficient values used by each frame.
<!--l. 24--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">6.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">6.2.1
</span> <a
id="x1-920006.2.1"></a>header decode</h5>
<!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
packet). configuration decode proceeds as follows:
<div class="fancyvrb" id="fancyvrb26">
<a
id="x1-92002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [floor0_order]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [floor0_order]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-92004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [floor0_rate]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 16</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [floor0_rate]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 16</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-92006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [floor0_bark_map_size]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> 16</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [floor0_bark_map_size]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> 16</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-92008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [floor0_amplitude_bits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> six</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [floor0_amplitude_bits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> six</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-92010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [floor0_amplitude_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> eight</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [floor0_amplitude_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> eight</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-92012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [floor0_number_of_books]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> four</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [floor0_number_of_books]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> four</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-92014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [floor0_book_list]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> list</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [floor0_number_of_books]</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integers</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> eight</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> each;</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [floor0_book_list]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> list</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [floor0_number_of_books]</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integers</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> eight</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> each;</span>
</div>
-
+
-
-<!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable. In
-addition, any element of the array <span
-class="cmtt-10x-x-109">[floor0_book_list] </span>that is greater than the maximum
+
+<!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
+In addition, any element of the array <span
+class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum
codebook number for this bitstream is an error condition that also renders the stream
undecodable.
<!--l. 48--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">6.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">6.2.2
</span> <a
id="x1-930006.2.2"></a>packet decode</h5>
-<!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve amplitude and
-<span
-class="cmtt-10x-x-109">[floor0_order] </span>LSP coefficient values from the bitstream, and then computing the floor curve,
-which is defined as the frequency response of the decoded LSP filter.
+<!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve
+amplitude and <span
+class="cmtt-12">[floor0_order] </span>LSP coefficient values from the bitstream, and then
+computing the floor curve, which is defined as the frequency response of the decoded LSP
+filter.
<!--l. 56--><p class="noindent" >Packet decode proceeds as follows:
<div class="fancyvrb" id="fancyvrb27">
<a
id="x1-93002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [amplitude]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [floor0_amplitude_bits]</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [amplitude]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [floor0_amplitude_bits]</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-93004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [amplitude]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [amplitude]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-93006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [coefficients]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> empty,</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> length</span><span
-class="cmtt-10"> vector</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [coefficients]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> empty,</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> length</span><span
+class="cmtt-8"> vector</span>
<br class="fancyvrb" /><a
id="x1-93008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [booknumber]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [booknumber]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> </span><a
href="#x1-1170009.2.1"><span
-class="cmtt-10">ilog</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> [floor0_number_of_books]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> bits</span>
+class="cmtt-8">ilog</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> [floor0_number_of_books]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-93010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [booknumber]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> highest</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> decode</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> undecodable</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [booknumber]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> highest</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> decode</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> undecodable</span>
<br class="fancyvrb" /><a
id="x1-93012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> zero;</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> zero;</span>
<br class="fancyvrb" /><a
id="x1-93014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [temp_vector]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> bitstream</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [floor0_book_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [booknumber]</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> VQ</span><span
-class="cmtt-10"> context.</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [temp_vector]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> bitstream</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [floor0_book_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [booknumber]</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> VQ</span><span
+class="cmtt-8"> context.</span>
<br class="fancyvrb" /><a
id="x1-93016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> each</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [temp_vector]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> each</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [temp_vector]</span>
<br class="fancyvrb" /><a
id="x1-93018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [last]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> last</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [temp_vector]</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [last]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> last</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [temp_vector]</span>
<br class="fancyvrb" /><a
id="x1-93020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> concatenate</span><span
-class="cmtt-10"> [temp_vector]</span><span
-class="cmtt-10"> onto</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> end</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> [coefficients]</span><span
-class="cmtt-10"> vector</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> concatenate</span><span
+class="cmtt-8"> [temp_vector]</span><span
+class="cmtt-8"> onto</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> end</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> [coefficients]</span><span
+class="cmtt-8"> vector</span>
<br class="fancyvrb" /><a
id="x1-93022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (length</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [coefficients]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [floor0_order],</span><span
-class="cmtt-10"> continue</span><span
-class="cmtt-10"> at</span><span
-class="cmtt-10"> step</span><span
-class="cmtt-10"> 6</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (length</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [coefficients]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [floor0_order],</span><span
+class="cmtt-8"> continue</span><span
+class="cmtt-8"> at</span><span
+class="cmtt-8"> step</span><span
+class="cmtt-8"> 6</span>
<br class="fancyvrb" /><a
id="x1-93024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-93026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-93028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-93030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> done.</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> done.</span>
<br class="fancyvrb" /><a
id="x1-93032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 76--><p class="noindent" >Take note of the following properties of decode:
- <ul class="itemize1">
- <li class="itemize">An <span
-class="cmtt-10x-x-109">[amplitude] </span>value of zero must result in a return code that indicates this channel is
- unused in this frame (the output of the channel will be all-zeroes in synthesis). Several
- later stages of decode don’t occur for an unused channel.
- </li>
- <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
- if end-of-packet is reached during any read operation above, floor decode is to return
- ’unused’ status as if the <span
-class="cmtt-10x-x-109">[amplitude] </span>value had read zero at the beginning of decode.
- </li>
- <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
+ <li class="itemize">An <span
+class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
+ is unused in this frame (the output of the channel will be all-zeroes in synthesis).
+ Several later stages of decode don’t occur for an unused channel.
+ </li>
+ <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
+ if end-of-packet is reached during any read operation above, floor decode is to return
+ ’unused’ status as if the <span
+class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
+ </li>
+
<li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
href="#x1-1170009.2.1">ilog</a>(
- <span
-class="cmtt-10x-x-109">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
-
+
-
- and values greater than the maximum possible book value are reserved.
- </li>
- <li class="itemize">The number of scalars read into the vector <span
-class="cmtt-10x-x-109">[coefficients] </span>may be greater
- than <span
-class="cmtt-10x-x-109">[floor0_order]</span>, the number actually required for curve computation. For
- example, if the VQ codebook used for the floor currently being decoded has a
- <span
-class="cmtt-10x-x-109">[codebook_dimensions] </span>value of three and <span
-class="cmtt-10x-x-109">[floor0_order] </span>is ten, the only way to fill
- all the needed scalars in <span
-class="cmtt-10x-x-109">[coefficients] </span>is to to read a total of twelve scalars as four
- vectors of three scalars each. This is not an error condition, and care must be taken not
- to allow a buffer overflow in decode. The extra values are not used and may be ignored
- or discarded.</li></ul>
+
+ <span
+class="cmtt-12">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
+ and values greater than the maximum possible book value are reserved.
+ </li>
+ <li class="itemize">The number of scalars read into the vector <span
+class="cmtt-12">[coefficients] </span>may be greater
+ than <span
+class="cmtt-12">[floor0_order]</span>, the number actually required for curve computation. For
+ example, if the VQ codebook used for the floor currently being decoded has a
+ <span
+class="cmtt-12">[codebook_dimensions] </span>value of three and <span
+class="cmtt-12">[floor0_order] </span>is ten, the only way to
+ fill all the needed scalars in <span
+class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
+ as four vectors of three scalars each. This is not an error condition, and care must
+ be taken not to allow a buffer overflow in decode. The extra values are not used and
+ may be ignored or discarded.</li></ul>
<!--l. 104--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">6.2.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">6.2.3
</span> <a
id="x1-940006.2.3"></a>curve computation</h5>
<!--l. 106--><p class="noindent" >Given an <span
-class="cmtt-10x-x-109">[amplitude] </span>integer and <span
-class="cmtt-10x-x-109">[coefficients] </span>vector from packet decode as well as the
-[floor0˙order], [floor0˙rate], [floor0˙bark˙map˙size], [floor0˙amplitude˙bits] and [floor0˙amplitude˙offset]
-values from floor setup, and an output vector size <span
-class="cmtt-10x-x-109">[n] </span>specified by the decode process, we compute
-a floor output vector.
+class="cmtt-12">[amplitude] </span>integer and <span
+class="cmtt-12">[coefficients] </span>vector from packet decode as well
+as the [floor0˙order], [floor0˙rate], [floor0˙bark˙map˙size], [floor0˙amplitude˙bits] and
+[floor0˙amplitude˙offset] values from floor setup, and an output vector size <span
+class="cmtt-12">[n] </span>specified by the
+decode process, we compute a floor output vector.
<!--l. 113--><p class="noindent" >If the value <span
-class="cmtt-10x-x-109">[amplitude] </span>is zero, the return value is a length <span
-class="cmtt-10x-x-109">[n] </span>vector with all-zero
+class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span
+class="cmtt-12">[n] </span>vector with all-zero
scalars. Otherwise, begin by assuming the following definitions for the given vector to be
synthesized:
<center class="par-math-display" >
<img
src="Vorbis_I_spec7x.png" alt=" {
- min (floor0xbarkxmapxsize - 1,foobar) for i ∈ [0,n - 1]
-mapi = - 1 for i = n
+ min (floor0xbarkxmapxsize - 1,f oobar) for i ∈ [0, n - 1]
+mapi = - 1 for i = n
" class="par-math-display" ></center>
<!--l. 128--><p class="nopar" >
<!--l. 130--><p class="noindent" >where
<center class="par-math-display" >
<img
-src="Vorbis_I_spec8x.png" alt=" ⌊ ( ) ⌋
-f oobar = bark floor0xrate-⋅i- ⋅ floor0xbarkxmapxsize-
- 2n bark(.5 ⋅floor0xrate )
+src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋
+ (floor0xrate ⋅ i) floor0xbarkxmapxsize
+foobar = bark -------2n------- ⋅-bark(.5 ⋅-floor0xrate-)
" class="par-math-display" ></center>
+
+
+
<!--l. 137--><p class="nopar" >
<!--l. 139--><p class="noindent" >and
-
-
-
<center class="par-math-display" >
<img
-src="Vorbis_I_spec9x.png" alt="bark(x) = 13.1 arctan (.00074x) + 2.24 arctan (.0000000185x2 + .0001x)
+src="Vorbis_I_spec9x.png" alt=" 2
+bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x )
" class="par-math-display" ></center>
<!--l. 143--><p class="nopar" >
-<!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the result
-to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output LSP
-curve <span
-class="cmtt-10x-x-109">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
+<!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
+result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
+LSP curve <span
+class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
step:
-<!--l. 15
1--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+<!--l. 15
0--><p class="noindent" >
+
<ol class="enumerate1" >
+ <li
class="enumerate" id="x1-94002x1"><span
-class="cmtt-10x-x-109">[i] </span>= 0
- </li>
- <li
+class="cmtt-12">[i] </span>= 0
+ </li>
+ <li
class="enumerate" id="x1-94004x2"><span
-class="cmtt-10x-x-109">[</span><span
-class="cmmi-10x-x-109">ω</span><span
-class="cmtt-10x-x-109">] </span>= <span
-class="cmmi-10x-x-109">π </span>* map element <span
-class="cmtt-10x-x-109">[i] </span>/ <span
-class="cmtt-10x-x-109">[floor0_bark_map_size]</span>
- </li>
- <li
+class="cmtt-12">[</span><span
+class="cmmi-12">ω</span><span
+class="cmtt-12">] </span>= <span
+class="cmmi-12">π </span>* map element <span
+class="cmtt-12">[i] </span>/ <span
+class="cmtt-12">[floor0_bark_map_size]</span>
+ </li>
+ <li
class="enumerate" id="x1-94006x3">if ( <span
-class="cmtt-10x-x-109">[floor0_order] </span>is odd )
- <ol class="enumerate2" >
- <li
+class="cmtt-12">[floor0_order] </span>is odd )
+
<ol class="enumerate2" >
+ <li
class="enumerate" id="x1-94008x1">calculate <span
-class="cmtt-10x-x-109">[p] </span>and <span
-class="cmtt-1
0x-x-109">[q] </span>according to: <div class="eqnarray">
- <center class="math-display" >
- <img
-src="Vorbis_I_spec10x.png" alt=" floor0x2order-3
-p = (1- cos2ω ) ∏ 4(cos([coefficients ] )- cosω )2
- j=0 2j+1
- floor0xorder-1
- 1 ---∏2-----
-q = -- 4(cos([coefficients ]2j) - cosω)2
+class="cmtt-12">[p] </span>and <span
+class="cmtt-1
2">[q] </span>according to: <div class="eqnarray">
+ <center class="math-display" >
+src="Vorbis_I_spec10x.png" alt=" floor0xorder-3
+ 2 ∏2 2
+p = (1 - cos ω) 4(cos([coefficients ]2j+1) - cosω )
+ j=0
+ floor0x∏or2der-1
+q = 1- 4(cos([coefficients ]2j) - cosω )2
4 j=0
- " class="math-display" ></center>
- </div>
- </li></ol>
- <!--l. 162--><p class="noindent" >else <span
-class="cmtt-10x-x-109">[floor0_order] </span>is even
- <ol class="enumerate2" >
- <li
- class="enumerate" id="x1-94011x1">calculate <span
-class="cmtt-10x-x-109">[p] </span>and <span
-class="cmtt-10x-x-109">[q] </span>according to: <div class="eqnarray">
-
+
-
- <center class="math-display" >
- <img
-src="Vorbis_I_spec11x.png" alt=" floor0xorder-2
- (1--cos2ω-) ∏2 2
-p = 2 4(cos([coefficients ]2j+1)- cosω )
- j=0
- (1+ cos2ω )floor0x∏o2rder-2
-q = ----------- 4(cos([coefficients ]2j)- cosω )2
- 2 j=0
- " class="math-display" ></center>
- </div>
- </li></ol>
- </li>
- <li
+
+ " class="math-display" ></center>
+ </div>
+ </li></ol>
+ <!--l. 162--><p class="noindent" >else <span
+class="cmtt-12">[floor0_order] </span>is even
+ <ol class="enumerate2" >
+ <li
+ class="enumerate" id="x1-94011x1">calculate <span
+class="cmtt-12">[p] </span>and <span
+class="cmtt-12">[q] </span>according to: <div class="eqnarray">
+ <center class="math-display" >
+ <img
+src="Vorbis_I_spec11x.png" alt=" floor0xorder-2
+ (1 - cos2ω) ∏2 2
+p = -----2------ 4(cos([coefficients ]2j+1) - cosω )
+ j=0
+ 2 floor0xor2der-2
+q = (1 +-cos-ω)- ∏ 4(cos([coefficients ] ) - cosω )2
+ 2 j=0 2j
+ " class="math-display" ></center>
+ </div>
+ </li></ol>
+ </li>
+ <li
class="enumerate" id="x1-94014x4">calculate <span
-class="cmtt-10x-x-109">[linear_floor_value] </span>according to:
- <center class="math-display" >
- <img
-src="Vorbis_I_spec12x.png" alt=" ( ( ))
-exp .11512925 amplitude--⋅floor0xamplitutex√offset-- - floor0xamplitudexoffset
- (2floor0xamplitudexbits - 1) p + q
- " class="math-display" ></center>
- <!--l. 177--><p class="nopar" >
- </li>
- <li
+class="cmtt-12">[linear_floor_value] </span>according to:
+ <center class="math-display" >
+src="Vorbis_I_spec12x.png" alt=" ( ( ))
+ amplitude---⋅ floor0xamplitutexoffset---
+exp .11512925 (2floor0xamplitudexbits - 1)√ p + q - floor0xamplitudexoffset
+ " class="math-display" ></center>
+
<!--l. 177--><p class="nopar" >
+ </li>
+ <li
class="enumerate" id="x1-94016x5"><span
-class="cmtt-10x-x-109">[iteration_condition] </span>= map element <span
-class="cmtt-10x-x-109">[i]</span>
- </li>
- <li
+class="cmtt-12">[iteration_condition] </span>= map element <span
+class="cmtt-12">[i]</span>
+
+
+
+ </li>
+ <li
class="enumerate" id="x1-94018x6"><span
-class="cmtt-10x-x-109">[output] </span>element <span
-class="cmtt-10x-x-109">[i] </span>= <span
-class="cmtt-10x-x-109">[linear_floor_value]</span>
- </li>
- <li
+class="cmtt-12">[output] </span>element <span
+class="cmtt-12">[i] </span>= <span
+class="cmtt-12">[linear_floor_value]</span>
+ </li>
+ <li
class="enumerate" id="x1-94020x7">increment <span
-class="cmtt-10x-x-109">[i]</span>
- </li>
- <li
+class="cmtt-12">[i]</span>
+ </li>
+ <li
class="enumerate" id="x1-94022x8">if ( map element <span
-class="cmtt-10x-x-109">[i] </span>is equal to <span
-class="cmtt-10x-x-109">[iteration_condition] </span>) continue at step 5
- </li>
- <li
+class="cmtt-12">[i] </span>is equal to <span
+class="cmtt-12">[iteration_condition] </span>) continue at step
+ 5
+ </li>
+ <li
class="enumerate" id="x1-94024x9">if ( <span
-class="cmtt-10x-x-109">[i] </span>is less than <span
-class="cmtt-10x-x-109">[n] </span>) continue at step 2
- </li>
- <li
+class="cmtt-12">[i] </span>is less than <span
+class="cmtt-12">[n] </span>) continue at step 2
+ </li>
+ <li
class="enumerate" id="x1-94026x10">done</li></ol>
-
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">7 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">7
</span> <a
id="x1-950007"></a>Floor type 1 setup and decode</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">7.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">7.1
</span> <a
id="x1-960007.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
curve. The representation plots this curve mechanically on a linear frequency axis and a
logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
algorithm.
<!--l. 16--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">7.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">7.2
</span> <a
id="x1-970007.2"></a>Floor 1 format</h4>
<!--l. 18--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">7.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">7.2.1
</span> <a
id="x1-980007.2.1"></a>model</h5>
-<!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a floor
-curve using iterative prediction in a process roughly equivalent to the following simplified
+<!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
+floor curve using iterative prediction in a process roughly equivalent to the following simplified
description:
- <ul class="itemize1">
- <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1 where
- in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be computed.
- </li>
- <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
- produces a y˙new value at that point computed from the existing line’s y value at x˙new
- (as plotted by the line) and a difference value decoded from the bitstream packet.
- </li>
- <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
- x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
- y˙new represents no change to the amplitude value at x˙new so that later refinement is
- additionally bounded at x˙new.
-
+ <ul class="itemize1">
+ <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
+ where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
+ computed.
+ </li>
+ <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
+ produces a y˙new value at that point computed from the existing line’s y value at
+ x˙new (as plotted by the line) and a difference value decoded from the bitstream
+ packet.
+
-
- </li>
- <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
- at floor 1 initialization time. Computation is completed at the end of the x value list.
- </li></ul>
+
+ </li>
+ <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
+ x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
+ y˙new represents no change to the amplitude value at x˙new so that later refinement
+ is additionally bounded at x˙new.
+ </li>
+ <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
+ at floor 1 initialization time. Computation is completed at the end of the x value list.
+ </li></ul>
<!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
representing typical configuration:
-<!--l. 51--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values in
-increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0, 128, 64,
-32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an example
-packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following way,
-beginning with the first line:
+<!--l. 51--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values
+in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
+128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
+example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
+way, beginning with the first line:
<div class="center"
>
<!--l. 59--><p class="noindent" >
><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 7: </td><td
class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980017 -->
</div>
-<!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32 and
-96:
+<!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
+and 96:
<div class="center"
>
<!--l. 67--><p class="noindent" >
class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980028 -->
</div>
<!--l. 72--><p class="noindent" >Although the new Y value at X position 96 is unchanged, it is still used later as an endpoint for
-further refinement. From here on, the pattern should be clear; we complete the floor computation as
-follows:
+further refinement. From here on, the pattern should be clear; we complete the floor computation
+as follows:
+
+
+
<div class="center"
>
<!--l. 76--><p class="noindent" >
><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 9: </td><td
class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980039 -->
</div>
-
-
-
<div class="center"
>
<!--l. 81--><p class="noindent" >
class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-9800410 -->
</div>
<!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
-decode, as described later. The actual algorithm splits Y value computation and line plotting into
-two steps with modifications to the above algorithm to eliminate noise accumulation through integer
-roundoff/truncation.
+decode, as described later. The actual algorithm splits Y value computation and line plotting
+into two steps with modifications to the above algorithm to eliminate noise accumulation
+through integer roundoff/truncation.
<!--l. 94--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">7.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">7.2.2
</span> <a
id="x1-990007.2.2"></a>header decode</h5>
-<!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order during
-packet decode and synthesis). This list is split into partitions, and each partition is assigned to a
-partition class. X positions 0 and [n] are implicit and do not belong to an explicit partition or
-partition class.
-<!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which the
-partition class encodes at once), a ’subclass’ value representing the number of alternate entropy
-books the partition class may use in representing Y values, the list of [subclass] books and a master
-book used to encode which alternate books were chosen for representation in a given packet. The
-master/subclass mechanism is meant to be used as a flexible representation cascade while still using
-codebooks only in a scalar context.
+<!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
+during packet decode and synthesis). This list is split into partitions, and each partition is
+assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
+partition or partition class.
+<!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
+the partition class encodes at once), a ’subclass’ value representing the number of
+alternate entropy books the partition class may use in representing Y values, the list of
+[subclass] books and a master book used to encode which alternate books were chosen
+for representation in a given packet. The master/subclass mechanism is meant to be
+used as a flexible representation cascade while still using codebooks only in a scalar
+context.
+
+
+
<!--l. 112--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb28">
<a
id="x1-99002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [floor1_partitions]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [floor1_partitions]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [maximum_class]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> -1</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [maximum_class]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> -1</span>
<br class="fancyvrb" /><a
id="x1-99008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [floor1_partitions]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [floor1_partitions]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_partition_class_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_partition_class_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [maximum_class]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> largest</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_partition_class_list]</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [maximum_class]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> largest</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_partition_class_list]</span>
<br class="fancyvrb" /><a
id="x1-99022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [maximum_class]</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [maximum_class]</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_dimensions]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_dimensions]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-99028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  8)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_subclasses]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
-
-
-
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  8)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_subclasses]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_subclasses]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> nonzero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_subclasses]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> nonzero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99034r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_masterbooks]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_masterbooks]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99036r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99038r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99040r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99042r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> (2</span><span
-class="cmtt-10"> exponent</span><span
-class="cmtt-10"> [floor1_class_subclasses]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i])</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> (2</span><span
+class="cmtt-8"> exponent</span><span
+class="cmtt-8"> [floor1_class_subclasses]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i])</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99044r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99046r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [floor1_subclass_books]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i],[j]</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [floor1_subclass_books]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i],[j]</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-99048r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> subtract</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> subtract</span><span
+class="cmtt-8"> one</span>
<br class="fancyvrb" /><a
id="x1-99050r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99052r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99054r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99056r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> [floor1_multiplier]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> [floor1_multiplier]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> one</span>
<br class="fancyvrb" /><a
id="x1-99058r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> [rangebits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> [rangebits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99060r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-99062r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [1]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> exponent</span><span
-class="cmtt-10"> [rangebits];</span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [1]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> exponent</span><span
+class="cmtt-8"> [rangebits];</span>
<br class="fancyvrb" /><a
id="x1-99064r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 17)</span><span
-class="cmtt-10"> [floor1_values]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 17)</span><span
+class="cmtt-8"> [floor1_values]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-99066r33"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 18)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [floor1_partitions]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">33</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 18)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [floor1_partitions]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99068r34"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">34</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99070r35"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 19)</span><span
-class="cmtt-10"> [current_class_number]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_partition_class_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">35</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 19)</span><span
+class="cmtt-8"> [current_class_number]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_partition_class_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-99072r36"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 20)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> ([floor1_class_dimensions]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [current_class_number])-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">36</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 20)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> ([floor1_class_dimensions]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [current_class_number])-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-99074r37"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 21)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([floor1_values])</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">37</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 21)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([floor1_values])</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-99076r38"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> [rangebits]</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">38</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> [rangebits]</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-99078r39"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 22)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [floor1_values]</span><span
-class="cmtt-10"> by</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">39</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 22)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [floor1_values]</span><span
+class="cmtt-8"> by</span><span
+class="cmtt-8"> one</span>
<br class="fancyvrb" /><a
id="x1-99080r40"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">40</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99082r41"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">41</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-99084r42"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">42</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-99086r43"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 23)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">43</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 23)</span><span
+class="cmtt-8"> done</span>
</div>
-<!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during setup renders
-a stream undecodable. In addition, a <span
-class="cmtt-10x-x-109">[floor1_class_masterbooks] </span>or <span
-class="cmtt-10x-x-109">[floor1_subclass_books]</span>
-scalar element greater than the highest numbered codebook configured in this stream is an error
-condition that renders the stream undecodable.
+<!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
+setup renders a stream undecodable. In addition, a <span
+class="cmtt-12">[floor1_class_masterbooks] </span>or
+<span
+class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook
+configured in this stream is an error condition that renders the stream undecodable.
<!--l. 165--><p class="noindent" ><span class="paragraphHead"><a
id="x1-1000007.2.2"></a><span
-class="cmbx-10x-x-109">packet decode</span></span>
+class="cmbx-12">packet decode</span></span>
Packet decode begins by checking the <span
-class="cmtt-10x-x-109">[nonzero] </span>flag:
+class="cmtt-12">[nonzero] </span>flag:
+
+
+
<!--l. 169--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb29">
<a
id="x1-100002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [nonzero]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> boolean</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [nonzero]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> boolean</span>
</div>
<!--l. 173--><p class="noindent" >If <span
-class="cmtt-10x-x-109">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame. Decode
-immediately returns a status indicating this floor curve (and thus this channel) is unused
+class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
+Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
this frame. (A return status of ’unused’ is different from decoding a floor that has all
-
-
-
points set to minimum representation amplitude, which happens to be approximately
-140dB).
<!--l. 181--><p class="noindent" >Assuming <span
-class="cmtt-10x-x-109">[nonzero] </span>is set, decode proceeds as follows:
+class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
<!--l. 183--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb30">
<a
id="x1-100004r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [range]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span><span
-class="cmtt-10"> 256,</span><span
-class="cmtt-10"> 128,</span><span
-class="cmtt-10"> 86,</span><span
-class="cmtt-10"> 64</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([floor1_multiplier]-1)</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [range]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span><span
+class="cmtt-8"> 256,</span><span
+class="cmtt-8"> 128,</span><span
+class="cmtt-8"> 86,</span><span
+class="cmtt-8"> 64</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([floor1_multiplier]-1)</span>
<br class="fancyvrb" /><a
id="x1-100006r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> </span><a
href="#x1-1170009.2.1"><span
-class="cmtt-10">ilog</span></a><span
-class="cmtt-10">([range]-1)</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmtt-8">ilog</span></a><span
+class="cmtt-8">([range]-1)</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-100008r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [1]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [1]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> </span><a
href="#x1-1170009.2.1"><span
-class="cmtt-10">ilog</span></a><span
-class="cmtt-10">([range]-1)</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmtt-8">ilog</span></a><span
+class="cmtt-8">([range]-1)</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-100010r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2;</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2;</span>
<br class="fancyvrb" /><a
id="x1-100012r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [floor1_partitions]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [floor1_partitions]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-100014r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100016r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [class]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_partition_class]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [class]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_partition_class]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-100018r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [cdim]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_dimensions]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [class]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [cdim]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_dimensions]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [class]</span>
<br class="fancyvrb" /><a
id="x1-100020r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> [cbits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_class_subclasses]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [class]</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> [cbits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_class_subclasses]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [class]</span>
<br class="fancyvrb" /><a
id="x1-100022r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [csub]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> (2</span><span
-class="cmtt-10"> exponent</span><span
-class="cmtt-10"> [cbits])-1</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [csub]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> (2</span><span
+class="cmtt-8"> exponent</span><span
+class="cmtt-8"> [cbits])-1</span>
<br class="fancyvrb" /><a
id="x1-100024r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> [cval]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> [cval]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-100026r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [cbits]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [cbits]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-100028r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100030r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> [cval]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> number</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> [cval]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> number</span>
<br class="fancyvrb" /><a
id="x1-100032r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> (vector</span><span
-class="cmtt-10"> [floor1_class_masterbooks]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [class])</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> (vector</span><span
+class="cmtt-8"> [floor1_class_masterbooks]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [class])</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-100034r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-100036r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100038r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [cdim]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [cdim]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-100040r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100042r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> [book]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [floor1_subclass_books]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [class],([cval]</span><span
-class="cmtt-10"> bitwise</span><span
-class="cmtt-10"> AND</span><span
-class="cmtt-10"> [csub])</span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> [book]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [floor1_subclass_books]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [class],([cval]</span><span
+class="cmtt-8"> bitwise</span><span
+class="cmtt-8"> AND</span><span
+class="cmtt-8"> [csub])</span>
<br class="fancyvrb" /><a
id="x1-100044r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> [cval]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [cval]</span><span
-class="cmtt-10"> right</span><span
-class="cmtt-10"> shifted</span><span
-class="cmtt-10"> [cbits]</span><span
-class="cmtt-10"> bits</span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> [cval]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [cval]</span><span
+class="cmtt-8"> right</span><span
+class="cmtt-8"> shifted</span><span
+class="cmtt-8"> [cbits]</span><span
+class="cmtt-8"> bits</span>
<br class="fancyvrb" /><a
id="x1-100046r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [book]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [book]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-100048r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100050r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 17)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([j]+[offset])</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> codebook</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 17)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([j]+[offset])</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> codebook</span>
<br class="fancyvrb" /><a
id="x1-100052r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [book]</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [book]</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-100054r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100056r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [book]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [book]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-100058r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100060r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 18)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([j]+[offset])</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 18)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([j]+[offset])</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-100062r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100064r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-100066r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-100068r33"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">33</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100070r34"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 19)</span><span
-class="cmtt-10"> [offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [offset]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [cdim]</span>
+class="cmr-6">34</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 19)</span><span
+class="cmtt-8"> [offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [offset]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [cdim]</span>
<br class="fancyvrb" /><a
id="x1-100072r35"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">35</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100074r36"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">36</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-100076r37"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">37</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-100078r38"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 20)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">38</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 20)</span><span
+class="cmtt-8"> done</span>
</div>
<!--l. 224--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
-end-of-packet is reached during any read operation above, floor decode is to return ’unused’ status
-as if the <span
-class="cmtt-10x-x-109">[nonzero] </span>flag had been unset at the beginning of decode.
-<!--l. 230--><p class="noindent" >Vector <span
-class="cmtt-10x-x-109">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
-
+
-
+
+end-of-packet is reached during any read operation above, floor decode is to return ’unused’
+status as if the <span
+class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
+<!--l. 230--><p class="noindent" >Vector <span
+class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
<!--l. 235--><p class="noindent" ><span class="paragraphHead"><a
id="x1-1010007.2.2"></a><span
-class="cmbx-10x-x-109">curve computation</span></span>
-Curve computation is split into two logical steps; the first step derives final Y amplitude values from
-the encoded, wrapped difference values taken from the bitstream. The second step plots the curve
-lines. Also, although zero-difference values are used in the iterative prediction to find final Y values,
-these points are conditionally skipped during final line computation in step two. Skipping
-zero-difference values allows a smoother line fit.
-<!--l. 245--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations, implementors
-are warned to follow the details closely. Deviation from implementing a strictly equivalent algorithm
-can result in serious decoding errors.
-<!--l. 251--><p class="noindent" >
- <dl class="description"><dt class="description">
+class="cmbx-12">curve computation</span></span>
+Curve computation is split into two logical steps; the first step derives final Y amplitude values
+from the encoded, wrapped difference values taken from the bitstream. The second step
+plots the curve lines. Also, although zero-difference values are used in the iterative
+prediction to find final Y values, these points are conditionally skipped during final
+line computation in step two. Skipping zero-difference values allows a smoother line
+fit.
+<!--l. 245--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations,
+implementors are warned to follow the details closely. Deviation from implementing a strictly
+equivalent algorithm can result in serious decoding errors.
+<!--l. 250--><p class="noindent" >
+ <dl class="description"><dt class="description">
<span
-class="cmssbx-10x-x-109">step 1: amplitude value synthesis</span> </dt><dd
+class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd
class="description">
- <!--l. 253--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
- values, then apply to line prediction.
- <!--l. 256--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb31">
+
<!--l. 253--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
+ values, then apply to line prediction.
+
<!--l. 256--><p class="noindent" >
+
<div class="fancyvrb" id="fancyvrb31">
<a
id="x1-101002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [range]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span><span
-class="cmtt-10"> 256,</span><span
-class="cmtt-10"> 128,</span><span
-class="cmtt-10"> 86,</span><span
-class="cmtt-10"> 64</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([floor1_multiplier]-1)</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [range]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span><span
+class="cmtt-8"> 256,</span><span
+class="cmtt-8"> 128,</span><span
+class="cmtt-8"> 86,</span><span
+class="cmtt-8"> 64</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([floor1_multiplier]-1)</span>
<br class="fancyvrb" /><a
id="x1-101004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> set</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> set</span>
<br class="fancyvrb" /><a
id="x1-101006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [1]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> set</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [1]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> set</span>
<br class="fancyvrb" /><a
id="x1-101008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span>
<br class="fancyvrb" /><a
id="x1-101010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [1]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [1]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [1]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [1]</span>
<br class="fancyvrb" /><a
id="x1-101012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [floor1_values]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [floor1_values]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [low_neighbor_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [low_neighbor_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1200009.2.4"><span
-class="cmtt-10">low_neighbor</span></a><span
-class="cmtt-10">([floor1_X_list],[i])</span>
+class="cmtt-8">low_neighbor</span></a><span
+class="cmtt-8">([floor1_X_list],[i])</span>
<br class="fancyvrb" /><a
id="x1-101018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> [high_neighbor_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> [high_neighbor_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1210009.2.5"><span
-class="cmtt-10">high_neighbor</span></a><span
-class="cmtt-10">([floor1_X_list],[i])</span>
+class="cmtt-8">high_neighbor</span></a><span
+class="cmtt-8">([floor1_X_list],[i])</span>
<br class="fancyvrb" /><a
id="x1-101020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [predicted]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [predicted]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> </span><a
href="#x1-1220009.2.6"><span
-class="cmtt-10">render_point</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [low_neighbor_offset],</span>
+class="cmtt-8">render_point</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [low_neighbor_offset],</span>
<br class="fancyvrb" /><a
id="x1-101024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [low_neighbor_offset],</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [low_neighbor_offset],</span>
<br class="fancyvrb" /><a
id="x1-101026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [high_neighbor_offset],</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [high_neighbor_offset],</span>
<br class="fancyvrb" /><a
id="x1-101028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [high_neighbor_offset],</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [high_neighbor_offset],</span>
<br class="fancyvrb" /><a
id="x1-101030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_X_list]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> )</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_X_list]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> )</span>
<br class="fancyvrb" /><a
id="x1-101032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101034r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-101036r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [range]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [predicted]</span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [range]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [predicted]</span>
<br class="fancyvrb" /><a
id="x1-101038r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [predicted]</span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [predicted]</span>
<br class="fancyvrb" /><a
id="x1-101040r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101042r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101044r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> [room]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> [room]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-101046r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
+
+
+
<br class="fancyvrb" /><a
id="x1-101048r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101050r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101052r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> [room]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> [room]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-101054r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
-
-
-
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101056r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101058r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101060r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> nonzero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> nonzero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101062r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101064r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 17)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [low_neighbor_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> set</span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 17)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [low_neighbor_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> set</span>
<br class="fancyvrb" /><a
id="x1-101066r33"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 18)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [high_neighbor_offset]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> set</span>
+class="cmr-6">33</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 18)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [high_neighbor_offset]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> set</span>
<br class="fancyvrb" /><a
id="x1-101068r34"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 19)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> set</span>
+class="cmr-6">34</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 19)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> set</span>
<br class="fancyvrb" /><a
id="x1-101070r35"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 20)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> or</span><span
-class="cmtt-10"> equal</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> [room]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">35</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 20)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> or</span><span
+class="cmtt-8"> equal</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> [room]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101072r36"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">36</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101074r37"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 21)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">37</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 21)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101076r38"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">38</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101078r39"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 22)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [predicted]</span>
+class="cmr-6">39</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 22)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [predicted]</span>
<br class="fancyvrb" /><a
id="x1-101080r40"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">40</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101082r41"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [lowroom]</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">41</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [lowroom]</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101084r42"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">42</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101086r43"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 23)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [predicted]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [highroom]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">43</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 23)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [predicted]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [highroom]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-101088r44"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">44</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101090r45"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">45</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101092r46"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">46</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101094r47"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [room]</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">47</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [room]</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101096r48"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">48</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101098r49"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 24)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> ([val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> odd)</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">49</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 24)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> ([val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> odd)</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101100r50"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">50</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101102r51"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 25)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">51</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 25)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-101104r52"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [predicted]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> (([val]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> divided</span><span
-class="cmtt-10"> by</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> division)</span>
+class="cmr-6">52</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [predicted]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> (([val]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> divided</span><span
+class="cmtt-8"> by</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> division)</span>
<br class="fancyvrb" /><a
id="x1-101106r53"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">53</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101108r54"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> even</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">54</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> even</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101110r55"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">55</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101112r56"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 26)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">56</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 26)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-101114r57"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [predicted]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> ([val]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> division)</span>
+class="cmr-6">57</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [predicted]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> ([val]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> division)</span>
<br class="fancyvrb" /><a
id="x1-101116r58"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">58</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101118r59"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">59</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101120r60"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">60</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101122r61"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">61</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101124r62"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">62</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101126r63"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> [val]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">63</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> [val]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101128r64"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">64</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101130r65"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 27)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_step2_flag]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> unset</span>
+class="cmr-6">65</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 27)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_step2_flag]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> unset</span>
<br class="fancyvrb" /><a
id="x1-101132r66"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 28)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [predicted]</span>
+class="cmr-6">66</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 28)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [predicted]</span>
<br class="fancyvrb" /><a
id="x1-101134r67"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">67</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101136r68"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">68</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101138r69"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">69</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101140r70"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">70</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101142r71"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">71</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101144r72"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 29)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">72</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 29)</span><span
+class="cmtt-8"> done</span>
<br class="fancyvrb" /><a
id="x1-101146r73"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">73</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
- </dd><dt class="description">
+ </dd><dt class="description">
<span
-class="cmssbx-10x-x-109">step 2: curve synthesis</span> </dt><dd
+class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
class="description">
- <!--l. 336--><p class="noindent" >Curve synthesis generates a return vector <span
-class="cmtt-10x-x-109">[floor] </span>of length <span
-class="cmtt-10x-x-109">[n] </span>(where <span
-class="cmtt-10x-x-109">[n] </span>is provided by the
-
+ <!--l. 336--><p class="noindent" >Curve synthesis generates a return vector <span
+class="cmtt-12">[floor] </span>of length <span
+class="cmtt-12">[n] </span>(where <span
+class="cmtt-12">[n] </span>is provided by
+ the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
+ <span
+class="cmtt-12">[floor1_X_list]</span>, <span
+class="cmtt-12">[floor1_final_Y] </span>and <span
+class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as
+ [floor1˙multiplier] and [floor1˙values] values.
+ <!--l. 343--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
+class="cmtt-12">[floor1_X_list]</span>, <span
+class="cmtt-12">[floor1_final_Y] </span>and
+
-
- decode process calling to floor decode). Floor 1 curve synthesis makes use of the
- <span
-class="cmtt-10x-x-109">[floor1_X_list]</span>, <span
-class="cmtt-10x-x-109">[floor1_final_Y] </span>and <span
-class="cmtt-10x-x-109">[floor1_step2_flag] </span>vectors, as well as
- [floor1˙multiplier] and [floor1˙values] values.
- <!--l. 343--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
-class="cmtt-10x-x-109">[floor1_X_list]</span>, <span
-class="cmtt-10x-x-109">[floor1_final_Y] </span>and
- <span
-class="cmtt-10x-x-109">[floor1_step2_flag] </span>together into new vectors <span
-class="cmtt-10x-x-109">[floor1_X_list]’</span>, <span
-class="cmtt-10x-x-109">[floor1_final_Y]’</span>
- and <span
-class="cmtt-10x-x-109">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
- <span
-class="cmtt-10x-x-109">[floor1_X_list]</span>. That is, sort the values of <span
-class="cmtt-10x-x-109">[floor1_X_list] </span>and then apply the same
- permutation to elements of the other two vectors so that the X, Y and step2˙flag values still
- match.
- <!--l. 353--><p class="noindent" >Then compute the final curve in one pass:
- <!--l. 355--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb32">
+
+ <span
+class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span
+class="cmtt-12">[floor1_X_list]’</span>, <span
+class="cmtt-12">[floor1_final_Y]’</span>
+ and <span
+class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
+ <span
+class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span
+class="cmtt-12">[floor1_X_list] </span>and then apply the same
+ permutation to elements of the other two vectors so that the X, Y and step2˙flag values still
+ match.
+ <!--l. 353--><p class="noindent" >Then compute the final curve in one pass:
+ <!--l. 355--><p class="noindent" >
+ <div class="fancyvrb" id="fancyvrb32">
<a
id="x1-101148r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [hx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [hx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-101150r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [lx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [lx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-101152r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [ly]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor1_final_Y]’</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [0]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [floor1_multiplier]</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [ly]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor1_final_Y]’</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [0]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [floor1_multiplier]</span>
<br class="fancyvrb" /><a
id="x1-101154r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [floor1_values]-1</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [floor1_values]-1</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101156r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101158r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [floor1_step2_flag]’</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [floor1_step2_flag]’</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101160r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101162r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> [hy]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [floor1_final_Y]’</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [floor1_multiplier]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> [hy]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [floor1_final_Y]’</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [floor1_multiplier]</span>
<br class="fancyvrb" /><a
id="x1-101164r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [hx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [floor1_X_list]’</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [hx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [floor1_X_list]’</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-101166r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> </span><a
href="#x1-1230009.2.7"><span
-class="cmtt-10">render_line</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> [lx],</span><span
-class="cmtt-10"> [ly],</span><span
-class="cmtt-10"> [hx],</span><span
-class="cmtt-10"> [hy],</span><span
-class="cmtt-10"> [floor]</span><span
-class="cmtt-10"> )</span>
+class="cmtt-8">render_line</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> [lx],</span><span
+class="cmtt-8"> [ly],</span><span
+class="cmtt-8"> [hx],</span><span
+class="cmtt-8"> [hy],</span><span
+class="cmtt-8"> [floor]</span><span
+class="cmtt-8"> )</span>
<br class="fancyvrb" /><a
id="x1-101168r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [lx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [hx]</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [lx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [hx]</span>
<br class="fancyvrb" /><a
id="x1-101170r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> [ly]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [hy]</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> [ly]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [hy]</span>
<br class="fancyvrb" /><a
id="x1-101172r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101174r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101176r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101178r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [hx]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [n]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [hx]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [n]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101180r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101182r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> </span><a
href="#x1-1230009.2.7"><span
-class="cmtt-10">render_line</span></a><span
-class="cmtt-10">(</span><span
-class="cmtt-10"> [hx],</span><span
-class="cmtt-10"> [hy],</span><span
-class="cmtt-10"> [n],</span><span
-class="cmtt-10"> [hy],</span><span
-class="cmtt-10"> [floor]</span><span
-class="cmtt-10"> )</span>
+class="cmtt-8">render_line</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8"> [hx],</span><span
+class="cmtt-8"> [hy],</span><span
+class="cmtt-8"> [n],</span><span
+class="cmtt-8"> [hy],</span><span
+class="cmtt-8"> [floor]</span><span
+class="cmtt-8"> )</span>
<br class="fancyvrb" /><a
id="x1-101184r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101186r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101188r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101190r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [hx]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [n]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">{</span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [hx]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [n]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">{</span>
<br class="fancyvrb" /><a
id="x1-101192r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101194r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> truncate</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor]</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> [n]</span><span
-class="cmtt-10"> elements</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> truncate</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor]</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> [n]</span><span
+class="cmtt-8"> elements</span>
<br class="fancyvrb" /><a
id="x1-101196r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101198r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmsy-10">}</span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmsy-8">}</span>
<br class="fancyvrb" /><a
id="x1-101200r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101202r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> for</span><span
-class="cmtt-10"> each</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [floor],</span><span
-class="cmtt-10"> perform</span><span
-class="cmtt-10"> a</span><span
-class="cmtt-10"> lookup</span><span
-class="cmtt-10"> substitution</span><span
-class="cmtt-10"> using</span>
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> for</span><span
+class="cmtt-8"> each</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [floor],</span><span
+class="cmtt-8"> perform</span><span
+class="cmtt-8"> a</span><span
+class="cmtt-8"> lookup</span><span
+class="cmtt-8"> substitution</span><span
+class="cmtt-8"> using</span>
<br class="fancyvrb" /><a
id="x1-101204r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> [floor]</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> an</span><span
-class="cmtt-10"> offset</span><span
-class="cmtt-10"> into</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> </span><a
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> [floor]</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> an</span><span
+class="cmtt-8"> offset</span><span
+class="cmtt-8"> into</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> </span><a
href="#x1-12500010.1"><span
-class="cmtt-10">[floor1_inverse_dB_static_table]</span></a>
+class="cmtt-8">[floor1_inverse_dB_static_table]</span></a>
<br class="fancyvrb" /><a
id="x1-101206r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-101208r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> done</span>
<br class="fancyvrb" /><a
id="x1-101210r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
- </dd></dl>
-
+ </dd></dl>
+
-
-<h3 class="sectionHead"><span class="titlemark">8 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">8
</span> <a
id="x1-1020008"></a>Residue setup and decode</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">8.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.1
</span> <a
id="x1-1030008.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
-may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by
-channel coupling. The exact semantic content of the vector does not matter to the residue
+may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel
+coupling. The exact semantic content of the vector does not matter to the residue
abstraction.
<!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
abstraction.
<!--l. 23--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">8.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.2
</span> <a
id="x1-1040008.2"></a>Residue format</h4>
-<!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each chunk,
-encodes the chunk classifications and finally encodes the chunks themselves using the the specific
-VQ arrangement defined for each selected classification. The exact interleaving and partitioning
-vary by residue encoding number, however the high-level process used to classify and encode the
-residue vector is the same in all three variants.
-<!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring
-for the moment exactly how a partition is encoded and simply trusting that it is, is as
+<!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
+chunk, encodes the chunk classifications and finally encodes the chunks themselves
+using the the specific VQ arrangement defined for each selected classification. The
+exact interleaving and partitioning vary by residue encoding number, however the
+high-level process used to classify and encode the residue vector is the same in all three
+variants.
+<!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
+the moment exactly how a partition is encoded and simply trusting that it is, is as
follows:
- <ul class="itemize1">
- <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
- specified. If we have a vector size of <span
-class="cmti-10x-x-109">n</span>, a partition size <span
-class="cmti-10x-x-109">residue˙partition˙size</span>, and
- a total of <span
-class="cmti-10x-x-109">ch </span>residue vectors, the total number of partitioned chunks coded is
- <span
-class="cmti-10x-x-109">n</span>/<span
-class="cmti-10x-x-109">residue˙partition˙size</span>*<span
-class="cmti-10x-x-109">ch</span>. It is important to note that the integer division truncates.
- In the below example, we assume an example <span
-class="cmti-10x-x-109">residue˙partition˙size </span>of 8.
- </li>
- <li class="itemize">Each partition in each vector has a classification number that specifies which of multiple
- configured VQ codebook setups are used to decode that partition. The classification
-
+ <ul class="itemize1">
+ <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
+ specified. If we have a vector size of <span
+class="cmti-12">n</span>, a partition size <span
+class="cmti-12">residue˙partition˙size</span>, and
+ a total of <span
+class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded is
+
-
- numbers of each partition can be thought of as forming a vector in their own right, as
- in the illustration below. Just as the residue vectors are coded in grouped partitions
- to increase encoding efficiency, the classification vector is also partitioned into chunks.
- The integer elements of each scalar in a classification chunk are built into a single scalar
- that represents the classification numbers in that chunk. In the below example, the
- classification codeword encodes two classification numbers.
- </li>
- <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
- the residue vector, but more often efficient codebook design dictates that each vector
- is encoded as the additive sum of several passes through the residue vector using more
- than one VQ codebook. Thus, each residue value potentially accumulates values from
- multiple decode passes. The classification value associated with a partition is the same
- in each pass, thus the classification codeword is coded only in the first pass.
- </li></ul>
+
+ <span
+class="cmti-12">n</span>/<span
+class="cmti-12">residue˙partition˙size</span>*<span
+class="cmti-12">ch</span>. It is important to note that the integer division truncates.
+ In the below example, we assume an example <span
+class="cmti-12">residue˙partition˙size </span>of 8.
+ </li>
+ <li class="itemize">Each partition in each vector has a classification number that specifies which of
+ multiple configured VQ codebook setups are used to decode that partition. The
+ classification numbers of each partition can be thought of as forming a vector in
+ their own right, as in the illustration below. Just as the residue vectors are coded
+ in grouped partitions to increase encoding efficiency, the classification vector is also
+ partitioned into chunks. The integer elements of each scalar in a classification chunk
+ are built into a single scalar that represents the classification numbers in that chunk.
+ In the below example, the classification codeword encodes two classification numbers.
+ </li>
+ <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
+ the residue vector, but more often efficient codebook design dictates that each vector
+ is encoded as the additive sum of several passes through the residue vector using
+ more than one VQ codebook. Thus, each residue value potentially accumulates values
+ from multiple decode passes. The classification value associated with a partition is
+ the same in each pass, thus the classification codeword is coded only in the first pass.
+ </li></ul>
<div class="center"
>
<!--l. 70--><p class="noindent" >
class="content">illustration of residue vector format</td></tr></table><!--tex4ht:label?: x1-10400111 -->
</div>
<!--l. 77--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">8.3 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.3
</span> <a
id="x1-1050008.3"></a>residue 0</h4>
<!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
partition encoding (visually treated as a black box–or cyan box or brown box–in the above
figure).
<!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
+
+
+
encode a partition in a specific pass. The dimension of the codebook need not be the same in
multiple passes, however the partition size must be an even multiple of the codebook
dimension.
-<!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using codebook
-sizes of 8, 4, 2 and 1:
+<!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
+codebook sizes of 8, 4, 2 and 1:
<!--l. 92--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb33">
-
-
-
<a
id="x1-105002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-105004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> original</span><span
-class="cmtt-10"> residue</span><span
-class="cmtt-10"> vector:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> original</span><span
+class="cmtt-8"> residue</span><span
+class="cmtt-8"> vector:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-105006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-105008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-105010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-105012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-105014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-105016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-105018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-105020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-105022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
<!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
restricted to a power of two.
<!--l. 111--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">8.4 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.4
</span> <a
id="x1-1060008.4"></a>residue 1</h4>
-<!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As with
-residue 0, however, partition length must be an integer multiple of the codebook dimension,
+<!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As
+with residue 0, however, partition length must be an integer multiple of the codebook dimension,
although dimension may vary from pass to pass.
-<!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using codebook
-sizes of 8, 4, 2 and 1:
+<!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
+codebook sizes of 8, 4, 2 and 1:
<!--l. 121--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb34">
<a
id="x1-106002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-106004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> original</span><span
-class="cmtt-10"> residue</span><span
-class="cmtt-10"> vector:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> original</span><span
+class="cmtt-8"> residue</span><span
+class="cmtt-8"> vector:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-106006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-106008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-106010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-106012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-106014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-106016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-106018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-106020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> dimensions</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> encoded</span><span
-class="cmtt-10"> as:</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 1</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 4</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 5</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> ],</span><span
-class="cmtt-10"> [</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> ]</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> dimensions</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> encoded</span><span
+class="cmtt-8"> as:</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 1</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 4</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 5</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> ],</span><span
+class="cmtt-8"> [</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> ]</span>
<br class="fancyvrb" /><a
id="x1-106022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
+
+
+
</div>
<!--l. 137--><p class="noindent" >
-
-
-
-<h4 class="subsectionHead"><span class="titlemark">8.5 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.5 </span> <a
id="x1-1070008.5"></a>residue 2</h4>
<!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
passed-in vectors as in residue type 1, the <span
-class="cmti-10x-x-109">ch </span>passed in vectors of length <span
-class="cmti-10x-x-109">n </span>are first interleaved and
-flattened into a single vector of length <span
-class="cmti-10x-x-109">ch</span>*<span
-class="cmti-10x-x-109">n</span>. Encoding then proceeds as in type 1. Decoding is as in
-type 1 with decode interleave reversed. If operating on a single vector to begin with, residue type 1
-and type 2 are equivalent.
+class="cmti-12">ch </span>passed in vectors of length <span
+class="cmti-12">n </span>are first interleaved
+and flattened into a single vector of length <span
+class="cmti-12">ch</span>*<span
+class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
+is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
+residue type 1 and type 2 are equivalent.
<div class="center"
>
<!--l. 147--><p class="noindent" >
class="content">illustration of residue type 2</td></tr></table><!--tex4ht:label?: x1-10700112 -->
</div>
<!--l. 153--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">8.6 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">8.6
</span> <a
id="x1-1080008.6"></a>Residue decode</h4>
<!--l. 155--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">8.6.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">8.6.1
</span> <a
id="x1-1090008.6.1"></a>header decode</h5>
<!--l. 157--><p class="noindent" >Header decode for all three residue types is identical.
<div class="fancyvrb" id="fancyvrb35">
<a
id="x1-109002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [residue_begin]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 24</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [residue_begin]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 24</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-109004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [residue_end]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 24</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [residue_end]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 24</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-109006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [residue_partition_size]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 24</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [residue_partition_size]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 24</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> one</span>
<br class="fancyvrb" /><a
id="x1-109008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [residue_classifications]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 6</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> add</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [residue_classifications]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 6</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> add</span><span
+class="cmtt-8"> one</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-109010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [residue_classbook]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [residue_classbook]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
</div>
<!--l. 166--><p class="noindent" ><span
-class="cmtt-10x-x-109">[residue_begin] </span>and <span
-class="cmtt-10x-x-109">[residue_end] </span>select the specific sub-portion of each vector that is
+class="cmtt-12">[residue_begin] </span>and <span
+class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is
actually coded; it implements akin to a bandpass where, for coding purposes, the vector
effectively begins at element <span
-class="cmtt-10x-x-109">[residue_begin] </span>and ends at <span
-class="cmtt-10x-x-109">[residue_end]</span>. Preceding
-and following values in the unpacked vectors are zeroed. Note that for residue type 2,
-these values as well as <span
-class="cmtt-10x-x-109">[residue_partition_size]</span>apply to the interleaved vector, not
-the individual vectors before interleave. <span
-class="cmtt-10x-x-109">[residue_partition_size] </span>is as explained
-above, <span
-class="cmtt-10x-x-109">[residue_classifications] </span>is the number of possible classification to which a
-partition can belong and <span
-class="cmtt-10x-x-109">[residue_classbook] </span>is the codebook number used to code
-
-
-
-classification codewords. The number of dimensions in book <span
-class="cmtt-10x-x-109">[residue_classbook] </span>determines
-how many classification values are grouped into a single classification codeword. Note
-that the number of entries and dimensions in book <span
-class="cmtt-10x-x-109">[residue_classbook]</span>, along with
+class="cmtt-12">[residue_begin] </span>and ends at <span
+class="cmtt-12">[residue_end]</span>. Preceding and
+following values in the unpacked vectors are zeroed. Note that for residue type 2, these
+values as well as <span
+class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the
+individual vectors before interleave. <span
+class="cmtt-12">[residue_partition_size] </span>is as explained above,
+<span
+class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can
+belong and <span
+class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification
+codewords. The number of dimensions in book <span
+class="cmtt-12">[residue_classbook] </span>determines how
+many classification values are grouped into a single classification codeword. Note that
+the number of entries and dimensions in book <span
+class="cmtt-12">[residue_classbook]</span>, along with
<span
-class="cmtt-10x-x-109">[residue_classifications]</span>, overdetermines to possible number of classification
+class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification
codewords. If <span
-class="cmtt-10x-x-109">[residue_classifications]</span>ˆ<span
-class="cmtt-10x-x-109">[residue_classbook]</span>.dimensions exceeds
+class="cmtt-12">[residue_classifications]</span>ˆ<span
+class="cmtt-12">[residue_classbook]</span>.dimensions exceeds
<span
-class="cmtt-10x-x-109">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
+class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
<!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
passes.
<!--l. 193--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb36">
<a
id="x1-109012r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [residue_classifications]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [residue_classifications]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-109014r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109016r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [high_bits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [high_bits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-109018r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [low_bits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 3</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [low_bits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 3</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-109020r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [bitflag]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> one</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> boolean</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [bitflag]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> one</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> boolean</span>
<br class="fancyvrb" /><a
id="x1-109022r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [bitflag]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> [high_bits]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> five</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [bitflag]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> [high_bits]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> five</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-109024r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [residue_cascade]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [high_bits]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [low_bits]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [residue_cascade]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [high_bits]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [low_bits]</span>
<br class="fancyvrb" /><a
id="x1-109026r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-109028r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> done</span>
</div>
<!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
bitmap. We loop over the possible codebook classifications and the maximum possible number of
<div class="fancyvrb" id="fancyvrb37">
<a
id="x1-109030r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [residue_classifications]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [residue_classifications]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-109032r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109034r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-109036r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109038r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [residue_cascade]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> set</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [residue_cascade]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> set</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-109040r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109042r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [residue_books]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i][j]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> 8</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> as</span><span
-class="cmtt-10"> unsigned</span><span
-class="cmtt-10"> integer</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [residue_books]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i][j]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> 8</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> as</span><span
+class="cmtt-8"> unsigned</span><span
+class="cmtt-8"> integer</span>
<br class="fancyvrb" /><a
id="x1-109044r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109046r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> {</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-109048r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109050r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [residue_books]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i][j]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> unused</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [residue_books]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i][j]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> unused</span>
<br class="fancyvrb" /><a
id="x1-109052r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109054r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-109056r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-109058r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-109060r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-109062r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> done</span>
</div>
<!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable. In
-
-
-
addition, any codebook number greater than the maximum numbered codebook set up in this
stream also renders the stream undecodable.
<!--l. 238--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">8.6.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">8.6.2
</span> <a
id="x1-1100008.6.2"></a>packet decode</h5>
<!--l. 240--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
decode can be built out of the format 1 decode process. Thus we describe first the decode
infrastructure identical to all three formats.
-<!--l. 245--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of vectors
-in the submap bundle and a vector of flags indicating if any of the vectors are not to be decoded. If
-the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’, decode skips
-vector 1 during the decode loop. However, even ’do not decode’ vectors are allocated and
-zeroed.
+<!--l. 245--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
+vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
+decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
+decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
+allocated and zeroed.
<!--l. 252--><p class="noindent" >Depending on the values of <span
-class="cmtt-10x-x-109">[residue_begin] </span>and <span
-class="cmtt-10x-x-109">[residue_end]</span>, it is obvious that the encoded
-portion of a residue vector may be the entire possible residue vector or some other strict subset of
-the actual residue vector size with zero padding at either uncoded end. However, it is also
-possible to set <span
-class="cmtt-10x-x-109">[residue_begin] </span>and <span
-class="cmtt-10x-x-109">[residue_end] </span>to specify a range partially or wholly
+class="cmtt-12">[residue_begin] </span>and <span
+class="cmtt-12">[residue_end]</span>, it is obvious that the
+encoded portion of a residue vector may be the entire possible residue vector or some other strict
+subset of the actual residue vector size with zero padding at either uncoded end. However, it is
+also possible to set <span
+class="cmtt-12">[residue_begin] </span>and <span
+class="cmtt-12">[residue_end] </span>to specify a range partially or wholly
beyond the maximum vector size. Before beginning residue decode, limit <span
-class="cmtt-10x-x-109">[residue_begin]</span>
+class="cmtt-12">[residue_begin]</span>
and <span
-class="cmtt-10x-x-109">[residue_end] </span>to the maximum possible vector size as follows. We assume that
+class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that
the number of vectors being encoded, <span
-class="cmtt-10x-x-109">[ch] </span>is provided by the higher level decoding
+class="cmtt-12">[ch] </span>is provided by the higher level decoding
process.
<!--l. 266--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb38">
<a
id="x1-110002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [actual_size]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> current</span><span
-class="cmtt-10"> blocksize/2;</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [actual_size]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> current</span><span
+class="cmtt-8"> blocksize/2;</span>
<br class="fancyvrb" /><a
id="x1-110004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> residue</span><span
-class="cmtt-10"> encoding</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> format</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> residue</span><span
+class="cmtt-8"> encoding</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> format</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-110006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [actual_size]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [actual_size]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [ch];</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [actual_size]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [actual_size]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [ch];</span>
<br class="fancyvrb" /><a
id="x1-110008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [limit_residue_begin]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> maximum</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> ([residue_begin],[actual_size]);</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [limit_residue_begin]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> maximum</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> ([residue_begin],[actual_size]);</span>
<br class="fancyvrb" /><a
id="x1-110010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [limit_residue_end]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> maximum</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> ([residue_end],[actual_size]);</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [limit_residue_end]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> maximum</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> ([residue_end],[actual_size]);</span>
</div>
+
+
+
<!--l. 274--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
<!--l. 277--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb39">
<a
id="x1-110012r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [classwords_per_codeword]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [codebook_dimensions]</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> [residue_classbook]</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [classwords_per_codeword]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [codebook_dimensions]</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> [residue_classbook]</span>
<br class="fancyvrb" /><a
id="x1-110014r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [n_to_read]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [limit_residue_end]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [limit_residue_begin]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [n_to_read]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [limit_residue_end]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [limit_residue_begin]</span>
<br class="fancyvrb" /><a
id="x1-110016r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [partitions_to_read]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [n_to_read]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> [residue_partition_size]</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [partitions_to_read]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [n_to_read]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> [residue_partition_size]</span>
</div>
<!--l. 283--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
-
-
-
<div class="fancyvrb" id="fancyvrb40">
<a
id="x1-110018r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> allocate</span><span
-class="cmtt-10"> and</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> all</span><span
-class="cmtt-10"> vectors</span><span
-class="cmtt-10"> that</span><span
-class="cmtt-10"> will</span><span
-class="cmtt-10"> be</span><span
-class="cmtt-10"> returned.</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> allocate</span><span
+class="cmtt-8"> and</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> all</span><span
+class="cmtt-8"> vectors</span><span
+class="cmtt-8"> that</span><span
+class="cmtt-8"> will</span><span
+class="cmtt-8"> be</span><span
+class="cmtt-8"> returned.</span>
<br class="fancyvrb" /><a
id="x1-110020r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> ([n_to_read]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> zero),</span><span
-class="cmtt-10"> stop;</span><span
-class="cmtt-10"> there</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> no</span><span
-class="cmtt-10"> residue</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> decode.</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> ([n_to_read]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> zero),</span><span
+class="cmtt-8"> stop;</span><span
+class="cmtt-8"> there</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> no</span><span
+class="cmtt-8"> residue</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> decode.</span>
<br class="fancyvrb" /><a
id="x1-110022r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [pass]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> 7</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [pass]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> 7</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110024r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110026r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [partition_count]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [partition_count]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-110028r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110030r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> while</span><span
-class="cmtt-10"> [partition_count]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [partitions_to_read]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> while</span><span
+class="cmtt-8"> [partition_count]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [partitions_to_read]</span>
<br class="fancyvrb" /><a
id="x1-110032r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110034r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> ([pass]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> zero)</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> ([pass]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> zero)</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110036r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110038r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ..</span><span
-class="cmtt-10"> [ch]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ..</span><span
+class="cmtt-8"> [ch]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110040r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110042r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> marked</span><span
-class="cmtt-10"> ’do</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> decode’</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> marked</span><span
+class="cmtt-8"> ’do</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> decode’</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110044r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110046r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [temp]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> [residue_classbook]</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> scalar</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [temp]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> [residue_classbook]</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> scalar</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-110048r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> descending</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> [classwords_per_codeword]-1</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> descending</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> [classwords_per_codeword]-1</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110050r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110052r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [classifications]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [j],([i]+[partition_count])</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [classifications]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [j],([i]+[partition_count])</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-110054r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [temp]</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> modulo</span><span
-class="cmtt-10"> [residue_classifications]</span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
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+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [temp]</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> modulo</span><span
+class="cmtt-8"> [residue_classifications]</span>
<br class="fancyvrb" /><a
id="x1-110056r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> [temp]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [temp]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> [residue_classifications]</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> division</span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
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+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> [temp]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [temp]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> [residue_classifications]</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> division</span>
<br class="fancyvrb" /><a
id="x1-110058r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110060r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110062r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110064r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110066r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110068r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110070r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110072r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110074r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110076r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ..</span><span
-class="cmtt-10"> ([classwords_per_codeword]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> while</span><span
-class="cmtt-10"> [partition_count]</span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ..</span><span
+class="cmtt-8"> ([classwords_per_codeword]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> while</span><span
+class="cmtt-8"> [partition_count]</span>
<br class="fancyvrb" /><a
id="x1-110078r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> also</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [partitions_to_read]</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> also</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [partitions_to_read]</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110080r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110082r33"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ..</span><span
-class="cmtt-10"> [ch]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">33</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ..</span><span
+class="cmtt-8"> [ch]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110084r34"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">34</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110086r35"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> marked</span><span
-class="cmtt-10"> ’do</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> decode’</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">35</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> marked</span><span
+class="cmtt-8"> ’do</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> decode’</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110088r36"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">36</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110090r37"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> [vqclass]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [classifications]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [j],[partition_count]</span>
+class="cmr-6">37</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> [vqclass]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [classifications]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [j],[partition_count]</span>
<br class="fancyvrb" /><a
id="x1-110092r38"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 17)</span><span
-class="cmtt-10"> [vqbook]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> array</span><span
-class="cmtt-10"> [residue_books]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [vqclass],[pass]</span>
+class="cmr-6">38</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 17)</span><span
+class="cmtt-8"> [vqbook]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> array</span><span
+class="cmtt-8"> [residue_books]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [vqclass],[pass]</span>
<br class="fancyvrb" /><a
id="x1-110094r39"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 18)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> ([vqbook]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> not</span><span
-class="cmtt-10"> ’unused’)</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">39</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 18)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> ([vqbook]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> not</span><span
+class="cmtt-8"> ’unused’)</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-110096r40"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">40</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110098r41"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 19)</span><span
-class="cmtt-10"> decode</span><span
-class="cmtt-10"> partition</span><span
-class="cmtt-10"> into</span><span
-class="cmtt-10"> output</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [j],</span><span
-class="cmtt-10"> starting</span><span
-class="cmtt-10"> at</span><span
-class="cmtt-10"> scalar</span>
+class="cmr-6">41</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 19)</span><span
+class="cmtt-8"> decode</span><span
+class="cmtt-8"> partition</span><span
+class="cmtt-8"> into</span><span
+class="cmtt-8"> output</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [j],</span><span
+class="cmtt-8"> starting</span><span
+class="cmtt-8"> at</span><span
+class="cmtt-8"> scalar</span>
<br class="fancyvrb" /><a
id="x1-110100r42"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> offset</span><span
-class="cmtt-10"> [limit_residue_begin]+[partition_count]*[residue_partition_size]</span><span
-class="cmtt-10"> using</span>
+class="cmr-6">42</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> offset</span><span
+class="cmtt-8"> [limit_residue_begin]+[partition_count]*[residue_partition_size]</span><span
+class="cmtt-8"> using</span>
<br class="fancyvrb" /><a
id="x1-110102r43"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [vqbook]</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> VQ</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">43</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [vqbook]</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> VQ</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-110104r44"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">44</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110106r45"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">45</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110108r46"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">46</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110110r47"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 20)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [partition_count]</span><span
-class="cmtt-10"> by</span><span
-class="cmtt-10"> one</span>
+class="cmr-6">47</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 20)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [partition_count]</span><span
+class="cmtt-8"> by</span><span
+class="cmtt-8"> one</span>
<br class="fancyvrb" /><a
id="x1-110112r48"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">48</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110114r49"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">49</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-110116r50"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">50</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110118r51"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">51</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-110120r52"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
-
-
-
+class="cmr-6">52</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-110122r53"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 21)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">53</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 21)</span><span
+class="cmtt-8"> done</span>
<br class="fancyvrb" /><a
id="x1-110124r54"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">54</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
-<!--l. 341--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence. Decode
-returns the result of vector decode up to that point.
+<!--l. 341--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
+Decode returns the result of vector decode up to that point.
<!--l. 347--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">8.6.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">8.6.3
</span> <a
id="x1-1110008.6.3"></a>format 0 specifics</h5>
<!--l. 349--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
section. The following pseudocode presents the same algorithm. Assume:
- <ul class="itemize1">
- <li class="itemize"><span
-class="cmtt-10x-x-109">[n] </span>is the value in <span
-class="cmtt-10x-x-109">[residue_partition_size]</span>
- </li>
- <li class="itemize"><span
-class="cmtt-10x-x-109">[v] </span>is the residue vector
- </li>
- <li class="itemize"><span
-class="cmtt-10x-x-109">[offset] </span>is the beginning read offset in [v]</li></ul>
+ <li class="itemize"><span
+class="cmtt-12">[n] </span>is the value in <span
+class="cmtt-12">[residue_partition_size]</span>
+ </li>
+ <li class="itemize"><span
+class="cmtt-12">[v] </span>is the residue vector
+ </li>
+ <li class="itemize"><span
+class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
<!--l. 360--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb41">
<a
id="x1-111002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [step]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [n]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> [codebook_dimensions]</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [step]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [n]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> [codebook_dimensions]</span>
<br class="fancyvrb" /><a
id="x1-111004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [step]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [step]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-111006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-111008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [entry_temp]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> current</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> VQ</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [entry_temp]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> current</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> VQ</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-111010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [codebook_dimensions]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [codebook_dimensions]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-111012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-111014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([offset]+[i]+[j]*[step])</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-111016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([offset]+[i]+[j]*[step])</span><span
-class="cmtt-10"> +</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
+class="cmtt-8"> +</span>
<br class="fancyvrb" /><a
id="x1-111018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [entry_temp]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [j]</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [entry_temp]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [j]</span>
<br class="fancyvrb" /><a
id="x1-111020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-111022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-111024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-111026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-111028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-111030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> done</span>
<br class="fancyvrb" /><a
id="x1-111032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
</div>
-
+
-
+
<!--l. 381--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">8.6.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">8.6.4
</span> <a
id="x1-1120008.6.4"></a>format 1 specifics</h5>
-<!--l. 383--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’ section.
-The following pseudocode presents the same algorithm. Assume:
- <ul class="itemize1">
- <li class="itemize"><span
-class="cmtt-10x-x-109">[n] </span>is the value in <span
-class="cmtt-10x-x-109">[residue_partition_size]</span>
- </li>
- <li class="itemize"><span
-class="cmtt-10x-x-109">[v] </span>is the residue vector
- </li>
- <li class="itemize"><span
-class="cmtt-10x-x-109">[offset] </span>is the beginning read offset in [v]</li></ul>
+<!--l. 383--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
+section. The following pseudocode presents the same algorithm. Assume:
+ <li class="itemize"><span
+class="cmtt-12">[n] </span>is the value in <span
+class="cmtt-12">[residue_partition_size]</span>
+ </li>
+ <li class="itemize"><span
+class="cmtt-12">[v] </span>is the residue vector
+ </li>
+ <li class="itemize"><span
+class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
<!--l. 395--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb42">
<a
id="x1-112002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-112004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [entry_temp]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> read</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> from</span><span
-class="cmtt-10"> packet</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> current</span><span
-class="cmtt-10"> codebook</span><span
-class="cmtt-10"> in</span><span
-class="cmtt-10"> VQ</span><span
-class="cmtt-10"> context</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [entry_temp]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> read</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> from</span><span
+class="cmtt-8"> packet</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> current</span><span
+class="cmtt-8"> codebook</span><span
+class="cmtt-8"> in</span><span
+class="cmtt-8"> VQ</span><span
+class="cmtt-8"> context</span>
<br class="fancyvrb" /><a
id="x1-112006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [codebook_dimensions]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [codebook_dimensions]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-112008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-112010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([offset]+[i])</span><span
-class="cmtt-10"> =</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([offset]+[i])</span><span
+class="cmtt-8"> =</span>
<br class="fancyvrb" /><a
id="x1-112012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10">  </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([offset]+[i])</span><span
-class="cmtt-10"> +</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8">  </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([offset]+[i])</span><span
+class="cmtt-8"> +</span>
<br class="fancyvrb" /><a
id="x1-112014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [entry_temp]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [j]</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [entry_temp]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [j]</span>
<br class="fancyvrb" /><a
id="x1-112016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [i]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [i]</span>
<br class="fancyvrb" /><a
id="x1-112018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-112020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-112022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-112024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> [n]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> continue</span><span
-class="cmtt-10"> at</span><span
-class="cmtt-10"> step</span><span
-class="cmtt-10"> 2</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> [n]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> continue</span><span
+class="cmtt-8"> at</span><span
+class="cmtt-8"> step</span><span
+class="cmtt-8"> 2</span>
<br class="fancyvrb" /><a
id="x1-112026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> done</span>
</div>
<!--l. 413--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">8.6.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">8.6.5
</span> <a
id="x1-1130008.6.5"></a>format 2 specifics</h5>
<!--l. 415--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
additional post-decode step after a normal format 1 decode.
-<!--l. 418--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors
-are marked ’do not decode’, no decode occurrs. However, if at least one vector is to be
-decoded, all the vectors are decoded. We then request normal format 1 to decode a single
-vector representing all output channels, rather than a vector for each channel. After
-decode, deinterleave the vector into independent vectors, one for each output channel. That
-is:
-
+<!--l. 418--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
+’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
+the vectors are decoded. We then request normal format 1 to decode a single vector
+representing all output channels, rather than a vector for each channel. After decode,
+deinterleave the vector into independent vectors, one for each output channel. That
+
-
-<!--l. 426--><p class="noindent" >
- <ol class="enumerate1" >
- <li
+
+is:
+<!--l. 425--><p class="noindent" >
+ <ol class="enumerate1" >
+ <li
class="enumerate" id="x1-113002x1">If all vectors 0 through <span
-class="cmti-10x-x-109">ch</span>-1 are marked ’do not decode’, allocate and clear a single
- vector <span
-class="cmtt-10x-x-109">[v]</span>of length <span
-class="cmti-10x-x-109">ch*n </span>and skip step 2 below; proceed directly to the post-decode
- step.
- </li>
- <li
+class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
+ vector <span
+class="cmtt-12">[v]</span>of length <span
+class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
+ step.
+ </li>
+ <li
class="enumerate" id="x1-113004x2">Rather than performing format 1 decode to produce <span
-class="cmti-10x-x-109">ch </span>vectors of length <span
-class="cmti-10x-x-109">n </span>each, call
- format 1 decode to produce a single vector <span
-class="cmtt-10x-x-109">[v] </span>of length <span
-class="cmti-10x-x-109">ch*n</span>.
- </li>
- <li
+class="cmti-12">ch </span>vectors of length <span
+class="cmti-12">n </span>each, call
+ format 1 decode to produce a single vector <span
+class="cmtt-12">[v] </span>of length <span
+class="cmti-12">ch*n</span>.
+ </li>
+ <li
class="enumerate" id="x1-113006x3">Post decode: Deinterleave the single vector <span
-class="cmtt-10x-x-109">[v] </span>returned by format 1 decode as
- described above into <span
-class="cmti-10x-x-109">ch </span>independent vectors, one for each outputchannel, according
- to:
- <div class="fancyvrb" id="fancyvrb43">
+class="cmtt-12">[v] </span>returned by format 1 decode as
+ described above into <span
+class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
+ to:
+
<div class="fancyvrb" id="fancyvrb43">
<a
id="x1-113008r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [n]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [n]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-113010r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-113012r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [ch]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [ch]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-113014r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-113016r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> output</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> number</span><span
-class="cmtt-10"> [j]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [i]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> ([i]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [ch]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [j])</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> output</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> number</span><span
+class="cmtt-8"> [j]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [i]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> ([i]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [ch]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [j])</span>
<br class="fancyvrb" /><a
id="x1-113018r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-113020r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-113022r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-113024r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-113026r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> done</span>
</div>
- </li></ol>
-
+ </li></ol>
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">9 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">9
</span> <a
id="x1-1140009"></a>Helper equations</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">9.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">9.1
</span> <a
id="x1-1150009.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
cluttering up the main specification documents, they are defined here and referenced where
appropriate.
<!--l. 13--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">9.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">9.2
</span> <a
id="x1-1160009.2"></a>Functions</h4>
<!--l. 15--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.1
</span> <a
id="x1-1170009.2.1"></a>ilog</h5>
<!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
two’s complement integer value <span
-class="cmtt-10x-x-109">[x]</span>. Values of <span
-class="cmtt-10x-x-109">[x] </span>less than zero are defined to return
+class="cmtt-12">[x]</span>. Values of <span
+class="cmtt-12">[x] </span>less than zero are defined to return
zero.
<!--l. 20--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb44">
<a
id="x1-117002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [return_value]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0;</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [return_value]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0;</span>
<br class="fancyvrb" /><a
id="x1-117004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> greater</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> greater</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-117006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-117008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> increment</span><span
-class="cmtt-10"> [return_value];</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> increment</span><span
+class="cmtt-8"> [return_value];</span>
<br class="fancyvrb" /><a
id="x1-117010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> logical</span><span
-class="cmtt-10"> shift</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> one</span><span
-class="cmtt-10"> bit</span><span
-class="cmtt-10"> to</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> right,</span><span
-class="cmtt-10"> padding</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> MSb</span><span
-class="cmtt-10"> with</span><span
-class="cmtt-10"> zero</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> logical</span><span
+class="cmtt-8"> shift</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> one</span><span
+class="cmtt-8"> bit</span><span
+class="cmtt-8"> to</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> right,</span><span
+class="cmtt-8"> padding</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> MSb</span><span
+class="cmtt-8"> with</span><span
+class="cmtt-8"> zero</span>
<br class="fancyvrb" /><a
id="x1-117012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> repeat</span><span
-class="cmtt-10"> at</span><span
-class="cmtt-10"> step</span><span
-class="cmtt-10"> 2)</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> repeat</span><span
+class="cmtt-8"> at</span><span
+class="cmtt-8"> step</span><span
+class="cmtt-8"> 2)</span>
<br class="fancyvrb" /><a
id="x1-117014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-117016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-117018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-117020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> done</span>
</div>
-<!--l. 33--><p class="noindent" >Examples:
-
+
-
- <ul class="itemize1">
- <li class="itemize">ilog(0) = 0;
- </li>
- <li class="itemize">ilog(1) = 1;
- </li>
- <li class="itemize">ilog(2) = 2;
- </li>
- <li class="itemize">ilog(3) = 2;
- </li>
- <li class="itemize">ilog(4) = 3;
- </li>
- <li class="itemize">ilog(7) = 3;
- </li>
- <li class="itemize">ilog(negative number) = 0;</li></ul>
+
+<!--l. 33--><p class="noindent" >Examples:
+ <ul class="itemize1">
+ <li class="itemize">ilog(0) = 0;
+ </li>
+ <li class="itemize">ilog(1) = 1;
+ </li>
+ <li class="itemize">ilog(2) = 2;
+ </li>
+ <li class="itemize">ilog(3) = 2;
+ </li>
+ <li class="itemize">ilog(4) = 3;
+ </li>
+ <li class="itemize">ilog(7) = 3;
+ </li>
+ <li class="itemize">ilog(negative number) = 0;</li></ul>
<!--l. 48--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.2
</span> <a
id="x1-1180009.2.2"></a>float32˙unpack</h5>
-<!--l. 50--><p class="noindent" >”float32˙unpack(x)” is intended to translate the packed binary representation of a Vorbis codebook
-float value into the representation used by the decoder for floating point numbers. For
+<!--l. 50--><p class="noindent" >”float32˙unpack(x)” is intended to translate the packed binary representation of a Vorbis
+codebook float value into the representation used by the decoder for floating point numbers. For
purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
number.
<!--l. 56--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb45">
<a
id="x1-118002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> [mantissa]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> bitwise</span><span
-class="cmtt-10"> AND</span><span
-class="cmtt-10"> 0x1fffff</span><span
-class="cmtt-10"> (unsigned</span><span
-class="cmtt-10"> result)</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> [mantissa]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> bitwise</span><span
+class="cmtt-8"> AND</span><span
+class="cmtt-8"> 0x1fffff</span><span
+class="cmtt-8"> (unsigned</span><span
+class="cmtt-8"> result)</span>
<br class="fancyvrb" /><a
id="x1-118004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [sign]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> bitwise</span><span
-class="cmtt-10"> AND</span><span
-class="cmtt-10"> 0x80000000</span><span
-class="cmtt-10"> (unsigned</span><span
-class="cmtt-10"> result)</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [sign]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> bitwise</span><span
+class="cmtt-8"> AND</span><span
+class="cmtt-8"> 0x80000000</span><span
+class="cmtt-8"> (unsigned</span><span
+class="cmtt-8"> result)</span>
<br class="fancyvrb" /><a
id="x1-118006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [exponent]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> bitwise</span><span
-class="cmtt-10"> AND</span><span
-class="cmtt-10"> 0x7fe00000)</span><span
-class="cmtt-10"> shifted</span><span
-class="cmtt-10"> right</span><span
-class="cmtt-10"> 21</span><span
-class="cmtt-10"> bits</span><span
-class="cmtt-10"> (unsigned</span><span
-class="cmtt-10"> result)</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [exponent]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> bitwise</span><span
+class="cmtt-8"> AND</span><span
+class="cmtt-8"> 0x7fe00000)</span><span
+class="cmtt-8"> shifted</span><span
+class="cmtt-8"> right</span><span
+class="cmtt-8"> 21</span><span
+class="cmtt-8"> bits</span><span
+class="cmtt-8"> (unsigned</span><span
+class="cmtt-8"> result)</span>
<br class="fancyvrb" /><a
id="x1-118008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [sign]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> nonzero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> then</span><span
-class="cmtt-10"> negate</span><span
-class="cmtt-10"> [mantissa]</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [sign]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> nonzero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> then</span><span
+class="cmtt-8"> negate</span><span
+class="cmtt-8"> [mantissa]</span>
<br class="fancyvrb" /><a
id="x1-118010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> return</span><span
-class="cmtt-10"> [mantissa]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> 2</span><span
-class="cmtt-10"> ^</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [exponent]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> 788</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> )</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> return</span><span
+class="cmtt-8"> [mantissa]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> 2</span><span
+class="cmtt-8"> ^</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [exponent]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> 788</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> )</span>
</div>
+
+
+
<!--l. 66--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.3 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.3
</span> <a
id="x1-1190009.2.3"></a>lookup1˙values</h5>
<!--l. 68--><p class="noindent" >”lookup1˙values(codebook˙entries,codebook˙dimensions)” is used to compute the correct length of
the value index for a codebook VQ lookup table of lookup type 1. The values on this list are
-
-
-
permuted to construct the VQ vector lookup table of size <span
-class="cmtt-10x-x-109">[codebook_entries]</span>.
+class="cmtt-12">[codebook_entries]</span>.
<!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
<span
-class="cmtt-10x-x-109">[return_value] </span>to the power of <span
-class="cmtt-10x-x-109">[codebook_dimensions] </span>is less than or equal to
+class="cmtt-12">[return_value] </span>to the power of <span
+class="cmtt-12">[codebook_dimensions] </span>is less than or equal to
<span
-class="cmtt-10x-x-109">[codebook_entries]</span>’.
+class="cmtt-12">[codebook_entries]</span>’.
<!--l. 81--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.4 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.4
</span> <a
id="x1-1200009.2.4"></a>low˙neighbor</h5>
<!--l. 83--><p class="noindent" >”low˙neighbor(v,x)” finds the position <span
-class="cmtt-10x-x-109">n </span>in vector <span
-class="cmtt-10x-x-109">[v] </span>of the greatest value scalar element
-for which <span
-class="cmtt-10x-x-109">n </span>is less than <span
-class="cmtt-10x-x-109">[x] </span>and vector <span
-class="cmtt-10x-x-109">[v] </span>element <span
-class="cmtt-10x-x-109">n </span>is less than vector <span
-class="cmtt-10x-x-109">[v] </span>element
+class="cmtt-12">n </span>in vector <span
+class="cmtt-12">[v] </span>of the greatest value scalar element for
+which <span
+class="cmtt-12">n </span>is less than <span
+class="cmtt-12">[x] </span>and vector <span
+class="cmtt-12">[v] </span>element <span
+class="cmtt-12">n </span>is less than vector <span
+class="cmtt-12">[v] </span>element
<span
-class="cmtt-10x-x-109">[x]</span>.
+class="cmtt-12">[x]</span>.
<!--l. 88--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.5 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.5
</span> <a
id="x1-1210009.2.5"></a>high˙neighbor</h5>
<!--l. 90--><p class="noindent" >”high˙neighbor(v,x)” finds the position <span
-class="cmtt-10x-x-109">n </span>in vector [v] of the lowest value scalar element for
+class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
which <span
-class="cmtt-10x-x-109">n </span>is less than <span
-class="cmtt-10x-x-109">[x] </span>and vector <span
-class="cmtt-10x-x-109">[v] </span>element <span
-class="cmtt-10x-x-109">n </span>is greater than vector <span
-class="cmtt-10x-x-109">[v] </span>element
+class="cmtt-12">n </span>is less than <span
+class="cmtt-12">[x] </span>and vector <span
+class="cmtt-12">[v] </span>element <span
+class="cmtt-12">n </span>is greater than vector <span
+class="cmtt-12">[v] </span>element
<span
-class="cmtt-10x-x-109">[x]</span>.
+class="cmtt-12">[x]</span>.
<!--l. 97--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.6 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.6
</span> <a
id="x1-1220009.2.6"></a>render˙point</h5>
-<!--l. 99--><p class="noindent" >”render˙point(x0,y0,x1,y1,X)” is used to find the Y value at point X along the line specified by x0,
-x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
+<!--l. 99--><p class="noindent" >”render˙point(x0,y0,x1,y1,X)” is used to find the Y value at point X along the line specified by
+x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
calculating intervening values along the line.
<!--l. 104--><p class="noindent" >
+
+
+
<div class="fancyvrb" id="fancyvrb46">
<a
id="x1-122002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [dy]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y1]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [y0]</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [dy]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y1]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [y0]</span>
<br class="fancyvrb" /><a
id="x1-122004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> [adx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [x1]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [x0]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> [adx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [x1]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [x0]</span>
<br class="fancyvrb" /><a
id="x1-122006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> [ady]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> absolute</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [dy]</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> [ady]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> absolute</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [dy]</span>
<br class="fancyvrb" /><a
id="x1-122008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [ady]</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> ([X]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [x0])</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [ady]</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> ([X]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [x0])</span>
<br class="fancyvrb" /><a
id="x1-122010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> [off]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> [adx]</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> division</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> [off]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> [adx]</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> division</span>
<br class="fancyvrb" /><a
id="x1-122012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [dy]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> zero</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [dy]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> zero</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-122014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-122016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> [Y]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y0]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [off]</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> [Y]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y0]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [off]</span>
<br class="fancyvrb" /><a
id="x1-122018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
-
-
-
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-122020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-122022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-122024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> [Y]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y0]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [off]</span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> [Y]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y0]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [off]</span>
<br class="fancyvrb" /><a
id="x1-122026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-122028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-122030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-122032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> done</span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> done</span>
</div>
<!--l. 125--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">9.2.7 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">9.2.7
</span> <a
id="x1-1230009.2.7"></a>render˙line</h5>
-<!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render˙line(x0, y0, x1, y1, v)” to
-construct an integer floor curve for contiguous piecewise line segments. Note that it has not been
-relevant elsewhere, but here we must define integer division as rounding division of both positive
-and negative numbers toward zero.
+<!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render˙line(x0, y0, x1, y1, v)”
+to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
+been relevant elsewhere, but here we must define integer division as rounding division of both
+positive and negative numbers toward zero.
<!--l. 134--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb47">
<a
id="x1-123002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [dy]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y1]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [y0]</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [dy]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y1]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [y0]</span>
<br class="fancyvrb" /><a
id="x1-123004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [adx]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [x1]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [x0]</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [adx]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [x1]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [x0]</span>
<br class="fancyvrb" /><a
id="x1-123006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [ady]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> absolute</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [dy]</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [ady]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> absolute</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [dy]</span>
<br class="fancyvrb" /><a
id="x1-123008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4)</span><span
-class="cmtt-10"> [base]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [dy]</span><span
-class="cmtt-10"> /</span><span
-class="cmtt-10"> [adx]</span><span
-class="cmtt-10"> using</span><span
-class="cmtt-10"> integer</span><span
-class="cmtt-10"> division</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4)</span><span
+class="cmtt-8"> [base]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [dy]</span><span
+class="cmtt-8"> /</span><span
+class="cmtt-8"> [adx]</span><span
+class="cmtt-8"> using</span><span
+class="cmtt-8"> integer</span><span
+class="cmtt-8"> division</span>
<br class="fancyvrb" /><a
id="x1-123010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 5)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [x0]</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 5)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [x0]</span>
<br class="fancyvrb" /><a
id="x1-123012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [y]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y0]</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [y]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y0]</span>
<br class="fancyvrb" /><a
id="x1-123014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> 0</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> 0</span>
<br class="fancyvrb" /><a
id="x1-123016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 8)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [dy]</span><span
-class="cmtt-10"> is</span><span
-class="cmtt-10"> less</span><span
-class="cmtt-10"> than</span><span
-class="cmtt-10"> 0</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 8)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [dy]</span><span
+class="cmtt-8"> is</span><span
+class="cmtt-8"> less</span><span
+class="cmtt-8"> than</span><span
+class="cmtt-8"> 0</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-123020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 9)</span><span
-class="cmtt-10"> [sy]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [base]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 9)</span><span
+class="cmtt-8"> [sy]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [base]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-123024r12"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">12</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123026r13"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">13</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-123028r14"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">14</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123030r15"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 10)</span><span
-class="cmtt-10"> [sy]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [base]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> 1</span>
+class="cmr-6">15</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 10)</span><span
+class="cmtt-8"> [sy]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [base]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> 1</span>
<br class="fancyvrb" /><a
id="x1-123032r16"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">16</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123034r17"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">17</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-123036r18"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">18</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123038r19"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 11)</span><span
-class="cmtt-10"> [ady]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [ady]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> (absolute</span><span
-class="cmtt-10"> value</span><span
-class="cmtt-10"> of</span><span
-class="cmtt-10"> [base])</span><span
-class="cmtt-10"> *</span><span
-class="cmtt-10"> [adx]</span>
+class="cmr-6">19</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 11)</span><span
+class="cmtt-8"> [ady]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [ady]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> (absolute</span><span
+class="cmtt-8"> value</span><span
+class="cmtt-8"> of</span><span
+class="cmtt-8"> [base])</span><span
+class="cmtt-8"> *</span><span
+class="cmtt-8"> [adx]</span>
<br class="fancyvrb" /><a
id="x1-123040r20"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 12)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y]</span>
+class="cmr-6">20</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 12)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y]</span>
<br class="fancyvrb" /><a
id="x1-123042r21"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">21</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123044r22"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 13)</span><span
-class="cmtt-10"> iterate</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> over</span><span
-class="cmtt-10"> the</span><span
-class="cmtt-10"> range</span><span
-class="cmtt-10"> [x0]+1</span><span
-class="cmtt-10"> ...</span><span
-class="cmtt-10"> [x1]-1</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">22</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 13)</span><span
+class="cmtt-8"> iterate</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> over</span><span
+class="cmtt-8"> the</span><span
+class="cmtt-8"> range</span><span
+class="cmtt-8"> [x0]+1</span><span
+class="cmtt-8"> ...</span><span
+class="cmtt-8"> [x1]-1</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-123046r23"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">23</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123048r24"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 14)</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [ady];</span>
+class="cmr-6">24</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 14)</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [ady];</span>
+
+
+
<br class="fancyvrb" /><a
id="x1-123050r25"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 15)</span><span
-class="cmtt-10"> if</span><span
-class="cmtt-10"> (</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> >=</span><span
-class="cmtt-10"> [adx]</span><span
-class="cmtt-10"> )</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">25</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 15)</span><span
+class="cmtt-8"> if</span><span
+class="cmtt-8"> (</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> >=</span><span
+class="cmtt-8"> [adx]</span><span
+class="cmtt-8"> )</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-123052r26"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">26</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123054r27"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 16)</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [err]</span><span
-class="cmtt-10"> -</span><span
-class="cmtt-10"> [adx]</span>
+class="cmr-6">27</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 16)</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [err]</span><span
+class="cmtt-8"> -</span><span
+class="cmtt-8"> [adx]</span>
<br class="fancyvrb" /><a
id="x1-123056r28"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 17)</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> [y]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [sy]</span>
-
-
-
+class="cmr-6">28</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 17)</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> [y]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [sy]</span>
<br class="fancyvrb" /><a
id="x1-123058r29"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">29</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123060r30"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span><span
-class="cmtt-10"> else</span><span
-class="cmtt-10"> {</span>
+class="cmr-6">30</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span><span
+class="cmtt-8"> else</span><span
+class="cmtt-8"> {</span>
<br class="fancyvrb" /><a
id="x1-123062r31"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">31</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123064r32"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 18)</span><span
-class="cmtt-10"> [y]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y]</span><span
-class="cmtt-10"> +</span><span
-class="cmtt-10"> [base]</span>
+class="cmr-6">32</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 18)</span><span
+class="cmtt-8"> [y]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y]</span><span
+class="cmtt-8"> +</span><span
+class="cmtt-8"> [base]</span>
<br class="fancyvrb" /><a
id="x1-123066r33"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">33</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123068r34"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">34</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
<br class="fancyvrb" /><a
id="x1-123070r35"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">35</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123072r36"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 19)</span><span
-class="cmtt-10"> vector</span><span
-class="cmtt-10"> [v]</span><span
-class="cmtt-10"> element</span><span
-class="cmtt-10"> [x]</span><span
-class="cmtt-10"> =</span><span
-class="cmtt-10"> [y]</span>
+class="cmr-6">36</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 19)</span><span
+class="cmtt-8"> vector</span><span
+class="cmtt-8"> [v]</span><span
+class="cmtt-8"> element</span><span
+class="cmtt-8"> [x]</span><span
+class="cmtt-8"> =</span><span
+class="cmtt-8"> [y]</span>
<br class="fancyvrb" /><a
id="x1-123074r37"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span>
+class="cmr-6">37</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span>
<br class="fancyvrb" /><a
id="x1-123076r38"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> }</span>
+class="cmr-6">38</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> }</span>
</div>
-
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">10 </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">10
</span> <a
id="x1-12400010"></a>Tables</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">10.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">10.1
</span> <a
id="x1-12500010.1"></a>floor1_inverse_dB_table</h4>
<!--l. 8--><p class="noindent" >The vector <span
-class="cmtt-10x-x-109">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consiting of the
+class="cmtt-12">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consiting of the
following values (read left to right then top to bottom):
<!--l. 12--><p class="noindent" >
<div class="fancyvrb" id="fancyvrb48">
<a
id="x1-125002r1"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.0649863e-07,</span><span
-class="cmtt-10"> 1.1341951e-07,</span><span
-class="cmtt-10"> 1.2079015e-07,</span><span
-class="cmtt-10"> 1.2863978e-07,</span>
+class="cmr-6">1</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.0649863e-07,</span><span
+class="cmtt-8"> 1.1341951e-07,</span><span
+class="cmtt-8"> 1.2079015e-07,</span><span
+class="cmtt-8"> 1.2863978e-07,</span>
<br class="fancyvrb" /><a
id="x1-125004r2"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.3699951e-07,</span><span
-class="cmtt-10"> 1.4590251e-07,</span><span
-class="cmtt-10"> 1.5538408e-07,</span><span
-class="cmtt-10"> 1.6548181e-07,</span>
+class="cmr-6">2</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.3699951e-07,</span><span
+class="cmtt-8"> 1.4590251e-07,</span><span
+class="cmtt-8"> 1.5538408e-07,</span><span
+class="cmtt-8"> 1.6548181e-07,</span>
<br class="fancyvrb" /><a
id="x1-125006r3"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.7623575e-07,</span><span
-class="cmtt-10"> 1.8768855e-07,</span><span
-class="cmtt-10"> 1.9988561e-07,</span><span
-class="cmtt-10"> 2.1287530e-07,</span>
+class="cmr-6">3</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.7623575e-07,</span><span
+class="cmtt-8"> 1.8768855e-07,</span><span
+class="cmtt-8"> 1.9988561e-07,</span><span
+class="cmtt-8"> 2.1287530e-07,</span>
<br class="fancyvrb" /><a
id="x1-125008r4"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2.2670913e-07,</span><span
-class="cmtt-10"> 2.4144197e-07,</span><span
-class="cmtt-10"> 2.5713223e-07,</span><span
-class="cmtt-10"> 2.7384213e-07,</span>
+class="cmr-6">4</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2.2670913e-07,</span><span
+class="cmtt-8"> 2.4144197e-07,</span><span
+class="cmtt-8"> 2.5713223e-07,</span><span
+class="cmtt-8"> 2.7384213e-07,</span>
<br class="fancyvrb" /><a
id="x1-125010r5"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 2.9163793e-07,</span><span
-class="cmtt-10"> 3.1059021e-07,</span><span
-class="cmtt-10"> 3.3077411e-07,</span><span
-class="cmtt-10"> 3.5226968e-07,</span>
+class="cmr-6">5</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 2.9163793e-07,</span><span
+class="cmtt-8"> 3.1059021e-07,</span><span
+class="cmtt-8"> 3.3077411e-07,</span><span
+class="cmtt-8"> 3.5226968e-07,</span>
<br class="fancyvrb" /><a
id="x1-125012r6"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 3.7516214e-07,</span><span
-class="cmtt-10"> 3.9954229e-07,</span><span
-class="cmtt-10"> 4.2550680e-07,</span><span
-class="cmtt-10"> 4.5315863e-07,</span>
+class="cmr-6">6</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 3.7516214e-07,</span><span
+class="cmtt-8"> 3.9954229e-07,</span><span
+class="cmtt-8"> 4.2550680e-07,</span><span
+class="cmtt-8"> 4.5315863e-07,</span>
<br class="fancyvrb" /><a
id="x1-125014r7"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 4.8260743e-07,</span><span
-class="cmtt-10"> 5.1396998e-07,</span><span
-class="cmtt-10"> 5.4737065e-07,</span><span
-class="cmtt-10"> 5.8294187e-07,</span>
+class="cmr-6">7</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 4.8260743e-07,</span><span
+class="cmtt-8"> 5.1396998e-07,</span><span
+class="cmtt-8"> 5.4737065e-07,</span><span
+class="cmtt-8"> 5.8294187e-07,</span>
<br class="fancyvrb" /><a
id="x1-125016r8"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 6.2082472e-07,</span><span
-class="cmtt-10"> 6.6116941e-07,</span><span
-class="cmtt-10"> 7.0413592e-07,</span><span
-class="cmtt-10"> 7.4989464e-07,</span>
+class="cmr-6">8</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 6.2082472e-07,</span><span
+class="cmtt-8"> 6.6116941e-07,</span><span
+class="cmtt-8"> 7.0413592e-07,</span><span
+class="cmtt-8"> 7.4989464e-07,</span>
<br class="fancyvrb" /><a
id="x1-125018r9"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 7.9862701e-07,</span><span
-class="cmtt-10"> 8.5052630e-07,</span><span
-class="cmtt-10"> 9.0579828e-07,</span><span
-class="cmtt-10"> 9.6466216e-07,</span>
+class="cmr-6">9</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 7.9862701e-07,</span><span
+class="cmtt-8"> 8.5052630e-07,</span><span
+class="cmtt-8"> 9.0579828e-07,</span><span
+class="cmtt-8"> 9.6466216e-07,</span>
<br class="fancyvrb" /><a
id="x1-125020r10"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.0273513e-06,</span><span
-class="cmtt-10"> 1.0941144e-06,</span><span
-class="cmtt-10"> 1.1652161e-06,</span><span
-class="cmtt-10"> 1.2409384e-06,</span>
+class="cmr-6">10</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.0273513e-06,</span><span
+class="cmtt-8"> 1.0941144e-06,</span><span
+class="cmtt-8"> 1.1652161e-06,</span><span
+class="cmtt-8"> 1.2409384e-06,</span>
<br class="fancyvrb" /><a
id="x1-125022r11"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.3215816e-06,</span><span
-class="cmtt-10"> 1.4074654e-06,</span><span
-class="cmtt-10"> 1.4989305e-06,</span><span
-class="cmtt-10"> 1.5963394e-06,</span>
+class="cmr-6">11</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.3215816e-06,</span><span
+class="cmtt-8"> 1.4074654e-06,</span><span
+class="cmtt-8"> 1.4989305e-06,</span><span
+class="cmtt-8"> 1.5963394e-06,</span>
<br class="fancyvrb" /><a
id="x1-125024r12"></a><span
-class="cmtt-10"> </span><span
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-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.11039993,</span><span
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-class="cmtt-10"> 0.11757434,</span><span
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-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.13335215,</span>
+class="cmr-6">56</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.11039993,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.11757434,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.12521498,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.13335215,</span>
<br class="fancyvrb" /><a
id="x1-125114r57"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.14201813,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.15124727,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.16107617,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.17154380,</span>
+class="cmr-6">57</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.14201813,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.15124727,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.16107617,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.17154380,</span>
<br class="fancyvrb" /><a
id="x1-125116r58"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.18269168,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.19456402,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.20720788,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.22067342,</span>
+class="cmr-6">58</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.18269168,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.19456402,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.20720788,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.22067342,</span>
<br class="fancyvrb" /><a
id="x1-125118r59"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.23501402,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.25028656,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.26655159,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.28387361,</span>
+class="cmr-6">59</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.23501402,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.25028656,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.26655159,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.28387361,</span>
<br class="fancyvrb" /><a
id="x1-125120r60"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.30232132,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.32196786,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.34289114,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.36517414,</span>
+class="cmr-6">60</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.30232132,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.32196786,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.34289114,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.36517414,</span>
<br class="fancyvrb" /><a
id="x1-125122r61"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.38890521,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.41417847,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.44109412,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.46975890,</span>
+class="cmr-6">61</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.38890521,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.41417847,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.44109412,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.46975890,</span>
<br class="fancyvrb" /><a
id="x1-125124r62"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.50028648,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.53279791,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.56742212,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.60429640,</span>
+class="cmr-6">62</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.50028648,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.53279791,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.56742212,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.60429640,</span>
<br class="fancyvrb" /><a
id="x1-125126r63"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.64356699,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.68538959,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.72993007,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.77736504,</span>
+class="cmr-6">63</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.64356699,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.68538959,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.72993007,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.77736504,</span>
<br class="fancyvrb" /><a
id="x1-125128r64"></a><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.82788260,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.88168307,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 0.9389798,</span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> </span><span
-class="cmtt-10"> 1.</span>
+class="cmr-6">64</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.82788260,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.88168307,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 0.9389798,</span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> </span><span
+class="cmtt-8"> 1.</span>
</div>
-
+
-
-
+
+
-
-<h3 class="sectionHead"><span class="titlemark">A </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">A
</span> <a
id="x1-126000A"></a>Embedding Vorbis into an Ogg stream</h3>
<!--l. 6--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">A.1 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">A.1
</span> <a
id="x1-127000A.1"></a>Overview</h4>
<!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
compressed audio packet data into file form.
<!--l. 12--><p class="noindent" >The <a
href="#x1-20001">Section 1<!--tex4ht:ref: vorbis:spec:intro --></a>, “<a
-href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of Vorbis
-audio packets.
+href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of
+Vorbis audio packets.
<!--l. 15--><p class="noindent" >The <a
href="oggstream.html" >Ogg bitstream overview</a> and <a
href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
knowledge of the concepts covered in these named backround documents. Please read them
first.
<!--l. 22--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">A.1.1 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">A.1.1
</span> <a
id="x1-128000A.1.1"></a>Restrictions</h5>
<!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
streams in degenerate, unmultiplexed form only. That is:
- <ul class="itemize1">
- <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
- </li>
- <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams (links).
- </li>
- <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream, per
- link)
- </li></ul>
-<!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media types into a
-multi-stream Ogg file. At the time this document was written, Ogg was becoming a popular
-container for low-bitrate movies consisting of DivX video and Vorbis audio. However, a ’Vorbis I
-audio file’ is taken to imply Vorbis audio existing alone within a degenerate Ogg stream. A
-compliant ’Vorbis audio player’ is not required to implement Ogg support beyond the specific
-support of Vorbis within a degenrate Ogg stream (naturally, application authors are encouraged to
-support full multiplexed Ogg handling).
-
+ <ul class="itemize1">
+ <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
+ </li>
+ <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
+ (links).
+ </li>
+ <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
+ per link)
+ </li></ul>
+
-
+
+<!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
+types into a multi-stream Ogg file. At the time this document was written, Ogg was
+becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
+audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
+within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
+implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
+stream (naturally, application authors are encouraged to support full multiplexed Ogg
+handling).
<!--l. 55--><p class="noindent" >
-<h5 class="subsubsectionHead"><span class="titlemark">A.1.2 </span> <a
+<h5 class="subsubsectionHead"><span class="titlemark">A.1.2
</span> <a
id="x1-129000A.1.2"></a>MIME type</h5>
<!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
applications should use <span
-class="cmtt-10x-x-109">application/ogg</span>, while visual media should use <span
-class="cmtt-10x-x-109">video/ogg</span>, and audio
+class="cmtt-12">application/ogg</span>, while visual media should use <span
+class="cmtt-12">video/ogg</span>, and audio
<span
-class="cmtt-10x-x-109">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP encapsulated
-Vorbis should use <span
-class="cmtt-10x-x-109">audio/vorbis </span>+ <span
-class="cmtt-10x-x-109">audio/vorbis-config</span>.
+class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP
+encapsulated Vorbis should use <span
+class="cmtt-12">audio/vorbis </span>+ <span
+class="cmtt-12">audio/vorbis-config</span>.
<!--l. 65--><p class="noindent" >
-<h4 class="subsectionHead"><span class="titlemark">A.2 </span> <a
+<h4 class="subsectionHead"><span class="titlemark">A.2
</span> <a
id="x1-130000A.2"></a>Encapsulation</h4>
<!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
- <ul class="itemize1">
- <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
- as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This results
- in a first Ogg page of exactly 58 bytes at the very beginning of the logical stream.
- </li>
- <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
- </li>
- <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
- more pages beginning on the second page of the logical stream. However many pages
- they span, the third header packet finishes the page on which it ends. The next (first
- audio) packet must begin on a fresh page.
- </li>
- <li class="itemize">The granule position of these first pages containing only headers is zero.
- </li>
- <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
- </li>
- <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
- </li>
- <li class="itemize">The last page is marked ’end of stream’ in the page flags.
- </li>
- <li class="itemize">Vorbis packets may span page boundaries.
-
+ <ul class="itemize1">
+ <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
+ as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
+ results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
+ stream.
+ </li>
+ <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
+ </li>
+ <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
+ more pages beginning on the second page of the logical stream. However many pages
+ they span, the third header packet finishes the page on which it ends. The next (first
+ audio) packet must begin on a fresh page.
+
-
- </li>
- <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio samples
- (per channel; a stereo stream’s granule position does not increment at twice the speed
- of a mono stream).
- </li>
- <li class="itemize">The granule position of a page represents the end PCM sample position of the last
- packet <span
-class="cmti-10x-x-109">completed </span>on that page. The ’last PCM sample’ is the last complete sample
- returned by decode, not an internal sample awaiting lapping with a subsequent block. A
- page that is entirely spanned by a single packet (that completes on a subsequent page)
- has no granule position, and the granule position is set to ’-1’.
- <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
- necessarily the middle sample from that block. If, eg, the current Vorbis packet
- encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
- decodable sample from the current packet be at position (3*long_block_length/4) -
- (short_block_length/4).
- </li>
- <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream started
- at position zero. Although the granule position belongs to the last completed packet
- on the page and a valid granule position must be positive, by inference it may indicate
- that the PCM position of the beginning of audio is positive or negative.
- <ul class="itemize2">
- <li class="itemize">A positive starting value simply indicates that this stream begins at some positive
- time offset, potentially within a larger program. This is a common case when
- connecting to the middle of broadcast stream.
- </li>
- <li class="itemize">A negative value indicates that output samples preceeding time zero should be
- discarded during decoding; this technique is used to allow sample-granularity
- editing of the stream start time of already-encoded Vorbis streams. The number
- of samples to be discarded must not exceed the overlap-add span of the first two
- audio packets.
- </li></ul>
- <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the second
- finished audio packet must flush the page on which it appears and the third packet begin a
- fresh page. This allows the decoder to always be able to perform PCM position adjustments
- before needing to return any PCM data from synthesis, resulting in correct positioning
- information without any aditional seeking logic.
- <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
- id="x1-131000A.2"></a><span
-class="cmbx-10x-x-109">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return incorrect
- positioning information for seeking operations at the very beginning of the stream.
-
+
+ </li>
+ <li class="itemize">The granule position of these first pages containing only headers is zero.
+ </li>
+ <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
+ </li>
+ <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
+ </li>
+ <li class="itemize">The last page is marked ’end of stream’ in the page flags.
+ </li>
+ <li class="itemize">Vorbis packets may span page boundaries.
+ </li>
+ <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
+ samples (per channel; a stereo stream’s granule position does not increment at twice
+ the speed of a mono stream).
+ </li>
+ <li class="itemize">The granule position of a page represents the end PCM sample position of the last
+ packet <span
+class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
+ returned by decode, not an internal sample awaiting lapping with a subsequent block.
+ A page that is entirely spanned by a single packet (that completes on a subsequent
+ page) has no granule position, and the granule position is set to ’-1’.
+ <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
+ necessarily the middle sample from that block. If, eg, the current Vorbis packet
+ encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
+ decodable sample from the current packet be at position (3*long_block_length/4) -
+ (short_block_length/4).
+ </li>
+ <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
+ started at position zero. Although the granule position belongs to the last completed
+ packet on the page and a valid granule position must be positive, by inference it may
+ indicate that the PCM position of the beginning of audio is positive or negative.
+ <ul class="itemize2">
+ <li class="itemize">A positive starting value simply indicates that this stream begins at some
+ positive time offset, potentially within a larger program. This is a common case
+ when connecting to the middle of broadcast stream.
+ </li>
+ <li class="itemize">A negative value indicates that output samples preceeding time zero should be
+
-
- </li>
- <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the final
- packet would normally return is used to end the stream on other than even frame
- boundaries. The difference between the actual available data returned and the
- declared amount indicates how many trailing samples to discard from the decoding
- process.
- </li></ul>
-
+
+ discarded during decoding; this technique is used to allow sample-granularity
+ editing of the stream start time of already-encoded Vorbis streams. The number
+ of samples to be discarded must not exceed the overlap-add span of the first two
+ audio packets.
+ </li></ul>
+ <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
+ second finished audio packet must flush the page on which it appears and the
+ third packet begin a fresh page. This allows the decoder to always be able to
+ perform PCM position adjustments before needing to return any PCM data from
+ synthesis, resulting in correct positioning information without any aditional seeking
+ logic.
+ <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
+ id="x1-131000A.2"></a><span
+class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return
+ incorrect positioning information for seeking operations at the very beginning of the
+ stream.
+ </li>
+ <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the
+ final packet would normally return is used to end the stream on other than even frame
+ boundaries. The difference between the actual available data returned and the
+ declared amount indicates how many trailing samples to discard from the decoding
+ process.
+ </li></ul>
+
-
-<h3 class="sectionHead"><span class="titlemark">B </span> <a
+
+<h3 class="sectionHead"><span class="titlemark">B
</span> <a
id="x1-132000B"></a>Vorbis encapsulation in RTP</h3>
<!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
-class="cmti-10x-x-109">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of how
-to embed Vorbis audio in an RTP stream.
-
+class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
+how to embed Vorbis audio in an RTP stream.
+
-
-
+
+
-
+
<h3 class="likesectionHead"><a
id="x1-133000B"></a>Colophon</h3>
<!--l. 6--><p class="noindent" ><img
-->
<!--l. 10--><p class="noindent" >Ogg is a <a
href="http://www.xiph.org/" >Xiph.org Foundation</a> effort to protect essential tenets of Internet multimedia from
-corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See <a
-href="http://www.xiph.org/about.html" >About
-the Xiph.org Foundation</a> for details.
+corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
+<a
+href="http://www.xiph.org/about.html" >About the Xiph.org Foundation</a> for details.
<!--l. 17--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.org
-Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification and
-certify specification compliance.
+Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification
+and certify specification compliance.
<!--l. 23--><p class="noindent" >Xiph.org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
does not restrict third parties from distributing independent implementations of Vorbis software
under other licenses.
reserved.
<!--l. 33--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
class="E">E</span>X</span></span>.
-
+
-
+
<h3 class="likesectionHead"><a
id="x1-134000B"></a>References</h3>
-<!--l. 1
30--><p class="noindent" >
- <div class="thebibliography">
- <p class="bibitem" ><span class="biblabel">
+<!--l. 1
23--><p class="noindent" >
+
<div class="thebibliography">
+
<p class="bibitem" ><span class="biblabel">
[1]<span class="bibsp">   </span></span><a
- id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg
- and B. Edler, The use of multirate filter banks for coding of high quality digital audio,
- <a
+ id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
+ B. Edler, The use of multirate filter banks for coding of high quality digital audio,
href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span
-class="cmtt-10x-x-109">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.
+class="cmtt-12">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.
</p>
- </div>
+ </div>
</body></html>
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projects / platform / upstream / libvorbis.git / commitdiff