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22 <h2 class="titleHead">Vorbis I specification</h2>
23 <div class="author" ><span
24 class="cmr-17">Xiph.Org Foundation</span></div><br />
25 <div class="date" ><span
26 class="cmr-17">February 3, 2012</span></div>
28 <h3 class="likesectionHead"><a
29 id="x1-1000"></a>Contents</h3>
30 <div class="tableofcontents">
31  <span class="sectionToc" >1 <a
32 href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
33 <br />  <span class="subsectionToc" >1.1 <a
34 href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
35 <br />   <span class="subsubsectionToc" >1.1.1 <a
36 href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
37 <br />   <span class="subsubsectionToc" >1.1.2 <a
38 href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
39 <br />   <span class="subsubsectionToc" >1.1.3 <a
40 href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
41 <br />   <span class="subsubsectionToc" >1.1.4 <a
42 href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
43 <br />   <span class="subsubsectionToc" >1.1.5 <a
44 href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
45 <br />   <span class="subsubsectionToc" >1.1.6 <a
46 href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
47 <br />  <span class="subsectionToc" >1.2 <a
48 href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
49 <br />   <span class="subsubsectionToc" >1.2.1 <a
50 href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
51 <br />   <span class="subsubsectionToc" >1.2.2 <a
52 href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
53 <br />   <span class="subsubsectionToc" >1.2.3 <a
54 href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
58 <br />   <span class="subsubsectionToc" >1.2.4 <a
59 href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
60 <br />   <span class="subsubsectionToc" >1.2.5 <a
61 href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
62 <br />   <span class="subsubsectionToc" >1.2.6 <a
63 href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
64 <br />  <span class="subsectionToc" >1.3 <a
65 href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
66 <br />   <span class="subsubsectionToc" >1.3.1 <a
67 href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
68 <br />   <span class="subsubsectionToc" >1.3.2 <a
69 href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
70 <br /> <span class="sectionToc" >2 <a
71 href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
72 <br />  <span class="subsectionToc" >2.1 <a
73 href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
74 <br />   <span class="subsubsectionToc" >2.1.1 <a
75 href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
76 <br />   <span class="subsubsectionToc" >2.1.2 <a
77 href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
78 <br />   <span class="subsubsectionToc" >2.1.3 <a
79 href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
80 <br />   <span class="subsubsectionToc" >2.1.4 <a
81 href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
82 <br />   <span class="subsubsectionToc" >2.1.5 <a
83 href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
84 <br />   <span class="subsubsectionToc" >2.1.6 <a
85 href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
86 <br />   <span class="subsubsectionToc" >2.1.7 <a
87 href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
88 <br />   <span class="subsubsectionToc" >2.1.8 <a
89 href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
90 <br />   <span class="subsubsectionToc" >2.1.9 <a
91 href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
92 <br /> <span class="sectionToc" >3 <a
93 href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
94 <br />  <span class="subsectionToc" >3.1 <a
95 href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
96 <br />   <span class="subsubsectionToc" >3.1.1 <a
97 href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
98 <br />  <span class="subsectionToc" >3.2 <a
99 href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
100 <br />   <span class="subsubsectionToc" >3.2.1 <a
101 href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
102 <br />  <span class="subsectionToc" >3.3 <a
103 href="#x1-570003.3" id="QQ2-1-62">Use of the codebook abstraction</a></span>
104 <br /> <span class="sectionToc" >4 <a
105 href="#x1-580004" id="QQ2-1-63">Codec Setup and Packet Decode</a></span>
106 <br />  <span class="subsectionToc" >4.1 <a
107 href="#x1-590004.1" id="QQ2-1-64">Overview</a></span>
108 <br />  <span class="subsectionToc" >4.2 <a
109 href="#x1-600004.2" id="QQ2-1-65">Header decode and decode setup</a></span>
110 <br />   <span class="subsubsectionToc" >4.2.1 <a
111 href="#x1-610004.2.1" id="QQ2-1-66">Common header decode</a></span>
112 <br />   <span class="subsubsectionToc" >4.2.2 <a
113 href="#x1-620004.2.2" id="QQ2-1-67">Identification header</a></span>
114 <br />   <span class="subsubsectionToc" >4.2.3 <a
115 href="#x1-630004.2.3" id="QQ2-1-68">Comment header</a></span>
119 <br />   <span class="subsubsectionToc" >4.2.4 <a
120 href="#x1-640004.2.4" id="QQ2-1-69">Setup header</a></span>
121 <br />  <span class="subsectionToc" >4.3 <a
122 href="#x1-710004.3" id="QQ2-1-77">Audio packet decode and synthesis</a></span>
123 <br />   <span class="subsubsectionToc" >4.3.1 <a
124 href="#x1-720004.3.1" id="QQ2-1-78">packet type, mode and window decode</a></span>
125 <br />   <span class="subsubsectionToc" >4.3.2 <a
126 href="#x1-730004.3.2" id="QQ2-1-79">floor curve decode</a></span>
127 <br />   <span class="subsubsectionToc" >4.3.3 <a
128 href="#x1-740004.3.3" id="QQ2-1-80">nonzero vector propagate</a></span>
129 <br />   <span class="subsubsectionToc" >4.3.4 <a
130 href="#x1-750004.3.4" id="QQ2-1-81">residue decode</a></span>
131 <br />   <span class="subsubsectionToc" >4.3.5 <a
132 href="#x1-760004.3.5" id="QQ2-1-82">inverse coupling</a></span>
133 <br />   <span class="subsubsectionToc" >4.3.6 <a
134 href="#x1-770004.3.6" id="QQ2-1-83">dot product</a></span>
135 <br />   <span class="subsubsectionToc" >4.3.7 <a
136 href="#x1-780004.3.7" id="QQ2-1-84">inverse MDCT</a></span>
137 <br />   <span class="subsubsectionToc" >4.3.8 <a
138 href="#x1-790004.3.8" id="QQ2-1-85">overlap_add</a></span>
139 <br />   <span class="subsubsectionToc" >4.3.9 <a
140 href="#x1-800004.3.9" id="QQ2-1-86">output channel order</a></span>
141 <br /> <span class="sectionToc" >5 <a
142 href="#x1-810005" id="QQ2-1-87">comment field and header specification</a></span>
143 <br />  <span class="subsectionToc" >5.1 <a
144 href="#x1-820005.1" id="QQ2-1-88">Overview</a></span>
145 <br />  <span class="subsectionToc" >5.2 <a
146 href="#x1-830005.2" id="QQ2-1-89">Comment encoding</a></span>
147 <br />   <span class="subsubsectionToc" >5.2.1 <a
148 href="#x1-840005.2.1" id="QQ2-1-90">Structure</a></span>
149 <br />   <span class="subsubsectionToc" >5.2.2 <a
150 href="#x1-850005.2.2" id="QQ2-1-91">Content vector format</a></span>
151 <br />   <span class="subsubsectionToc" >5.2.3 <a
152 href="#x1-880005.2.3" id="QQ2-1-94">Encoding</a></span>
153 <br /> <span class="sectionToc" >6 <a
154 href="#x1-890006" id="QQ2-1-95">Floor type 0 setup and decode</a></span>
155 <br />  <span class="subsectionToc" >6.1 <a
156 href="#x1-900006.1" id="QQ2-1-96">Overview</a></span>
157 <br />  <span class="subsectionToc" >6.2 <a
158 href="#x1-910006.2" id="QQ2-1-97">Floor 0 format</a></span>
159 <br />   <span class="subsubsectionToc" >6.2.1 <a
160 href="#x1-920006.2.1" id="QQ2-1-98">header decode</a></span>
161 <br />   <span class="subsubsectionToc" >6.2.2 <a
162 href="#x1-930006.2.2" id="QQ2-1-99">packet decode</a></span>
163 <br />   <span class="subsubsectionToc" >6.2.3 <a
164 href="#x1-940006.2.3" id="QQ2-1-100">curve computation</a></span>
165 <br /> <span class="sectionToc" >7 <a
166 href="#x1-950007" id="QQ2-1-101">Floor type 1 setup and decode</a></span>
167 <br />  <span class="subsectionToc" >7.1 <a
168 href="#x1-960007.1" id="QQ2-1-102">Overview</a></span>
169 <br />  <span class="subsectionToc" >7.2 <a
170 href="#x1-970007.2" id="QQ2-1-103">Floor 1 format</a></span>
171 <br />   <span class="subsubsectionToc" >7.2.1 <a
172 href="#x1-980007.2.1" id="QQ2-1-104">model</a></span>
173 <br />   <span class="subsubsectionToc" >7.2.2 <a
174 href="#x1-990007.2.2" id="QQ2-1-109">header decode</a></span>
175 <br />   <span class="subsubsectionToc" >7.2.3 <a
176 href="#x1-1000007.2.3" id="QQ2-1-110">packet decode</a></span>
180 <br />   <span class="subsubsectionToc" >7.2.4 <a
181 href="#x1-1010007.2.4" id="QQ2-1-111">curve computation</a></span>
182 <br /> <span class="sectionToc" >8 <a
183 href="#x1-1020008" id="QQ2-1-112">Residue setup and decode</a></span>
184 <br />  <span class="subsectionToc" >8.1 <a
185 href="#x1-1030008.1" id="QQ2-1-113">Overview</a></span>
186 <br />  <span class="subsectionToc" >8.2 <a
187 href="#x1-1040008.2" id="QQ2-1-114">Residue format</a></span>
188 <br />  <span class="subsectionToc" >8.3 <a
189 href="#x1-1050008.3" id="QQ2-1-116">residue 0</a></span>
190 <br />  <span class="subsectionToc" >8.4 <a
191 href="#x1-1060008.4" id="QQ2-1-117">residue 1</a></span>
192 <br />  <span class="subsectionToc" >8.5 <a
193 href="#x1-1070008.5" id="QQ2-1-118">residue 2</a></span>
194 <br />  <span class="subsectionToc" >8.6 <a
195 href="#x1-1080008.6" id="QQ2-1-120">Residue decode</a></span>
196 <br />   <span class="subsubsectionToc" >8.6.1 <a
197 href="#x1-1090008.6.1" id="QQ2-1-121">header decode</a></span>
198 <br />   <span class="subsubsectionToc" >8.6.2 <a
199 href="#x1-1100008.6.2" id="QQ2-1-122">packet decode</a></span>
200 <br />   <span class="subsubsectionToc" >8.6.3 <a
201 href="#x1-1110008.6.3" id="QQ2-1-123">format 0 specifics</a></span>
202 <br />   <span class="subsubsectionToc" >8.6.4 <a
203 href="#x1-1120008.6.4" id="QQ2-1-124">format 1 specifics</a></span>
204 <br />   <span class="subsubsectionToc" >8.6.5 <a
205 href="#x1-1130008.6.5" id="QQ2-1-125">format 2 specifics</a></span>
206 <br /> <span class="sectionToc" >9 <a
207 href="#x1-1140009" id="QQ2-1-126">Helper equations</a></span>
208 <br />  <span class="subsectionToc" >9.1 <a
209 href="#x1-1150009.1" id="QQ2-1-127">Overview</a></span>
210 <br />  <span class="subsectionToc" >9.2 <a
211 href="#x1-1160009.2" id="QQ2-1-128">Functions</a></span>
212 <br />   <span class="subsubsectionToc" >9.2.1 <a
213 href="#x1-1170009.2.1" id="QQ2-1-129">ilog</a></span>
214 <br />   <span class="subsubsectionToc" >9.2.2 <a
215 href="#x1-1180009.2.2" id="QQ2-1-130">float32_unpack</a></span>
216 <br />   <span class="subsubsectionToc" >9.2.3 <a
217 href="#x1-1190009.2.3" id="QQ2-1-131">lookup1_values</a></span>
218 <br />   <span class="subsubsectionToc" >9.2.4 <a
219 href="#x1-1200009.2.4" id="QQ2-1-132">low_neighbor</a></span>
220 <br />   <span class="subsubsectionToc" >9.2.5 <a
221 href="#x1-1210009.2.5" id="QQ2-1-133">high_neighbor</a></span>
222 <br />   <span class="subsubsectionToc" >9.2.6 <a
223 href="#x1-1220009.2.6" id="QQ2-1-134">render_point</a></span>
224 <br />   <span class="subsubsectionToc" >9.2.7 <a
225 href="#x1-1230009.2.7" id="QQ2-1-135">render_line</a></span>
226 <br /> <span class="sectionToc" >10 <a
227 href="#x1-12400010" id="QQ2-1-136">Tables</a></span>
228 <br />  <span class="subsectionToc" >10.1 <a
229 href="#x1-12500010.1" id="QQ2-1-137">floor1_inverse_dB_table</a></span>
230 <br /> <span class="sectionToc" >A <a
231 href="#x1-126000A" id="QQ2-1-138">Embedding Vorbis into an Ogg stream</a></span>
232 <br />  <span class="subsectionToc" >A.1 <a
233 href="#x1-127000A.1" id="QQ2-1-139">Overview</a></span>
234 <br />   <span class="subsubsectionToc" >A.1.1 <a
235 href="#x1-128000A.1.1" id="QQ2-1-140">Restrictions</a></span>
236 <br />   <span class="subsubsectionToc" >A.1.2 <a
237 href="#x1-129000A.1.2" id="QQ2-1-141">MIME type</a></span>
241 <br />  <span class="subsectionToc" >A.2 <a
242 href="#x1-130000A.2" id="QQ2-1-142">Encapsulation</a></span>
243 <br /> <span class="sectionToc" >B <a
244 href="#x1-132000B" id="QQ2-1-144">Vorbis encapsulation in RTP</a></span>
249 <h3 class="sectionHead"><span class="titlemark">1. </span> <a
250 id="x1-20001"></a>Introduction and Description</h3>
251 <!--l. 6--><p class="noindent" >
252 <h4 class="subsectionHead"><span class="titlemark">1.1. </span> <a
253 id="x1-30001.1"></a>Overview</h4>
254 <!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
255 specification appears beginning in <a
256 href="#x1-580004">Section 4</a>, “<a
257 href="#x1-580004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later
258 sections assume a high-level understanding of the Vorbis decode process, which is provided
260 <!--l. 15--><p class="noindent" >
261 <h5 class="subsubsectionHead"><span class="titlemark">1.1.1. </span> <a
262 id="x1-40001.1.1"></a>Application</h5>
263 <!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
264 flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At
265 the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same
266 league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT
267 rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower
268 and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
269 representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
271 <!--l. 29--><p class="noindent" >
272 <h5 class="subsubsectionHead"><span class="titlemark">1.1.2. </span> <a
273 id="x1-50001.1.2"></a>Classification</h5>
274 <!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete
275 Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in
276 Vorbis II to offer better transient response and reproduction using a transform better suited to
277 localized time events.
281 <!--l. 37--><p class="noindent" >
282 <h5 class="subsubsectionHead"><span class="titlemark">1.1.3. </span> <a
283 id="x1-60001.1.3"></a>Assumptions</h5>
284 <!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
285 low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
286 require more working memory as Vorbis has no static probability model; the vector codebooks
287 used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
288 bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to
289 which they are pre-decoded into a cache is the dominant factor in decoder memory
291 <!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it
292 is solely a method of accepting input audio, dividing it into individual frames and
293 compressing these frames into raw, unformatted ’packets’. The decoder then accepts
294 these raw packets in sequence, decodes them, synthesizes audio frames from them, and
295 reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form
296 variable bit rate (VBR) codec and packets have no minimum size, maximum size, or
297 fixed/expected size. Packets are designed that they may be truncated (or padded)
298 and remain decodable; this is not to be considered an error condition and is used
299 extensively in bitrate management in peeling. Both the transport mechanism and
300 decoder must allow that a packet may be any size, or end before or after packet decode
302 <!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
303 framing, sync, positioning and error correction in accordance with these design assumptions, such
304 as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
305 document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
306 although this is by no means a requirement or fundamental assumption in the Vorbis
308 <!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
309 href="#x1-126000A">Section A</a>,
311 href="#x1-126000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
312 <!--l. 77--><p class="noindent" >
313 <h5 class="subsubsectionHead"><span class="titlemark">1.1.4. </span> <a
314 id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
315 <!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
316 decades of continuous encoder improvement before running out of room within the codec
317 specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
318 extreme of forward adaptive.
322 <!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis
323 developer to keep in mind) is that the entire probability model of the codec, the Huffman and
324 VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
325 parameters (often several hundred fields). This makes it impossible, as it would be with
326 MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
327 decode at any frame in the stream without having previously fetched the codec setup
329 <!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a
330 id="x1-80001.1.4"></a><span
331 class="cmbx-12">Note:</span></span> Vorbis <span
332 class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
333 has been initialized/setup with the setup headers.
334 <!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream
335 headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less
336 is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
337 <!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is
338 an unusual design and thus causes some amount of complaint among engineers as this runs
339 against current design trends (and also points out limitations in some existing software/interface
340 designs, such as Windows’ ACM codec framework). However, we find that it does not
341 fundamentally limit Vorbis’ suitable application space.
342 <!--l. 115--><p class="noindent" >
343 <h5 class="subsubsectionHead"><span class="titlemark">1.1.5. </span> <a
344 id="x1-90001.1.5"></a>Format Specification</h5>
345 <!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets
346 that are correctly decoded by the reference Vorbis decoder described below may be considered
347 a proper Vorbis encoder. A decoder must faithfully and completely implement the
348 specification defined below (except where noted) to be considered a proper Vorbis
350 <!--l. 123--><p class="noindent" >
351 <h5 class="subsubsectionHead"><span class="titlemark">1.1.6. </span> <a
352 id="x1-100001.1.6"></a>Hardware Profile</h5>
356 <!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
357 embedded design. For this reason, embedded designs are allowed to deviate in limited ways from
358 the ‘full’ decode specification yet still be certified compliant. These optional omissions are
359 labelled in the spec where relevant.
360 <!--l. 131--><p class="noindent" >
361 <h4 class="subsectionHead"><span class="titlemark">1.2. </span> <a
362 id="x1-110001.2"></a>Decoder Configuration</h4>
363 <!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
364 perform specific functions in the decode pipeline. Each different component instance of a specific
365 type is semantically interchangeable; decoder configuration consists both of internal component
366 configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
367 arrangement is roughly as follows:
370 <!--l. 141--><p class="noindent" >
372 <!--l. 142--><p class="noindent" ><img
373 src="components.png" alt="PIC"
375 <br /> <div class="caption"
376 ><span class="id">Figure 1: </span><span
377 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-110011 -->
379 <!--l. 146--><p class="noindent" >
380 <h5 class="subsubsectionHead"><span class="titlemark">1.2.1. </span> <a
381 id="x1-120001.2.1"></a>Global Config</h5>
382 <!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
383 version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
384 configuration is in the context of specific components.
385 <!--l. 152--><p class="noindent" >
386 <h5 class="subsubsectionHead"><span class="titlemark">1.2.2. </span> <a
387 id="x1-130001.2.2"></a>Mode</h5>
391 <!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
393 <!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
394 methods with the intention of choosing a method best suited to that frame. Different
395 modes are, e.g. how frame size is changed from frame to frame. The mode number of a
396 frame serves as a top level configuration switch for all other specific aspects of frame
398 <!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis
399 window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping
400 number. The mapping number specifies which mapping configuration instance to use for low-level
401 packet decode and synthesis.
402 <!--l. 171--><p class="noindent" >
403 <h5 class="subsubsectionHead"><span class="titlemark">1.2.3. </span> <a
404 id="x1-140001.2.3"></a>Mapping</h5>
405 <!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets
406 of channel vectors together for grouped encoding and decoding. These submaps are
407 not references to external components; the submap list is internal and specific to a
409 <!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors
410 within a mapping. The submap functions as a last layer of indirection such that specific special
411 floor or residue settings can be applied not only to all the vectors in a given mode, but also
412 specific vectors in a specific mode. Each submap specifies the proper floor and residue
413 instance number to use for decoding that submap’s spectral floor and spectral residue
415 <!--l. 186--><p class="noindent" >As an example:
416 <!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth
417 channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a
418 full-spectrum version of it as with the other channels. The submapping mechanism can be used
419 to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only
420 representation to the bass channel, thus saving space. In this example, channels 0-4 belong to
421 submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which
422 uses a bass-only representation.
426 <!--l. 199--><p class="noindent" >
427 <h5 class="subsubsectionHead"><span class="titlemark">1.2.4. </span> <a
428 id="x1-150001.2.4"></a>Floor</h5>
429 <!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
430 representation of the audio spectrum for the given channel in the current frame, generally used
431 akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has
432 historically used it as a unit-baseline for spectral resolution.
433 <!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
434 amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
435 interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
436 are semantically interchangeable in encoding/decoding. However, floor type 1 provides more
437 stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and
438 high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
440 <!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
441 encoder past Xiph.Org’s own beta 4 makes use of floor 0.
442 <!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy
443 coding to save space. For this reason, a floor configuration generally refers to multiple
444 codebooks in the codebook component list. Entropy coding is thus provided as an
445 abstraction, and each floor instance may choose from any and all available codebooks when
447 <!--l. 230--><p class="noindent" >
448 <h5 class="subsubsectionHead"><span class="titlemark">1.2.5. </span> <a
449 id="x1-160001.2.5"></a>Residue</h5>
450 <!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been
451 subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector
452 quantization according to one of three specific packing/coding algorithms numbered
453 0 through 2. The packing algorithm details are configured by residue instance. As
454 with the floor components, the final VQ/entropy encoding is provided by external
455 codebook instances and each residue instance may choose from any and all available
457 <!--l. 241--><p class="noindent" >
461 <h5 class="subsubsectionHead"><span class="titlemark">1.2.6. </span> <a
462 id="x1-170001.2.6"></a>Codebooks</h5>
463 <!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use
464 the entropy-decoded integer value as an offset into an index of output value vectors, returning
465 the indicated vector of values.
466 <!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
467 representation. This tree is tightly packed using one of several methods, depending on whether
468 codeword lengths are ordered or unordered, or the tree is sparse.
469 <!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
470 the vector index is encoded as a single list of values of possible values that are then permuted
471 into a list of n-dimensional rows (lattice VQ).
472 <!--l. 260--><p class="noindent" >
473 <h4 class="subsectionHead"><span class="titlemark">1.3. </span> <a
474 id="x1-180001.3"></a>High-level Decode Process</h4>
475 <!--l. 262--><p class="noindent" >
476 <h5 class="subsubsectionHead"><span class="titlemark">1.3.1. </span> <a
477 id="x1-190001.3.1"></a>Decode Setup</h5>
478 <!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
479 stream to be decoded. Vorbis uses three header packets; all are required, in-order, by
480 this specification. Once set up, decode may begin at any audio packet belonging to
481 the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio
483 <!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
485 <!--l. 274--><p class="noindent" ><span class="paragraphHead"><a
486 id="x1-200001.3.1"></a><span
487 class="cmbx-12">Identification Header</span></span>
488 The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
489 characteristics of the stream such as sample rate and number of channels.
493 <!--l. 279--><p class="noindent" ><span class="paragraphHead"><a
494 id="x1-210001.3.1"></a><span
495 class="cmbx-12">Comment Header</span></span>
496 The comment header includes user text comments (“tags”) and a vendor string for the
497 application/library that produced the bitstream. The encoding and proper use of the comment
498 header is described in <a
499 href="#x1-810005">Section 5</a>, “<a
500 href="#x1-810005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
501 <!--l. 284--><p class="noindent" ><span class="paragraphHead"><a
502 id="x1-220001.3.1"></a><span
503 class="cmbx-12">Setup Header</span></span>
504 The setup header includes extensive CODEC setup information as well as the complete VQ and
505 Huffman codebooks needed for decode.
506 <!--l. 289--><p class="noindent" >
507 <h5 class="subsubsectionHead"><span class="titlemark">1.3.2. </span> <a
508 id="x1-230001.3.2"></a>Decode Procedure</h5>
509 <!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
510 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
512 class="enumerate-enumitem">decode packet type flag
513 </dd><dt class="enumerate-enumitem">
515 class="enumerate-enumitem">decode mode number
516 </dd><dt class="enumerate-enumitem">
518 class="enumerate-enumitem">decode window shape (long windows only)
519 </dd><dt class="enumerate-enumitem">
521 class="enumerate-enumitem">decode floor
522 </dd><dt class="enumerate-enumitem">
524 class="enumerate-enumitem">decode residue into residue vectors
525 </dd><dt class="enumerate-enumitem">
527 class="enumerate-enumitem">inverse channel coupling of residue vectors
528 </dd><dt class="enumerate-enumitem">
530 class="enumerate-enumitem">generate floor curve from decoded floor data
531 </dd><dt class="enumerate-enumitem">
533 class="enumerate-enumitem">compute dot product of floor and residue, producing audio spectrum vector
534 </dd><dt class="enumerate-enumitem">
536 class="enumerate-enumitem">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis
541 </dd><dt class="enumerate-enumitem">
543 class="enumerate-enumitem">overlap/add left-hand output of transform with right-hand output of previous frame
544 </dd><dt class="enumerate-enumitem">
546 class="enumerate-enumitem">store right hand-data from transform of current frame for future lapping
547 </dd><dt class="enumerate-enumitem">
549 class="enumerate-enumitem">if not first frame, return results of overlap/add as audio result of current frame</dd></dl>
550 <!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can
551 take advantage of symmetries in the MDCT to store the right-hand transform data of a partial
552 MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before
553 overlap/add with the next frame. This optimization produces entirely equivalent output and is
554 naturally perfectly legal. The decoder must be <span
555 class="cmti-12">entirely mathematically equivalent </span>to the
556 specification, it need not be a literal semantic implementation.
557 <!--l. 317--><p class="noindent" ><span class="paragraphHead"><a
558 id="x1-240001.3.2"></a><span
559 class="cmbx-12">Packet type decode</span></span>
560 Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis
561 headers described above. The fourth packet type marks an audio packet. All other packet types
562 are reserved; packets marked with a reserved type should be ignored.
563 <!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
564 audio packet decode is to read and verify the packet type; <span
565 class="cmti-12">a non-audio packet when audio is</span>
567 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
569 class="cmti-12">packet and not attempt decoding it to audio</span>.
570 <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
571 id="x1-250001.3.2"></a><span
572 class="cmbx-12">Mode decode</span></span>
573 Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
574 which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
575 offset into the mode instance index.
576 <!--l. 341--><p class="noindent" ><span class="paragraphHead"><a
577 id="x1-260001.3.2"></a><span
578 class="cmbx-12">Window shape decode (long windows only)</span></span>
579 Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I,
580 legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis
581 handles channels as independent vectors and these frame sizes are in samples per
586 <!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
587 avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
588 according to MDCT requirements, overlapped 50% with the output of the previous frame and
589 added. The window shape assures seamless reconstruction.
590 <!--l. 354--><p class="noindent" >This is easy to visualize in the case of equal sized-windows:
593 <!--l. 356--><p class="noindent" >
595 <!--l. 357--><p class="noindent" ><img
596 src="window1.png" alt="PIC"
598 <br /> <div class="caption"
599 ><span class="id">Figure 2: </span><span
600 class="content">overlap of two equal-sized windows</span></div><!--tex4ht:label?: x1-260012 -->
602 <!--l. 361--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows:
605 <!--l. 364--><p class="noindent" >
607 <!--l. 365--><p class="noindent" ><img
608 src="window2.png" alt="PIC"
610 <br /> <div class="caption"
611 ><span class="id">Figure 3: </span><span
612 class="content">overlap of a long and a short window</span></div><!--tex4ht:label?: x1-260023 -->
614 <!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
615 seamless lapping as above. It is possible to correctly infer window shape to be applied to the
616 current window from knowing the sizes of the current, previous and next window. It is legal for a
617 decoder to use this method. However, in the case of a long window (short windows require no
618 modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although
619 not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to
620 the point of lapping entirely independently of any other packet, allowing easier abstraction of
621 decode layers as well as allowing a greater level of easy parallelism in encode and
623 <!--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
624 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
625 Vorbis windows all use the slope function
626 <center class="math-display" >
628 src="Vorbis_I_spec0x.png" alt="y = sin (.5 ∗ π sin2((x + .5)∕n ∗ π)).
632 " class="math-display" ></center>
633 <!--l. 385--><p class="nopar" >
634 <!--l. 389--><p class="noindent" ><span class="paragraphHead"><a
635 id="x1-270001.3.2"></a><span
636 class="cmbx-12">floor decode</span></span>
637 Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
638 specifies which floor configuration to use. All floors are decoded before residue decode
640 <!--l. 395--><p class="noindent" ><span class="paragraphHead"><a
641 id="x1-280001.3.2"></a><span
642 class="cmbx-12">residue decode</span></span>
643 Although the number of residue vectors equals the number of channels, channel coupling may
644 mean that the raw residue vectors extracted during decode do not map directly to specific
645 channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or
646 angle. The coupling relationships are described in the codec setup and may differ from frame to
647 frame, due to different mode numbers.
648 <!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from
649 submap 0 through n-1. This differs from floors which are coded using a configuration provided by
650 submap number, but are coded individually in channel order.
651 <!--l. 411--><p class="noindent" ><span class="paragraphHead"><a
652 id="x1-290001.3.2"></a><span
653 class="cmbx-12">inverse channel coupling</span></span>
654 A detailed discussion of stereo in the Vorbis codec can be found in the document
656 href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo
657 coupling, but the stereo document also gives a good overview of the generic coupling
659 <!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a
660 pair at a time in the order and using the vectors specified in the current mapping
661 configuration. The decoupling operation is the same for all pairs, converting square polar
662 representation (where one vector is magnitude and the second angle) back to Cartesian
664 <!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
665 represent the fine spectral detail of each output channel.
669 <!--l. 432--><p class="noindent" ><span class="paragraphHead"><a
670 id="x1-300001.3.2"></a><span
671 class="cmbx-12">generate floor curve</span></span>
672 The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to
673 generate the output curve when the floor data is decoded from the raw packet, or it
674 can be generated after inverse coupling and applied to the spectral residue directly,
675 combining generation and the dot product into one step and eliminating some working
677 <!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied
678 (dot product) by the linear-range, linear-domain spectral residue.
679 <!--l. 447--><p class="noindent" ><span class="paragraphHead"><a
680 id="x1-310001.3.2"></a><span
681 class="cmbx-12">compute floor/residue dot product</span></span>
682 This step is straightforward; for each output channel, the decoder multiplies the floor curve and
683 residue vectors element by element, producing the finished audio spectrum of each
685 <!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
686 implementation might be to assume that a 32 bit fixed-point representation for floor and
687 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
688 in all cases because it happens to mostly work with the current Xiph.Org reference
690 <!--l. 462--><p class="noindent" >However, floor vector values can span <span
691 class="cmsy-10x-x-120">∼</span>140dB (<span
692 class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
693 vector should represent a minimum of 120dB (<span
694 class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
695 bit PCM device. For the residue vector to represent full scale if the floor is nailed
697 class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
698 full scale if the floor is nailed at 0dB, it must be able to represent <span
699 class="cmsy-10x-x-120">−</span>140dB to +0dB.
700 Thus, in order to handle full range dynamics, a residue vector may span <span
701 class="cmsy-10x-x-120">−</span>140dB to
702 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
703 residue vector must be able to represent a 48 bit range and the dot product must
704 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
705 achieved using large (64 bit or larger) integers, or implementing a movable binary point
707 <!--l. 479--><p class="noindent" ><span class="paragraphHead"><a
708 id="x1-320001.3.2"></a><span
709 class="cmbx-12">inverse monolithic transform (MDCT)</span></span>
710 The audio spectrum is converted back into time domain PCM audio via an inverse Modified
711 Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
712 <span class="cite">[<a
713 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
714 <!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be
718 lapped with surrounding frames using an appropriate window (such as the Vorbis window) before
719 the MDCT can be considered orthogonal.
720 <!--l. 492--><p class="noindent" ><span class="paragraphHead"><a
721 id="x1-330001.3.2"></a><span
722 class="cmbx-12">overlap/add data</span></span>
723 Windowed MDCT output is overlapped and added with the right hand data of the previous
724 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
725 current window (as illustrated in the window overlap diagram). At this point, the audio data
726 between the center of the previous frame and the center of the current frame is now finished and
727 ready to be returned.
728 <!--l. 501--><p class="noindent" ><span class="paragraphHead"><a
729 id="x1-340001.3.2"></a><span
730 class="cmbx-12">cache right hand data</span></span>
731 The decoder must cache the right hand portion of the current frame to be lapped with the left
732 hand portion of the next frame.
733 <!--l. 507--><p class="noindent" ><span class="paragraphHead"><a
734 id="x1-350001.3.2"></a><span
735 class="cmbx-12">return finished audio data</span></span>
736 The overlapped portion produced from overlapping the previous and current frame data
737 is finished data to be returned by the decoder. This data spans from the center of
738 the previous window to the center of the current window. In the case of same-sized
739 windows, the amount of data to return is one-half block consisting of and only of the
740 overlapped portions. When overlapping a short and long window, much of the returned
741 range is not actually overlap. This does not damage transform orthogonality. Pay
742 attention however to returning the correct data range; the amount of data to be returned
744 <!--l. 519--><p class="noindent" >
745 <div class="fancyvrb" id="fancyvrb1">
747 id="x1-35002r1"></a><span
748 class="cmr-6">1</span><span
749 class="cmtt-8"> </span><span
750 class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
752 <!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
753 <!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
754 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
755 PCM output offset is ’0’ (as no data has been returned yet).
762 <h3 class="sectionHead"><span class="titlemark">2. </span> <a
763 id="x1-360002"></a>Bitpacking Convention</h3>
764 <!--l. 6--><p class="noindent" >
765 <h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a
766 id="x1-370002.1"></a>Overview</h4>
767 <!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
768 integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
769 encoder and then read one-by-one in the same monotonically increasing order by the decoder.
770 Most current binary storage arrangements group bits into a native word size of eight bits
771 (octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
772 bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
773 representation in fixed-width words.
774 <!--l. 19--><p class="noindent" >
775 <h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a
776 id="x1-380002.1.1"></a>octets, bytes and words</h5>
777 <!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
778 This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
779 For purposes of the bitpacking convention, a byte implies the native, smallest integer
780 storage representation offered by a platform. On modern platforms, this is generally
781 assumed to be eight bits (not necessarily because of the processor but because of the
782 filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
783 atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
785 <!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
786 to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
787 bitpacking convention is still well defined for any native byte size; Vorbis uses the native
788 bit-width of a given storage system. This document assumes that a byte is one octet for purposes
790 <!--l. 39--><p class="noindent" >
794 <h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a
795 id="x1-390002.1.2"></a>bit order</h5>
796 <!--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
797 storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
798 opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
799 class="cmmi-12">n </span>(<span
800 class="cmmi-12">n </span>= 7 in an
802 <!--l. 50--><p class="noindent" >
803 <h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a
804 id="x1-400002.1.3"></a>byte order</h5>
805 <!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
806 common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
807 highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
808 which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
810 <!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
811 word, level, thus host word ordering is of a concern only during optimization when writing high
812 performance code that operates on a word of storage at a time rather than by byte.
813 Logically, bytes are always coded and decoded in order from byte zero through byte
815 class="cmmi-12">n</span>.
816 <!--l. 68--><p class="noindent" >
817 <h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a
818 id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
819 <!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
820 wide, into packets. These integer fields are not aligned to the boundaries of the byte
821 representation; the next field is written at the bit position at which the previous field
823 <!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
824 bitstream first, followed by next least significant bit, etc, until the requested number of bits
825 have been coded. When packing the bits into bytes, the encoder begins by placing
826 the LSb of the integer to be written into the least significant unused bit position of
827 the destination byte, followed by the next-least significant bit of the source integer
828 and so on up to the requested number of bits. When all bits of the destination byte
829 have been filled, encoding continues by zeroing all bits of the next byte and writing
830 the next bit into the bit position 0 of that byte. Decoding follows the same process
834 as encoding, but by reading bits from the byte stream and reassembling them into
836 <!--l. 90--><p class="noindent" >
837 <h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a
838 id="x1-420002.1.5"></a>signedness</h5>
839 <!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
840 given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
841 either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
842 encoder and decoder are responsible for knowing if fields are to be treated as signed or
844 <!--l. 101--><p class="noindent" >
845 <h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a
846 id="x1-430002.1.6"></a>coding example</h5>
847 <!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
848 <!--l. 106--><p class="noindent" >
849 <div class="fancyvrb" id="fancyvrb2">
851 id="x1-43002r1"></a><span
852 class="cmr-6">1</span><span
853 class="cmtt-8"> </span><span
854 class="cmtt-8"> </span><span
855 class="cmtt-8"> </span><span
856 class="cmtt-8"> </span><span
857 class="cmtt-8"> </span><span
858 class="cmtt-8"> </span><span
859 class="cmtt-8"> </span><span
860 class="cmtt-8"> </span><span
861 class="cmtt-8"> </span><span
862 class="cmtt-8"> </span><span
863 class="cmtt-8"> </span><span
864 class="cmtt-8"> </span><span
865 class="cmtt-8"> </span><span
866 class="cmtt-8"> </span><span
867 class="cmtt-8"> </span><span
868 class="cmtt-8"> |</span>
869 <br class="fancyvrb" /><a
870 id="x1-43004r2"></a><span
871 class="cmr-6">2</span><span
872 class="cmtt-8"> </span><span
873 class="cmtt-8"> </span><span
874 class="cmtt-8"> </span><span
875 class="cmtt-8"> </span><span
876 class="cmtt-8"> </span><span
877 class="cmtt-8"> </span><span
878 class="cmtt-8"> </span><span
879 class="cmtt-8"> </span><span
880 class="cmtt-8"> </span><span
881 class="cmtt-8"> </span><span
882 class="cmtt-8"> </span><span
883 class="cmtt-8"> </span><span
884 class="cmtt-8"> </span><span
885 class="cmtt-8"> </span><span
886 class="cmtt-8"> </span><span
887 class="cmtt-8"> V</span>
888 <br class="fancyvrb" /><a
889 id="x1-43006r3"></a><span
890 class="cmr-6">3</span><span
891 class="cmtt-8"> </span><span
892 class="cmtt-8"> </span>
893 <br class="fancyvrb" /><a
894 id="x1-43008r4"></a><span
895 class="cmr-6">4</span><span
896 class="cmtt-8"> </span><span
897 class="cmtt-8"> </span><span
898 class="cmtt-8"> </span><span
899 class="cmtt-8"> </span><span
900 class="cmtt-8"> </span><span
901 class="cmtt-8"> </span><span
902 class="cmtt-8"> </span><span
903 class="cmtt-8"> </span><span
904 class="cmtt-8"> </span><span
905 class="cmtt-8"> 7</span><span
906 class="cmtt-8"> 6</span><span
907 class="cmtt-8"> 5</span><span
908 class="cmtt-8"> 4</span><span
909 class="cmtt-8"> 3</span><span
910 class="cmtt-8"> 2</span><span
911 class="cmtt-8"> 1</span><span
912 class="cmtt-8"> 0</span>
913 <br class="fancyvrb" /><a
914 id="x1-43010r5"></a><span
915 class="cmr-6">5</span><span
916 class="cmtt-8"> </span><span
917 class="cmtt-8"> byte</span><span
918 class="cmtt-8"> 0</span><span
919 class="cmtt-8"> [0</span><span
920 class="cmtt-8"> 0</span><span
921 class="cmtt-8"> 0</span><span
922 class="cmtt-8"> 0</span><span
923 class="cmtt-8"> 1</span><span
924 class="cmtt-8"> 1</span><span
925 class="cmtt-8"> 0</span><span
926 class="cmtt-8"> 0]</span><span
927 class="cmtt-8"> </span><span
928 class="cmtt-8"> <-</span>
929 <br class="fancyvrb" /><a
930 id="x1-43012r6"></a><span
931 class="cmr-6">6</span><span
932 class="cmtt-8"> </span><span
933 class="cmtt-8"> byte</span><span
934 class="cmtt-8"> 1</span><span
935 class="cmtt-8"> [</span><span
936 class="cmtt-8"> </span><span
937 class="cmtt-8"> </span><span
938 class="cmtt-8"> </span><span
939 class="cmtt-8"> </span><span
940 class="cmtt-8"> </span><span
941 class="cmtt-8"> </span><span
942 class="cmtt-8"> </span><span
943 class="cmtt-8"> </span><span
944 class="cmtt-8"> </span><span
945 class="cmtt-8"> </span><span
946 class="cmtt-8"> </span><span
947 class="cmtt-8"> </span><span
948 class="cmtt-8"> </span><span
949 class="cmtt-8"> </span><span
950 class="cmtt-8"> ]</span>
951 <br class="fancyvrb" /><a
952 id="x1-43014r7"></a><span
953 class="cmr-6">7</span><span
954 class="cmtt-8"> </span><span
955 class="cmtt-8"> byte</span><span
956 class="cmtt-8"> 2</span><span
957 class="cmtt-8"> [</span><span
958 class="cmtt-8"> </span><span
959 class="cmtt-8"> </span><span
960 class="cmtt-8"> </span><span
961 class="cmtt-8"> </span><span
962 class="cmtt-8"> </span><span
963 class="cmtt-8"> </span><span
964 class="cmtt-8"> </span><span
965 class="cmtt-8"> </span><span
966 class="cmtt-8"> </span><span
967 class="cmtt-8"> </span><span
968 class="cmtt-8"> </span><span
969 class="cmtt-8"> </span><span
970 class="cmtt-8"> </span><span
971 class="cmtt-8"> </span><span
972 class="cmtt-8"> ]</span>
973 <br class="fancyvrb" /><a
974 id="x1-43016r8"></a><span
975 class="cmr-6">8</span><span
976 class="cmtt-8"> </span><span
977 class="cmtt-8"> byte</span><span
978 class="cmtt-8"> 3</span><span
979 class="cmtt-8"> [</span><span
980 class="cmtt-8"> </span><span
981 class="cmtt-8"> </span><span
982 class="cmtt-8"> </span><span
983 class="cmtt-8"> </span><span
984 class="cmtt-8"> </span><span
985 class="cmtt-8"> </span><span
986 class="cmtt-8"> </span><span
987 class="cmtt-8"> </span><span
988 class="cmtt-8"> </span><span
989 class="cmtt-8"> </span><span
990 class="cmtt-8"> </span><span
991 class="cmtt-8"> </span><span
992 class="cmtt-8"> </span><span
993 class="cmtt-8"> </span><span
994 class="cmtt-8"> ]</span>
995 <br class="fancyvrb" /><a
996 id="x1-43018r9"></a><span
997 class="cmr-6">9</span><span
998 class="cmtt-8"> </span><span
999 class="cmtt-8"> </span><span
1000 class="cmtt-8"> </span><span
1001 class="cmtt-8"> </span><span
1002 class="cmtt-8"> </span><span
1003 class="cmtt-8"> </span><span
1004 class="cmtt-8"> </span><span
1005 class="cmtt-8"> </span><span
1006 class="cmtt-8"> </span><span
1007 class="cmtt-8"> </span><span
1008 class="cmtt-8"> </span><span
1009 class="cmtt-8"> </span><span
1010 class="cmtt-8"> </span><span
1011 class="cmtt-8"> </span><span
1012 class="cmtt-8"> ...</span>
1013 <br class="fancyvrb" /><a
1014 id="x1-43020r10"></a><span
1015 class="cmr-6">10</span><span
1016 class="cmtt-8"> </span><span
1017 class="cmtt-8"> byte</span><span
1018 class="cmtt-8"> n</span><span
1019 class="cmtt-8"> [</span><span
1020 class="cmtt-8"> </span><span
1021 class="cmtt-8"> </span><span
1022 class="cmtt-8"> </span><span
1023 class="cmtt-8"> </span><span
1024 class="cmtt-8"> </span><span
1025 class="cmtt-8"> </span><span
1026 class="cmtt-8"> </span><span
1027 class="cmtt-8"> </span><span
1028 class="cmtt-8"> </span><span
1029 class="cmtt-8"> </span><span
1030 class="cmtt-8"> </span><span
1031 class="cmtt-8"> </span><span
1032 class="cmtt-8"> </span><span
1033 class="cmtt-8"> </span><span
1034 class="cmtt-8"> ]</span><span
1035 class="cmtt-8"> </span><span
1036 class="cmtt-8"> bytestream</span><span
1037 class="cmtt-8"> length</span><span
1038 class="cmtt-8"> ==</span><span
1039 class="cmtt-8"> 1</span><span
1040 class="cmtt-8"> byte</span>
1041 <br class="fancyvrb" /><a
1042 id="x1-43022r11"></a><span
1043 class="cmr-6">11</span><span
1044 class="cmtt-8"> </span><span
1045 class="cmtt-8"> </span>
1047 <!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
1048 <!--l. 123--><p class="noindent" >
1049 <div class="fancyvrb" id="fancyvrb3">
1051 id="x1-43024r1"></a><span
1052 class="cmr-6">1</span><span
1053 class="cmtt-8"> </span><span
1054 class="cmtt-8"> </span><span
1055 class="cmtt-8"> </span><span
1056 class="cmtt-8"> </span><span
1057 class="cmtt-8"> </span><span
1058 class="cmtt-8"> </span><span
1059 class="cmtt-8"> </span><span
1060 class="cmtt-8"> </span><span
1061 class="cmtt-8"> </span><span
1062 class="cmtt-8"> |</span>
1063 <br class="fancyvrb" /><a
1064 id="x1-43026r2"></a><span
1065 class="cmr-6">2</span><span
1066 class="cmtt-8"> </span><span
1067 class="cmtt-8"> </span><span
1068 class="cmtt-8"> </span><span
1069 class="cmtt-8"> </span><span
1070 class="cmtt-8"> </span><span
1071 class="cmtt-8"> </span><span
1072 class="cmtt-8"> </span><span
1073 class="cmtt-8"> </span><span
1074 class="cmtt-8"> </span><span
1075 class="cmtt-8"> V</span>
1076 <br class="fancyvrb" /><a
1077 id="x1-43028r3"></a><span
1078 class="cmr-6">3</span><span
1079 class="cmtt-8"> </span><span
1080 class="cmtt-8"> </span>
1081 <br class="fancyvrb" /><a
1082 id="x1-43030r4"></a><span
1083 class="cmr-6">4</span><span
1084 class="cmtt-8"> </span><span
1085 class="cmtt-8"> </span><span
1086 class="cmtt-8"> </span><span
1087 class="cmtt-8"> </span><span
1088 class="cmtt-8"> </span><span
1089 class="cmtt-8"> </span><span
1090 class="cmtt-8"> </span><span
1091 class="cmtt-8"> </span><span
1092 class="cmtt-8"> </span><span
1093 class="cmtt-8"> 7</span><span
1094 class="cmtt-8"> 6</span><span
1095 class="cmtt-8"> 5</span><span
1096 class="cmtt-8"> 4</span><span
1097 class="cmtt-8"> 3</span><span
1098 class="cmtt-8"> 2</span><span
1099 class="cmtt-8"> 1</span><span
1100 class="cmtt-8"> 0</span>
1101 <br class="fancyvrb" /><a
1102 id="x1-43032r5"></a><span
1103 class="cmr-6">5</span><span
1104 class="cmtt-8"> </span><span
1105 class="cmtt-8"> byte</span><span
1106 class="cmtt-8"> 0</span><span
1107 class="cmtt-8"> [0</span><span
1108 class="cmtt-8"> 1</span><span
1109 class="cmtt-8"> 1</span><span
1110 class="cmtt-8"> 1</span><span
1111 class="cmtt-8"> 1</span><span
1112 class="cmtt-8"> 1</span><span
1113 class="cmtt-8"> 0</span><span
1114 class="cmtt-8"> 0]</span><span
1115 class="cmtt-8"> </span><span
1116 class="cmtt-8"> <-</span>
1117 <br class="fancyvrb" /><a
1118 id="x1-43034r6"></a><span
1119 class="cmr-6">6</span><span
1120 class="cmtt-8"> </span><span
1121 class="cmtt-8"> byte</span><span
1122 class="cmtt-8"> 1</span><span
1123 class="cmtt-8"> [</span><span
1124 class="cmtt-8"> </span><span
1125 class="cmtt-8"> </span><span
1126 class="cmtt-8"> </span><span
1127 class="cmtt-8"> </span><span
1128 class="cmtt-8"> </span><span
1129 class="cmtt-8"> </span><span
1130 class="cmtt-8"> </span><span
1131 class="cmtt-8"> </span><span
1132 class="cmtt-8"> </span><span
1133 class="cmtt-8"> </span><span
1134 class="cmtt-8"> </span><span
1135 class="cmtt-8"> </span><span
1136 class="cmtt-8"> </span><span
1137 class="cmtt-8"> </span><span
1138 class="cmtt-8"> ]</span>
1142 <br class="fancyvrb" /><a
1143 id="x1-43036r7"></a><span
1144 class="cmr-6">7</span><span
1145 class="cmtt-8"> </span><span
1146 class="cmtt-8"> byte</span><span
1147 class="cmtt-8"> 2</span><span
1148 class="cmtt-8"> [</span><span
1149 class="cmtt-8"> </span><span
1150 class="cmtt-8"> </span><span
1151 class="cmtt-8"> </span><span
1152 class="cmtt-8"> </span><span
1153 class="cmtt-8"> </span><span
1154 class="cmtt-8"> </span><span
1155 class="cmtt-8"> </span><span
1156 class="cmtt-8"> </span><span
1157 class="cmtt-8"> </span><span
1158 class="cmtt-8"> </span><span
1159 class="cmtt-8"> </span><span
1160 class="cmtt-8"> </span><span
1161 class="cmtt-8"> </span><span
1162 class="cmtt-8"> </span><span
1163 class="cmtt-8"> ]</span>
1164 <br class="fancyvrb" /><a
1165 id="x1-43038r8"></a><span
1166 class="cmr-6">8</span><span
1167 class="cmtt-8"> </span><span
1168 class="cmtt-8"> byte</span><span
1169 class="cmtt-8"> 3</span><span
1170 class="cmtt-8"> [</span><span
1171 class="cmtt-8"> </span><span
1172 class="cmtt-8"> </span><span
1173 class="cmtt-8"> </span><span
1174 class="cmtt-8"> </span><span
1175 class="cmtt-8"> </span><span
1176 class="cmtt-8"> </span><span
1177 class="cmtt-8"> </span><span
1178 class="cmtt-8"> </span><span
1179 class="cmtt-8"> </span><span
1180 class="cmtt-8"> </span><span
1181 class="cmtt-8"> </span><span
1182 class="cmtt-8"> </span><span
1183 class="cmtt-8"> </span><span
1184 class="cmtt-8"> </span><span
1185 class="cmtt-8"> ]</span>
1186 <br class="fancyvrb" /><a
1187 id="x1-43040r9"></a><span
1188 class="cmr-6">9</span><span
1189 class="cmtt-8"> </span><span
1190 class="cmtt-8"> </span><span
1191 class="cmtt-8"> </span><span
1192 class="cmtt-8"> </span><span
1193 class="cmtt-8"> </span><span
1194 class="cmtt-8"> </span><span
1195 class="cmtt-8"> </span><span
1196 class="cmtt-8"> </span><span
1197 class="cmtt-8"> </span><span
1198 class="cmtt-8"> </span><span
1199 class="cmtt-8"> </span><span
1200 class="cmtt-8"> </span><span
1201 class="cmtt-8"> </span><span
1202 class="cmtt-8"> </span><span
1203 class="cmtt-8"> ...</span>
1204 <br class="fancyvrb" /><a
1205 id="x1-43042r10"></a><span
1206 class="cmr-6">10</span><span
1207 class="cmtt-8"> </span><span
1208 class="cmtt-8"> byte</span><span
1209 class="cmtt-8"> n</span><span
1210 class="cmtt-8"> [</span><span
1211 class="cmtt-8"> </span><span
1212 class="cmtt-8"> </span><span
1213 class="cmtt-8"> </span><span
1214 class="cmtt-8"> </span><span
1215 class="cmtt-8"> </span><span
1216 class="cmtt-8"> </span><span
1217 class="cmtt-8"> </span><span
1218 class="cmtt-8"> </span><span
1219 class="cmtt-8"> </span><span
1220 class="cmtt-8"> </span><span
1221 class="cmtt-8"> </span><span
1222 class="cmtt-8"> </span><span
1223 class="cmtt-8"> </span><span
1224 class="cmtt-8"> </span><span
1225 class="cmtt-8"> ]</span><span
1226 class="cmtt-8"> </span><span
1227 class="cmtt-8"> bytestream</span><span
1228 class="cmtt-8"> length</span><span
1229 class="cmtt-8"> ==</span><span
1230 class="cmtt-8"> 1</span><span
1231 class="cmtt-8"> byte</span>
1233 <!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
1234 <!--l. 139--><p class="noindent" >
1235 <div class="fancyvrb" id="fancyvrb4">
1237 id="x1-43044r1"></a><span
1238 class="cmr-6">1</span><span
1239 class="cmtt-8"> </span><span
1240 class="cmtt-8"> </span><span
1241 class="cmtt-8"> </span><span
1242 class="cmtt-8"> </span><span
1243 class="cmtt-8"> </span><span
1244 class="cmtt-8"> </span><span
1245 class="cmtt-8"> </span><span
1246 class="cmtt-8"> </span><span
1247 class="cmtt-8"> </span><span
1248 class="cmtt-8"> </span><span
1249 class="cmtt-8"> </span><span
1250 class="cmtt-8"> |</span>
1251 <br class="fancyvrb" /><a
1252 id="x1-43046r2"></a><span
1253 class="cmr-6">2</span><span
1254 class="cmtt-8"> </span><span
1255 class="cmtt-8"> </span><span
1256 class="cmtt-8"> </span><span
1257 class="cmtt-8"> </span><span
1258 class="cmtt-8"> </span><span
1259 class="cmtt-8"> </span><span
1260 class="cmtt-8"> </span><span
1261 class="cmtt-8"> </span><span
1262 class="cmtt-8"> </span><span
1263 class="cmtt-8"> </span><span
1264 class="cmtt-8"> </span><span
1265 class="cmtt-8"> V</span>
1266 <br class="fancyvrb" /><a
1267 id="x1-43048r3"></a><span
1268 class="cmr-6">3</span><span
1269 class="cmtt-8"> </span><span
1270 class="cmtt-8"> </span>
1271 <br class="fancyvrb" /><a
1272 id="x1-43050r4"></a><span
1273 class="cmr-6">4</span><span
1274 class="cmtt-8"> </span><span
1275 class="cmtt-8"> </span><span
1276 class="cmtt-8"> </span><span
1277 class="cmtt-8"> </span><span
1278 class="cmtt-8"> </span><span
1279 class="cmtt-8"> </span><span
1280 class="cmtt-8"> </span><span
1281 class="cmtt-8"> </span><span
1282 class="cmtt-8"> </span><span
1283 class="cmtt-8"> 7</span><span
1284 class="cmtt-8"> 6</span><span
1285 class="cmtt-8"> 5</span><span
1286 class="cmtt-8"> 4</span><span
1287 class="cmtt-8"> 3</span><span
1288 class="cmtt-8"> 2</span><span
1289 class="cmtt-8"> 1</span><span
1290 class="cmtt-8"> 0</span>
1291 <br class="fancyvrb" /><a
1292 id="x1-43052r5"></a><span
1293 class="cmr-6">5</span><span
1294 class="cmtt-8"> </span><span
1295 class="cmtt-8"> byte</span><span
1296 class="cmtt-8"> 0</span><span
1297 class="cmtt-8"> [1</span><span
1298 class="cmtt-8"> 1</span><span
1299 class="cmtt-8"> 1</span><span
1300 class="cmtt-8"> 1</span><span
1301 class="cmtt-8"> 1</span><span
1302 class="cmtt-8"> 1</span><span
1303 class="cmtt-8"> 0</span><span
1304 class="cmtt-8"> 0]</span>
1305 <br class="fancyvrb" /><a
1306 id="x1-43054r6"></a><span
1307 class="cmr-6">6</span><span
1308 class="cmtt-8"> </span><span
1309 class="cmtt-8"> byte</span><span
1310 class="cmtt-8"> 1</span><span
1311 class="cmtt-8"> [0</span><span
1312 class="cmtt-8"> 0</span><span
1313 class="cmtt-8"> 0</span><span
1314 class="cmtt-8"> 0</span><span
1315 class="cmtt-8"> 1</span><span
1316 class="cmtt-8"> 0</span><span
1317 class="cmtt-8"> 0</span><span
1318 class="cmtt-8"> 0]</span><span
1319 class="cmtt-8"> </span><span
1320 class="cmtt-8"> <-</span>
1321 <br class="fancyvrb" /><a
1322 id="x1-43056r7"></a><span
1323 class="cmr-6">7</span><span
1324 class="cmtt-8"> </span><span
1325 class="cmtt-8"> byte</span><span
1326 class="cmtt-8"> 2</span><span
1327 class="cmtt-8"> [</span><span
1328 class="cmtt-8"> </span><span
1329 class="cmtt-8"> </span><span
1330 class="cmtt-8"> </span><span
1331 class="cmtt-8"> </span><span
1332 class="cmtt-8"> </span><span
1333 class="cmtt-8"> </span><span
1334 class="cmtt-8"> </span><span
1335 class="cmtt-8"> </span><span
1336 class="cmtt-8"> </span><span
1337 class="cmtt-8"> </span><span
1338 class="cmtt-8"> </span><span
1339 class="cmtt-8"> </span><span
1340 class="cmtt-8"> </span><span
1341 class="cmtt-8"> </span><span
1342 class="cmtt-8"> ]</span>
1343 <br class="fancyvrb" /><a
1344 id="x1-43058r8"></a><span
1345 class="cmr-6">8</span><span
1346 class="cmtt-8"> </span><span
1347 class="cmtt-8"> byte</span><span
1348 class="cmtt-8"> 3</span><span
1349 class="cmtt-8"> [</span><span
1350 class="cmtt-8"> </span><span
1351 class="cmtt-8"> </span><span
1352 class="cmtt-8"> </span><span
1353 class="cmtt-8"> </span><span
1354 class="cmtt-8"> </span><span
1355 class="cmtt-8"> </span><span
1356 class="cmtt-8"> </span><span
1357 class="cmtt-8"> </span><span
1358 class="cmtt-8"> </span><span
1359 class="cmtt-8"> </span><span
1360 class="cmtt-8"> </span><span
1361 class="cmtt-8"> </span><span
1362 class="cmtt-8"> </span><span
1363 class="cmtt-8"> </span><span
1364 class="cmtt-8"> ]</span>
1365 <br class="fancyvrb" /><a
1366 id="x1-43060r9"></a><span
1367 class="cmr-6">9</span><span
1368 class="cmtt-8"> </span><span
1369 class="cmtt-8"> </span><span
1370 class="cmtt-8"> </span><span
1371 class="cmtt-8"> </span><span
1372 class="cmtt-8"> </span><span
1373 class="cmtt-8"> </span><span
1374 class="cmtt-8"> </span><span
1375 class="cmtt-8"> </span><span
1376 class="cmtt-8"> </span><span
1377 class="cmtt-8"> </span><span
1378 class="cmtt-8"> </span><span
1379 class="cmtt-8"> </span><span
1380 class="cmtt-8"> </span><span
1381 class="cmtt-8"> </span><span
1382 class="cmtt-8"> ...</span>
1383 <br class="fancyvrb" /><a
1384 id="x1-43062r10"></a><span
1385 class="cmr-6">10</span><span
1386 class="cmtt-8"> </span><span
1387 class="cmtt-8"> byte</span><span
1388 class="cmtt-8"> n</span><span
1389 class="cmtt-8"> [</span><span
1390 class="cmtt-8"> </span><span
1391 class="cmtt-8"> </span><span
1392 class="cmtt-8"> </span><span
1393 class="cmtt-8"> </span><span
1394 class="cmtt-8"> </span><span
1395 class="cmtt-8"> </span><span
1396 class="cmtt-8"> </span><span
1397 class="cmtt-8"> </span><span
1398 class="cmtt-8"> </span><span
1399 class="cmtt-8"> </span><span
1400 class="cmtt-8"> </span><span
1401 class="cmtt-8"> </span><span
1402 class="cmtt-8"> </span><span
1403 class="cmtt-8"> </span><span
1404 class="cmtt-8"> ]</span><span
1405 class="cmtt-8"> </span><span
1406 class="cmtt-8"> bytestream</span><span
1407 class="cmtt-8"> length</span><span
1408 class="cmtt-8"> ==</span><span
1409 class="cmtt-8"> 2</span><span
1410 class="cmtt-8"> bytes</span>
1411 <br class="fancyvrb" /><a
1412 id="x1-43064r11"></a><span
1413 class="cmr-6">11</span><span
1414 class="cmtt-8"> </span><span
1415 class="cmtt-8"> </span><span
1416 class="cmtt-8"> </span><span
1417 class="cmtt-8"> </span><span
1418 class="cmtt-8"> </span><span
1419 class="cmtt-8"> </span><span
1420 class="cmtt-8"> </span><span
1421 class="cmtt-8"> </span><span
1422 class="cmtt-8"> </span><span
1423 class="cmtt-8"> </span><span
1424 class="cmtt-8"> </span><span
1425 class="cmtt-8"> </span><span
1426 class="cmtt-8"> </span><span
1427 class="cmtt-8"> </span><span
1428 class="cmtt-8"> </span><span
1429 class="cmtt-8"> </span><span
1430 class="cmtt-8"> </span><span
1431 class="cmtt-8"> </span><span
1432 class="cmtt-8"> </span><span
1433 class="cmtt-8"> </span><span
1434 class="cmtt-8"> </span><span
1435 class="cmtt-8"> </span><span
1436 class="cmtt-8"> </span><span
1437 class="cmtt-8"> </span><span
1438 class="cmtt-8"> </span><span
1439 class="cmtt-8"> </span><span
1440 class="cmtt-8"> </span><span
1441 class="cmtt-8"> bit</span><span
1442 class="cmtt-8"> cursor</span><span
1443 class="cmtt-8"> ==</span><span
1444 class="cmtt-8"> 6</span>
1446 <!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
1447 <!--l. 156--><p class="noindent" >
1448 <div class="fancyvrb" id="fancyvrb5">
1450 id="x1-43066r1"></a><span
1451 class="cmr-6">1</span><span
1452 class="cmtt-8"> </span><span
1453 class="cmtt-8"> </span><span
1454 class="cmtt-8"> </span><span
1455 class="cmtt-8"> </span><span
1456 class="cmtt-8"> </span><span
1457 class="cmtt-8"> </span><span
1458 class="cmtt-8"> </span><span
1459 class="cmtt-8"> </span><span
1460 class="cmtt-8"> </span><span
1461 class="cmtt-8"> </span><span
1462 class="cmtt-8"> </span><span
1463 class="cmtt-8"> </span><span
1464 class="cmtt-8"> </span><span
1465 class="cmtt-8"> </span><span
1466 class="cmtt-8"> </span><span
1467 class="cmtt-8"> </span><span
1468 class="cmtt-8"> </span><span
1469 class="cmtt-8"> |</span>
1470 <br class="fancyvrb" /><a
1471 id="x1-43068r2"></a><span
1472 class="cmr-6">2</span><span
1473 class="cmtt-8"> </span><span
1474 class="cmtt-8"> </span><span
1475 class="cmtt-8"> </span><span
1476 class="cmtt-8"> </span><span
1477 class="cmtt-8"> </span><span
1478 class="cmtt-8"> </span><span
1479 class="cmtt-8"> </span><span
1480 class="cmtt-8"> </span><span
1481 class="cmtt-8"> </span><span
1482 class="cmtt-8"> </span><span
1483 class="cmtt-8"> </span><span
1484 class="cmtt-8"> </span><span
1485 class="cmtt-8"> </span><span
1486 class="cmtt-8"> </span><span
1487 class="cmtt-8"> </span><span
1488 class="cmtt-8"> </span><span
1489 class="cmtt-8"> </span><span
1490 class="cmtt-8"> V</span>
1491 <br class="fancyvrb" /><a
1492 id="x1-43070r3"></a><span
1493 class="cmr-6">3</span><span
1494 class="cmtt-8"> </span><span
1495 class="cmtt-8"> </span>
1496 <br class="fancyvrb" /><a
1497 id="x1-43072r4"></a><span
1498 class="cmr-6">4</span><span
1499 class="cmtt-8"> </span><span
1500 class="cmtt-8"> </span><span
1501 class="cmtt-8"> </span><span
1502 class="cmtt-8"> </span><span
1503 class="cmtt-8"> </span><span
1504 class="cmtt-8"> </span><span
1505 class="cmtt-8"> </span><span
1506 class="cmtt-8"> </span><span
1507 class="cmtt-8"> </span><span
1508 class="cmtt-8"> 7</span><span
1509 class="cmtt-8"> 6</span><span
1510 class="cmtt-8"> 5</span><span
1511 class="cmtt-8"> 4</span><span
1512 class="cmtt-8"> 3</span><span
1513 class="cmtt-8"> 2</span><span
1514 class="cmtt-8"> 1</span><span
1515 class="cmtt-8"> 0</span>
1516 <br class="fancyvrb" /><a
1517 id="x1-43074r5"></a><span
1518 class="cmr-6">5</span><span
1519 class="cmtt-8"> </span><span
1520 class="cmtt-8"> byte</span><span
1521 class="cmtt-8"> 0</span><span
1522 class="cmtt-8"> [1</span><span
1523 class="cmtt-8"> 1</span><span
1524 class="cmtt-8"> 1</span><span
1525 class="cmtt-8"> 1</span><span
1526 class="cmtt-8"> 1</span><span
1527 class="cmtt-8"> 1</span><span
1528 class="cmtt-8"> 0</span><span
1529 class="cmtt-8"> 0]</span>
1530 <br class="fancyvrb" /><a
1531 id="x1-43076r6"></a><span
1532 class="cmr-6">6</span><span
1533 class="cmtt-8"> </span><span
1534 class="cmtt-8"> byte</span><span
1535 class="cmtt-8"> 1</span><span
1536 class="cmtt-8"> [0</span><span
1537 class="cmtt-8"> 1</span><span
1538 class="cmtt-8"> 0</span><span
1539 class="cmtt-8"> 0</span><span
1540 class="cmtt-8"> 1</span><span
1541 class="cmtt-8"> 0</span><span
1542 class="cmtt-8"> 0</span><span
1543 class="cmtt-8"> 0]</span>
1544 <br class="fancyvrb" /><a
1545 id="x1-43078r7"></a><span
1546 class="cmr-6">7</span><span
1547 class="cmtt-8"> </span><span
1548 class="cmtt-8"> byte</span><span
1549 class="cmtt-8"> 2</span><span
1550 class="cmtt-8"> [1</span><span
1551 class="cmtt-8"> 1</span><span
1552 class="cmtt-8"> 0</span><span
1553 class="cmtt-8"> 0</span><span
1554 class="cmtt-8"> 1</span><span
1555 class="cmtt-8"> 1</span><span
1556 class="cmtt-8"> 1</span><span
1557 class="cmtt-8"> 0]</span>
1558 <br class="fancyvrb" /><a
1559 id="x1-43080r8"></a><span
1560 class="cmr-6">8</span><span
1561 class="cmtt-8"> </span><span
1562 class="cmtt-8"> byte</span><span
1563 class="cmtt-8"> 3</span><span
1564 class="cmtt-8"> [0</span><span
1565 class="cmtt-8"> 0</span><span
1566 class="cmtt-8"> 0</span><span
1567 class="cmtt-8"> 0</span><span
1568 class="cmtt-8"> 0</span><span
1569 class="cmtt-8"> 1</span><span
1570 class="cmtt-8"> 1</span><span
1571 class="cmtt-8"> 0]</span><span
1572 class="cmtt-8"> </span><span
1573 class="cmtt-8"> <-</span>
1574 <br class="fancyvrb" /><a
1575 id="x1-43082r9"></a><span
1576 class="cmr-6">9</span><span
1577 class="cmtt-8"> </span><span
1578 class="cmtt-8"> </span><span
1579 class="cmtt-8"> </span><span
1580 class="cmtt-8"> </span><span
1581 class="cmtt-8"> </span><span
1582 class="cmtt-8"> </span><span
1583 class="cmtt-8"> </span><span
1584 class="cmtt-8"> </span><span
1585 class="cmtt-8"> </span><span
1586 class="cmtt-8"> </span><span
1587 class="cmtt-8"> </span><span
1588 class="cmtt-8"> </span><span
1589 class="cmtt-8"> </span><span
1590 class="cmtt-8"> </span><span
1591 class="cmtt-8"> ...</span>
1592 <br class="fancyvrb" /><a
1593 id="x1-43084r10"></a><span
1594 class="cmr-6">10</span><span
1595 class="cmtt-8"> </span><span
1596 class="cmtt-8"> byte</span><span
1597 class="cmtt-8"> n</span><span
1598 class="cmtt-8"> [</span><span
1599 class="cmtt-8"> </span><span
1600 class="cmtt-8"> </span><span
1601 class="cmtt-8"> </span><span
1602 class="cmtt-8"> </span><span
1603 class="cmtt-8"> </span><span
1604 class="cmtt-8"> </span><span
1605 class="cmtt-8"> </span><span
1606 class="cmtt-8"> </span><span
1607 class="cmtt-8"> </span><span
1608 class="cmtt-8"> </span><span
1609 class="cmtt-8"> </span><span
1610 class="cmtt-8"> </span><span
1611 class="cmtt-8"> </span><span
1612 class="cmtt-8"> </span><span
1613 class="cmtt-8"> ]</span><span
1614 class="cmtt-8"> </span><span
1615 class="cmtt-8"> bytestream</span><span
1616 class="cmtt-8"> length</span><span
1617 class="cmtt-8"> ==</span><span
1618 class="cmtt-8"> 4</span><span
1619 class="cmtt-8"> bytes</span>
1620 <br class="fancyvrb" /><a
1621 id="x1-43086r11"></a><span
1622 class="cmr-6">11</span><span
1623 class="cmtt-8"> </span><span
1624 class="cmtt-8"> </span>
1626 <!--l. 173--><p class="noindent" >
1627 <h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a
1628 id="x1-440002.1.7"></a>decoding example</h5>
1629 <!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
1630 <!--l. 177--><p class="noindent" >
1631 <div class="fancyvrb" id="fancyvrb6">
1636 id="x1-44002r1"></a><span
1637 class="cmr-6">1</span><span
1638 class="cmtt-8"> </span><span
1639 class="cmtt-8"> </span><span
1640 class="cmtt-8"> </span><span
1641 class="cmtt-8"> </span><span
1642 class="cmtt-8"> </span><span
1643 class="cmtt-8"> </span><span
1644 class="cmtt-8"> </span><span
1645 class="cmtt-8"> </span><span
1646 class="cmtt-8"> </span><span
1647 class="cmtt-8"> </span><span
1648 class="cmtt-8"> </span><span
1649 class="cmtt-8"> </span><span
1650 class="cmtt-8"> </span><span
1651 class="cmtt-8"> </span><span
1652 class="cmtt-8"> </span><span
1653 class="cmtt-8"> </span><span
1654 class="cmtt-8"> </span><span
1655 class="cmtt-8"> </span><span
1656 class="cmtt-8"> </span><span
1657 class="cmtt-8"> </span><span
1658 class="cmtt-8"> </span><span
1659 class="cmtt-8"> </span><span
1660 class="cmtt-8"> </span><span
1661 class="cmtt-8"> |</span>
1662 <br class="fancyvrb" /><a
1663 id="x1-44004r2"></a><span
1664 class="cmr-6">2</span><span
1665 class="cmtt-8"> </span><span
1666 class="cmtt-8"> </span><span
1667 class="cmtt-8"> </span><span
1668 class="cmtt-8"> </span><span
1669 class="cmtt-8"> </span><span
1670 class="cmtt-8"> </span><span
1671 class="cmtt-8"> </span><span
1672 class="cmtt-8"> </span><span
1673 class="cmtt-8"> </span><span
1674 class="cmtt-8"> </span><span
1675 class="cmtt-8"> </span><span
1676 class="cmtt-8"> </span><span
1677 class="cmtt-8"> </span><span
1678 class="cmtt-8"> </span><span
1679 class="cmtt-8"> </span><span
1680 class="cmtt-8"> </span><span
1681 class="cmtt-8"> </span><span
1682 class="cmtt-8"> </span><span
1683 class="cmtt-8"> </span><span
1684 class="cmtt-8"> </span><span
1685 class="cmtt-8"> </span><span
1686 class="cmtt-8"> </span><span
1687 class="cmtt-8"> </span><span
1688 class="cmtt-8"> V</span>
1689 <br class="fancyvrb" /><a
1690 id="x1-44006r3"></a><span
1691 class="cmr-6">3</span><span
1692 class="cmtt-8"> </span><span
1693 class="cmtt-8"> </span>
1694 <br class="fancyvrb" /><a
1695 id="x1-44008r4"></a><span
1696 class="cmr-6">4</span><span
1697 class="cmtt-8"> </span><span
1698 class="cmtt-8"> </span><span
1699 class="cmtt-8"> </span><span
1700 class="cmtt-8"> </span><span
1701 class="cmtt-8"> </span><span
1702 class="cmtt-8"> </span><span
1703 class="cmtt-8"> </span><span
1704 class="cmtt-8"> </span><span
1705 class="cmtt-8"> </span><span
1706 class="cmtt-8"> 7</span><span
1707 class="cmtt-8"> 6</span><span
1708 class="cmtt-8"> 5</span><span
1709 class="cmtt-8"> 4</span><span
1710 class="cmtt-8"> 3</span><span
1711 class="cmtt-8"> 2</span><span
1712 class="cmtt-8"> 1</span><span
1713 class="cmtt-8"> 0</span>
1714 <br class="fancyvrb" /><a
1715 id="x1-44010r5"></a><span
1716 class="cmr-6">5</span><span
1717 class="cmtt-8"> </span><span
1718 class="cmtt-8"> byte</span><span
1719 class="cmtt-8"> 0</span><span
1720 class="cmtt-8"> [1</span><span
1721 class="cmtt-8"> 1</span><span
1722 class="cmtt-8"> 1</span><span
1723 class="cmtt-8"> 1</span><span
1724 class="cmtt-8"> 1</span><span
1725 class="cmtt-8"> 1</span><span
1726 class="cmtt-8"> 0</span><span
1727 class="cmtt-8"> 0]</span><span
1728 class="cmtt-8"> </span><span
1729 class="cmtt-8"> <-</span>
1730 <br class="fancyvrb" /><a
1731 id="x1-44012r6"></a><span
1732 class="cmr-6">6</span><span
1733 class="cmtt-8"> </span><span
1734 class="cmtt-8"> byte</span><span
1735 class="cmtt-8"> 1</span><span
1736 class="cmtt-8"> [0</span><span
1737 class="cmtt-8"> 1</span><span
1738 class="cmtt-8"> 0</span><span
1739 class="cmtt-8"> 0</span><span
1740 class="cmtt-8"> 1</span><span
1741 class="cmtt-8"> 0</span><span
1742 class="cmtt-8"> 0</span><span
1743 class="cmtt-8"> 0]</span>
1744 <br class="fancyvrb" /><a
1745 id="x1-44014r7"></a><span
1746 class="cmr-6">7</span><span
1747 class="cmtt-8"> </span><span
1748 class="cmtt-8"> byte</span><span
1749 class="cmtt-8"> 2</span><span
1750 class="cmtt-8"> [1</span><span
1751 class="cmtt-8"> 1</span><span
1752 class="cmtt-8"> 0</span><span
1753 class="cmtt-8"> 0</span><span
1754 class="cmtt-8"> 1</span><span
1755 class="cmtt-8"> 1</span><span
1756 class="cmtt-8"> 1</span><span
1757 class="cmtt-8"> 0]</span>
1758 <br class="fancyvrb" /><a
1759 id="x1-44016r8"></a><span
1760 class="cmr-6">8</span><span
1761 class="cmtt-8"> </span><span
1762 class="cmtt-8"> byte</span><span
1763 class="cmtt-8"> 3</span><span
1764 class="cmtt-8"> [0</span><span
1765 class="cmtt-8"> 0</span><span
1766 class="cmtt-8"> 0</span><span
1767 class="cmtt-8"> 0</span><span
1768 class="cmtt-8"> 0</span><span
1769 class="cmtt-8"> 1</span><span
1770 class="cmtt-8"> 1</span><span
1771 class="cmtt-8"> 0]</span><span
1772 class="cmtt-8"> </span><span
1773 class="cmtt-8"> bytestream</span><span
1774 class="cmtt-8"> length</span><span
1775 class="cmtt-8"> ==</span><span
1776 class="cmtt-8"> 4</span><span
1777 class="cmtt-8"> bytes</span>
1778 <br class="fancyvrb" /><a
1779 id="x1-44018r9"></a><span
1780 class="cmr-6">9</span><span
1781 class="cmtt-8"> </span><span
1782 class="cmtt-8"> </span>
1784 <!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
1785 are worth noting here:
1786 <ul class="itemize1">
1787 <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
1788 some other combination of bit-widths from the bitstream is well defined. There are
1789 no artificial alignment boundaries maintained in the bitstream.
1791 <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
1792 either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
1793 decode context.</li></ul>
1794 <!--l. 208--><p class="noindent" >
1795 <h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a
1796 id="x1-450002.1.8"></a>end-of-packet alignment</h5>
1797 <!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
1798 embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
1799 Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
1800 the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
1801 in the last byte of a packet.
1802 <!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
1803 should this unused space be read, it will return binary zeroes.
1804 <!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
1805 End-of-packet is not to be considered an error; it is merely a state indicating that there is
1806 insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
1807 normal mode of operation, and as such, decoders must handle reading past the end of a packet as
1808 a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
1809 also return ’end-of-packet’.
1813 <!--l. 233--><p class="noindent" >
1814 <h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a
1815 id="x1-460002.1.9"></a>reading zero bits</h5>
1816 <!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
1817 Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
1818 triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
1819 end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
1820 shall also fail with ’end-of-packet’.
1827 <h3 class="sectionHead"><span class="titlemark">3. </span> <a
1828 id="x1-470003"></a>Probability Model and Codebooks</h3>
1829 <!--l. 6--><p class="noindent" >
1830 <h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a
1831 id="x1-480003.1"></a>Overview</h4>
1832 <!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
1833 probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
1834 bitstream itself in the third header, the codec setup header. This packed configuration consists of
1835 multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
1836 compressed codewords as well as an optional lookup table of output vector values to which a
1837 decoded Huffman value is applied as an offset, generating the final decoded output corresponding
1838 to a given compressed codeword.
1839 <!--l. 18--><p class="noindent" >
1840 <h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a
1841 id="x1-490003.1.1"></a>Bitwise operation</h5>
1842 <!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
1843 and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
1844 read from the stream according to <a
1845 href="#x1-360002">Section 2</a>, “<a
1846 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
1847 <!--l. 27--><p class="noindent" >
1848 <h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a
1849 id="x1-500003.2"></a>Packed codebook format</h4>
1850 <!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
1851 eight bits. This is not universally true; see <a
1852 href="#x1-360002">Section 2</a>, “<a
1853 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
1854 relating to non-eight-bit bytes.
1858 <!--l. 34--><p class="noindent" >
1859 <h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a
1860 id="x1-510003.2.1"></a>codebook decode</h5>
1861 <!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
1862 <!--l. 38--><p class="noindent" >
1863 <div class="fancyvrb" id="fancyvrb7">
1865 id="x1-51002r1"></a><span
1866 class="cmr-6">1</span><span
1867 class="cmtt-8"> </span><span
1868 class="cmtt-8"> byte</span><span
1869 class="cmtt-8"> 0:</span><span
1870 class="cmtt-8"> [</span><span
1871 class="cmtt-8"> 0</span><span
1872 class="cmtt-8"> 1</span><span
1873 class="cmtt-8"> 0</span><span
1874 class="cmtt-8"> 0</span><span
1875 class="cmtt-8"> 0</span><span
1876 class="cmtt-8"> 0</span><span
1877 class="cmtt-8"> 1</span><span
1878 class="cmtt-8"> 0</span><span
1879 class="cmtt-8"> ]</span><span
1880 class="cmtt-8"> (0x42)</span>
1881 <br class="fancyvrb" /><a
1882 id="x1-51004r2"></a><span
1883 class="cmr-6">2</span><span
1884 class="cmtt-8"> </span><span
1885 class="cmtt-8"> byte</span><span
1886 class="cmtt-8"> 1:</span><span
1887 class="cmtt-8"> [</span><span
1888 class="cmtt-8"> 0</span><span
1889 class="cmtt-8"> 1</span><span
1890 class="cmtt-8"> 0</span><span
1891 class="cmtt-8"> 0</span><span
1892 class="cmtt-8"> 0</span><span
1893 class="cmtt-8"> 0</span><span
1894 class="cmtt-8"> 1</span><span
1895 class="cmtt-8"> 1</span><span
1896 class="cmtt-8"> ]</span><span
1897 class="cmtt-8"> (0x43)</span>
1898 <br class="fancyvrb" /><a
1899 id="x1-51006r3"></a><span
1900 class="cmr-6">3</span><span
1901 class="cmtt-8"> </span><span
1902 class="cmtt-8"> byte</span><span
1903 class="cmtt-8"> 2:</span><span
1904 class="cmtt-8"> [</span><span
1905 class="cmtt-8"> 0</span><span
1906 class="cmtt-8"> 1</span><span
1907 class="cmtt-8"> 0</span><span
1908 class="cmtt-8"> 1</span><span
1909 class="cmtt-8"> 0</span><span
1910 class="cmtt-8"> 1</span><span
1911 class="cmtt-8"> 1</span><span
1912 class="cmtt-8"> 0</span><span
1913 class="cmtt-8"> ]</span><span
1914 class="cmtt-8"> (0x56)</span>
1916 <!--l. 44--><p class="noindent" >16 bit <span
1917 class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span
1918 class="cmtt-12">[codebook_entries] </span>fields:
1919 <!--l. 46--><p class="noindent" >
1920 <div class="fancyvrb" id="fancyvrb8">
1922 id="x1-51008r1"></a><span
1923 class="cmr-6">1</span><span
1924 class="cmtt-8"> </span><span
1925 class="cmtt-8"> </span>
1926 <br class="fancyvrb" /><a
1927 id="x1-51010r2"></a><span
1928 class="cmr-6">2</span><span
1929 class="cmtt-8"> </span><span
1930 class="cmtt-8"> byte</span><span
1931 class="cmtt-8"> 3:</span><span
1932 class="cmtt-8"> [</span><span
1933 class="cmtt-8"> X</span><span
1934 class="cmtt-8"> X</span><span
1935 class="cmtt-8"> X</span><span
1936 class="cmtt-8"> X</span><span
1937 class="cmtt-8"> X</span><span
1938 class="cmtt-8"> X</span><span
1939 class="cmtt-8"> X</span><span
1940 class="cmtt-8"> X</span><span
1941 class="cmtt-8"> ]</span>
1942 <br class="fancyvrb" /><a
1943 id="x1-51012r3"></a><span
1944 class="cmr-6">3</span><span
1945 class="cmtt-8"> </span><span
1946 class="cmtt-8"> byte</span><span
1947 class="cmtt-8"> 4:</span><span
1948 class="cmtt-8"> [</span><span
1949 class="cmtt-8"> X</span><span
1950 class="cmtt-8"> X</span><span
1951 class="cmtt-8"> X</span><span
1952 class="cmtt-8"> X</span><span
1953 class="cmtt-8"> X</span><span
1954 class="cmtt-8"> X</span><span
1955 class="cmtt-8"> X</span><span
1956 class="cmtt-8"> X</span><span
1957 class="cmtt-8"> ]</span><span
1958 class="cmtt-8"> [codebook_dimensions]</span><span
1959 class="cmtt-8"> (16</span><span
1960 class="cmtt-8"> bit</span><span
1961 class="cmtt-8"> unsigned)</span>
1962 <br class="fancyvrb" /><a
1963 id="x1-51014r4"></a><span
1964 class="cmr-6">4</span><span
1965 class="cmtt-8"> </span><span
1966 class="cmtt-8"> </span>
1967 <br class="fancyvrb" /><a
1968 id="x1-51016r5"></a><span
1969 class="cmr-6">5</span><span
1970 class="cmtt-8"> </span><span
1971 class="cmtt-8"> byte</span><span
1972 class="cmtt-8"> 5:</span><span
1973 class="cmtt-8"> [</span><span
1974 class="cmtt-8"> X</span><span
1975 class="cmtt-8"> X</span><span
1976 class="cmtt-8"> X</span><span
1977 class="cmtt-8"> X</span><span
1978 class="cmtt-8"> X</span><span
1979 class="cmtt-8"> X</span><span
1980 class="cmtt-8"> X</span><span
1981 class="cmtt-8"> X</span><span
1982 class="cmtt-8"> ]</span>
1983 <br class="fancyvrb" /><a
1984 id="x1-51018r6"></a><span
1985 class="cmr-6">6</span><span
1986 class="cmtt-8"> </span><span
1987 class="cmtt-8"> byte</span><span
1988 class="cmtt-8"> 6:</span><span
1989 class="cmtt-8"> [</span><span
1990 class="cmtt-8"> X</span><span
1991 class="cmtt-8"> X</span><span
1992 class="cmtt-8"> X</span><span
1993 class="cmtt-8"> X</span><span
1994 class="cmtt-8"> X</span><span
1995 class="cmtt-8"> X</span><span
1996 class="cmtt-8"> X</span><span
1997 class="cmtt-8"> X</span><span
1998 class="cmtt-8"> ]</span>
1999 <br class="fancyvrb" /><a
2000 id="x1-51020r7"></a><span
2001 class="cmr-6">7</span><span
2002 class="cmtt-8"> </span><span
2003 class="cmtt-8"> byte</span><span
2004 class="cmtt-8"> 7:</span><span
2005 class="cmtt-8"> [</span><span
2006 class="cmtt-8"> X</span><span
2007 class="cmtt-8"> X</span><span
2008 class="cmtt-8"> X</span><span
2009 class="cmtt-8"> X</span><span
2010 class="cmtt-8"> X</span><span
2011 class="cmtt-8"> X</span><span
2012 class="cmtt-8"> X</span><span
2013 class="cmtt-8"> X</span><span
2014 class="cmtt-8"> ]</span><span
2015 class="cmtt-8"> [codebook_entries]</span><span
2016 class="cmtt-8"> (24</span><span
2017 class="cmtt-8"> bit</span><span
2018 class="cmtt-8"> unsigned)</span>
2019 <br class="fancyvrb" /><a
2020 id="x1-51022r8"></a><span
2021 class="cmr-6">8</span><span
2022 class="cmtt-8"> </span><span
2023 class="cmtt-8"> </span>
2025 <!--l. 57--><p class="noindent" >Next is the <span
2026 class="cmtt-12">[ordered] </span>bit flag:
2027 <!--l. 59--><p class="noindent" >
2028 <div class="fancyvrb" id="fancyvrb9">
2030 id="x1-51024r1"></a><span
2031 class="cmr-6">1</span><span
2032 class="cmtt-8"> </span><span
2033 class="cmtt-8"> </span>
2034 <br class="fancyvrb" /><a
2035 id="x1-51026r2"></a><span
2036 class="cmr-6">2</span><span
2037 class="cmtt-8"> </span><span
2038 class="cmtt-8"> byte</span><span
2039 class="cmtt-8"> 8:</span><span
2040 class="cmtt-8"> [</span><span
2041 class="cmtt-8"> </span><span
2042 class="cmtt-8"> </span><span
2043 class="cmtt-8"> </span><span
2044 class="cmtt-8"> </span><span
2045 class="cmtt-8"> </span><span
2046 class="cmtt-8"> </span><span
2047 class="cmtt-8"> </span><span
2048 class="cmtt-8"> </span><span
2049 class="cmtt-8"> </span><span
2050 class="cmtt-8"> </span><span
2051 class="cmtt-8"> </span><span
2052 class="cmtt-8"> </span><span
2053 class="cmtt-8"> </span><span
2054 class="cmtt-8"> </span><span
2055 class="cmtt-8"> X</span><span
2056 class="cmtt-8"> ]</span><span
2057 class="cmtt-8"> [ordered]</span><span
2058 class="cmtt-8"> (1</span><span
2059 class="cmtt-8"> bit)</span>
2060 <br class="fancyvrb" /><a
2061 id="x1-51028r3"></a><span
2062 class="cmr-6">3</span><span
2063 class="cmtt-8"> </span><span
2064 class="cmtt-8"> </span>
2066 <!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
2067 class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length.
2068 We now read the list of codeword lengths and store these lengths in the array
2070 class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span
2071 class="cmtt-12">[ordered] </span>flag
2073 <ul class="itemize1">
2074 <li class="itemize">If the <span
2075 class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
2076 needs to read each codeword length one-by-one.
2077 <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
2078 class="cmtt-12">[sparse] </span>flag. This flag determines
2079 whether or not the codebook contains unused entries that are not to be included in
2083 the codeword decode tree:
2084 <!--l. 82--><p class="noindent" >
2085 <div class="fancyvrb" id="fancyvrb10">
2087 id="x1-51030r1"></a><span
2088 class="cmr-6">1</span><span
2089 class="cmtt-8"> </span><span
2090 class="cmtt-8"> byte</span><span
2091 class="cmtt-8"> 8:</span><span
2092 class="cmtt-8"> [</span><span
2093 class="cmtt-8"> </span><span
2094 class="cmtt-8"> </span><span
2095 class="cmtt-8"> </span><span
2096 class="cmtt-8"> </span><span
2097 class="cmtt-8"> </span><span
2098 class="cmtt-8"> </span><span
2099 class="cmtt-8"> </span><span
2100 class="cmtt-8"> </span><span
2101 class="cmtt-8"> </span><span
2102 class="cmtt-8"> </span><span
2103 class="cmtt-8"> </span><span
2104 class="cmtt-8"> </span><span
2105 class="cmtt-8"> X</span><span
2106 class="cmtt-8"> 1</span><span
2107 class="cmtt-8"> ]</span><span
2108 class="cmtt-8"> [sparse]</span><span
2109 class="cmtt-8"> flag</span><span
2110 class="cmtt-8"> (1</span><span
2111 class="cmtt-8"> bit)</span>
2113 <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
2114 class="cmtt-12">[codebook_entries] </span>codebook entries:
2115 <!--l. 89--><p class="noindent" >
2116 <div class="fancyvrb" id="fancyvrb11">
2118 id="x1-51032r1"></a><span
2119 class="cmr-6">1</span><span
2120 class="cmtt-8"> </span><span
2121 class="cmtt-8"> </span>
2122 <br class="fancyvrb" /><a
2123 id="x1-51034r2"></a><span
2124 class="cmr-6">2</span><span
2125 class="cmtt-8"> </span><span
2126 class="cmtt-8"> </span><span
2127 class="cmtt-8"> </span><span
2128 class="cmtt-8"> 1)</span><span
2129 class="cmtt-8"> if([sparse]</span><span
2130 class="cmtt-8"> is</span><span
2131 class="cmtt-8"> set)</span><span
2132 class="cmtt-8"> </span><span
2133 class="cmsy-8">{</span>
2134 <br class="fancyvrb" /><a
2135 id="x1-51036r3"></a><span
2136 class="cmr-6">3</span><span
2137 class="cmtt-8"> </span><span
2138 class="cmtt-8"> </span>
2139 <br class="fancyvrb" /><a
2140 id="x1-51038r4"></a><span
2141 class="cmr-6">4</span><span
2142 class="cmtt-8"> </span><span
2143 class="cmtt-8"> </span><span
2144 class="cmtt-8"> </span><span
2145 class="cmtt-8"> </span><span
2146 class="cmtt-8"> </span><span
2147 class="cmtt-8"> </span><span
2148 class="cmtt-8"> </span><span
2149 class="cmtt-8"> </span><span
2150 class="cmtt-8"> </span><span
2151 class="cmtt-8"> </span><span
2152 class="cmtt-8"> 2)</span><span
2153 class="cmtt-8"> [flag]</span><span
2154 class="cmtt-8"> =</span><span
2155 class="cmtt-8"> read</span><span
2156 class="cmtt-8"> one</span><span
2157 class="cmtt-8"> bit;</span>
2158 <br class="fancyvrb" /><a
2159 id="x1-51040r5"></a><span
2160 class="cmr-6">5</span><span
2161 class="cmtt-8"> </span><span
2162 class="cmtt-8"> </span><span
2163 class="cmtt-8"> </span><span
2164 class="cmtt-8"> </span><span
2165 class="cmtt-8"> </span><span
2166 class="cmtt-8"> </span><span
2167 class="cmtt-8"> </span><span
2168 class="cmtt-8"> </span><span
2169 class="cmtt-8"> </span><span
2170 class="cmtt-8"> </span><span
2171 class="cmtt-8"> 3)</span><span
2172 class="cmtt-8"> if([flag]</span><span
2173 class="cmtt-8"> is</span><span
2174 class="cmtt-8"> set)</span><span
2175 class="cmtt-8"> </span><span
2176 class="cmsy-8">{</span>
2177 <br class="fancyvrb" /><a
2178 id="x1-51042r6"></a><span
2179 class="cmr-6">6</span><span
2180 class="cmtt-8"> </span><span
2181 class="cmtt-8"> </span>
2182 <br class="fancyvrb" /><a
2183 id="x1-51044r7"></a><span
2184 class="cmr-6">7</span><span
2185 class="cmtt-8"> </span><span
2186 class="cmtt-8"> </span><span
2187 class="cmtt-8"> </span><span
2188 class="cmtt-8"> </span><span
2189 class="cmtt-8"> </span><span
2190 class="cmtt-8"> </span><span
2191 class="cmtt-8"> </span><span
2192 class="cmtt-8"> </span><span
2193 class="cmtt-8"> </span><span
2194 class="cmtt-8"> </span><span
2195 class="cmtt-8"> </span><span
2196 class="cmtt-8"> </span><span
2197 class="cmtt-8"> </span><span
2198 class="cmtt-8"> </span><span
2199 class="cmtt-8"> </span><span
2200 class="cmtt-8"> 4)</span><span
2201 class="cmtt-8"> [length]</span><span
2202 class="cmtt-8"> =</span><span
2203 class="cmtt-8"> read</span><span
2204 class="cmtt-8"> a</span><span
2205 class="cmtt-8"> five</span><span
2206 class="cmtt-8"> bit</span><span
2207 class="cmtt-8"> unsigned</span><span
2208 class="cmtt-8"> integer;</span>
2209 <br class="fancyvrb" /><a
2210 id="x1-51046r8"></a><span
2211 class="cmr-6">8</span><span
2212 class="cmtt-8"> </span><span
2213 class="cmtt-8"> </span><span
2214 class="cmtt-8"> </span><span
2215 class="cmtt-8"> </span><span
2216 class="cmtt-8"> </span><span
2217 class="cmtt-8"> </span><span
2218 class="cmtt-8"> </span><span
2219 class="cmtt-8"> </span><span
2220 class="cmtt-8"> </span><span
2221 class="cmtt-8"> </span><span
2222 class="cmtt-8"> </span><span
2223 class="cmtt-8"> </span><span
2224 class="cmtt-8"> </span><span
2225 class="cmtt-8"> </span><span
2226 class="cmtt-8"> </span><span
2227 class="cmtt-8"> 5)</span><span
2228 class="cmtt-8"> codeword</span><span
2229 class="cmtt-8"> length</span><span
2230 class="cmtt-8"> for</span><span
2231 class="cmtt-8"> this</span><span
2232 class="cmtt-8"> entry</span><span
2233 class="cmtt-8"> is</span><span
2234 class="cmtt-8"> [length]+1;</span>
2235 <br class="fancyvrb" /><a
2236 id="x1-51048r9"></a><span
2237 class="cmr-6">9</span><span
2238 class="cmtt-8"> </span><span
2239 class="cmtt-8"> </span>
2240 <br class="fancyvrb" /><a
2241 id="x1-51050r10"></a><span
2242 class="cmr-6">10</span><span
2243 class="cmtt-8"> </span><span
2244 class="cmtt-8"> </span><span
2245 class="cmtt-8"> </span><span
2246 class="cmtt-8"> </span><span
2247 class="cmtt-8"> </span><span
2248 class="cmtt-8"> </span><span
2249 class="cmtt-8"> </span><span
2250 class="cmtt-8"> </span><span
2251 class="cmtt-8"> </span><span
2252 class="cmtt-8"> </span><span
2253 class="cmtt-8"> </span><span
2254 class="cmtt-8"> </span><span
2255 class="cmtt-8"> </span><span
2256 class="cmtt-8"> </span><span
2257 class="cmsy-8">}</span><span
2258 class="cmtt-8"> else</span><span
2259 class="cmtt-8"> </span><span
2260 class="cmsy-8">{</span>
2261 <br class="fancyvrb" /><a
2262 id="x1-51052r11"></a><span
2263 class="cmr-6">11</span><span
2264 class="cmtt-8"> </span><span
2265 class="cmtt-8"> </span>
2266 <br class="fancyvrb" /><a
2267 id="x1-51054r12"></a><span
2268 class="cmr-6">12</span><span
2269 class="cmtt-8"> </span><span
2270 class="cmtt-8"> </span><span
2271 class="cmtt-8"> </span><span
2272 class="cmtt-8"> </span><span
2273 class="cmtt-8"> </span><span
2274 class="cmtt-8"> </span><span
2275 class="cmtt-8"> </span><span
2276 class="cmtt-8"> </span><span
2277 class="cmtt-8"> </span><span
2278 class="cmtt-8"> </span><span
2279 class="cmtt-8"> </span><span
2280 class="cmtt-8"> </span><span
2281 class="cmtt-8"> </span><span
2282 class="cmtt-8"> </span><span
2283 class="cmtt-8"> </span><span
2284 class="cmtt-8"> 6)</span><span
2285 class="cmtt-8"> this</span><span
2286 class="cmtt-8"> entry</span><span
2287 class="cmtt-8"> is</span><span
2288 class="cmtt-8"> unused.</span><span
2289 class="cmtt-8"> </span><span
2290 class="cmtt-8"> mark</span><span
2291 class="cmtt-8"> it</span><span
2292 class="cmtt-8"> as</span><span
2293 class="cmtt-8"> such.</span>
2294 <br class="fancyvrb" /><a
2295 id="x1-51056r13"></a><span
2296 class="cmr-6">13</span><span
2297 class="cmtt-8"> </span><span
2298 class="cmtt-8"> </span>
2299 <br class="fancyvrb" /><a
2300 id="x1-51058r14"></a><span
2301 class="cmr-6">14</span><span
2302 class="cmtt-8"> </span><span
2303 class="cmtt-8"> </span><span
2304 class="cmtt-8"> </span><span
2305 class="cmtt-8"> </span><span
2306 class="cmtt-8"> </span><span
2307 class="cmtt-8"> </span><span
2308 class="cmtt-8"> </span><span
2309 class="cmtt-8"> </span><span
2310 class="cmtt-8"> </span><span
2311 class="cmtt-8"> </span><span
2312 class="cmtt-8"> </span><span
2313 class="cmtt-8"> </span><span
2314 class="cmtt-8"> </span><span
2315 class="cmtt-8"> </span><span
2316 class="cmsy-8">}</span>
2317 <br class="fancyvrb" /><a
2318 id="x1-51060r15"></a><span
2319 class="cmr-6">15</span><span
2320 class="cmtt-8"> </span><span
2321 class="cmtt-8"> </span>
2322 <br class="fancyvrb" /><a
2323 id="x1-51062r16"></a><span
2324 class="cmr-6">16</span><span
2325 class="cmtt-8"> </span><span
2326 class="cmtt-8"> </span><span
2327 class="cmtt-8"> </span><span
2328 class="cmtt-8"> </span><span
2329 class="cmtt-8"> </span><span
2330 class="cmtt-8"> </span><span
2331 class="cmtt-8"> </span><span
2332 class="cmsy-8">}</span><span
2333 class="cmtt-8"> else</span><span
2334 class="cmtt-8"> the</span><span
2335 class="cmtt-8"> sparse</span><span
2336 class="cmtt-8"> flag</span><span
2337 class="cmtt-8"> is</span><span
2338 class="cmtt-8"> not</span><span
2339 class="cmtt-8"> set</span><span
2340 class="cmtt-8"> </span><span
2341 class="cmsy-8">{</span>
2342 <br class="fancyvrb" /><a
2343 id="x1-51064r17"></a><span
2344 class="cmr-6">17</span><span
2345 class="cmtt-8"> </span><span
2346 class="cmtt-8"> </span>
2347 <br class="fancyvrb" /><a
2348 id="x1-51066r18"></a><span
2349 class="cmr-6">18</span><span
2350 class="cmtt-8"> </span><span
2351 class="cmtt-8"> </span><span
2352 class="cmtt-8"> </span><span
2353 class="cmtt-8"> </span><span
2354 class="cmtt-8"> </span><span
2355 class="cmtt-8"> </span><span
2356 class="cmtt-8"> </span><span
2357 class="cmtt-8"> </span><span
2358 class="cmtt-8"> </span><span
2359 class="cmtt-8"> 7)</span><span
2360 class="cmtt-8"> [length]</span><span
2361 class="cmtt-8"> =</span><span
2362 class="cmtt-8"> read</span><span
2363 class="cmtt-8"> a</span><span
2364 class="cmtt-8"> five</span><span
2365 class="cmtt-8"> bit</span><span
2366 class="cmtt-8"> unsigned</span><span
2367 class="cmtt-8"> integer;</span>
2368 <br class="fancyvrb" /><a
2369 id="x1-51068r19"></a><span
2370 class="cmr-6">19</span><span
2371 class="cmtt-8"> </span><span
2372 class="cmtt-8"> </span><span
2373 class="cmtt-8"> </span><span
2374 class="cmtt-8"> </span><span
2375 class="cmtt-8"> </span><span
2376 class="cmtt-8"> </span><span
2377 class="cmtt-8"> </span><span
2378 class="cmtt-8"> </span><span
2379 class="cmtt-8"> </span><span
2380 class="cmtt-8"> 8)</span><span
2381 class="cmtt-8"> the</span><span
2382 class="cmtt-8"> codeword</span><span
2383 class="cmtt-8"> length</span><span
2384 class="cmtt-8"> for</span><span
2385 class="cmtt-8"> this</span><span
2386 class="cmtt-8"> entry</span><span
2387 class="cmtt-8"> is</span><span
2388 class="cmtt-8"> [length]+1;</span>
2389 <br class="fancyvrb" /><a
2390 id="x1-51070r20"></a><span
2391 class="cmr-6">20</span><span
2392 class="cmtt-8"> </span><span
2393 class="cmtt-8"> </span>
2394 <br class="fancyvrb" /><a
2395 id="x1-51072r21"></a><span
2396 class="cmr-6">21</span><span
2397 class="cmtt-8"> </span><span
2398 class="cmtt-8"> </span><span
2399 class="cmtt-8"> </span><span
2400 class="cmtt-8"> </span><span
2401 class="cmtt-8"> </span><span
2402 class="cmtt-8"> </span><span
2403 class="cmtt-8"> </span><span
2404 class="cmsy-8">}</span>
2405 <br class="fancyvrb" /><a
2406 id="x1-51074r22"></a><span
2407 class="cmr-6">22</span><span
2408 class="cmtt-8"> </span><span
2409 class="cmtt-8"> </span>
2412 <li class="itemize">If the <span
2413 class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
2414 ascending length order. Rather than reading a length for every codeword, the
2415 encoder reads the number of codewords per length. That is, beginning at entry
2417 <!--l. 120--><p class="noindent" >
2418 <div class="fancyvrb" id="fancyvrb12">
2420 id="x1-51076r1"></a><span
2421 class="cmr-6">1</span><span
2422 class="cmtt-8"> </span><span
2423 class="cmtt-8"> </span><span
2424 class="cmtt-8"> </span><span
2425 class="cmtt-8"> 1)</span><span
2426 class="cmtt-8"> [current_entry]</span><span
2427 class="cmtt-8"> =</span><span
2428 class="cmtt-8"> 0;</span>
2429 <br class="fancyvrb" /><a
2430 id="x1-51078r2"></a><span
2431 class="cmr-6">2</span><span
2432 class="cmtt-8"> </span><span
2433 class="cmtt-8"> </span><span
2434 class="cmtt-8"> </span><span
2435 class="cmtt-8"> 2)</span><span
2436 class="cmtt-8"> [current_length]</span><span
2437 class="cmtt-8"> =</span><span
2438 class="cmtt-8"> read</span><span
2439 class="cmtt-8"> a</span><span
2440 class="cmtt-8"> five</span><span
2441 class="cmtt-8"> bit</span><span
2442 class="cmtt-8"> unsigned</span><span
2443 class="cmtt-8"> integer</span><span
2444 class="cmtt-8"> and</span><span
2445 class="cmtt-8"> add</span><span
2446 class="cmtt-8"> 1;</span>
2447 <br class="fancyvrb" /><a
2448 id="x1-51080r3"></a><span
2449 class="cmr-6">3</span><span
2450 class="cmtt-8"> </span><span
2451 class="cmtt-8"> </span><span
2452 class="cmtt-8"> </span><span
2453 class="cmtt-8"> 3)</span><span
2454 class="cmtt-8"> [number]</span><span
2455 class="cmtt-8"> =</span><span
2456 class="cmtt-8"> read</span><span
2457 class="cmtt-8"> </span><a
2458 href="#x1-1170009.2.1"><span
2459 class="cmtt-8">ilog</span></a><span
2460 class="cmtt-8">([codebook_entries]</span><span
2461 class="cmtt-8"> -</span><span
2462 class="cmtt-8"> [current_entry])</span><span
2463 class="cmtt-8"> bits</span><span
2464 class="cmtt-8"> as</span><span
2465 class="cmtt-8"> an</span><span
2466 class="cmtt-8"> unsigned</span><span
2467 class="cmtt-8"> integer</span>
2468 <br class="fancyvrb" /><a
2469 id="x1-51082r4"></a><span
2470 class="cmr-6">4</span><span
2471 class="cmtt-8"> </span><span
2472 class="cmtt-8"> </span><span
2473 class="cmtt-8"> </span><span
2474 class="cmtt-8"> 4)</span><span
2475 class="cmtt-8"> set</span><span
2476 class="cmtt-8"> the</span><span
2477 class="cmtt-8"> entries</span><span
2478 class="cmtt-8"> [current_entry]</span><span
2479 class="cmtt-8"> through</span><span
2480 class="cmtt-8"> [current_entry]+[number]-1,</span><span
2481 class="cmtt-8"> inclusive,</span>
2482 <br class="fancyvrb" /><a
2483 id="x1-51084r5"></a><span
2484 class="cmr-6">5</span><span
2485 class="cmtt-8"> </span><span
2486 class="cmtt-8"> </span><span
2487 class="cmtt-8"> </span><span
2488 class="cmtt-8"> </span><span
2489 class="cmtt-8"> </span><span
2490 class="cmtt-8"> of</span><span
2491 class="cmtt-8"> the</span><span
2492 class="cmtt-8"> [codebook_codeword_lengths]</span><span
2493 class="cmtt-8"> array</span><span
2494 class="cmtt-8"> to</span><span
2495 class="cmtt-8"> [current_length]</span>
2496 <br class="fancyvrb" /><a
2497 id="x1-51086r6"></a><span
2498 class="cmr-6">6</span><span
2499 class="cmtt-8"> </span><span
2500 class="cmtt-8"> </span><span
2501 class="cmtt-8"> </span><span
2502 class="cmtt-8"> 5)</span><span
2503 class="cmtt-8"> set</span><span
2504 class="cmtt-8"> [current_entry]</span><span
2505 class="cmtt-8"> to</span><span
2506 class="cmtt-8"> [number]</span><span
2507 class="cmtt-8"> +</span><span
2508 class="cmtt-8"> [current_entry]</span>
2509 <br class="fancyvrb" /><a
2510 id="x1-51088r7"></a><span
2511 class="cmr-6">7</span><span
2512 class="cmtt-8"> </span><span
2513 class="cmtt-8"> </span><span
2514 class="cmtt-8"> </span><span
2515 class="cmtt-8"> 6)</span><span
2516 class="cmtt-8"> increment</span><span
2517 class="cmtt-8"> [current_length]</span><span
2518 class="cmtt-8"> by</span><span
2519 class="cmtt-8"> 1</span>
2520 <br class="fancyvrb" /><a
2521 id="x1-51090r8"></a><span
2522 class="cmr-6">8</span><span
2523 class="cmtt-8"> </span><span
2524 class="cmtt-8"> </span><span
2525 class="cmtt-8"> </span><span
2526 class="cmtt-8"> 7)</span><span
2527 class="cmtt-8"> if</span><span
2528 class="cmtt-8"> [current_entry]</span><span
2529 class="cmtt-8"> is</span><span
2530 class="cmtt-8"> greater</span><span
2531 class="cmtt-8"> than</span><span
2532 class="cmtt-8"> [codebook_entries]</span><span
2533 class="cmtt-8"> ERROR</span><span
2534 class="cmtt-8"> CONDITION;</span>
2535 <br class="fancyvrb" /><a
2536 id="x1-51092r9"></a><span
2537 class="cmr-6">9</span><span
2538 class="cmtt-8"> </span><span
2539 class="cmtt-8"> </span><span
2540 class="cmtt-8"> </span><span
2541 class="cmtt-8"> </span><span
2542 class="cmtt-8"> </span><span
2543 class="cmtt-8"> the</span><span
2544 class="cmtt-8"> decoder</span><span
2545 class="cmtt-8"> will</span><span
2546 class="cmtt-8"> not</span><span
2547 class="cmtt-8"> be</span><span
2548 class="cmtt-8"> able</span><span
2549 class="cmtt-8"> to</span><span
2550 class="cmtt-8"> read</span><span
2551 class="cmtt-8"> this</span><span
2552 class="cmtt-8"> stream.</span>
2553 <br class="fancyvrb" /><a
2554 id="x1-51094r10"></a><span
2555 class="cmr-6">10</span><span
2556 class="cmtt-8"> </span><span
2557 class="cmtt-8"> </span><span
2558 class="cmtt-8"> </span><span
2559 class="cmtt-8"> 8)</span><span
2560 class="cmtt-8"> if</span><span
2561 class="cmtt-8"> [current_entry]</span><span
2562 class="cmtt-8"> is</span><span
2563 class="cmtt-8"> less</span><span
2564 class="cmtt-8"> than</span><span
2565 class="cmtt-8"> [codebook_entries],</span><span
2566 class="cmtt-8"> repeat</span><span
2567 class="cmtt-8"> process</span><span
2568 class="cmtt-8"> starting</span><span
2569 class="cmtt-8"> at</span><span
2570 class="cmtt-8"> 3)</span>
2571 <br class="fancyvrb" /><a
2572 id="x1-51096r11"></a><span
2573 class="cmr-6">11</span><span
2574 class="cmtt-8"> </span><span
2575 class="cmtt-8"> </span><span
2576 class="cmtt-8"> </span><span
2577 class="cmtt-8"> 9)</span><span
2578 class="cmtt-8"> done.</span>
2584 <!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
2585 I supports three lookup types:
2586 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
2588 class="enumerate-enumitem">No lookup
2589 </dd><dt class="enumerate-enumitem">
2591 class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ)
2592 </dd><dt class="enumerate-enumitem">
2594 class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl>
2595 <!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
2596 <div class="fancyvrb" id="fancyvrb13">
2598 id="x1-51101r1"></a><span
2599 class="cmr-6">1</span><span
2600 class="cmtt-8"> </span><span
2601 class="cmtt-8"> </span><span
2602 class="cmtt-8"> </span><span
2603 class="cmtt-8"> 1)</span><span
2604 class="cmtt-8"> [codebook_lookup_type]</span><span
2605 class="cmtt-8"> =</span><span
2606 class="cmtt-8"> read</span><span
2607 class="cmtt-8"> four</span><span
2608 class="cmtt-8"> bits</span><span
2609 class="cmtt-8"> as</span><span
2610 class="cmtt-8"> an</span><span
2611 class="cmtt-8"> unsigned</span><span
2612 class="cmtt-8"> integer</span>
2614 <!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
2615 class="cmtt-12">[codebook_lookup_type]</span>:
2616 <ul class="itemize1">
2617 <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
2619 <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
2620 be read. Lookup type one reads a list of values that are permuted in a set pattern to
2621 build a list of vectors, each vector of order <span
2622 class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup
2623 type two builds the same vector list, but reads each scalar for each vector explicitly,
2624 rather than building vectors from a smaller list of possible scalar values. Lookup
2625 decode proceeds as follows:
2626 <!--l. 168--><p class="noindent" >
2627 <div class="fancyvrb" id="fancyvrb14">
2629 id="x1-51103r1"></a><span
2630 class="cmr-6">1</span><span
2631 class="cmtt-8"> </span><span
2632 class="cmtt-8"> </span><span
2633 class="cmtt-8"> </span><span
2634 class="cmtt-8"> 1)</span><span
2635 class="cmtt-8"> [codebook_minimum_value]</span><span
2636 class="cmtt-8"> =</span><span
2637 class="cmtt-8"> </span><a
2638 href="#x1-1180009.2.2"><span
2639 class="cmtt-8">float32_unpack</span></a><span
2640 class="cmtt-8">(</span><span
2641 class="cmtt-8"> read</span><span
2642 class="cmtt-8"> 32</span><span
2643 class="cmtt-8"> bits</span><span
2644 class="cmtt-8"> as</span><span
2645 class="cmtt-8"> an</span><span
2646 class="cmtt-8"> unsigned</span><span
2647 class="cmtt-8"> integer)</span>
2648 <br class="fancyvrb" /><a
2649 id="x1-51105r2"></a><span
2650 class="cmr-6">2</span><span
2651 class="cmtt-8"> </span><span
2652 class="cmtt-8"> </span><span
2653 class="cmtt-8"> </span><span
2654 class="cmtt-8"> 2)</span><span
2655 class="cmtt-8"> [codebook_delta_value]</span><span
2656 class="cmtt-8"> =</span><span
2657 class="cmtt-8"> </span><a
2658 href="#x1-1180009.2.2"><span
2659 class="cmtt-8">float32_unpack</span></a><span
2660 class="cmtt-8">(</span><span
2661 class="cmtt-8"> read</span><span
2662 class="cmtt-8"> 32</span><span
2663 class="cmtt-8"> bits</span><span
2664 class="cmtt-8"> as</span><span
2665 class="cmtt-8"> an</span><span
2666 class="cmtt-8"> unsigned</span><span
2667 class="cmtt-8"> integer)</span>
2668 <br class="fancyvrb" /><a
2669 id="x1-51107r3"></a><span
2670 class="cmr-6">3</span><span
2671 class="cmtt-8"> </span><span
2672 class="cmtt-8"> </span><span
2673 class="cmtt-8"> </span><span
2674 class="cmtt-8"> 3)</span><span
2675 class="cmtt-8"> [codebook_value_bits]</span><span
2676 class="cmtt-8"> =</span><span
2677 class="cmtt-8"> read</span><span
2678 class="cmtt-8"> 4</span><span
2679 class="cmtt-8"> bits</span><span
2680 class="cmtt-8"> as</span><span
2681 class="cmtt-8"> an</span><span
2682 class="cmtt-8"> unsigned</span><span
2683 class="cmtt-8"> integer</span><span
2684 class="cmtt-8"> and</span><span
2685 class="cmtt-8"> add</span><span
2686 class="cmtt-8"> 1</span>
2687 <br class="fancyvrb" /><a
2688 id="x1-51109r4"></a><span
2689 class="cmr-6">4</span><span
2690 class="cmtt-8"> </span><span
2691 class="cmtt-8"> </span><span
2692 class="cmtt-8"> </span><span
2693 class="cmtt-8"> 4)</span><span
2694 class="cmtt-8"> [codebook_sequence_p]</span><span
2695 class="cmtt-8"> =</span><span
2696 class="cmtt-8"> read</span><span
2697 class="cmtt-8"> 1</span><span
2698 class="cmtt-8"> bit</span><span
2699 class="cmtt-8"> as</span><span
2700 class="cmtt-8"> a</span><span
2701 class="cmtt-8"> boolean</span><span
2702 class="cmtt-8"> flag</span>
2703 <br class="fancyvrb" /><a
2704 id="x1-51111r5"></a><span
2705 class="cmr-6">5</span><span
2706 class="cmtt-8"> </span><span
2707 class="cmtt-8"> </span>
2708 <br class="fancyvrb" /><a
2709 id="x1-51113r6"></a><span
2710 class="cmr-6">6</span><span
2711 class="cmtt-8"> </span><span
2712 class="cmtt-8"> </span><span
2713 class="cmtt-8"> </span><span
2714 class="cmtt-8"> if</span><span
2715 class="cmtt-8"> (</span><span
2716 class="cmtt-8"> [codebook_lookup_type]</span><span
2717 class="cmtt-8"> is</span><span
2718 class="cmtt-8"> 1</span><span
2719 class="cmtt-8"> )</span><span
2720 class="cmtt-8"> </span><span
2721 class="cmsy-8">{</span>
2722 <br class="fancyvrb" /><a
2723 id="x1-51115r7"></a><span
2724 class="cmr-6">7</span><span
2725 class="cmtt-8"> </span><span
2726 class="cmtt-8"> </span>
2727 <br class="fancyvrb" /><a
2728 id="x1-51117r8"></a><span
2729 class="cmr-6">8</span><span
2730 class="cmtt-8"> </span><span
2731 class="cmtt-8"> </span><span
2732 class="cmtt-8"> </span><span
2733 class="cmtt-8"> </span><span
2734 class="cmtt-8"> </span><span
2735 class="cmtt-8"> </span><span
2736 class="cmtt-8"> 5)</span><span
2737 class="cmtt-8"> [codebook_lookup_values]</span><span
2738 class="cmtt-8"> =</span><span
2739 class="cmtt-8"> </span><a
2740 href="#x1-1190009.2.3"><span
2741 class="cmtt-8">lookup1_values</span></a><span
2742 class="cmtt-8">([codebook_entries],</span><span
2743 class="cmtt-8"> [codebook_dimensions]</span><span
2744 class="cmtt-8"> )</span>
2745 <br class="fancyvrb" /><a
2746 id="x1-51119r9"></a><span
2747 class="cmr-6">9</span><span
2748 class="cmtt-8"> </span><span
2749 class="cmtt-8"> </span>
2750 <br class="fancyvrb" /><a
2751 id="x1-51121r10"></a><span
2752 class="cmr-6">10</span><span
2753 class="cmtt-8"> </span><span
2754 class="cmtt-8"> </span><span
2755 class="cmtt-8"> </span><span
2756 class="cmtt-8"> </span><span
2757 class="cmsy-8">}</span><span
2758 class="cmtt-8"> else</span><span
2759 class="cmtt-8"> </span><span
2760 class="cmsy-8">{</span>
2761 <br class="fancyvrb" /><a
2762 id="x1-51123r11"></a><span
2763 class="cmr-6">11</span><span
2764 class="cmtt-8"> </span><span
2765 class="cmtt-8"> </span>
2766 <br class="fancyvrb" /><a
2767 id="x1-51125r12"></a><span
2768 class="cmr-6">12</span><span
2769 class="cmtt-8"> </span><span
2770 class="cmtt-8"> </span><span
2771 class="cmtt-8"> </span><span
2772 class="cmtt-8"> </span><span
2773 class="cmtt-8"> </span><span
2774 class="cmtt-8"> </span><span
2775 class="cmtt-8"> 6)</span><span
2776 class="cmtt-8"> [codebook_lookup_values]</span><span
2777 class="cmtt-8"> =</span><span
2778 class="cmtt-8"> [codebook_entries]</span><span
2779 class="cmtt-8"> *</span><span
2780 class="cmtt-8"> [codebook_dimensions]</span>
2781 <br class="fancyvrb" /><a
2782 id="x1-51127r13"></a><span
2783 class="cmr-6">13</span><span
2784 class="cmtt-8"> </span><span
2785 class="cmtt-8"> </span>
2786 <br class="fancyvrb" /><a
2787 id="x1-51129r14"></a><span
2788 class="cmr-6">14</span><span
2789 class="cmtt-8"> </span><span
2790 class="cmtt-8"> </span><span
2791 class="cmtt-8"> </span><span
2792 class="cmtt-8"> </span><span
2793 class="cmsy-8">}</span>
2794 <br class="fancyvrb" /><a
2795 id="x1-51131r15"></a><span
2796 class="cmr-6">15</span><span
2797 class="cmtt-8"> </span><span
2798 class="cmtt-8"> </span>
2799 <br class="fancyvrb" /><a
2800 id="x1-51133r16"></a><span
2801 class="cmr-6">16</span><span
2802 class="cmtt-8"> </span><span
2803 class="cmtt-8"> </span><span
2804 class="cmtt-8"> </span><span
2805 class="cmtt-8"> 7)</span><span
2806 class="cmtt-8"> read</span><span
2807 class="cmtt-8"> a</span><span
2808 class="cmtt-8"> total</span><span
2809 class="cmtt-8"> of</span><span
2810 class="cmtt-8"> [codebook_lookup_values]</span><span
2811 class="cmtt-8"> unsigned</span><span
2812 class="cmtt-8"> integers</span><span
2813 class="cmtt-8"> of</span><span
2814 class="cmtt-8"> [codebook_value_bits]</span><span
2815 class="cmtt-8"> each;</span>
2819 <br class="fancyvrb" /><a
2820 id="x1-51135r17"></a><span
2821 class="cmr-6">17</span><span
2822 class="cmtt-8"> </span><span
2823 class="cmtt-8"> </span><span
2824 class="cmtt-8"> </span><span
2825 class="cmtt-8"> </span><span
2826 class="cmtt-8"> </span><span
2827 class="cmtt-8"> </span><span
2828 class="cmtt-8"> store</span><span
2829 class="cmtt-8"> these</span><span
2830 class="cmtt-8"> in</span><span
2831 class="cmtt-8"> order</span><span
2832 class="cmtt-8"> in</span><span
2833 class="cmtt-8"> the</span><span
2834 class="cmtt-8"> array</span><span
2835 class="cmtt-8"> [codebook_multiplicands]</span>
2838 <li class="itemize">A <span
2839 class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is
2840 not decodable by the specification in this document.
2842 <!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
2843 rendering the stream undecodable.
2844 <!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
2845 id="x1-520003.2.1"></a><span
2846 class="cmbx-12">Huffman decision tree representation</span></span>
2848 class="cmtt-12">[codebook_codeword_lengths] </span>array and <span
2849 class="cmtt-12">[codebook_entries] </span>value uniquely define the
2850 Huffman decision tree used for entropy decoding.
2851 <!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
2852 codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
2853 possible. Assume the following codeword length list:
2854 <!--l. 209--><p class="noindent" >
2855 <div class="fancyvrb" id="fancyvrb15">
2857 id="x1-52002r1"></a><span
2858 class="cmr-6">1</span><span
2859 class="cmtt-8"> </span><span
2860 class="cmtt-8"> entry</span><span
2861 class="cmtt-8"> 0:</span><span
2862 class="cmtt-8"> length</span><span
2863 class="cmtt-8"> 2</span>
2864 <br class="fancyvrb" /><a
2865 id="x1-52004r2"></a><span
2866 class="cmr-6">2</span><span
2867 class="cmtt-8"> </span><span
2868 class="cmtt-8"> entry</span><span
2869 class="cmtt-8"> 1:</span><span
2870 class="cmtt-8"> length</span><span
2871 class="cmtt-8"> 4</span>
2872 <br class="fancyvrb" /><a
2873 id="x1-52006r3"></a><span
2874 class="cmr-6">3</span><span
2875 class="cmtt-8"> </span><span
2876 class="cmtt-8"> entry</span><span
2877 class="cmtt-8"> 2:</span><span
2878 class="cmtt-8"> length</span><span
2879 class="cmtt-8"> 4</span>
2880 <br class="fancyvrb" /><a
2881 id="x1-52008r4"></a><span
2882 class="cmr-6">4</span><span
2883 class="cmtt-8"> </span><span
2884 class="cmtt-8"> entry</span><span
2885 class="cmtt-8"> 3:</span><span
2886 class="cmtt-8"> length</span><span
2887 class="cmtt-8"> 4</span>
2888 <br class="fancyvrb" /><a
2889 id="x1-52010r5"></a><span
2890 class="cmr-6">5</span><span
2891 class="cmtt-8"> </span><span
2892 class="cmtt-8"> entry</span><span
2893 class="cmtt-8"> 4:</span><span
2894 class="cmtt-8"> length</span><span
2895 class="cmtt-8"> 4</span>
2896 <br class="fancyvrb" /><a
2897 id="x1-52012r6"></a><span
2898 class="cmr-6">6</span><span
2899 class="cmtt-8"> </span><span
2900 class="cmtt-8"> entry</span><span
2901 class="cmtt-8"> 5:</span><span
2902 class="cmtt-8"> length</span><span
2903 class="cmtt-8"> 2</span>
2904 <br class="fancyvrb" /><a
2905 id="x1-52014r7"></a><span
2906 class="cmr-6">7</span><span
2907 class="cmtt-8"> </span><span
2908 class="cmtt-8"> entry</span><span
2909 class="cmtt-8"> 6:</span><span
2910 class="cmtt-8"> length</span><span
2911 class="cmtt-8"> 3</span>
2912 <br class="fancyvrb" /><a
2913 id="x1-52016r8"></a><span
2914 class="cmr-6">8</span><span
2915 class="cmtt-8"> </span><span
2916 class="cmtt-8"> entry</span><span
2917 class="cmtt-8"> 7:</span><span
2918 class="cmtt-8"> length</span><span
2919 class="cmtt-8"> 3</span>
2921 <!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
2922 in the following codeword list:
2923 <!--l. 223--><p class="noindent" >
2924 <div class="fancyvrb" id="fancyvrb16">
2926 id="x1-52018r1"></a><span
2927 class="cmr-6">1</span><span
2928 class="cmtt-8"> </span><span
2929 class="cmtt-8"> entry</span><span
2930 class="cmtt-8"> 0:</span><span
2931 class="cmtt-8"> length</span><span
2932 class="cmtt-8"> 2</span><span
2933 class="cmtt-8"> codeword</span><span
2934 class="cmtt-8"> 00</span>
2935 <br class="fancyvrb" /><a
2936 id="x1-52020r2"></a><span
2937 class="cmr-6">2</span><span
2938 class="cmtt-8"> </span><span
2939 class="cmtt-8"> entry</span><span
2940 class="cmtt-8"> 1:</span><span
2941 class="cmtt-8"> length</span><span
2942 class="cmtt-8"> 4</span><span
2943 class="cmtt-8"> codeword</span><span
2944 class="cmtt-8"> 0100</span>
2945 <br class="fancyvrb" /><a
2946 id="x1-52022r3"></a><span
2947 class="cmr-6">3</span><span
2948 class="cmtt-8"> </span><span
2949 class="cmtt-8"> entry</span><span
2950 class="cmtt-8"> 2:</span><span
2951 class="cmtt-8"> length</span><span
2952 class="cmtt-8"> 4</span><span
2953 class="cmtt-8"> codeword</span><span
2954 class="cmtt-8"> 0101</span>
2955 <br class="fancyvrb" /><a
2956 id="x1-52024r4"></a><span
2957 class="cmr-6">4</span><span
2958 class="cmtt-8"> </span><span
2959 class="cmtt-8"> entry</span><span
2960 class="cmtt-8"> 3:</span><span
2961 class="cmtt-8"> length</span><span
2962 class="cmtt-8"> 4</span><span
2963 class="cmtt-8"> codeword</span><span
2964 class="cmtt-8"> 0110</span>
2965 <br class="fancyvrb" /><a
2966 id="x1-52026r5"></a><span
2967 class="cmr-6">5</span><span
2968 class="cmtt-8"> </span><span
2969 class="cmtt-8"> entry</span><span
2970 class="cmtt-8"> 4:</span><span
2971 class="cmtt-8"> length</span><span
2972 class="cmtt-8"> 4</span><span
2973 class="cmtt-8"> codeword</span><span
2974 class="cmtt-8"> 0111</span>
2975 <br class="fancyvrb" /><a
2976 id="x1-52028r6"></a><span
2977 class="cmr-6">6</span><span
2978 class="cmtt-8"> </span><span
2979 class="cmtt-8"> entry</span><span
2980 class="cmtt-8"> 5:</span><span
2981 class="cmtt-8"> length</span><span
2982 class="cmtt-8"> 2</span><span
2983 class="cmtt-8"> codeword</span><span
2984 class="cmtt-8"> 10</span>
2985 <br class="fancyvrb" /><a
2986 id="x1-52030r7"></a><span
2987 class="cmr-6">7</span><span
2988 class="cmtt-8"> </span><span
2989 class="cmtt-8"> entry</span><span
2990 class="cmtt-8"> 6:</span><span
2991 class="cmtt-8"> length</span><span
2992 class="cmtt-8"> 3</span><span
2993 class="cmtt-8"> codeword</span><span
2994 class="cmtt-8"> 110</span>
2995 <br class="fancyvrb" /><a
2996 id="x1-52032r8"></a><span
2997 class="cmr-6">8</span><span
2998 class="cmtt-8"> </span><span
2999 class="cmtt-8"> entry</span><span
3000 class="cmtt-8"> 7:</span><span
3001 class="cmtt-8"> length</span><span
3002 class="cmtt-8"> 3</span><span
3003 class="cmtt-8"> codeword</span><span
3004 class="cmtt-8"> 111</span>
3009 <!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
3010 id="x1-530003.2.1"></a><span
3011 class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
3012 be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
3013 one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
3015 <!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
3016 numbers equivalent to the leaves numbered left-to-right:
3019 <!--l. 247--><p class="noindent" >
3021 <!--l. 248--><p class="noindent" ><img
3022 src="hufftree.png" alt="PIC"
3024 <br /> <div class="caption"
3025 ><span class="id">Figure 4: </span><span
3026 class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 -->
3028 <!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
3030 <!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
3031 In the above example, if codeword seven were eliminated, it’s clear that the tree is
3035 <!--l. 260--><p class="noindent" >
3037 <!--l. 261--><p class="noindent" ><img
3038 src="hufftree-under.png" alt="PIC"
3040 <br /> <div class="caption"
3041 ><span class="id">Figure 5: </span><span
3042 class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 -->
3044 <!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
3045 codeword is impossible. Both underspecified and overspecified trees are an error condition
3046 rendering the stream undecodable. Take special care that a codebook with a single used
3047 entry is handled properly; it consists of a single codework of zero bits and ’reading’
3048 a value out of such a codebook always returns the single used value and sinks zero
3050 <!--l. 274--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
3051 codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
3052 from the stream to decode to that entry number.
3056 <!--l. 281--><p class="noindent" ><span class="paragraphHead"><a
3057 id="x1-540003.2.1"></a><span
3058 class="cmbx-12">VQ lookup table vector representation</span></span>
3059 Unpacking the VQ lookup table vectors relies on the following values:
3060 <div class="fancyvrb" id="fancyvrb17">
3062 id="x1-54002r1"></a><span
3063 class="cmr-6">1</span><span
3064 class="cmtt-8"> </span><span
3065 class="cmtt-8"> the</span><span
3066 class="cmtt-8"> [codebook\_multiplicands]</span><span
3067 class="cmtt-8"> array</span>
3068 <br class="fancyvrb" /><a
3069 id="x1-54004r2"></a><span
3070 class="cmr-6">2</span><span
3071 class="cmtt-8"> </span><span
3072 class="cmtt-8"> [codebook\_minimum\_value]</span>
3073 <br class="fancyvrb" /><a
3074 id="x1-54006r3"></a><span
3075 class="cmr-6">3</span><span
3076 class="cmtt-8"> </span><span
3077 class="cmtt-8"> [codebook\_delta\_value]</span>
3078 <br class="fancyvrb" /><a
3079 id="x1-54008r4"></a><span
3080 class="cmr-6">4</span><span
3081 class="cmtt-8"> </span><span
3082 class="cmtt-8"> [codebook\_sequence\_p]</span>
3083 <br class="fancyvrb" /><a
3084 id="x1-54010r5"></a><span
3085 class="cmr-6">5</span><span
3086 class="cmtt-8"> </span><span
3087 class="cmtt-8"> [codebook\_lookup\_type]</span>
3088 <br class="fancyvrb" /><a
3089 id="x1-54012r6"></a><span
3090 class="cmr-6">6</span><span
3091 class="cmtt-8"> </span><span
3092 class="cmtt-8"> [codebook\_entries]</span>
3093 <br class="fancyvrb" /><a
3094 id="x1-54014r7"></a><span
3095 class="cmr-6">7</span><span
3096 class="cmtt-8"> </span><span
3097 class="cmtt-8"> [codebook\_dimensions]</span>
3098 <br class="fancyvrb" /><a
3099 id="x1-54016r8"></a><span
3100 class="cmr-6">8</span><span
3101 class="cmtt-8"> </span><span
3102 class="cmtt-8"> [codebook\_lookup\_values]</span>
3104 <!--l. 297--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
3106 class="cmtt-12">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return
3107 during audio packet decode in a VQ context.
3108 <!--l. 302--><p class="noindent" ><span class="paragraphHead"><a
3109 id="x1-550003.2.1"></a><span
3110 class="cmbx-12">Vector value decode: Lookup type 1</span></span>
3111 Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of
3112 scalar values. Calculate (unpack) the final values of a codebook entry vector from
3113 the entries in <span
3114 class="cmtt-12">[codebook_multiplicands] </span>as follows (<span
3115 class="cmtt-12">[value_vector] </span>is the output
3116 vector representing the vector of values for entry number <span
3117 class="cmtt-12">[lookup_offset] </span>in this
3119 <!--l. 311--><p class="noindent" >
3120 <div class="fancyvrb" id="fancyvrb18">
3122 id="x1-55002r1"></a><span
3123 class="cmr-6">1</span><span
3124 class="cmtt-8"> </span><span
3125 class="cmtt-8"> </span><span
3126 class="cmtt-8"> </span><span
3127 class="cmtt-8"> 1)</span><span
3128 class="cmtt-8"> [last]</span><span
3129 class="cmtt-8"> =</span><span
3130 class="cmtt-8"> 0;</span>
3131 <br class="fancyvrb" /><a
3132 id="x1-55004r2"></a><span
3133 class="cmr-6">2</span><span
3134 class="cmtt-8"> </span><span
3135 class="cmtt-8"> </span><span
3136 class="cmtt-8"> </span><span
3137 class="cmtt-8"> 2)</span><span
3138 class="cmtt-8"> [index_divisor]</span><span
3139 class="cmtt-8"> =</span><span
3140 class="cmtt-8"> 1;</span>
3141 <br class="fancyvrb" /><a
3142 id="x1-55006r3"></a><span
3143 class="cmr-6">3</span><span
3144 class="cmtt-8"> </span><span
3145 class="cmtt-8"> </span><span
3146 class="cmtt-8"> </span><span
3147 class="cmtt-8"> 3)</span><span
3148 class="cmtt-8"> iterate</span><span
3149 class="cmtt-8"> [i]</span><span
3150 class="cmtt-8"> over</span><span
3151 class="cmtt-8"> the</span><span
3152 class="cmtt-8"> range</span><span
3153 class="cmtt-8"> 0</span><span
3154 class="cmtt-8"> ...</span><span
3155 class="cmtt-8"> [codebook_dimensions]-1</span><span
3156 class="cmtt-8"> (once</span><span
3157 class="cmtt-8"> for</span><span
3158 class="cmtt-8"> each</span><span
3159 class="cmtt-8"> scalar</span><span
3160 class="cmtt-8"> value</span><span
3161 class="cmtt-8"> in</span><span
3162 class="cmtt-8"> the</span><span
3163 class="cmtt-8"> value</span><span
3164 class="cmtt-8"> vector)</span><span
3165 class="cmtt-8"> </span><span
3166 class="cmsy-8">{</span>
3167 <br class="fancyvrb" /><a
3168 id="x1-55008r4"></a><span
3169 class="cmr-6">4</span><span
3170 class="cmtt-8"> </span><span
3171 class="cmtt-8"> </span>
3172 <br class="fancyvrb" /><a
3173 id="x1-55010r5"></a><span
3174 class="cmr-6">5</span><span
3175 class="cmtt-8"> </span><span
3176 class="cmtt-8"> </span><span
3177 class="cmtt-8"> </span><span
3178 class="cmtt-8"> </span><span
3179 class="cmtt-8"> </span><span
3180 class="cmtt-8"> </span><span
3181 class="cmtt-8"> </span><span
3182 class="cmtt-8"> </span><span
3183 class="cmtt-8"> 4)</span><span
3184 class="cmtt-8"> [multiplicand_offset]</span><span
3185 class="cmtt-8"> =</span><span
3186 class="cmtt-8"> (</span><span
3187 class="cmtt-8"> [lookup_offset]</span><span
3188 class="cmtt-8"> divided</span><span
3189 class="cmtt-8"> by</span><span
3190 class="cmtt-8"> [index_divisor]</span><span
3191 class="cmtt-8"> using</span><span
3192 class="cmtt-8"> integer</span>
3193 <br class="fancyvrb" /><a
3194 id="x1-55012r6"></a><span
3195 class="cmr-6">6</span><span
3196 class="cmtt-8"> </span><span
3197 class="cmtt-8"> </span><span
3198 class="cmtt-8"> </span><span
3199 class="cmtt-8"> </span><span
3200 class="cmtt-8"> </span><span
3201 class="cmtt-8"> </span><span
3202 class="cmtt-8"> </span><span
3203 class="cmtt-8"> </span><span
3204 class="cmtt-8"> </span><span
3205 class="cmtt-8"> </span><span
3206 class="cmtt-8"> </span><span
3207 class="cmtt-8"> division</span><span
3208 class="cmtt-8"> )</span><span
3209 class="cmtt-8"> integer</span><span
3210 class="cmtt-8"> modulo</span><span
3211 class="cmtt-8"> [codebook_lookup_values]</span>
3212 <br class="fancyvrb" /><a
3213 id="x1-55014r7"></a><span
3214 class="cmr-6">7</span><span
3215 class="cmtt-8"> </span><span
3216 class="cmtt-8"> </span>
3217 <br class="fancyvrb" /><a
3218 id="x1-55016r8"></a><span
3219 class="cmr-6">8</span><span
3220 class="cmtt-8"> </span><span
3221 class="cmtt-8"> </span><span
3222 class="cmtt-8"> </span><span
3223 class="cmtt-8"> </span><span
3224 class="cmtt-8"> </span><span
3225 class="cmtt-8"> </span><span
3226 class="cmtt-8"> </span><span
3227 class="cmtt-8"> </span><span
3228 class="cmtt-8"> 5)</span><span
3229 class="cmtt-8"> vector</span><span
3230 class="cmtt-8"> [value_vector]</span><span
3231 class="cmtt-8"> element</span><span
3232 class="cmtt-8"> [i]</span><span
3233 class="cmtt-8"> =</span>
3234 <br class="fancyvrb" /><a
3235 id="x1-55018r9"></a><span
3236 class="cmr-6">9</span><span
3237 class="cmtt-8"> </span><span
3238 class="cmtt-8"> </span><span
3239 class="cmtt-8"> </span><span
3240 class="cmtt-8"> </span><span
3241 class="cmtt-8"> </span><span
3242 class="cmtt-8"> </span><span
3243 class="cmtt-8"> </span><span
3244 class="cmtt-8"> </span><span
3245 class="cmtt-8"> </span><span
3246 class="cmtt-8"> </span><span
3247 class="cmtt-8"> </span><span
3248 class="cmtt-8"> </span><span
3249 class="cmtt-8"> </span><span
3250 class="cmtt-8"> (</span><span
3251 class="cmtt-8"> [codebook_multiplicands]</span><span
3252 class="cmtt-8"> array</span><span
3253 class="cmtt-8"> element</span><span
3254 class="cmtt-8"> number</span><span
3255 class="cmtt-8"> [multiplicand_offset]</span><span
3256 class="cmtt-8"> )</span><span
3257 class="cmtt-8"> *</span>
3258 <br class="fancyvrb" /><a
3259 id="x1-55020r10"></a><span
3260 class="cmr-6">10</span><span
3261 class="cmtt-8"> </span><span
3262 class="cmtt-8"> </span><span
3263 class="cmtt-8"> </span><span
3264 class="cmtt-8"> </span><span
3265 class="cmtt-8"> </span><span
3266 class="cmtt-8"> </span><span
3267 class="cmtt-8"> </span><span
3268 class="cmtt-8"> </span><span
3269 class="cmtt-8"> </span><span
3270 class="cmtt-8"> </span><span
3271 class="cmtt-8"> </span><span
3272 class="cmtt-8"> </span><span
3273 class="cmtt-8"> </span><span
3274 class="cmtt-8"> [codebook_delta_value]</span><span
3275 class="cmtt-8"> +</span><span
3276 class="cmtt-8"> [codebook_minimum_value]</span><span
3277 class="cmtt-8"> +</span><span
3278 class="cmtt-8"> [last];</span>
3279 <br class="fancyvrb" /><a
3280 id="x1-55022r11"></a><span
3281 class="cmr-6">11</span><span
3282 class="cmtt-8"> </span><span
3283 class="cmtt-8"> </span>
3284 <br class="fancyvrb" /><a
3285 id="x1-55024r12"></a><span
3286 class="cmr-6">12</span><span
3287 class="cmtt-8"> </span><span
3288 class="cmtt-8"> </span><span
3289 class="cmtt-8"> </span><span
3290 class="cmtt-8"> </span><span
3291 class="cmtt-8"> </span><span
3292 class="cmtt-8"> </span><span
3293 class="cmtt-8"> </span><span
3294 class="cmtt-8"> </span><span
3295 class="cmtt-8"> 6)</span><span
3296 class="cmtt-8"> if</span><span
3297 class="cmtt-8"> (</span><span
3298 class="cmtt-8"> [codebook_sequence_p]</span><span
3299 class="cmtt-8"> is</span><span
3300 class="cmtt-8"> set</span><span
3301 class="cmtt-8"> )</span><span
3302 class="cmtt-8"> then</span><span
3303 class="cmtt-8"> set</span><span
3304 class="cmtt-8"> [last]</span><span
3305 class="cmtt-8"> =</span><span
3306 class="cmtt-8"> vector</span><span
3307 class="cmtt-8"> [value_vector]</span><span
3308 class="cmtt-8"> element</span><span
3309 class="cmtt-8"> [i]</span>
3310 <br class="fancyvrb" /><a
3311 id="x1-55026r13"></a><span
3312 class="cmr-6">13</span><span
3313 class="cmtt-8"> </span><span
3314 class="cmtt-8"> </span>
3315 <br class="fancyvrb" /><a
3316 id="x1-55028r14"></a><span
3317 class="cmr-6">14</span><span
3318 class="cmtt-8"> </span><span
3319 class="cmtt-8"> </span><span
3320 class="cmtt-8"> </span><span
3321 class="cmtt-8"> </span><span
3322 class="cmtt-8"> </span><span
3323 class="cmtt-8"> </span><span
3324 class="cmtt-8"> </span><span
3325 class="cmtt-8"> </span><span
3326 class="cmtt-8"> 7)</span><span
3327 class="cmtt-8"> [index_divisor]</span><span
3328 class="cmtt-8"> =</span><span
3329 class="cmtt-8"> [index_divisor]</span><span
3330 class="cmtt-8"> *</span><span
3331 class="cmtt-8"> [codebook_lookup_values]</span>
3332 <br class="fancyvrb" /><a
3333 id="x1-55030r15"></a><span
3334 class="cmr-6">15</span><span
3335 class="cmtt-8"> </span><span
3336 class="cmtt-8"> </span>
3337 <br class="fancyvrb" /><a
3338 id="x1-55032r16"></a><span
3339 class="cmr-6">16</span><span
3340 class="cmtt-8"> </span><span
3341 class="cmtt-8"> </span><span
3342 class="cmtt-8"> </span><span
3343 class="cmtt-8"> </span><span
3344 class="cmtt-8"> </span><span
3345 class="cmtt-8"> </span><span
3346 class="cmtt-8"> </span><span
3347 class="cmsy-8">}</span>
3348 <br class="fancyvrb" /><a
3349 id="x1-55034r17"></a><span
3350 class="cmr-6">17</span><span
3351 class="cmtt-8"> </span><span
3352 class="cmtt-8"> </span>
3353 <br class="fancyvrb" /><a
3354 id="x1-55036r18"></a><span
3355 class="cmr-6">18</span><span
3356 class="cmtt-8"> </span><span
3357 class="cmtt-8"> </span><span
3358 class="cmtt-8"> </span><span
3359 class="cmtt-8"> 8)</span><span
3360 class="cmtt-8"> vector</span><span
3361 class="cmtt-8"> calculation</span><span
3362 class="cmtt-8"> completed.</span>
3367 <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
3368 id="x1-560003.2.1"></a><span
3369 class="cmbx-12">Vector value decode: Lookup type 2</span></span>
3370 Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set
3372 class="cmtt-12">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final
3373 values of a codebook entry vector from the entries in <span
3374 class="cmtt-12">[codebook_multiplicands] </span>as follows
3376 class="cmtt-12">[value_vector] </span>is the output vector representing the vector of values for entry number
3378 class="cmtt-12">[lookup_offset] </span>in this codebook):
3379 <!--l. 344--><p class="noindent" >
3380 <div class="fancyvrb" id="fancyvrb19">
3382 id="x1-56002r1"></a><span
3383 class="cmr-6">1</span><span
3384 class="cmtt-8"> </span><span
3385 class="cmtt-8"> </span><span
3386 class="cmtt-8"> </span><span
3387 class="cmtt-8"> 1)</span><span
3388 class="cmtt-8"> [last]</span><span
3389 class="cmtt-8"> =</span><span
3390 class="cmtt-8"> 0;</span>
3391 <br class="fancyvrb" /><a
3392 id="x1-56004r2"></a><span
3393 class="cmr-6">2</span><span
3394 class="cmtt-8"> </span><span
3395 class="cmtt-8"> </span><span
3396 class="cmtt-8"> </span><span
3397 class="cmtt-8"> 2)</span><span
3398 class="cmtt-8"> [multiplicand_offset]</span><span
3399 class="cmtt-8"> =</span><span
3400 class="cmtt-8"> [lookup_offset]</span><span
3401 class="cmtt-8"> *</span><span
3402 class="cmtt-8"> [codebook_dimensions]</span>
3403 <br class="fancyvrb" /><a
3404 id="x1-56006r3"></a><span
3405 class="cmr-6">3</span><span
3406 class="cmtt-8"> </span><span
3407 class="cmtt-8"> </span><span
3408 class="cmtt-8"> </span><span
3409 class="cmtt-8"> 3)</span><span
3410 class="cmtt-8"> iterate</span><span
3411 class="cmtt-8"> [i]</span><span
3412 class="cmtt-8"> over</span><span
3413 class="cmtt-8"> the</span><span
3414 class="cmtt-8"> range</span><span
3415 class="cmtt-8"> 0</span><span
3416 class="cmtt-8"> ...</span><span
3417 class="cmtt-8"> [codebook_dimensions]-1</span><span
3418 class="cmtt-8"> (once</span><span
3419 class="cmtt-8"> for</span><span
3420 class="cmtt-8"> each</span><span
3421 class="cmtt-8"> scalar</span><span
3422 class="cmtt-8"> value</span><span
3423 class="cmtt-8"> in</span><span
3424 class="cmtt-8"> the</span><span
3425 class="cmtt-8"> value</span><span
3426 class="cmtt-8"> vector)</span><span
3427 class="cmtt-8"> </span><span
3428 class="cmsy-8">{</span>
3429 <br class="fancyvrb" /><a
3430 id="x1-56008r4"></a><span
3431 class="cmr-6">4</span><span
3432 class="cmtt-8"> </span><span
3433 class="cmtt-8"> </span>
3434 <br class="fancyvrb" /><a
3435 id="x1-56010r5"></a><span
3436 class="cmr-6">5</span><span
3437 class="cmtt-8"> </span><span
3438 class="cmtt-8"> </span><span
3439 class="cmtt-8"> </span><span
3440 class="cmtt-8"> </span><span
3441 class="cmtt-8"> </span><span
3442 class="cmtt-8"> </span><span
3443 class="cmtt-8"> </span><span
3444 class="cmtt-8"> </span><span
3445 class="cmtt-8"> 4)</span><span
3446 class="cmtt-8"> vector</span><span
3447 class="cmtt-8"> [value_vector]</span><span
3448 class="cmtt-8"> element</span><span
3449 class="cmtt-8"> [i]</span><span
3450 class="cmtt-8"> =</span>
3451 <br class="fancyvrb" /><a
3452 id="x1-56012r6"></a><span
3453 class="cmr-6">6</span><span
3454 class="cmtt-8"> </span><span
3455 class="cmtt-8"> </span><span
3456 class="cmtt-8"> </span><span
3457 class="cmtt-8"> </span><span
3458 class="cmtt-8"> </span><span
3459 class="cmtt-8"> </span><span
3460 class="cmtt-8"> </span><span
3461 class="cmtt-8"> </span><span
3462 class="cmtt-8"> </span><span
3463 class="cmtt-8"> </span><span
3464 class="cmtt-8"> </span><span
3465 class="cmtt-8"> </span><span
3466 class="cmtt-8"> </span><span
3467 class="cmtt-8"> (</span><span
3468 class="cmtt-8"> [codebook_multiplicands]</span><span
3469 class="cmtt-8"> array</span><span
3470 class="cmtt-8"> element</span><span
3471 class="cmtt-8"> number</span><span
3472 class="cmtt-8"> [multiplicand_offset]</span><span
3473 class="cmtt-8"> )</span><span
3474 class="cmtt-8"> *</span>
3475 <br class="fancyvrb" /><a
3476 id="x1-56014r7"></a><span
3477 class="cmr-6">7</span><span
3478 class="cmtt-8"> </span><span
3479 class="cmtt-8"> </span><span
3480 class="cmtt-8"> </span><span
3481 class="cmtt-8"> </span><span
3482 class="cmtt-8"> </span><span
3483 class="cmtt-8"> </span><span
3484 class="cmtt-8"> </span><span
3485 class="cmtt-8"> </span><span
3486 class="cmtt-8"> </span><span
3487 class="cmtt-8"> </span><span
3488 class="cmtt-8"> </span><span
3489 class="cmtt-8"> </span><span
3490 class="cmtt-8"> </span><span
3491 class="cmtt-8"> [codebook_delta_value]</span><span
3492 class="cmtt-8"> +</span><span
3493 class="cmtt-8"> [codebook_minimum_value]</span><span
3494 class="cmtt-8"> +</span><span
3495 class="cmtt-8"> [last];</span>
3496 <br class="fancyvrb" /><a
3497 id="x1-56016r8"></a><span
3498 class="cmr-6">8</span><span
3499 class="cmtt-8"> </span><span
3500 class="cmtt-8"> </span>
3501 <br class="fancyvrb" /><a
3502 id="x1-56018r9"></a><span
3503 class="cmr-6">9</span><span
3504 class="cmtt-8"> </span><span
3505 class="cmtt-8"> </span><span
3506 class="cmtt-8"> </span><span
3507 class="cmtt-8"> </span><span
3508 class="cmtt-8"> </span><span
3509 class="cmtt-8"> </span><span
3510 class="cmtt-8"> </span><span
3511 class="cmtt-8"> </span><span
3512 class="cmtt-8"> 5)</span><span
3513 class="cmtt-8"> if</span><span
3514 class="cmtt-8"> (</span><span
3515 class="cmtt-8"> [codebook_sequence_p]</span><span
3516 class="cmtt-8"> is</span><span
3517 class="cmtt-8"> set</span><span
3518 class="cmtt-8"> )</span><span
3519 class="cmtt-8"> then</span><span
3520 class="cmtt-8"> set</span><span
3521 class="cmtt-8"> [last]</span><span
3522 class="cmtt-8"> =</span><span
3523 class="cmtt-8"> vector</span><span
3524 class="cmtt-8"> [value_vector]</span><span
3525 class="cmtt-8"> element</span><span
3526 class="cmtt-8"> [i]</span>
3527 <br class="fancyvrb" /><a
3528 id="x1-56020r10"></a><span
3529 class="cmr-6">10</span><span
3530 class="cmtt-8"> </span><span
3531 class="cmtt-8"> </span>
3532 <br class="fancyvrb" /><a
3533 id="x1-56022r11"></a><span
3534 class="cmr-6">11</span><span
3535 class="cmtt-8"> </span><span
3536 class="cmtt-8"> </span><span
3537 class="cmtt-8"> </span><span
3538 class="cmtt-8"> </span><span
3539 class="cmtt-8"> </span><span
3540 class="cmtt-8"> </span><span
3541 class="cmtt-8"> </span><span
3542 class="cmtt-8"> </span><span
3543 class="cmtt-8"> 6)</span><span
3544 class="cmtt-8"> increment</span><span
3545 class="cmtt-8"> [multiplicand_offset]</span>
3546 <br class="fancyvrb" /><a
3547 id="x1-56024r12"></a><span
3548 class="cmr-6">12</span><span
3549 class="cmtt-8"> </span><span
3550 class="cmtt-8"> </span>
3551 <br class="fancyvrb" /><a
3552 id="x1-56026r13"></a><span
3553 class="cmr-6">13</span><span
3554 class="cmtt-8"> </span><span
3555 class="cmtt-8"> </span><span
3556 class="cmtt-8"> </span><span
3557 class="cmtt-8"> </span><span
3558 class="cmtt-8"> </span><span
3559 class="cmtt-8"> </span><span
3560 class="cmtt-8"> </span><span
3561 class="cmsy-8">}</span>
3562 <br class="fancyvrb" /><a
3563 id="x1-56028r14"></a><span
3564 class="cmr-6">14</span><span
3565 class="cmtt-8"> </span><span
3566 class="cmtt-8"> </span>
3567 <br class="fancyvrb" /><a
3568 id="x1-56030r15"></a><span
3569 class="cmr-6">15</span><span
3570 class="cmtt-8"> </span><span
3571 class="cmtt-8"> </span><span
3572 class="cmtt-8"> </span><span
3573 class="cmtt-8"> 7)</span><span
3574 class="cmtt-8"> vector</span><span
3575 class="cmtt-8"> calculation</span><span
3576 class="cmtt-8"> completed.</span>
3578 <!--l. 370--><p class="noindent" >
3579 <h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a
3580 id="x1-570003.3"></a>Use of the codebook abstraction</h4>
3581 <!--l. 372--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a
3582 specific codebook reads a codeword from the bitstream, decoding it into an entry number, and
3583 then returns that entry number to the decoder (when used in a scalar entropy coding context), or
3584 uses that entry number as an offset into the VQ lookup table, returning a vector of values (when
3585 used in a context desiring a VQ value). Scalar or VQ context is always explicit; any
3586 call to the codebook mechanism requests either a scalar entry number or a lookup
3588 <!--l. 382--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting
3589 decode using a codebook of lookup type 0 in any context expecting a vector return
3590 value (even in a case where a vector of dimension one) is forbidden. If decoder setup
3591 or decode requests such an action, that is an error condition rendering the packet
3596 <!--l. 389--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
3597 next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
3598 codeword in the codebook. This process can be though of as logically walking the
3599 Huffman decode tree by reading one bit at a time from the bitstream, and using the
3600 bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
3601 branch (right in the above examples). Walking the tree finishes when the decode process
3602 hits a leaf in the decision tree; the result is the entry number corresponding to that
3603 leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
3605 <!--l. 401--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
3607 <!--l. 404--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
3608 table. The value returned to the decoder is the vector of scalars corresponding to this
3616 <h3 class="sectionHead"><span class="titlemark">4. </span> <a
3617 id="x1-580004"></a>Codec Setup and Packet Decode</h3>
3618 <!--l. 7--><p class="noindent" >
3619 <h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a
3620 id="x1-590004.1"></a>Overview</h4>
3621 <!--l. 9--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
3622 of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
3623 process, which is provided in <a
3624 href="#x1-20001">Section 1</a>, “<a
3625 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
3626 href="#x1-360002">Section 2</a>,
3628 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
3630 <!--l. 17--><p class="noindent" >
3631 <h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a
3632 id="x1-600004.2"></a>Header decode and decode setup</h4>
3633 <!--l. 19--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
3634 identification header, the comments header, and the setup header. All are required for decode
3635 compliance. An end-of-packet condition during decoding the first or third header packet renders
3636 the stream undecodable. End-of-packet decoding the comment header is a non-fatal error
3638 <!--l. 26--><p class="noindent" >
3639 <h5 class="subsubsectionHead"><span class="titlemark">4.2.1. </span> <a
3640 id="x1-610004.2.1"></a>Common header decode</h5>
3641 <!--l. 28--><p class="noindent" >Each header packet begins with the same header fields.
3642 <!--l. 31--><p class="noindent" >
3643 <div class="fancyvrb" id="fancyvrb20">
3645 id="x1-61002r1"></a><span
3646 class="cmr-6">1</span><span
3647 class="cmtt-8"> </span><span
3648 class="cmtt-8"> </span><span
3649 class="cmtt-8"> </span><span
3650 class="cmtt-8"> 1)</span><span
3651 class="cmtt-8"> [packet_type]</span><span
3652 class="cmtt-8"> :</span><span
3653 class="cmtt-8"> 8</span><span
3654 class="cmtt-8"> bit</span><span
3655 class="cmtt-8"> value</span>
3656 <br class="fancyvrb" /><a
3657 id="x1-61004r2"></a><span
3658 class="cmr-6">2</span><span
3659 class="cmtt-8"> </span><span
3660 class="cmtt-8"> </span><span
3661 class="cmtt-8"> </span><span
3662 class="cmtt-8"> 2)</span><span
3663 class="cmtt-8"> 0x76,</span><span
3664 class="cmtt-8"> 0x6f,</span><span
3665 class="cmtt-8"> 0x72,</span><span
3666 class="cmtt-8"> 0x62,</span><span
3667 class="cmtt-8"> 0x69,</span><span
3668 class="cmtt-8"> 0x73:</span><span
3669 class="cmtt-8"> the</span><span
3670 class="cmtt-8"> characters</span><span
3671 class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
3672 class="cmtt-8"> as</span><span
3673 class="cmtt-8"> six</span><span
3674 class="cmtt-8"> octets</span>
3679 <!--l. 36--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
3680 header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
3681 single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
3683 <!--l. 44--><p class="noindent" >
3684 <h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a
3685 id="x1-620004.2.2"></a>Identification header</h5>
3686 <!--l. 46--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream
3687 definitively as Vorbis, and provide a few externally relevant pieces of information about the audio
3688 stream. The identification header is coded as follows:
3689 <!--l. 51--><p class="noindent" >
3690 <div class="fancyvrb" id="fancyvrb21">
3692 id="x1-62002r1"></a><span
3693 class="cmr-6">1</span><span
3694 class="cmtt-8"> </span><span
3695 class="cmtt-8"> </span><span
3696 class="cmtt-8"> 1)</span><span
3697 class="cmtt-8"> [vorbis_version]</span><span
3698 class="cmtt-8"> =</span><span
3699 class="cmtt-8"> read</span><span
3700 class="cmtt-8"> 32</span><span
3701 class="cmtt-8"> bits</span><span
3702 class="cmtt-8"> as</span><span
3703 class="cmtt-8"> unsigned</span><span
3704 class="cmtt-8"> integer</span>
3705 <br class="fancyvrb" /><a
3706 id="x1-62004r2"></a><span
3707 class="cmr-6">2</span><span
3708 class="cmtt-8"> </span><span
3709 class="cmtt-8"> </span><span
3710 class="cmtt-8"> 2)</span><span
3711 class="cmtt-8"> [audio_channels]</span><span
3712 class="cmtt-8"> =</span><span
3713 class="cmtt-8"> read</span><span
3714 class="cmtt-8"> 8</span><span
3715 class="cmtt-8"> bit</span><span
3716 class="cmtt-8"> integer</span><span
3717 class="cmtt-8"> as</span><span
3718 class="cmtt-8"> unsigned</span>
3719 <br class="fancyvrb" /><a
3720 id="x1-62006r3"></a><span
3721 class="cmr-6">3</span><span
3722 class="cmtt-8"> </span><span
3723 class="cmtt-8"> </span><span
3724 class="cmtt-8"> 3)</span><span
3725 class="cmtt-8"> [audio_sample_rate]</span><span
3726 class="cmtt-8"> =</span><span
3727 class="cmtt-8"> read</span><span
3728 class="cmtt-8"> 32</span><span
3729 class="cmtt-8"> bits</span><span
3730 class="cmtt-8"> as</span><span
3731 class="cmtt-8"> unsigned</span><span
3732 class="cmtt-8"> integer</span>
3733 <br class="fancyvrb" /><a
3734 id="x1-62008r4"></a><span
3735 class="cmr-6">4</span><span
3736 class="cmtt-8"> </span><span
3737 class="cmtt-8"> </span><span
3738 class="cmtt-8"> 4)</span><span
3739 class="cmtt-8"> [bitrate_maximum]</span><span
3740 class="cmtt-8"> =</span><span
3741 class="cmtt-8"> read</span><span
3742 class="cmtt-8"> 32</span><span
3743 class="cmtt-8"> bits</span><span
3744 class="cmtt-8"> as</span><span
3745 class="cmtt-8"> signed</span><span
3746 class="cmtt-8"> integer</span>
3747 <br class="fancyvrb" /><a
3748 id="x1-62010r5"></a><span
3749 class="cmr-6">5</span><span
3750 class="cmtt-8"> </span><span
3751 class="cmtt-8"> </span><span
3752 class="cmtt-8"> 5)</span><span
3753 class="cmtt-8"> [bitrate_nominal]</span><span
3754 class="cmtt-8"> =</span><span
3755 class="cmtt-8"> read</span><span
3756 class="cmtt-8"> 32</span><span
3757 class="cmtt-8"> bits</span><span
3758 class="cmtt-8"> as</span><span
3759 class="cmtt-8"> signed</span><span
3760 class="cmtt-8"> integer</span>
3761 <br class="fancyvrb" /><a
3762 id="x1-62012r6"></a><span
3763 class="cmr-6">6</span><span
3764 class="cmtt-8"> </span><span
3765 class="cmtt-8"> </span><span
3766 class="cmtt-8"> 6)</span><span
3767 class="cmtt-8"> [bitrate_minimum]</span><span
3768 class="cmtt-8"> =</span><span
3769 class="cmtt-8"> read</span><span
3770 class="cmtt-8"> 32</span><span
3771 class="cmtt-8"> bits</span><span
3772 class="cmtt-8"> as</span><span
3773 class="cmtt-8"> signed</span><span
3774 class="cmtt-8"> integer</span>
3775 <br class="fancyvrb" /><a
3776 id="x1-62014r7"></a><span
3777 class="cmr-6">7</span><span
3778 class="cmtt-8"> </span><span
3779 class="cmtt-8"> </span><span
3780 class="cmtt-8"> 7)</span><span
3781 class="cmtt-8"> [blocksize_0]</span><span
3782 class="cmtt-8"> =</span><span
3783 class="cmtt-8"> 2</span><span
3784 class="cmtt-8"> exponent</span><span
3785 class="cmtt-8"> (read</span><span
3786 class="cmtt-8"> 4</span><span
3787 class="cmtt-8"> bits</span><span
3788 class="cmtt-8"> as</span><span
3789 class="cmtt-8"> unsigned</span><span
3790 class="cmtt-8"> integer)</span>
3791 <br class="fancyvrb" /><a
3792 id="x1-62016r8"></a><span
3793 class="cmr-6">8</span><span
3794 class="cmtt-8"> </span><span
3795 class="cmtt-8"> </span><span
3796 class="cmtt-8"> 8)</span><span
3797 class="cmtt-8"> [blocksize_1]</span><span
3798 class="cmtt-8"> =</span><span
3799 class="cmtt-8"> 2</span><span
3800 class="cmtt-8"> exponent</span><span
3801 class="cmtt-8"> (read</span><span
3802 class="cmtt-8"> 4</span><span
3803 class="cmtt-8"> bits</span><span
3804 class="cmtt-8"> as</span><span
3805 class="cmtt-8"> unsigned</span><span
3806 class="cmtt-8"> integer)</span>
3807 <br class="fancyvrb" /><a
3808 id="x1-62018r9"></a><span
3809 class="cmr-6">9</span><span
3810 class="cmtt-8"> </span><span
3811 class="cmtt-8"> </span><span
3812 class="cmtt-8"> 9)</span><span
3813 class="cmtt-8"> [framing_flag]</span><span
3814 class="cmtt-8"> =</span><span
3815 class="cmtt-8"> read</span><span
3816 class="cmtt-8"> one</span><span
3817 class="cmtt-8"> bit</span>
3819 <!--l. 63--><p class="noindent" ><span
3820 class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
3822 class="cmtt-12">[audio_channels] </span>and <span
3823 class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final
3824 blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
3825 class="cmtt-12">[blocksize_0]</span>
3826 must be less than or equal to <span
3827 class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet
3828 any of these conditions renders a stream undecodable.
3829 <!--l. 71--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
3830 considerably off in purely VBR streams. The fields are meaningful only when greater than
3832 <ul class="itemize1">
3833 <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
3834 fixed-rate bitstream
3836 <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
3841 <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
3843 <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
3844 <!--l. 85--><p class="noindent" >
3845 <h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a
3846 id="x1-630004.2.3"></a>Comment header</h5>
3847 <!--l. 86--><p class="noindent" >Comment header decode and data specification is covered in <a
3848 href="#x1-810005">Section 5</a>, “<a
3849 href="#x1-810005">comment field and
3850 header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
3851 <!--l. 90--><p class="noindent" >
3852 <h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a
3853 id="x1-640004.2.4"></a>Setup header</h5>
3854 <!--l. 92--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
3857 <!--l. 94--><p class="noindent" >
3859 <!--l. 95--><p class="noindent" ><img
3860 src="components.png" alt="PIC"
3862 <br /> <div class="caption"
3863 ><span class="id">Figure 6: </span><span
3864 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-640016 -->
3866 <!--l. 100--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
3867 header contains, in order, the lists of codebook configurations, time-domain transform
3868 configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
3869 mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
3870 decode proceeds in the following order:
3871 <!--l. 108--><p class="noindent" ><span class="paragraphHead"><a
3872 id="x1-650004.2.4"></a><span
3873 class="cmbx-12">Codebooks</span></span>
3877 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3879 class="enumerate-enumitem"><span
3880 class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
3881 </dd><dt class="enumerate-enumitem">
3883 class="enumerate-enumitem">Decode <span
3884 class="cmtt-12">[vorbis_codebook_count] </span>codebooks in order as defined in <a
3885 href="#x1-470003">Section 3</a>,
3887 href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
3888 of codebook configurations <span
3889 class="cmtt-12">[vorbis_codebook_configurations]</span>.</dd></dl>
3890 <!--l. 120--><p class="noindent" ><span class="paragraphHead"><a
3891 id="x1-660004.2.4"></a><span
3892 class="cmbx-12">Time domain transforms</span></span>
3893 These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must
3894 be read to maintain bitstream sync.
3895 <!--l. 127--><p class="noindent" >
3896 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3898 class="enumerate-enumitem"><span
3899 class="cmtt-12">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
3900 </dd><dt class="enumerate-enumitem">
3902 class="enumerate-enumitem">read <span
3903 class="cmtt-12">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
3904 nonzero, this is an error condition and the stream is undecodable.</dd></dl>
3905 <!--l. 133--><p class="noindent" ><span class="paragraphHead"><a
3906 id="x1-670004.2.4"></a><span
3907 class="cmbx-12">Floors</span></span>
3908 Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
3910 <!--l. 139--><p class="noindent" >
3911 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3913 class="enumerate-enumitem"><span
3914 class="cmtt-12">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
3915 </dd><dt class="enumerate-enumitem">
3917 class="enumerate-enumitem">For each <span
3918 class="cmtt-12">[i] </span>of <span
3919 class="cmtt-12">[vorbis_floor_count] </span>floor numbers:
3920 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3922 class="enumerate-enumitem">read the floor type: vector <span
3923 class="cmtt-12">[vorbis_floor_types] </span>element <span
3924 class="cmtt-12">[i] </span>= read 16 bits
3926 </dd><dt class="enumerate-enumitem">
3928 class="enumerate-enumitem">If the floor type is zero, decode the floor configuration as defined in <a
3929 href="#x1-890006">Section 6</a>,
3931 href="#x1-890006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
3932 class="cmtt-12">[i] </span>of the floor
3933 configuration array <span
3934 class="cmtt-12">[vorbis_floor_configurations]</span>.
3938 </dd><dt class="enumerate-enumitem">
3940 class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a
3941 href="#x1-950007">Section 7</a>,
3943 href="#x1-950007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
3944 class="cmtt-12">[i] </span>of the floor
3945 configuration array <span
3946 class="cmtt-12">[vorbis_floor_configurations]</span>.
3947 </dd><dt class="enumerate-enumitem">
3949 class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR
3952 <!--l. 157--><p class="noindent" ><span class="paragraphHead"><a
3953 id="x1-680004.2.4"></a><span
3954 class="cmbx-12">Residues</span></span>
3955 Vorbis uses three residue types; header decode of each type is identical.
3956 <!--l. 163--><p class="noindent" >
3957 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3959 class="enumerate-enumitem"><span
3960 class="cmtt-12">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
3961 </dd><dt class="enumerate-enumitem">
3963 class="enumerate-enumitem">For each of <span
3964 class="cmtt-12">[vorbis_residue_count] </span>residue numbers:
3965 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3967 class="enumerate-enumitem">read the residue type; vector <span
3968 class="cmtt-12">[vorbis_residue_types] </span>element <span
3969 class="cmtt-12">[i] </span>= read 16
3970 bits as unsigned integer
3971 </dd><dt class="enumerate-enumitem">
3973 class="enumerate-enumitem">If the residue type is zero, one or two, decode the residue configuration as defined
3975 href="#x1-1020008">Section 8</a>, “<a
3976 href="#x1-1020008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
3977 class="cmtt-12">[i] </span>of
3978 the residue configuration array <span
3979 class="cmtt-12">[vorbis_residue_configurations]</span>.
3980 </dd><dt class="enumerate-enumitem">
3982 class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR
3985 <!--l. 177--><p class="noindent" ><span class="paragraphHead"><a
3986 id="x1-690004.2.4"></a><span
3987 class="cmbx-12">Mappings</span></span>
3988 Mappings are used to set up specific pipelines for encoding multichannel audio with varying
3989 channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
3994 <!--l. 188--><p class="noindent" >
3995 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3997 class="enumerate-enumitem"><span
3998 class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
3999 </dd><dt class="enumerate-enumitem">
4001 class="enumerate-enumitem">For each <span
4002 class="cmtt-12">[i] </span>of <span
4003 class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers:
4004 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4006 class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
4007 the mapping type in Vorbis I.
4008 </dd><dt class="enumerate-enumitem">
4010 class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable
4011 </dd><dt class="enumerate-enumitem">
4013 class="enumerate-enumitem">If the mapping type is zero:
4014 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4016 class="enumerate-enumitem">read 1 bit as a boolean flag
4017 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4019 class="enumerate-enumitem">if set, <span
4020 class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer
4022 </dd><dt class="enumerate-enumitem">
4024 class="enumerate-enumitem">if unset, <span
4025 class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</dd></dl>
4026 </dd><dt class="enumerate-enumitem">
4028 class="enumerate-enumitem">read 1 bit as a boolean flag
4029 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4031 class="enumerate-enumitem">if set, square polar channel mapping is in use:
4032 <ul class="itemize1">
4033 <li class="itemize"><span
4034 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned
4037 <li class="itemize">for <span
4038 class="cmtt-12">[j] </span>each of <span
4039 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps:
4040 <ul class="itemize2">
4041 <li class="itemize">vector <span
4042 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
4043 class="cmtt-12">[j]</span>= read
4045 href="#x1-1170009.2.1">ilog</a>(<span
4046 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
4048 <li class="itemize">vector <span
4049 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
4050 class="cmtt-12">[j]</span>= read
4052 href="#x1-1170009.2.1">ilog</a>(<span
4053 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
4058 <li class="itemize">the numbers read in the above two steps are channel numbers
4059 representing the channel to treat as magnitude and the channel
4060 to treat as angle, respectively. If for any coupling step the
4061 angle channel number equals the magnitude channel number, the
4062 magnitude channel number is greater than <span
4063 class="cmtt-12">[audio_channels]</span>-1, or
4064 the angle channel is greater than <span
4065 class="cmtt-12">[audio_channels]</span>-1, the stream
4066 is undecodable.</li></ul>
4068 </dd><dt class="enumerate-enumitem">
4070 class="enumerate-enumitem">if unset, <span
4071 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= 0</dd></dl>
4072 </dd><dt class="enumerate-enumitem">
4074 class="enumerate-enumitem">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
4075 </dd><dt class="enumerate-enumitem">
4077 class="enumerate-enumitem">if <span
4078 class="cmtt-12">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
4079 settings. For each <span
4080 class="cmtt-12">[j] </span>of <span
4081 class="cmtt-12">[audio_channels] </span>channels:
4082 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4084 class="enumerate-enumitem">vector <span
4085 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4086 class="cmtt-12">[j] </span>= read 4 bits as unsigned
4088 </dd><dt class="enumerate-enumitem">
4090 class="enumerate-enumitem">if the value is greater than the highest numbered submap
4092 class="cmtt-12">[vorbis_mapping_submaps] </span>- 1), this in an error condition rendering
4093 the stream undecodable</dd></dl>
4094 </dd><dt class="enumerate-enumitem">
4096 class="enumerate-enumitem">for each submap <span
4097 class="cmtt-12">[j] </span>of <span
4098 class="cmtt-12">[vorbis_mapping_submaps] </span>submaps, read the floor and
4099 residue numbers for use in decoding that submap:
4100 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4102 class="enumerate-enumitem">read and discard 8 bits (the unused time configuration placeholder)
4103 </dd><dt class="enumerate-enumitem">
4105 class="enumerate-enumitem">read 8 bits as unsigned integer for the floor number; save in vector
4107 class="cmtt-12">[vorbis_mapping_submap_floor] </span>element <span
4108 class="cmtt-12">[j]</span>
4109 </dd><dt class="enumerate-enumitem">
4111 class="enumerate-enumitem">verify the floor number is not greater than the highest number floor
4112 configured for the bitstream. If it is, the bitstream is undecodable
4113 </dd><dt class="enumerate-enumitem">
4115 class="enumerate-enumitem">read 8 bits as unsigned integer for the residue number; save in vector
4117 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
4118 class="cmtt-12">[j]</span>
4122 </dd><dt class="enumerate-enumitem">
4124 class="enumerate-enumitem">verify the residue number is not greater than the highest number residue
4125 configured for the bitstream. If it is, the bitstream is undecodable</dd></dl>
4126 </dd><dt class="enumerate-enumitem">
4128 class="enumerate-enumitem">save this mapping configuration in slot <span
4129 class="cmtt-12">[i] </span>of the mapping configuration array
4131 class="cmtt-12">[vorbis_mapping_configurations]</span>.</dd></dl>
4134 <!--l. 247--><p class="noindent" ><span class="paragraphHead"><a
4135 id="x1-700004.2.4"></a><span
4136 class="cmbx-12">Modes</span></span>
4137 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4139 class="enumerate-enumitem"><span
4140 class="cmtt-12">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
4141 </dd><dt class="enumerate-enumitem">
4143 class="enumerate-enumitem">For each of <span
4144 class="cmtt-12">[vorbis_mode_count] </span>mode numbers:
4145 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4147 class="enumerate-enumitem"><span
4148 class="cmtt-12">[vorbis_mode_blockflag] </span>= read 1 bit
4149 </dd><dt class="enumerate-enumitem">
4151 class="enumerate-enumitem"><span
4152 class="cmtt-12">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
4153 </dd><dt class="enumerate-enumitem">
4155 class="enumerate-enumitem"><span
4156 class="cmtt-12">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
4157 </dd><dt class="enumerate-enumitem">
4159 class="enumerate-enumitem"><span
4160 class="cmtt-12">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
4161 </dd><dt class="enumerate-enumitem">
4163 class="enumerate-enumitem">verify ranges; zero is the only legal value in
4165 class="cmtt-12">[vorbis_mode_windowtype] </span>and <span
4166 class="cmtt-12">[vorbis_mode_transformtype]</span>.
4168 class="cmtt-12">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
4169 in use. Any illegal values render the stream undecodable.
4170 </dd><dt class="enumerate-enumitem">
4172 class="enumerate-enumitem">save this mode configuration in slot <span
4173 class="cmtt-12">[i] </span>of the mode configuration array
4175 class="cmtt-12">[vorbis_mode_configurations]</span>.</dd></dl>
4176 </dd><dt class="enumerate-enumitem">
4178 class="enumerate-enumitem">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
4179 decodable.</dd></dl>
4183 <!--l. 268--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
4184 <!--l. 277--><p class="noindent" >
4185 <h4 class="subsectionHead"><span class="titlemark">4.3. </span> <a
4186 id="x1-710004.3"></a>Audio packet decode and synthesis</h4>
4187 <!--l. 279--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
4188 audio packet decode is to read and verify the packet type. <span
4189 class="cmti-12">A non-audio packet when audio is</span>
4191 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
4193 class="cmti-12">packet and not attempt decoding it to audio</span>.
4194 <!--l. 286--><p class="noindent" >
4195 <h5 class="subsubsectionHead"><span class="titlemark">4.3.1. </span> <a
4196 id="x1-720004.3.1"></a>packet type, mode and window decode</h5>
4197 <!--l. 289--><p class="noindent" >
4198 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4200 class="enumerate-enumitem">read 1 bit <span
4201 class="cmtt-12">[packet_type]</span>; check that packet type is 0 (audio)
4202 </dd><dt class="enumerate-enumitem">
4204 class="enumerate-enumitem">read <a
4205 href="#x1-1170009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span
4206 class="cmtt-12">[mode_number]</span>
4207 </dd><dt class="enumerate-enumitem">
4209 class="enumerate-enumitem">decode blocksize <span
4210 class="cmtt-12">[n] </span>is equal to <span
4211 class="cmtt-12">[blocksize_0] </span>if <span
4212 class="cmtt-12">[vorbis_mode_blockflag] </span>is 0,
4214 class="cmtt-12">[n] </span>is equal to <span
4215 class="cmtt-12">[blocksize_1]</span>.
4216 </dd><dt class="enumerate-enumitem">
4218 class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse
4220 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4222 class="enumerate-enumitem">if this is a long window (the <span
4223 class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is
4225 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4227 class="enumerate-enumitem">read 1 bit for <span
4228 class="cmtt-12">[previous_window_flag]</span>
4229 </dd><dt class="enumerate-enumitem">
4231 class="enumerate-enumitem">read 1 bit for <span
4232 class="cmtt-12">[next_window_flag]</span>
4236 </dd><dt class="enumerate-enumitem">
4238 class="enumerate-enumitem">if <span
4239 class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will
4240 be a hybrid window for lapping with a short block. See <a
4241 href="#paragraph.1" >paragraph <a
4242 href="#x1-260001.3.2">1.3.2</a></a>,
4244 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4245 overlapping dissimilar windows. Else, the left half window will have normal
4247 </dd><dt class="enumerate-enumitem">
4249 class="enumerate-enumitem">if <span
4250 class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be
4251 a hybrid window for lapping with a short block. See <a
4252 href="#x1-260001.3.2">paragraph 1.3.2</a>,
4254 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4255 overlapping dissimilar windows. Else, the left right window will have normal
4256 long shape.</dd></dl>
4257 </dd><dt class="enumerate-enumitem">
4259 class="enumerate-enumitem">if this is a short window, the window is always the same short-window
4262 <!--l. 321--><p class="noindent" >Vorbis windows all use the slope function <span
4263 class="cmmi-12">y </span>= sin(<img
4264 src="Vorbis_I_spec1x.png" alt="π2" class="frac" align="middle"> <span
4265 class="cmsy-10x-x-120">∗</span> sin <sup><span
4266 class="cmr-8">2</span></sup>((<span
4267 class="cmmi-12">x </span>+ 0<span
4268 class="cmmi-12">.</span>5)<span
4269 class="cmmi-12">∕n </span><span
4270 class="cmsy-10x-x-120">∗ </span><span
4271 class="cmmi-12">π</span>)), where <span
4272 class="cmmi-12">n </span>is window
4274 class="cmmi-12">x </span>ranges 0<span
4275 class="cmmi-12">…</span><span
4276 class="cmmi-12">n</span><span
4277 class="cmsy-10x-x-120">− </span>1, but dissimilar lapping requirements can affect overall shape. Window
4278 generation proceeds as follows:
4279 <!--l. 327--><p class="noindent" >
4280 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4282 class="enumerate-enumitem"><span
4283 class="cmtt-12">[window_center] </span>= <span
4284 class="cmtt-12">[n] </span>/ 2
4285 </dd><dt class="enumerate-enumitem">
4287 class="enumerate-enumitem">if (<span
4288 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4289 class="cmtt-12">[previous_window_flag] </span>is not set)
4291 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4293 class="enumerate-enumitem"><span
4294 class="cmtt-12">[left_window_start] </span>= <span
4295 class="cmtt-12">[n]</span>/4 - <span
4296 class="cmtt-12">[blocksize_0]</span>/4
4297 </dd><dt class="enumerate-enumitem">
4299 class="enumerate-enumitem"><span
4300 class="cmtt-12">[left_window_end] </span>= <span
4301 class="cmtt-12">[n]</span>/4 + <span
4302 class="cmtt-12">[blocksize_0]</span>/4
4303 </dd><dt class="enumerate-enumitem">
4305 class="enumerate-enumitem"><span
4306 class="cmtt-12">[left_n] </span>= <span
4307 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4308 <!--l. 336--><p class="noindent" >else
4309 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4311 class="enumerate-enumitem"><span
4312 class="cmtt-12">[left_window_start] </span>= 0
4313 </dd><dt class="enumerate-enumitem">
4315 class="enumerate-enumitem"><span
4316 class="cmtt-12">[left_window_end] </span>= <span
4317 class="cmtt-12">[window_center]</span>
4321 </dd><dt class="enumerate-enumitem">
4323 class="enumerate-enumitem"><span
4324 class="cmtt-12">[left_n] </span>= <span
4325 class="cmtt-12">[n]</span>/2</dd></dl>
4326 </dd><dt class="enumerate-enumitem">
4328 class="enumerate-enumitem">if (<span
4329 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4330 class="cmtt-12">[next_window_flag] </span>is not set) then
4331 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4333 class="enumerate-enumitem"><span
4334 class="cmtt-12">[right_window_start] </span>= <span
4335 class="cmtt-12">[n]*3</span>/4 - <span
4336 class="cmtt-12">[blocksize_0]</span>/4
4337 </dd><dt class="enumerate-enumitem">
4339 class="enumerate-enumitem"><span
4340 class="cmtt-12">[right_window_end] </span>= <span
4341 class="cmtt-12">[n]*3</span>/4 + <span
4342 class="cmtt-12">[blocksize_0]</span>/4
4343 </dd><dt class="enumerate-enumitem">
4345 class="enumerate-enumitem"><span
4346 class="cmtt-12">[right_n] </span>= <span
4347 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4348 <!--l. 352--><p class="noindent" >else
4349 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4351 class="enumerate-enumitem"><span
4352 class="cmtt-12">[right_window_start] </span>= <span
4353 class="cmtt-12">[window_center]</span>
4354 </dd><dt class="enumerate-enumitem">
4356 class="enumerate-enumitem"><span
4357 class="cmtt-12">[right_window_end] </span>= <span
4358 class="cmtt-12">[n]</span>
4359 </dd><dt class="enumerate-enumitem">
4361 class="enumerate-enumitem"><span
4362 class="cmtt-12">[right_n] </span>= <span
4363 class="cmtt-12">[n]</span>/2</dd></dl>
4364 </dd><dt class="enumerate-enumitem">
4366 class="enumerate-enumitem">window from range 0 ... <span
4367 class="cmtt-12">[left_window_start]</span>-1 inclusive is zero
4368 </dd><dt class="enumerate-enumitem">
4370 class="enumerate-enumitem">for <span
4371 class="cmtt-12">[i] </span>in range <span
4372 class="cmtt-12">[left_window_start] </span>... <span
4373 class="cmtt-12">[left_window_end]</span>-1, window(<span
4374 class="cmtt-12">[i]</span>) =
4376 src="Vorbis_I_spec2x.png" alt="π
4377 2" class="frac" align="middle"> <span
4378 class="cmsy-10x-x-120">∗</span> sin <sup><span
4379 class="cmr-8">2</span></sup>( (<span
4380 class="cmtt-12">[i]</span>-<span
4381 class="cmtt-12">[left_window_start]</span>+0.5) / <span
4382 class="cmtt-12">[left_n] </span><span
4383 class="cmsy-10x-x-120">∗</span><img
4384 src="Vorbis_I_spec3x.png" alt="π
4385 2" class="frac" align="middle">) )
4386 </dd><dt class="enumerate-enumitem">
4388 class="enumerate-enumitem">window from range <span
4389 class="cmtt-12">[left_window_end] </span>... <span
4390 class="cmtt-12">[right_window_start]</span>-1 inclusive is
4392 </dd><dt class="enumerate-enumitem">
4394 class="enumerate-enumitem">for <span
4395 class="cmtt-12">[i] </span>in range <span
4396 class="cmtt-12">[right_window_start] </span>... <span
4397 class="cmtt-12">[right_window_end]</span>-1, window(<span
4398 class="cmtt-12">[i]</span>) =
4400 src="Vorbis_I_spec4x.png" alt="π
4401 2" class="frac" align="middle"> <span
4402 class="cmsy-10x-x-120">∗</span> sin <sup><span
4403 class="cmr-8">2</span></sup>( (<span
4404 class="cmtt-12">[i]</span>-<span
4405 class="cmtt-12">[right_window_start]</span>+0.5) / <span
4406 class="cmtt-12">[right_n] </span><span
4407 class="cmsy-10x-x-120">∗</span><img
4408 src="Vorbis_I_spec5x.png" alt="π
4409 2" class="frac" align="middle"> + <img
4410 src="Vorbis_I_spec6x.png" alt="π
4411 2" class="frac" align="middle">) )
4412 </dd><dt class="enumerate-enumitem">
4414 class="enumerate-enumitem">window from range <span
4415 class="cmtt-12">[right_window_start] </span>... <span
4416 class="cmtt-12">[n]</span>-1 is zero</dd></dl>
4417 <!--l. 368--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this
4418 packet from the stream. An end of packet condition past this point is to be considered a possible
4423 <!--l. 375--><p class="noindent" >
4424 <h5 class="subsubsectionHead"><span class="titlemark">4.3.2. </span> <a
4425 id="x1-730004.3.2"></a>floor curve decode</h5>
4426 <!--l. 377--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
4427 class="cmtt-12">[mode_number]</span>
4428 from configuration array <span
4429 class="cmtt-12">[vorbis_mode_configurations] </span>and the map number
4431 class="cmtt-12">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
4433 class="cmtt-12">[vorbis_mapping_configurations]</span>.
4434 <!--l. 384--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
4435 <!--l. 386--><p class="noindent" >For each floor <span
4436 class="cmtt-12">[i] </span>of <span
4437 class="cmtt-12">[audio_channels]</span>
4438 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4440 class="enumerate-enumitem"><span
4441 class="cmtt-12">[submap_number] </span>= element <span
4442 class="cmtt-12">[i] </span>of vector [vorbis_mapping_mux]
4443 </dd><dt class="enumerate-enumitem">
4445 class="enumerate-enumitem"><span
4446 class="cmtt-12">[floor_number] </span>= element <span
4447 class="cmtt-12">[submap_number] </span>of vector [vorbis_submap_floor]
4448 </dd><dt class="enumerate-enumitem">
4450 class="enumerate-enumitem">if the floor type of this floor (vector
4452 class="cmtt-12">[vorbis_floor_types] </span>element <span
4453 class="cmtt-12">[floor_number]</span>) is zero then decode the floor for
4455 class="cmtt-12">[i] </span>according to the <a
4456 href="#x1-930006.2.2">subsubsection 6.2.2</a>, “<a
4457 href="#x1-930006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
4458 </dd><dt class="enumerate-enumitem">
4460 class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span
4461 class="cmtt-12">[i] </span>according to the
4463 href="#x1-1000007.2.3">subsubsection 7.2.3</a>, “<a
4464 href="#x1-1000007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
4465 </dd><dt class="enumerate-enumitem">
4467 class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis
4468 </dd><dt class="enumerate-enumitem">
4470 class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span
4471 class="cmtt-12">[no_residue] </span>element <span
4472 class="cmtt-12">[i] </span>to true,
4473 else set vector <span
4474 class="cmtt-12">[no_residue] </span>element <span
4475 class="cmtt-12">[i] </span>to false</dd></dl>
4476 <!--l. 406--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
4477 output vectors and skipping to the add/overlap output stage.
4478 <!--l. 412--><p class="noindent" >
4479 <h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a
4480 id="x1-740004.3.3"></a>nonzero vector propagate</h5>
4481 <!--l. 414--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
4482 that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
4483 coded in the stream, save for one complication. If some vectors are used and some are not,
4487 channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
4489 <!--l. 421--><p class="noindent" >for each <span
4490 class="cmtt-12">[i] </span>from 0 ... <span
4491 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1
4492 <!--l. 424--><p class="noindent" >
4493 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4495 class="enumerate-enumitem">if either <span
4496 class="cmtt-12">[no_residue] </span>entry for channel (<span
4497 class="cmtt-12">[vorbis_mapping_magnitude] </span>element
4499 class="cmtt-12">[i]</span>) or channel (<span
4500 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
4501 class="cmtt-12">[i]</span>) are set to false, then both
4502 must be set to false. Note that an ’unused’ floor has no decoded floor information; it
4503 is important that this is remembered at floor curve synthesis time.</dd></dl>
4504 <!--l. 436--><p class="noindent" >
4505 <h5 class="subsubsectionHead"><span class="titlemark">4.3.4. </span> <a
4506 id="x1-750004.3.4"></a>residue decode</h5>
4507 <!--l. 438--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
4509 <!--l. 441--><p class="noindent" >for each submap <span
4510 class="cmtt-12">[i] </span>in order from 0 ... <span
4511 class="cmtt-12">[vorbis_mapping_submaps]</span>-1
4512 <!--l. 444--><p class="noindent" >
4513 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4515 class="enumerate-enumitem"><span
4516 class="cmtt-12">[ch] </span>= 0
4517 </dd><dt class="enumerate-enumitem">
4519 class="enumerate-enumitem">for each channel <span
4520 class="cmtt-12">[j] </span>in order from 0 ... <span
4521 class="cmtt-12">[audio_channels] </span>- 1
4522 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4524 class="enumerate-enumitem">if channel <span
4525 class="cmtt-12">[j] </span>in submap <span
4526 class="cmtt-12">[i] </span>(vector <span
4527 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4528 class="cmtt-12">[j] </span>is equal to
4530 class="cmtt-12">[i]</span>)
4531 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4533 class="enumerate-enumitem">if vector <span
4534 class="cmtt-12">[no_residue] </span>element <span
4535 class="cmtt-12">[j] </span>is true
4536 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4538 class="enumerate-enumitem">vector <span
4539 class="cmtt-12">[do_not_decode_flag] </span>element <span
4540 class="cmtt-12">[ch] </span>is set</dd></dl>
4541 <!--l. 453--><p class="noindent" >else
4542 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4544 class="enumerate-enumitem">vector <span
4545 class="cmtt-12">[do_not_decode_flag] </span>element <span
4546 class="cmtt-12">[ch] </span>is unset</dd></dl>
4547 </dd><dt class="enumerate-enumitem">
4549 class="enumerate-enumitem">increment <span
4550 class="cmtt-12">[ch]</span></dd></dl>
4555 </dd><dt class="enumerate-enumitem">
4557 class="enumerate-enumitem"><span
4558 class="cmtt-12">[residue_number] </span>= vector <span
4559 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
4560 class="cmtt-12">[i]</span>
4561 </dd><dt class="enumerate-enumitem">
4563 class="enumerate-enumitem"><span
4564 class="cmtt-12">[residue_type] </span>= vector <span
4565 class="cmtt-12">[vorbis_residue_types] </span>element <span
4566 class="cmtt-12">[residue_number]</span>
4567 </dd><dt class="enumerate-enumitem">
4569 class="enumerate-enumitem">decode <span
4570 class="cmtt-12">[ch] </span>vectors using residue <span
4571 class="cmtt-12">[residue_number]</span>, according to type <span
4572 class="cmtt-12">[residue_type]</span>,
4573 also passing vector <span
4574 class="cmtt-12">[do_not_decode_flag] </span>to indicate which vectors in the bundle should
4575 not be decoded. Correct per-vector decode length is <span
4576 class="cmtt-12">[n]</span>/2.
4577 </dd><dt class="enumerate-enumitem">
4579 class="enumerate-enumitem"><span
4580 class="cmtt-12">[ch] </span>= 0
4581 </dd><dt class="enumerate-enumitem">
4583 class="enumerate-enumitem">for each channel <span
4584 class="cmtt-12">[j] </span>in order from 0 ... <span
4585 class="cmtt-12">[audio_channels]</span>
4586 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4588 class="enumerate-enumitem">if channel <span
4589 class="cmtt-12">[j] </span>is in submap <span
4590 class="cmtt-12">[i] </span>(vector <span
4591 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4592 class="cmtt-12">[j] </span>is equal
4594 class="cmtt-12">[i]</span>)
4595 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4597 class="enumerate-enumitem">residue vector for channel <span
4598 class="cmtt-12">[j] </span>is set to decoded residue vector <span
4599 class="cmtt-12">[ch]</span>
4600 </dd><dt class="enumerate-enumitem">
4602 class="enumerate-enumitem">increment <span
4603 class="cmtt-12">[ch]</span></dd></dl>
4606 <!--l. 480--><p class="noindent" >
4607 <h5 class="subsubsectionHead"><span class="titlemark">4.3.5. </span> <a
4608 id="x1-760004.3.5"></a>inverse coupling</h5>
4609 <!--l. 482--><p class="noindent" >for each <span
4610 class="cmtt-12">[i] </span>from <span
4611 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
4612 <!--l. 485--><p class="noindent" >
4613 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4615 class="enumerate-enumitem"><span
4616 class="cmtt-12">[magnitude_vector] </span>= the residue vector for channel (vector
4618 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
4619 class="cmtt-12">[i]</span>)
4620 </dd><dt class="enumerate-enumitem">
4622 class="enumerate-enumitem"><span
4623 class="cmtt-12">[angle_vector] </span>= the residue vector for channel (vector <span
4624 class="cmtt-12">[vorbis_mapping_angle]</span>
4629 class="cmtt-12">[i]</span>)
4630 </dd><dt class="enumerate-enumitem">
4632 class="enumerate-enumitem">for each scalar value <span
4633 class="cmtt-12">[M] </span>in vector <span
4634 class="cmtt-12">[magnitude_vector] </span>and the corresponding scalar value
4636 class="cmtt-12">[A] </span>in vector <span
4637 class="cmtt-12">[angle_vector]</span>:
4638 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4640 class="enumerate-enumitem">if (<span
4641 class="cmtt-12">[M] </span>is greater than zero)
4642 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4644 class="enumerate-enumitem">if (<span
4645 class="cmtt-12">[A] </span>is greater than zero)
4646 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4648 class="enumerate-enumitem"><span
4649 class="cmtt-12">[new_M] </span>= <span
4650 class="cmtt-12">[M]</span>
4651 </dd><dt class="enumerate-enumitem">
4653 class="enumerate-enumitem"><span
4654 class="cmtt-12">[new_A] </span>= <span
4655 class="cmtt-12">[M]</span>-<span
4656 class="cmtt-12">[A]</span></dd></dl>
4657 <!--l. 498--><p class="noindent" >else
4658 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4660 class="enumerate-enumitem"><span
4661 class="cmtt-12">[new_A] </span>= <span
4662 class="cmtt-12">[M]</span>
4663 </dd><dt class="enumerate-enumitem">
4665 class="enumerate-enumitem"><span
4666 class="cmtt-12">[new_M] </span>= <span
4667 class="cmtt-12">[M]</span>+<span
4668 class="cmtt-12">[A]</span></dd></dl>
4670 <!--l. 505--><p class="noindent" >else
4671 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4673 class="enumerate-enumitem">if (<span
4674 class="cmtt-12">[A] </span>is greater than zero)
4675 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4677 class="enumerate-enumitem"><span
4678 class="cmtt-12">[new_M] </span>= <span
4679 class="cmtt-12">[M]</span>
4680 </dd><dt class="enumerate-enumitem">
4682 class="enumerate-enumitem"><span
4683 class="cmtt-12">[new_A] </span>= <span
4684 class="cmtt-12">[M]</span>+<span
4685 class="cmtt-12">[A]</span></dd></dl>
4686 <!--l. 512--><p class="noindent" >else
4687 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4689 class="enumerate-enumitem"><span
4690 class="cmtt-12">[new_A] </span>= <span
4691 class="cmtt-12">[M]</span>
4692 </dd><dt class="enumerate-enumitem">
4694 class="enumerate-enumitem"><span
4695 class="cmtt-12">[new_M] </span>= <span
4696 class="cmtt-12">[M]</span>-<span
4697 class="cmtt-12">[A]</span></dd></dl>
4699 </dd><dt class="enumerate-enumitem">
4701 class="enumerate-enumitem">set scalar value <span
4702 class="cmtt-12">[M] </span>in vector <span
4703 class="cmtt-12">[magnitude_vector] </span>to <span
4704 class="cmtt-12">[new_M]</span>
4708 </dd><dt class="enumerate-enumitem">
4710 class="enumerate-enumitem">set scalar value <span
4711 class="cmtt-12">[A] </span>in vector <span
4712 class="cmtt-12">[angle_vector] </span>to <span
4713 class="cmtt-12">[new_A]</span></dd></dl>
4715 <!--l. 529--><p class="noindent" >
4716 <h5 class="subsubsectionHead"><span class="titlemark">4.3.6. </span> <a
4717 id="x1-770004.3.6"></a>dot product</h5>
4718 <!--l. 531--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
4719 packet type. Note that the vector synthesis length for floor computation is <span
4720 class="cmtt-12">[n]</span>/2.
4721 <!--l. 535--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
4722 channel’s residue vector. The result is the dot product of the floor and residue vectors for
4723 each channel; the produced vectors are the length <span
4724 class="cmtt-12">[n]</span>/2 audio spectrum for each
4726 <!--l. 543--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
4727 implementation might be to assume that a 32 bit fixed-point representation for floor and
4728 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
4729 in all cases because it happens to mostly work with the current Xiph.Org reference
4731 <!--l. 550--><p class="noindent" >However, floor vector values can span <span
4732 class="cmsy-10x-x-120">∼</span>140dB (<span
4733 class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
4734 vector should represent a minimum of 120dB (<span
4735 class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
4736 bit PCM device. For the residue vector to represent full scale if the floor is nailed
4738 class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
4739 full scale if the floor is nailed at 0dB, it must be able to represent <span
4740 class="cmsy-10x-x-120">−</span>140dB to +0dB.
4741 Thus, in order to handle full range dynamics, a residue vector may span <span
4742 class="cmsy-10x-x-120">−</span>140dB to
4743 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
4744 residue vector must be able to represent a 48 bit range and the dot product must
4745 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
4746 achieved using large (64 bit or larger) integers, or implementing a movable binary point
4748 <!--l. 567--><p class="noindent" >
4749 <h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a
4750 id="x1-780004.3.7"></a>inverse MDCT</h5>
4751 <!--l. 569--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
4755 inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is
4756 available in <span class="cite">[<a
4757 href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
4759 <!--l. 576--><p class="noindent" >
4760 <h5 class="subsubsectionHead"><span class="titlemark">4.3.8. </span> <a
4761 id="x1-790004.3.8"></a>overlap_add</h5>
4762 <!--l. 578--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
4763 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
4764 current window (as illustrated in <a
4765 href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a
4766 href="#x1-260001.3.2">Window shape decode (long windows
4767 only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
4768 is finished data to be returned by the decoder. This data spans from the center of
4769 the previous window to the center of the current window. In the case of same-sized
4770 windows, the amount of data to return is one-half block consisting of and only of the
4771 overlapped portions. When overlapping a short and long window, much of the returned
4772 range does not actually overlap. This does not damage transform orthogonality. Pay
4773 attention however to returning the correct data range; the amount of data to be returned
4775 <!--l. 592--><p class="noindent" >
4776 <div class="fancyvrb" id="fancyvrb22">
4778 id="x1-79002r1"></a><span
4779 class="cmr-6">1</span><span
4780 class="cmtt-8"> </span><span
4781 class="cmtt-8"> window\_blocksize(previous\_window)/4+window\_blocksize(current\_window)/4</span>
4783 <!--l. 596--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
4784 windowsize/2-1, inclusive) of the current window.
4785 <!--l. 599--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
4786 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
4787 PCM output offset is ’0’ (as no data has been returned yet).
4788 <!--l. 606--><p class="noindent" >
4789 <h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a
4790 id="x1-800004.3.9"></a>output channel order</h5>
4791 <!--l. 608--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
4792 implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the
4793 specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for
4797 greater-than-eight channels remains ’left to the implementation’.
4798 <!--l. 614--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a
4799 decoder to produce output with channels in any order. Any such decoder should explicitly
4800 document channel reordering behavior.
4801 <!--l. 620--><p class="noindent" >
4802 <dl class="description"><dt class="description">
4804 class="cmssbx-10x-x-120">one channel</span> </dt><dd
4805 class="description">the stream is monophonic
4806 </dd><dt class="description">
4808 class="cmssbx-10x-x-120">two channels</span> </dt><dd
4809 class="description">the stream is stereo. channel order: left, right
4810 </dd><dt class="description">
4812 class="cmssbx-10x-x-120">three channels</span> </dt><dd
4813 class="description">the stream is a 1d-surround encoding. channel order: left, center, right
4814 </dd><dt class="description">
4816 class="cmssbx-10x-x-120">four channels</span> </dt><dd
4817 class="description">the stream is quadraphonic surround. channel order: front left, front right,
4818 rear left, rear right
4819 </dd><dt class="description">
4821 class="cmssbx-10x-x-120">five channels</span> </dt><dd
4822 class="description">the stream is five-channel surround. channel order: front left, center, front
4823 right, rear left, rear right
4824 </dd><dt class="description">
4826 class="cmssbx-10x-x-120">six channels</span> </dt><dd
4827 class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear
4828 left, rear right, LFE
4829 </dd><dt class="description">
4831 class="cmssbx-10x-x-120">seven channels</span> </dt><dd
4832 class="description">the stream is 6.1 surround. channel order: front left, center, front right,
4833 side left, side right, rear center, LFE
4834 </dd><dt class="description">
4836 class="cmssbx-10x-x-120">eight channels</span> </dt><dd
4837 class="description">the stream is 7.1 surround. channel order: front left, center, front right,
4838 side left, side right, rear left, rear right, LFE
4839 </dd><dt class="description">
4841 class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd
4842 class="description">channel use and order is defined by the application
4844 <!--l. 656--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
4845 channel mappings (such as three and four channel <a
4846 href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
4847 mappings other than mapping 0.
4854 <h3 class="sectionHead"><span class="titlemark">5. </span> <a
4855 id="x1-810005"></a>comment field and header specification</h3>
4856 <!--l. 6--><p class="noindent" >
4857 <h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a
4858 id="x1-820005.1"></a>Overview</h4>
4859 <!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
4860 bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
4861 belongs in a separate logical bitstream (usually an XML stream type) that provides greater
4862 structure and machine parseability.
4863 <!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
4864 a CDR. It should be a little information to remember the disc by and explain it to others; a
4865 short, to-the-point text note that need not only be a couple words, but isn’t going to be more
4866 than a short paragraph. The essentials, in other words, whatever they turn out to be,
4868 <!--l. 21--><p class="noindent" >
4870 <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
4871 class="cmti-12">“I’m Still Around”</span>, opening
4872 for Moxy Früvous, 1997.</div>
4873 <!--l. 29--><p class="noindent" >
4874 <h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a
4875 id="x1-830005.2"></a>Comment encoding</h4>
4876 <!--l. 31--><p class="noindent" >
4877 <h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a
4878 id="x1-840005.2.1"></a>Structure</h5>
4879 <!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
4880 bounded to 2<sup><span
4881 class="cmr-8">32</span></sup> <span
4882 class="cmsy-10x-x-120">− </span>1 and the length of each vector is limited to 2<sup><span
4883 class="cmr-8">32</span></sup> <span
4884 class="cmsy-10x-x-120">− </span>1 bytes. The vector length is
4888 encoded; the vector contents themselves are not null terminated. In addition to the vector list,
4889 there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
4890 example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
4892 <!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
4893 packing conventions of the vorbis codec. However, since data in the comment header
4894 is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
4896 <!--l. 46--><p class="noindent" >The comment header is decoded as follows:
4897 <!--l. 48--><p class="noindent" >
4898 <div class="fancyvrb" id="fancyvrb23">
4900 id="x1-84002r1"></a><span
4901 class="cmr-6">1</span><span
4902 class="cmtt-8"> </span><span
4903 class="cmtt-8"> </span><span
4904 class="cmtt-8"> </span><span
4905 class="cmtt-8"> 1)</span><span
4906 class="cmtt-8"> [vendor\_length]</span><span
4907 class="cmtt-8"> =</span><span
4908 class="cmtt-8"> read</span><span
4909 class="cmtt-8"> an</span><span
4910 class="cmtt-8"> unsigned</span><span
4911 class="cmtt-8"> integer</span><span
4912 class="cmtt-8"> of</span><span
4913 class="cmtt-8"> 32</span><span
4914 class="cmtt-8"> bits</span>
4915 <br class="fancyvrb" /><a
4916 id="x1-84004r2"></a><span
4917 class="cmr-6">2</span><span
4918 class="cmtt-8"> </span><span
4919 class="cmtt-8"> </span><span
4920 class="cmtt-8"> </span><span
4921 class="cmtt-8"> 2)</span><span
4922 class="cmtt-8"> [vendor\_string]</span><span
4923 class="cmtt-8"> =</span><span
4924 class="cmtt-8"> read</span><span
4925 class="cmtt-8"> a</span><span
4926 class="cmtt-8"> UTF-8</span><span
4927 class="cmtt-8"> vector</span><span
4928 class="cmtt-8"> as</span><span
4929 class="cmtt-8"> [vendor\_length]</span><span
4930 class="cmtt-8"> octets</span>
4931 <br class="fancyvrb" /><a
4932 id="x1-84006r3"></a><span
4933 class="cmr-6">3</span><span
4934 class="cmtt-8"> </span><span
4935 class="cmtt-8"> </span><span
4936 class="cmtt-8"> </span><span
4937 class="cmtt-8"> 3)</span><span
4938 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4939 class="cmtt-8"> =</span><span
4940 class="cmtt-8"> read</span><span
4941 class="cmtt-8"> an</span><span
4942 class="cmtt-8"> unsigned</span><span
4943 class="cmtt-8"> integer</span><span
4944 class="cmtt-8"> of</span><span
4945 class="cmtt-8"> 32</span><span
4946 class="cmtt-8"> bits</span>
4947 <br class="fancyvrb" /><a
4948 id="x1-84008r4"></a><span
4949 class="cmr-6">4</span><span
4950 class="cmtt-8"> </span><span
4951 class="cmtt-8"> </span><span
4952 class="cmtt-8"> </span><span
4953 class="cmtt-8"> 4)</span><span
4954 class="cmtt-8"> iterate</span><span
4955 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4956 class="cmtt-8"> times</span><span
4957 class="cmtt-8"> {</span>
4958 <br class="fancyvrb" /><a
4959 id="x1-84010r5"></a><span
4960 class="cmr-6">5</span><span
4961 class="cmtt-8"> </span><span
4962 class="cmtt-8"> </span><span
4963 class="cmtt-8"> </span><span
4964 class="cmtt-8"> </span><span
4965 class="cmtt-8"> </span><span
4966 class="cmtt-8"> </span><span
4967 class="cmtt-8"> </span><span
4968 class="cmtt-8"> </span><span
4969 class="cmtt-8"> 5)</span><span
4970 class="cmtt-8"> [length]</span><span
4971 class="cmtt-8"> =</span><span
4972 class="cmtt-8"> read</span><span
4973 class="cmtt-8"> an</span><span
4974 class="cmtt-8"> unsigned</span><span
4975 class="cmtt-8"> integer</span><span
4976 class="cmtt-8"> of</span><span
4977 class="cmtt-8"> 32</span><span
4978 class="cmtt-8"> bits</span>
4979 <br class="fancyvrb" /><a
4980 id="x1-84012r6"></a><span
4981 class="cmr-6">6</span><span
4982 class="cmtt-8"> </span><span
4983 class="cmtt-8"> </span><span
4984 class="cmtt-8"> </span><span
4985 class="cmtt-8"> </span><span
4986 class="cmtt-8"> </span><span
4987 class="cmtt-8"> </span><span
4988 class="cmtt-8"> </span><span
4989 class="cmtt-8"> </span><span
4990 class="cmtt-8"> 6)</span><span
4991 class="cmtt-8"> this</span><span
4992 class="cmtt-8"> iteration’s</span><span
4993 class="cmtt-8"> user</span><span
4994 class="cmtt-8"> comment</span><span
4995 class="cmtt-8"> =</span><span
4996 class="cmtt-8"> read</span><span
4997 class="cmtt-8"> a</span><span
4998 class="cmtt-8"> UTF-8</span><span
4999 class="cmtt-8"> vector</span><span
5000 class="cmtt-8"> as</span><span
5001 class="cmtt-8"> [length]</span><span
5002 class="cmtt-8"> octets</span>
5003 <br class="fancyvrb" /><a
5004 id="x1-84014r7"></a><span
5005 class="cmr-6">7</span><span
5006 class="cmtt-8"> </span><span
5007 class="cmtt-8"> </span><span
5008 class="cmtt-8"> </span><span
5009 class="cmtt-8"> </span><span
5010 class="cmtt-8"> </span><span
5011 class="cmtt-8"> </span><span
5012 class="cmtt-8"> }</span>
5013 <br class="fancyvrb" /><a
5014 id="x1-84016r8"></a><span
5015 class="cmr-6">8</span><span
5016 class="cmtt-8"> </span><span
5017 class="cmtt-8"> </span><span
5018 class="cmtt-8"> </span><span
5019 class="cmtt-8"> 7)</span><span
5020 class="cmtt-8"> [framing\_bit]</span><span
5021 class="cmtt-8"> =</span><span
5022 class="cmtt-8"> read</span><span
5023 class="cmtt-8"> a</span><span
5024 class="cmtt-8"> single</span><span
5025 class="cmtt-8"> bit</span><span
5026 class="cmtt-8"> as</span><span
5027 class="cmtt-8"> boolean</span>
5028 <br class="fancyvrb" /><a
5029 id="x1-84018r9"></a><span
5030 class="cmr-6">9</span><span
5031 class="cmtt-8"> </span><span
5032 class="cmtt-8"> </span><span
5033 class="cmtt-8"> </span><span
5034 class="cmtt-8"> 8)</span><span
5035 class="cmtt-8"> if</span><span
5036 class="cmtt-8"> (</span><span
5037 class="cmtt-8"> [framing\_bit]</span><span
5038 class="cmtt-8"> unset</span><span
5039 class="cmtt-8"> or</span><span
5040 class="cmtt-8"> end-of-packet</span><span
5041 class="cmtt-8"> )</span><span
5042 class="cmtt-8"> then</span><span
5043 class="cmtt-8"> ERROR</span>
5044 <br class="fancyvrb" /><a
5045 id="x1-84020r10"></a><span
5046 class="cmr-6">10</span><span
5047 class="cmtt-8"> </span><span
5048 class="cmtt-8"> </span><span
5049 class="cmtt-8"> </span><span
5050 class="cmtt-8"> 9)</span><span
5051 class="cmtt-8"> done.</span>
5053 <!--l. 64--><p class="noindent" >
5054 <h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a
5055 id="x1-850005.2.2"></a>Content vector format</h5>
5056 <!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is,
5057 comment fields consist of a field name and a corresponding value and look like:
5058 <!--l. 70--><p class="noindent" >
5060 <!--l. 71--><p class="noindent" >
5061 <div class="fancyvrb" id="fancyvrb24">
5063 id="x1-85002r1"></a><span
5064 class="cmr-6">1</span><span
5065 class="cmtt-8"> </span><span
5066 class="cmtt-8"> comment[0]="ARTIST=me";</span>
5067 <br class="fancyvrb" /><a
5068 id="x1-85004r2"></a><span
5069 class="cmr-6">2</span><span
5070 class="cmtt-8"> </span><span
5071 class="cmtt-8"> comment[1]="TITLE=the</span><span
5072 class="cmtt-8"> sound</span><span
5073 class="cmtt-8"> of</span><span
5074 class="cmtt-8"> Vorbis";</span>
5080 <!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
5081 excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
5082 ASCII 0x61 through 0x7A inclusive (characters a-z).
5083 <!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
5084 terminate the field name.
5085 <!--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
5087 <!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
5088 id="x1-860005.2.2"></a><span
5089 class="cmbx-12">Field names</span></span>
5090 Below is a proposed, minimal list of standard field names with a description of intended use. No
5091 single or group of field names is mandatory; a comment header may contain one, all or none of
5092 the names in this list.
5093 <!--l. 99--><p class="noindent" >
5094 <dl class="description"><dt class="description">
5096 class="cmssbx-10x-x-120">TITLE</span> </dt><dd
5097 class="description">Track/Work name
5098 </dd><dt class="description">
5100 class="cmssbx-10x-x-120">VERSION</span> </dt><dd
5101 class="description">The version field may be used to differentiate multiple versions of the same
5102 track title in a single collection. (e.g. remix info)
5103 </dd><dt class="description">
5105 class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
5106 class="description">The collection name to which this track belongs
5107 </dd><dt class="description">
5109 class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
5110 class="description">The track number of this piece if part of a specific larger collection or
5112 </dd><dt class="description">
5114 class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
5115 class="description">The artist generally considered responsible for the work. In popular music this is
5116 usually the performing band or singer. For classical music it would be the composer.
5117 For an audio book it would be the author of the original text.
5118 </dd><dt class="description">
5120 class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
5121 class="description">The artist(s) who performed the work. In classical music this would be the
5122 conductor, orchestra, soloists. In an audio book it would be the actor who did the
5123 reading. In popular music this is typically the same as the ARTIST and is omitted.
5124 </dd><dt class="description">
5126 class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
5127 class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
5128 </dd><dt class="description">
5133 class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
5134 class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to
5135 a license such as a Creative
5136 Commons license (”www.creativecommons.org/blahblah/license.html”) or the EFF
5137 Open Audio License (’distributed under the terms of the Open Audio License. see
5138 http://www.eff.org/IP/Open_licenses/eff_oal.html for details’), etc.
5139 </dd><dt class="description">
5141 class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
5142 class="description">Name of the organization producing the track (i.e. the ’record label’)
5143 </dd><dt class="description">
5145 class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
5146 class="description">A short text description of the contents
5147 </dd><dt class="description">
5149 class="cmssbx-10x-x-120">GENRE</span> </dt><dd
5150 class="description">A short text indication of music genre
5151 </dd><dt class="description">
5153 class="cmssbx-10x-x-120">DATE</span> </dt><dd
5154 class="description">Date the track was recorded
5155 </dd><dt class="description">
5157 class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
5158 class="description">Location where track was recorded
5159 </dd><dt class="description">
5161 class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
5162 class="description">Contact information for the creators or distributors of the track. This could
5163 be a URL, an email address, the physical address of the producing label.
5164 </dd><dt class="description">
5166 class="cmssbx-10x-x-120">ISRC</span> </dt><dd
5167 class="description">International Standard Recording Code for the track; see <a
5168 href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for
5169 more information on ISRC numbers.
5171 <!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
5172 id="x1-870005.2.2"></a><span
5173 class="cmbx-12">Implications</span></span>
5174 Field names should not be ’internationalized’; this is a concession to simplicity not
5175 an attempt to exclude the majority of the world that doesn’t speak English. Field
5177 class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
5179 <!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
5180 the field name is bounded in a known way. Thus we also have the length of the field
5182 <!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
5183 use of comment fields should be clear through context at this point. Abuse will be
5188 <!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
5189 to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
5190 tags here to help with standardization.
5191 <!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
5192 example, assume a track was recorded by three well know artists; the following is permissible,
5194 <!--l. 183--><p class="noindent" >
5196 <!--l. 184--><p class="noindent" >
5197 <div class="fancyvrb" id="fancyvrb25">
5199 id="x1-87002r1"></a><span
5200 class="cmr-6">1</span><span
5201 class="cmtt-8"> </span><span
5202 class="cmtt-8"> ARTIST=Dizzy</span><span
5203 class="cmtt-8"> Gillespie</span>
5204 <br class="fancyvrb" /><a
5205 id="x1-87004r2"></a><span
5206 class="cmr-6">2</span><span
5207 class="cmtt-8"> </span><span
5208 class="cmtt-8"> ARTIST=Sonny</span><span
5209 class="cmtt-8"> Rollins</span>
5210 <br class="fancyvrb" /><a
5211 id="x1-87006r3"></a><span
5212 class="cmr-6">3</span><span
5213 class="cmtt-8"> </span><span
5214 class="cmtt-8"> ARTIST=Sonny</span><span
5215 class="cmtt-8"> Stitt</span>
5218 <!--l. 197--><p class="noindent" >
5219 <h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a
5220 id="x1-880005.2.3"></a>Encoding</h5>
5221 <!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
5222 first bitstream header packet, it is not generally the only packet on the second page and may not
5223 be restricted to within the second bitstream page. The length of the comment header packet is
5224 (practically) unbounded. The comment header packet is not optional; it must be present in the
5225 bitstream even if it is effectively empty.
5226 <!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
5227 renders least-significant-bit of the word to be coded into the least significant available bit of the
5228 current bitstream octet first):
5229 <!--l. 213--><p class="noindent" >
5230 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5232 class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets)
5233 </dd><dt class="enumerate-enumitem">
5235 class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of
5236 string, not null terminated)
5240 </dd><dt class="enumerate-enumitem">
5242 class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields)
5243 </dd><dt class="enumerate-enumitem">
5245 class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span
5246 class="cmmi-12">> </span>0; 32 bit unsigned quantity
5247 specifying number of octets)
5248 </dd><dt class="enumerate-enumitem">
5250 class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
5251 end of string, not null terminated)
5252 </dd><dt class="enumerate-enumitem">
5254 class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span
5255 class="cmmi-12">> </span>1...)...
5257 <!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
5259 class="cmtt-12">vorbis/lib/info.c</span>, <span
5260 class="cmtt-12">_vorbis_pack_comment() </span>and <span
5261 class="cmtt-12">_vorbis_unpack_comment()</span>.
5268 <h3 class="sectionHead"><span class="titlemark">6. </span> <a
5269 id="x1-890006"></a>Floor type 0 setup and decode</h3>
5270 <!--l. 6--><p class="noindent" >
5271 <h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a
5272 id="x1-900006.1"></a>Overview</h4>
5273 <!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
5274 Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
5275 response of the LSP filter. This representation is equivalent to a traditional all-pole infinite
5276 impulse response filter as would be used in linear predictive coding; LSP representation may be
5277 converted to LPC representation and vice-versa.
5278 <!--l. 18--><p class="noindent" >
5279 <h4 class="subsectionHead"><span class="titlemark">6.2. </span> <a
5280 id="x1-910006.2"></a>Floor 0 format</h4>
5281 <!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
5282 coding/decoding the LSP filter coefficient values used by each frame.
5283 <!--l. 24--><p class="noindent" >
5284 <h5 class="subsubsectionHead"><span class="titlemark">6.2.1. </span> <a
5285 id="x1-920006.2.1"></a>header decode</h5>
5286 <!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
5287 packet). configuration decode proceeds as follows:
5288 <!--l. 30--><p class="noindent" >
5289 <div class="fancyvrb" id="fancyvrb26">
5291 id="x1-92002r1"></a><span
5292 class="cmr-6">1</span><span
5293 class="cmtt-8"> </span><span
5294 class="cmtt-8"> </span><span
5295 class="cmtt-8"> </span><span
5296 class="cmtt-8"> 1)</span><span
5297 class="cmtt-8"> [floor0_order]</span><span
5298 class="cmtt-8"> =</span><span
5299 class="cmtt-8"> read</span><span
5300 class="cmtt-8"> an</span><span
5301 class="cmtt-8"> unsigned</span><span
5302 class="cmtt-8"> integer</span><span
5303 class="cmtt-8"> of</span><span
5304 class="cmtt-8"> 8</span><span
5305 class="cmtt-8"> bits</span>
5306 <br class="fancyvrb" /><a
5307 id="x1-92004r2"></a><span
5308 class="cmr-6">2</span><span
5309 class="cmtt-8"> </span><span
5310 class="cmtt-8"> </span><span
5311 class="cmtt-8"> </span><span
5312 class="cmtt-8"> 2)</span><span
5313 class="cmtt-8"> [floor0_rate]</span><span
5314 class="cmtt-8"> =</span><span
5315 class="cmtt-8"> read</span><span
5316 class="cmtt-8"> an</span><span
5317 class="cmtt-8"> unsigned</span><span
5318 class="cmtt-8"> integer</span><span
5319 class="cmtt-8"> of</span><span
5320 class="cmtt-8"> 16</span><span
5321 class="cmtt-8"> bits</span>
5322 <br class="fancyvrb" /><a
5323 id="x1-92006r3"></a><span
5324 class="cmr-6">3</span><span
5325 class="cmtt-8"> </span><span
5326 class="cmtt-8"> </span><span
5327 class="cmtt-8"> </span><span
5328 class="cmtt-8"> 3)</span><span
5329 class="cmtt-8"> [floor0_bark_map_size]</span><span
5330 class="cmtt-8"> =</span><span
5331 class="cmtt-8"> read</span><span
5332 class="cmtt-8"> an</span><span
5333 class="cmtt-8"> unsigned</span><span
5334 class="cmtt-8"> integer</span><span
5335 class="cmtt-8"> of</span><span
5336 class="cmtt-8"> 16</span><span
5337 class="cmtt-8"> bits</span>
5338 <br class="fancyvrb" /><a
5339 id="x1-92008r4"></a><span
5340 class="cmr-6">4</span><span
5341 class="cmtt-8"> </span><span
5342 class="cmtt-8"> </span><span
5343 class="cmtt-8"> </span><span
5344 class="cmtt-8"> 4)</span><span
5345 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5346 class="cmtt-8"> =</span><span
5347 class="cmtt-8"> read</span><span
5348 class="cmtt-8"> an</span><span
5349 class="cmtt-8"> unsigned</span><span
5350 class="cmtt-8"> integer</span><span
5351 class="cmtt-8"> of</span><span
5352 class="cmtt-8"> six</span><span
5353 class="cmtt-8"> bits</span>
5354 <br class="fancyvrb" /><a
5355 id="x1-92010r5"></a><span
5356 class="cmr-6">5</span><span
5357 class="cmtt-8"> </span><span
5358 class="cmtt-8"> </span><span
5359 class="cmtt-8"> </span><span
5360 class="cmtt-8"> 5)</span><span
5361 class="cmtt-8"> [floor0_amplitude_offset]</span><span
5362 class="cmtt-8"> =</span><span
5363 class="cmtt-8"> read</span><span
5364 class="cmtt-8"> an</span><span
5365 class="cmtt-8"> unsigned</span><span
5366 class="cmtt-8"> integer</span><span
5367 class="cmtt-8"> of</span><span
5368 class="cmtt-8"> eight</span><span
5369 class="cmtt-8"> bits</span>
5370 <br class="fancyvrb" /><a
5371 id="x1-92012r6"></a><span
5372 class="cmr-6">6</span><span
5373 class="cmtt-8"> </span><span
5374 class="cmtt-8"> </span><span
5375 class="cmtt-8"> </span><span
5376 class="cmtt-8"> 6)</span><span
5377 class="cmtt-8"> [floor0_number_of_books]</span><span
5378 class="cmtt-8"> =</span><span
5379 class="cmtt-8"> read</span><span
5380 class="cmtt-8"> an</span><span
5381 class="cmtt-8"> unsigned</span><span
5382 class="cmtt-8"> integer</span><span
5383 class="cmtt-8"> of</span><span
5384 class="cmtt-8"> four</span><span
5385 class="cmtt-8"> bits</span><span
5386 class="cmtt-8"> and</span><span
5387 class="cmtt-8"> add</span><span
5388 class="cmtt-8"> 1</span>
5389 <br class="fancyvrb" /><a
5390 id="x1-92014r7"></a><span
5391 class="cmr-6">7</span><span
5392 class="cmtt-8"> </span><span
5393 class="cmtt-8"> </span><span
5394 class="cmtt-8"> </span><span
5395 class="cmtt-8"> 7)</span><span
5396 class="cmtt-8"> array</span><span
5397 class="cmtt-8"> [floor0_book_list]</span><span
5398 class="cmtt-8"> =</span><span
5399 class="cmtt-8"> read</span><span
5400 class="cmtt-8"> a</span><span
5401 class="cmtt-8"> list</span><span
5402 class="cmtt-8"> of</span><span
5403 class="cmtt-8"> [floor0_number_of_books]</span><span
5404 class="cmtt-8"> unsigned</span><span
5405 class="cmtt-8"> integers</span><span
5406 class="cmtt-8"> of</span><span
5407 class="cmtt-8"> eight</span><span
5408 class="cmtt-8"> bits</span><span
5409 class="cmtt-8"> each;</span>
5414 <!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
5415 In addition, any element of the array <span
5416 class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum
5417 codebook number for this bitstream is an error condition that also renders the stream
5419 <!--l. 48--><p class="noindent" >
5420 <h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a
5421 id="x1-930006.2.2"></a>packet decode</h5>
5422 <!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve
5424 class="cmtt-12">[floor0_order] </span>LSP coefficient values from the bitstream, and then
5425 computing the floor curve, which is defined as the frequency response of the decoded LSP
5427 <!--l. 56--><p class="noindent" >Packet decode proceeds as follows:
5428 <div class="fancyvrb" id="fancyvrb27">
5430 id="x1-93002r1"></a><span
5431 class="cmr-6">1</span><span
5432 class="cmtt-8"> </span><span
5433 class="cmtt-8"> </span><span
5434 class="cmtt-8"> </span><span
5435 class="cmtt-8"> 1)</span><span
5436 class="cmtt-8"> [amplitude]</span><span
5437 class="cmtt-8"> =</span><span
5438 class="cmtt-8"> read</span><span
5439 class="cmtt-8"> an</span><span
5440 class="cmtt-8"> unsigned</span><span
5441 class="cmtt-8"> integer</span><span
5442 class="cmtt-8"> of</span><span
5443 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5444 class="cmtt-8"> bits</span>
5445 <br class="fancyvrb" /><a
5446 id="x1-93004r2"></a><span
5447 class="cmr-6">2</span><span
5448 class="cmtt-8"> </span><span
5449 class="cmtt-8"> </span><span
5450 class="cmtt-8"> </span><span
5451 class="cmtt-8"> 2)</span><span
5452 class="cmtt-8"> if</span><span
5453 class="cmtt-8"> (</span><span
5454 class="cmtt-8"> [amplitude]</span><span
5455 class="cmtt-8"> is</span><span
5456 class="cmtt-8"> greater</span><span
5457 class="cmtt-8"> than</span><span
5458 class="cmtt-8"> zero</span><span
5459 class="cmtt-8"> )</span><span
5460 class="cmtt-8"> </span><span
5461 class="cmsy-8">{</span>
5462 <br class="fancyvrb" /><a
5463 id="x1-93006r3"></a><span
5464 class="cmr-6">3</span><span
5465 class="cmtt-8"> </span><span
5466 class="cmtt-8"> </span><span
5467 class="cmtt-8"> </span><span
5468 class="cmtt-8"> </span><span
5469 class="cmtt-8"> </span><span
5470 class="cmtt-8"> </span><span
5471 class="cmtt-8"> </span><span
5472 class="cmtt-8"> </span><span
5473 class="cmtt-8"> 3)</span><span
5474 class="cmtt-8"> [coefficients]</span><span
5475 class="cmtt-8"> is</span><span
5476 class="cmtt-8"> an</span><span
5477 class="cmtt-8"> empty,</span><span
5478 class="cmtt-8"> zero</span><span
5479 class="cmtt-8"> length</span><span
5480 class="cmtt-8"> vector</span>
5481 <br class="fancyvrb" /><a
5482 id="x1-93008r4"></a><span
5483 class="cmr-6">4</span><span
5484 class="cmtt-8"> </span><span
5485 class="cmtt-8"> </span><span
5486 class="cmtt-8"> </span><span
5487 class="cmtt-8"> </span><span
5488 class="cmtt-8"> </span><span
5489 class="cmtt-8"> </span><span
5490 class="cmtt-8"> </span><span
5491 class="cmtt-8"> </span><span
5492 class="cmtt-8"> 4)</span><span
5493 class="cmtt-8"> [booknumber]</span><span
5494 class="cmtt-8"> =</span><span
5495 class="cmtt-8"> read</span><span
5496 class="cmtt-8"> an</span><span
5497 class="cmtt-8"> unsigned</span><span
5498 class="cmtt-8"> integer</span><span
5499 class="cmtt-8"> of</span><span
5500 class="cmtt-8"> </span><a
5501 href="#x1-1170009.2.1"><span
5502 class="cmtt-8">ilog</span></a><span
5503 class="cmtt-8">(</span><span
5504 class="cmtt-8"> [floor0_number_of_books]</span><span
5505 class="cmtt-8"> )</span><span
5506 class="cmtt-8"> bits</span>
5507 <br class="fancyvrb" /><a
5508 id="x1-93010r5"></a><span
5509 class="cmr-6">5</span><span
5510 class="cmtt-8"> </span><span
5511 class="cmtt-8"> </span><span
5512 class="cmtt-8"> </span><span
5513 class="cmtt-8"> </span><span
5514 class="cmtt-8"> </span><span
5515 class="cmtt-8"> </span><span
5516 class="cmtt-8"> </span><span
5517 class="cmtt-8"> </span><span
5518 class="cmtt-8"> 5)</span><span
5519 class="cmtt-8"> if</span><span
5520 class="cmtt-8"> (</span><span
5521 class="cmtt-8"> [booknumber]</span><span
5522 class="cmtt-8"> is</span><span
5523 class="cmtt-8"> greater</span><span
5524 class="cmtt-8"> than</span><span
5525 class="cmtt-8"> the</span><span
5526 class="cmtt-8"> highest</span><span
5527 class="cmtt-8"> number</span><span
5528 class="cmtt-8"> decode</span><span
5529 class="cmtt-8"> codebook</span><span
5530 class="cmtt-8"> )</span><span
5531 class="cmtt-8"> then</span><span
5532 class="cmtt-8"> packet</span><span
5533 class="cmtt-8"> is</span><span
5534 class="cmtt-8"> undecodable</span>
5535 <br class="fancyvrb" /><a
5536 id="x1-93012r6"></a><span
5537 class="cmr-6">6</span><span
5538 class="cmtt-8"> </span><span
5539 class="cmtt-8"> </span><span
5540 class="cmtt-8"> </span><span
5541 class="cmtt-8"> </span><span
5542 class="cmtt-8"> </span><span
5543 class="cmtt-8"> </span><span
5544 class="cmtt-8"> </span><span
5545 class="cmtt-8"> </span><span
5546 class="cmtt-8"> 6)</span><span
5547 class="cmtt-8"> [last]</span><span
5548 class="cmtt-8"> =</span><span
5549 class="cmtt-8"> zero;</span>
5550 <br class="fancyvrb" /><a
5551 id="x1-93014r7"></a><span
5552 class="cmr-6">7</span><span
5553 class="cmtt-8"> </span><span
5554 class="cmtt-8"> </span><span
5555 class="cmtt-8"> </span><span
5556 class="cmtt-8"> </span><span
5557 class="cmtt-8"> </span><span
5558 class="cmtt-8"> </span><span
5559 class="cmtt-8"> </span><span
5560 class="cmtt-8"> </span><span
5561 class="cmtt-8"> 7)</span><span
5562 class="cmtt-8"> vector</span><span
5563 class="cmtt-8"> [temp_vector]</span><span
5564 class="cmtt-8"> =</span><span
5565 class="cmtt-8"> read</span><span
5566 class="cmtt-8"> vector</span><span
5567 class="cmtt-8"> from</span><span
5568 class="cmtt-8"> bitstream</span><span
5569 class="cmtt-8"> using</span><span
5570 class="cmtt-8"> codebook</span><span
5571 class="cmtt-8"> number</span><span
5572 class="cmtt-8"> [floor0_book_list]</span><span
5573 class="cmtt-8"> element</span><span
5574 class="cmtt-8"> [booknumber]</span><span
5575 class="cmtt-8"> in</span><span
5576 class="cmtt-8"> VQ</span><span
5577 class="cmtt-8"> context.</span>
5578 <br class="fancyvrb" /><a
5579 id="x1-93016r8"></a><span
5580 class="cmr-6">8</span><span
5581 class="cmtt-8"> </span><span
5582 class="cmtt-8"> </span><span
5583 class="cmtt-8"> </span><span
5584 class="cmtt-8"> </span><span
5585 class="cmtt-8"> </span><span
5586 class="cmtt-8"> </span><span
5587 class="cmtt-8"> </span><span
5588 class="cmtt-8"> </span><span
5589 class="cmtt-8"> 8)</span><span
5590 class="cmtt-8"> add</span><span
5591 class="cmtt-8"> the</span><span
5592 class="cmtt-8"> scalar</span><span
5593 class="cmtt-8"> value</span><span
5594 class="cmtt-8"> [last]</span><span
5595 class="cmtt-8"> to</span><span
5596 class="cmtt-8"> each</span><span
5597 class="cmtt-8"> scalar</span><span
5598 class="cmtt-8"> in</span><span
5599 class="cmtt-8"> vector</span><span
5600 class="cmtt-8"> [temp_vector]</span>
5601 <br class="fancyvrb" /><a
5602 id="x1-93018r9"></a><span
5603 class="cmr-6">9</span><span
5604 class="cmtt-8"> </span><span
5605 class="cmtt-8"> </span><span
5606 class="cmtt-8"> </span><span
5607 class="cmtt-8"> </span><span
5608 class="cmtt-8"> </span><span
5609 class="cmtt-8"> </span><span
5610 class="cmtt-8"> </span><span
5611 class="cmtt-8"> </span><span
5612 class="cmtt-8"> 9)</span><span
5613 class="cmtt-8"> [last]</span><span
5614 class="cmtt-8"> =</span><span
5615 class="cmtt-8"> the</span><span
5616 class="cmtt-8"> value</span><span
5617 class="cmtt-8"> of</span><span
5618 class="cmtt-8"> the</span><span
5619 class="cmtt-8"> last</span><span
5620 class="cmtt-8"> scalar</span><span
5621 class="cmtt-8"> in</span><span
5622 class="cmtt-8"> vector</span><span
5623 class="cmtt-8"> [temp_vector]</span>
5624 <br class="fancyvrb" /><a
5625 id="x1-93020r10"></a><span
5626 class="cmr-6">10</span><span
5627 class="cmtt-8"> </span><span
5628 class="cmtt-8"> </span><span
5629 class="cmtt-8"> </span><span
5630 class="cmtt-8"> </span><span
5631 class="cmtt-8"> </span><span
5632 class="cmtt-8"> </span><span
5633 class="cmtt-8"> </span><span
5634 class="cmtt-8"> 10)</span><span
5635 class="cmtt-8"> concatenate</span><span
5636 class="cmtt-8"> [temp_vector]</span><span
5637 class="cmtt-8"> onto</span><span
5638 class="cmtt-8"> the</span><span
5639 class="cmtt-8"> end</span><span
5640 class="cmtt-8"> of</span><span
5641 class="cmtt-8"> the</span><span
5642 class="cmtt-8"> [coefficients]</span><span
5643 class="cmtt-8"> vector</span>
5644 <br class="fancyvrb" /><a
5645 id="x1-93022r11"></a><span
5646 class="cmr-6">11</span><span
5647 class="cmtt-8"> </span><span
5648 class="cmtt-8"> </span><span
5649 class="cmtt-8"> </span><span
5650 class="cmtt-8"> </span><span
5651 class="cmtt-8"> </span><span
5652 class="cmtt-8"> </span><span
5653 class="cmtt-8"> </span><span
5654 class="cmtt-8"> 11)</span><span
5655 class="cmtt-8"> if</span><span
5656 class="cmtt-8"> (length</span><span
5657 class="cmtt-8"> of</span><span
5658 class="cmtt-8"> vector</span><span
5659 class="cmtt-8"> [coefficients]</span><span
5660 class="cmtt-8"> is</span><span
5661 class="cmtt-8"> less</span><span
5662 class="cmtt-8"> than</span><span
5663 class="cmtt-8"> [floor0_order],</span><span
5664 class="cmtt-8"> continue</span><span
5665 class="cmtt-8"> at</span><span
5666 class="cmtt-8"> step</span><span
5667 class="cmtt-8"> 6</span>
5668 <br class="fancyvrb" /><a
5669 id="x1-93024r12"></a><span
5670 class="cmr-6">12</span><span
5671 class="cmtt-8"> </span><span
5672 class="cmtt-8"> </span>
5673 <br class="fancyvrb" /><a
5674 id="x1-93026r13"></a><span
5675 class="cmr-6">13</span><span
5676 class="cmtt-8"> </span><span
5677 class="cmtt-8"> </span><span
5678 class="cmtt-8"> </span><span
5679 class="cmtt-8"> </span><span
5680 class="cmtt-8"> </span><span
5681 class="cmtt-8"> </span><span
5682 class="cmtt-8"> </span><span
5683 class="cmsy-8">}</span>
5684 <br class="fancyvrb" /><a
5685 id="x1-93028r14"></a><span
5686 class="cmr-6">14</span><span
5687 class="cmtt-8"> </span><span
5688 class="cmtt-8"> </span>
5689 <br class="fancyvrb" /><a
5690 id="x1-93030r15"></a><span
5691 class="cmr-6">15</span><span
5692 class="cmtt-8"> </span><span
5693 class="cmtt-8"> </span><span
5694 class="cmtt-8"> 12)</span><span
5695 class="cmtt-8"> done.</span>
5696 <br class="fancyvrb" /><a
5697 id="x1-93032r16"></a><span
5698 class="cmr-6">16</span><span
5699 class="cmtt-8"> </span><span
5700 class="cmtt-8"> </span>
5702 <!--l. 76--><p class="noindent" >Take note of the following properties of decode:
5703 <ul class="itemize1">
5704 <li class="itemize">An <span
5705 class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
5706 is unused in this frame (the output of the channel will be all-zeroes in synthesis).
5707 Several later stages of decode don’t occur for an unused channel.
5709 <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
5710 if end-of-packet is reached during any read operation above, floor decode is to return
5711 ’unused’ status as if the <span
5712 class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
5714 <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
5715 href="#x1-1170009.2.1">ilog</a>(
5720 class="cmtt-12">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
5721 and values greater than the maximum possible book value are reserved.
5723 <li class="itemize">The number of scalars read into the vector <span
5724 class="cmtt-12">[coefficients] </span>may be greater
5726 class="cmtt-12">[floor0_order]</span>, the number actually required for curve computation. For
5727 example, if the VQ codebook used for the floor currently being decoded has a
5729 class="cmtt-12">[codebook_dimensions] </span>value of three and <span
5730 class="cmtt-12">[floor0_order] </span>is ten, the only way to
5731 fill all the needed scalars in <span
5732 class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
5733 as four vectors of three scalars each. This is not an error condition, and care must
5734 be taken not to allow a buffer overflow in decode. The extra values are not used and
5735 may be ignored or discarded.</li></ul>
5736 <!--l. 104--><p class="noindent" >
5737 <h5 class="subsubsectionHead"><span class="titlemark">6.2.3. </span> <a
5738 id="x1-940006.2.3"></a>curve computation</h5>
5739 <!--l. 106--><p class="noindent" >Given an <span
5740 class="cmtt-12">[amplitude] </span>integer and <span
5741 class="cmtt-12">[coefficients] </span>vector from packet decode as well as
5742 the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and
5743 [floor0_amplitude_offset] values from floor setup, and an output vector size <span
5744 class="cmtt-12">[n] </span>specified by the
5745 decode process, we compute a floor output vector.
5746 <!--l. 113--><p class="noindent" >If the value <span
5747 class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span
5748 class="cmtt-12">[n] </span>vector with all-zero
5749 scalars. Otherwise, begin by assuming the following definitions for the given vector to be
5751 <center class="par-math-display" >
5753 src="Vorbis_I_spec7x.png" alt=" {
5754 min (floor0_bark_map_size − 1,foobar ) for i ∈ [0,n − 1 ]
5755 mapi = − 1 for i = n
5756 " class="par-math-display" ></center>
5757 <!--l. 128--><p class="nopar" >
5758 <!--l. 130--><p class="noindent" >where
5759 <center class="par-math-display" >
5761 src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋
5762 (floor0_rate ⋅ i) floor0_bark_map_size
5763 foobar = bark -------2n------- ⋅-bark(.5 ⋅ floor0_rate-)
5764 " class="par-math-display" ></center>
5768 <!--l. 137--><p class="nopar" >
5769 <!--l. 139--><p class="noindent" >and
5770 <center class="par-math-display" >
5772 src="Vorbis_I_spec9x.png" alt=" 2
5773 bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x )
5774 " class="par-math-display" ></center>
5775 <!--l. 143--><p class="nopar" >
5776 <!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
5777 result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
5779 class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
5781 <!--l. 151--><p class="noindent" >
5782 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5784 class="enumerate-enumitem"><span
5785 class="cmtt-12">[i] </span>= 0
5786 </dd><dt class="enumerate-enumitem">
5788 class="enumerate-enumitem"><span
5789 class="cmtt-12">[</span><span
5790 class="cmmi-12">ω</span><span
5791 class="cmtt-12">] </span>= <span
5792 class="cmmi-12">π </span>* map element <span
5793 class="cmtt-12">[i] </span>/ <span
5794 class="cmtt-12">[floor0_bark_map_size]</span>
5795 </dd><dt class="enumerate-enumitem">
5797 class="enumerate-enumitem">if ( <span
5798 class="cmtt-12">[floor0_order] </span>is odd )
5799 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5801 class="enumerate-enumitem">calculate <span
5802 class="cmtt-12">[p] </span>and <span
5803 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5804 <center class="math-display" >
5806 src="Vorbis_I_spec10x.png" alt=" floor0_order−3
5808 p = (1 − cos ω) 4(cos([coefficients ]2j+1) − cosω )
5809 floor0_order−1 j=0
5811 q = -- 4(cos([coefficients ]2j) − cosω )2
5816 " class="math-display" ></center>
5819 <!--l. 162--><p class="noindent" >else <span
5820 class="cmtt-12">[floor0_order] </span>is even
5821 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5823 class="enumerate-enumitem">calculate <span
5824 class="cmtt-12">[p] </span>and <span
5825 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5826 <center class="math-display" >
5828 src="Vorbis_I_spec11x.png" alt=" floor0_order−2
5829 (1-−-cosω-) ∏2 2
5830 p = 2 4(cos([coefficients ]2j+1) − cosω)
5832 floor0_∏o2rder−-2
5833 q = (1-+-cosω-) 4(cos([coefficients ]2j) − cos ω)2
5835 " class="math-display" ></center>
5838 </dd><dt class="enumerate-enumitem">
5840 class="enumerate-enumitem">calculate <span
5841 class="cmtt-12">[linear_floor_value] </span>according to:
5842 <center class="math-display" >
5844 src="Vorbis_I_spec12x.png" alt=" ( ( ))
5845 exp .11512925 amplitude---⋅ floor0_amplitute_√offset---− floor0_amplitude_offset
5846 (2floor0_amplitude_bits − 1) p + q
5847 " class="math-display" ></center>
5848 <!--l. 177--><p class="nopar" >
5849 </dd><dt class="enumerate-enumitem">
5851 class="enumerate-enumitem"><span
5852 class="cmtt-12">[iteration_condition] </span>= map element <span
5853 class="cmtt-12">[i]</span>
5857 </dd><dt class="enumerate-enumitem">
5859 class="enumerate-enumitem"><span
5860 class="cmtt-12">[output] </span>element <span
5861 class="cmtt-12">[i] </span>= <span
5862 class="cmtt-12">[linear_floor_value]</span>
5863 </dd><dt class="enumerate-enumitem">
5865 class="enumerate-enumitem">increment <span
5866 class="cmtt-12">[i]</span>
5867 </dd><dt class="enumerate-enumitem">
5869 class="enumerate-enumitem">if ( map element <span
5870 class="cmtt-12">[i] </span>is equal to <span
5871 class="cmtt-12">[iteration_condition] </span>) continue at step
5873 </dd><dt class="enumerate-enumitem">
5875 class="enumerate-enumitem">if ( <span
5876 class="cmtt-12">[i] </span>is less than <span
5877 class="cmtt-12">[n] </span>) continue at step 2
5878 </dd><dt class="enumerate-enumitem">
5880 class="enumerate-enumitem">done</dd></dl>
5887 <h3 class="sectionHead"><span class="titlemark">7. </span> <a
5888 id="x1-950007"></a>Floor type 1 setup and decode</h3>
5889 <!--l. 6--><p class="noindent" >
5890 <h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a
5891 id="x1-960007.1"></a>Overview</h4>
5892 <!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
5893 curve. The representation plots this curve mechanically on a linear frequency axis and a
5894 logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
5896 <!--l. 16--><p class="noindent" >
5897 <h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a
5898 id="x1-970007.2"></a>Floor 1 format</h4>
5899 <!--l. 18--><p class="noindent" >
5900 <h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a
5901 id="x1-980007.2.1"></a>model</h5>
5902 <!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
5903 floor curve using iterative prediction in a process roughly equivalent to the following simplified
5905 <ul class="itemize1">
5906 <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
5907 where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
5910 <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
5911 produces a y˙new value at that point computed from the existing line’s y value at
5912 x˙new (as plotted by the line) and a difference value decoded from the bitstream
5918 <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
5919 x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
5920 y˙new represents no change to the amplitude value at x˙new so that later refinement
5921 is additionally bounded at x˙new.
5923 <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
5924 at floor 1 initialization time. Computation is completed at the end of the x value list.
5926 <!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
5927 representing typical configuration:
5928 <!--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
5929 in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
5930 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
5931 example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
5932 way, beginning with the first line:
5935 <!--l. 59--><p class="noindent" >
5937 <!--l. 60--><p class="noindent" ><img
5938 src="floor1-1.png" alt="PIC"
5940 <br /> <div class="caption"
5941 ><span class="id">Figure 7: </span><span
5942 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980017 -->
5944 <!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
5948 <!--l. 67--><p class="noindent" >
5950 <!--l. 68--><p class="noindent" ><img
5951 src="floor1-2.png" alt="PIC"
5953 <br /> <div class="caption"
5954 ><span class="id">Figure 8: </span><span
5955 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980028 -->
5957 <!--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
5958 further refinement. From here on, the pattern should be clear; we complete the floor computation
5965 <!--l. 76--><p class="noindent" >
5967 <!--l. 77--><p class="noindent" ><img
5968 src="floor1-3.png" alt="PIC"
5970 <br /> <div class="caption"
5971 ><span class="id">Figure 9: </span><span
5972 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980039 -->
5976 <!--l. 81--><p class="noindent" >
5978 <!--l. 82--><p class="noindent" ><img
5979 src="floor1-4.png" alt="PIC"
5981 <br /> <div class="caption"
5982 ><span class="id">Figure 10: </span><span
5983 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-9800410 -->
5985 <!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
5986 decode, as described later. The actual algorithm splits Y value computation and line plotting
5987 into two steps with modifications to the above algorithm to eliminate noise accumulation
5988 through integer roundoff/truncation.
5989 <!--l. 94--><p class="noindent" >
5990 <h5 class="subsubsectionHead"><span class="titlemark">7.2.2. </span> <a
5991 id="x1-990007.2.2"></a>header decode</h5>
5992 <!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
5993 during packet decode and synthesis). This list is split into partitions, and each partition is
5994 assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
5995 partition or partition class.
5996 <!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
5997 the partition class encodes at once), a ’subclass’ value representing the number of
5998 alternate entropy books the partition class may use in representing Y values, the list of
5999 [subclass] books and a master book used to encode which alternate books were chosen
6000 for representation in a given packet. The master/subclass mechanism is meant to be
6001 used as a flexible representation cascade while still using codebooks only in a scalar
6006 <!--l. 112--><p class="noindent" >
6007 <div class="fancyvrb" id="fancyvrb28">
6009 id="x1-99002r1"></a><span
6010 class="cmr-6">1</span><span
6011 class="cmtt-8"> </span><span
6012 class="cmtt-8"> </span>
6013 <br class="fancyvrb" /><a
6014 id="x1-99004r2"></a><span
6015 class="cmr-6">2</span><span
6016 class="cmtt-8"> </span><span
6017 class="cmtt-8"> </span><span
6018 class="cmtt-8"> </span><span
6019 class="cmtt-8"> 1)</span><span
6020 class="cmtt-8"> [floor1_partitions]</span><span
6021 class="cmtt-8"> =</span><span
6022 class="cmtt-8"> read</span><span
6023 class="cmtt-8"> 5</span><span
6024 class="cmtt-8"> bits</span><span
6025 class="cmtt-8"> as</span><span
6026 class="cmtt-8"> unsigned</span><span
6027 class="cmtt-8"> integer</span>
6028 <br class="fancyvrb" /><a
6029 id="x1-99006r3"></a><span
6030 class="cmr-6">3</span><span
6031 class="cmtt-8"> </span><span
6032 class="cmtt-8"> </span><span
6033 class="cmtt-8"> </span><span
6034 class="cmtt-8"> 2)</span><span
6035 class="cmtt-8"> [maximum_class]</span><span
6036 class="cmtt-8"> =</span><span
6037 class="cmtt-8"> -1</span>
6038 <br class="fancyvrb" /><a
6039 id="x1-99008r4"></a><span
6040 class="cmr-6">4</span><span
6041 class="cmtt-8"> </span><span
6042 class="cmtt-8"> </span><span
6043 class="cmtt-8"> </span><span
6044 class="cmtt-8"> 3)</span><span
6045 class="cmtt-8"> iterate</span><span
6046 class="cmtt-8"> [i]</span><span
6047 class="cmtt-8"> over</span><span
6048 class="cmtt-8"> the</span><span
6049 class="cmtt-8"> range</span><span
6050 class="cmtt-8"> 0</span><span
6051 class="cmtt-8"> ...</span><span
6052 class="cmtt-8"> [floor1_partitions]-1</span><span
6053 class="cmtt-8"> </span><span
6054 class="cmsy-8">{</span>
6055 <br class="fancyvrb" /><a
6056 id="x1-99010r5"></a><span
6057 class="cmr-6">5</span><span
6058 class="cmtt-8"> </span><span
6059 class="cmtt-8"> </span>
6060 <br class="fancyvrb" /><a
6061 id="x1-99012r6"></a><span
6062 class="cmr-6">6</span><span
6063 class="cmtt-8"> </span><span
6064 class="cmtt-8"> </span><span
6065 class="cmtt-8"> </span><span
6066 class="cmtt-8"> </span><span
6067 class="cmtt-8"> </span><span
6068 class="cmtt-8"> </span><span
6069 class="cmtt-8"> </span><span
6070 class="cmtt-8"> </span><span
6071 class="cmtt-8"> </span><span
6072 class="cmtt-8"> 4)</span><span
6073 class="cmtt-8"> vector</span><span
6074 class="cmtt-8"> [floor1_partition_class_list]</span><span
6075 class="cmtt-8"> element</span><span
6076 class="cmtt-8"> [i]</span><span
6077 class="cmtt-8"> =</span><span
6078 class="cmtt-8"> read</span><span
6079 class="cmtt-8"> 4</span><span
6080 class="cmtt-8"> bits</span><span
6081 class="cmtt-8"> as</span><span
6082 class="cmtt-8"> unsigned</span><span
6083 class="cmtt-8"> integer</span>
6084 <br class="fancyvrb" /><a
6085 id="x1-99014r7"></a><span
6086 class="cmr-6">7</span><span
6087 class="cmtt-8"> </span><span
6088 class="cmtt-8"> </span>
6089 <br class="fancyvrb" /><a
6090 id="x1-99016r8"></a><span
6091 class="cmr-6">8</span><span
6092 class="cmtt-8"> </span><span
6093 class="cmtt-8"> </span><span
6094 class="cmtt-8"> </span><span
6095 class="cmtt-8"> </span><span
6096 class="cmtt-8"> </span><span
6097 class="cmtt-8"> </span><span
6098 class="cmtt-8"> </span><span
6099 class="cmsy-8">}</span>
6100 <br class="fancyvrb" /><a
6101 id="x1-99018r9"></a><span
6102 class="cmr-6">9</span><span
6103 class="cmtt-8"> </span><span
6104 class="cmtt-8"> </span>
6105 <br class="fancyvrb" /><a
6106 id="x1-99020r10"></a><span
6107 class="cmr-6">10</span><span
6108 class="cmtt-8"> </span><span
6109 class="cmtt-8"> </span><span
6110 class="cmtt-8"> </span><span
6111 class="cmtt-8"> 5)</span><span
6112 class="cmtt-8"> [maximum_class]</span><span
6113 class="cmtt-8"> =</span><span
6114 class="cmtt-8"> largest</span><span
6115 class="cmtt-8"> integer</span><span
6116 class="cmtt-8"> scalar</span><span
6117 class="cmtt-8"> value</span><span
6118 class="cmtt-8"> in</span><span
6119 class="cmtt-8"> vector</span><span
6120 class="cmtt-8"> [floor1_partition_class_list]</span>
6121 <br class="fancyvrb" /><a
6122 id="x1-99022r11"></a><span
6123 class="cmr-6">11</span><span
6124 class="cmtt-8"> </span><span
6125 class="cmtt-8"> </span><span
6126 class="cmtt-8"> </span><span
6127 class="cmtt-8"> 6)</span><span
6128 class="cmtt-8"> iterate</span><span
6129 class="cmtt-8"> [i]</span><span
6130 class="cmtt-8"> over</span><span
6131 class="cmtt-8"> the</span><span
6132 class="cmtt-8"> range</span><span
6133 class="cmtt-8"> 0</span><span
6134 class="cmtt-8"> ...</span><span
6135 class="cmtt-8"> [maximum_class]</span><span
6136 class="cmtt-8"> </span><span
6137 class="cmsy-8">{</span>
6138 <br class="fancyvrb" /><a
6139 id="x1-99024r12"></a><span
6140 class="cmr-6">12</span><span
6141 class="cmtt-8"> </span><span
6142 class="cmtt-8"> </span>
6143 <br class="fancyvrb" /><a
6144 id="x1-99026r13"></a><span
6145 class="cmr-6">13</span><span
6146 class="cmtt-8"> </span><span
6147 class="cmtt-8"> </span><span
6148 class="cmtt-8"> </span><span
6149 class="cmtt-8"> </span><span
6150 class="cmtt-8"> </span><span
6151 class="cmtt-8"> </span><span
6152 class="cmtt-8"> </span><span
6153 class="cmtt-8"> </span><span
6154 class="cmtt-8"> </span><span
6155 class="cmtt-8"> 7)</span><span
6156 class="cmtt-8"> vector</span><span
6157 class="cmtt-8"> [floor1_class_dimensions]</span><span
6158 class="cmtt-8"> element</span><span
6159 class="cmtt-8"> [i]</span><span
6160 class="cmtt-8"> =</span><span
6161 class="cmtt-8"> read</span><span
6162 class="cmtt-8"> 3</span><span
6163 class="cmtt-8"> bits</span><span
6164 class="cmtt-8"> as</span><span
6165 class="cmtt-8"> unsigned</span><span
6166 class="cmtt-8"> integer</span><span
6167 class="cmtt-8"> and</span><span
6168 class="cmtt-8"> add</span><span
6169 class="cmtt-8"> 1</span>
6170 <br class="fancyvrb" /><a
6171 id="x1-99028r14"></a><span
6172 class="cmr-6">14</span><span
6173 class="cmtt-8"> </span><span
6174 class="cmtt-8">  8)</span><span
6175 class="cmtt-8"> vector</span><span
6176 class="cmtt-8"> [floor1_class_subclasses]</span><span
6177 class="cmtt-8"> element</span><span
6178 class="cmtt-8"> [i]</span><span
6179 class="cmtt-8"> =</span><span
6180 class="cmtt-8"> read</span><span
6181 class="cmtt-8"> 2</span><span
6182 class="cmtt-8"> bits</span><span
6183 class="cmtt-8"> as</span><span
6184 class="cmtt-8"> unsigned</span><span
6185 class="cmtt-8"> integer</span>
6186 <br class="fancyvrb" /><a
6187 id="x1-99030r15"></a><span
6188 class="cmr-6">15</span><span
6189 class="cmtt-8"> </span><span
6190 class="cmtt-8"> </span><span
6191 class="cmtt-8"> </span><span
6192 class="cmtt-8"> </span><span
6193 class="cmtt-8"> </span><span
6194 class="cmtt-8"> </span><span
6195 class="cmtt-8"> </span><span
6196 class="cmtt-8"> </span><span
6197 class="cmtt-8"> </span><span
6198 class="cmtt-8"> 9)</span><span
6199 class="cmtt-8"> if</span><span
6200 class="cmtt-8"> (</span><span
6201 class="cmtt-8"> vector</span><span
6202 class="cmtt-8"> [floor1_class_subclasses]</span><span
6203 class="cmtt-8"> element</span><span
6204 class="cmtt-8"> [i]</span><span
6205 class="cmtt-8"> is</span><span
6206 class="cmtt-8"> nonzero</span><span
6207 class="cmtt-8"> )</span><span
6208 class="cmtt-8"> </span><span
6209 class="cmsy-8">{</span>
6210 <br class="fancyvrb" /><a
6211 id="x1-99032r16"></a><span
6212 class="cmr-6">16</span><span
6213 class="cmtt-8"> </span><span
6214 class="cmtt-8"> </span>
6215 <br class="fancyvrb" /><a
6216 id="x1-99034r17"></a><span
6217 class="cmr-6">17</span><span
6218 class="cmtt-8"> </span><span
6219 class="cmtt-8"> </span><span
6220 class="cmtt-8"> </span><span
6221 class="cmtt-8"> </span><span
6222 class="cmtt-8"> </span><span
6223 class="cmtt-8"> </span><span
6224 class="cmtt-8"> </span><span
6225 class="cmtt-8"> </span><span
6226 class="cmtt-8"> </span><span
6227 class="cmtt-8"> </span><span
6228 class="cmtt-8"> </span><span
6229 class="cmtt-8"> </span><span
6230 class="cmtt-8"> </span><span
6231 class="cmtt-8"> </span><span
6232 class="cmtt-8"> 10)</span><span
6233 class="cmtt-8"> vector</span><span
6234 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6235 class="cmtt-8"> element</span><span
6236 class="cmtt-8"> [i]</span><span
6237 class="cmtt-8"> =</span><span
6238 class="cmtt-8"> read</span><span
6239 class="cmtt-8"> 8</span><span
6240 class="cmtt-8"> bits</span><span
6241 class="cmtt-8"> as</span><span
6242 class="cmtt-8"> unsigned</span><span
6243 class="cmtt-8"> integer</span>
6244 <br class="fancyvrb" /><a
6245 id="x1-99036r18"></a><span
6246 class="cmr-6">18</span><span
6247 class="cmtt-8"> </span><span
6248 class="cmtt-8"> </span>
6249 <br class="fancyvrb" /><a
6250 id="x1-99038r19"></a><span
6251 class="cmr-6">19</span><span
6252 class="cmtt-8"> </span><span
6253 class="cmtt-8"> </span><span
6254 class="cmtt-8"> </span><span
6255 class="cmtt-8"> </span><span
6256 class="cmtt-8"> </span><span
6257 class="cmtt-8"> </span><span
6258 class="cmtt-8"> </span><span
6259 class="cmtt-8"> </span><span
6260 class="cmtt-8"> </span><span
6261 class="cmtt-8"> </span><span
6262 class="cmtt-8"> </span><span
6263 class="cmtt-8"> </span><span
6264 class="cmtt-8"> </span><span
6265 class="cmsy-8">}</span>
6266 <br class="fancyvrb" /><a
6267 id="x1-99040r20"></a><span
6268 class="cmr-6">20</span><span
6269 class="cmtt-8"> </span><span
6270 class="cmtt-8"> </span>
6271 <br class="fancyvrb" /><a
6272 id="x1-99042r21"></a><span
6273 class="cmr-6">21</span><span
6274 class="cmtt-8"> </span><span
6275 class="cmtt-8"> </span><span
6276 class="cmtt-8"> </span><span
6277 class="cmtt-8"> </span><span
6278 class="cmtt-8"> </span><span
6279 class="cmtt-8"> </span><span
6280 class="cmtt-8"> </span><span
6281 class="cmtt-8"> </span><span
6282 class="cmtt-8"> 11)</span><span
6283 class="cmtt-8"> iterate</span><span
6284 class="cmtt-8"> [j]</span><span
6285 class="cmtt-8"> over</span><span
6286 class="cmtt-8"> the</span><span
6287 class="cmtt-8"> range</span><span
6288 class="cmtt-8"> 0</span><span
6289 class="cmtt-8"> ...</span><span
6290 class="cmtt-8"> (2</span><span
6291 class="cmtt-8"> exponent</span><span
6292 class="cmtt-8"> [floor1_class_subclasses]</span><span
6293 class="cmtt-8"> element</span><span
6294 class="cmtt-8"> [i])</span><span
6295 class="cmtt-8"> -</span><span
6296 class="cmtt-8"> 1</span><span
6297 class="cmtt-8"> </span><span
6298 class="cmsy-8">{</span>
6299 <br class="fancyvrb" /><a
6300 id="x1-99044r22"></a><span
6301 class="cmr-6">22</span><span
6302 class="cmtt-8"> </span><span
6303 class="cmtt-8"> </span>
6304 <br class="fancyvrb" /><a
6305 id="x1-99046r23"></a><span
6306 class="cmr-6">23</span><span
6307 class="cmtt-8"> </span><span
6308 class="cmtt-8"> </span><span
6309 class="cmtt-8"> </span><span
6310 class="cmtt-8"> </span><span
6311 class="cmtt-8"> </span><span
6312 class="cmtt-8"> </span><span
6313 class="cmtt-8"> </span><span
6314 class="cmtt-8"> </span><span
6315 class="cmtt-8"> </span><span
6316 class="cmtt-8"> </span><span
6317 class="cmtt-8"> </span><span
6318 class="cmtt-8"> </span><span
6319 class="cmtt-8"> </span><span
6320 class="cmtt-8"> </span><span
6321 class="cmtt-8"> 12)</span><span
6322 class="cmtt-8"> array</span><span
6323 class="cmtt-8"> [floor1_subclass_books]</span><span
6324 class="cmtt-8"> element</span><span
6325 class="cmtt-8"> [i],[j]</span><span
6326 class="cmtt-8"> =</span>
6327 <br class="fancyvrb" /><a
6328 id="x1-99048r24"></a><span
6329 class="cmr-6">24</span><span
6330 class="cmtt-8"> </span><span
6331 class="cmtt-8"> </span><span
6332 class="cmtt-8"> </span><span
6333 class="cmtt-8"> </span><span
6334 class="cmtt-8"> </span><span
6335 class="cmtt-8"> </span><span
6336 class="cmtt-8"> </span><span
6337 class="cmtt-8"> </span><span
6338 class="cmtt-8"> </span><span
6339 class="cmtt-8"> </span><span
6340 class="cmtt-8"> </span><span
6341 class="cmtt-8"> </span><span
6342 class="cmtt-8"> </span><span
6343 class="cmtt-8"> </span><span
6344 class="cmtt-8"> </span><span
6345 class="cmtt-8"> </span><span
6346 class="cmtt-8"> </span><span
6347 class="cmtt-8"> </span><span
6348 class="cmtt-8"> read</span><span
6349 class="cmtt-8"> 8</span><span
6350 class="cmtt-8"> bits</span><span
6351 class="cmtt-8"> as</span><span
6352 class="cmtt-8"> unsigned</span><span
6353 class="cmtt-8"> integer</span><span
6354 class="cmtt-8"> and</span><span
6355 class="cmtt-8"> subtract</span><span
6356 class="cmtt-8"> one</span>
6357 <br class="fancyvrb" /><a
6358 id="x1-99050r25"></a><span
6359 class="cmr-6">25</span><span
6360 class="cmtt-8"> </span><span
6361 class="cmtt-8"> </span><span
6362 class="cmtt-8"> </span><span
6363 class="cmtt-8"> </span><span
6364 class="cmtt-8"> </span><span
6365 class="cmtt-8"> </span><span
6366 class="cmtt-8"> </span><span
6367 class="cmtt-8"> </span><span
6368 class="cmtt-8"> </span><span
6369 class="cmtt-8"> </span><span
6370 class="cmtt-8"> </span><span
6371 class="cmtt-8"> </span><span
6372 class="cmtt-8"> </span><span
6373 class="cmsy-8">}</span>
6374 <br class="fancyvrb" /><a
6375 id="x1-99052r26"></a><span
6376 class="cmr-6">26</span><span
6377 class="cmtt-8"> </span><span
6378 class="cmtt-8"> </span><span
6379 class="cmtt-8"> </span><span
6380 class="cmtt-8"> </span><span
6381 class="cmtt-8"> </span><span
6382 class="cmtt-8"> </span><span
6383 class="cmtt-8"> </span><span
6384 class="cmtt-8"> </span><span
6385 class="cmsy-8">}</span>
6386 <br class="fancyvrb" /><a
6387 id="x1-99054r27"></a><span
6388 class="cmr-6">27</span><span
6389 class="cmtt-8"> </span><span
6390 class="cmtt-8"> </span>
6391 <br class="fancyvrb" /><a
6392 id="x1-99056r28"></a><span
6393 class="cmr-6">28</span><span
6394 class="cmtt-8"> </span><span
6395 class="cmtt-8"> </span><span
6396 class="cmtt-8"> 13)</span><span
6397 class="cmtt-8"> [floor1_multiplier]</span><span
6398 class="cmtt-8"> =</span><span
6399 class="cmtt-8"> read</span><span
6400 class="cmtt-8"> 2</span><span
6401 class="cmtt-8"> bits</span><span
6402 class="cmtt-8"> as</span><span
6403 class="cmtt-8"> unsigned</span><span
6404 class="cmtt-8"> integer</span><span
6405 class="cmtt-8"> and</span><span
6406 class="cmtt-8"> add</span><span
6407 class="cmtt-8"> one</span>
6408 <br class="fancyvrb" /><a
6409 id="x1-99058r29"></a><span
6410 class="cmr-6">29</span><span
6411 class="cmtt-8"> </span><span
6412 class="cmtt-8"> </span><span
6413 class="cmtt-8"> 14)</span><span
6414 class="cmtt-8"> [rangebits]</span><span
6415 class="cmtt-8"> =</span><span
6416 class="cmtt-8"> read</span><span
6417 class="cmtt-8"> 4</span><span
6418 class="cmtt-8"> bits</span><span
6419 class="cmtt-8"> as</span><span
6420 class="cmtt-8"> unsigned</span><span
6421 class="cmtt-8"> integer</span>
6422 <br class="fancyvrb" /><a
6423 id="x1-99060r30"></a><span
6424 class="cmr-6">30</span><span
6425 class="cmtt-8"> </span><span
6426 class="cmtt-8"> </span><span
6427 class="cmtt-8"> 15)</span><span
6428 class="cmtt-8"> vector</span><span
6429 class="cmtt-8"> [floor1_X_list]</span><span
6430 class="cmtt-8"> element</span><span
6431 class="cmtt-8"> [0]</span><span
6432 class="cmtt-8"> =</span><span
6433 class="cmtt-8"> 0</span>
6434 <br class="fancyvrb" /><a
6435 id="x1-99062r31"></a><span
6436 class="cmr-6">31</span><span
6437 class="cmtt-8"> </span><span
6438 class="cmtt-8"> </span><span
6439 class="cmtt-8"> 16)</span><span
6440 class="cmtt-8"> vector</span><span
6441 class="cmtt-8"> [floor1_X_list]</span><span
6442 class="cmtt-8"> element</span><span
6443 class="cmtt-8"> [1]</span><span
6444 class="cmtt-8"> =</span><span
6445 class="cmtt-8"> 2</span><span
6446 class="cmtt-8"> exponent</span><span
6447 class="cmtt-8"> [rangebits];</span>
6448 <br class="fancyvrb" /><a
6449 id="x1-99064r32"></a><span
6450 class="cmr-6">32</span><span
6451 class="cmtt-8"> </span><span
6452 class="cmtt-8"> </span><span
6453 class="cmtt-8"> 17)</span><span
6454 class="cmtt-8"> [floor1_values]</span><span
6455 class="cmtt-8"> =</span><span
6456 class="cmtt-8"> 2</span>
6457 <br class="fancyvrb" /><a
6458 id="x1-99066r33"></a><span
6459 class="cmr-6">33</span><span
6460 class="cmtt-8"> </span><span
6461 class="cmtt-8"> </span><span
6462 class="cmtt-8"> 18)</span><span
6463 class="cmtt-8"> iterate</span><span
6464 class="cmtt-8"> [i]</span><span
6465 class="cmtt-8"> over</span><span
6466 class="cmtt-8"> the</span><span
6467 class="cmtt-8"> range</span><span
6468 class="cmtt-8"> 0</span><span
6469 class="cmtt-8"> ...</span><span
6470 class="cmtt-8"> [floor1_partitions]-1</span><span
6471 class="cmtt-8"> </span><span
6472 class="cmsy-8">{</span>
6473 <br class="fancyvrb" /><a
6474 id="x1-99068r34"></a><span
6475 class="cmr-6">34</span><span
6476 class="cmtt-8"> </span><span
6477 class="cmtt-8"> </span>
6478 <br class="fancyvrb" /><a
6479 id="x1-99070r35"></a><span
6480 class="cmr-6">35</span><span
6481 class="cmtt-8"> </span><span
6482 class="cmtt-8"> </span><span
6483 class="cmtt-8"> </span><span
6484 class="cmtt-8"> </span><span
6485 class="cmtt-8"> </span><span
6486 class="cmtt-8"> </span><span
6487 class="cmtt-8"> </span><span
6488 class="cmtt-8"> </span><span
6489 class="cmtt-8"> 19)</span><span
6490 class="cmtt-8"> [current_class_number]</span><span
6491 class="cmtt-8"> =</span><span
6492 class="cmtt-8"> vector</span><span
6493 class="cmtt-8"> [floor1_partition_class_list]</span><span
6494 class="cmtt-8"> element</span><span
6495 class="cmtt-8"> [i]</span>
6496 <br class="fancyvrb" /><a
6497 id="x1-99072r36"></a><span
6498 class="cmr-6">36</span><span
6499 class="cmtt-8"> </span><span
6500 class="cmtt-8"> </span><span
6501 class="cmtt-8"> </span><span
6502 class="cmtt-8"> </span><span
6503 class="cmtt-8"> </span><span
6504 class="cmtt-8"> </span><span
6505 class="cmtt-8"> </span><span
6506 class="cmtt-8"> </span><span
6507 class="cmtt-8"> 20)</span><span
6508 class="cmtt-8"> iterate</span><span
6509 class="cmtt-8"> [j]</span><span
6510 class="cmtt-8"> over</span><span
6511 class="cmtt-8"> the</span><span
6512 class="cmtt-8"> range</span><span
6513 class="cmtt-8"> 0</span><span
6514 class="cmtt-8"> ...</span><span
6515 class="cmtt-8"> ([floor1_class_dimensions]</span><span
6516 class="cmtt-8"> element</span><span
6517 class="cmtt-8"> [current_class_number])-1</span><span
6518 class="cmtt-8"> </span><span
6519 class="cmsy-8">{</span>
6520 <br class="fancyvrb" /><a
6521 id="x1-99074r37"></a><span
6522 class="cmr-6">37</span><span
6523 class="cmtt-8"> </span><span
6524 class="cmtt-8"> </span><span
6525 class="cmtt-8"> </span><span
6526 class="cmtt-8"> </span><span
6527 class="cmtt-8"> </span><span
6528 class="cmtt-8"> </span><span
6529 class="cmtt-8"> </span><span
6530 class="cmtt-8"> </span><span
6531 class="cmtt-8"> </span><span
6532 class="cmtt-8"> </span><span
6533 class="cmtt-8"> </span><span
6534 class="cmtt-8"> </span><span
6535 class="cmtt-8"> </span><span
6536 class="cmtt-8"> </span><span
6537 class="cmtt-8"> 21)</span><span
6538 class="cmtt-8"> vector</span><span
6539 class="cmtt-8"> [floor1_X_list]</span><span
6540 class="cmtt-8"> element</span><span
6541 class="cmtt-8"> ([floor1_values])</span><span
6542 class="cmtt-8"> =</span>
6543 <br class="fancyvrb" /><a
6544 id="x1-99076r38"></a><span
6545 class="cmr-6">38</span><span
6546 class="cmtt-8"> </span><span
6547 class="cmtt-8"> </span><span
6548 class="cmtt-8"> </span><span
6549 class="cmtt-8"> </span><span
6550 class="cmtt-8"> </span><span
6551 class="cmtt-8"> </span><span
6552 class="cmtt-8"> </span><span
6553 class="cmtt-8"> </span><span
6554 class="cmtt-8"> </span><span
6555 class="cmtt-8"> </span><span
6556 class="cmtt-8"> </span><span
6557 class="cmtt-8"> </span><span
6558 class="cmtt-8"> </span><span
6559 class="cmtt-8"> </span><span
6560 class="cmtt-8"> </span><span
6561 class="cmtt-8"> </span><span
6562 class="cmtt-8"> </span><span
6563 class="cmtt-8"> </span><span
6564 class="cmtt-8"> read</span><span
6565 class="cmtt-8"> [rangebits]</span><span
6566 class="cmtt-8"> bits</span><span
6567 class="cmtt-8"> as</span><span
6568 class="cmtt-8"> unsigned</span><span
6569 class="cmtt-8"> integer</span>
6570 <br class="fancyvrb" /><a
6571 id="x1-99078r39"></a><span
6572 class="cmr-6">39</span><span
6573 class="cmtt-8"> </span><span
6574 class="cmtt-8"> </span><span
6575 class="cmtt-8"> </span><span
6576 class="cmtt-8"> </span><span
6577 class="cmtt-8"> </span><span
6578 class="cmtt-8"> </span><span
6579 class="cmtt-8"> </span><span
6580 class="cmtt-8"> </span><span
6581 class="cmtt-8"> </span><span
6582 class="cmtt-8"> </span><span
6583 class="cmtt-8"> </span><span
6584 class="cmtt-8"> </span><span
6585 class="cmtt-8"> </span><span
6586 class="cmtt-8"> </span><span
6587 class="cmtt-8"> 22)</span><span
6588 class="cmtt-8"> increment</span><span
6589 class="cmtt-8"> [floor1_values]</span><span
6590 class="cmtt-8"> by</span><span
6591 class="cmtt-8"> one</span>
6592 <br class="fancyvrb" /><a
6593 id="x1-99080r40"></a><span
6594 class="cmr-6">40</span><span
6595 class="cmtt-8"> </span><span
6596 class="cmtt-8"> </span><span
6597 class="cmtt-8"> </span><span
6598 class="cmtt-8"> </span><span
6599 class="cmtt-8"> </span><span
6600 class="cmtt-8"> </span><span
6601 class="cmtt-8"> </span><span
6602 class="cmtt-8"> </span><span
6603 class="cmtt-8"> </span><span
6604 class="cmtt-8"> </span><span
6605 class="cmtt-8"> </span><span
6606 class="cmtt-8"> </span><span
6607 class="cmtt-8"> </span><span
6608 class="cmsy-8">}</span>
6609 <br class="fancyvrb" /><a
6610 id="x1-99082r41"></a><span
6611 class="cmr-6">41</span><span
6612 class="cmtt-8"> </span><span
6613 class="cmtt-8"> </span><span
6614 class="cmtt-8"> </span><span
6615 class="cmtt-8"> </span><span
6616 class="cmtt-8"> </span><span
6617 class="cmtt-8"> </span><span
6618 class="cmtt-8"> </span><span
6619 class="cmsy-8">}</span>
6620 <br class="fancyvrb" /><a
6621 id="x1-99084r42"></a><span
6622 class="cmr-6">42</span><span
6623 class="cmtt-8"> </span><span
6624 class="cmtt-8"> </span>
6625 <br class="fancyvrb" /><a
6626 id="x1-99086r43"></a><span
6627 class="cmr-6">43</span><span
6628 class="cmtt-8"> </span><span
6629 class="cmtt-8"> </span><span
6630 class="cmtt-8"> 23)</span><span
6631 class="cmtt-8"> done</span>
6633 <!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
6634 setup renders a stream undecodable. In addition, a <span
6635 class="cmtt-12">[floor1_class_masterbooks] </span>or
6637 class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook
6638 configured in this stream is an error condition that renders the stream undecodable. Vector
6639 [floor1_x_list] is limited to a maximum length of 65 elements; a setup indicating more than 65
6640 total elements (including elements 0 and 1 set prior to the read loop) renders the stream
6641 undecodable. All vector [floor1_x_list] element values must be unique within the vector; a
6642 non-unique value renders the stream undecodable.
6646 <!--l. 170--><p class="noindent" >
6647 <h5 class="subsubsectionHead"><span class="titlemark">7.2.3. </span> <a
6648 id="x1-1000007.2.3"></a>packet decode</h5>
6649 <!--l. 172--><p class="noindent" >Packet decode begins by checking the <span
6650 class="cmtt-12">[nonzero] </span>flag:
6651 <!--l. 174--><p class="noindent" >
6652 <div class="fancyvrb" id="fancyvrb29">
6654 id="x1-100002r1"></a><span
6655 class="cmr-6">1</span><span
6656 class="cmtt-8"> </span><span
6657 class="cmtt-8"> </span><span
6658 class="cmtt-8"> </span><span
6659 class="cmtt-8"> 1)</span><span
6660 class="cmtt-8"> [nonzero]</span><span
6661 class="cmtt-8"> =</span><span
6662 class="cmtt-8"> read</span><span
6663 class="cmtt-8"> 1</span><span
6664 class="cmtt-8"> bit</span><span
6665 class="cmtt-8"> as</span><span
6666 class="cmtt-8"> boolean</span>
6668 <!--l. 178--><p class="noindent" >If <span
6669 class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
6670 Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
6671 this frame. (A return status of ’unused’ is different from decoding a floor that has all
6672 points set to minimum representation amplitude, which happens to be approximately
6674 <!--l. 186--><p class="noindent" >Assuming <span
6675 class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
6676 <!--l. 188--><p class="noindent" >
6677 <div class="fancyvrb" id="fancyvrb30">
6679 id="x1-100004r1"></a><span
6680 class="cmr-6">1</span><span
6681 class="cmtt-8"> </span><span
6682 class="cmtt-8"> </span><span
6683 class="cmtt-8"> </span><span
6684 class="cmtt-8"> 1)</span><span
6685 class="cmtt-8"> [range]</span><span
6686 class="cmtt-8"> =</span><span
6687 class="cmtt-8"> vector</span><span
6688 class="cmtt-8"> </span><span
6689 class="cmsy-8">{</span><span
6690 class="cmtt-8"> 256,</span><span
6691 class="cmtt-8"> 128,</span><span
6692 class="cmtt-8"> 86,</span><span
6693 class="cmtt-8"> 64</span><span
6694 class="cmtt-8"> </span><span
6695 class="cmsy-8">}</span><span
6696 class="cmtt-8"> element</span><span
6697 class="cmtt-8"> ([floor1_multiplier]-1)</span>
6698 <br class="fancyvrb" /><a
6699 id="x1-100006r2"></a><span
6700 class="cmr-6">2</span><span
6701 class="cmtt-8"> </span><span
6702 class="cmtt-8"> </span><span
6703 class="cmtt-8"> </span><span
6704 class="cmtt-8"> 2)</span><span
6705 class="cmtt-8"> vector</span><span
6706 class="cmtt-8"> [floor1_Y]</span><span
6707 class="cmtt-8"> element</span><span
6708 class="cmtt-8"> [0]</span><span
6709 class="cmtt-8"> =</span><span
6710 class="cmtt-8"> read</span><span
6711 class="cmtt-8"> </span><a
6712 href="#x1-1170009.2.1"><span
6713 class="cmtt-8">ilog</span></a><span
6714 class="cmtt-8">([range]-1)</span><span
6715 class="cmtt-8"> bits</span><span
6716 class="cmtt-8"> as</span><span
6717 class="cmtt-8"> unsigned</span><span
6718 class="cmtt-8"> integer</span>
6719 <br class="fancyvrb" /><a
6720 id="x1-100008r3"></a><span
6721 class="cmr-6">3</span><span
6722 class="cmtt-8"> </span><span
6723 class="cmtt-8"> </span><span
6724 class="cmtt-8"> </span><span
6725 class="cmtt-8"> 3)</span><span
6726 class="cmtt-8"> vector</span><span
6727 class="cmtt-8"> [floor1_Y]</span><span
6728 class="cmtt-8"> element</span><span
6729 class="cmtt-8"> [1]</span><span
6730 class="cmtt-8"> =</span><span
6731 class="cmtt-8"> read</span><span
6732 class="cmtt-8"> </span><a
6733 href="#x1-1170009.2.1"><span
6734 class="cmtt-8">ilog</span></a><span
6735 class="cmtt-8">([range]-1)</span><span
6736 class="cmtt-8"> bits</span><span
6737 class="cmtt-8"> as</span><span
6738 class="cmtt-8"> unsigned</span><span
6739 class="cmtt-8"> integer</span>
6740 <br class="fancyvrb" /><a
6741 id="x1-100010r4"></a><span
6742 class="cmr-6">4</span><span
6743 class="cmtt-8"> </span><span
6744 class="cmtt-8"> </span><span
6745 class="cmtt-8"> </span><span
6746 class="cmtt-8"> 4)</span><span
6747 class="cmtt-8"> [offset]</span><span
6748 class="cmtt-8"> =</span><span
6749 class="cmtt-8"> 2;</span>
6750 <br class="fancyvrb" /><a
6751 id="x1-100012r5"></a><span
6752 class="cmr-6">5</span><span
6753 class="cmtt-8"> </span><span
6754 class="cmtt-8"> </span><span
6755 class="cmtt-8"> </span><span
6756 class="cmtt-8"> 5)</span><span
6757 class="cmtt-8"> iterate</span><span
6758 class="cmtt-8"> [i]</span><span
6759 class="cmtt-8"> over</span><span
6760 class="cmtt-8"> the</span><span
6761 class="cmtt-8"> range</span><span
6762 class="cmtt-8"> 0</span><span
6763 class="cmtt-8"> ...</span><span
6764 class="cmtt-8"> [floor1_partitions]-1</span><span
6765 class="cmtt-8"> </span><span
6766 class="cmsy-8">{</span>
6767 <br class="fancyvrb" /><a
6768 id="x1-100014r6"></a><span
6769 class="cmr-6">6</span><span
6770 class="cmtt-8"> </span><span
6771 class="cmtt-8"> </span>
6772 <br class="fancyvrb" /><a
6773 id="x1-100016r7"></a><span
6774 class="cmr-6">7</span><span
6775 class="cmtt-8"> </span><span
6776 class="cmtt-8"> </span><span
6777 class="cmtt-8"> </span><span
6778 class="cmtt-8"> </span><span
6779 class="cmtt-8"> </span><span
6780 class="cmtt-8"> </span><span
6781 class="cmtt-8"> </span><span
6782 class="cmtt-8"> </span><span
6783 class="cmtt-8"> 6)</span><span
6784 class="cmtt-8"> [class]</span><span
6785 class="cmtt-8"> =</span><span
6786 class="cmtt-8"> vector</span><span
6787 class="cmtt-8"> [floor1_partition_class]</span><span
6788 class="cmtt-8"> </span><span
6789 class="cmtt-8"> element</span><span
6790 class="cmtt-8"> [i]</span>
6791 <br class="fancyvrb" /><a
6792 id="x1-100018r8"></a><span
6793 class="cmr-6">8</span><span
6794 class="cmtt-8"> </span><span
6795 class="cmtt-8"> </span><span
6796 class="cmtt-8"> </span><span
6797 class="cmtt-8"> </span><span
6798 class="cmtt-8"> </span><span
6799 class="cmtt-8"> </span><span
6800 class="cmtt-8"> </span><span
6801 class="cmtt-8"> </span><span
6802 class="cmtt-8"> 7)</span><span
6803 class="cmtt-8"> [cdim]</span><span
6804 class="cmtt-8"> </span><span
6805 class="cmtt-8"> =</span><span
6806 class="cmtt-8"> vector</span><span
6807 class="cmtt-8"> [floor1_class_dimensions]</span><span
6808 class="cmtt-8"> element</span><span
6809 class="cmtt-8"> [class]</span>
6810 <br class="fancyvrb" /><a
6811 id="x1-100020r9"></a><span
6812 class="cmr-6">9</span><span
6813 class="cmtt-8"> </span><span
6814 class="cmtt-8"> </span><span
6815 class="cmtt-8"> </span><span
6816 class="cmtt-8"> </span><span
6817 class="cmtt-8"> </span><span
6818 class="cmtt-8"> </span><span
6819 class="cmtt-8"> </span><span
6820 class="cmtt-8"> </span><span
6821 class="cmtt-8"> 8)</span><span
6822 class="cmtt-8"> [cbits]</span><span
6823 class="cmtt-8"> =</span><span
6824 class="cmtt-8"> vector</span><span
6825 class="cmtt-8"> [floor1_class_subclasses]</span><span
6826 class="cmtt-8"> element</span><span
6827 class="cmtt-8"> [class]</span>
6828 <br class="fancyvrb" /><a
6829 id="x1-100022r10"></a><span
6830 class="cmr-6">10</span><span
6831 class="cmtt-8"> </span><span
6832 class="cmtt-8"> </span><span
6833 class="cmtt-8"> </span><span
6834 class="cmtt-8"> </span><span
6835 class="cmtt-8"> </span><span
6836 class="cmtt-8"> </span><span
6837 class="cmtt-8"> </span><span
6838 class="cmtt-8"> </span><span
6839 class="cmtt-8"> 9)</span><span
6840 class="cmtt-8"> [csub]</span><span
6841 class="cmtt-8"> </span><span
6842 class="cmtt-8"> =</span><span
6843 class="cmtt-8"> (2</span><span
6844 class="cmtt-8"> exponent</span><span
6845 class="cmtt-8"> [cbits])-1</span>
6846 <br class="fancyvrb" /><a
6847 id="x1-100024r11"></a><span
6848 class="cmr-6">11</span><span
6849 class="cmtt-8"> </span><span
6850 class="cmtt-8"> </span><span
6851 class="cmtt-8"> </span><span
6852 class="cmtt-8"> </span><span
6853 class="cmtt-8"> </span><span
6854 class="cmtt-8"> </span><span
6855 class="cmtt-8"> </span><span
6856 class="cmtt-8"> 10)</span><span
6857 class="cmtt-8"> [cval]</span><span
6858 class="cmtt-8"> </span><span
6859 class="cmtt-8"> =</span><span
6860 class="cmtt-8"> 0</span>
6861 <br class="fancyvrb" /><a
6862 id="x1-100026r12"></a><span
6863 class="cmr-6">12</span><span
6864 class="cmtt-8"> </span><span
6865 class="cmtt-8"> </span><span
6866 class="cmtt-8"> </span><span
6867 class="cmtt-8"> </span><span
6868 class="cmtt-8"> </span><span
6869 class="cmtt-8"> </span><span
6870 class="cmtt-8"> </span><span
6871 class="cmtt-8"> 11)</span><span
6872 class="cmtt-8"> if</span><span
6873 class="cmtt-8"> (</span><span
6874 class="cmtt-8"> [cbits]</span><span
6875 class="cmtt-8"> is</span><span
6876 class="cmtt-8"> greater</span><span
6877 class="cmtt-8"> than</span><span
6878 class="cmtt-8"> zero</span><span
6879 class="cmtt-8"> )</span><span
6880 class="cmtt-8"> </span><span
6881 class="cmsy-8">{</span>
6882 <br class="fancyvrb" /><a
6883 id="x1-100028r13"></a><span
6884 class="cmr-6">13</span><span
6885 class="cmtt-8"> </span><span
6886 class="cmtt-8"> </span>
6887 <br class="fancyvrb" /><a
6888 id="x1-100030r14"></a><span
6889 class="cmr-6">14</span><span
6890 class="cmtt-8"> </span><span
6891 class="cmtt-8"> </span><span
6892 class="cmtt-8"> </span><span
6893 class="cmtt-8"> </span><span
6894 class="cmtt-8"> </span><span
6895 class="cmtt-8"> </span><span
6896 class="cmtt-8"> </span><span
6897 class="cmtt-8"> </span><span
6898 class="cmtt-8"> </span><span
6899 class="cmtt-8"> </span><span
6900 class="cmtt-8"> </span><span
6901 class="cmtt-8"> </span><span
6902 class="cmtt-8"> </span><span
6903 class="cmtt-8"> </span><span
6904 class="cmtt-8"> 12)</span><span
6905 class="cmtt-8"> [cval]</span><span
6906 class="cmtt-8"> =</span><span
6907 class="cmtt-8"> read</span><span
6908 class="cmtt-8"> from</span><span
6909 class="cmtt-8"> packet</span><span
6910 class="cmtt-8"> using</span><span
6911 class="cmtt-8"> codebook</span><span
6912 class="cmtt-8"> number</span>
6913 <br class="fancyvrb" /><a
6914 id="x1-100032r15"></a><span
6915 class="cmr-6">15</span><span
6916 class="cmtt-8"> </span><span
6917 class="cmtt-8"> </span><span
6918 class="cmtt-8"> </span><span
6919 class="cmtt-8"> </span><span
6920 class="cmtt-8"> </span><span
6921 class="cmtt-8"> </span><span
6922 class="cmtt-8"> </span><span
6923 class="cmtt-8"> </span><span
6924 class="cmtt-8"> </span><span
6925 class="cmtt-8"> </span><span
6926 class="cmtt-8"> </span><span
6927 class="cmtt-8"> </span><span
6928 class="cmtt-8"> </span><span
6929 class="cmtt-8"> </span><span
6930 class="cmtt-8"> </span><span
6931 class="cmtt-8"> </span><span
6932 class="cmtt-8"> </span><span
6933 class="cmtt-8"> </span><span
6934 class="cmtt-8"> (vector</span><span
6935 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6936 class="cmtt-8"> element</span><span
6937 class="cmtt-8"> [class])</span><span
6938 class="cmtt-8"> in</span><span
6939 class="cmtt-8"> scalar</span><span
6940 class="cmtt-8"> context</span>
6941 <br class="fancyvrb" /><a
6942 id="x1-100034r16"></a><span
6943 class="cmr-6">16</span><span
6944 class="cmtt-8"> </span><span
6945 class="cmtt-8"> </span><span
6946 class="cmtt-8"> </span><span
6947 class="cmtt-8"> </span><span
6948 class="cmtt-8"> </span><span
6949 class="cmtt-8"> </span><span
6950 class="cmtt-8"> </span><span
6951 class="cmtt-8"> </span><span
6952 class="cmtt-8"> </span><span
6953 class="cmtt-8"> </span><span
6954 class="cmtt-8"> </span><span
6955 class="cmtt-8"> </span><span
6956 class="cmsy-8">}</span>
6957 <br class="fancyvrb" /><a
6958 id="x1-100036r17"></a><span
6959 class="cmr-6">17</span><span
6960 class="cmtt-8"> </span><span
6961 class="cmtt-8"> </span>
6962 <br class="fancyvrb" /><a
6963 id="x1-100038r18"></a><span
6964 class="cmr-6">18</span><span
6965 class="cmtt-8"> </span><span
6966 class="cmtt-8"> </span><span
6967 class="cmtt-8"> </span><span
6968 class="cmtt-8"> </span><span
6969 class="cmtt-8"> </span><span
6970 class="cmtt-8"> </span><span
6971 class="cmtt-8"> </span><span
6972 class="cmtt-8"> 13)</span><span
6973 class="cmtt-8"> iterate</span><span
6974 class="cmtt-8"> [j]</span><span
6975 class="cmtt-8"> over</span><span
6976 class="cmtt-8"> the</span><span
6977 class="cmtt-8"> range</span><span
6978 class="cmtt-8"> 0</span><span
6979 class="cmtt-8"> ...</span><span
6980 class="cmtt-8"> [cdim]-1</span><span
6981 class="cmtt-8"> </span><span
6982 class="cmsy-8">{</span>
6983 <br class="fancyvrb" /><a
6984 id="x1-100040r19"></a><span
6985 class="cmr-6">19</span><span
6986 class="cmtt-8"> </span><span
6987 class="cmtt-8"> </span>
6988 <br class="fancyvrb" /><a
6989 id="x1-100042r20"></a><span
6990 class="cmr-6">20</span><span
6991 class="cmtt-8"> </span><span
6992 class="cmtt-8"> </span><span
6993 class="cmtt-8"> </span><span
6994 class="cmtt-8"> </span><span
6995 class="cmtt-8"> </span><span
6996 class="cmtt-8"> </span><span
6997 class="cmtt-8"> </span><span
6998 class="cmtt-8"> </span><span
6999 class="cmtt-8"> </span><span
7000 class="cmtt-8"> </span><span
7001 class="cmtt-8"> </span><span
7002 class="cmtt-8"> </span><span
7003 class="cmtt-8"> </span><span
7004 class="cmtt-8"> </span><span
7005 class="cmtt-8"> 14)</span><span
7006 class="cmtt-8"> [book]</span><span
7007 class="cmtt-8"> =</span><span
7008 class="cmtt-8"> array</span><span
7009 class="cmtt-8"> [floor1_subclass_books]</span><span
7010 class="cmtt-8"> element</span><span
7011 class="cmtt-8"> [class],([cval]</span><span
7012 class="cmtt-8"> bitwise</span><span
7013 class="cmtt-8"> AND</span><span
7014 class="cmtt-8"> [csub])</span>
7015 <br class="fancyvrb" /><a
7016 id="x1-100044r21"></a><span
7017 class="cmr-6">21</span><span
7018 class="cmtt-8"> </span><span
7019 class="cmtt-8"> </span><span
7020 class="cmtt-8"> </span><span
7021 class="cmtt-8"> </span><span
7022 class="cmtt-8"> </span><span
7023 class="cmtt-8"> </span><span
7024 class="cmtt-8"> </span><span
7025 class="cmtt-8"> </span><span
7026 class="cmtt-8"> </span><span
7027 class="cmtt-8"> </span><span
7028 class="cmtt-8"> </span><span
7029 class="cmtt-8"> </span><span
7030 class="cmtt-8"> </span><span
7031 class="cmtt-8"> </span><span
7032 class="cmtt-8"> 15)</span><span
7033 class="cmtt-8"> [cval]</span><span
7034 class="cmtt-8"> =</span><span
7035 class="cmtt-8"> [cval]</span><span
7036 class="cmtt-8"> right</span><span
7037 class="cmtt-8"> shifted</span><span
7038 class="cmtt-8"> [cbits]</span><span
7039 class="cmtt-8"> bits</span>
7040 <br class="fancyvrb" /><a
7041 id="x1-100046r22"></a><span
7042 class="cmr-6">22</span><span
7043 class="cmtt-8"> </span><span
7044 class="cmtt-8">  </span><span
7045 class="cmtt-8"> </span><span
7046 class="cmtt-8"> </span><span
7047 class="cmtt-8"> </span><span
7048 class="cmtt-8"> </span><span
7049 class="cmtt-8"> 16)</span><span
7050 class="cmtt-8"> if</span><span
7051 class="cmtt-8"> (</span><span
7052 class="cmtt-8"> [book]</span><span
7053 class="cmtt-8"> is</span><span
7054 class="cmtt-8"> not</span><span
7055 class="cmtt-8"> less</span><span
7056 class="cmtt-8"> than</span><span
7057 class="cmtt-8"> zero</span><span
7058 class="cmtt-8"> )</span><span
7059 class="cmtt-8"> </span><span
7060 class="cmsy-8">{</span>
7061 <br class="fancyvrb" /><a
7062 id="x1-100048r23"></a><span
7063 class="cmr-6">23</span><span
7064 class="cmtt-8"> </span><span
7065 class="cmtt-8"> </span>
7066 <br class="fancyvrb" /><a
7067 id="x1-100050r24"></a><span
7068 class="cmr-6">24</span><span
7069 class="cmtt-8"> </span><span
7070 class="cmtt-8">  </span><span
7071 class="cmtt-8"> </span><span
7072 class="cmtt-8"> </span><span
7073 class="cmtt-8"> </span><span
7074 class="cmtt-8"> </span><span
7075 class="cmtt-8"> </span><span
7076 class="cmtt-8"> </span><span
7077 class="cmtt-8"> </span><span
7078 class="cmtt-8"> </span><span
7079 class="cmtt-8"> </span><span
7080 class="cmtt-8"> </span><span
7081 class="cmtt-8"> 17)</span><span
7082 class="cmtt-8"> vector</span><span
7083 class="cmtt-8"> [floor1_Y]</span><span
7084 class="cmtt-8"> element</span><span
7085 class="cmtt-8"> ([j]+[offset])</span><span
7086 class="cmtt-8"> =</span><span
7087 class="cmtt-8"> read</span><span
7088 class="cmtt-8"> from</span><span
7089 class="cmtt-8"> packet</span><span
7090 class="cmtt-8"> using</span><span
7091 class="cmtt-8"> codebook</span>
7092 <br class="fancyvrb" /><a
7093 id="x1-100052r25"></a><span
7094 class="cmr-6">25</span><span
7095 class="cmtt-8"> </span><span
7096 class="cmtt-8"> </span><span
7097 class="cmtt-8"> </span><span
7098 class="cmtt-8"> </span><span
7099 class="cmtt-8"> </span><span
7100 class="cmtt-8"> </span><span
7101 class="cmtt-8"> </span><span
7102 class="cmtt-8"> </span><span
7103 class="cmtt-8"> </span><span
7104 class="cmtt-8"> </span><span
7105 class="cmtt-8"> </span><span
7106 class="cmtt-8"> </span><span
7107 class="cmtt-8"> </span><span
7108 class="cmtt-8"> </span><span
7109 class="cmtt-8"> </span><span
7110 class="cmtt-8"> </span><span
7111 class="cmtt-8"> </span><span
7112 class="cmtt-8"> </span><span
7113 class="cmtt-8"> </span><span
7114 class="cmtt-8"> </span><span
7115 class="cmtt-8"> </span><span
7116 class="cmtt-8"> </span><span
7117 class="cmtt-8"> </span><span
7118 class="cmtt-8"> </span><span
7119 class="cmtt-8"> [book]</span><span
7120 class="cmtt-8"> in</span><span
7121 class="cmtt-8"> scalar</span><span
7122 class="cmtt-8"> context</span>
7123 <br class="fancyvrb" /><a
7124 id="x1-100054r26"></a><span
7125 class="cmr-6">26</span><span
7126 class="cmtt-8"> </span><span
7127 class="cmtt-8"> </span>
7128 <br class="fancyvrb" /><a
7129 id="x1-100056r27"></a><span
7130 class="cmr-6">27</span><span
7131 class="cmtt-8"> </span><span
7132 class="cmtt-8"> </span><span
7133 class="cmtt-8"> </span><span
7134 class="cmtt-8"> </span><span
7135 class="cmtt-8"> </span><span
7136 class="cmtt-8"> </span><span
7137 class="cmtt-8"> </span><span
7138 class="cmtt-8"> </span><span
7139 class="cmtt-8"> </span><span
7140 class="cmtt-8"> </span><span
7141 class="cmtt-8"> </span><span
7142 class="cmtt-8"> </span><span
7143 class="cmtt-8"> </span><span
7144 class="cmtt-8"> </span><span
7145 class="cmtt-8"> </span><span
7146 class="cmtt-8"> </span><span
7147 class="cmtt-8"> </span><span
7148 class="cmtt-8"> </span><span
7149 class="cmtt-8"> </span><span
7150 class="cmsy-8">}</span><span
7151 class="cmtt-8"> else</span><span
7152 class="cmtt-8"> [book]</span><span
7153 class="cmtt-8"> is</span><span
7154 class="cmtt-8"> less</span><span
7155 class="cmtt-8"> than</span><span
7156 class="cmtt-8"> zero</span><span
7157 class="cmtt-8"> </span><span
7158 class="cmsy-8">{</span>
7159 <br class="fancyvrb" /><a
7160 id="x1-100058r28"></a><span
7161 class="cmr-6">28</span><span
7162 class="cmtt-8"> </span><span
7163 class="cmtt-8"> </span>
7164 <br class="fancyvrb" /><a
7165 id="x1-100060r29"></a><span
7166 class="cmr-6">29</span><span
7167 class="cmtt-8"> </span><span
7168 class="cmtt-8">  </span><span
7169 class="cmtt-8"> </span><span
7170 class="cmtt-8"> </span><span
7171 class="cmtt-8"> </span><span
7172 class="cmtt-8"> </span><span
7173 class="cmtt-8"> </span><span
7174 class="cmtt-8"> </span><span
7175 class="cmtt-8"> </span><span
7176 class="cmtt-8"> </span><span
7177 class="cmtt-8"> </span><span
7178 class="cmtt-8"> </span><span
7179 class="cmtt-8"> 18)</span><span
7180 class="cmtt-8"> vector</span><span
7181 class="cmtt-8"> [floor1_Y]</span><span
7182 class="cmtt-8"> element</span><span
7183 class="cmtt-8"> ([j]+[offset])</span><span
7184 class="cmtt-8"> =</span><span
7185 class="cmtt-8"> 0</span>
7186 <br class="fancyvrb" /><a
7187 id="x1-100062r30"></a><span
7188 class="cmr-6">30</span><span
7189 class="cmtt-8"> </span><span
7190 class="cmtt-8"> </span>
7191 <br class="fancyvrb" /><a
7192 id="x1-100064r31"></a><span
7193 class="cmr-6">31</span><span
7194 class="cmtt-8"> </span><span
7195 class="cmtt-8"> </span><span
7196 class="cmtt-8"> </span><span
7197 class="cmtt-8"> </span><span
7198 class="cmtt-8"> </span><span
7199 class="cmtt-8"> </span><span
7200 class="cmtt-8"> </span><span
7201 class="cmtt-8"> </span><span
7202 class="cmtt-8"> </span><span
7203 class="cmtt-8"> </span><span
7204 class="cmtt-8"> </span><span
7205 class="cmtt-8"> </span><span
7206 class="cmtt-8"> </span><span
7207 class="cmtt-8"> </span><span
7208 class="cmtt-8"> </span><span
7209 class="cmtt-8"> </span><span
7210 class="cmtt-8"> </span><span
7211 class="cmtt-8"> </span><span
7212 class="cmtt-8"> </span><span
7213 class="cmsy-8">}</span>
7214 <br class="fancyvrb" /><a
7215 id="x1-100066r32"></a><span
7216 class="cmr-6">32</span><span
7217 class="cmtt-8"> </span><span
7218 class="cmtt-8"> </span><span
7219 class="cmtt-8"> </span><span
7220 class="cmtt-8"> </span><span
7221 class="cmtt-8"> </span><span
7222 class="cmtt-8"> </span><span
7223 class="cmtt-8"> </span><span
7224 class="cmtt-8"> </span><span
7225 class="cmtt-8"> </span><span
7226 class="cmtt-8"> </span><span
7227 class="cmtt-8"> </span><span
7228 class="cmtt-8"> </span><span
7229 class="cmsy-8">}</span>
7230 <br class="fancyvrb" /><a
7231 id="x1-100068r33"></a><span
7232 class="cmr-6">33</span><span
7233 class="cmtt-8"> </span><span
7234 class="cmtt-8"> </span>
7235 <br class="fancyvrb" /><a
7236 id="x1-100070r34"></a><span
7237 class="cmr-6">34</span><span
7238 class="cmtt-8"> </span><span
7239 class="cmtt-8"> </span><span
7240 class="cmtt-8"> </span><span
7241 class="cmtt-8"> </span><span
7242 class="cmtt-8"> </span><span
7243 class="cmtt-8"> </span><span
7244 class="cmtt-8"> </span><span
7245 class="cmtt-8"> 19)</span><span
7246 class="cmtt-8"> [offset]</span><span
7247 class="cmtt-8"> =</span><span
7248 class="cmtt-8"> [offset]</span><span
7249 class="cmtt-8"> +</span><span
7250 class="cmtt-8"> [cdim]</span>
7254 <br class="fancyvrb" /><a
7255 id="x1-100072r35"></a><span
7256 class="cmr-6">35</span><span
7257 class="cmtt-8"> </span><span
7258 class="cmtt-8"> </span>
7259 <br class="fancyvrb" /><a
7260 id="x1-100074r36"></a><span
7261 class="cmr-6">36</span><span
7262 class="cmtt-8"> </span><span
7263 class="cmtt-8"> </span><span
7264 class="cmtt-8"> </span><span
7265 class="cmtt-8"> </span><span
7266 class="cmtt-8"> </span><span
7267 class="cmtt-8"> </span><span
7268 class="cmtt-8"> </span><span
7269 class="cmsy-8">}</span>
7270 <br class="fancyvrb" /><a
7271 id="x1-100076r37"></a><span
7272 class="cmr-6">37</span><span
7273 class="cmtt-8"> </span><span
7274 class="cmtt-8"> </span>
7275 <br class="fancyvrb" /><a
7276 id="x1-100078r38"></a><span
7277 class="cmr-6">38</span><span
7278 class="cmtt-8"> </span><span
7279 class="cmtt-8"> </span><span
7280 class="cmtt-8"> 20)</span><span
7281 class="cmtt-8"> done</span>
7283 <!--l. 229--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
7284 end-of-packet is reached during any read operation above, floor decode is to return ’unused’
7285 status as if the <span
7286 class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
7287 <!--l. 235--><p class="noindent" >Vector <span
7288 class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
7289 <!--l. 240--><p class="noindent" >
7290 <h5 class="subsubsectionHead"><span class="titlemark">7.2.4. </span> <a
7291 id="x1-1010007.2.4"></a>curve computation</h5>
7292 <!--l. 242--><p class="noindent" >Curve computation is split into two logical steps; the first step derives final Y amplitude values
7293 from the encoded, wrapped difference values taken from the bitstream. The second step
7294 plots the curve lines. Also, although zero-difference values are used in the iterative
7295 prediction to find final Y values, these points are conditionally skipped during final
7296 line computation in step two. Skipping zero-difference values allows a smoother line
7298 <!--l. 250--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations,
7299 implementors are warned to follow the details closely. Deviation from implementing a strictly
7300 equivalent algorithm can result in serious decoding errors.
7301 <!--l. 255--><p class="noindent" ><span
7302 class="cmti-12">Additional note: </span>Although <span
7303 class="cmtt-12">[floor1_final_Y] </span>values in the prediction loop and at the end of
7304 step 1 are inherently limited by the prediction algorithm to [0, <span
7305 class="cmtt-12">[range]</span>), it is possible to abuse
7306 the setup and codebook machinery to produce negative or over-range results. We suggest that
7307 decoder implementations guard the values in vector <span
7308 class="cmtt-12">[floor1_final_Y] </span>by clamping each
7309 element to [0, <span
7310 class="cmtt-12">[range]</span>) after step 1. Variants of this suggestion are acceptable as valid floor1
7311 setups cannot produce out of range values.
7312 <!--l. 266--><p class="noindent" >
7313 <dl class="description"><dt class="description">
7315 class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd
7316 class="description">
7317 <!--l. 268--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
7318 values, then apply to line prediction.
7319 <!--l. 271--><p class="noindent" >
7320 <div class="fancyvrb" id="fancyvrb31">
7325 id="x1-101002r1"></a><span
7326 class="cmr-6">1</span><span
7327 class="cmtt-8"> </span><span
7328 class="cmtt-8"> </span><span
7329 class="cmtt-8"> </span><span
7330 class="cmtt-8"> 1)</span><span
7331 class="cmtt-8"> [range]</span><span
7332 class="cmtt-8"> =</span><span
7333 class="cmtt-8"> vector</span><span
7334 class="cmtt-8"> </span><span
7335 class="cmsy-8">{</span><span
7336 class="cmtt-8"> 256,</span><span
7337 class="cmtt-8"> 128,</span><span
7338 class="cmtt-8"> 86,</span><span
7339 class="cmtt-8"> 64</span><span
7340 class="cmtt-8"> </span><span
7341 class="cmsy-8">}</span><span
7342 class="cmtt-8"> element</span><span
7343 class="cmtt-8"> ([floor1_multiplier]-1)</span>
7344 <br class="fancyvrb" /><a
7345 id="x1-101004r2"></a><span
7346 class="cmr-6">2</span><span
7347 class="cmtt-8"> </span><span
7348 class="cmtt-8"> </span><span
7349 class="cmtt-8"> </span><span
7350 class="cmtt-8"> 2)</span><span
7351 class="cmtt-8"> vector</span><span
7352 class="cmtt-8"> [floor1_step2_flag]</span><span
7353 class="cmtt-8"> element</span><span
7354 class="cmtt-8"> [0]</span><span
7355 class="cmtt-8"> =</span><span
7356 class="cmtt-8"> set</span>
7357 <br class="fancyvrb" /><a
7358 id="x1-101006r3"></a><span
7359 class="cmr-6">3</span><span
7360 class="cmtt-8"> </span><span
7361 class="cmtt-8"> </span><span
7362 class="cmtt-8"> </span><span
7363 class="cmtt-8"> 3)</span><span
7364 class="cmtt-8"> vector</span><span
7365 class="cmtt-8"> [floor1_step2_flag]</span><span
7366 class="cmtt-8"> element</span><span
7367 class="cmtt-8"> [1]</span><span
7368 class="cmtt-8"> =</span><span
7369 class="cmtt-8"> set</span>
7370 <br class="fancyvrb" /><a
7371 id="x1-101008r4"></a><span
7372 class="cmr-6">4</span><span
7373 class="cmtt-8"> </span><span
7374 class="cmtt-8"> </span><span
7375 class="cmtt-8"> </span><span
7376 class="cmtt-8"> 4)</span><span
7377 class="cmtt-8"> vector</span><span
7378 class="cmtt-8"> [floor1_final_Y]</span><span
7379 class="cmtt-8"> element</span><span
7380 class="cmtt-8"> [0]</span><span
7381 class="cmtt-8"> =</span><span
7382 class="cmtt-8"> vector</span><span
7383 class="cmtt-8"> [floor1_Y]</span><span
7384 class="cmtt-8"> element</span><span
7385 class="cmtt-8"> [0]</span>
7386 <br class="fancyvrb" /><a
7387 id="x1-101010r5"></a><span
7388 class="cmr-6">5</span><span
7389 class="cmtt-8"> </span><span
7390 class="cmtt-8"> </span><span
7391 class="cmtt-8"> </span><span
7392 class="cmtt-8"> 5)</span><span
7393 class="cmtt-8"> vector</span><span
7394 class="cmtt-8"> [floor1_final_Y]</span><span
7395 class="cmtt-8"> element</span><span
7396 class="cmtt-8"> [1]</span><span
7397 class="cmtt-8"> =</span><span
7398 class="cmtt-8"> vector</span><span
7399 class="cmtt-8"> [floor1_Y]</span><span
7400 class="cmtt-8"> element</span><span
7401 class="cmtt-8"> [1]</span>
7402 <br class="fancyvrb" /><a
7403 id="x1-101012r6"></a><span
7404 class="cmr-6">6</span><span
7405 class="cmtt-8"> </span><span
7406 class="cmtt-8"> </span><span
7407 class="cmtt-8"> </span><span
7408 class="cmtt-8"> 6)</span><span
7409 class="cmtt-8"> iterate</span><span
7410 class="cmtt-8"> [i]</span><span
7411 class="cmtt-8"> over</span><span
7412 class="cmtt-8"> the</span><span
7413 class="cmtt-8"> range</span><span
7414 class="cmtt-8"> 2</span><span
7415 class="cmtt-8"> ...</span><span
7416 class="cmtt-8"> [floor1_values]-1</span><span
7417 class="cmtt-8"> </span><span
7418 class="cmsy-8">{</span>
7419 <br class="fancyvrb" /><a
7420 id="x1-101014r7"></a><span
7421 class="cmr-6">7</span><span
7422 class="cmtt-8"> </span><span
7423 class="cmtt-8"> </span>
7424 <br class="fancyvrb" /><a
7425 id="x1-101016r8"></a><span
7426 class="cmr-6">8</span><span
7427 class="cmtt-8"> </span><span
7428 class="cmtt-8"> </span><span
7429 class="cmtt-8"> </span><span
7430 class="cmtt-8"> </span><span
7431 class="cmtt-8"> </span><span
7432 class="cmtt-8"> </span><span
7433 class="cmtt-8"> </span><span
7434 class="cmtt-8"> </span><span
7435 class="cmtt-8"> 7)</span><span
7436 class="cmtt-8"> [low_neighbor_offset]</span><span
7437 class="cmtt-8"> =</span><span
7438 class="cmtt-8"> </span><a
7439 href="#x1-1200009.2.4"><span
7440 class="cmtt-8">low_neighbor</span></a><span
7441 class="cmtt-8">([floor1_X_list],[i])</span>
7442 <br class="fancyvrb" /><a
7443 id="x1-101018r9"></a><span
7444 class="cmr-6">9</span><span
7445 class="cmtt-8"> </span><span
7446 class="cmtt-8"> </span><span
7447 class="cmtt-8"> </span><span
7448 class="cmtt-8"> </span><span
7449 class="cmtt-8"> </span><span
7450 class="cmtt-8"> </span><span
7451 class="cmtt-8"> </span><span
7452 class="cmtt-8"> </span><span
7453 class="cmtt-8"> 8)</span><span
7454 class="cmtt-8"> [high_neighbor_offset]</span><span
7455 class="cmtt-8"> =</span><span
7456 class="cmtt-8"> </span><a
7457 href="#x1-1210009.2.5"><span
7458 class="cmtt-8">high_neighbor</span></a><span
7459 class="cmtt-8">([floor1_X_list],[i])</span>
7460 <br class="fancyvrb" /><a
7461 id="x1-101020r10"></a><span
7462 class="cmr-6">10</span><span
7463 class="cmtt-8"> </span><span
7464 class="cmtt-8"> </span>
7465 <br class="fancyvrb" /><a
7466 id="x1-101022r11"></a><span
7467 class="cmr-6">11</span><span
7468 class="cmtt-8"> </span><span
7469 class="cmtt-8"> </span><span
7470 class="cmtt-8"> </span><span
7471 class="cmtt-8"> </span><span
7472 class="cmtt-8"> </span><span
7473 class="cmtt-8"> </span><span
7474 class="cmtt-8"> </span><span
7475 class="cmtt-8"> </span><span
7476 class="cmtt-8"> 9)</span><span
7477 class="cmtt-8"> [predicted]</span><span
7478 class="cmtt-8"> =</span><span
7479 class="cmtt-8"> </span><a
7480 href="#x1-1220009.2.6"><span
7481 class="cmtt-8">render_point</span></a><span
7482 class="cmtt-8">(</span><span
7483 class="cmtt-8"> vector</span><span
7484 class="cmtt-8"> [floor1_X_list]</span><span
7485 class="cmtt-8"> element</span><span
7486 class="cmtt-8"> [low_neighbor_offset],</span>
7487 <br class="fancyvrb" /><a
7488 id="x1-101024r12"></a><span
7489 class="cmr-6">12</span><span
7490 class="cmtt-8"> </span><span
7491 class="cmtt-8">  </span><span
7492 class="cmtt-8"> </span><span
7493 class="cmtt-8"> </span><span
7494 class="cmtt-8"> </span><span
7495 class="cmtt-8"> </span><span
7496 class="cmtt-8"> </span><span
7497 class="cmtt-8"> vector</span><span
7498 class="cmtt-8"> [floor1_final_Y]</span><span
7499 class="cmtt-8"> element</span><span
7500 class="cmtt-8"> [low_neighbor_offset],</span>
7501 <br class="fancyvrb" /><a
7502 id="x1-101026r13"></a><span
7503 class="cmr-6">13</span><span
7504 class="cmtt-8"> </span><span
7505 class="cmtt-8"> </span><span
7506 class="cmtt-8"> </span><span
7507 class="cmtt-8"> </span><span
7508 class="cmtt-8"> </span><span
7509 class="cmtt-8"> </span><span
7510 class="cmtt-8"> </span><span
7511 class="cmtt-8"> </span><span
7512 class="cmtt-8"> </span><span
7513 class="cmtt-8"> </span><span
7514 class="cmtt-8"> </span><span
7515 class="cmtt-8"> </span><span
7516 class="cmtt-8"> </span><span
7517 class="cmtt-8"> </span><span
7518 class="cmtt-8"> </span><span
7519 class="cmtt-8"> </span><span
7520 class="cmtt-8"> </span><span
7521 class="cmtt-8"> </span><span
7522 class="cmtt-8"> </span><span
7523 class="cmtt-8"> </span><span
7524 class="cmtt-8"> </span><span
7525 class="cmtt-8"> </span><span
7526 class="cmtt-8"> </span><span
7527 class="cmtt-8"> </span><span
7528 class="cmtt-8"> </span><span
7529 class="cmtt-8"> </span><span
7530 class="cmtt-8"> </span><span
7531 class="cmtt-8"> </span><span
7532 class="cmtt-8"> </span><span
7533 class="cmtt-8"> </span><span
7534 class="cmtt-8"> </span><span
7535 class="cmtt-8"> </span><span
7536 class="cmtt-8"> </span><span
7537 class="cmtt-8"> </span><span
7538 class="cmtt-8"> </span><span
7539 class="cmtt-8"> </span><span
7540 class="cmtt-8"> </span><span
7541 class="cmtt-8"> </span><span
7542 class="cmtt-8"> </span><span
7543 class="cmtt-8"> vector</span><span
7544 class="cmtt-8"> [floor1_X_list]</span><span
7545 class="cmtt-8"> element</span><span
7546 class="cmtt-8"> [high_neighbor_offset],</span>
7547 <br class="fancyvrb" /><a
7548 id="x1-101028r14"></a><span
7549 class="cmr-6">14</span><span
7550 class="cmtt-8"> </span><span
7551 class="cmtt-8">  </span><span
7552 class="cmtt-8"> </span><span
7553 class="cmtt-8"> </span><span
7554 class="cmtt-8"> </span><span
7555 class="cmtt-8"> </span><span
7556 class="cmtt-8"> </span><span
7557 class="cmtt-8"> vector</span><span
7558 class="cmtt-8"> [floor1_final_Y]</span><span
7559 class="cmtt-8"> element</span><span
7560 class="cmtt-8"> [high_neighbor_offset],</span>
7561 <br class="fancyvrb" /><a
7562 id="x1-101030r15"></a><span
7563 class="cmr-6">15</span><span
7564 class="cmtt-8"> </span><span
7565 class="cmtt-8"> </span><span
7566 class="cmtt-8"> </span><span
7567 class="cmtt-8"> </span><span
7568 class="cmtt-8"> </span><span
7569 class="cmtt-8"> </span><span
7570 class="cmtt-8"> </span><span
7571 class="cmtt-8"> </span><span
7572 class="cmtt-8"> </span><span
7573 class="cmtt-8"> </span><span
7574 class="cmtt-8"> </span><span
7575 class="cmtt-8"> </span><span
7576 class="cmtt-8"> </span><span
7577 class="cmtt-8"> </span><span
7578 class="cmtt-8"> </span><span
7579 class="cmtt-8"> </span><span
7580 class="cmtt-8"> </span><span
7581 class="cmtt-8"> </span><span
7582 class="cmtt-8"> </span><span
7583 class="cmtt-8"> </span><span
7584 class="cmtt-8"> </span><span
7585 class="cmtt-8"> </span><span
7586 class="cmtt-8"> </span><span
7587 class="cmtt-8"> </span><span
7588 class="cmtt-8"> </span><span
7589 class="cmtt-8"> </span><span
7590 class="cmtt-8"> </span><span
7591 class="cmtt-8"> </span><span
7592 class="cmtt-8"> </span><span
7593 class="cmtt-8"> </span><span
7594 class="cmtt-8"> </span><span
7595 class="cmtt-8"> </span><span
7596 class="cmtt-8"> </span><span
7597 class="cmtt-8"> </span><span
7598 class="cmtt-8"> </span><span
7599 class="cmtt-8"> </span><span
7600 class="cmtt-8"> </span><span
7601 class="cmtt-8"> </span><span
7602 class="cmtt-8"> </span><span
7603 class="cmtt-8"> vector</span><span
7604 class="cmtt-8"> [floor1_X_list]</span><span
7605 class="cmtt-8"> element</span><span
7606 class="cmtt-8"> [i]</span><span
7607 class="cmtt-8"> )</span>
7608 <br class="fancyvrb" /><a
7609 id="x1-101032r16"></a><span
7610 class="cmr-6">16</span><span
7611 class="cmtt-8"> </span><span
7612 class="cmtt-8"> </span>
7613 <br class="fancyvrb" /><a
7614 id="x1-101034r17"></a><span
7615 class="cmr-6">17</span><span
7616 class="cmtt-8"> </span><span
7617 class="cmtt-8"> </span><span
7618 class="cmtt-8"> </span><span
7619 class="cmtt-8"> </span><span
7620 class="cmtt-8"> </span><span
7621 class="cmtt-8"> </span><span
7622 class="cmtt-8"> </span><span
7623 class="cmtt-8"> 10)</span><span
7624 class="cmtt-8"> [val]</span><span
7625 class="cmtt-8"> =</span><span
7626 class="cmtt-8"> vector</span><span
7627 class="cmtt-8"> [floor1_Y]</span><span
7628 class="cmtt-8"> element</span><span
7629 class="cmtt-8"> [i]</span>
7630 <br class="fancyvrb" /><a
7631 id="x1-101036r18"></a><span
7632 class="cmr-6">18</span><span
7633 class="cmtt-8"> </span><span
7634 class="cmtt-8"> </span><span
7635 class="cmtt-8"> </span><span
7636 class="cmtt-8"> </span><span
7637 class="cmtt-8"> </span><span
7638 class="cmtt-8"> </span><span
7639 class="cmtt-8"> </span><span
7640 class="cmtt-8"> 11)</span><span
7641 class="cmtt-8"> [highroom]</span><span
7642 class="cmtt-8"> =</span><span
7643 class="cmtt-8"> [range]</span><span
7644 class="cmtt-8"> -</span><span
7645 class="cmtt-8"> [predicted]</span>
7646 <br class="fancyvrb" /><a
7647 id="x1-101038r19"></a><span
7648 class="cmr-6">19</span><span
7649 class="cmtt-8"> </span><span
7650 class="cmtt-8"> </span><span
7651 class="cmtt-8"> </span><span
7652 class="cmtt-8"> </span><span
7653 class="cmtt-8"> </span><span
7654 class="cmtt-8"> </span><span
7655 class="cmtt-8"> </span><span
7656 class="cmtt-8"> 12)</span><span
7657 class="cmtt-8"> [lowroom]</span><span
7658 class="cmtt-8"> </span><span
7659 class="cmtt-8"> =</span><span
7660 class="cmtt-8"> [predicted]</span>
7661 <br class="fancyvrb" /><a
7662 id="x1-101040r20"></a><span
7663 class="cmr-6">20</span><span
7664 class="cmtt-8"> </span><span
7665 class="cmtt-8"> </span><span
7666 class="cmtt-8"> </span><span
7667 class="cmtt-8"> </span><span
7668 class="cmtt-8"> </span><span
7669 class="cmtt-8"> </span><span
7670 class="cmtt-8"> </span><span
7671 class="cmtt-8"> 13)</span><span
7672 class="cmtt-8"> if</span><span
7673 class="cmtt-8"> (</span><span
7674 class="cmtt-8"> [highroom]</span><span
7675 class="cmtt-8"> is</span><span
7676 class="cmtt-8"> less</span><span
7677 class="cmtt-8"> than</span><span
7678 class="cmtt-8"> [lowroom]</span><span
7679 class="cmtt-8"> )</span><span
7680 class="cmtt-8"> </span><span
7681 class="cmsy-8">{</span>
7682 <br class="fancyvrb" /><a
7683 id="x1-101042r21"></a><span
7684 class="cmr-6">21</span><span
7685 class="cmtt-8"> </span><span
7686 class="cmtt-8"> </span>
7687 <br class="fancyvrb" /><a
7688 id="x1-101044r22"></a><span
7689 class="cmr-6">22</span><span
7690 class="cmtt-8"> </span><span
7691 class="cmtt-8"> </span><span
7692 class="cmtt-8"> </span><span
7693 class="cmtt-8"> </span><span
7694 class="cmtt-8"> </span><span
7695 class="cmtt-8"> </span><span
7696 class="cmtt-8"> </span><span
7697 class="cmtt-8"> </span><span
7698 class="cmtt-8"> </span><span
7699 class="cmtt-8"> </span><span
7700 class="cmtt-8"> </span><span
7701 class="cmtt-8"> </span><span
7702 class="cmtt-8"> </span><span
7703 class="cmtt-8"> 14)</span><span
7704 class="cmtt-8"> [room]</span><span
7705 class="cmtt-8"> =</span><span
7706 class="cmtt-8"> [highroom]</span><span
7707 class="cmtt-8"> *</span><span
7708 class="cmtt-8"> 2</span>
7709 <br class="fancyvrb" /><a
7710 id="x1-101046r23"></a><span
7711 class="cmr-6">23</span><span
7712 class="cmtt-8"> </span><span
7713 class="cmtt-8"> </span>
7714 <br class="fancyvrb" /><a
7715 id="x1-101048r24"></a><span
7716 class="cmr-6">24</span><span
7717 class="cmtt-8"> </span><span
7718 class="cmtt-8"> </span><span
7719 class="cmtt-8"> </span><span
7720 class="cmtt-8"> </span><span
7721 class="cmtt-8"> </span><span
7722 class="cmtt-8"> </span><span
7723 class="cmtt-8"> </span><span
7724 class="cmtt-8"> </span><span
7725 class="cmtt-8"> </span><span
7726 class="cmtt-8"> </span><span
7727 class="cmtt-8"> </span><span
7728 class="cmtt-8"> </span><span
7729 class="cmsy-8">}</span><span
7730 class="cmtt-8"> else</span><span
7731 class="cmtt-8"> [highroom]</span><span
7732 class="cmtt-8"> is</span><span
7733 class="cmtt-8"> not</span><span
7734 class="cmtt-8"> less</span><span
7735 class="cmtt-8"> than</span><span
7736 class="cmtt-8"> [lowroom]</span><span
7737 class="cmtt-8"> </span><span
7738 class="cmsy-8">{</span>
7739 <br class="fancyvrb" /><a
7740 id="x1-101050r25"></a><span
7741 class="cmr-6">25</span><span
7742 class="cmtt-8"> </span><span
7743 class="cmtt-8"> </span>
7744 <br class="fancyvrb" /><a
7745 id="x1-101052r26"></a><span
7746 class="cmr-6">26</span><span
7747 class="cmtt-8"> </span><span
7748 class="cmtt-8"> </span><span
7749 class="cmtt-8"> </span><span
7750 class="cmtt-8"> </span><span
7751 class="cmtt-8"> </span><span
7752 class="cmtt-8"> </span><span
7753 class="cmtt-8"> </span><span
7754 class="cmtt-8"> </span><span
7755 class="cmtt-8"> </span><span
7756 class="cmtt-8"> </span><span
7757 class="cmtt-8"> </span><span
7758 class="cmtt-8"> </span><span
7759 class="cmtt-8"> </span><span
7760 class="cmtt-8"> 15)</span><span
7761 class="cmtt-8"> [room]</span><span
7762 class="cmtt-8"> =</span><span
7763 class="cmtt-8"> [lowroom]</span><span
7764 class="cmtt-8"> *</span><span
7765 class="cmtt-8"> 2</span>
7766 <br class="fancyvrb" /><a
7767 id="x1-101054r27"></a><span
7768 class="cmr-6">27</span><span
7769 class="cmtt-8"> </span><span
7770 class="cmtt-8"> </span>
7771 <br class="fancyvrb" /><a
7772 id="x1-101056r28"></a><span
7773 class="cmr-6">28</span><span
7774 class="cmtt-8"> </span><span
7775 class="cmtt-8"> </span><span
7776 class="cmtt-8"> </span><span
7777 class="cmtt-8"> </span><span
7778 class="cmtt-8"> </span><span
7779 class="cmtt-8"> </span><span
7780 class="cmtt-8"> </span><span
7781 class="cmtt-8"> </span><span
7782 class="cmtt-8"> </span><span
7783 class="cmtt-8"> </span><span
7784 class="cmtt-8"> </span><span
7785 class="cmtt-8"> </span><span
7786 class="cmsy-8">}</span>
7787 <br class="fancyvrb" /><a
7788 id="x1-101058r29"></a><span
7789 class="cmr-6">29</span><span
7790 class="cmtt-8"> </span><span
7791 class="cmtt-8"> </span>
7792 <br class="fancyvrb" /><a
7793 id="x1-101060r30"></a><span
7794 class="cmr-6">30</span><span
7795 class="cmtt-8"> </span><span
7796 class="cmtt-8"> </span><span
7797 class="cmtt-8"> </span><span
7798 class="cmtt-8"> </span><span
7799 class="cmtt-8"> </span><span
7800 class="cmtt-8"> </span><span
7801 class="cmtt-8"> </span><span
7802 class="cmtt-8"> 16)</span><span
7803 class="cmtt-8"> if</span><span
7804 class="cmtt-8"> (</span><span
7805 class="cmtt-8"> [val]</span><span
7806 class="cmtt-8"> is</span><span
7807 class="cmtt-8"> nonzero</span><span
7808 class="cmtt-8"> )</span><span
7809 class="cmtt-8"> </span><span
7810 class="cmsy-8">{</span>
7811 <br class="fancyvrb" /><a
7812 id="x1-101062r31"></a><span
7813 class="cmr-6">31</span><span
7814 class="cmtt-8"> </span><span
7815 class="cmtt-8"> </span>
7816 <br class="fancyvrb" /><a
7817 id="x1-101064r32"></a><span
7818 class="cmr-6">32</span><span
7819 class="cmtt-8"> </span><span
7820 class="cmtt-8"> </span><span
7821 class="cmtt-8"> </span><span
7822 class="cmtt-8"> </span><span
7823 class="cmtt-8"> </span><span
7824 class="cmtt-8"> </span><span
7825 class="cmtt-8"> </span><span
7826 class="cmtt-8"> </span><span
7827 class="cmtt-8"> </span><span
7828 class="cmtt-8"> </span><span
7829 class="cmtt-8"> </span><span
7830 class="cmtt-8"> </span><span
7831 class="cmtt-8"> </span><span
7832 class="cmtt-8"> 17)</span><span
7833 class="cmtt-8"> vector</span><span
7834 class="cmtt-8"> [floor1_step2_flag]</span><span
7835 class="cmtt-8"> element</span><span
7836 class="cmtt-8"> [low_neighbor_offset]</span><span
7837 class="cmtt-8"> =</span><span
7838 class="cmtt-8"> set</span>
7839 <br class="fancyvrb" /><a
7840 id="x1-101066r33"></a><span
7841 class="cmr-6">33</span><span
7842 class="cmtt-8"> </span><span
7843 class="cmtt-8"> </span><span
7844 class="cmtt-8"> </span><span
7845 class="cmtt-8"> </span><span
7846 class="cmtt-8"> </span><span
7847 class="cmtt-8"> </span><span
7848 class="cmtt-8"> </span><span
7849 class="cmtt-8"> </span><span
7850 class="cmtt-8"> </span><span
7851 class="cmtt-8"> </span><span
7852 class="cmtt-8"> </span><span
7853 class="cmtt-8"> </span><span
7854 class="cmtt-8"> </span><span
7855 class="cmtt-8"> 18)</span><span
7856 class="cmtt-8"> vector</span><span
7857 class="cmtt-8"> [floor1_step2_flag]</span><span
7858 class="cmtt-8"> element</span><span
7859 class="cmtt-8"> [high_neighbor_offset]</span><span
7860 class="cmtt-8"> =</span><span
7861 class="cmtt-8"> set</span>
7862 <br class="fancyvrb" /><a
7863 id="x1-101068r34"></a><span
7864 class="cmr-6">34</span><span
7865 class="cmtt-8"> </span><span
7866 class="cmtt-8"> </span><span
7867 class="cmtt-8"> </span><span
7868 class="cmtt-8"> </span><span
7869 class="cmtt-8"> </span><span
7870 class="cmtt-8"> </span><span
7871 class="cmtt-8"> </span><span
7872 class="cmtt-8"> </span><span
7873 class="cmtt-8"> </span><span
7874 class="cmtt-8"> </span><span
7875 class="cmtt-8"> </span><span
7876 class="cmtt-8"> </span><span
7877 class="cmtt-8"> </span><span
7878 class="cmtt-8"> 19)</span><span
7879 class="cmtt-8"> vector</span><span
7880 class="cmtt-8"> [floor1_step2_flag]</span><span
7881 class="cmtt-8"> element</span><span
7882 class="cmtt-8"> [i]</span><span
7883 class="cmtt-8"> =</span><span
7884 class="cmtt-8"> set</span>
7885 <br class="fancyvrb" /><a
7886 id="x1-101070r35"></a><span
7887 class="cmr-6">35</span><span
7888 class="cmtt-8"> </span><span
7889 class="cmtt-8"> </span><span
7890 class="cmtt-8"> </span><span
7891 class="cmtt-8"> </span><span
7892 class="cmtt-8"> </span><span
7893 class="cmtt-8"> </span><span
7894 class="cmtt-8"> </span><span
7895 class="cmtt-8"> </span><span
7896 class="cmtt-8"> </span><span
7897 class="cmtt-8"> </span><span
7898 class="cmtt-8"> </span><span
7899 class="cmtt-8"> </span><span
7900 class="cmtt-8"> </span><span
7901 class="cmtt-8"> 20)</span><span
7902 class="cmtt-8"> if</span><span
7903 class="cmtt-8"> (</span><span
7904 class="cmtt-8"> [val]</span><span
7905 class="cmtt-8"> is</span><span
7906 class="cmtt-8"> greater</span><span
7907 class="cmtt-8"> than</span><span
7908 class="cmtt-8"> or</span><span
7909 class="cmtt-8"> equal</span><span
7910 class="cmtt-8"> to</span><span
7911 class="cmtt-8"> [room]</span><span
7912 class="cmtt-8"> )</span><span
7913 class="cmtt-8"> </span><span
7914 class="cmsy-8">{</span>
7915 <br class="fancyvrb" /><a
7916 id="x1-101072r36"></a><span
7917 class="cmr-6">36</span><span
7918 class="cmtt-8"> </span><span
7919 class="cmtt-8"> </span>
7920 <br class="fancyvrb" /><a
7921 id="x1-101074r37"></a><span
7922 class="cmr-6">37</span><span
7923 class="cmtt-8"> </span><span
7924 class="cmtt-8"> </span><span
7925 class="cmtt-8"> </span><span
7926 class="cmtt-8"> </span><span
7927 class="cmtt-8"> </span><span
7928 class="cmtt-8"> </span><span
7929 class="cmtt-8"> </span><span
7930 class="cmtt-8"> </span><span
7931 class="cmtt-8"> </span><span
7932 class="cmtt-8"> </span><span
7933 class="cmtt-8"> </span><span
7934 class="cmtt-8"> </span><span
7935 class="cmtt-8"> </span><span
7936 class="cmtt-8"> </span><span
7937 class="cmtt-8"> </span><span
7938 class="cmtt-8"> </span><span
7939 class="cmtt-8"> </span><span
7940 class="cmtt-8"> </span><span
7941 class="cmtt-8"> </span><span
7942 class="cmtt-8"> 21)</span><span
7943 class="cmtt-8"> if</span><span
7944 class="cmtt-8"> (</span><span
7945 class="cmtt-8"> [highroom]</span><span
7946 class="cmtt-8"> is</span><span
7947 class="cmtt-8"> greater</span><span
7948 class="cmtt-8"> than</span><span
7949 class="cmtt-8"> [lowroom]</span><span
7950 class="cmtt-8"> )</span><span
7951 class="cmtt-8"> </span><span
7952 class="cmsy-8">{</span>
7953 <br class="fancyvrb" /><a
7954 id="x1-101076r38"></a><span
7955 class="cmr-6">38</span><span
7956 class="cmtt-8"> </span><span
7957 class="cmtt-8"> </span>
7958 <br class="fancyvrb" /><a
7959 id="x1-101078r39"></a><span
7960 class="cmr-6">39</span><span
7961 class="cmtt-8"> </span><span
7962 class="cmtt-8"> </span><span
7963 class="cmtt-8"> </span><span
7964 class="cmtt-8"> </span><span
7965 class="cmtt-8"> </span><span
7966 class="cmtt-8"> </span><span
7967 class="cmtt-8"> </span><span
7968 class="cmtt-8"> </span><span
7969 class="cmtt-8"> </span><span
7970 class="cmtt-8"> </span><span
7971 class="cmtt-8"> </span><span
7972 class="cmtt-8"> </span><span
7973 class="cmtt-8"> </span><span
7974 class="cmtt-8"> </span><span
7975 class="cmtt-8"> </span><span
7976 class="cmtt-8"> </span><span
7977 class="cmtt-8"> </span><span
7978 class="cmtt-8"> </span><span
7979 class="cmtt-8"> </span><span
7980 class="cmtt-8"> </span><span
7981 class="cmtt-8"> </span><span
7982 class="cmtt-8"> </span><span
7983 class="cmtt-8"> </span><span
7984 class="cmtt-8"> </span><span
7985 class="cmtt-8"> </span><span
7986 class="cmtt-8"> 22)</span><span
7987 class="cmtt-8"> vector</span><span
7988 class="cmtt-8"> [floor1_final_Y]</span><span
7989 class="cmtt-8"> element</span><span
7990 class="cmtt-8"> [i]</span><span
7991 class="cmtt-8"> =</span><span
7992 class="cmtt-8"> [val]</span><span
7993 class="cmtt-8"> -</span><span
7994 class="cmtt-8"> [lowroom]</span><span
7995 class="cmtt-8"> +</span><span
7996 class="cmtt-8"> [predicted]</span>
7997 <br class="fancyvrb" /><a
7998 id="x1-101080r40"></a><span
7999 class="cmr-6">40</span><span
8000 class="cmtt-8"> </span><span
8001 class="cmtt-8"> </span>
8002 <br class="fancyvrb" /><a
8003 id="x1-101082r41"></a><span
8004 class="cmr-6">41</span><span
8005 class="cmtt-8"> </span><span
8006 class="cmtt-8">  </span><span
8007 class="cmtt-8"> </span><span
8008 class="cmtt-8"> </span><span
8009 class="cmtt-8"> </span><span
8010 class="cmtt-8"> </span><span
8011 class="cmtt-8"> </span><span
8012 class="cmtt-8"> </span><span
8013 class="cmsy-8">}</span><span
8014 class="cmtt-8"> else</span><span
8015 class="cmtt-8"> [highroom]</span><span
8016 class="cmtt-8"> is</span><span
8017 class="cmtt-8"> not</span><span
8018 class="cmtt-8"> greater</span><span
8019 class="cmtt-8"> than</span><span
8020 class="cmtt-8"> [lowroom]</span><span
8021 class="cmtt-8"> </span><span
8022 class="cmsy-8">{</span>
8023 <br class="fancyvrb" /><a
8024 id="x1-101084r42"></a><span
8025 class="cmr-6">42</span><span
8026 class="cmtt-8"> </span><span
8027 class="cmtt-8"> </span>
8028 <br class="fancyvrb" /><a
8029 id="x1-101086r43"></a><span
8030 class="cmr-6">43</span><span
8031 class="cmtt-8"> </span><span
8032 class="cmtt-8"> </span><span
8033 class="cmtt-8"> </span><span
8034 class="cmtt-8"> </span><span
8035 class="cmtt-8"> </span><span
8036 class="cmtt-8"> </span><span
8037 class="cmtt-8"> </span><span
8038 class="cmtt-8"> </span><span
8039 class="cmtt-8"> </span><span
8040 class="cmtt-8"> </span><span
8041 class="cmtt-8"> </span><span
8042 class="cmtt-8"> </span><span
8043 class="cmtt-8"> </span><span
8044 class="cmtt-8"> </span><span
8045 class="cmtt-8"> </span><span
8046 class="cmtt-8"> </span><span
8047 class="cmtt-8"> </span><span
8048 class="cmtt-8"> </span><span
8049 class="cmtt-8"> </span><span
8050 class="cmtt-8"> </span><span
8051 class="cmtt-8"> </span><span
8052 class="cmtt-8"> </span><span
8053 class="cmtt-8"> </span><span
8054 class="cmtt-8"> </span><span
8055 class="cmtt-8"> </span><span
8056 class="cmtt-8"> 23)</span><span
8057 class="cmtt-8"> vector</span><span
8058 class="cmtt-8"> [floor1_final_Y]</span><span
8059 class="cmtt-8"> element</span><span
8060 class="cmtt-8"> [i]</span><span
8061 class="cmtt-8"> =</span><span
8062 class="cmtt-8"> [predicted]</span><span
8063 class="cmtt-8"> -</span><span
8064 class="cmtt-8"> [val]</span><span
8065 class="cmtt-8"> +</span><span
8066 class="cmtt-8"> [highroom]</span><span
8067 class="cmtt-8"> -</span><span
8068 class="cmtt-8"> 1</span>
8069 <br class="fancyvrb" /><a
8070 id="x1-101088r44"></a><span
8071 class="cmr-6">44</span><span
8072 class="cmtt-8"> </span><span
8073 class="cmtt-8"> </span>
8074 <br class="fancyvrb" /><a
8075 id="x1-101090r45"></a><span
8076 class="cmr-6">45</span><span
8077 class="cmtt-8"> </span><span
8078 class="cmtt-8"> </span><span
8079 class="cmtt-8"> </span><span
8080 class="cmtt-8"> </span><span
8081 class="cmtt-8"> </span><span
8082 class="cmtt-8"> </span><span
8083 class="cmtt-8"> </span><span
8084 class="cmtt-8"> </span><span
8085 class="cmtt-8"> </span><span
8086 class="cmtt-8"> </span><span
8087 class="cmtt-8"> </span><span
8088 class="cmtt-8"> </span><span
8089 class="cmtt-8"> </span><span
8090 class="cmtt-8"> </span><span
8091 class="cmtt-8"> </span><span
8092 class="cmtt-8"> </span><span
8093 class="cmtt-8"> </span><span
8094 class="cmtt-8"> </span><span
8095 class="cmtt-8"> </span><span
8096 class="cmtt-8"> </span><span
8097 class="cmtt-8"> </span><span
8098 class="cmtt-8"> </span><span
8099 class="cmtt-8"> </span><span
8100 class="cmtt-8"> </span><span
8101 class="cmsy-8">}</span>
8102 <br class="fancyvrb" /><a
8103 id="x1-101092r46"></a><span
8104 class="cmr-6">46</span><span
8105 class="cmtt-8"> </span><span
8106 class="cmtt-8"> </span>
8107 <br class="fancyvrb" /><a
8108 id="x1-101094r47"></a><span
8109 class="cmr-6">47</span><span
8110 class="cmtt-8"> </span><span
8111 class="cmtt-8"> </span><span
8112 class="cmtt-8"> </span><span
8113 class="cmtt-8"> </span><span
8114 class="cmtt-8"> </span><span
8115 class="cmtt-8"> </span><span
8116 class="cmtt-8"> </span><span
8117 class="cmtt-8"> </span><span
8118 class="cmtt-8"> </span><span
8119 class="cmtt-8"> </span><span
8120 class="cmtt-8"> </span><span
8121 class="cmtt-8"> </span><span
8122 class="cmtt-8"> </span><span
8123 class="cmtt-8"> </span><span
8124 class="cmtt-8"> </span><span
8125 class="cmtt-8"> </span><span
8126 class="cmtt-8"> </span><span
8127 class="cmtt-8"> </span><span
8128 class="cmsy-8">}</span><span
8129 class="cmtt-8"> else</span><span
8130 class="cmtt-8"> [val]</span><span
8131 class="cmtt-8"> is</span><span
8132 class="cmtt-8"> less</span><span
8133 class="cmtt-8"> than</span><span
8134 class="cmtt-8"> [room]</span><span
8135 class="cmtt-8"> </span><span
8136 class="cmsy-8">{</span>
8137 <br class="fancyvrb" /><a
8138 id="x1-101096r48"></a><span
8139 class="cmr-6">48</span><span
8140 class="cmtt-8"> </span><span
8141 class="cmtt-8"> </span>
8142 <br class="fancyvrb" /><a
8143 id="x1-101098r49"></a><span
8144 class="cmr-6">49</span><span
8145 class="cmtt-8"> </span><span
8146 class="cmtt-8"> </span><span
8147 class="cmtt-8"> </span><span
8148 class="cmtt-8"> </span><span
8149 class="cmtt-8"> </span><span
8150 class="cmtt-8"> </span><span
8151 class="cmtt-8"> </span><span
8152 class="cmtt-8"> </span><span
8153 class="cmtt-8"> </span><span
8154 class="cmtt-8"> </span><span
8155 class="cmtt-8"> </span><span
8156 class="cmtt-8"> </span><span
8157 class="cmtt-8"> </span><span
8158 class="cmtt-8"> </span><span
8159 class="cmtt-8"> </span><span
8160 class="cmtt-8"> </span><span
8161 class="cmtt-8"> </span><span
8162 class="cmtt-8"> </span><span
8163 class="cmtt-8"> </span><span
8164 class="cmtt-8"> </span><span
8165 class="cmtt-8"> </span><span
8166 class="cmtt-8"> 24)</span><span
8167 class="cmtt-8"> if</span><span
8168 class="cmtt-8"> ([val]</span><span
8169 class="cmtt-8"> is</span><span
8170 class="cmtt-8"> odd)</span><span
8171 class="cmtt-8"> </span><span
8172 class="cmsy-8">{</span>
8173 <br class="fancyvrb" /><a
8174 id="x1-101100r50"></a><span
8175 class="cmr-6">50</span><span
8176 class="cmtt-8"> </span><span
8177 class="cmtt-8"> </span>
8178 <br class="fancyvrb" /><a
8179 id="x1-101102r51"></a><span
8180 class="cmr-6">51</span><span
8181 class="cmtt-8"> </span><span
8182 class="cmtt-8"> </span><span
8183 class="cmtt-8"> </span><span
8184 class="cmtt-8"> </span><span
8185 class="cmtt-8"> </span><span
8186 class="cmtt-8"> </span><span
8187 class="cmtt-8"> </span><span
8188 class="cmtt-8"> </span><span
8189 class="cmtt-8"> </span><span
8190 class="cmtt-8"> </span><span
8191 class="cmtt-8"> </span><span
8192 class="cmtt-8"> </span><span
8193 class="cmtt-8"> </span><span
8194 class="cmtt-8"> </span><span
8195 class="cmtt-8"> </span><span
8196 class="cmtt-8"> </span><span
8197 class="cmtt-8"> </span><span
8198 class="cmtt-8"> </span><span
8199 class="cmtt-8"> </span><span
8200 class="cmtt-8"> </span><span
8201 class="cmtt-8"> </span><span
8202 class="cmtt-8"> </span><span
8203 class="cmtt-8"> </span><span
8204 class="cmtt-8"> </span><span
8205 class="cmtt-8"> </span><span
8206 class="cmtt-8"> 25)</span><span
8207 class="cmtt-8"> vector</span><span
8208 class="cmtt-8"> [floor1_final_Y]</span><span
8209 class="cmtt-8"> element</span><span
8210 class="cmtt-8"> [i]</span><span
8211 class="cmtt-8"> =</span>
8212 <br class="fancyvrb" /><a
8213 id="x1-101104r52"></a><span
8214 class="cmr-6">52</span><span
8215 class="cmtt-8"> </span><span
8216 class="cmtt-8"> </span><span
8217 class="cmtt-8"> </span><span
8218 class="cmtt-8"> </span><span
8219 class="cmtt-8"> </span><span
8220 class="cmtt-8"> </span><span
8221 class="cmtt-8"> </span><span
8222 class="cmtt-8"> </span><span
8223 class="cmtt-8"> </span><span
8224 class="cmtt-8"> </span><span
8225 class="cmtt-8"> </span><span
8226 class="cmtt-8"> </span><span
8227 class="cmtt-8"> </span><span
8228 class="cmtt-8"> </span><span
8229 class="cmtt-8"> </span><span
8230 class="cmtt-8"> </span><span
8231 class="cmtt-8"> </span><span
8232 class="cmtt-8"> </span><span
8233 class="cmtt-8"> </span><span
8234 class="cmtt-8"> </span><span
8235 class="cmtt-8"> </span><span
8236 class="cmtt-8"> </span><span
8237 class="cmtt-8"> </span><span
8238 class="cmtt-8"> </span><span
8239 class="cmtt-8"> </span><span
8240 class="cmtt-8"> </span><span
8241 class="cmtt-8"> </span><span
8242 class="cmtt-8"> </span><span
8243 class="cmtt-8"> </span><span
8244 class="cmtt-8"> [predicted]</span><span
8245 class="cmtt-8"> -</span><span
8246 class="cmtt-8"> (([val]</span><span
8247 class="cmtt-8"> +</span><span
8248 class="cmtt-8"> 1)</span><span
8249 class="cmtt-8"> divided</span><span
8250 class="cmtt-8"> by</span><span
8251 class="cmtt-8"> </span><span
8252 class="cmtt-8"> 2</span><span
8253 class="cmtt-8"> using</span><span
8254 class="cmtt-8"> integer</span><span
8255 class="cmtt-8"> division)</span>
8256 <br class="fancyvrb" /><a
8257 id="x1-101106r53"></a><span
8258 class="cmr-6">53</span><span
8259 class="cmtt-8"> </span><span
8260 class="cmtt-8"> </span>
8261 <br class="fancyvrb" /><a
8262 id="x1-101108r54"></a><span
8263 class="cmr-6">54</span><span
8264 class="cmtt-8"> </span><span
8265 class="cmtt-8"> </span><span
8266 class="cmtt-8"> </span><span
8267 class="cmtt-8"> </span><span
8268 class="cmtt-8"> </span><span
8269 class="cmtt-8"> </span><span
8270 class="cmtt-8"> </span><span
8271 class="cmtt-8"> </span><span
8272 class="cmtt-8"> </span><span
8273 class="cmtt-8"> </span><span
8274 class="cmtt-8"> </span><span
8275 class="cmtt-8"> </span><span
8276 class="cmtt-8"> </span><span
8277 class="cmtt-8"> </span><span
8278 class="cmtt-8"> </span><span
8279 class="cmtt-8"> </span><span
8280 class="cmtt-8"> </span><span
8281 class="cmtt-8"> </span><span
8282 class="cmtt-8"> </span><span
8283 class="cmtt-8"> </span><span
8284 class="cmtt-8"> </span><span
8285 class="cmtt-8"> </span><span
8286 class="cmtt-8"> </span><span
8287 class="cmtt-8"> </span><span
8288 class="cmsy-8">}</span><span
8289 class="cmtt-8"> else</span><span
8290 class="cmtt-8"> [val]</span><span
8291 class="cmtt-8"> is</span><span
8292 class="cmtt-8"> even</span><span
8293 class="cmtt-8"> </span><span
8294 class="cmsy-8">{</span>
8295 <br class="fancyvrb" /><a
8296 id="x1-101110r55"></a><span
8297 class="cmr-6">55</span><span
8298 class="cmtt-8"> </span><span
8299 class="cmtt-8"> </span>
8300 <br class="fancyvrb" /><a
8301 id="x1-101112r56"></a><span
8302 class="cmr-6">56</span><span
8303 class="cmtt-8"> </span><span
8304 class="cmtt-8"> </span><span
8305 class="cmtt-8"> </span><span
8306 class="cmtt-8"> </span><span
8307 class="cmtt-8"> </span><span
8308 class="cmtt-8"> </span><span
8309 class="cmtt-8"> </span><span
8310 class="cmtt-8"> </span><span
8311 class="cmtt-8"> </span><span
8312 class="cmtt-8"> </span><span
8313 class="cmtt-8"> </span><span
8314 class="cmtt-8"> </span><span
8315 class="cmtt-8"> </span><span
8316 class="cmtt-8"> </span><span
8317 class="cmtt-8"> </span><span
8318 class="cmtt-8"> </span><span
8319 class="cmtt-8"> </span><span
8320 class="cmtt-8"> </span><span
8321 class="cmtt-8"> </span><span
8322 class="cmtt-8"> </span><span
8323 class="cmtt-8"> </span><span
8324 class="cmtt-8"> </span><span
8325 class="cmtt-8"> </span><span
8326 class="cmtt-8"> </span><span
8327 class="cmtt-8"> </span><span
8328 class="cmtt-8"> 26)</span><span
8329 class="cmtt-8"> vector</span><span
8330 class="cmtt-8"> [floor1_final_Y]</span><span
8331 class="cmtt-8"> element</span><span
8332 class="cmtt-8"> [i]</span><span
8333 class="cmtt-8"> =</span>
8334 <br class="fancyvrb" /><a
8335 id="x1-101114r57"></a><span
8336 class="cmr-6">57</span><span
8337 class="cmtt-8"> </span><span
8338 class="cmtt-8"> </span><span
8339 class="cmtt-8"> </span><span
8340 class="cmtt-8"> </span><span
8341 class="cmtt-8"> </span><span
8342 class="cmtt-8"> </span><span
8343 class="cmtt-8"> </span><span
8344 class="cmtt-8"> </span><span
8345 class="cmtt-8"> </span><span
8346 class="cmtt-8"> </span><span
8347 class="cmtt-8"> </span><span
8348 class="cmtt-8"> </span><span
8349 class="cmtt-8"> </span><span
8350 class="cmtt-8"> </span><span
8351 class="cmtt-8"> </span><span
8352 class="cmtt-8"> </span><span
8353 class="cmtt-8"> </span><span
8354 class="cmtt-8"> </span><span
8355 class="cmtt-8"> </span><span
8356 class="cmtt-8"> </span><span
8357 class="cmtt-8"> </span><span
8358 class="cmtt-8"> </span><span
8359 class="cmtt-8"> </span><span
8360 class="cmtt-8"> </span><span
8361 class="cmtt-8"> </span><span
8362 class="cmtt-8"> </span><span
8363 class="cmtt-8"> </span><span
8364 class="cmtt-8"> </span><span
8365 class="cmtt-8"> </span><span
8366 class="cmtt-8"> [predicted]</span><span
8367 class="cmtt-8"> +</span><span
8368 class="cmtt-8"> ([val]</span><span
8369 class="cmtt-8"> /</span><span
8370 class="cmtt-8"> 2</span><span
8371 class="cmtt-8"> using</span><span
8372 class="cmtt-8"> integer</span><span
8373 class="cmtt-8"> division)</span>
8374 <br class="fancyvrb" /><a
8375 id="x1-101116r58"></a><span
8376 class="cmr-6">58</span><span
8377 class="cmtt-8"> </span><span
8378 class="cmtt-8"> </span>
8379 <br class="fancyvrb" /><a
8380 id="x1-101118r59"></a><span
8381 class="cmr-6">59</span><span
8382 class="cmtt-8"> </span><span
8383 class="cmtt-8"> </span><span
8384 class="cmtt-8"> </span><span
8385 class="cmtt-8"> </span><span
8386 class="cmtt-8"> </span><span
8387 class="cmtt-8"> </span><span
8388 class="cmtt-8"> </span><span
8389 class="cmtt-8"> </span><span
8390 class="cmtt-8"> </span><span
8391 class="cmtt-8"> </span><span
8392 class="cmtt-8"> </span><span
8393 class="cmtt-8"> </span><span
8394 class="cmtt-8"> </span><span
8395 class="cmtt-8"> </span><span
8396 class="cmtt-8"> </span><span
8397 class="cmtt-8"> </span><span
8398 class="cmtt-8"> </span><span
8399 class="cmtt-8"> </span><span
8400 class="cmtt-8"> </span><span
8401 class="cmtt-8"> </span><span
8402 class="cmtt-8"> </span><span
8403 class="cmtt-8"> </span><span
8404 class="cmtt-8"> </span><span
8405 class="cmtt-8"> </span><span
8406 class="cmsy-8">}</span>
8407 <br class="fancyvrb" /><a
8408 id="x1-101120r60"></a><span
8409 class="cmr-6">60</span><span
8410 class="cmtt-8"> </span><span
8411 class="cmtt-8"> </span>
8412 <br class="fancyvrb" /><a
8413 id="x1-101122r61"></a><span
8414 class="cmr-6">61</span><span
8415 class="cmtt-8"> </span><span
8416 class="cmtt-8"> </span><span
8417 class="cmtt-8"> </span><span
8418 class="cmtt-8"> </span><span
8419 class="cmtt-8"> </span><span
8420 class="cmtt-8"> </span><span
8421 class="cmtt-8"> </span><span
8422 class="cmtt-8"> </span><span
8423 class="cmtt-8"> </span><span
8424 class="cmtt-8"> </span><span
8425 class="cmtt-8"> </span><span
8426 class="cmtt-8"> </span><span
8427 class="cmtt-8"> </span><span
8428 class="cmtt-8"> </span><span
8429 class="cmtt-8"> </span><span
8430 class="cmtt-8"> </span><span
8431 class="cmtt-8"> </span><span
8432 class="cmtt-8"> </span><span
8433 class="cmsy-8">}</span>
8434 <br class="fancyvrb" /><a
8435 id="x1-101124r62"></a><span
8436 class="cmr-6">62</span><span
8437 class="cmtt-8"> </span><span
8438 class="cmtt-8"> </span>
8439 <br class="fancyvrb" /><a
8440 id="x1-101126r63"></a><span
8441 class="cmr-6">63</span><span
8442 class="cmtt-8"> </span><span
8443 class="cmtt-8"> </span><span
8444 class="cmtt-8"> </span><span
8445 class="cmtt-8"> </span><span
8446 class="cmtt-8"> </span><span
8447 class="cmtt-8"> </span><span
8448 class="cmtt-8"> </span><span
8449 class="cmtt-8"> </span><span
8450 class="cmtt-8"> </span><span
8451 class="cmtt-8"> </span><span
8452 class="cmtt-8"> </span><span
8453 class="cmtt-8"> </span><span
8454 class="cmsy-8">}</span><span
8455 class="cmtt-8"> else</span><span
8456 class="cmtt-8"> [val]</span><span
8457 class="cmtt-8"> is</span><span
8458 class="cmtt-8"> zero</span><span
8459 class="cmtt-8"> </span><span
8460 class="cmsy-8">{</span>
8461 <br class="fancyvrb" /><a
8462 id="x1-101128r64"></a><span
8463 class="cmr-6">64</span><span
8464 class="cmtt-8"> </span><span
8465 class="cmtt-8"> </span>
8466 <br class="fancyvrb" /><a
8467 id="x1-101130r65"></a><span
8468 class="cmr-6">65</span><span
8469 class="cmtt-8"> </span><span
8470 class="cmtt-8"> </span><span
8471 class="cmtt-8"> </span><span
8472 class="cmtt-8"> </span><span
8473 class="cmtt-8"> </span><span
8474 class="cmtt-8"> </span><span
8475 class="cmtt-8"> </span><span
8476 class="cmtt-8"> </span><span
8477 class="cmtt-8"> </span><span
8478 class="cmtt-8"> </span><span
8479 class="cmtt-8"> </span><span
8480 class="cmtt-8"> </span><span
8481 class="cmtt-8"> </span><span
8482 class="cmtt-8"> 27)</span><span
8483 class="cmtt-8"> vector</span><span
8484 class="cmtt-8"> [floor1_step2_flag]</span><span
8485 class="cmtt-8"> element</span><span
8486 class="cmtt-8"> [i]</span><span
8487 class="cmtt-8"> =</span><span
8488 class="cmtt-8"> unset</span>
8492 <br class="fancyvrb" /><a
8493 id="x1-101132r66"></a><span
8494 class="cmr-6">66</span><span
8495 class="cmtt-8"> </span><span
8496 class="cmtt-8"> </span><span
8497 class="cmtt-8"> </span><span
8498 class="cmtt-8"> </span><span
8499 class="cmtt-8"> </span><span
8500 class="cmtt-8"> </span><span
8501 class="cmtt-8"> </span><span
8502 class="cmtt-8"> </span><span
8503 class="cmtt-8"> </span><span
8504 class="cmtt-8"> </span><span
8505 class="cmtt-8"> </span><span
8506 class="cmtt-8"> </span><span
8507 class="cmtt-8"> </span><span
8508 class="cmtt-8"> 28)</span><span
8509 class="cmtt-8"> vector</span><span
8510 class="cmtt-8"> [floor1_final_Y]</span><span
8511 class="cmtt-8"> element</span><span
8512 class="cmtt-8"> [i]</span><span
8513 class="cmtt-8"> =</span><span
8514 class="cmtt-8"> [predicted]</span>
8515 <br class="fancyvrb" /><a
8516 id="x1-101134r67"></a><span
8517 class="cmr-6">67</span><span
8518 class="cmtt-8"> </span><span
8519 class="cmtt-8"> </span>
8520 <br class="fancyvrb" /><a
8521 id="x1-101136r68"></a><span
8522 class="cmr-6">68</span><span
8523 class="cmtt-8"> </span><span
8524 class="cmtt-8"> </span><span
8525 class="cmtt-8"> </span><span
8526 class="cmtt-8"> </span><span
8527 class="cmtt-8"> </span><span
8528 class="cmtt-8"> </span><span
8529 class="cmtt-8"> </span><span
8530 class="cmtt-8"> </span><span
8531 class="cmtt-8"> </span><span
8532 class="cmtt-8"> </span><span
8533 class="cmtt-8"> </span><span
8534 class="cmtt-8"> </span><span
8535 class="cmsy-8">}</span>
8536 <br class="fancyvrb" /><a
8537 id="x1-101138r69"></a><span
8538 class="cmr-6">69</span><span
8539 class="cmtt-8"> </span><span
8540 class="cmtt-8"> </span>
8541 <br class="fancyvrb" /><a
8542 id="x1-101140r70"></a><span
8543 class="cmr-6">70</span><span
8544 class="cmtt-8"> </span><span
8545 class="cmtt-8"> </span><span
8546 class="cmtt-8"> </span><span
8547 class="cmtt-8"> </span><span
8548 class="cmtt-8"> </span><span
8549 class="cmtt-8"> </span><span
8550 class="cmtt-8"> </span><span
8551 class="cmsy-8">}</span>
8552 <br class="fancyvrb" /><a
8553 id="x1-101142r71"></a><span
8554 class="cmr-6">71</span><span
8555 class="cmtt-8"> </span><span
8556 class="cmtt-8"> </span>
8557 <br class="fancyvrb" /><a
8558 id="x1-101144r72"></a><span
8559 class="cmr-6">72</span><span
8560 class="cmtt-8"> </span><span
8561 class="cmtt-8"> </span><span
8562 class="cmtt-8"> 29)</span><span
8563 class="cmtt-8"> done</span>
8564 <br class="fancyvrb" /><a
8565 id="x1-101146r73"></a><span
8566 class="cmr-6">73</span><span
8567 class="cmtt-8"> </span><span
8568 class="cmtt-8"> </span>
8570 </dd><dt class="description">
8572 class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
8573 class="description">
8574 <!--l. 351--><p class="noindent" >Curve synthesis generates a return vector <span
8575 class="cmtt-12">[floor] </span>of length <span
8576 class="cmtt-12">[n] </span>(where <span
8577 class="cmtt-12">[n] </span>is provided by
8578 the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
8580 class="cmtt-12">[floor1_X_list]</span>, <span
8581 class="cmtt-12">[floor1_final_Y] </span>and <span
8582 class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as
8583 [floor1_multiplier] and [floor1_values] values.
8584 <!--l. 358--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
8585 class="cmtt-12">[floor1_X_list]</span>, <span
8586 class="cmtt-12">[floor1_final_Y] </span>and
8588 class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span
8589 class="cmtt-12">[floor1_X_list]’</span>, <span
8590 class="cmtt-12">[floor1_final_Y]’</span>
8592 class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
8594 class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span
8595 class="cmtt-12">[floor1_X_list] </span>and then apply the same
8596 permutation to elements of the other two vectors so that the X, Y and step2_flag values
8598 <!--l. 368--><p class="noindent" >Then compute the final curve in one pass:
8599 <!--l. 370--><p class="noindent" >
8600 <div class="fancyvrb" id="fancyvrb32">
8602 id="x1-101148r1"></a><span
8603 class="cmr-6">1</span><span
8604 class="cmtt-8"> </span><span
8605 class="cmtt-8"> </span><span
8606 class="cmtt-8"> </span><span
8607 class="cmtt-8"> 1)</span><span
8608 class="cmtt-8"> [hx]</span><span
8609 class="cmtt-8"> =</span><span
8610 class="cmtt-8"> 0</span>
8611 <br class="fancyvrb" /><a
8612 id="x1-101150r2"></a><span
8613 class="cmr-6">2</span><span
8614 class="cmtt-8"> </span><span
8615 class="cmtt-8"> </span><span
8616 class="cmtt-8"> </span><span
8617 class="cmtt-8"> 2)</span><span
8618 class="cmtt-8"> [lx]</span><span
8619 class="cmtt-8"> =</span><span
8620 class="cmtt-8"> 0</span>
8621 <br class="fancyvrb" /><a
8622 id="x1-101152r3"></a><span
8623 class="cmr-6">3</span><span
8624 class="cmtt-8"> </span><span
8625 class="cmtt-8"> </span><span
8626 class="cmtt-8"> </span><span
8627 class="cmtt-8"> 3)</span><span
8628 class="cmtt-8"> [ly]</span><span
8629 class="cmtt-8"> =</span><span
8630 class="cmtt-8"> vector</span><span
8631 class="cmtt-8"> [floor1_final_Y]’</span><span
8632 class="cmtt-8"> element</span><span
8633 class="cmtt-8"> [0]</span><span
8634 class="cmtt-8"> *</span><span
8635 class="cmtt-8"> [floor1_multiplier]</span>
8636 <br class="fancyvrb" /><a
8637 id="x1-101154r4"></a><span
8638 class="cmr-6">4</span><span
8639 class="cmtt-8"> </span><span
8640 class="cmtt-8"> </span><span
8641 class="cmtt-8"> </span><span
8642 class="cmtt-8"> 4)</span><span
8643 class="cmtt-8"> iterate</span><span
8644 class="cmtt-8"> [i]</span><span
8645 class="cmtt-8"> over</span><span
8646 class="cmtt-8"> the</span><span
8647 class="cmtt-8"> range</span><span
8648 class="cmtt-8"> 1</span><span
8649 class="cmtt-8"> ...</span><span
8650 class="cmtt-8"> [floor1_values]-1</span><span
8651 class="cmtt-8"> </span><span
8652 class="cmsy-8">{</span>
8653 <br class="fancyvrb" /><a
8654 id="x1-101156r5"></a><span
8655 class="cmr-6">5</span><span
8656 class="cmtt-8"> </span><span
8657 class="cmtt-8"> </span>
8658 <br class="fancyvrb" /><a
8659 id="x1-101158r6"></a><span
8660 class="cmr-6">6</span><span
8661 class="cmtt-8"> </span><span
8662 class="cmtt-8"> </span><span
8663 class="cmtt-8"> </span><span
8664 class="cmtt-8"> </span><span
8665 class="cmtt-8"> </span><span
8666 class="cmtt-8"> </span><span
8667 class="cmtt-8"> </span><span
8668 class="cmtt-8"> </span><span
8669 class="cmtt-8"> 5)</span><span
8670 class="cmtt-8"> if</span><span
8671 class="cmtt-8"> (</span><span
8672 class="cmtt-8"> [floor1_step2_flag]’</span><span
8673 class="cmtt-8"> element</span><span
8674 class="cmtt-8"> [i]</span><span
8675 class="cmtt-8"> is</span><span
8676 class="cmtt-8"> set</span><span
8677 class="cmtt-8"> )</span><span
8678 class="cmtt-8"> </span><span
8679 class="cmsy-8">{</span>
8680 <br class="fancyvrb" /><a
8681 id="x1-101160r7"></a><span
8682 class="cmr-6">7</span><span
8683 class="cmtt-8"> </span><span
8684 class="cmtt-8"> </span>
8685 <br class="fancyvrb" /><a
8686 id="x1-101162r8"></a><span
8687 class="cmr-6">8</span><span
8688 class="cmtt-8"> </span><span
8689 class="cmtt-8"> </span><span
8690 class="cmtt-8"> </span><span
8691 class="cmtt-8"> </span><span
8692 class="cmtt-8"> </span><span
8693 class="cmtt-8"> </span><span
8694 class="cmtt-8"> </span><span
8695 class="cmtt-8"> </span><span
8696 class="cmtt-8"> </span><span
8697 class="cmtt-8"> </span><span
8698 class="cmtt-8"> </span><span
8699 class="cmtt-8"> </span><span
8700 class="cmtt-8"> </span><span
8701 class="cmtt-8"> </span><span
8702 class="cmtt-8"> 6)</span><span
8703 class="cmtt-8"> [hy]</span><span
8704 class="cmtt-8"> =</span><span
8705 class="cmtt-8"> [floor1_final_Y]’</span><span
8706 class="cmtt-8"> element</span><span
8707 class="cmtt-8"> [i]</span><span
8708 class="cmtt-8"> *</span><span
8709 class="cmtt-8"> [floor1_multiplier]</span>
8710 <br class="fancyvrb" /><a
8711 id="x1-101164r9"></a><span
8712 class="cmr-6">9</span><span
8713 class="cmtt-8"> </span><span
8714 class="cmtt-8"> </span><span
8715 class="cmtt-8">  </span><span
8716 class="cmtt-8"> </span><span
8717 class="cmtt-8"> </span><span
8718 class="cmtt-8"> </span><span
8719 class="cmtt-8"> </span><span
8720 class="cmtt-8"> 7)</span><span
8721 class="cmtt-8"> [hx]</span><span
8722 class="cmtt-8"> =</span><span
8723 class="cmtt-8"> [floor1_X_list]’</span><span
8724 class="cmtt-8"> element</span><span
8725 class="cmtt-8"> [i]</span>
8726 <br class="fancyvrb" /><a
8727 id="x1-101166r10"></a><span
8728 class="cmr-6">10</span><span
8729 class="cmtt-8"> </span><span
8730 class="cmtt-8"> </span><span
8731 class="cmtt-8"> </span><span
8732 class="cmtt-8"> </span><span
8733 class="cmtt-8"> </span><span
8734 class="cmtt-8"> </span><span
8735 class="cmtt-8"> </span><span
8736 class="cmtt-8"> </span><span
8737 class="cmtt-8"> </span><span
8738 class="cmtt-8"> </span><span
8739 class="cmtt-8"> </span><span
8740 class="cmtt-8"> </span><span
8741 class="cmtt-8"> </span><span
8742 class="cmtt-8"> </span><span
8743 class="cmtt-8"> 8)</span><span
8744 class="cmtt-8"> </span><a
8745 href="#x1-1230009.2.7"><span
8746 class="cmtt-8">render_line</span></a><span
8747 class="cmtt-8">(</span><span
8748 class="cmtt-8"> [lx],</span><span
8749 class="cmtt-8"> [ly],</span><span
8750 class="cmtt-8"> [hx],</span><span
8751 class="cmtt-8"> [hy],</span><span
8752 class="cmtt-8"> [floor]</span><span
8753 class="cmtt-8"> )</span>
8754 <br class="fancyvrb" /><a
8755 id="x1-101168r11"></a><span
8756 class="cmr-6">11</span><span
8757 class="cmtt-8"> </span><span
8758 class="cmtt-8"> </span><span
8759 class="cmtt-8"> </span><span
8760 class="cmtt-8"> </span><span
8761 class="cmtt-8"> </span><span
8762 class="cmtt-8"> </span><span
8763 class="cmtt-8"> </span><span
8764 class="cmtt-8"> </span><span
8765 class="cmtt-8"> </span><span
8766 class="cmtt-8"> </span><span
8767 class="cmtt-8"> </span><span
8768 class="cmtt-8"> </span><span
8769 class="cmtt-8"> </span><span
8770 class="cmtt-8"> </span><span
8771 class="cmtt-8"> 9)</span><span
8772 class="cmtt-8"> [lx]</span><span
8773 class="cmtt-8"> =</span><span
8774 class="cmtt-8"> [hx]</span>
8775 <br class="fancyvrb" /><a
8776 id="x1-101170r12"></a><span
8777 class="cmr-6">12</span><span
8778 class="cmtt-8"> </span><span
8779 class="cmtt-8">  </span><span
8780 class="cmtt-8"> </span><span
8781 class="cmtt-8"> </span><span
8782 class="cmtt-8"> </span><span
8783 class="cmtt-8"> 10)</span><span
8784 class="cmtt-8"> [ly]</span><span
8785 class="cmtt-8"> =</span><span
8786 class="cmtt-8"> [hy]</span>
8787 <br class="fancyvrb" /><a
8788 id="x1-101172r13"></a><span
8789 class="cmr-6">13</span><span
8790 class="cmtt-8"> </span><span
8791 class="cmtt-8"> </span><span
8792 class="cmtt-8"> </span><span
8793 class="cmtt-8"> </span><span
8794 class="cmtt-8"> </span><span
8795 class="cmtt-8"> </span><span
8796 class="cmtt-8"> </span><span
8797 class="cmtt-8"> </span><span
8798 class="cmtt-8"> </span><span
8799 class="cmtt-8"> </span><span
8800 class="cmtt-8"> </span><span
8801 class="cmtt-8"> </span><span
8802 class="cmsy-8">}</span>
8803 <br class="fancyvrb" /><a
8804 id="x1-101174r14"></a><span
8805 class="cmr-6">14</span><span
8806 class="cmtt-8"> </span><span
8807 class="cmtt-8"> </span><span
8808 class="cmtt-8"> </span><span
8809 class="cmtt-8"> </span><span
8810 class="cmtt-8"> </span><span
8811 class="cmtt-8"> </span><span
8812 class="cmtt-8"> </span><span
8813 class="cmsy-8">}</span>
8814 <br class="fancyvrb" /><a
8815 id="x1-101176r15"></a><span
8816 class="cmr-6">15</span><span
8817 class="cmtt-8"> </span><span
8818 class="cmtt-8"> </span>
8819 <br class="fancyvrb" /><a
8820 id="x1-101178r16"></a><span
8821 class="cmr-6">16</span><span
8822 class="cmtt-8"> </span><span
8823 class="cmtt-8"> </span><span
8824 class="cmtt-8"> 11)</span><span
8825 class="cmtt-8"> if</span><span
8826 class="cmtt-8"> (</span><span
8827 class="cmtt-8"> [hx]</span><span
8828 class="cmtt-8"> is</span><span
8829 class="cmtt-8"> less</span><span
8830 class="cmtt-8"> than</span><span
8831 class="cmtt-8"> [n]</span><span
8832 class="cmtt-8"> )</span><span
8833 class="cmtt-8"> </span><span
8834 class="cmsy-8">{</span>
8835 <br class="fancyvrb" /><a
8836 id="x1-101180r17"></a><span
8837 class="cmr-6">17</span><span
8838 class="cmtt-8"> </span><span
8839 class="cmtt-8"> </span>
8840 <br class="fancyvrb" /><a
8841 id="x1-101182r18"></a><span
8842 class="cmr-6">18</span><span
8843 class="cmtt-8"> </span><span
8844 class="cmtt-8"> </span><span
8845 class="cmtt-8"> </span><span
8846 class="cmtt-8"> </span><span
8847 class="cmtt-8"> </span><span
8848 class="cmtt-8"> </span><span
8849 class="cmtt-8"> </span><span
8850 class="cmtt-8"> </span><span
8851 class="cmtt-8"> </span><span
8852 class="cmtt-8"> 12)</span><span
8853 class="cmtt-8"> </span><a
8854 href="#x1-1230009.2.7"><span
8855 class="cmtt-8">render_line</span></a><span
8856 class="cmtt-8">(</span><span
8857 class="cmtt-8"> [hx],</span><span
8858 class="cmtt-8"> [hy],</span><span
8859 class="cmtt-8"> [n],</span><span
8860 class="cmtt-8"> [hy],</span><span
8861 class="cmtt-8"> [floor]</span><span
8862 class="cmtt-8"> )</span>
8863 <br class="fancyvrb" /><a
8864 id="x1-101184r19"></a><span
8865 class="cmr-6">19</span><span
8866 class="cmtt-8"> </span><span
8867 class="cmtt-8"> </span>
8868 <br class="fancyvrb" /><a
8869 id="x1-101186r20"></a><span
8870 class="cmr-6">20</span><span
8871 class="cmtt-8"> </span><span
8872 class="cmtt-8"> </span><span
8873 class="cmtt-8"> </span><span
8874 class="cmtt-8"> </span><span
8875 class="cmtt-8"> </span><span
8876 class="cmtt-8"> </span><span
8877 class="cmtt-8"> </span><span
8878 class="cmsy-8">}</span>
8879 <br class="fancyvrb" /><a
8880 id="x1-101188r21"></a><span
8881 class="cmr-6">21</span><span
8882 class="cmtt-8"> </span><span
8883 class="cmtt-8"> </span>
8884 <br class="fancyvrb" /><a
8885 id="x1-101190r22"></a><span
8886 class="cmr-6">22</span><span
8887 class="cmtt-8"> </span><span
8888 class="cmtt-8"> </span><span
8889 class="cmtt-8"> 13)</span><span
8890 class="cmtt-8"> if</span><span
8891 class="cmtt-8"> (</span><span
8892 class="cmtt-8"> [hx]</span><span
8893 class="cmtt-8"> is</span><span
8894 class="cmtt-8"> greater</span><span
8895 class="cmtt-8"> than</span><span
8896 class="cmtt-8"> [n]</span><span
8897 class="cmtt-8"> )</span><span
8898 class="cmtt-8"> </span><span
8899 class="cmsy-8">{</span>
8900 <br class="fancyvrb" /><a
8901 id="x1-101192r23"></a><span
8902 class="cmr-6">23</span><span
8903 class="cmtt-8"> </span><span
8904 class="cmtt-8"> </span>
8905 <br class="fancyvrb" /><a
8906 id="x1-101194r24"></a><span
8907 class="cmr-6">24</span><span
8908 class="cmtt-8"> </span><span
8909 class="cmtt-8"> </span><span
8910 class="cmtt-8"> </span><span
8911 class="cmtt-8"> </span><span
8912 class="cmtt-8"> </span><span
8913 class="cmtt-8"> </span><span
8914 class="cmtt-8"> </span><span
8915 class="cmtt-8"> </span><span
8916 class="cmtt-8"> </span><span
8917 class="cmtt-8"> </span><span
8918 class="cmtt-8"> </span><span
8919 class="cmtt-8"> </span><span
8920 class="cmtt-8"> </span><span
8921 class="cmtt-8"> 14)</span><span
8922 class="cmtt-8"> truncate</span><span
8923 class="cmtt-8"> vector</span><span
8924 class="cmtt-8"> [floor]</span><span
8925 class="cmtt-8"> to</span><span
8926 class="cmtt-8"> [n]</span><span
8927 class="cmtt-8"> elements</span>
8928 <br class="fancyvrb" /><a
8929 id="x1-101196r25"></a><span
8930 class="cmr-6">25</span><span
8931 class="cmtt-8"> </span><span
8932 class="cmtt-8"> </span>
8933 <br class="fancyvrb" /><a
8934 id="x1-101198r26"></a><span
8935 class="cmr-6">26</span><span
8936 class="cmtt-8"> </span><span
8937 class="cmtt-8"> </span><span
8938 class="cmtt-8"> </span><span
8939 class="cmtt-8"> </span><span
8940 class="cmtt-8"> </span><span
8941 class="cmtt-8"> </span><span
8942 class="cmtt-8"> </span><span
8943 class="cmsy-8">}</span>
8944 <br class="fancyvrb" /><a
8945 id="x1-101200r27"></a><span
8946 class="cmr-6">27</span><span
8947 class="cmtt-8"> </span><span
8948 class="cmtt-8"> </span>
8952 <br class="fancyvrb" /><a
8953 id="x1-101202r28"></a><span
8954 class="cmr-6">28</span><span
8955 class="cmtt-8"> </span><span
8956 class="cmtt-8"> </span><span
8957 class="cmtt-8"> 15)</span><span
8958 class="cmtt-8"> for</span><span
8959 class="cmtt-8"> each</span><span
8960 class="cmtt-8"> scalar</span><span
8961 class="cmtt-8"> in</span><span
8962 class="cmtt-8"> vector</span><span
8963 class="cmtt-8"> [floor],</span><span
8964 class="cmtt-8"> perform</span><span
8965 class="cmtt-8"> a</span><span
8966 class="cmtt-8"> lookup</span><span
8967 class="cmtt-8"> substitution</span><span
8968 class="cmtt-8"> using</span>
8969 <br class="fancyvrb" /><a
8970 id="x1-101204r29"></a><span
8971 class="cmr-6">29</span><span
8972 class="cmtt-8"> </span><span
8973 class="cmtt-8"> </span><span
8974 class="cmtt-8"> </span><span
8975 class="cmtt-8"> </span><span
8976 class="cmtt-8"> </span><span
8977 class="cmtt-8"> </span><span
8978 class="cmtt-8"> the</span><span
8979 class="cmtt-8"> scalar</span><span
8980 class="cmtt-8"> value</span><span
8981 class="cmtt-8"> from</span><span
8982 class="cmtt-8"> [floor]</span><span
8983 class="cmtt-8"> as</span><span
8984 class="cmtt-8"> an</span><span
8985 class="cmtt-8"> offset</span><span
8986 class="cmtt-8"> into</span><span
8987 class="cmtt-8"> the</span><span
8988 class="cmtt-8"> vector</span><span
8989 class="cmtt-8"> </span><a
8990 href="#x1-12500010.1"><span
8991 class="cmtt-8">[floor1_inverse_dB_static_table]</span></a>
8992 <br class="fancyvrb" /><a
8993 id="x1-101206r30"></a><span
8994 class="cmr-6">30</span><span
8995 class="cmtt-8"> </span><span
8996 class="cmtt-8"> </span>
8997 <br class="fancyvrb" /><a
8998 id="x1-101208r31"></a><span
8999 class="cmr-6">31</span><span
9000 class="cmtt-8"> </span><span
9001 class="cmtt-8"> </span><span
9002 class="cmtt-8"> 16)</span><span
9003 class="cmtt-8"> done</span>
9004 <br class="fancyvrb" /><a
9005 id="x1-101210r32"></a><span
9006 class="cmr-6">32</span><span
9007 class="cmtt-8"> </span><span
9008 class="cmtt-8"> </span>
9014 <h3 class="sectionHead"><span class="titlemark">8. </span> <a
9015 id="x1-1020008"></a>Residue setup and decode</h3>
9016 <!--l. 6--><p class="noindent" >
9017 <h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a
9018 id="x1-1030008.1"></a>Overview</h4>
9019 <!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
9020 after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
9021 may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel
9022 coupling. The exact semantic content of the vector does not matter to the residue
9024 <!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
9025 bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
9026 different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
9028 <!--l. 23--><p class="noindent" >
9029 <h4 class="subsectionHead"><span class="titlemark">8.2. </span> <a
9030 id="x1-1040008.2"></a>Residue format</h4>
9031 <!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
9032 chunk, encodes the chunk classifications and finally encodes the chunks themselves
9033 using the the specific VQ arrangement defined for each selected classification. The
9034 exact interleaving and partitioning vary by residue encoding number, however the
9035 high-level process used to classify and encode the residue vector is the same in all three
9037 <!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
9038 the moment exactly how a partition is encoded and simply trusting that it is, is as
9040 <ul class="itemize1">
9041 <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
9042 specified. If we have a vector size of <span
9043 class="cmti-12">n</span>, a partition size <span
9044 class="cmti-12">residue</span><span
9045 class="cmti-12">_partition</span><span
9046 class="cmti-12">_size</span>,
9047 and a total of <span
9048 class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded
9053 class="cmti-12">n</span>/<span
9054 class="cmti-12">residue</span><span
9055 class="cmti-12">_partition</span><span
9056 class="cmti-12">_size</span>*<span
9057 class="cmti-12">ch</span>. It is important to note that the integer division
9058 truncates. In the below example, we assume an example <span
9059 class="cmti-12">residue</span><span
9060 class="cmti-12">_partition</span><span
9061 class="cmti-12">_size </span>of 8.
9063 <li class="itemize">Each partition in each vector has a classification number that specifies which of
9064 multiple configured VQ codebook setups are used to decode that partition. The
9065 classification numbers of each partition can be thought of as forming a vector in
9066 their own right, as in the illustration below. Just as the residue vectors are coded
9067 in grouped partitions to increase encoding efficiency, the classification vector is also
9068 partitioned into chunks. The integer elements of each scalar in a classification chunk
9069 are built into a single scalar that represents the classification numbers in that chunk.
9070 In the below example, the classification codeword encodes two classification numbers.
9072 <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
9073 the residue vector, but more often efficient codebook design dictates that each vector
9074 is encoded as the additive sum of several passes through the residue vector using
9075 more than one VQ codebook. Thus, each residue value potentially accumulates values
9076 from multiple decode passes. The classification value associated with a partition is
9077 the same in each pass, thus the classification codeword is coded only in the first pass.
9081 <!--l. 70--><p class="noindent" >
9083 <!--l. 71--><p class="noindent" ><img
9084 src="residue-pack.png" alt="PIC"
9086 <br /> <div class="caption"
9087 ><span class="id">Figure 11: </span><span
9088 class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10400111 -->
9090 <!--l. 77--><p class="noindent" >
9091 <h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a
9092 id="x1-1050008.3"></a>residue 0</h4>
9093 <!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
9094 partition encoding (visually treated as a black box–or cyan box or brown box–in the above
9096 <!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
9100 encode a partition in a specific pass. The dimension of the codebook need not be the same in
9101 multiple passes, however the partition size must be an even multiple of the codebook
9103 <!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
9104 codebook sizes of 8, 4, 2 and 1:
9105 <!--l. 92--><p class="noindent" >
9106 <div class="fancyvrb" id="fancyvrb33">
9108 id="x1-105002r1"></a><span
9109 class="cmr-6">1</span><span
9110 class="cmtt-8"> </span><span
9111 class="cmtt-8"> </span>
9112 <br class="fancyvrb" /><a
9113 id="x1-105004r2"></a><span
9114 class="cmr-6">2</span><span
9115 class="cmtt-8"> </span><span
9116 class="cmtt-8"> </span><span
9117 class="cmtt-8"> </span><span
9118 class="cmtt-8"> </span><span
9119 class="cmtt-8"> </span><span
9120 class="cmtt-8"> </span><span
9121 class="cmtt-8"> </span><span
9122 class="cmtt-8"> </span><span
9123 class="cmtt-8"> </span><span
9124 class="cmtt-8"> </span><span
9125 class="cmtt-8"> </span><span
9126 class="cmtt-8"> </span><span
9127 class="cmtt-8"> </span><span
9128 class="cmtt-8"> original</span><span
9129 class="cmtt-8"> residue</span><span
9130 class="cmtt-8"> vector:</span><span
9131 class="cmtt-8"> [</span><span
9132 class="cmtt-8"> 0</span><span
9133 class="cmtt-8"> 1</span><span
9134 class="cmtt-8"> 2</span><span
9135 class="cmtt-8"> 3</span><span
9136 class="cmtt-8"> 4</span><span
9137 class="cmtt-8"> 5</span><span
9138 class="cmtt-8"> 6</span><span
9139 class="cmtt-8"> 7</span><span
9140 class="cmtt-8"> ]</span>
9141 <br class="fancyvrb" /><a
9142 id="x1-105006r3"></a><span
9143 class="cmr-6">3</span><span
9144 class="cmtt-8"> </span><span
9145 class="cmtt-8"> </span>
9146 <br class="fancyvrb" /><a
9147 id="x1-105008r4"></a><span
9148 class="cmr-6">4</span><span
9149 class="cmtt-8"> </span><span
9150 class="cmtt-8"> codebook</span><span
9151 class="cmtt-8"> dimensions</span><span
9152 class="cmtt-8"> =</span><span
9153 class="cmtt-8"> 8</span><span
9154 class="cmtt-8"> </span><span
9155 class="cmtt-8"> encoded</span><span
9156 class="cmtt-8"> as:</span><span
9157 class="cmtt-8"> [</span><span
9158 class="cmtt-8"> 0</span><span
9159 class="cmtt-8"> 1</span><span
9160 class="cmtt-8"> 2</span><span
9161 class="cmtt-8"> 3</span><span
9162 class="cmtt-8"> 4</span><span
9163 class="cmtt-8"> 5</span><span
9164 class="cmtt-8"> 6</span><span
9165 class="cmtt-8"> 7</span><span
9166 class="cmtt-8"> ]</span>
9167 <br class="fancyvrb" /><a
9168 id="x1-105010r5"></a><span
9169 class="cmr-6">5</span><span
9170 class="cmtt-8"> </span><span
9171 class="cmtt-8"> </span>
9172 <br class="fancyvrb" /><a
9173 id="x1-105012r6"></a><span
9174 class="cmr-6">6</span><span
9175 class="cmtt-8"> </span><span
9176 class="cmtt-8"> codebook</span><span
9177 class="cmtt-8"> dimensions</span><span
9178 class="cmtt-8"> =</span><span
9179 class="cmtt-8"> 4</span><span
9180 class="cmtt-8"> </span><span
9181 class="cmtt-8"> encoded</span><span
9182 class="cmtt-8"> as:</span><span
9183 class="cmtt-8"> [</span><span
9184 class="cmtt-8"> 0</span><span
9185 class="cmtt-8"> 2</span><span
9186 class="cmtt-8"> 4</span><span
9187 class="cmtt-8"> 6</span><span
9188 class="cmtt-8"> ],</span><span
9189 class="cmtt-8"> [</span><span
9190 class="cmtt-8"> 1</span><span
9191 class="cmtt-8"> 3</span><span
9192 class="cmtt-8"> 5</span><span
9193 class="cmtt-8"> 7</span><span
9194 class="cmtt-8"> ]</span>
9195 <br class="fancyvrb" /><a
9196 id="x1-105014r7"></a><span
9197 class="cmr-6">7</span><span
9198 class="cmtt-8"> </span><span
9199 class="cmtt-8"> </span>
9200 <br class="fancyvrb" /><a
9201 id="x1-105016r8"></a><span
9202 class="cmr-6">8</span><span
9203 class="cmtt-8"> </span><span
9204 class="cmtt-8"> codebook</span><span
9205 class="cmtt-8"> dimensions</span><span
9206 class="cmtt-8"> =</span><span
9207 class="cmtt-8"> 2</span><span
9208 class="cmtt-8"> </span><span
9209 class="cmtt-8"> encoded</span><span
9210 class="cmtt-8"> as:</span><span
9211 class="cmtt-8"> [</span><span
9212 class="cmtt-8"> 0</span><span
9213 class="cmtt-8"> 4</span><span
9214 class="cmtt-8"> ],</span><span
9215 class="cmtt-8"> [</span><span
9216 class="cmtt-8"> 1</span><span
9217 class="cmtt-8"> 5</span><span
9218 class="cmtt-8"> ],</span><span
9219 class="cmtt-8"> [</span><span
9220 class="cmtt-8"> 2</span><span
9221 class="cmtt-8"> 6</span><span
9222 class="cmtt-8"> ],</span><span
9223 class="cmtt-8"> [</span><span
9224 class="cmtt-8"> 3</span><span
9225 class="cmtt-8"> 7</span><span
9226 class="cmtt-8"> ]</span>
9227 <br class="fancyvrb" /><a
9228 id="x1-105018r9"></a><span
9229 class="cmr-6">9</span><span
9230 class="cmtt-8"> </span><span
9231 class="cmtt-8"> </span>
9232 <br class="fancyvrb" /><a
9233 id="x1-105020r10"></a><span
9234 class="cmr-6">10</span><span
9235 class="cmtt-8"> </span><span
9236 class="cmtt-8"> codebook</span><span
9237 class="cmtt-8"> dimensions</span><span
9238 class="cmtt-8"> =</span><span
9239 class="cmtt-8"> 1</span><span
9240 class="cmtt-8"> </span><span
9241 class="cmtt-8"> encoded</span><span
9242 class="cmtt-8"> as:</span><span
9243 class="cmtt-8"> [</span><span
9244 class="cmtt-8"> 0</span><span
9245 class="cmtt-8"> ],</span><span
9246 class="cmtt-8"> [</span><span
9247 class="cmtt-8"> 1</span><span
9248 class="cmtt-8"> ],</span><span
9249 class="cmtt-8"> [</span><span
9250 class="cmtt-8"> 2</span><span
9251 class="cmtt-8"> ],</span><span
9252 class="cmtt-8"> [</span><span
9253 class="cmtt-8"> 3</span><span
9254 class="cmtt-8"> ],</span><span
9255 class="cmtt-8"> [</span><span
9256 class="cmtt-8"> 4</span><span
9257 class="cmtt-8"> ],</span><span
9258 class="cmtt-8"> [</span><span
9259 class="cmtt-8"> 5</span><span
9260 class="cmtt-8"> ],</span><span
9261 class="cmtt-8"> [</span><span
9262 class="cmtt-8"> 6</span><span
9263 class="cmtt-8"> ],</span><span
9264 class="cmtt-8"> [</span><span
9265 class="cmtt-8"> 7</span><span
9266 class="cmtt-8"> ]</span>
9267 <br class="fancyvrb" /><a
9268 id="x1-105022r11"></a><span
9269 class="cmr-6">11</span><span
9270 class="cmtt-8"> </span><span
9271 class="cmtt-8"> </span>
9273 <!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
9274 restricted to a power of two.
9275 <!--l. 111--><p class="noindent" >
9276 <h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a
9277 id="x1-1060008.4"></a>residue 1</h4>
9278 <!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As
9279 with residue 0, however, partition length must be an integer multiple of the codebook dimension,
9280 although dimension may vary from pass to pass.
9281 <!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
9282 codebook sizes of 8, 4, 2 and 1:
9283 <!--l. 121--><p class="noindent" >
9284 <div class="fancyvrb" id="fancyvrb34">
9286 id="x1-106002r1"></a><span
9287 class="cmr-6">1</span><span
9288 class="cmtt-8"> </span><span
9289 class="cmtt-8"> </span>
9290 <br class="fancyvrb" /><a
9291 id="x1-106004r2"></a><span
9292 class="cmr-6">2</span><span
9293 class="cmtt-8"> </span><span
9294 class="cmtt-8"> </span><span
9295 class="cmtt-8"> </span><span
9296 class="cmtt-8"> </span><span
9297 class="cmtt-8"> </span><span
9298 class="cmtt-8"> </span><span
9299 class="cmtt-8"> </span><span
9300 class="cmtt-8"> </span><span
9301 class="cmtt-8"> </span><span
9302 class="cmtt-8"> </span><span
9303 class="cmtt-8"> </span><span
9304 class="cmtt-8"> </span><span
9305 class="cmtt-8"> </span><span
9306 class="cmtt-8"> original</span><span
9307 class="cmtt-8"> residue</span><span
9308 class="cmtt-8"> vector:</span><span
9309 class="cmtt-8"> [</span><span
9310 class="cmtt-8"> 0</span><span
9311 class="cmtt-8"> 1</span><span
9312 class="cmtt-8"> 2</span><span
9313 class="cmtt-8"> 3</span><span
9314 class="cmtt-8"> 4</span><span
9315 class="cmtt-8"> 5</span><span
9316 class="cmtt-8"> 6</span><span
9317 class="cmtt-8"> 7</span><span
9318 class="cmtt-8"> ]</span>
9319 <br class="fancyvrb" /><a
9320 id="x1-106006r3"></a><span
9321 class="cmr-6">3</span><span
9322 class="cmtt-8"> </span><span
9323 class="cmtt-8"> </span>
9324 <br class="fancyvrb" /><a
9325 id="x1-106008r4"></a><span
9326 class="cmr-6">4</span><span
9327 class="cmtt-8"> </span><span
9328 class="cmtt-8"> codebook</span><span
9329 class="cmtt-8"> dimensions</span><span
9330 class="cmtt-8"> =</span><span
9331 class="cmtt-8"> 8</span><span
9332 class="cmtt-8"> </span><span
9333 class="cmtt-8"> encoded</span><span
9334 class="cmtt-8"> as:</span><span
9335 class="cmtt-8"> [</span><span
9336 class="cmtt-8"> 0</span><span
9337 class="cmtt-8"> 1</span><span
9338 class="cmtt-8"> 2</span><span
9339 class="cmtt-8"> 3</span><span
9340 class="cmtt-8"> 4</span><span
9341 class="cmtt-8"> 5</span><span
9342 class="cmtt-8"> 6</span><span
9343 class="cmtt-8"> 7</span><span
9344 class="cmtt-8"> ]</span>
9345 <br class="fancyvrb" /><a
9346 id="x1-106010r5"></a><span
9347 class="cmr-6">5</span><span
9348 class="cmtt-8"> </span><span
9349 class="cmtt-8"> </span>
9350 <br class="fancyvrb" /><a
9351 id="x1-106012r6"></a><span
9352 class="cmr-6">6</span><span
9353 class="cmtt-8"> </span><span
9354 class="cmtt-8"> codebook</span><span
9355 class="cmtt-8"> dimensions</span><span
9356 class="cmtt-8"> =</span><span
9357 class="cmtt-8"> 4</span><span
9358 class="cmtt-8"> </span><span
9359 class="cmtt-8"> encoded</span><span
9360 class="cmtt-8"> as:</span><span
9361 class="cmtt-8"> [</span><span
9362 class="cmtt-8"> 0</span><span
9363 class="cmtt-8"> 1</span><span
9364 class="cmtt-8"> 2</span><span
9365 class="cmtt-8"> 3</span><span
9366 class="cmtt-8"> ],</span><span
9367 class="cmtt-8"> [</span><span
9368 class="cmtt-8"> 4</span><span
9369 class="cmtt-8"> 5</span><span
9370 class="cmtt-8"> 6</span><span
9371 class="cmtt-8"> 7</span><span
9372 class="cmtt-8"> ]</span>
9373 <br class="fancyvrb" /><a
9374 id="x1-106014r7"></a><span
9375 class="cmr-6">7</span><span
9376 class="cmtt-8"> </span><span
9377 class="cmtt-8"> </span>
9378 <br class="fancyvrb" /><a
9379 id="x1-106016r8"></a><span
9380 class="cmr-6">8</span><span
9381 class="cmtt-8"> </span><span
9382 class="cmtt-8"> codebook</span><span
9383 class="cmtt-8"> dimensions</span><span
9384 class="cmtt-8"> =</span><span
9385 class="cmtt-8"> 2</span><span
9386 class="cmtt-8"> </span><span
9387 class="cmtt-8"> encoded</span><span
9388 class="cmtt-8"> as:</span><span
9389 class="cmtt-8"> [</span><span
9390 class="cmtt-8"> 0</span><span
9391 class="cmtt-8"> 1</span><span
9392 class="cmtt-8"> ],</span><span
9393 class="cmtt-8"> [</span><span
9394 class="cmtt-8"> 2</span><span
9395 class="cmtt-8"> 3</span><span
9396 class="cmtt-8"> ],</span><span
9397 class="cmtt-8"> [</span><span
9398 class="cmtt-8"> 4</span><span
9399 class="cmtt-8"> 5</span><span
9400 class="cmtt-8"> ],</span><span
9401 class="cmtt-8"> [</span><span
9402 class="cmtt-8"> 6</span><span
9403 class="cmtt-8"> 7</span><span
9404 class="cmtt-8"> ]</span>
9405 <br class="fancyvrb" /><a
9406 id="x1-106018r9"></a><span
9407 class="cmr-6">9</span><span
9408 class="cmtt-8"> </span><span
9409 class="cmtt-8"> </span>
9410 <br class="fancyvrb" /><a
9411 id="x1-106020r10"></a><span
9412 class="cmr-6">10</span><span
9413 class="cmtt-8"> </span><span
9414 class="cmtt-8"> codebook</span><span
9415 class="cmtt-8"> dimensions</span><span
9416 class="cmtt-8"> =</span><span
9417 class="cmtt-8"> 1</span><span
9418 class="cmtt-8"> </span><span
9419 class="cmtt-8"> encoded</span><span
9420 class="cmtt-8"> as:</span><span
9421 class="cmtt-8"> [</span><span
9422 class="cmtt-8"> 0</span><span
9423 class="cmtt-8"> ],</span><span
9424 class="cmtt-8"> [</span><span
9425 class="cmtt-8"> 1</span><span
9426 class="cmtt-8"> ],</span><span
9427 class="cmtt-8"> [</span><span
9428 class="cmtt-8"> 2</span><span
9429 class="cmtt-8"> ],</span><span
9430 class="cmtt-8"> [</span><span
9431 class="cmtt-8"> 3</span><span
9432 class="cmtt-8"> ],</span><span
9433 class="cmtt-8"> [</span><span
9434 class="cmtt-8"> 4</span><span
9435 class="cmtt-8"> ],</span><span
9436 class="cmtt-8"> [</span><span
9437 class="cmtt-8"> 5</span><span
9438 class="cmtt-8"> ],</span><span
9439 class="cmtt-8"> [</span><span
9440 class="cmtt-8"> 6</span><span
9441 class="cmtt-8"> ],</span><span
9442 class="cmtt-8"> [</span><span
9443 class="cmtt-8"> 7</span><span
9444 class="cmtt-8"> ]</span>
9445 <br class="fancyvrb" /><a
9446 id="x1-106022r11"></a><span
9447 class="cmr-6">11</span><span
9448 class="cmtt-8"> </span><span
9449 class="cmtt-8"> </span>
9454 <!--l. 137--><p class="noindent" >
9455 <h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a
9456 id="x1-1070008.5"></a>residue 2</h4>
9457 <!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
9458 passed-in vectors as in residue type 1, the <span
9459 class="cmti-12">ch </span>passed in vectors of length <span
9460 class="cmti-12">n </span>are first interleaved
9461 and flattened into a single vector of length <span
9462 class="cmti-12">ch</span>*<span
9463 class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
9464 is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
9465 residue type 1 and type 2 are equivalent.
9468 <!--l. 147--><p class="noindent" >
9470 <!--l. 148--><p class="noindent" ><img
9471 src="residue2.png" alt="PIC"
9473 <br /> <div class="caption"
9474 ><span class="id">Figure 12: </span><span
9475 class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10700112 -->
9477 <!--l. 153--><p class="noindent" >
9478 <h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a
9479 id="x1-1080008.6"></a>Residue decode</h4>
9480 <!--l. 155--><p class="noindent" >
9481 <h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a
9482 id="x1-1090008.6.1"></a>header decode</h5>
9483 <!--l. 157--><p class="noindent" >Header decode for all three residue types is identical.
9484 <div class="fancyvrb" id="fancyvrb35">
9486 id="x1-109002r1"></a><span
9487 class="cmr-6">1</span><span
9488 class="cmtt-8"> </span><span
9489 class="cmtt-8"> </span><span
9490 class="cmtt-8"> </span><span
9491 class="cmtt-8"> 1)</span><span
9492 class="cmtt-8"> [residue\_begin]</span><span
9493 class="cmtt-8"> =</span><span
9494 class="cmtt-8"> read</span><span
9495 class="cmtt-8"> 24</span><span
9496 class="cmtt-8"> bits</span><span
9497 class="cmtt-8"> as</span><span
9498 class="cmtt-8"> unsigned</span><span
9499 class="cmtt-8"> integer</span>
9500 <br class="fancyvrb" /><a
9501 id="x1-109004r2"></a><span
9502 class="cmr-6">2</span><span
9503 class="cmtt-8"> </span><span
9504 class="cmtt-8"> </span><span
9505 class="cmtt-8"> </span><span
9506 class="cmtt-8"> 2)</span><span
9507 class="cmtt-8"> [residue\_end]</span><span
9508 class="cmtt-8"> =</span><span
9509 class="cmtt-8"> read</span><span
9510 class="cmtt-8"> 24</span><span
9511 class="cmtt-8"> bits</span><span
9512 class="cmtt-8"> as</span><span
9513 class="cmtt-8"> unsigned</span><span
9514 class="cmtt-8"> integer</span>
9515 <br class="fancyvrb" /><a
9516 id="x1-109006r3"></a><span
9517 class="cmr-6">3</span><span
9518 class="cmtt-8"> </span><span
9519 class="cmtt-8"> </span><span
9520 class="cmtt-8"> </span><span
9521 class="cmtt-8"> 3)</span><span
9522 class="cmtt-8"> [residue\_partition\_size]</span><span
9523 class="cmtt-8"> =</span><span
9524 class="cmtt-8"> read</span><span
9525 class="cmtt-8"> 24</span><span
9526 class="cmtt-8"> bits</span><span
9527 class="cmtt-8"> as</span><span
9528 class="cmtt-8"> unsigned</span><span
9529 class="cmtt-8"> integer</span><span
9530 class="cmtt-8"> and</span><span
9531 class="cmtt-8"> add</span><span
9532 class="cmtt-8"> one</span>
9533 <br class="fancyvrb" /><a
9534 id="x1-109008r4"></a><span
9535 class="cmr-6">4</span><span
9536 class="cmtt-8"> </span><span
9537 class="cmtt-8"> </span><span
9538 class="cmtt-8"> </span><span
9539 class="cmtt-8"> 4)</span><span
9540 class="cmtt-8"> [residue\_classifications]</span><span
9541 class="cmtt-8"> =</span><span
9542 class="cmtt-8"> read</span><span
9543 class="cmtt-8"> 6</span><span
9544 class="cmtt-8"> bits</span><span
9545 class="cmtt-8"> as</span><span
9546 class="cmtt-8"> unsigned</span><span
9547 class="cmtt-8"> integer</span><span
9548 class="cmtt-8"> and</span><span
9549 class="cmtt-8"> add</span><span
9550 class="cmtt-8"> one</span>
9554 <br class="fancyvrb" /><a
9555 id="x1-109010r5"></a><span
9556 class="cmr-6">5</span><span
9557 class="cmtt-8"> </span><span
9558 class="cmtt-8"> </span><span
9559 class="cmtt-8"> </span><span
9560 class="cmtt-8"> 5)</span><span
9561 class="cmtt-8"> [residue\_classbook]</span><span
9562 class="cmtt-8"> =</span><span
9563 class="cmtt-8"> read</span><span
9564 class="cmtt-8"> 8</span><span
9565 class="cmtt-8"> bits</span><span
9566 class="cmtt-8"> as</span><span
9567 class="cmtt-8"> unsigned</span><span
9568 class="cmtt-8"> integer</span>
9570 <!--l. 166--><p class="noindent" ><span
9571 class="cmtt-12">[residue_begin] </span>and <span
9572 class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is
9573 actually coded; it implements akin to a bandpass where, for coding purposes, the vector
9574 effectively begins at element <span
9575 class="cmtt-12">[residue_begin] </span>and ends at <span
9576 class="cmtt-12">[residue_end]</span>. Preceding and
9577 following values in the unpacked vectors are zeroed. Note that for residue type 2, these
9578 values as well as <span
9579 class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the
9580 individual vectors before interleave. <span
9581 class="cmtt-12">[residue_partition_size] </span>is as explained above,
9583 class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can
9585 class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification
9586 codewords. The number of dimensions in book <span
9587 class="cmtt-12">[residue_classbook] </span>determines how
9588 many classification values are grouped into a single classification codeword. Note that
9589 the number of entries and dimensions in book <span
9590 class="cmtt-12">[residue_classbook]</span>, along with
9592 class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification
9594 class="cmtt-12">[residue_classifications]</span>ˆ<span
9595 class="cmtt-12">[residue_classbook]</span>.dimensions exceeds
9597 class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
9598 <!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
9600 <!--l. 193--><p class="noindent" >
9601 <div class="fancyvrb" id="fancyvrb36">
9603 id="x1-109012r1"></a><span
9604 class="cmr-6">1</span><span
9605 class="cmtt-8"> </span><span
9606 class="cmtt-8"> </span><span
9607 class="cmtt-8"> </span><span
9608 class="cmtt-8"> 1)</span><span
9609 class="cmtt-8"> iterate</span><span
9610 class="cmtt-8"> [i]</span><span
9611 class="cmtt-8"> over</span><span
9612 class="cmtt-8"> the</span><span
9613 class="cmtt-8"> range</span><span
9614 class="cmtt-8"> 0</span><span
9615 class="cmtt-8"> ...</span><span
9616 class="cmtt-8"> [residue\_classifications]-1</span><span
9617 class="cmtt-8"> {</span>
9618 <br class="fancyvrb" /><a
9619 id="x1-109014r2"></a><span
9620 class="cmr-6">2</span><span
9621 class="cmtt-8"> </span><span
9622 class="cmtt-8"> </span>
9623 <br class="fancyvrb" /><a
9624 id="x1-109016r3"></a><span
9625 class="cmr-6">3</span><span
9626 class="cmtt-8"> </span><span
9627 class="cmtt-8"> </span><span
9628 class="cmtt-8"> </span><span
9629 class="cmtt-8"> </span><span
9630 class="cmtt-8"> </span><span
9631 class="cmtt-8"> </span><span
9632 class="cmtt-8"> </span><span
9633 class="cmtt-8"> </span><span
9634 class="cmtt-8"> 2)</span><span
9635 class="cmtt-8"> [high\_bits]</span><span
9636 class="cmtt-8"> =</span><span
9637 class="cmtt-8"> 0</span>
9638 <br class="fancyvrb" /><a
9639 id="x1-109018r4"></a><span
9640 class="cmr-6">4</span><span
9641 class="cmtt-8"> </span><span
9642 class="cmtt-8"> </span><span
9643 class="cmtt-8"> </span><span
9644 class="cmtt-8"> </span><span
9645 class="cmtt-8"> </span><span
9646 class="cmtt-8"> </span><span
9647 class="cmtt-8"> </span><span
9648 class="cmtt-8"> </span><span
9649 class="cmtt-8"> 3)</span><span
9650 class="cmtt-8"> [low\_bits]</span><span
9651 class="cmtt-8"> =</span><span
9652 class="cmtt-8"> read</span><span
9653 class="cmtt-8"> 3</span><span
9654 class="cmtt-8"> bits</span><span
9655 class="cmtt-8"> as</span><span
9656 class="cmtt-8"> unsigned</span><span
9657 class="cmtt-8"> integer</span>
9658 <br class="fancyvrb" /><a
9659 id="x1-109020r5"></a><span
9660 class="cmr-6">5</span><span
9661 class="cmtt-8"> </span><span
9662 class="cmtt-8"> </span><span
9663 class="cmtt-8"> </span><span
9664 class="cmtt-8"> </span><span
9665 class="cmtt-8"> </span><span
9666 class="cmtt-8"> </span><span
9667 class="cmtt-8"> </span><span
9668 class="cmtt-8"> </span><span
9669 class="cmtt-8"> 4)</span><span
9670 class="cmtt-8"> [bitflag]</span><span
9671 class="cmtt-8"> =</span><span
9672 class="cmtt-8"> read</span><span
9673 class="cmtt-8"> one</span><span
9674 class="cmtt-8"> bit</span><span
9675 class="cmtt-8"> as</span><span
9676 class="cmtt-8"> boolean</span>
9677 <br class="fancyvrb" /><a
9678 id="x1-109022r6"></a><span
9679 class="cmr-6">6</span><span
9680 class="cmtt-8"> </span><span
9681 class="cmtt-8"> </span><span
9682 class="cmtt-8"> </span><span
9683 class="cmtt-8"> </span><span
9684 class="cmtt-8"> </span><span
9685 class="cmtt-8"> </span><span
9686 class="cmtt-8"> </span><span
9687 class="cmtt-8"> </span><span
9688 class="cmtt-8"> 5)</span><span
9689 class="cmtt-8"> if</span><span
9690 class="cmtt-8"> (</span><span
9691 class="cmtt-8"> [bitflag]</span><span
9692 class="cmtt-8"> is</span><span
9693 class="cmtt-8"> set</span><span
9694 class="cmtt-8"> )</span><span
9695 class="cmtt-8"> then</span><span
9696 class="cmtt-8"> [high\_bits]</span><span
9697 class="cmtt-8"> =</span><span
9698 class="cmtt-8"> read</span><span
9699 class="cmtt-8"> five</span><span
9700 class="cmtt-8"> bits</span><span
9701 class="cmtt-8"> as</span><span
9702 class="cmtt-8"> unsigned</span><span
9703 class="cmtt-8"> integer</span>
9704 <br class="fancyvrb" /><a
9705 id="x1-109024r7"></a><span
9706 class="cmr-6">7</span><span
9707 class="cmtt-8"> </span><span
9708 class="cmtt-8"> </span><span
9709 class="cmtt-8"> </span><span
9710 class="cmtt-8"> </span><span
9711 class="cmtt-8"> </span><span
9712 class="cmtt-8"> </span><span
9713 class="cmtt-8"> </span><span
9714 class="cmtt-8"> </span><span
9715 class="cmtt-8"> 6)</span><span
9716 class="cmtt-8"> vector</span><span
9717 class="cmtt-8"> [residue\_cascade]</span><span
9718 class="cmtt-8"> element</span><span
9719 class="cmtt-8"> [i]</span><span
9720 class="cmtt-8"> =</span><span
9721 class="cmtt-8"> [high\_bits]</span><span
9722 class="cmtt-8"> *</span><span
9723 class="cmtt-8"> 8</span><span
9724 class="cmtt-8"> +</span><span
9725 class="cmtt-8"> [low\_bits]</span>
9726 <br class="fancyvrb" /><a
9727 id="x1-109026r8"></a><span
9728 class="cmr-6">8</span><span
9729 class="cmtt-8"> </span><span
9730 class="cmtt-8"> </span><span
9731 class="cmtt-8"> </span><span
9732 class="cmtt-8"> </span><span
9733 class="cmtt-8"> </span><span
9734 class="cmtt-8"> </span><span
9735 class="cmtt-8"> }</span>
9736 <br class="fancyvrb" /><a
9737 id="x1-109028r9"></a><span
9738 class="cmr-6">9</span><span
9739 class="cmtt-8"> </span><span
9740 class="cmtt-8"> </span><span
9741 class="cmtt-8"> </span><span
9742 class="cmtt-8"> 7)</span><span
9743 class="cmtt-8"> done</span>
9745 <!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
9746 bitmap. We loop over the possible codebook classifications and the maximum possible number of
9747 encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
9749 <!--l. 211--><p class="noindent" >
9750 <div class="fancyvrb" id="fancyvrb37">
9752 id="x1-109030r1"></a><span
9753 class="cmr-6">1</span><span
9754 class="cmtt-8"> </span><span
9755 class="cmtt-8"> </span><span
9756 class="cmtt-8"> </span><span
9757 class="cmtt-8"> 1)</span><span
9758 class="cmtt-8"> iterate</span><span
9759 class="cmtt-8"> [i]</span><span
9760 class="cmtt-8"> over</span><span
9761 class="cmtt-8"> the</span><span
9762 class="cmtt-8"> range</span><span
9763 class="cmtt-8"> 0</span><span
9764 class="cmtt-8"> ...</span><span
9765 class="cmtt-8"> [residue\_classifications]-1</span><span
9766 class="cmtt-8"> {</span>
9767 <br class="fancyvrb" /><a
9768 id="x1-109032r2"></a><span
9769 class="cmr-6">2</span><span
9770 class="cmtt-8"> </span><span
9771 class="cmtt-8"> </span>
9772 <br class="fancyvrb" /><a
9773 id="x1-109034r3"></a><span
9774 class="cmr-6">3</span><span
9775 class="cmtt-8"> </span><span
9776 class="cmtt-8"> </span><span
9777 class="cmtt-8"> </span><span
9778 class="cmtt-8"> </span><span
9779 class="cmtt-8"> </span><span
9780 class="cmtt-8"> </span><span
9781 class="cmtt-8"> </span><span
9782 class="cmtt-8"> </span><span
9783 class="cmtt-8"> 2)</span><span
9784 class="cmtt-8"> iterate</span><span
9785 class="cmtt-8"> [j]</span><span
9786 class="cmtt-8"> over</span><span
9787 class="cmtt-8"> the</span><span
9788 class="cmtt-8"> range</span><span
9789 class="cmtt-8"> 0</span><span
9790 class="cmtt-8"> ...</span><span
9791 class="cmtt-8"> 7</span><span
9792 class="cmtt-8"> {</span>
9793 <br class="fancyvrb" /><a
9794 id="x1-109036r4"></a><span
9795 class="cmr-6">4</span><span
9796 class="cmtt-8"> </span><span
9797 class="cmtt-8"> </span>
9798 <br class="fancyvrb" /><a
9799 id="x1-109038r5"></a><span
9800 class="cmr-6">5</span><span
9801 class="cmtt-8"> </span><span
9802 class="cmtt-8"> </span><span
9803 class="cmtt-8"> </span><span
9804 class="cmtt-8"> </span><span
9805 class="cmtt-8"> </span><span
9806 class="cmtt-8"> </span><span
9807 class="cmtt-8"> </span><span
9808 class="cmtt-8"> </span><span
9809 class="cmtt-8"> </span><span
9810 class="cmtt-8"> </span><span
9811 class="cmtt-8"> </span><span
9812 class="cmtt-8"> </span><span
9813 class="cmtt-8"> </span><span
9814 class="cmtt-8"> 3)</span><span
9815 class="cmtt-8"> if</span><span
9816 class="cmtt-8"> (</span><span
9817 class="cmtt-8"> vector</span><span
9818 class="cmtt-8"> [residue\_cascade]</span><span
9819 class="cmtt-8"> element</span><span
9820 class="cmtt-8"> [i]</span><span
9821 class="cmtt-8"> bit</span><span
9822 class="cmtt-8"> [j]</span><span
9823 class="cmtt-8"> is</span><span
9824 class="cmtt-8"> set</span><span
9825 class="cmtt-8"> )</span><span
9826 class="cmtt-8"> {</span>
9827 <br class="fancyvrb" /><a
9828 id="x1-109040r6"></a><span
9829 class="cmr-6">6</span><span
9830 class="cmtt-8"> </span><span
9831 class="cmtt-8"> </span>
9832 <br class="fancyvrb" /><a
9833 id="x1-109042r7"></a><span
9834 class="cmr-6">7</span><span
9835 class="cmtt-8"> </span><span
9836 class="cmtt-8"> </span><span
9837 class="cmtt-8"> </span><span
9838 class="cmtt-8"> </span><span
9839 class="cmtt-8"> </span><span
9840 class="cmtt-8"> </span><span
9841 class="cmtt-8"> </span><span
9842 class="cmtt-8"> </span><span
9843 class="cmtt-8"> </span><span
9844 class="cmtt-8"> </span><span
9845 class="cmtt-8"> </span><span
9846 class="cmtt-8"> </span><span
9847 class="cmtt-8"> </span><span
9848 class="cmtt-8"> </span><span
9849 class="cmtt-8"> </span><span
9850 class="cmtt-8"> </span><span
9851 class="cmtt-8"> </span><span
9852 class="cmtt-8"> </span><span
9853 class="cmtt-8"> 4)</span><span
9854 class="cmtt-8"> array</span><span
9855 class="cmtt-8"> [residue\_books]</span><span
9856 class="cmtt-8"> element</span><span
9857 class="cmtt-8"> [i][j]</span><span
9858 class="cmtt-8"> =</span><span
9859 class="cmtt-8"> read</span><span
9860 class="cmtt-8"> 8</span><span
9861 class="cmtt-8"> bits</span><span
9862 class="cmtt-8"> as</span><span
9863 class="cmtt-8"> unsigned</span><span
9864 class="cmtt-8"> integer</span>
9865 <br class="fancyvrb" /><a
9866 id="x1-109044r8"></a><span
9867 class="cmr-6">8</span><span
9868 class="cmtt-8"> </span><span
9869 class="cmtt-8"> </span>
9870 <br class="fancyvrb" /><a
9871 id="x1-109046r9"></a><span
9872 class="cmr-6">9</span><span
9873 class="cmtt-8"> </span><span
9874 class="cmtt-8"> </span><span
9875 class="cmtt-8"> </span><span
9876 class="cmtt-8"> </span><span
9877 class="cmtt-8"> </span><span
9878 class="cmtt-8"> </span><span
9879 class="cmtt-8"> </span><span
9880 class="cmtt-8"> </span><span
9881 class="cmtt-8"> </span><span
9882 class="cmtt-8"> </span><span
9883 class="cmtt-8"> </span><span
9884 class="cmtt-8"> </span><span
9885 class="cmtt-8"> </span><span
9886 class="cmtt-8"> </span><span
9887 class="cmtt-8"> </span><span
9888 class="cmtt-8"> </span><span
9889 class="cmtt-8"> }</span><span
9890 class="cmtt-8"> else</span><span
9891 class="cmtt-8"> {</span>
9895 <br class="fancyvrb" /><a
9896 id="x1-109048r10"></a><span
9897 class="cmr-6">10</span><span
9898 class="cmtt-8"> </span><span
9899 class="cmtt-8"> </span>
9900 <br class="fancyvrb" /><a
9901 id="x1-109050r11"></a><span
9902 class="cmr-6">11</span><span
9903 class="cmtt-8"> </span><span
9904 class="cmtt-8"> </span><span
9905 class="cmtt-8"> </span><span
9906 class="cmtt-8"> </span><span
9907 class="cmtt-8"> </span><span
9908 class="cmtt-8"> </span><span
9909 class="cmtt-8"> </span><span
9910 class="cmtt-8"> </span><span
9911 class="cmtt-8"> </span><span
9912 class="cmtt-8"> </span><span
9913 class="cmtt-8"> </span><span
9914 class="cmtt-8"> </span><span
9915 class="cmtt-8"> </span><span
9916 class="cmtt-8"> </span><span
9917 class="cmtt-8"> </span><span
9918 class="cmtt-8"> </span><span
9919 class="cmtt-8"> </span><span
9920 class="cmtt-8"> </span><span
9921 class="cmtt-8"> 5)</span><span
9922 class="cmtt-8"> array</span><span
9923 class="cmtt-8"> [residue\_books]</span><span
9924 class="cmtt-8"> element</span><span
9925 class="cmtt-8"> [i][j]</span><span
9926 class="cmtt-8"> =</span><span
9927 class="cmtt-8"> unused</span>
9928 <br class="fancyvrb" /><a
9929 id="x1-109052r12"></a><span
9930 class="cmr-6">12</span><span
9931 class="cmtt-8"> </span><span
9932 class="cmtt-8"> </span>
9933 <br class="fancyvrb" /><a
9934 id="x1-109054r13"></a><span
9935 class="cmr-6">13</span><span
9936 class="cmtt-8"> </span><span
9937 class="cmtt-8"> </span><span
9938 class="cmtt-8"> </span><span
9939 class="cmtt-8"> </span><span
9940 class="cmtt-8"> </span><span
9941 class="cmtt-8"> </span><span
9942 class="cmtt-8"> </span><span
9943 class="cmtt-8"> </span><span
9944 class="cmtt-8"> </span><span
9945 class="cmtt-8"> </span><span
9946 class="cmtt-8"> </span><span
9947 class="cmtt-8"> </span><span
9948 class="cmtt-8"> </span><span
9949 class="cmtt-8"> </span><span
9950 class="cmtt-8"> </span><span
9951 class="cmtt-8"> </span><span
9952 class="cmtt-8"> }</span>
9953 <br class="fancyvrb" /><a
9954 id="x1-109056r14"></a><span
9955 class="cmr-6">14</span><span
9956 class="cmtt-8"> </span><span
9957 class="cmtt-8"> </span><span
9958 class="cmtt-8"> </span><span
9959 class="cmtt-8"> </span><span
9960 class="cmtt-8"> </span><span
9961 class="cmtt-8"> </span><span
9962 class="cmtt-8"> </span><span
9963 class="cmtt-8"> </span><span
9964 class="cmtt-8"> </span><span
9965 class="cmtt-8"> </span><span
9966 class="cmtt-8"> </span><span
9967 class="cmtt-8"> }</span>
9968 <br class="fancyvrb" /><a
9969 id="x1-109058r15"></a><span
9970 class="cmr-6">15</span><span
9971 class="cmtt-8"> </span><span
9972 class="cmtt-8"> </span><span
9973 class="cmtt-8"> </span><span
9974 class="cmtt-8"> </span><span
9975 class="cmtt-8"> </span><span
9976 class="cmtt-8"> </span><span
9977 class="cmtt-8"> </span><span
9978 class="cmtt-8"> }</span>
9979 <br class="fancyvrb" /><a
9980 id="x1-109060r16"></a><span
9981 class="cmr-6">16</span><span
9982 class="cmtt-8"> </span><span
9983 class="cmtt-8"> </span>
9984 <br class="fancyvrb" /><a
9985 id="x1-109062r17"></a><span
9986 class="cmr-6">17</span><span
9987 class="cmtt-8"> </span><span
9988 class="cmtt-8"> </span><span
9989 class="cmtt-8"> </span><span
9990 class="cmtt-8"> 6)</span><span
9991 class="cmtt-8"> done</span>
9993 <!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable.
9994 In addition, any codebook number greater than the maximum numbered codebook
9995 set up in this stream also renders the stream undecodable. All codebooks in array
9996 [residue_books] are required to have a value mapping. The presence of codebook in array
9997 [residue_books] without a value mapping (maptype equals zero) renders the stream
9999 <!--l. 241--><p class="noindent" >
10000 <h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a
10001 id="x1-1100008.6.2"></a>packet decode</h5>
10002 <!--l. 243--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
10003 decode can be built out of the format 1 decode process. Thus we describe first the decode
10004 infrastructure identical to all three formats.
10005 <!--l. 248--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
10006 vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
10007 decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
10008 decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
10009 allocated and zeroed.
10010 <!--l. 255--><p class="noindent" >Depending on the values of <span
10011 class="cmtt-12">[residue_begin] </span>and <span
10012 class="cmtt-12">[residue_end]</span>, it is obvious that the
10013 encoded portion of a residue vector may be the entire possible residue vector or some other strict
10014 subset of the actual residue vector size with zero padding at either uncoded end. However, it is
10015 also possible to set <span
10016 class="cmtt-12">[residue_begin] </span>and <span
10017 class="cmtt-12">[residue_end] </span>to specify a range partially or wholly
10018 beyond the maximum vector size. Before beginning residue decode, limit <span
10019 class="cmtt-12">[residue_begin]</span>
10021 class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that
10022 the number of vectors being encoded, <span
10023 class="cmtt-12">[ch] </span>is provided by the higher level decoding
10025 <!--l. 269--><p class="noindent" >
10026 <div class="fancyvrb" id="fancyvrb38">
10028 id="x1-110002r1"></a><span
10029 class="cmr-6">1</span><span
10030 class="cmtt-8"> </span><span
10031 class="cmtt-8"> </span><span
10032 class="cmtt-8"> </span><span
10033 class="cmtt-8"> 1)</span><span
10034 class="cmtt-8"> [actual\_size]</span><span
10035 class="cmtt-8"> =</span><span
10036 class="cmtt-8"> current</span><span
10037 class="cmtt-8"> blocksize/2;</span>
10038 <br class="fancyvrb" /><a
10039 id="x1-110004r2"></a><span
10040 class="cmr-6">2</span><span
10041 class="cmtt-8"> </span><span
10042 class="cmtt-8"> </span><span
10043 class="cmtt-8"> </span><span
10044 class="cmtt-8"> 2)</span><span
10045 class="cmtt-8"> if</span><span
10046 class="cmtt-8"> residue</span><span
10047 class="cmtt-8"> encoding</span><span
10048 class="cmtt-8"> is</span><span
10049 class="cmtt-8"> format</span><span
10050 class="cmtt-8"> 2</span>
10051 <br class="fancyvrb" /><a
10052 id="x1-110006r3"></a><span
10053 class="cmr-6">3</span><span
10054 class="cmtt-8"> </span><span
10055 class="cmtt-8"> </span><span
10056 class="cmtt-8"> </span><span
10057 class="cmtt-8"> </span><span
10058 class="cmtt-8"> </span><span
10059 class="cmtt-8"> </span><span
10060 class="cmtt-8"> </span><span
10061 class="cmtt-8"> </span><span
10062 class="cmtt-8"> 3)</span><span
10063 class="cmtt-8"> [actual\_size]</span><span
10064 class="cmtt-8"> =</span><span
10065 class="cmtt-8"> [actual\_size]</span><span
10066 class="cmtt-8"> *</span><span
10067 class="cmtt-8"> [ch];</span>
10071 <br class="fancyvrb" /><a
10072 id="x1-110008r4"></a><span
10073 class="cmr-6">4</span><span
10074 class="cmtt-8"> </span><span
10075 class="cmtt-8"> </span><span
10076 class="cmtt-8"> </span><span
10077 class="cmtt-8"> 4)</span><span
10078 class="cmtt-8"> [limit\_residue\_begin]</span><span
10079 class="cmtt-8"> =</span><span
10080 class="cmtt-8"> maximum</span><span
10081 class="cmtt-8"> of</span><span
10082 class="cmtt-8"> ([residue\_begin],[actual\_size]);</span>
10083 <br class="fancyvrb" /><a
10084 id="x1-110010r5"></a><span
10085 class="cmr-6">5</span><span
10086 class="cmtt-8"> </span><span
10087 class="cmtt-8"> </span><span
10088 class="cmtt-8"> </span><span
10089 class="cmtt-8"> 5)</span><span
10090 class="cmtt-8"> [limit\_residue\_end]</span><span
10091 class="cmtt-8"> =</span><span
10092 class="cmtt-8"> maximum</span><span
10093 class="cmtt-8"> of</span><span
10094 class="cmtt-8"> ([residue\_end],[actual\_size]);</span>
10096 <!--l. 277--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
10097 <!--l. 280--><p class="noindent" >
10098 <div class="fancyvrb" id="fancyvrb39">
10100 id="x1-110012r1"></a><span
10101 class="cmr-6">1</span><span
10102 class="cmtt-8"> </span><span
10103 class="cmtt-8"> </span><span
10104 class="cmtt-8"> </span><span
10105 class="cmtt-8"> 1)</span><span
10106 class="cmtt-8"> [classwords\_per\_codeword]</span><span
10107 class="cmtt-8"> =</span><span
10108 class="cmtt-8"> [codebook\_dimensions]</span><span
10109 class="cmtt-8"> value</span><span
10110 class="cmtt-8"> of</span><span
10111 class="cmtt-8"> codebook</span><span
10112 class="cmtt-8"> [residue\_classbook]</span>
10113 <br class="fancyvrb" /><a
10114 id="x1-110014r2"></a><span
10115 class="cmr-6">2</span><span
10116 class="cmtt-8"> </span><span
10117 class="cmtt-8"> </span><span
10118 class="cmtt-8"> </span><span
10119 class="cmtt-8"> 2)</span><span
10120 class="cmtt-8"> [n\_to\_read]</span><span
10121 class="cmtt-8"> =</span><span
10122 class="cmtt-8"> [limit\_residue\_end]</span><span
10123 class="cmtt-8"> -</span><span
10124 class="cmtt-8"> [limit\_residue\_begin]</span>
10125 <br class="fancyvrb" /><a
10126 id="x1-110016r3"></a><span
10127 class="cmr-6">3</span><span
10128 class="cmtt-8"> </span><span
10129 class="cmtt-8"> </span><span
10130 class="cmtt-8"> </span><span
10131 class="cmtt-8"> 3)</span><span
10132 class="cmtt-8"> [partitions\_to\_read]</span><span
10133 class="cmtt-8"> =</span><span
10134 class="cmtt-8"> [n\_to\_read]</span><span
10135 class="cmtt-8"> /</span><span
10136 class="cmtt-8"> [residue\_partition\_size]</span>
10138 <!--l. 286--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
10139 <div class="fancyvrb" id="fancyvrb40">
10141 id="x1-110018r1"></a><span
10142 class="cmr-6">1</span><span
10143 class="cmtt-8"> </span><span
10144 class="cmtt-8"> </span><span
10145 class="cmtt-8"> </span><span
10146 class="cmtt-8"> 1)</span><span
10147 class="cmtt-8"> allocate</span><span
10148 class="cmtt-8"> and</span><span
10149 class="cmtt-8"> zero</span><span
10150 class="cmtt-8"> all</span><span
10151 class="cmtt-8"> vectors</span><span
10152 class="cmtt-8"> that</span><span
10153 class="cmtt-8"> will</span><span
10154 class="cmtt-8"> be</span><span
10155 class="cmtt-8"> returned.</span>
10156 <br class="fancyvrb" /><a
10157 id="x1-110020r2"></a><span
10158 class="cmr-6">2</span><span
10159 class="cmtt-8"> </span><span
10160 class="cmtt-8"> </span><span
10161 class="cmtt-8"> </span><span
10162 class="cmtt-8"> 2)</span><span
10163 class="cmtt-8"> if</span><span
10164 class="cmtt-8"> ([n\_to\_read]</span><span
10165 class="cmtt-8"> is</span><span
10166 class="cmtt-8"> zero),</span><span
10167 class="cmtt-8"> stop;</span><span
10168 class="cmtt-8"> there</span><span
10169 class="cmtt-8"> is</span><span
10170 class="cmtt-8"> no</span><span
10171 class="cmtt-8"> residue</span><span
10172 class="cmtt-8"> to</span><span
10173 class="cmtt-8"> decode.</span>
10174 <br class="fancyvrb" /><a
10175 id="x1-110022r3"></a><span
10176 class="cmr-6">3</span><span
10177 class="cmtt-8"> </span><span
10178 class="cmtt-8"> </span><span
10179 class="cmtt-8"> </span><span
10180 class="cmtt-8"> 3)</span><span
10181 class="cmtt-8"> iterate</span><span
10182 class="cmtt-8"> [pass]</span><span
10183 class="cmtt-8"> over</span><span
10184 class="cmtt-8"> the</span><span
10185 class="cmtt-8"> range</span><span
10186 class="cmtt-8"> 0</span><span
10187 class="cmtt-8"> ...</span><span
10188 class="cmtt-8"> 7</span><span
10189 class="cmtt-8"> {</span>
10190 <br class="fancyvrb" /><a
10191 id="x1-110024r4"></a><span
10192 class="cmr-6">4</span><span
10193 class="cmtt-8"> </span><span
10194 class="cmtt-8"> </span>
10195 <br class="fancyvrb" /><a
10196 id="x1-110026r5"></a><span
10197 class="cmr-6">5</span><span
10198 class="cmtt-8"> </span><span
10199 class="cmtt-8"> </span><span
10200 class="cmtt-8"> </span><span
10201 class="cmtt-8"> </span><span
10202 class="cmtt-8"> </span><span
10203 class="cmtt-8"> </span><span
10204 class="cmtt-8"> </span><span
10205 class="cmtt-8"> </span><span
10206 class="cmtt-8"> 4)</span><span
10207 class="cmtt-8"> [partition\_count]</span><span
10208 class="cmtt-8"> =</span><span
10209 class="cmtt-8"> 0</span>
10210 <br class="fancyvrb" /><a
10211 id="x1-110028r6"></a><span
10212 class="cmr-6">6</span><span
10213 class="cmtt-8"> </span><span
10214 class="cmtt-8"> </span>
10215 <br class="fancyvrb" /><a
10216 id="x1-110030r7"></a><span
10217 class="cmr-6">7</span><span
10218 class="cmtt-8"> </span><span
10219 class="cmtt-8"> </span><span
10220 class="cmtt-8"> </span><span
10221 class="cmtt-8"> </span><span
10222 class="cmtt-8"> </span><span
10223 class="cmtt-8"> </span><span
10224 class="cmtt-8"> </span><span
10225 class="cmtt-8"> </span><span
10226 class="cmtt-8"> 5)</span><span
10227 class="cmtt-8"> while</span><span
10228 class="cmtt-8"> [partition\_count]</span><span
10229 class="cmtt-8"> is</span><span
10230 class="cmtt-8"> less</span><span
10231 class="cmtt-8"> than</span><span
10232 class="cmtt-8"> [partitions\_to\_read]</span>
10233 <br class="fancyvrb" /><a
10234 id="x1-110032r8"></a><span
10235 class="cmr-6">8</span><span
10236 class="cmtt-8"> </span><span
10237 class="cmtt-8"> </span>
10238 <br class="fancyvrb" /><a
10239 id="x1-110034r9"></a><span
10240 class="cmr-6">9</span><span
10241 class="cmtt-8"> </span><span
10242 class="cmtt-8"> </span><span
10243 class="cmtt-8"> </span><span
10244 class="cmtt-8"> </span><span
10245 class="cmtt-8"> </span><span
10246 class="cmtt-8"> </span><span
10247 class="cmtt-8"> </span><span
10248 class="cmtt-8"> </span><span
10249 class="cmtt-8"> </span><span
10250 class="cmtt-8"> </span><span
10251 class="cmtt-8"> </span><span
10252 class="cmtt-8"> </span><span
10253 class="cmtt-8"> </span><span
10254 class="cmtt-8"> 6)</span><span
10255 class="cmtt-8"> if</span><span
10256 class="cmtt-8"> ([pass]</span><span
10257 class="cmtt-8"> is</span><span
10258 class="cmtt-8"> zero)</span><span
10259 class="cmtt-8"> {</span>
10260 <br class="fancyvrb" /><a
10261 id="x1-110036r10"></a><span
10262 class="cmr-6">10</span><span
10263 class="cmtt-8"> </span><span
10264 class="cmtt-8"> </span>
10265 <br class="fancyvrb" /><a
10266 id="x1-110038r11"></a><span
10267 class="cmr-6">11</span><span
10268 class="cmtt-8"> </span><span
10269 class="cmtt-8"> </span><span
10270 class="cmtt-8"> </span><span
10271 class="cmtt-8"> </span><span
10272 class="cmtt-8"> </span><span
10273 class="cmtt-8"> </span><span
10274 class="cmtt-8"> </span><span
10275 class="cmtt-8"> </span><span
10276 class="cmtt-8"> </span><span
10277 class="cmtt-8"> </span><span
10278 class="cmtt-8"> </span><span
10279 class="cmtt-8"> </span><span
10280 class="cmtt-8"> </span><span
10281 class="cmtt-8"> </span><span
10282 class="cmtt-8"> </span><span
10283 class="cmtt-8"> </span><span
10284 class="cmtt-8"> </span><span
10285 class="cmtt-8"> </span><span
10286 class="cmtt-8"> 7)</span><span
10287 class="cmtt-8"> iterate</span><span
10288 class="cmtt-8"> [j]</span><span
10289 class="cmtt-8"> over</span><span
10290 class="cmtt-8"> the</span><span
10291 class="cmtt-8"> range</span><span
10292 class="cmtt-8"> 0</span><span
10293 class="cmtt-8"> ..</span><span
10294 class="cmtt-8"> [ch]-1</span><span
10295 class="cmtt-8"> {</span>
10296 <br class="fancyvrb" /><a
10297 id="x1-110040r12"></a><span
10298 class="cmr-6">12</span><span
10299 class="cmtt-8"> </span><span
10300 class="cmtt-8"> </span>
10301 <br class="fancyvrb" /><a
10302 id="x1-110042r13"></a><span
10303 class="cmr-6">13</span><span
10304 class="cmtt-8"> </span><span
10305 class="cmtt-8"> </span><span
10306 class="cmtt-8"> </span><span
10307 class="cmtt-8"> </span><span
10308 class="cmtt-8"> </span><span
10309 class="cmtt-8"> </span><span
10310 class="cmtt-8"> </span><span
10311 class="cmtt-8"> </span><span
10312 class="cmtt-8"> </span><span
10313 class="cmtt-8"> </span><span
10314 class="cmtt-8"> </span><span
10315 class="cmtt-8"> </span><span
10316 class="cmtt-8"> </span><span
10317 class="cmtt-8"> </span><span
10318 class="cmtt-8"> </span><span
10319 class="cmtt-8"> </span><span
10320 class="cmtt-8"> </span><span
10321 class="cmtt-8"> </span><span
10322 class="cmtt-8"> </span><span
10323 class="cmtt-8"> </span><span
10324 class="cmtt-8"> </span><span
10325 class="cmtt-8"> </span><span
10326 class="cmtt-8"> </span><span
10327 class="cmtt-8"> 8)</span><span
10328 class="cmtt-8"> if</span><span
10329 class="cmtt-8"> vector</span><span
10330 class="cmtt-8"> [j]</span><span
10331 class="cmtt-8"> is</span><span
10332 class="cmtt-8"> not</span><span
10333 class="cmtt-8"> marked</span><span
10334 class="cmtt-8"> ’do</span><span
10335 class="cmtt-8"> not</span><span
10336 class="cmtt-8"> decode’</span><span
10337 class="cmtt-8"> {</span>
10338 <br class="fancyvrb" /><a
10339 id="x1-110044r14"></a><span
10340 class="cmr-6">14</span><span
10341 class="cmtt-8"> </span><span
10342 class="cmtt-8"> </span>
10343 <br class="fancyvrb" /><a
10344 id="x1-110046r15"></a><span
10345 class="cmr-6">15</span><span
10346 class="cmtt-8"> </span><span
10347 class="cmtt-8"> </span><span
10348 class="cmtt-8"> </span><span
10349 class="cmtt-8"> </span><span
10350 class="cmtt-8"> </span><span
10351 class="cmtt-8"> </span><span
10352 class="cmtt-8"> </span><span
10353 class="cmtt-8"> </span><span
10354 class="cmtt-8"> </span><span
10355 class="cmtt-8"> </span><span
10356 class="cmtt-8"> </span><span
10357 class="cmtt-8"> </span><span
10358 class="cmtt-8"> </span><span
10359 class="cmtt-8"> </span><span
10360 class="cmtt-8"> </span><span
10361 class="cmtt-8"> </span><span
10362 class="cmtt-8"> </span><span
10363 class="cmtt-8"> </span><span
10364 class="cmtt-8"> </span><span
10365 class="cmtt-8"> </span><span
10366 class="cmtt-8"> </span><span
10367 class="cmtt-8"> </span><span
10368 class="cmtt-8"> </span><span
10369 class="cmtt-8"> </span><span
10370 class="cmtt-8"> </span><span
10371 class="cmtt-8"> </span><span
10372 class="cmtt-8"> </span><span
10373 class="cmtt-8"> </span><span
10374 class="cmtt-8"> 9)</span><span
10375 class="cmtt-8"> [temp]</span><span
10376 class="cmtt-8"> =</span><span
10377 class="cmtt-8"> read</span><span
10378 class="cmtt-8"> from</span><span
10379 class="cmtt-8"> packet</span><span
10380 class="cmtt-8"> using</span><span
10381 class="cmtt-8"> codebook</span><span
10382 class="cmtt-8"> [residue\_classbook]</span><span
10383 class="cmtt-8"> in</span><span
10384 class="cmtt-8"> scalar</span><span
10385 class="cmtt-8"> context</span>
10386 <br class="fancyvrb" /><a
10387 id="x1-110048r16"></a><span
10388 class="cmr-6">16</span><span
10389 class="cmtt-8"> </span><span
10390 class="cmtt-8"> </span><span
10391 class="cmtt-8"> </span><span
10392 class="cmtt-8"> </span><span
10393 class="cmtt-8"> </span><span
10394 class="cmtt-8"> </span><span
10395 class="cmtt-8"> </span><span
10396 class="cmtt-8"> </span><span
10397 class="cmtt-8"> </span><span
10398 class="cmtt-8"> </span><span
10399 class="cmtt-8"> </span><span
10400 class="cmtt-8"> </span><span
10401 class="cmtt-8"> </span><span
10402 class="cmtt-8"> </span><span
10403 class="cmtt-8"> </span><span
10404 class="cmtt-8"> </span><span
10405 class="cmtt-8"> </span><span
10406 class="cmtt-8"> </span><span
10407 class="cmtt-8"> </span><span
10408 class="cmtt-8"> </span><span
10409 class="cmtt-8"> </span><span
10410 class="cmtt-8"> </span><span
10411 class="cmtt-8"> </span><span
10412 class="cmtt-8"> </span><span
10413 class="cmtt-8"> </span><span
10414 class="cmtt-8"> </span><span
10415 class="cmtt-8"> </span><span
10416 class="cmtt-8"> 10)</span><span
10417 class="cmtt-8"> iterate</span><span
10418 class="cmtt-8"> [i]</span><span
10419 class="cmtt-8"> descending</span><span
10420 class="cmtt-8"> over</span><span
10421 class="cmtt-8"> the</span><span
10422 class="cmtt-8"> range</span><span
10423 class="cmtt-8"> [classwords\_per\_codeword]-1</span><span
10424 class="cmtt-8"> ...</span><span
10425 class="cmtt-8"> 0</span><span
10426 class="cmtt-8"> {</span>
10427 <br class="fancyvrb" /><a
10428 id="x1-110050r17"></a><span
10429 class="cmr-6">17</span><span
10430 class="cmtt-8"> </span><span
10431 class="cmtt-8"> </span>
10432 <br class="fancyvrb" /><a
10433 id="x1-110052r18"></a><span
10434 class="cmr-6">18</span><span
10435 class="cmtt-8"> </span><span
10436 class="cmtt-8"> </span><span
10437 class="cmtt-8"> </span><span
10438 class="cmtt-8"> </span><span
10439 class="cmtt-8"> </span><span
10440 class="cmtt-8"> </span><span
10441 class="cmtt-8"> </span><span
10442 class="cmtt-8"> </span><span
10443 class="cmtt-8"> </span><span
10444 class="cmtt-8"> </span><span
10445 class="cmtt-8"> </span><span
10446 class="cmtt-8"> </span><span
10447 class="cmtt-8"> </span><span
10448 class="cmtt-8"> </span><span
10449 class="cmtt-8"> </span><span
10450 class="cmtt-8"> </span><span
10451 class="cmtt-8"> </span><span
10452 class="cmtt-8"> </span><span
10453 class="cmtt-8"> </span><span
10454 class="cmtt-8"> </span><span
10455 class="cmtt-8"> </span><span
10456 class="cmtt-8"> </span><span
10457 class="cmtt-8"> </span><span
10458 class="cmtt-8"> </span><span
10459 class="cmtt-8"> </span><span
10460 class="cmtt-8"> </span><span
10461 class="cmtt-8"> </span><span
10462 class="cmtt-8"> </span><span
10463 class="cmtt-8"> </span><span
10464 class="cmtt-8"> </span><span
10465 class="cmtt-8"> </span><span
10466 class="cmtt-8"> </span><span
10467 class="cmtt-8"> 11)</span><span
10468 class="cmtt-8"> array</span><span
10469 class="cmtt-8"> [classifications]</span><span
10470 class="cmtt-8"> element</span><span
10471 class="cmtt-8"> [j],([i]+[partition\_count])</span><span
10472 class="cmtt-8"> =</span>
10473 <br class="fancyvrb" /><a
10474 id="x1-110054r19"></a><span
10475 class="cmr-6">19</span><span
10476 class="cmtt-8"> </span><span
10477 class="cmtt-8"> </span><span
10478 class="cmtt-8"> </span><span
10479 class="cmtt-8"> </span><span
10480 class="cmtt-8"> </span><span
10481 class="cmtt-8"> </span><span
10482 class="cmtt-8"> </span><span
10483 class="cmtt-8"> </span><span
10484 class="cmtt-8"> </span><span
10485 class="cmtt-8"> </span><span
10486 class="cmtt-8"> </span><span
10487 class="cmtt-8"> </span><span
10488 class="cmtt-8"> </span><span
10489 class="cmtt-8"> </span><span
10490 class="cmtt-8"> </span><span
10491 class="cmtt-8"> </span><span
10492 class="cmtt-8"> </span><span
10493 class="cmtt-8"> </span><span
10494 class="cmtt-8"> </span><span
10495 class="cmtt-8"> </span><span
10496 class="cmtt-8"> </span><span
10497 class="cmtt-8"> </span><span
10498 class="cmtt-8"> </span><span
10499 class="cmtt-8"> </span><span
10500 class="cmtt-8"> </span><span
10501 class="cmtt-8"> </span><span
10502 class="cmtt-8"> </span><span
10503 class="cmtt-8"> </span><span
10504 class="cmtt-8"> </span><span
10505 class="cmtt-8"> </span><span
10506 class="cmtt-8"> </span><span
10507 class="cmtt-8"> </span><span
10508 class="cmtt-8"> </span><span
10509 class="cmtt-8"> </span><span
10510 class="cmtt-8"> </span><span
10511 class="cmtt-8"> </span><span
10512 class="cmtt-8"> [temp]</span><span
10513 class="cmtt-8"> integer</span><span
10514 class="cmtt-8"> modulo</span><span
10515 class="cmtt-8"> [residue\_classifications]</span>
10516 <br class="fancyvrb" /><a
10517 id="x1-110056r20"></a><span
10518 class="cmr-6">20</span><span
10519 class="cmtt-8"> </span><span
10520 class="cmtt-8"> </span><span
10521 class="cmtt-8"> </span><span
10522 class="cmtt-8"> </span><span
10523 class="cmtt-8"> </span><span
10524 class="cmtt-8"> </span><span
10525 class="cmtt-8"> </span><span
10526 class="cmtt-8"> </span><span
10527 class="cmtt-8"> </span><span
10528 class="cmtt-8"> </span><span
10529 class="cmtt-8"> </span><span
10530 class="cmtt-8"> </span><span
10531 class="cmtt-8"> </span><span
10532 class="cmtt-8"> </span><span
10533 class="cmtt-8"> </span><span
10534 class="cmtt-8"> </span><span
10535 class="cmtt-8"> </span><span
10536 class="cmtt-8"> </span><span
10537 class="cmtt-8"> </span><span
10538 class="cmtt-8"> </span><span
10539 class="cmtt-8"> </span><span
10540 class="cmtt-8"> </span><span
10541 class="cmtt-8"> </span><span
10542 class="cmtt-8"> </span><span
10543 class="cmtt-8"> </span><span
10544 class="cmtt-8"> </span><span
10545 class="cmtt-8"> </span><span
10546 class="cmtt-8"> </span><span
10547 class="cmtt-8"> </span><span
10548 class="cmtt-8"> </span><span
10549 class="cmtt-8"> </span><span
10550 class="cmtt-8"> </span><span
10551 class="cmtt-8"> 12)</span><span
10552 class="cmtt-8"> [temp]</span><span
10553 class="cmtt-8"> =</span><span
10554 class="cmtt-8"> [temp]</span><span
10555 class="cmtt-8"> /</span><span
10556 class="cmtt-8"> [residue\_classifications]</span><span
10557 class="cmtt-8"> using</span><span
10558 class="cmtt-8"> integer</span><span
10559 class="cmtt-8"> division</span>
10560 <br class="fancyvrb" /><a
10561 id="x1-110058r21"></a><span
10562 class="cmr-6">21</span><span
10563 class="cmtt-8"> </span><span
10564 class="cmtt-8"> </span>
10565 <br class="fancyvrb" /><a
10566 id="x1-110060r22"></a><span
10567 class="cmr-6">22</span><span
10568 class="cmtt-8"> </span><span
10569 class="cmtt-8"> </span><span
10570 class="cmtt-8"> </span><span
10571 class="cmtt-8"> </span><span
10572 class="cmtt-8"> </span><span
10573 class="cmtt-8"> </span><span
10574 class="cmtt-8"> </span><span
10575 class="cmtt-8"> </span><span
10576 class="cmtt-8"> </span><span
10577 class="cmtt-8"> </span><span
10578 class="cmtt-8"> </span><span
10579 class="cmtt-8"> </span><span
10580 class="cmtt-8"> </span><span
10581 class="cmtt-8"> </span><span
10582 class="cmtt-8"> </span><span
10583 class="cmtt-8"> </span><span
10584 class="cmtt-8"> </span><span
10585 class="cmtt-8"> </span><span
10586 class="cmtt-8"> </span><span
10587 class="cmtt-8"> </span><span
10588 class="cmtt-8"> </span><span
10589 class="cmtt-8"> </span><span
10590 class="cmtt-8"> </span><span
10591 class="cmtt-8"> </span><span
10592 class="cmtt-8"> </span><span
10593 class="cmtt-8"> </span><span
10594 class="cmtt-8"> </span><span
10595 class="cmtt-8"> </span><span
10596 class="cmtt-8"> </span><span
10597 class="cmtt-8"> </span><span
10598 class="cmtt-8"> </span><span
10599 class="cmtt-8"> }</span>
10600 <br class="fancyvrb" /><a
10601 id="x1-110062r23"></a><span
10602 class="cmr-6">23</span><span
10603 class="cmtt-8"> </span><span
10604 class="cmtt-8"> </span>
10605 <br class="fancyvrb" /><a
10606 id="x1-110064r24"></a><span
10607 class="cmr-6">24</span><span
10608 class="cmtt-8"> </span><span
10609 class="cmtt-8"> </span><span
10610 class="cmtt-8"> </span><span
10611 class="cmtt-8"> </span><span
10612 class="cmtt-8"> </span><span
10613 class="cmtt-8"> </span><span
10614 class="cmtt-8"> </span><span
10615 class="cmtt-8"> </span><span
10616 class="cmtt-8"> </span><span
10617 class="cmtt-8"> </span><span
10618 class="cmtt-8"> </span><span
10619 class="cmtt-8"> </span><span
10620 class="cmtt-8"> </span><span
10621 class="cmtt-8"> </span><span
10622 class="cmtt-8"> </span><span
10623 class="cmtt-8"> </span><span
10624 class="cmtt-8"> </span><span
10625 class="cmtt-8"> </span><span
10626 class="cmtt-8"> </span><span
10627 class="cmtt-8"> </span><span
10628 class="cmtt-8"> </span><span
10629 class="cmtt-8"> </span><span
10630 class="cmtt-8"> </span><span
10631 class="cmtt-8"> </span><span
10632 class="cmtt-8"> </span><span
10633 class="cmtt-8"> </span><span
10634 class="cmtt-8"> }</span>
10635 <br class="fancyvrb" /><a
10636 id="x1-110066r25"></a><span
10637 class="cmr-6">25</span><span
10638 class="cmtt-8"> </span><span
10639 class="cmtt-8"> </span>
10640 <br class="fancyvrb" /><a
10641 id="x1-110068r26"></a><span
10642 class="cmr-6">26</span><span
10643 class="cmtt-8"> </span><span
10644 class="cmtt-8"> </span><span
10645 class="cmtt-8"> </span><span
10646 class="cmtt-8"> </span><span
10647 class="cmtt-8"> </span><span
10648 class="cmtt-8"> </span><span
10649 class="cmtt-8"> </span><span
10650 class="cmtt-8"> </span><span
10651 class="cmtt-8"> </span><span
10652 class="cmtt-8"> </span><span
10653 class="cmtt-8"> </span><span
10654 class="cmtt-8"> </span><span
10655 class="cmtt-8"> </span><span
10656 class="cmtt-8"> </span><span
10657 class="cmtt-8"> </span><span
10658 class="cmtt-8"> </span><span
10659 class="cmtt-8"> </span><span
10660 class="cmtt-8"> </span><span
10661 class="cmtt-8"> </span><span
10662 class="cmtt-8"> </span><span
10663 class="cmtt-8"> </span><span
10664 class="cmtt-8"> }</span>
10665 <br class="fancyvrb" /><a
10666 id="x1-110070r27"></a><span
10667 class="cmr-6">27</span><span
10668 class="cmtt-8"> </span><span
10669 class="cmtt-8"> </span>
10670 <br class="fancyvrb" /><a
10671 id="x1-110072r28"></a><span
10672 class="cmr-6">28</span><span
10673 class="cmtt-8"> </span><span
10674 class="cmtt-8"> </span><span
10675 class="cmtt-8"> </span><span
10676 class="cmtt-8"> </span><span
10677 class="cmtt-8"> </span><span
10678 class="cmtt-8"> </span><span
10679 class="cmtt-8"> </span><span
10680 class="cmtt-8"> </span><span
10681 class="cmtt-8"> </span><span
10682 class="cmtt-8"> </span><span
10683 class="cmtt-8"> </span><span
10684 class="cmtt-8"> </span><span
10685 class="cmtt-8"> </span><span
10686 class="cmtt-8"> </span><span
10687 class="cmtt-8"> </span><span
10688 class="cmtt-8"> </span><span
10689 class="cmtt-8"> }</span>
10690 <br class="fancyvrb" /><a
10691 id="x1-110074r29"></a><span
10692 class="cmr-6">29</span><span
10693 class="cmtt-8"> </span><span
10694 class="cmtt-8"> </span>
10695 <br class="fancyvrb" /><a
10696 id="x1-110076r30"></a><span
10697 class="cmr-6">30</span><span
10698 class="cmtt-8"> </span><span
10699 class="cmtt-8"> </span><span
10700 class="cmtt-8"> </span><span
10701 class="cmtt-8"> </span><span
10702 class="cmtt-8"> </span><span
10703 class="cmtt-8"> </span><span
10704 class="cmtt-8"> </span><span
10705 class="cmtt-8"> </span><span
10706 class="cmtt-8"> </span><span
10707 class="cmtt-8"> </span><span
10708 class="cmtt-8"> </span><span
10709 class="cmtt-8"> </span><span
10710 class="cmtt-8"> 13)</span><span
10711 class="cmtt-8"> iterate</span><span
10712 class="cmtt-8"> [i]</span><span
10713 class="cmtt-8"> over</span><span
10714 class="cmtt-8"> the</span><span
10715 class="cmtt-8"> range</span><span
10716 class="cmtt-8"> 0</span><span
10717 class="cmtt-8"> ..</span><span
10718 class="cmtt-8"> ([classwords\_per\_codeword]</span><span
10719 class="cmtt-8"> -</span><span
10720 class="cmtt-8"> 1)</span><span
10721 class="cmtt-8"> while</span><span
10722 class="cmtt-8"> [partition\_count]</span>
10723 <br class="fancyvrb" /><a
10724 id="x1-110078r31"></a><span
10725 class="cmr-6">31</span><span
10726 class="cmtt-8"> </span><span
10727 class="cmtt-8"> </span><span
10728 class="cmtt-8"> </span><span
10729 class="cmtt-8"> </span><span
10730 class="cmtt-8"> </span><span
10731 class="cmtt-8"> </span><span
10732 class="cmtt-8"> </span><span
10733 class="cmtt-8"> </span><span
10734 class="cmtt-8"> </span><span
10735 class="cmtt-8"> </span><span
10736 class="cmtt-8"> </span><span
10737 class="cmtt-8"> </span><span
10738 class="cmtt-8"> </span><span
10739 class="cmtt-8"> </span><span
10740 class="cmtt-8"> </span><span
10741 class="cmtt-8"> </span><span
10742 class="cmtt-8"> is</span><span
10743 class="cmtt-8"> also</span><span
10744 class="cmtt-8"> less</span><span
10745 class="cmtt-8"> than</span><span
10746 class="cmtt-8"> [partitions\_to\_read]</span><span
10747 class="cmtt-8"> {</span>
10748 <br class="fancyvrb" /><a
10749 id="x1-110080r32"></a><span
10750 class="cmr-6">32</span><span
10751 class="cmtt-8"> </span><span
10752 class="cmtt-8"> </span>
10753 <br class="fancyvrb" /><a
10754 id="x1-110082r33"></a><span
10755 class="cmr-6">33</span><span
10756 class="cmtt-8"> </span><span
10757 class="cmtt-8"> </span><span
10758 class="cmtt-8"> </span><span
10759 class="cmtt-8"> </span><span
10760 class="cmtt-8"> </span><span
10761 class="cmtt-8"> </span><span
10762 class="cmtt-8"> </span><span
10763 class="cmtt-8"> </span><span
10764 class="cmtt-8"> </span><span
10765 class="cmtt-8"> </span><span
10766 class="cmtt-8"> </span><span
10767 class="cmtt-8"> </span><span
10768 class="cmtt-8"> </span><span
10769 class="cmtt-8"> </span><span
10770 class="cmtt-8"> </span><span
10771 class="cmtt-8"> </span><span
10772 class="cmtt-8"> </span><span
10773 class="cmtt-8"> </span><span
10774 class="cmtt-8"> 14)</span><span
10775 class="cmtt-8"> iterate</span><span
10776 class="cmtt-8"> [j]</span><span
10777 class="cmtt-8"> over</span><span
10778 class="cmtt-8"> the</span><span
10779 class="cmtt-8"> range</span><span
10780 class="cmtt-8"> 0</span><span
10781 class="cmtt-8"> ..</span><span
10782 class="cmtt-8"> [ch]-1</span><span
10783 class="cmtt-8"> {</span>
10784 <br class="fancyvrb" /><a
10785 id="x1-110084r34"></a><span
10786 class="cmr-6">34</span><span
10787 class="cmtt-8"> </span><span
10788 class="cmtt-8"> </span>
10789 <br class="fancyvrb" /><a
10790 id="x1-110086r35"></a><span
10791 class="cmr-6">35</span><span
10792 class="cmtt-8"> </span><span
10793 class="cmtt-8"> </span><span
10794 class="cmtt-8"> </span><span
10795 class="cmtt-8"> </span><span
10796 class="cmtt-8"> </span><span
10797 class="cmtt-8"> </span><span
10798 class="cmtt-8"> </span><span
10799 class="cmtt-8"> </span><span
10800 class="cmtt-8"> </span><span
10801 class="cmtt-8"> </span><span
10802 class="cmtt-8"> </span><span
10803 class="cmtt-8"> </span><span
10804 class="cmtt-8"> </span><span
10805 class="cmtt-8"> </span><span
10806 class="cmtt-8"> </span><span
10807 class="cmtt-8"> </span><span
10808 class="cmtt-8"> </span><span
10809 class="cmtt-8"> </span><span
10810 class="cmtt-8"> </span><span
10811 class="cmtt-8"> </span><span
10812 class="cmtt-8"> </span><span
10813 class="cmtt-8"> </span><span
10814 class="cmtt-8"> </span><span
10815 class="cmtt-8"> 15)</span><span
10816 class="cmtt-8"> if</span><span
10817 class="cmtt-8"> vector</span><span
10818 class="cmtt-8"> [j]</span><span
10819 class="cmtt-8"> is</span><span
10820 class="cmtt-8"> not</span><span
10821 class="cmtt-8"> marked</span><span
10822 class="cmtt-8"> ’do</span><span
10823 class="cmtt-8"> not</span><span
10824 class="cmtt-8"> decode’</span><span
10825 class="cmtt-8"> {</span>
10826 <br class="fancyvrb" /><a
10827 id="x1-110088r36"></a><span
10828 class="cmr-6">36</span><span
10829 class="cmtt-8"> </span><span
10830 class="cmtt-8"> </span>
10831 <br class="fancyvrb" /><a
10832 id="x1-110090r37"></a><span
10833 class="cmr-6">37</span><span
10834 class="cmtt-8"> </span><span
10835 class="cmtt-8"> </span><span
10836 class="cmtt-8"> </span><span
10837 class="cmtt-8"> </span><span
10838 class="cmtt-8"> </span><span
10839 class="cmtt-8"> </span><span
10840 class="cmtt-8"> </span><span
10841 class="cmtt-8"> </span><span
10842 class="cmtt-8"> </span><span
10843 class="cmtt-8"> </span><span
10844 class="cmtt-8"> </span><span
10845 class="cmtt-8"> </span><span
10846 class="cmtt-8"> </span><span
10847 class="cmtt-8"> </span><span
10848 class="cmtt-8"> </span><span
10849 class="cmtt-8"> </span><span
10850 class="cmtt-8"> </span><span
10851 class="cmtt-8"> </span><span
10852 class="cmtt-8"> </span><span
10853 class="cmtt-8"> </span><span
10854 class="cmtt-8"> </span><span
10855 class="cmtt-8"> </span><span
10856 class="cmtt-8"> </span><span
10857 class="cmtt-8"> </span><span
10858 class="cmtt-8"> </span><span
10859 class="cmtt-8"> </span><span
10860 class="cmtt-8"> </span><span
10861 class="cmtt-8"> </span><span
10862 class="cmtt-8"> 16)</span><span
10863 class="cmtt-8"> [vqclass]</span><span
10864 class="cmtt-8"> =</span><span
10865 class="cmtt-8"> array</span><span
10866 class="cmtt-8"> [classifications]</span><span
10867 class="cmtt-8"> element</span><span
10868 class="cmtt-8"> [j],[partition\_count]</span>
10869 <br class="fancyvrb" /><a
10870 id="x1-110092r38"></a><span
10871 class="cmr-6">38</span><span
10872 class="cmtt-8"> </span><span
10873 class="cmtt-8"> </span><span
10874 class="cmtt-8"> </span><span
10875 class="cmtt-8"> </span><span
10876 class="cmtt-8"> </span><span
10877 class="cmtt-8"> </span><span
10878 class="cmtt-8"> </span><span
10879 class="cmtt-8"> </span><span
10880 class="cmtt-8"> </span><span
10881 class="cmtt-8"> </span><span
10882 class="cmtt-8"> </span><span
10883 class="cmtt-8"> </span><span
10884 class="cmtt-8"> </span><span
10885 class="cmtt-8"> </span><span
10886 class="cmtt-8"> </span><span
10887 class="cmtt-8"> </span><span
10888 class="cmtt-8"> </span><span
10889 class="cmtt-8"> </span><span
10890 class="cmtt-8"> </span><span
10891 class="cmtt-8"> </span><span
10892 class="cmtt-8"> </span><span
10893 class="cmtt-8"> </span><span
10894 class="cmtt-8"> </span><span
10895 class="cmtt-8"> </span><span
10896 class="cmtt-8"> </span><span
10897 class="cmtt-8"> </span><span
10898 class="cmtt-8"> </span><span
10899 class="cmtt-8"> </span><span
10900 class="cmtt-8"> 17)</span><span
10901 class="cmtt-8"> [vqbook]</span><span
10902 class="cmtt-8"> =</span><span
10903 class="cmtt-8"> array</span><span
10904 class="cmtt-8"> [residue\_books]</span><span
10905 class="cmtt-8"> element</span><span
10906 class="cmtt-8"> [vqclass],[pass]</span>
10907 <br class="fancyvrb" /><a
10908 id="x1-110094r39"></a><span
10909 class="cmr-6">39</span><span
10910 class="cmtt-8"> </span><span
10911 class="cmtt-8"> </span><span
10912 class="cmtt-8"> </span><span
10913 class="cmtt-8"> </span><span
10914 class="cmtt-8"> </span><span
10915 class="cmtt-8"> </span><span
10916 class="cmtt-8"> </span><span
10917 class="cmtt-8"> </span><span
10918 class="cmtt-8"> </span><span
10919 class="cmtt-8"> </span><span
10920 class="cmtt-8"> </span><span
10921 class="cmtt-8"> </span><span
10922 class="cmtt-8"> </span><span
10923 class="cmtt-8"> </span><span
10924 class="cmtt-8"> </span><span
10925 class="cmtt-8"> </span><span
10926 class="cmtt-8"> </span><span
10927 class="cmtt-8"> </span><span
10928 class="cmtt-8"> </span><span
10929 class="cmtt-8"> </span><span
10930 class="cmtt-8"> </span><span
10931 class="cmtt-8"> </span><span
10932 class="cmtt-8"> </span><span
10933 class="cmtt-8"> </span><span
10934 class="cmtt-8"> </span><span
10935 class="cmtt-8"> </span><span
10936 class="cmtt-8"> </span><span
10937 class="cmtt-8"> </span><span
10938 class="cmtt-8"> 18)</span><span
10939 class="cmtt-8"> if</span><span
10940 class="cmtt-8"> ([vqbook]</span><span
10941 class="cmtt-8"> is</span><span
10942 class="cmtt-8"> not</span><span
10943 class="cmtt-8"> ’unused’)</span><span
10944 class="cmtt-8"> {</span>
10945 <br class="fancyvrb" /><a
10946 id="x1-110096r40"></a><span
10947 class="cmr-6">40</span><span
10948 class="cmtt-8"> </span><span
10949 class="cmtt-8"> </span>
10950 <br class="fancyvrb" /><a
10951 id="x1-110098r41"></a><span
10952 class="cmr-6">41</span><span
10953 class="cmtt-8"> </span><span
10954 class="cmtt-8"> </span><span
10955 class="cmtt-8"> </span><span
10956 class="cmtt-8"> </span><span
10957 class="cmtt-8"> </span><span
10958 class="cmtt-8"> </span><span
10959 class="cmtt-8"> </span><span
10960 class="cmtt-8"> </span><span
10961 class="cmtt-8"> </span><span
10962 class="cmtt-8"> </span><span
10963 class="cmtt-8"> </span><span
10964 class="cmtt-8"> </span><span
10965 class="cmtt-8"> </span><span
10966 class="cmtt-8"> </span><span
10967 class="cmtt-8"> </span><span
10968 class="cmtt-8"> </span><span
10969 class="cmtt-8"> </span><span
10970 class="cmtt-8"> </span><span
10971 class="cmtt-8"> </span><span
10972 class="cmtt-8"> </span><span
10973 class="cmtt-8"> </span><span
10974 class="cmtt-8"> </span><span
10975 class="cmtt-8"> </span><span
10976 class="cmtt-8"> </span><span
10977 class="cmtt-8"> </span><span
10978 class="cmtt-8"> </span><span
10979 class="cmtt-8"> </span><span
10980 class="cmtt-8"> </span><span
10981 class="cmtt-8"> </span><span
10982 class="cmtt-8"> </span><span
10983 class="cmtt-8"> </span><span
10984 class="cmtt-8"> </span><span
10985 class="cmtt-8"> </span><span
10986 class="cmtt-8"> 19)</span><span
10987 class="cmtt-8"> decode</span><span
10988 class="cmtt-8"> partition</span><span
10989 class="cmtt-8"> into</span><span
10990 class="cmtt-8"> output</span><span
10991 class="cmtt-8"> vector</span><span
10992 class="cmtt-8"> number</span><span
10993 class="cmtt-8"> [j],</span><span
10994 class="cmtt-8"> starting</span><span
10995 class="cmtt-8"> at</span><span
10996 class="cmtt-8"> scalar</span>
10997 <br class="fancyvrb" /><a
10998 id="x1-110100r42"></a><span
10999 class="cmr-6">42</span><span
11000 class="cmtt-8"> </span><span
11001 class="cmtt-8"> </span><span
11002 class="cmtt-8"> </span><span
11003 class="cmtt-8"> </span><span
11004 class="cmtt-8"> </span><span
11005 class="cmtt-8"> </span><span
11006 class="cmtt-8"> </span><span
11007 class="cmtt-8"> </span><span
11008 class="cmtt-8"> </span><span
11009 class="cmtt-8"> </span><span
11010 class="cmtt-8"> </span><span
11011 class="cmtt-8"> </span><span
11012 class="cmtt-8"> </span><span
11013 class="cmtt-8"> </span><span
11014 class="cmtt-8"> </span><span
11015 class="cmtt-8"> </span><span
11016 class="cmtt-8"> </span><span
11017 class="cmtt-8"> </span><span
11018 class="cmtt-8"> </span><span
11019 class="cmtt-8"> </span><span
11020 class="cmtt-8"> </span><span
11021 class="cmtt-8"> </span><span
11022 class="cmtt-8"> </span><span
11023 class="cmtt-8"> </span><span
11024 class="cmtt-8"> </span><span
11025 class="cmtt-8"> </span><span
11026 class="cmtt-8"> </span><span
11027 class="cmtt-8"> </span><span
11028 class="cmtt-8"> </span><span
11029 class="cmtt-8"> </span><span
11030 class="cmtt-8"> </span><span
11031 class="cmtt-8"> </span><span
11032 class="cmtt-8"> </span><span
11033 class="cmtt-8"> </span><span
11034 class="cmtt-8"> </span><span
11035 class="cmtt-8"> </span><span
11036 class="cmtt-8"> </span><span
11037 class="cmtt-8"> offset</span><span
11038 class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span
11039 class="cmtt-8"> using</span>
11040 <br class="fancyvrb" /><a
11041 id="x1-110102r43"></a><span
11042 class="cmr-6">43</span><span
11043 class="cmtt-8"> </span><span
11044 class="cmtt-8"> </span><span
11045 class="cmtt-8"> </span><span
11046 class="cmtt-8"> </span><span
11047 class="cmtt-8"> </span><span
11048 class="cmtt-8"> </span><span
11049 class="cmtt-8"> </span><span
11050 class="cmtt-8"> </span><span
11051 class="cmtt-8"> </span><span
11052 class="cmtt-8"> </span><span
11053 class="cmtt-8"> </span><span
11054 class="cmtt-8"> </span><span
11055 class="cmtt-8"> </span><span
11056 class="cmtt-8"> </span><span
11057 class="cmtt-8"> </span><span
11058 class="cmtt-8"> </span><span
11059 class="cmtt-8"> </span><span
11060 class="cmtt-8"> </span><span
11061 class="cmtt-8"> </span><span
11062 class="cmtt-8"> </span><span
11063 class="cmtt-8"> </span><span
11064 class="cmtt-8"> </span><span
11065 class="cmtt-8"> </span><span
11066 class="cmtt-8"> </span><span
11067 class="cmtt-8"> </span><span
11068 class="cmtt-8"> </span><span
11069 class="cmtt-8"> </span><span
11070 class="cmtt-8"> </span><span
11071 class="cmtt-8"> </span><span
11072 class="cmtt-8"> </span><span
11073 class="cmtt-8"> </span><span
11074 class="cmtt-8"> </span><span
11075 class="cmtt-8"> </span><span
11076 class="cmtt-8"> </span><span
11077 class="cmtt-8"> </span><span
11078 class="cmtt-8"> </span><span
11079 class="cmtt-8"> </span><span
11080 class="cmtt-8"> codebook</span><span
11081 class="cmtt-8"> number</span><span
11082 class="cmtt-8"> [vqbook]</span><span
11083 class="cmtt-8"> in</span><span
11084 class="cmtt-8"> VQ</span><span
11085 class="cmtt-8"> context</span>
11086 <br class="fancyvrb" /><a
11087 id="x1-110104r44"></a><span
11088 class="cmr-6">44</span><span
11089 class="cmtt-8"> </span><span
11090 class="cmtt-8"> </span><span
11091 class="cmtt-8"> </span><span
11092 class="cmtt-8"> </span><span
11093 class="cmtt-8"> </span><span
11094 class="cmtt-8"> </span><span
11095 class="cmtt-8"> </span><span
11096 class="cmtt-8"> </span><span
11097 class="cmtt-8"> </span><span
11098 class="cmtt-8"> </span><span
11099 class="cmtt-8"> </span><span
11100 class="cmtt-8"> </span><span
11101 class="cmtt-8"> </span><span
11102 class="cmtt-8"> </span><span
11103 class="cmtt-8"> </span><span
11104 class="cmtt-8"> </span><span
11105 class="cmtt-8"> </span><span
11106 class="cmtt-8"> </span><span
11107 class="cmtt-8"> </span><span
11108 class="cmtt-8"> </span><span
11109 class="cmtt-8"> </span><span
11110 class="cmtt-8"> </span><span
11111 class="cmtt-8"> </span><span
11112 class="cmtt-8"> </span><span
11113 class="cmtt-8"> </span><span
11114 class="cmtt-8"> </span><span
11115 class="cmtt-8"> </span><span
11116 class="cmtt-8"> }</span>
11120 <br class="fancyvrb" /><a
11121 id="x1-110106r45"></a><span
11122 class="cmr-6">45</span><span
11123 class="cmtt-8"> </span><span
11124 class="cmtt-8"> </span><span
11125 class="cmtt-8"> </span><span
11126 class="cmtt-8"> </span><span
11127 class="cmtt-8"> </span><span
11128 class="cmtt-8"> </span><span
11129 class="cmtt-8"> </span><span
11130 class="cmtt-8"> </span><span
11131 class="cmtt-8"> </span><span
11132 class="cmtt-8"> </span><span
11133 class="cmtt-8"> </span><span
11134 class="cmtt-8"> </span><span
11135 class="cmtt-8"> </span><span
11136 class="cmtt-8"> </span><span
11137 class="cmtt-8"> </span><span
11138 class="cmtt-8"> </span><span
11139 class="cmtt-8"> </span><span
11140 class="cmtt-8"> </span><span
11141 class="cmtt-8"> </span><span
11142 class="cmtt-8"> </span><span
11143 class="cmtt-8"> </span><span
11144 class="cmtt-8"> </span><span
11145 class="cmtt-8"> }</span>
11146 <br class="fancyvrb" /><a
11147 id="x1-110108r46"></a><span
11148 class="cmr-6">46</span><span
11149 class="cmtt-8"> </span><span
11150 class="cmtt-8"> </span>
11151 <br class="fancyvrb" /><a
11152 id="x1-110110r47"></a><span
11153 class="cmr-6">47</span><span
11154 class="cmtt-8"> </span><span
11155 class="cmtt-8"> </span><span
11156 class="cmtt-8"> </span><span
11157 class="cmtt-8"> </span><span
11158 class="cmtt-8"> </span><span
11159 class="cmtt-8"> </span><span
11160 class="cmtt-8"> </span><span
11161 class="cmtt-8"> </span><span
11162 class="cmtt-8"> </span><span
11163 class="cmtt-8"> </span><span
11164 class="cmtt-8"> </span><span
11165 class="cmtt-8"> </span><span
11166 class="cmtt-8"> </span><span
11167 class="cmtt-8"> </span><span
11168 class="cmtt-8"> </span><span
11169 class="cmtt-8"> </span><span
11170 class="cmtt-8"> </span><span
11171 class="cmtt-8"> </span><span
11172 class="cmtt-8"> 20)</span><span
11173 class="cmtt-8"> increment</span><span
11174 class="cmtt-8"> [partition\_count]</span><span
11175 class="cmtt-8"> by</span><span
11176 class="cmtt-8"> one</span>
11177 <br class="fancyvrb" /><a
11178 id="x1-110112r48"></a><span
11179 class="cmr-6">48</span><span
11180 class="cmtt-8"> </span><span
11181 class="cmtt-8"> </span>
11182 <br class="fancyvrb" /><a
11183 id="x1-110114r49"></a><span
11184 class="cmr-6">49</span><span
11185 class="cmtt-8"> </span><span
11186 class="cmtt-8"> </span><span
11187 class="cmtt-8"> </span><span
11188 class="cmtt-8"> </span><span
11189 class="cmtt-8"> </span><span
11190 class="cmtt-8"> </span><span
11191 class="cmtt-8"> </span><span
11192 class="cmtt-8"> </span><span
11193 class="cmtt-8"> </span><span
11194 class="cmtt-8"> </span><span
11195 class="cmtt-8"> </span><span
11196 class="cmtt-8"> </span><span
11197 class="cmtt-8"> </span><span
11198 class="cmtt-8"> </span><span
11199 class="cmtt-8"> </span><span
11200 class="cmtt-8"> </span><span
11201 class="cmtt-8"> }</span>
11202 <br class="fancyvrb" /><a
11203 id="x1-110116r50"></a><span
11204 class="cmr-6">50</span><span
11205 class="cmtt-8"> </span><span
11206 class="cmtt-8"> </span><span
11207 class="cmtt-8"> </span><span
11208 class="cmtt-8"> </span><span
11209 class="cmtt-8"> </span><span
11210 class="cmtt-8"> </span><span
11211 class="cmtt-8"> </span><span
11212 class="cmtt-8"> </span><span
11213 class="cmtt-8"> </span><span
11214 class="cmtt-8"> </span><span
11215 class="cmtt-8"> </span><span
11216 class="cmtt-8"> }</span>
11217 <br class="fancyvrb" /><a
11218 id="x1-110118r51"></a><span
11219 class="cmr-6">51</span><span
11220 class="cmtt-8"> </span><span
11221 class="cmtt-8"> </span><span
11222 class="cmtt-8"> </span><span
11223 class="cmtt-8"> </span><span
11224 class="cmtt-8"> </span><span
11225 class="cmtt-8"> </span><span
11226 class="cmtt-8"> }</span>
11227 <br class="fancyvrb" /><a
11228 id="x1-110120r52"></a><span
11229 class="cmr-6">52</span><span
11230 class="cmtt-8"> </span><span
11231 class="cmtt-8"> </span>
11232 <br class="fancyvrb" /><a
11233 id="x1-110122r53"></a><span
11234 class="cmr-6">53</span><span
11235 class="cmtt-8"> </span><span
11236 class="cmtt-8"> </span><span
11237 class="cmtt-8"> 21)</span><span
11238 class="cmtt-8"> done</span>
11239 <br class="fancyvrb" /><a
11240 id="x1-110124r54"></a><span
11241 class="cmr-6">54</span><span
11242 class="cmtt-8"> </span><span
11243 class="cmtt-8"> </span>
11245 <!--l. 344--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
11246 Decode returns the result of vector decode up to that point.
11247 <!--l. 350--><p class="noindent" >
11248 <h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a
11249 id="x1-1110008.6.3"></a>format 0 specifics</h5>
11250 <!--l. 352--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
11251 section. The following pseudocode presents the same algorithm. Assume:
11252 <ul class="itemize1">
11253 <li class="itemize"><span
11254 class="cmtt-12">[n] </span>is the value in <span
11255 class="cmtt-12">[residue_partition_size]</span>
11257 <li class="itemize"><span
11258 class="cmtt-12">[v] </span>is the residue vector
11260 <li class="itemize"><span
11261 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
11262 <!--l. 363--><p class="noindent" >
11263 <div class="fancyvrb" id="fancyvrb41">
11265 id="x1-111002r1"></a><span
11266 class="cmr-6">1</span><span
11267 class="cmtt-8"> </span><span
11268 class="cmtt-8"> </span><span
11269 class="cmtt-8"> 1)</span><span
11270 class="cmtt-8"> [step]</span><span
11271 class="cmtt-8"> =</span><span
11272 class="cmtt-8"> [n]</span><span
11273 class="cmtt-8"> /</span><span
11274 class="cmtt-8"> [codebook\_dimensions]</span>
11275 <br class="fancyvrb" /><a
11276 id="x1-111004r2"></a><span
11277 class="cmr-6">2</span><span
11278 class="cmtt-8"> </span><span
11279 class="cmtt-8"> </span><span
11280 class="cmtt-8"> 2)</span><span
11281 class="cmtt-8"> iterate</span><span
11282 class="cmtt-8"> [i]</span><span
11283 class="cmtt-8"> over</span><span
11284 class="cmtt-8"> the</span><span
11285 class="cmtt-8"> range</span><span
11286 class="cmtt-8"> 0</span><span
11287 class="cmtt-8"> ...</span><span
11288 class="cmtt-8"> [step]-1</span><span
11289 class="cmtt-8"> {</span>
11290 <br class="fancyvrb" /><a
11291 id="x1-111006r3"></a><span
11292 class="cmr-6">3</span><span
11293 class="cmtt-8"> </span><span
11294 class="cmtt-8"> </span>
11295 <br class="fancyvrb" /><a
11296 id="x1-111008r4"></a><span
11297 class="cmr-6">4</span><span
11298 class="cmtt-8"> </span><span
11299 class="cmtt-8"> </span><span
11300 class="cmtt-8"> </span><span
11301 class="cmtt-8"> </span><span
11302 class="cmtt-8"> </span><span
11303 class="cmtt-8"> </span><span
11304 class="cmtt-8"> </span><span
11305 class="cmtt-8"> 3)</span><span
11306 class="cmtt-8"> vector</span><span
11307 class="cmtt-8"> [entry\_temp]</span><span
11308 class="cmtt-8"> =</span><span
11309 class="cmtt-8"> read</span><span
11310 class="cmtt-8"> vector</span><span
11311 class="cmtt-8"> from</span><span
11312 class="cmtt-8"> packet</span><span
11313 class="cmtt-8"> using</span><span
11314 class="cmtt-8"> current</span><span
11315 class="cmtt-8"> codebook</span><span
11316 class="cmtt-8"> in</span><span
11317 class="cmtt-8"> VQ</span><span
11318 class="cmtt-8"> context</span>
11319 <br class="fancyvrb" /><a
11320 id="x1-111010r5"></a><span
11321 class="cmr-6">5</span><span
11322 class="cmtt-8"> </span><span
11323 class="cmtt-8"> </span><span
11324 class="cmtt-8"> </span><span
11325 class="cmtt-8"> </span><span
11326 class="cmtt-8"> </span><span
11327 class="cmtt-8"> </span><span
11328 class="cmtt-8"> </span><span
11329 class="cmtt-8"> 4)</span><span
11330 class="cmtt-8"> iterate</span><span
11331 class="cmtt-8"> [j]</span><span
11332 class="cmtt-8"> over</span><span
11333 class="cmtt-8"> the</span><span
11334 class="cmtt-8"> range</span><span
11335 class="cmtt-8"> 0</span><span
11336 class="cmtt-8"> ...</span><span
11337 class="cmtt-8"> [codebook\_dimensions]-1</span><span
11338 class="cmtt-8"> {</span>
11339 <br class="fancyvrb" /><a
11340 id="x1-111012r6"></a><span
11341 class="cmr-6">6</span><span
11342 class="cmtt-8"> </span><span
11343 class="cmtt-8"> </span>
11344 <br class="fancyvrb" /><a
11345 id="x1-111014r7"></a><span
11346 class="cmr-6">7</span><span
11347 class="cmtt-8"> </span><span
11348 class="cmtt-8"> </span><span
11349 class="cmtt-8"> </span><span
11350 class="cmtt-8"> </span><span
11351 class="cmtt-8"> </span><span
11352 class="cmtt-8"> </span><span
11353 class="cmtt-8"> </span><span
11354 class="cmtt-8"> </span><span
11355 class="cmtt-8"> </span><span
11356 class="cmtt-8"> </span><span
11357 class="cmtt-8"> </span><span
11358 class="cmtt-8"> </span><span
11359 class="cmtt-8"> 5)</span><span
11360 class="cmtt-8"> vector</span><span
11361 class="cmtt-8"> [v]</span><span
11362 class="cmtt-8"> element</span><span
11363 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
11364 class="cmtt-8"> =</span>
11365 <br class="fancyvrb" /><a
11366 id="x1-111016r8"></a><span
11367 class="cmr-6">8</span><span
11368 class="cmtt-8"> </span><span
11369 class="cmtt-8">  </span><span
11370 class="cmtt-8"> </span><span
11371 class="cmtt-8"> </span><span
11372 class="cmtt-8"> </span><span
11373 class="cmtt-8"> </span><span
11374 class="cmtt-8"> </span><span
11375 class="cmtt-8"> </span><span
11376 class="cmtt-8"> </span><span
11377 class="cmtt-8"> vector</span><span
11378 class="cmtt-8"> [v]</span><span
11379 class="cmtt-8"> element</span><span
11380 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
11381 class="cmtt-8"> +</span>
11382 <br class="fancyvrb" /><a
11383 id="x1-111018r9"></a><span
11384 class="cmr-6">9</span><span
11385 class="cmtt-8"> </span><span
11386 class="cmtt-8"> </span><span
11387 class="cmtt-8"> </span><span
11388 class="cmtt-8"> </span><span
11389 class="cmtt-8"> </span><span
11390 class="cmtt-8"> </span><span
11391 class="cmtt-8"> </span><span
11392 class="cmtt-8"> </span><span
11393 class="cmtt-8"> </span><span
11394 class="cmtt-8"> </span><span
11395 class="cmtt-8"> </span><span
11396 class="cmtt-8"> </span><span
11397 class="cmtt-8"> </span><span
11398 class="cmtt-8"> </span><span
11399 class="cmtt-8"> </span><span
11400 class="cmtt-8"> </span><span
11401 class="cmtt-8"> </span><span
11402 class="cmtt-8"> vector</span><span
11403 class="cmtt-8"> [entry\_temp]</span><span
11404 class="cmtt-8"> element</span><span
11405 class="cmtt-8"> [j]</span>
11406 <br class="fancyvrb" /><a
11407 id="x1-111020r10"></a><span
11408 class="cmr-6">10</span><span
11409 class="cmtt-8"> </span><span
11410 class="cmtt-8"> </span>
11411 <br class="fancyvrb" /><a
11412 id="x1-111022r11"></a><span
11413 class="cmr-6">11</span><span
11414 class="cmtt-8"> </span><span
11415 class="cmtt-8"> </span><span
11416 class="cmtt-8"> </span><span
11417 class="cmtt-8"> </span><span
11418 class="cmtt-8"> </span><span
11419 class="cmtt-8"> </span><span
11420 class="cmtt-8"> </span><span
11421 class="cmtt-8"> </span><span
11422 class="cmtt-8"> </span><span
11423 class="cmtt-8"> </span><span
11424 class="cmtt-8"> }</span>
11425 <br class="fancyvrb" /><a
11426 id="x1-111024r12"></a><span
11427 class="cmr-6">12</span><span
11428 class="cmtt-8"> </span><span
11429 class="cmtt-8"> </span>
11430 <br class="fancyvrb" /><a
11431 id="x1-111026r13"></a><span
11432 class="cmr-6">13</span><span
11433 class="cmtt-8"> </span><span
11434 class="cmtt-8"> </span><span
11435 class="cmtt-8"> </span><span
11436 class="cmtt-8"> </span><span
11437 class="cmtt-8"> </span><span
11438 class="cmtt-8"> }</span>
11439 <br class="fancyvrb" /><a
11440 id="x1-111028r14"></a><span
11441 class="cmr-6">14</span><span
11442 class="cmtt-8"> </span><span
11443 class="cmtt-8"> </span>
11444 <br class="fancyvrb" /><a
11445 id="x1-111030r15"></a><span
11446 class="cmr-6">15</span><span
11447 class="cmtt-8"> </span><span
11448 class="cmtt-8"> </span><span
11449 class="cmtt-8"> </span><span
11450 class="cmtt-8"> 6)</span><span
11451 class="cmtt-8"> done</span>
11452 <br class="fancyvrb" /><a
11453 id="x1-111032r16"></a><span
11454 class="cmr-6">16</span><span
11455 class="cmtt-8"> </span><span
11456 class="cmtt-8"> </span>
11461 <!--l. 384--><p class="noindent" >
11462 <h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a
11463 id="x1-1120008.6.4"></a>format 1 specifics</h5>
11464 <!--l. 386--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
11465 section. The following pseudocode presents the same algorithm. Assume:
11466 <ul class="itemize1">
11467 <li class="itemize"><span
11468 class="cmtt-12">[n] </span>is the value in <span
11469 class="cmtt-12">[residue_partition_size]</span>
11471 <li class="itemize"><span
11472 class="cmtt-12">[v] </span>is the residue vector
11474 <li class="itemize"><span
11475 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
11476 <!--l. 398--><p class="noindent" >
11477 <div class="fancyvrb" id="fancyvrb42">
11479 id="x1-112002r1"></a><span
11480 class="cmr-6">1</span><span
11481 class="cmtt-8"> </span><span
11482 class="cmtt-8"> </span><span
11483 class="cmtt-8"> 1)</span><span
11484 class="cmtt-8"> [i]</span><span
11485 class="cmtt-8"> =</span><span
11486 class="cmtt-8"> 0</span>
11487 <br class="fancyvrb" /><a
11488 id="x1-112004r2"></a><span
11489 class="cmr-6">2</span><span
11490 class="cmtt-8"> </span><span
11491 class="cmtt-8"> </span><span
11492 class="cmtt-8"> 2)</span><span
11493 class="cmtt-8"> vector</span><span
11494 class="cmtt-8"> [entry\_temp]</span><span
11495 class="cmtt-8"> =</span><span
11496 class="cmtt-8"> read</span><span
11497 class="cmtt-8"> vector</span><span
11498 class="cmtt-8"> from</span><span
11499 class="cmtt-8"> packet</span><span
11500 class="cmtt-8"> using</span><span
11501 class="cmtt-8"> current</span><span
11502 class="cmtt-8"> codebook</span><span
11503 class="cmtt-8"> in</span><span
11504 class="cmtt-8"> VQ</span><span
11505 class="cmtt-8"> context</span>
11506 <br class="fancyvrb" /><a
11507 id="x1-112006r3"></a><span
11508 class="cmr-6">3</span><span
11509 class="cmtt-8"> </span><span
11510 class="cmtt-8"> </span><span
11511 class="cmtt-8"> 3)</span><span
11512 class="cmtt-8"> iterate</span><span
11513 class="cmtt-8"> [j]</span><span
11514 class="cmtt-8"> over</span><span
11515 class="cmtt-8"> the</span><span
11516 class="cmtt-8"> range</span><span
11517 class="cmtt-8"> 0</span><span
11518 class="cmtt-8"> ...</span><span
11519 class="cmtt-8"> [codebook\_dimensions]-1</span><span
11520 class="cmtt-8"> {</span>
11521 <br class="fancyvrb" /><a
11522 id="x1-112008r4"></a><span
11523 class="cmr-6">4</span><span
11524 class="cmtt-8"> </span><span
11525 class="cmtt-8"> </span>
11526 <br class="fancyvrb" /><a
11527 id="x1-112010r5"></a><span
11528 class="cmr-6">5</span><span
11529 class="cmtt-8"> </span><span
11530 class="cmtt-8"> </span><span
11531 class="cmtt-8"> </span><span
11532 class="cmtt-8"> </span><span
11533 class="cmtt-8"> </span><span
11534 class="cmtt-8"> </span><span
11535 class="cmtt-8"> </span><span
11536 class="cmtt-8"> 4)</span><span
11537 class="cmtt-8"> vector</span><span
11538 class="cmtt-8"> [v]</span><span
11539 class="cmtt-8"> element</span><span
11540 class="cmtt-8"> ([offset]+[i])</span><span
11541 class="cmtt-8"> =</span>
11542 <br class="fancyvrb" /><a
11543 id="x1-112012r6"></a><span
11544 class="cmr-6">6</span><span
11545 class="cmtt-8"> </span><span
11546 class="cmtt-8">  </span><span
11547 class="cmtt-8"> </span><span
11548 class="cmtt-8"> vector</span><span
11549 class="cmtt-8"> [v]</span><span
11550 class="cmtt-8"> element</span><span
11551 class="cmtt-8"> ([offset]+[i])</span><span
11552 class="cmtt-8"> +</span>
11553 <br class="fancyvrb" /><a
11554 id="x1-112014r7"></a><span
11555 class="cmr-6">7</span><span
11556 class="cmtt-8"> </span><span
11557 class="cmtt-8"> </span><span
11558 class="cmtt-8"> </span><span
11559 class="cmtt-8"> </span><span
11560 class="cmtt-8"> </span><span
11561 class="cmtt-8"> </span><span
11562 class="cmtt-8"> </span><span
11563 class="cmtt-8"> </span><span
11564 class="cmtt-8"> </span><span
11565 class="cmtt-8"> </span><span
11566 class="cmtt-8"> </span><span
11567 class="cmtt-8"> vector</span><span
11568 class="cmtt-8"> [entry\_temp]</span><span
11569 class="cmtt-8"> element</span><span
11570 class="cmtt-8"> [j]</span>
11571 <br class="fancyvrb" /><a
11572 id="x1-112016r8"></a><span
11573 class="cmr-6">8</span><span
11574 class="cmtt-8"> </span><span
11575 class="cmtt-8"> </span><span
11576 class="cmtt-8"> </span><span
11577 class="cmtt-8"> </span><span
11578 class="cmtt-8"> </span><span
11579 class="cmtt-8"> </span><span
11580 class="cmtt-8"> </span><span
11581 class="cmtt-8"> 5)</span><span
11582 class="cmtt-8"> increment</span><span
11583 class="cmtt-8"> [i]</span>
11584 <br class="fancyvrb" /><a
11585 id="x1-112018r9"></a><span
11586 class="cmr-6">9</span><span
11587 class="cmtt-8"> </span><span
11588 class="cmtt-8"> </span>
11589 <br class="fancyvrb" /><a
11590 id="x1-112020r10"></a><span
11591 class="cmr-6">10</span><span
11592 class="cmtt-8"> </span><span
11593 class="cmtt-8"> </span><span
11594 class="cmtt-8"> </span><span
11595 class="cmtt-8"> </span><span
11596 class="cmtt-8"> </span><span
11597 class="cmtt-8"> }</span>
11598 <br class="fancyvrb" /><a
11599 id="x1-112022r11"></a><span
11600 class="cmr-6">11</span><span
11601 class="cmtt-8"> </span><span
11602 class="cmtt-8"> </span>
11603 <br class="fancyvrb" /><a
11604 id="x1-112024r12"></a><span
11605 class="cmr-6">12</span><span
11606 class="cmtt-8"> </span><span
11607 class="cmtt-8"> </span><span
11608 class="cmtt-8"> </span><span
11609 class="cmtt-8"> 6)</span><span
11610 class="cmtt-8"> if</span><span
11611 class="cmtt-8"> (</span><span
11612 class="cmtt-8"> [i]</span><span
11613 class="cmtt-8"> is</span><span
11614 class="cmtt-8"> less</span><span
11615 class="cmtt-8"> than</span><span
11616 class="cmtt-8"> [n]</span><span
11617 class="cmtt-8"> )</span><span
11618 class="cmtt-8"> continue</span><span
11619 class="cmtt-8"> at</span><span
11620 class="cmtt-8"> step</span><span
11621 class="cmtt-8"> 2</span>
11622 <br class="fancyvrb" /><a
11623 id="x1-112026r13"></a><span
11624 class="cmr-6">13</span><span
11625 class="cmtt-8"> </span><span
11626 class="cmtt-8"> </span><span
11627 class="cmtt-8"> </span><span
11628 class="cmtt-8"> 7)</span><span
11629 class="cmtt-8"> done</span>
11631 <!--l. 416--><p class="noindent" >
11632 <h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a
11633 id="x1-1130008.6.5"></a>format 2 specifics</h5>
11634 <!--l. 418--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
11635 additional post-decode step after a normal format 1 decode.
11639 <!--l. 421--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
11640 ’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
11641 the vectors are decoded. We then request normal format 1 to decode a single vector
11642 representing all output channels, rather than a vector for each channel. After decode,
11643 deinterleave the vector into independent vectors, one for each output channel. That
11645 <!--l. 429--><p class="noindent" >
11646 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
11648 class="enumerate-enumitem">If all vectors 0 through <span
11649 class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
11651 class="cmtt-12">[v]</span>of length <span
11652 class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
11654 </dd><dt class="enumerate-enumitem">
11656 class="enumerate-enumitem">Rather than performing format 1 decode to produce <span
11657 class="cmti-12">ch </span>vectors of length <span
11658 class="cmti-12">n </span>each, call
11659 format 1 decode to produce a single vector <span
11660 class="cmtt-12">[v] </span>of length <span
11661 class="cmti-12">ch*n</span>.
11662 </dd><dt class="enumerate-enumitem">
11664 class="enumerate-enumitem">Post decode: Deinterleave the single vector <span
11665 class="cmtt-12">[v] </span>returned by format 1 decode as
11666 described above into <span
11667 class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
11669 <div class="fancyvrb" id="fancyvrb43">
11671 id="x1-113005r1"></a><span
11672 class="cmr-6">1</span><span
11673 class="cmtt-8"> </span><span
11674 class="cmtt-8"> </span><span
11675 class="cmtt-8"> </span><span
11676 class="cmtt-8"> 1)</span><span
11677 class="cmtt-8"> iterate</span><span
11678 class="cmtt-8"> [i]</span><span
11679 class="cmtt-8"> over</span><span
11680 class="cmtt-8"> the</span><span
11681 class="cmtt-8"> range</span><span
11682 class="cmtt-8"> 0</span><span
11683 class="cmtt-8"> ...</span><span
11684 class="cmtt-8"> [n]-1</span><span
11685 class="cmtt-8"> {</span>
11686 <br class="fancyvrb" /><a
11687 id="x1-113007r2"></a><span
11688 class="cmr-6">2</span><span
11689 class="cmtt-8"> </span><span
11690 class="cmtt-8"> </span>
11691 <br class="fancyvrb" /><a
11692 id="x1-113009r3"></a><span
11693 class="cmr-6">3</span><span
11694 class="cmtt-8"> </span><span
11695 class="cmtt-8"> </span><span
11696 class="cmtt-8"> </span><span
11697 class="cmtt-8"> </span><span
11698 class="cmtt-8"> </span><span
11699 class="cmtt-8"> </span><span
11700 class="cmtt-8"> </span><span
11701 class="cmtt-8"> </span><span
11702 class="cmtt-8"> 2)</span><span
11703 class="cmtt-8"> iterate</span><span
11704 class="cmtt-8"> [j]</span><span
11705 class="cmtt-8"> over</span><span
11706 class="cmtt-8"> the</span><span
11707 class="cmtt-8"> range</span><span
11708 class="cmtt-8"> 0</span><span
11709 class="cmtt-8"> ...</span><span
11710 class="cmtt-8"> [ch]-1</span><span
11711 class="cmtt-8"> {</span>
11712 <br class="fancyvrb" /><a
11713 id="x1-113011r4"></a><span
11714 class="cmr-6">4</span><span
11715 class="cmtt-8"> </span><span
11716 class="cmtt-8"> </span>
11717 <br class="fancyvrb" /><a
11718 id="x1-113013r5"></a><span
11719 class="cmr-6">5</span><span
11720 class="cmtt-8"> </span><span
11721 class="cmtt-8"> </span><span
11722 class="cmtt-8"> </span><span
11723 class="cmtt-8"> </span><span
11724 class="cmtt-8"> </span><span
11725 class="cmtt-8"> </span><span
11726 class="cmtt-8"> </span><span
11727 class="cmtt-8"> </span><span
11728 class="cmtt-8"> </span><span
11729 class="cmtt-8"> </span><span
11730 class="cmtt-8"> </span><span
11731 class="cmtt-8"> </span><span
11732 class="cmtt-8"> </span><span
11733 class="cmtt-8"> 3)</span><span
11734 class="cmtt-8"> output</span><span
11735 class="cmtt-8"> vector</span><span
11736 class="cmtt-8"> number</span><span
11737 class="cmtt-8"> [j]</span><span
11738 class="cmtt-8"> element</span><span
11739 class="cmtt-8"> [i]</span><span
11740 class="cmtt-8"> =</span><span
11741 class="cmtt-8"> vector</span><span
11742 class="cmtt-8"> [v]</span><span
11743 class="cmtt-8"> element</span><span
11744 class="cmtt-8"> ([i]</span><span
11745 class="cmtt-8"> *</span><span
11746 class="cmtt-8"> [ch]</span><span
11747 class="cmtt-8"> +</span><span
11748 class="cmtt-8"> [j])</span>
11749 <br class="fancyvrb" /><a
11750 id="x1-113015r6"></a><span
11751 class="cmr-6">6</span><span
11752 class="cmtt-8"> </span><span
11753 class="cmtt-8"> </span>
11754 <br class="fancyvrb" /><a
11755 id="x1-113017r7"></a><span
11756 class="cmr-6">7</span><span
11757 class="cmtt-8"> </span><span
11758 class="cmtt-8"> </span><span
11759 class="cmtt-8"> </span><span
11760 class="cmtt-8"> </span><span
11761 class="cmtt-8"> </span><span
11762 class="cmtt-8"> </span><span
11763 class="cmtt-8"> </span><span
11764 class="cmtt-8"> </span><span
11765 class="cmtt-8"> </span><span
11766 class="cmtt-8"> </span><span
11767 class="cmtt-8"> </span><span
11768 class="cmtt-8"> }</span>
11769 <br class="fancyvrb" /><a
11770 id="x1-113019r8"></a><span
11771 class="cmr-6">8</span><span
11772 class="cmtt-8"> </span><span
11773 class="cmtt-8"> </span><span
11774 class="cmtt-8"> </span><span
11775 class="cmtt-8"> </span><span
11776 class="cmtt-8"> </span><span
11777 class="cmtt-8"> </span><span
11778 class="cmtt-8"> }</span>
11779 <br class="fancyvrb" /><a
11780 id="x1-113021r9"></a><span
11781 class="cmr-6">9</span><span
11782 class="cmtt-8"> </span><span
11783 class="cmtt-8"> </span>
11784 <br class="fancyvrb" /><a
11785 id="x1-113023r10"></a><span
11786 class="cmr-6">10</span><span
11787 class="cmtt-8"> </span><span
11788 class="cmtt-8"> </span><span
11789 class="cmtt-8"> </span><span
11790 class="cmtt-8"> 4)</span><span
11791 class="cmtt-8"> done</span>
11800 <h3 class="sectionHead"><span class="titlemark">9. </span> <a
11801 id="x1-1140009"></a>Helper equations</h3>
11802 <!--l. 6--><p class="noindent" >
11803 <h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a
11804 id="x1-1150009.1"></a>Overview</h4>
11805 <!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
11806 cluttering up the main specification documents, they are defined here and referenced where
11808 <!--l. 13--><p class="noindent" >
11809 <h4 class="subsectionHead"><span class="titlemark">9.2. </span> <a
11810 id="x1-1160009.2"></a>Functions</h4>
11811 <!--l. 15--><p class="noindent" >
11812 <h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a
11813 id="x1-1170009.2.1"></a>ilog</h5>
11814 <!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
11815 two’s complement integer value <span
11816 class="cmtt-12">[x]</span>. Values of <span
11817 class="cmtt-12">[x] </span>less than zero are defined to return
11819 <!--l. 20--><p class="noindent" >
11820 <div class="fancyvrb" id="fancyvrb44">
11822 id="x1-117002r1"></a><span
11823 class="cmr-6">1</span><span
11824 class="cmtt-8"> </span><span
11825 class="cmtt-8"> </span><span
11826 class="cmtt-8"> </span><span
11827 class="cmtt-8"> 1)</span><span
11828 class="cmtt-8"> [return\_value]</span><span
11829 class="cmtt-8"> =</span><span
11830 class="cmtt-8"> 0;</span>
11831 <br class="fancyvrb" /><a
11832 id="x1-117004r2"></a><span
11833 class="cmr-6">2</span><span
11834 class="cmtt-8"> </span><span
11835 class="cmtt-8"> </span><span
11836 class="cmtt-8"> </span><span
11837 class="cmtt-8"> 2)</span><span
11838 class="cmtt-8"> if</span><span
11839 class="cmtt-8"> (</span><span
11840 class="cmtt-8"> [x]</span><span
11841 class="cmtt-8"> is</span><span
11842 class="cmtt-8"> greater</span><span
11843 class="cmtt-8"> than</span><span
11844 class="cmtt-8"> zero</span><span
11845 class="cmtt-8"> )</span><span
11846 class="cmtt-8"> {</span>
11847 <br class="fancyvrb" /><a
11848 id="x1-117006r3"></a><span
11849 class="cmr-6">3</span><span
11850 class="cmtt-8"> </span><span
11851 class="cmtt-8"> </span>
11852 <br class="fancyvrb" /><a
11853 id="x1-117008r4"></a><span
11854 class="cmr-6">4</span><span
11855 class="cmtt-8"> </span><span
11856 class="cmtt-8"> </span><span
11857 class="cmtt-8"> </span><span
11858 class="cmtt-8"> </span><span
11859 class="cmtt-8"> </span><span
11860 class="cmtt-8"> </span><span
11861 class="cmtt-8"> </span><span
11862 class="cmtt-8"> </span><span
11863 class="cmtt-8"> 3)</span><span
11864 class="cmtt-8"> increment</span><span
11865 class="cmtt-8"> [return\_value];</span>
11866 <br class="fancyvrb" /><a
11867 id="x1-117010r5"></a><span
11868 class="cmr-6">5</span><span
11869 class="cmtt-8"> </span><span
11870 class="cmtt-8"> </span><span
11871 class="cmtt-8"> </span><span
11872 class="cmtt-8"> </span><span
11873 class="cmtt-8"> </span><span
11874 class="cmtt-8"> </span><span
11875 class="cmtt-8"> </span><span
11876 class="cmtt-8"> </span><span
11877 class="cmtt-8"> 4)</span><span
11878 class="cmtt-8"> logical</span><span
11879 class="cmtt-8"> shift</span><span
11880 class="cmtt-8"> [x]</span><span
11881 class="cmtt-8"> one</span><span
11882 class="cmtt-8"> bit</span><span
11883 class="cmtt-8"> to</span><span
11884 class="cmtt-8"> the</span><span
11885 class="cmtt-8"> right,</span><span
11886 class="cmtt-8"> padding</span><span
11887 class="cmtt-8"> the</span><span
11888 class="cmtt-8"> MSb</span><span
11889 class="cmtt-8"> with</span><span
11890 class="cmtt-8"> zero</span>
11891 <br class="fancyvrb" /><a
11892 id="x1-117012r6"></a><span
11893 class="cmr-6">6</span><span
11894 class="cmtt-8"> </span><span
11895 class="cmtt-8"> </span><span
11896 class="cmtt-8"> </span><span
11897 class="cmtt-8"> </span><span
11898 class="cmtt-8"> </span><span
11899 class="cmtt-8"> </span><span
11900 class="cmtt-8"> </span><span
11901 class="cmtt-8"> </span><span
11902 class="cmtt-8"> 5)</span><span
11903 class="cmtt-8"> repeat</span><span
11904 class="cmtt-8"> at</span><span
11905 class="cmtt-8"> step</span><span
11906 class="cmtt-8"> 2)</span>
11907 <br class="fancyvrb" /><a
11908 id="x1-117014r7"></a><span
11909 class="cmr-6">7</span><span
11910 class="cmtt-8"> </span><span
11911 class="cmtt-8"> </span>
11912 <br class="fancyvrb" /><a
11913 id="x1-117016r8"></a><span
11914 class="cmr-6">8</span><span
11915 class="cmtt-8"> </span><span
11916 class="cmtt-8"> </span><span
11917 class="cmtt-8"> </span><span
11918 class="cmtt-8"> </span><span
11919 class="cmtt-8"> </span><span
11920 class="cmtt-8"> </span><span
11921 class="cmtt-8"> }</span>
11922 <br class="fancyvrb" /><a
11923 id="x1-117018r9"></a><span
11924 class="cmr-6">9</span><span
11925 class="cmtt-8"> </span><span
11926 class="cmtt-8"> </span>
11927 <br class="fancyvrb" /><a
11928 id="x1-117020r10"></a><span
11929 class="cmr-6">10</span><span
11930 class="cmtt-8"> </span><span
11931 class="cmtt-8"> </span><span
11932 class="cmtt-8"> </span><span
11933 class="cmtt-8"> </span><span
11934 class="cmtt-8"> 6)</span><span
11935 class="cmtt-8"> done</span>
11940 <!--l. 33--><p class="noindent" >Examples:
11941 <ul class="itemize1">
11942 <li class="itemize">ilog(0) = 0;
11944 <li class="itemize">ilog(1) = 1;
11946 <li class="itemize">ilog(2) = 2;
11948 <li class="itemize">ilog(3) = 2;
11950 <li class="itemize">ilog(4) = 3;
11952 <li class="itemize">ilog(7) = 3;
11954 <li class="itemize">ilog(negative number) = 0;</li></ul>
11955 <!--l. 48--><p class="noindent" >
11956 <h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a
11957 id="x1-1180009.2.2"></a>float32_unpack</h5>
11958 <!--l. 50--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis
11959 codebook float value into the representation used by the decoder for floating point numbers. For
11960 purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
11962 <!--l. 56--><p class="noindent" >
11963 <div class="fancyvrb" id="fancyvrb45">
11965 id="x1-118002r1"></a><span
11966 class="cmr-6">1</span><span
11967 class="cmtt-8"> </span><span
11968 class="cmtt-8"> </span><span
11969 class="cmtt-8"> </span><span
11970 class="cmtt-8"> 1)</span><span
11971 class="cmtt-8"> [mantissa]</span><span
11972 class="cmtt-8"> =</span><span
11973 class="cmtt-8"> [x]</span><span
11974 class="cmtt-8"> bitwise</span><span
11975 class="cmtt-8"> AND</span><span
11976 class="cmtt-8"> 0x1fffff</span><span
11977 class="cmtt-8"> (unsigned</span><span
11978 class="cmtt-8"> result)</span>
11979 <br class="fancyvrb" /><a
11980 id="x1-118004r2"></a><span
11981 class="cmr-6">2</span><span
11982 class="cmtt-8"> </span><span
11983 class="cmtt-8"> </span><span
11984 class="cmtt-8"> </span><span
11985 class="cmtt-8"> 2)</span><span
11986 class="cmtt-8"> [sign]</span><span
11987 class="cmtt-8"> =</span><span
11988 class="cmtt-8"> [x]</span><span
11989 class="cmtt-8"> bitwise</span><span
11990 class="cmtt-8"> AND</span><span
11991 class="cmtt-8"> 0x80000000</span><span
11992 class="cmtt-8"> (unsigned</span><span
11993 class="cmtt-8"> result)</span>
11994 <br class="fancyvrb" /><a
11995 id="x1-118006r3"></a><span
11996 class="cmr-6">3</span><span
11997 class="cmtt-8"> </span><span
11998 class="cmtt-8"> </span><span
11999 class="cmtt-8"> </span><span
12000 class="cmtt-8"> 3)</span><span
12001 class="cmtt-8"> [exponent]</span><span
12002 class="cmtt-8"> =</span><span
12003 class="cmtt-8"> (</span><span
12004 class="cmtt-8"> [x]</span><span
12005 class="cmtt-8"> bitwise</span><span
12006 class="cmtt-8"> AND</span><span
12007 class="cmtt-8"> 0x7fe00000)</span><span
12008 class="cmtt-8"> shifted</span><span
12009 class="cmtt-8"> right</span><span
12010 class="cmtt-8"> 21</span><span
12011 class="cmtt-8"> bits</span><span
12012 class="cmtt-8"> (unsigned</span><span
12013 class="cmtt-8"> result)</span>
12014 <br class="fancyvrb" /><a
12015 id="x1-118008r4"></a><span
12016 class="cmr-6">4</span><span
12017 class="cmtt-8"> </span><span
12018 class="cmtt-8"> </span><span
12019 class="cmtt-8"> </span><span
12020 class="cmtt-8"> 4)</span><span
12021 class="cmtt-8"> if</span><span
12022 class="cmtt-8"> (</span><span
12023 class="cmtt-8"> [sign]</span><span
12024 class="cmtt-8"> is</span><span
12025 class="cmtt-8"> nonzero</span><span
12026 class="cmtt-8"> )</span><span
12027 class="cmtt-8"> then</span><span
12028 class="cmtt-8"> negate</span><span
12029 class="cmtt-8"> [mantissa]</span>
12030 <br class="fancyvrb" /><a
12031 id="x1-118010r5"></a><span
12032 class="cmr-6">5</span><span
12033 class="cmtt-8"> </span><span
12034 class="cmtt-8"> </span><span
12035 class="cmtt-8"> </span><span
12036 class="cmtt-8"> 5)</span><span
12037 class="cmtt-8"> return</span><span
12038 class="cmtt-8"> [mantissa]</span><span
12039 class="cmtt-8"> *</span><span
12040 class="cmtt-8"> (</span><span
12041 class="cmtt-8"> 2</span><span
12042 class="cmtt-8"> ^</span><span
12043 class="cmtt-8"> (</span><span
12044 class="cmtt-8"> [exponent]</span><span
12045 class="cmtt-8"> -</span><span
12046 class="cmtt-8"> 788</span><span
12047 class="cmtt-8"> )</span><span
12048 class="cmtt-8"> )</span>
12053 <!--l. 66--><p class="noindent" >
12054 <h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a
12055 id="x1-1190009.2.3"></a>lookup1_values</h5>
12056 <!--l. 68--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the
12057 correct length of the value index for a codebook VQ lookup table of lookup type 1.
12058 The values on this list are permuted to construct the VQ vector lookup table of size
12060 class="cmtt-12">[codebook_entries]</span>.
12061 <!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
12063 class="cmtt-12">[return_value] </span>to the power of <span
12064 class="cmtt-12">[codebook_dimensions] </span>is less than or equal to
12066 class="cmtt-12">[codebook_entries]</span>’.
12067 <!--l. 81--><p class="noindent" >
12068 <h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a
12069 id="x1-1200009.2.4"></a>low_neighbor</h5>
12070 <!--l. 83--><p class="noindent" >”low_neighbor(v,x)” finds the position <span
12071 class="cmtt-12">n </span>in vector <span
12072 class="cmtt-12">[v] </span>of the greatest value scalar element for
12074 class="cmtt-12">n </span>is less than <span
12075 class="cmtt-12">[x] </span>and vector <span
12076 class="cmtt-12">[v] </span>element <span
12077 class="cmtt-12">n </span>is less than vector <span
12078 class="cmtt-12">[v] </span>element
12080 class="cmtt-12">[x]</span>.
12081 <!--l. 88--><p class="noindent" >
12082 <h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a
12083 id="x1-1210009.2.5"></a>high_neighbor</h5>
12084 <!--l. 90--><p class="noindent" >”high_neighbor(v,x)” finds the position <span
12085 class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
12087 class="cmtt-12">n </span>is less than <span
12088 class="cmtt-12">[x] </span>and vector <span
12089 class="cmtt-12">[v] </span>element <span
12090 class="cmtt-12">n </span>is greater than vector <span
12091 class="cmtt-12">[v] </span>element
12093 class="cmtt-12">[x]</span>.
12094 <!--l. 97--><p class="noindent" >
12095 <h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a
12096 id="x1-1220009.2.6"></a>render_point</h5>
12097 <!--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
12098 x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
12099 calculating intervening values along the line.
12103 <!--l. 104--><p class="noindent" >
12104 <div class="fancyvrb" id="fancyvrb46">
12106 id="x1-122002r1"></a><span
12107 class="cmr-6">1</span><span
12108 class="cmtt-8"> </span><span
12109 class="cmtt-8"> </span><span
12110 class="cmtt-8"> </span><span
12111 class="cmtt-8"> 1)</span><span
12112 class="cmtt-8"> </span><span
12113 class="cmtt-8"> [dy]</span><span
12114 class="cmtt-8"> =</span><span
12115 class="cmtt-8"> [y1]</span><span
12116 class="cmtt-8"> -</span><span
12117 class="cmtt-8"> [y0]</span>
12118 <br class="fancyvrb" /><a
12119 id="x1-122004r2"></a><span
12120 class="cmr-6">2</span><span
12121 class="cmtt-8"> </span><span
12122 class="cmtt-8"> </span><span
12123 class="cmtt-8"> </span><span
12124 class="cmtt-8"> 2)</span><span
12125 class="cmtt-8"> [adx]</span><span
12126 class="cmtt-8"> =</span><span
12127 class="cmtt-8"> [x1]</span><span
12128 class="cmtt-8"> -</span><span
12129 class="cmtt-8"> [x0]</span>
12130 <br class="fancyvrb" /><a
12131 id="x1-122006r3"></a><span
12132 class="cmr-6">3</span><span
12133 class="cmtt-8"> </span><span
12134 class="cmtt-8"> </span><span
12135 class="cmtt-8"> </span><span
12136 class="cmtt-8"> 3)</span><span
12137 class="cmtt-8"> [ady]</span><span
12138 class="cmtt-8"> =</span><span
12139 class="cmtt-8"> absolute</span><span
12140 class="cmtt-8"> value</span><span
12141 class="cmtt-8"> of</span><span
12142 class="cmtt-8"> [dy]</span>
12143 <br class="fancyvrb" /><a
12144 id="x1-122008r4"></a><span
12145 class="cmr-6">4</span><span
12146 class="cmtt-8"> </span><span
12147 class="cmtt-8"> </span><span
12148 class="cmtt-8"> </span><span
12149 class="cmtt-8"> 4)</span><span
12150 class="cmtt-8"> [err]</span><span
12151 class="cmtt-8"> =</span><span
12152 class="cmtt-8"> [ady]</span><span
12153 class="cmtt-8"> *</span><span
12154 class="cmtt-8"> ([X]</span><span
12155 class="cmtt-8"> -</span><span
12156 class="cmtt-8"> [x0])</span>
12157 <br class="fancyvrb" /><a
12158 id="x1-122010r5"></a><span
12159 class="cmr-6">5</span><span
12160 class="cmtt-8"> </span><span
12161 class="cmtt-8"> </span><span
12162 class="cmtt-8"> </span><span
12163 class="cmtt-8"> 5)</span><span
12164 class="cmtt-8"> [off]</span><span
12165 class="cmtt-8"> =</span><span
12166 class="cmtt-8"> [err]</span><span
12167 class="cmtt-8"> /</span><span
12168 class="cmtt-8"> [adx]</span><span
12169 class="cmtt-8"> using</span><span
12170 class="cmtt-8"> integer</span><span
12171 class="cmtt-8"> division</span>
12172 <br class="fancyvrb" /><a
12173 id="x1-122012r6"></a><span
12174 class="cmr-6">6</span><span
12175 class="cmtt-8"> </span><span
12176 class="cmtt-8"> </span><span
12177 class="cmtt-8"> </span><span
12178 class="cmtt-8"> 6)</span><span
12179 class="cmtt-8"> if</span><span
12180 class="cmtt-8"> (</span><span
12181 class="cmtt-8"> [dy]</span><span
12182 class="cmtt-8"> is</span><span
12183 class="cmtt-8"> less</span><span
12184 class="cmtt-8"> than</span><span
12185 class="cmtt-8"> zero</span><span
12186 class="cmtt-8"> )</span><span
12187 class="cmtt-8"> {</span>
12188 <br class="fancyvrb" /><a
12189 id="x1-122014r7"></a><span
12190 class="cmr-6">7</span><span
12191 class="cmtt-8"> </span><span
12192 class="cmtt-8"> </span>
12193 <br class="fancyvrb" /><a
12194 id="x1-122016r8"></a><span
12195 class="cmr-6">8</span><span
12196 class="cmtt-8"> </span><span
12197 class="cmtt-8"> </span><span
12198 class="cmtt-8"> </span><span
12199 class="cmtt-8"> </span><span
12200 class="cmtt-8"> </span><span
12201 class="cmtt-8"> </span><span
12202 class="cmtt-8"> </span><span
12203 class="cmtt-8"> </span><span
12204 class="cmtt-8"> 7)</span><span
12205 class="cmtt-8"> [Y]</span><span
12206 class="cmtt-8"> =</span><span
12207 class="cmtt-8"> [y0]</span><span
12208 class="cmtt-8"> -</span><span
12209 class="cmtt-8"> [off]</span>
12210 <br class="fancyvrb" /><a
12211 id="x1-122018r9"></a><span
12212 class="cmr-6">9</span><span
12213 class="cmtt-8"> </span><span
12214 class="cmtt-8"> </span>
12215 <br class="fancyvrb" /><a
12216 id="x1-122020r10"></a><span
12217 class="cmr-6">10</span><span
12218 class="cmtt-8"> </span><span
12219 class="cmtt-8"> </span><span
12220 class="cmtt-8"> </span><span
12221 class="cmtt-8"> </span><span
12222 class="cmtt-8"> </span><span
12223 class="cmtt-8"> </span><span
12224 class="cmtt-8"> }</span><span
12225 class="cmtt-8"> else</span><span
12226 class="cmtt-8"> {</span>
12227 <br class="fancyvrb" /><a
12228 id="x1-122022r11"></a><span
12229 class="cmr-6">11</span><span
12230 class="cmtt-8"> </span><span
12231 class="cmtt-8"> </span>
12232 <br class="fancyvrb" /><a
12233 id="x1-122024r12"></a><span
12234 class="cmr-6">12</span><span
12235 class="cmtt-8"> </span><span
12236 class="cmtt-8"> </span><span
12237 class="cmtt-8"> </span><span
12238 class="cmtt-8"> </span><span
12239 class="cmtt-8"> </span><span
12240 class="cmtt-8"> </span><span
12241 class="cmtt-8"> </span><span
12242 class="cmtt-8"> </span><span
12243 class="cmtt-8"> 8)</span><span
12244 class="cmtt-8"> [Y]</span><span
12245 class="cmtt-8"> =</span><span
12246 class="cmtt-8"> [y0]</span><span
12247 class="cmtt-8"> +</span><span
12248 class="cmtt-8"> [off]</span>
12249 <br class="fancyvrb" /><a
12250 id="x1-122026r13"></a><span
12251 class="cmr-6">13</span><span
12252 class="cmtt-8"> </span><span
12253 class="cmtt-8"> </span>
12254 <br class="fancyvrb" /><a
12255 id="x1-122028r14"></a><span
12256 class="cmr-6">14</span><span
12257 class="cmtt-8"> </span><span
12258 class="cmtt-8"> </span><span
12259 class="cmtt-8"> </span><span
12260 class="cmtt-8"> </span><span
12261 class="cmtt-8"> </span><span
12262 class="cmtt-8"> </span><span
12263 class="cmtt-8"> }</span>
12264 <br class="fancyvrb" /><a
12265 id="x1-122030r15"></a><span
12266 class="cmr-6">15</span><span
12267 class="cmtt-8"> </span><span
12268 class="cmtt-8"> </span>
12269 <br class="fancyvrb" /><a
12270 id="x1-122032r16"></a><span
12271 class="cmr-6">16</span><span
12272 class="cmtt-8"> </span><span
12273 class="cmtt-8"> </span><span
12274 class="cmtt-8"> </span><span
12275 class="cmtt-8"> 9)</span><span
12276 class="cmtt-8"> done</span>
12278 <!--l. 125--><p class="noindent" >
12279 <h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a
12280 id="x1-1230009.2.7"></a>render_line</h5>
12281 <!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)”
12282 to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
12283 been relevant elsewhere, but here we must define integer division as rounding division of both
12284 positive and negative numbers toward zero.
12285 <!--l. 134--><p class="noindent" >
12286 <div class="fancyvrb" id="fancyvrb47">
12288 id="x1-123002r1"></a><span
12289 class="cmr-6">1</span><span
12290 class="cmtt-8"> </span><span
12291 class="cmtt-8"> </span><span
12292 class="cmtt-8"> </span><span
12293 class="cmtt-8"> 1)</span><span
12294 class="cmtt-8"> </span><span
12295 class="cmtt-8"> </span><span
12296 class="cmtt-8"> [dy]</span><span
12297 class="cmtt-8"> =</span><span
12298 class="cmtt-8"> [y1]</span><span
12299 class="cmtt-8"> -</span><span
12300 class="cmtt-8"> [y0]</span>
12301 <br class="fancyvrb" /><a
12302 id="x1-123004r2"></a><span
12303 class="cmr-6">2</span><span
12304 class="cmtt-8"> </span><span
12305 class="cmtt-8"> </span><span
12306 class="cmtt-8"> </span><span
12307 class="cmtt-8"> 2)</span><span
12308 class="cmtt-8"> </span><span
12309 class="cmtt-8"> [adx]</span><span
12310 class="cmtt-8"> =</span><span
12311 class="cmtt-8"> [x1]</span><span
12312 class="cmtt-8"> -</span><span
12313 class="cmtt-8"> [x0]</span>
12314 <br class="fancyvrb" /><a
12315 id="x1-123006r3"></a><span
12316 class="cmr-6">3</span><span
12317 class="cmtt-8"> </span><span
12318 class="cmtt-8"> </span><span
12319 class="cmtt-8"> </span><span
12320 class="cmtt-8"> 3)</span><span
12321 class="cmtt-8"> </span><span
12322 class="cmtt-8"> [ady]</span><span
12323 class="cmtt-8"> =</span><span
12324 class="cmtt-8"> absolute</span><span
12325 class="cmtt-8"> value</span><span
12326 class="cmtt-8"> of</span><span
12327 class="cmtt-8"> [dy]</span>
12328 <br class="fancyvrb" /><a
12329 id="x1-123008r4"></a><span
12330 class="cmr-6">4</span><span
12331 class="cmtt-8"> </span><span
12332 class="cmtt-8"> </span><span
12333 class="cmtt-8"> </span><span
12334 class="cmtt-8"> 4)</span><span
12335 class="cmtt-8"> [base]</span><span
12336 class="cmtt-8"> =</span><span
12337 class="cmtt-8"> [dy]</span><span
12338 class="cmtt-8"> /</span><span
12339 class="cmtt-8"> [adx]</span><span
12340 class="cmtt-8"> using</span><span
12341 class="cmtt-8"> integer</span><span
12342 class="cmtt-8"> division</span>
12343 <br class="fancyvrb" /><a
12344 id="x1-123010r5"></a><span
12345 class="cmr-6">5</span><span
12346 class="cmtt-8"> </span><span
12347 class="cmtt-8"> </span><span
12348 class="cmtt-8"> </span><span
12349 class="cmtt-8"> 5)</span><span
12350 class="cmtt-8"> </span><span
12351 class="cmtt-8"> </span><span
12352 class="cmtt-8"> </span><span
12353 class="cmtt-8"> [x]</span><span
12354 class="cmtt-8"> =</span><span
12355 class="cmtt-8"> [x0]</span>
12356 <br class="fancyvrb" /><a
12357 id="x1-123012r6"></a><span
12358 class="cmr-6">6</span><span
12359 class="cmtt-8"> </span><span
12360 class="cmtt-8"> </span><span
12361 class="cmtt-8"> </span><span
12362 class="cmtt-8"> 6)</span><span
12363 class="cmtt-8"> </span><span
12364 class="cmtt-8"> </span><span
12365 class="cmtt-8"> </span><span
12366 class="cmtt-8"> [y]</span><span
12367 class="cmtt-8"> =</span><span
12368 class="cmtt-8"> [y0]</span>
12369 <br class="fancyvrb" /><a
12370 id="x1-123014r7"></a><span
12371 class="cmr-6">7</span><span
12372 class="cmtt-8"> </span><span
12373 class="cmtt-8"> </span><span
12374 class="cmtt-8"> </span><span
12375 class="cmtt-8"> 7)</span><span
12376 class="cmtt-8"> </span><span
12377 class="cmtt-8"> [err]</span><span
12378 class="cmtt-8"> =</span><span
12379 class="cmtt-8"> 0</span>
12380 <br class="fancyvrb" /><a
12381 id="x1-123016r8"></a><span
12382 class="cmr-6">8</span><span
12383 class="cmtt-8"> </span><span
12384 class="cmtt-8"> </span>
12385 <br class="fancyvrb" /><a
12386 id="x1-123018r9"></a><span
12387 class="cmr-6">9</span><span
12388 class="cmtt-8"> </span><span
12389 class="cmtt-8"> </span><span
12390 class="cmtt-8"> </span><span
12391 class="cmtt-8"> 8)</span><span
12392 class="cmtt-8"> if</span><span
12393 class="cmtt-8"> (</span><span
12394 class="cmtt-8"> [dy]</span><span
12395 class="cmtt-8"> is</span><span
12396 class="cmtt-8"> less</span><span
12397 class="cmtt-8"> than</span><span
12398 class="cmtt-8"> 0</span><span
12399 class="cmtt-8"> )</span><span
12400 class="cmtt-8"> {</span>
12401 <br class="fancyvrb" /><a
12402 id="x1-123020r10"></a><span
12403 class="cmr-6">10</span><span
12404 class="cmtt-8"> </span><span
12405 class="cmtt-8"> </span>
12406 <br class="fancyvrb" /><a
12407 id="x1-123022r11"></a><span
12408 class="cmr-6">11</span><span
12409 class="cmtt-8"> </span><span
12410 class="cmtt-8"> </span><span
12411 class="cmtt-8"> </span><span
12412 class="cmtt-8"> </span><span
12413 class="cmtt-8"> </span><span
12414 class="cmtt-8"> </span><span
12415 class="cmtt-8"> </span><span
12416 class="cmtt-8"> </span><span
12417 class="cmtt-8"> </span><span
12418 class="cmtt-8"> 9)</span><span
12419 class="cmtt-8"> [sy]</span><span
12420 class="cmtt-8"> =</span><span
12421 class="cmtt-8"> [base]</span><span
12422 class="cmtt-8"> -</span><span
12423 class="cmtt-8"> 1</span>
12424 <br class="fancyvrb" /><a
12425 id="x1-123024r12"></a><span
12426 class="cmr-6">12</span><span
12427 class="cmtt-8"> </span><span
12428 class="cmtt-8"> </span>
12429 <br class="fancyvrb" /><a
12430 id="x1-123026r13"></a><span
12431 class="cmr-6">13</span><span
12432 class="cmtt-8"> </span><span
12433 class="cmtt-8"> </span><span
12434 class="cmtt-8"> </span><span
12435 class="cmtt-8"> </span><span
12436 class="cmtt-8"> </span><span
12437 class="cmtt-8"> </span><span
12438 class="cmtt-8"> }</span><span
12439 class="cmtt-8"> else</span><span
12440 class="cmtt-8"> {</span>
12441 <br class="fancyvrb" /><a
12442 id="x1-123028r14"></a><span
12443 class="cmr-6">14</span><span
12444 class="cmtt-8"> </span><span
12445 class="cmtt-8"> </span>
12446 <br class="fancyvrb" /><a
12447 id="x1-123030r15"></a><span
12448 class="cmr-6">15</span><span
12449 class="cmtt-8"> </span><span
12450 class="cmtt-8"> </span><span
12451 class="cmtt-8"> </span><span
12452 class="cmtt-8"> </span><span
12453 class="cmtt-8"> </span><span
12454 class="cmtt-8"> </span><span
12455 class="cmtt-8"> </span><span
12456 class="cmtt-8"> </span><span
12457 class="cmtt-8"> 10)</span><span
12458 class="cmtt-8"> [sy]</span><span
12459 class="cmtt-8"> =</span><span
12460 class="cmtt-8"> [base]</span><span
12461 class="cmtt-8"> +</span><span
12462 class="cmtt-8"> 1</span>
12463 <br class="fancyvrb" /><a
12464 id="x1-123032r16"></a><span
12465 class="cmr-6">16</span><span
12466 class="cmtt-8"> </span><span
12467 class="cmtt-8"> </span>
12468 <br class="fancyvrb" /><a
12469 id="x1-123034r17"></a><span
12470 class="cmr-6">17</span><span
12471 class="cmtt-8"> </span><span
12472 class="cmtt-8"> </span><span
12473 class="cmtt-8"> </span><span
12474 class="cmtt-8"> </span><span
12475 class="cmtt-8"> </span><span
12476 class="cmtt-8"> </span><span
12477 class="cmtt-8"> }</span>
12478 <br class="fancyvrb" /><a
12479 id="x1-123036r18"></a><span
12480 class="cmr-6">18</span><span
12481 class="cmtt-8"> </span><span
12482 class="cmtt-8"> </span>
12483 <br class="fancyvrb" /><a
12484 id="x1-123038r19"></a><span
12485 class="cmr-6">19</span><span
12486 class="cmtt-8"> </span><span
12487 class="cmtt-8"> </span><span
12488 class="cmtt-8"> 11)</span><span
12489 class="cmtt-8"> [ady]</span><span
12490 class="cmtt-8"> =</span><span
12491 class="cmtt-8"> [ady]</span><span
12492 class="cmtt-8"> -</span><span
12493 class="cmtt-8"> (absolute</span><span
12494 class="cmtt-8"> value</span><span
12495 class="cmtt-8"> of</span><span
12496 class="cmtt-8"> [base])</span><span
12497 class="cmtt-8"> *</span><span
12498 class="cmtt-8"> [adx]</span>
12499 <br class="fancyvrb" /><a
12500 id="x1-123040r20"></a><span
12501 class="cmr-6">20</span><span
12502 class="cmtt-8"> </span><span
12503 class="cmtt-8"> </span><span
12504 class="cmtt-8"> 12)</span><span
12505 class="cmtt-8"> vector</span><span
12506 class="cmtt-8"> [v]</span><span
12507 class="cmtt-8"> element</span><span
12508 class="cmtt-8"> [x]</span><span
12509 class="cmtt-8"> =</span><span
12510 class="cmtt-8"> [y]</span>
12511 <br class="fancyvrb" /><a
12512 id="x1-123042r21"></a><span
12513 class="cmr-6">21</span><span
12514 class="cmtt-8"> </span><span
12515 class="cmtt-8"> </span>
12516 <br class="fancyvrb" /><a
12517 id="x1-123044r22"></a><span
12518 class="cmr-6">22</span><span
12519 class="cmtt-8"> </span><span
12520 class="cmtt-8"> </span><span
12521 class="cmtt-8"> 13)</span><span
12522 class="cmtt-8"> iterate</span><span
12523 class="cmtt-8"> [x]</span><span
12524 class="cmtt-8"> over</span><span
12525 class="cmtt-8"> the</span><span
12526 class="cmtt-8"> range</span><span
12527 class="cmtt-8"> [x0]+1</span><span
12528 class="cmtt-8"> ...</span><span
12529 class="cmtt-8"> [x1]-1</span><span
12530 class="cmtt-8"> {</span>
12534 <br class="fancyvrb" /><a
12535 id="x1-123046r23"></a><span
12536 class="cmr-6">23</span><span
12537 class="cmtt-8"> </span><span
12538 class="cmtt-8"> </span>
12539 <br class="fancyvrb" /><a
12540 id="x1-123048r24"></a><span
12541 class="cmr-6">24</span><span
12542 class="cmtt-8"> </span><span
12543 class="cmtt-8"> </span><span
12544 class="cmtt-8"> </span><span
12545 class="cmtt-8"> </span><span
12546 class="cmtt-8"> </span><span
12547 class="cmtt-8"> </span><span
12548 class="cmtt-8"> </span><span
12549 class="cmtt-8"> </span><span
12550 class="cmtt-8"> 14)</span><span
12551 class="cmtt-8"> [err]</span><span
12552 class="cmtt-8"> =</span><span
12553 class="cmtt-8"> [err]</span><span
12554 class="cmtt-8"> +</span><span
12555 class="cmtt-8"> [ady];</span>
12556 <br class="fancyvrb" /><a
12557 id="x1-123050r25"></a><span
12558 class="cmr-6">25</span><span
12559 class="cmtt-8"> </span><span
12560 class="cmtt-8"> </span><span
12561 class="cmtt-8"> </span><span
12562 class="cmtt-8"> </span><span
12563 class="cmtt-8"> </span><span
12564 class="cmtt-8"> </span><span
12565 class="cmtt-8"> </span><span
12566 class="cmtt-8"> </span><span
12567 class="cmtt-8"> 15)</span><span
12568 class="cmtt-8"> if</span><span
12569 class="cmtt-8"> (</span><span
12570 class="cmtt-8"> [err]</span><span
12571 class="cmtt-8"> >=</span><span
12572 class="cmtt-8"> [adx]</span><span
12573 class="cmtt-8"> )</span><span
12574 class="cmtt-8"> {</span>
12575 <br class="fancyvrb" /><a
12576 id="x1-123052r26"></a><span
12577 class="cmr-6">26</span><span
12578 class="cmtt-8"> </span><span
12579 class="cmtt-8"> </span>
12580 <br class="fancyvrb" /><a
12581 id="x1-123054r27"></a><span
12582 class="cmr-6">27</span><span
12583 class="cmtt-8"> </span><span
12584 class="cmtt-8"> </span><span
12585 class="cmtt-8"> </span><span
12586 class="cmtt-8"> </span><span
12587 class="cmtt-8"> </span><span
12588 class="cmtt-8"> </span><span
12589 class="cmtt-8"> </span><span
12590 class="cmtt-8"> </span><span
12591 class="cmtt-8"> </span><span
12592 class="cmtt-8"> </span><span
12593 class="cmtt-8"> </span><span
12594 class="cmtt-8"> </span><span
12595 class="cmtt-8"> </span><span
12596 class="cmtt-8"> </span><span
12597 class="cmtt-8"> 16)</span><span
12598 class="cmtt-8"> [err]</span><span
12599 class="cmtt-8"> =</span><span
12600 class="cmtt-8"> [err]</span><span
12601 class="cmtt-8"> -</span><span
12602 class="cmtt-8"> [adx]</span>
12603 <br class="fancyvrb" /><a
12604 id="x1-123056r28"></a><span
12605 class="cmr-6">28</span><span
12606 class="cmtt-8"> </span><span
12607 class="cmtt-8"> </span><span
12608 class="cmtt-8"> </span><span
12609 class="cmtt-8"> </span><span
12610 class="cmtt-8"> </span><span
12611 class="cmtt-8"> </span><span
12612 class="cmtt-8"> </span><span
12613 class="cmtt-8"> </span><span
12614 class="cmtt-8"> </span><span
12615 class="cmtt-8"> </span><span
12616 class="cmtt-8"> </span><span
12617 class="cmtt-8"> </span><span
12618 class="cmtt-8"> </span><span
12619 class="cmtt-8"> </span><span
12620 class="cmtt-8"> 17)</span><span
12621 class="cmtt-8"> </span><span
12622 class="cmtt-8"> </span><span
12623 class="cmtt-8"> [y]</span><span
12624 class="cmtt-8"> =</span><span
12625 class="cmtt-8"> [y]</span><span
12626 class="cmtt-8"> +</span><span
12627 class="cmtt-8"> [sy]</span>
12628 <br class="fancyvrb" /><a
12629 id="x1-123058r29"></a><span
12630 class="cmr-6">29</span><span
12631 class="cmtt-8"> </span><span
12632 class="cmtt-8"> </span>
12633 <br class="fancyvrb" /><a
12634 id="x1-123060r30"></a><span
12635 class="cmr-6">30</span><span
12636 class="cmtt-8"> </span><span
12637 class="cmtt-8"> </span><span
12638 class="cmtt-8"> </span><span
12639 class="cmtt-8"> </span><span
12640 class="cmtt-8"> </span><span
12641 class="cmtt-8"> </span><span
12642 class="cmtt-8"> </span><span
12643 class="cmtt-8"> </span><span
12644 class="cmtt-8"> </span><span
12645 class="cmtt-8"> </span><span
12646 class="cmtt-8"> </span><span
12647 class="cmtt-8"> </span><span
12648 class="cmtt-8"> }</span><span
12649 class="cmtt-8"> else</span><span
12650 class="cmtt-8"> {</span>
12651 <br class="fancyvrb" /><a
12652 id="x1-123062r31"></a><span
12653 class="cmr-6">31</span><span
12654 class="cmtt-8"> </span><span
12655 class="cmtt-8"> </span>
12656 <br class="fancyvrb" /><a
12657 id="x1-123064r32"></a><span
12658 class="cmr-6">32</span><span
12659 class="cmtt-8"> </span><span
12660 class="cmtt-8"> </span><span
12661 class="cmtt-8"> </span><span
12662 class="cmtt-8"> </span><span
12663 class="cmtt-8"> </span><span
12664 class="cmtt-8"> </span><span
12665 class="cmtt-8"> </span><span
12666 class="cmtt-8"> </span><span
12667 class="cmtt-8"> </span><span
12668 class="cmtt-8"> </span><span
12669 class="cmtt-8"> </span><span
12670 class="cmtt-8"> </span><span
12671 class="cmtt-8"> </span><span
12672 class="cmtt-8"> </span><span
12673 class="cmtt-8"> 18)</span><span
12674 class="cmtt-8"> [y]</span><span
12675 class="cmtt-8"> =</span><span
12676 class="cmtt-8"> [y]</span><span
12677 class="cmtt-8"> +</span><span
12678 class="cmtt-8"> [base]</span>
12679 <br class="fancyvrb" /><a
12680 id="x1-123066r33"></a><span
12681 class="cmr-6">33</span><span
12682 class="cmtt-8"> </span><span
12683 class="cmtt-8"> </span>
12684 <br class="fancyvrb" /><a
12685 id="x1-123068r34"></a><span
12686 class="cmr-6">34</span><span
12687 class="cmtt-8"> </span><span
12688 class="cmtt-8"> </span><span
12689 class="cmtt-8"> </span><span
12690 class="cmtt-8"> </span><span
12691 class="cmtt-8"> </span><span
12692 class="cmtt-8"> </span><span
12693 class="cmtt-8"> </span><span
12694 class="cmtt-8"> </span><span
12695 class="cmtt-8"> </span><span
12696 class="cmtt-8"> </span><span
12697 class="cmtt-8"> </span><span
12698 class="cmtt-8"> </span><span
12699 class="cmtt-8"> }</span>
12700 <br class="fancyvrb" /><a
12701 id="x1-123070r35"></a><span
12702 class="cmr-6">35</span><span
12703 class="cmtt-8"> </span><span
12704 class="cmtt-8"> </span>
12705 <br class="fancyvrb" /><a
12706 id="x1-123072r36"></a><span
12707 class="cmr-6">36</span><span
12708 class="cmtt-8"> </span><span
12709 class="cmtt-8"> </span><span
12710 class="cmtt-8"> </span><span
12711 class="cmtt-8"> </span><span
12712 class="cmtt-8"> </span><span
12713 class="cmtt-8"> </span><span
12714 class="cmtt-8"> </span><span
12715 class="cmtt-8"> </span><span
12716 class="cmtt-8"> 19)</span><span
12717 class="cmtt-8"> vector</span><span
12718 class="cmtt-8"> [v]</span><span
12719 class="cmtt-8"> element</span><span
12720 class="cmtt-8"> [x]</span><span
12721 class="cmtt-8"> =</span><span
12722 class="cmtt-8"> [y]</span>
12723 <br class="fancyvrb" /><a
12724 id="x1-123074r37"></a><span
12725 class="cmr-6">37</span><span
12726 class="cmtt-8"> </span><span
12727 class="cmtt-8"> </span>
12728 <br class="fancyvrb" /><a
12729 id="x1-123076r38"></a><span
12730 class="cmr-6">38</span><span
12731 class="cmtt-8"> </span><span
12732 class="cmtt-8"> </span><span
12733 class="cmtt-8"> </span><span
12734 class="cmtt-8"> </span><span
12735 class="cmtt-8"> </span><span
12736 class="cmtt-8"> </span><span
12737 class="cmtt-8"> }</span>
12745 <h3 class="sectionHead"><span class="titlemark">10. </span> <a
12746 id="x1-12400010"></a>Tables</h3>
12747 <!--l. 6--><p class="noindent" >
12748 <h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a
12749 id="x1-12500010.1"></a>floor1_inverse_dB_table</h4>
12750 <!--l. 8--><p class="noindent" >The vector <span
12751 class="cmtt-12">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consiting of the
12752 following values (read left to right then top to bottom):
12753 <!--l. 12--><p class="noindent" >
12754 <div class="fancyvrb" id="fancyvrb48">
12756 id="x1-125002r1"></a><span
12757 class="cmr-6">1</span><span
12758 class="cmtt-8"> </span><span
12759 class="cmtt-8"> </span><span
12760 class="cmtt-8"> </span><span
12761 class="cmtt-8"> 1.0649863e-07,</span><span
12762 class="cmtt-8"> 1.1341951e-07,</span><span
12763 class="cmtt-8"> 1.2079015e-07,</span><span
12764 class="cmtt-8"> 1.2863978e-07,</span>
12765 <br class="fancyvrb" /><a
12766 id="x1-125004r2"></a><span
12767 class="cmr-6">2</span><span
12768 class="cmtt-8"> </span><span
12769 class="cmtt-8"> </span><span
12770 class="cmtt-8"> </span><span
12771 class="cmtt-8"> 1.3699951e-07,</span><span
12772 class="cmtt-8"> 1.4590251e-07,</span><span
12773 class="cmtt-8"> 1.5538408e-07,</span><span
12774 class="cmtt-8"> 1.6548181e-07,</span>
12775 <br class="fancyvrb" /><a
12776 id="x1-125006r3"></a><span
12777 class="cmr-6">3</span><span
12778 class="cmtt-8"> </span><span
12779 class="cmtt-8"> </span><span
12780 class="cmtt-8"> </span><span
12781 class="cmtt-8"> 1.7623575e-07,</span><span
12782 class="cmtt-8"> 1.8768855e-07,</span><span
12783 class="cmtt-8"> 1.9988561e-07,</span><span
12784 class="cmtt-8"> 2.1287530e-07,</span>
12785 <br class="fancyvrb" /><a
12786 id="x1-125008r4"></a><span
12787 class="cmr-6">4</span><span
12788 class="cmtt-8"> </span><span
12789 class="cmtt-8"> </span><span
12790 class="cmtt-8"> </span><span
12791 class="cmtt-8"> 2.2670913e-07,</span><span
12792 class="cmtt-8"> 2.4144197e-07,</span><span
12793 class="cmtt-8"> 2.5713223e-07,</span><span
12794 class="cmtt-8"> 2.7384213e-07,</span>
12795 <br class="fancyvrb" /><a
12796 id="x1-125010r5"></a><span
12797 class="cmr-6">5</span><span
12798 class="cmtt-8"> </span><span
12799 class="cmtt-8"> </span><span
12800 class="cmtt-8"> </span><span
12801 class="cmtt-8"> 2.9163793e-07,</span><span
12802 class="cmtt-8"> 3.1059021e-07,</span><span
12803 class="cmtt-8"> 3.3077411e-07,</span><span
12804 class="cmtt-8"> 3.5226968e-07,</span>
12805 <br class="fancyvrb" /><a
12806 id="x1-125012r6"></a><span
12807 class="cmr-6">6</span><span
12808 class="cmtt-8"> </span><span
12809 class="cmtt-8"> </span><span
12810 class="cmtt-8"> </span><span
12811 class="cmtt-8"> 3.7516214e-07,</span><span
12812 class="cmtt-8"> 3.9954229e-07,</span><span
12813 class="cmtt-8"> 4.2550680e-07,</span><span
12814 class="cmtt-8"> 4.5315863e-07,</span>
12815 <br class="fancyvrb" /><a
12816 id="x1-125014r7"></a><span
12817 class="cmr-6">7</span><span
12818 class="cmtt-8"> </span><span
12819 class="cmtt-8"> </span><span
12820 class="cmtt-8"> </span><span
12821 class="cmtt-8"> 4.8260743e-07,</span><span
12822 class="cmtt-8"> 5.1396998e-07,</span><span
12823 class="cmtt-8"> 5.4737065e-07,</span><span
12824 class="cmtt-8"> 5.8294187e-07,</span>
12825 <br class="fancyvrb" /><a
12826 id="x1-125016r8"></a><span
12827 class="cmr-6">8</span><span
12828 class="cmtt-8"> </span><span
12829 class="cmtt-8"> </span><span
12830 class="cmtt-8"> </span><span
12831 class="cmtt-8"> 6.2082472e-07,</span><span
12832 class="cmtt-8"> 6.6116941e-07,</span><span
12833 class="cmtt-8"> 7.0413592e-07,</span><span
12834 class="cmtt-8"> 7.4989464e-07,</span>
12835 <br class="fancyvrb" /><a
12836 id="x1-125018r9"></a><span
12837 class="cmr-6">9</span><span
12838 class="cmtt-8"> </span><span
12839 class="cmtt-8"> </span><span
12840 class="cmtt-8"> </span><span
12841 class="cmtt-8"> 7.9862701e-07,</span><span
12842 class="cmtt-8"> 8.5052630e-07,</span><span
12843 class="cmtt-8"> 9.0579828e-07,</span><span
12844 class="cmtt-8"> 9.6466216e-07,</span>
12845 <br class="fancyvrb" /><a
12846 id="x1-125020r10"></a><span
12847 class="cmr-6">10</span><span
12848 class="cmtt-8"> </span><span
12849 class="cmtt-8"> </span><span
12850 class="cmtt-8"> </span><span
12851 class="cmtt-8"> 1.0273513e-06,</span><span
12852 class="cmtt-8"> 1.0941144e-06,</span><span
12853 class="cmtt-8"> 1.1652161e-06,</span><span
12854 class="cmtt-8"> 1.2409384e-06,</span>
12855 <br class="fancyvrb" /><a
12856 id="x1-125022r11"></a><span
12857 class="cmr-6">11</span><span
12858 class="cmtt-8"> </span><span
12859 class="cmtt-8"> </span><span
12860 class="cmtt-8"> </span><span
12861 class="cmtt-8"> 1.3215816e-06,</span><span
12862 class="cmtt-8"> 1.4074654e-06,</span><span
12863 class="cmtt-8"> 1.4989305e-06,</span><span
12864 class="cmtt-8"> 1.5963394e-06,</span>
12865 <br class="fancyvrb" /><a
12866 id="x1-125024r12"></a><span
12867 class="cmr-6">12</span><span
12868 class="cmtt-8"> </span><span
12869 class="cmtt-8"> </span><span
12870 class="cmtt-8"> </span><span
12871 class="cmtt-8"> 1.7000785e-06,</span><span
12872 class="cmtt-8"> 1.8105592e-06,</span><span
12873 class="cmtt-8"> 1.9282195e-06,</span><span
12874 class="cmtt-8"> 2.0535261e-06,</span>
12875 <br class="fancyvrb" /><a
12876 id="x1-125026r13"></a><span
12877 class="cmr-6">13</span><span
12878 class="cmtt-8"> </span><span
12879 class="cmtt-8"> </span><span
12880 class="cmtt-8"> </span><span
12881 class="cmtt-8"> 2.1869758e-06,</span><span
12882 class="cmtt-8"> 2.3290978e-06,</span><span
12883 class="cmtt-8"> 2.4804557e-06,</span><span
12884 class="cmtt-8"> 2.6416497e-06,</span>
12885 <br class="fancyvrb" /><a
12886 id="x1-125028r14"></a><span
12887 class="cmr-6">14</span><span
12888 class="cmtt-8"> </span><span
12889 class="cmtt-8"> </span><span
12890 class="cmtt-8"> </span><span
12891 class="cmtt-8"> 2.8133190e-06,</span><span
12892 class="cmtt-8"> 2.9961443e-06,</span><span
12893 class="cmtt-8"> 3.1908506e-06,</span><span
12894 class="cmtt-8"> 3.3982101e-06,</span>
12895 <br class="fancyvrb" /><a
12896 id="x1-125030r15"></a><span
12897 class="cmr-6">15</span><span
12898 class="cmtt-8"> </span><span
12899 class="cmtt-8"> </span><span
12900 class="cmtt-8"> </span><span
12901 class="cmtt-8"> 3.6190449e-06,</span><span
12902 class="cmtt-8"> 3.8542308e-06,</span><span
12903 class="cmtt-8"> 4.1047004e-06,</span><span
12904 class="cmtt-8"> 4.3714470e-06,</span>
12905 <br class="fancyvrb" /><a
12906 id="x1-125032r16"></a><span
12907 class="cmr-6">16</span><span
12908 class="cmtt-8"> </span><span
12909 class="cmtt-8"> </span><span
12910 class="cmtt-8"> </span><span
12911 class="cmtt-8"> 4.6555282e-06,</span><span
12912 class="cmtt-8"> 4.9580707e-06,</span><span
12913 class="cmtt-8"> 5.2802740e-06,</span><span
12914 class="cmtt-8"> 5.6234160e-06,</span>
12915 <br class="fancyvrb" /><a
12916 id="x1-125034r17"></a><span
12917 class="cmr-6">17</span><span
12918 class="cmtt-8"> </span><span
12919 class="cmtt-8"> </span><span
12920 class="cmtt-8"> </span><span
12921 class="cmtt-8"> 5.9888572e-06,</span><span
12922 class="cmtt-8"> 6.3780469e-06,</span><span
12923 class="cmtt-8"> 6.7925283e-06,</span><span
12924 class="cmtt-8"> 7.2339451e-06,</span>
12925 <br class="fancyvrb" /><a
12926 id="x1-125036r18"></a><span
12927 class="cmr-6">18</span><span
12928 class="cmtt-8"> </span><span
12929 class="cmtt-8"> </span><span
12930 class="cmtt-8"> </span><span
12931 class="cmtt-8"> 7.7040476e-06,</span><span
12932 class="cmtt-8"> 8.2047000e-06,</span><span
12933 class="cmtt-8"> 8.7378876e-06,</span><span
12934 class="cmtt-8"> 9.3057248e-06,</span>
12935 <br class="fancyvrb" /><a
12936 id="x1-125038r19"></a><span
12937 class="cmr-6">19</span><span
12938 class="cmtt-8"> </span><span
12939 class="cmtt-8"> </span><span
12940 class="cmtt-8"> </span><span
12941 class="cmtt-8"> 9.9104632e-06,</span><span
12942 class="cmtt-8"> 1.0554501e-05,</span><span
12943 class="cmtt-8"> 1.1240392e-05,</span><span
12944 class="cmtt-8"> 1.1970856e-05,</span>
12945 <br class="fancyvrb" /><a
12946 id="x1-125040r20"></a><span
12947 class="cmr-6">20</span><span
12948 class="cmtt-8"> </span><span
12949 class="cmtt-8"> </span><span
12950 class="cmtt-8"> </span><span
12951 class="cmtt-8"> 1.2748789e-05,</span><span
12952 class="cmtt-8"> 1.3577278e-05,</span><span
12953 class="cmtt-8"> 1.4459606e-05,</span><span
12954 class="cmtt-8"> 1.5399272e-05,</span>
12955 <br class="fancyvrb" /><a
12956 id="x1-125042r21"></a><span
12957 class="cmr-6">21</span><span
12958 class="cmtt-8"> </span><span
12959 class="cmtt-8"> </span><span
12960 class="cmtt-8"> </span><span
12961 class="cmtt-8"> 1.6400004e-05,</span><span
12962 class="cmtt-8"> 1.7465768e-05,</span><span
12963 class="cmtt-8"> 1.8600792e-05,</span><span
12964 class="cmtt-8"> 1.9809576e-05,</span>
12965 <br class="fancyvrb" /><a
12966 id="x1-125044r22"></a><span
12967 class="cmr-6">22</span><span
12968 class="cmtt-8"> </span><span
12969 class="cmtt-8"> </span><span
12970 class="cmtt-8"> </span><span
12971 class="cmtt-8"> 2.1096914e-05,</span><span
12972 class="cmtt-8"> 2.2467911e-05,</span><span
12973 class="cmtt-8"> 2.3928002e-05,</span><span
12974 class="cmtt-8"> 2.5482978e-05,</span>
12975 <br class="fancyvrb" /><a
12976 id="x1-125046r23"></a><span
12977 class="cmr-6">23</span><span
12978 class="cmtt-8"> </span><span
12979 class="cmtt-8"> </span><span
12980 class="cmtt-8"> </span><span
12981 class="cmtt-8"> 2.7139006e-05,</span><span
12982 class="cmtt-8"> 2.8902651e-05,</span><span
12983 class="cmtt-8"> 3.0780908e-05,</span><span
12984 class="cmtt-8"> 3.2781225e-05,</span>
12985 <br class="fancyvrb" /><a
12986 id="x1-125048r24"></a><span
12987 class="cmr-6">24</span><span
12988 class="cmtt-8"> </span><span
12989 class="cmtt-8"> </span><span
12990 class="cmtt-8"> </span><span
12991 class="cmtt-8"> 3.4911534e-05,</span><span
12992 class="cmtt-8"> 3.7180282e-05,</span><span
12993 class="cmtt-8"> 3.9596466e-05,</span><span
12994 class="cmtt-8"> 4.2169667e-05,</span>
12995 <br class="fancyvrb" /><a
12996 id="x1-125050r25"></a><span
12997 class="cmr-6">25</span><span
12998 class="cmtt-8"> </span><span
12999 class="cmtt-8"> </span><span
13000 class="cmtt-8"> </span><span
13001 class="cmtt-8"> 4.4910090e-05,</span><span
13002 class="cmtt-8"> 4.7828601e-05,</span><span
13003 class="cmtt-8"> 5.0936773e-05,</span><span
13004 class="cmtt-8"> 5.4246931e-05,</span>
13005 <br class="fancyvrb" /><a
13006 id="x1-125052r26"></a><span
13007 class="cmr-6">26</span><span
13008 class="cmtt-8"> </span><span
13009 class="cmtt-8"> </span><span
13010 class="cmtt-8"> </span><span
13011 class="cmtt-8"> 5.7772202e-05,</span><span
13012 class="cmtt-8"> 6.1526565e-05,</span><span
13013 class="cmtt-8"> 6.5524908e-05,</span><span
13014 class="cmtt-8"> 6.9783085e-05,</span>
13015 <br class="fancyvrb" /><a
13016 id="x1-125054r27"></a><span
13017 class="cmr-6">27</span><span
13018 class="cmtt-8"> </span><span
13019 class="cmtt-8"> </span><span
13020 class="cmtt-8"> </span><span
13021 class="cmtt-8"> 7.4317983e-05,</span><span
13022 class="cmtt-8"> 7.9147585e-05,</span><span
13023 class="cmtt-8"> 8.4291040e-05,</span><span
13024 class="cmtt-8"> 8.9768747e-05,</span>
13025 <br class="fancyvrb" /><a
13026 id="x1-125056r28"></a><span
13027 class="cmr-6">28</span><span
13028 class="cmtt-8"> </span><span
13029 class="cmtt-8"> </span><span
13030 class="cmtt-8"> </span><span
13031 class="cmtt-8"> 9.5602426e-05,</span><span
13032 class="cmtt-8"> 0.00010181521,</span><span
13033 class="cmtt-8"> 0.00010843174,</span><span
13034 class="cmtt-8"> 0.00011547824,</span>
13035 <br class="fancyvrb" /><a
13036 id="x1-125058r29"></a><span
13037 class="cmr-6">29</span><span
13038 class="cmtt-8"> </span><span
13039 class="cmtt-8"> </span><span
13040 class="cmtt-8"> </span><span
13041 class="cmtt-8"> 0.00012298267,</span><span
13042 class="cmtt-8"> 0.00013097477,</span><span
13043 class="cmtt-8"> 0.00013948625,</span><span
13044 class="cmtt-8"> 0.00014855085,</span>
13045 <br class="fancyvrb" /><a
13046 id="x1-125060r30"></a><span
13047 class="cmr-6">30</span><span
13048 class="cmtt-8"> </span><span
13049 class="cmtt-8"> </span><span
13050 class="cmtt-8"> </span><span
13051 class="cmtt-8"> 0.00015820453,</span><span
13052 class="cmtt-8"> 0.00016848555,</span><span
13053 class="cmtt-8"> 0.00017943469,</span><span
13054 class="cmtt-8"> 0.00019109536,</span>
13055 <br class="fancyvrb" /><a
13056 id="x1-125062r31"></a><span
13057 class="cmr-6">31</span><span
13058 class="cmtt-8"> </span><span
13059 class="cmtt-8"> </span><span
13060 class="cmtt-8"> </span><span
13061 class="cmtt-8"> 0.00020351382,</span><span
13062 class="cmtt-8"> 0.00021673929,</span><span
13063 class="cmtt-8"> 0.00023082423,</span><span
13064 class="cmtt-8"> 0.00024582449,</span>
13065 <br class="fancyvrb" /><a
13066 id="x1-125064r32"></a><span
13067 class="cmr-6">32</span><span
13068 class="cmtt-8"> </span><span
13069 class="cmtt-8"> </span><span
13070 class="cmtt-8"> </span><span
13071 class="cmtt-8"> 0.00026179955,</span><span
13072 class="cmtt-8"> 0.00027881276,</span><span
13073 class="cmtt-8"> 0.00029693158,</span><span
13074 class="cmtt-8"> 0.00031622787,</span>
13075 <br class="fancyvrb" /><a
13076 id="x1-125066r33"></a><span
13077 class="cmr-6">33</span><span
13078 class="cmtt-8"> </span><span
13079 class="cmtt-8"> </span><span
13080 class="cmtt-8"> </span><span
13081 class="cmtt-8"> 0.00033677814,</span><span
13082 class="cmtt-8"> 0.00035866388,</span><span
13083 class="cmtt-8"> 0.00038197188,</span><span
13084 class="cmtt-8"> 0.00040679456,</span>
13085 <br class="fancyvrb" /><a
13086 id="x1-125068r34"></a><span
13087 class="cmr-6">34</span><span
13088 class="cmtt-8"> </span><span
13089 class="cmtt-8"> </span><span
13090 class="cmtt-8"> </span><span
13091 class="cmtt-8"> 0.00043323036,</span><span
13092 class="cmtt-8"> 0.00046138411,</span><span
13093 class="cmtt-8"> 0.00049136745,</span><span
13094 class="cmtt-8"> 0.00052329927,</span>
13095 <br class="fancyvrb" /><a
13096 id="x1-125070r35"></a><span
13097 class="cmr-6">35</span><span
13098 class="cmtt-8"> </span><span
13099 class="cmtt-8"> </span><span
13100 class="cmtt-8"> </span><span
13101 class="cmtt-8"> 0.00055730621,</span><span
13102 class="cmtt-8"> 0.00059352311,</span><span
13103 class="cmtt-8"> 0.00063209358,</span><span
13104 class="cmtt-8"> 0.00067317058,</span>
13105 <br class="fancyvrb" /><a
13106 id="x1-125072r36"></a><span
13107 class="cmr-6">36</span><span
13108 class="cmtt-8"> </span><span
13109 class="cmtt-8"> </span><span
13110 class="cmtt-8"> </span><span
13111 class="cmtt-8"> 0.00071691700,</span><span
13112 class="cmtt-8"> 0.00076350630,</span><span
13113 class="cmtt-8"> 0.00081312324,</span><span
13114 class="cmtt-8"> 0.00086596457,</span>
13115 <br class="fancyvrb" /><a
13116 id="x1-125074r37"></a><span
13117 class="cmr-6">37</span><span
13118 class="cmtt-8"> </span><span
13119 class="cmtt-8"> </span><span
13120 class="cmtt-8"> </span><span
13121 class="cmtt-8"> 0.00092223983,</span><span
13122 class="cmtt-8"> 0.00098217216,</span><span
13123 class="cmtt-8"> 0.0010459992,</span><span
13124 class="cmtt-8"> </span><span
13125 class="cmtt-8"> 0.0011139742,</span>
13126 <br class="fancyvrb" /><a
13127 id="x1-125076r38"></a><span
13128 class="cmr-6">38</span><span
13129 class="cmtt-8"> </span><span
13130 class="cmtt-8"> </span><span
13131 class="cmtt-8"> </span><span
13132 class="cmtt-8"> 0.0011863665,</span><span
13133 class="cmtt-8"> </span><span
13134 class="cmtt-8"> 0.0012634633,</span><span
13135 class="cmtt-8"> </span><span
13136 class="cmtt-8"> 0.0013455702,</span><span
13137 class="cmtt-8"> </span><span
13138 class="cmtt-8"> 0.0014330129,</span>
13139 <br class="fancyvrb" /><a
13140 id="x1-125078r39"></a><span
13141 class="cmr-6">39</span><span
13142 class="cmtt-8"> </span><span
13143 class="cmtt-8"> </span><span
13144 class="cmtt-8"> </span><span
13145 class="cmtt-8"> 0.0015261382,</span><span
13146 class="cmtt-8"> </span><span
13147 class="cmtt-8"> 0.0016253153,</span><span
13148 class="cmtt-8"> </span><span
13149 class="cmtt-8"> 0.0017309374,</span><span
13150 class="cmtt-8"> </span><span
13151 class="cmtt-8"> 0.0018434235,</span>
13152 <br class="fancyvrb" /><a
13153 id="x1-125080r40"></a><span
13154 class="cmr-6">40</span><span
13155 class="cmtt-8"> </span><span
13156 class="cmtt-8"> </span><span
13157 class="cmtt-8"> </span><span
13158 class="cmtt-8"> 0.0019632195,</span><span
13159 class="cmtt-8"> </span><span
13160 class="cmtt-8"> 0.0020908006,</span><span
13161 class="cmtt-8"> </span><span
13162 class="cmtt-8"> 0.0022266726,</span><span
13163 class="cmtt-8"> </span><span
13164 class="cmtt-8"> 0.0023713743,</span>
13165 <br class="fancyvrb" /><a
13166 id="x1-125082r41"></a><span
13167 class="cmr-6">41</span><span
13168 class="cmtt-8"> </span><span
13169 class="cmtt-8"> </span><span
13170 class="cmtt-8"> </span><span
13171 class="cmtt-8"> 0.0025254795,</span><span
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13173 class="cmtt-8"> 0.0026895994,</span><span
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13175 class="cmtt-8"> 0.0028643847,</span><span
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13177 class="cmtt-8"> 0.0030505286,</span>
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13184 class="cmtt-8"> 0.0032487691,</span><span
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13186 class="cmtt-8"> 0.0034598925,</span><span
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13188 class="cmtt-8"> 0.0036847358,</span><span
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13190 class="cmtt-8"> 0.0039241906,</span>
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13202 class="cmtt-8"> 0.0044507950,</span><span
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13204 class="cmtt-8"> 0.0047400328,</span><span
13205 class="cmtt-8"> </span><span
13206 class="cmtt-8"> 0.0050480668,</span>
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13213 class="cmtt-8"> 0.0053761186,</span><span
13214 class="cmtt-8"> </span><span
13215 class="cmtt-8"> 0.0057254891,</span><span
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13217 class="cmtt-8"> 0.0060975636,</span><span
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13219 class="cmtt-8"> 0.0064938176,</span>
13220 <br class="fancyvrb" /><a
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13226 class="cmtt-8"> 0.0069158225,</span><span
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13232 class="cmtt-8"> 0.0083536271,</span>
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13263 class="cmtt-8"> 0.013823725,</span>
13264 <br class="fancyvrb" /><a
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13276 class="cmtt-8"> 0.016697687,</span><span
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13289 class="cmtt-8"> 0.020169149,</span><span
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13292 class="cmtt-8"> 0.021479854,</span><span
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13294 class="cmtt-8"> </span><span
13295 class="cmtt-8"> 0.022875735,</span>
13296 <br class="fancyvrb" /><a
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13301 class="cmtt-8"> </span><span
13302 class="cmtt-8"> 0.024362330,</span><span
13303 class="cmtt-8"> </span><span
13304 class="cmtt-8"> </span><span
13305 class="cmtt-8"> 0.025945531,</span><span
13306 class="cmtt-8"> </span><span
13307 class="cmtt-8"> </span><span
13308 class="cmtt-8"> 0.027631618,</span><span
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13310 class="cmtt-8"> </span><span
13311 class="cmtt-8"> 0.029427276,</span>
13312 <br class="fancyvrb" /><a
13313 id="x1-125102r51"></a><span
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13315 class="cmtt-8"> </span><span
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13317 class="cmtt-8"> </span><span
13318 class="cmtt-8"> 0.031339626,</span><span
13319 class="cmtt-8"> </span><span
13320 class="cmtt-8"> </span><span
13321 class="cmtt-8"> 0.033376252,</span><span
13322 class="cmtt-8"> </span><span
13323 class="cmtt-8"> </span><span
13324 class="cmtt-8"> 0.035545228,</span><span
13325 class="cmtt-8"> </span><span
13326 class="cmtt-8"> </span><span
13327 class="cmtt-8"> 0.037855157,</span>
13328 <br class="fancyvrb" /><a
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13334 class="cmtt-8"> 0.040315199,</span><span
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13336 class="cmtt-8"> </span><span
13337 class="cmtt-8"> 0.042935108,</span><span
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13340 class="cmtt-8"> 0.045725273,</span><span
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13343 class="cmtt-8"> 0.048696758,</span>
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13350 class="cmtt-8"> 0.051861348,</span><span
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13353 class="cmtt-8"> 0.055231591,</span><span
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13355 class="cmtt-8"> </span><span
13356 class="cmtt-8"> 0.058820850,</span><span
13357 class="cmtt-8"> </span><span
13358 class="cmtt-8"> </span><span
13359 class="cmtt-8"> 0.062643361,</span>
13360 <br class="fancyvrb" /><a
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13369 class="cmtt-8"> 0.071049749,</span><span
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13375 class="cmtt-8"> 0.080584227,</span>
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13382 class="cmtt-8"> 0.085821044,</span><span
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13385 class="cmtt-8"> 0.091398179,</span><span
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13387 class="cmtt-8"> </span><span
13388 class="cmtt-8"> 0.097337747,</span><span
13389 class="cmtt-8"> </span><span
13390 class="cmtt-8"> </span><span
13391 class="cmtt-8"> 0.10366330,</span>
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13398 class="cmtt-8"> 0.11039993,</span><span
13399 class="cmtt-8"> </span><span
13400 class="cmtt-8"> </span><span
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13416 class="cmtt-8"> </span><span
13417 class="cmtt-8"> 0.14201813,</span><span
13418 class="cmtt-8"> </span><span
13419 class="cmtt-8"> </span><span
13420 class="cmtt-8"> </span><span
13421 class="cmtt-8"> 0.15124727,</span><span
13422 class="cmtt-8"> </span><span
13423 class="cmtt-8"> </span><span
13424 class="cmtt-8"> </span><span
13425 class="cmtt-8"> 0.16107617,</span><span
13426 class="cmtt-8"> </span><span
13427 class="cmtt-8"> </span><span
13428 class="cmtt-8"> </span><span
13429 class="cmtt-8"> 0.17154380,</span>
13430 <br class="fancyvrb" /><a
13431 id="x1-125116r58"></a><span
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13436 class="cmtt-8"> 0.18269168,</span><span
13437 class="cmtt-8"> </span><span
13438 class="cmtt-8"> </span><span
13439 class="cmtt-8"> </span><span
13440 class="cmtt-8"> 0.19456402,</span><span
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13442 class="cmtt-8"> </span><span
13443 class="cmtt-8"> </span><span
13444 class="cmtt-8"> 0.20720788,</span><span
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13448 class="cmtt-8"> 0.22067342,</span>
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13455 class="cmtt-8"> 0.23501402,</span><span
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13459 class="cmtt-8"> 0.25028656,</span><span
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13462 class="cmtt-8"> </span><span
13463 class="cmtt-8"> 0.26655159,</span><span
13464 class="cmtt-8"> </span><span
13465 class="cmtt-8"> </span><span
13466 class="cmtt-8"> </span><span
13467 class="cmtt-8"> 0.28387361,</span>
13468 <br class="fancyvrb" /><a
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13474 class="cmtt-8"> 0.30232132,</span><span
13475 class="cmtt-8"> </span><span
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13477 class="cmtt-8"> </span><span
13478 class="cmtt-8"> 0.32196786,</span><span
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13480 class="cmtt-8"> </span><span
13481 class="cmtt-8"> </span><span
13482 class="cmtt-8"> 0.34289114,</span><span
13483 class="cmtt-8"> </span><span
13484 class="cmtt-8"> </span><span
13485 class="cmtt-8"> </span><span
13486 class="cmtt-8"> 0.36517414,</span>
13487 <br class="fancyvrb" /><a
13488 id="x1-125122r61"></a><span
13489 class="cmr-6">61</span><span
13490 class="cmtt-8"> </span><span
13491 class="cmtt-8"> </span><span
13492 class="cmtt-8"> </span><span
13493 class="cmtt-8"> 0.38890521,</span><span
13494 class="cmtt-8"> </span><span
13495 class="cmtt-8"> </span><span
13496 class="cmtt-8"> </span><span
13497 class="cmtt-8"> 0.41417847,</span><span
13498 class="cmtt-8"> </span><span
13499 class="cmtt-8"> </span><span
13500 class="cmtt-8"> </span><span
13501 class="cmtt-8"> 0.44109412,</span><span
13502 class="cmtt-8"> </span><span
13503 class="cmtt-8"> </span><span
13504 class="cmtt-8"> </span><span
13505 class="cmtt-8"> 0.46975890,</span>
13506 <br class="fancyvrb" /><a
13507 id="x1-125124r62"></a><span
13508 class="cmr-6">62</span><span
13509 class="cmtt-8"> </span><span
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13511 class="cmtt-8"> </span><span
13512 class="cmtt-8"> 0.50028648,</span><span
13513 class="cmtt-8"> </span><span
13514 class="cmtt-8"> </span><span
13515 class="cmtt-8"> </span><span
13516 class="cmtt-8"> 0.53279791,</span><span
13517 class="cmtt-8"> </span><span
13518 class="cmtt-8"> </span><span
13519 class="cmtt-8"> </span><span
13520 class="cmtt-8"> 0.56742212,</span><span
13521 class="cmtt-8"> </span><span
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13523 class="cmtt-8"> </span><span
13524 class="cmtt-8"> 0.60429640,</span>
13525 <br class="fancyvrb" /><a
13526 id="x1-125126r63"></a><span
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13530 class="cmtt-8"> </span><span
13531 class="cmtt-8"> 0.64356699,</span><span
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13535 class="cmtt-8"> 0.68538959,</span><span
13536 class="cmtt-8"> </span><span
13537 class="cmtt-8"> </span><span
13538 class="cmtt-8"> </span><span
13539 class="cmtt-8"> 0.72993007,</span><span
13540 class="cmtt-8"> </span><span
13541 class="cmtt-8"> </span><span
13542 class="cmtt-8"> </span><span
13543 class="cmtt-8"> 0.77736504,</span>
13544 <br class="fancyvrb" /><a
13545 id="x1-125128r64"></a><span
13546 class="cmr-6">64</span><span
13547 class="cmtt-8"> </span><span
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13549 class="cmtt-8"> </span><span
13550 class="cmtt-8"> 0.82788260,</span><span
13551 class="cmtt-8"> </span><span
13552 class="cmtt-8"> </span><span
13553 class="cmtt-8"> </span><span
13554 class="cmtt-8"> 0.88168307,</span><span
13555 class="cmtt-8"> </span><span
13556 class="cmtt-8"> </span><span
13557 class="cmtt-8"> </span><span
13558 class="cmtt-8"> 0.9389798,</span><span
13559 class="cmtt-8"> </span><span
13560 class="cmtt-8"> </span><span
13561 class="cmtt-8"> </span><span
13562 class="cmtt-8"> </span><span
13563 class="cmtt-8"> 1.</span>
13571 <h3 class="sectionHead"><span class="titlemark">A. </span> <a
13572 id="x1-126000A"></a>Embedding Vorbis into an Ogg stream</h3>
13573 <!--l. 6--><p class="noindent" >
13574 <h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a
13575 id="x1-127000A.1"></a>Overview</h4>
13576 <!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
13577 compressed audio packet data into file form.
13578 <!--l. 12--><p class="noindent" >The <a
13579 href="#x1-20001">Section 1</a>, “<a
13580 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of
13581 Vorbis audio packets.
13582 <!--l. 15--><p class="noindent" >The <a
13583 href="oggstream.html" >Ogg bitstream overview</a> and <a
13584 href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
13585 descriptions of Ogg transport streams. This specification document assumes a working
13586 knowledge of the concepts covered in these named backround documents. Please read them
13588 <!--l. 22--><p class="noindent" >
13589 <h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a
13590 id="x1-128000A.1.1"></a>Restrictions</h5>
13591 <!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
13592 streams in degenerate, unmultiplexed form only. That is:
13593 <ul class="itemize1">
13594 <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
13596 <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
13599 <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
13605 <!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
13606 types into a multi-stream Ogg file. At the time this document was written, Ogg was
13607 becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
13608 audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
13609 within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
13610 implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
13611 stream (naturally, application authors are encouraged to support full multiplexed Ogg
13613 <!--l. 55--><p class="noindent" >
13614 <h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a
13615 id="x1-129000A.1.2"></a>MIME type</h5>
13616 <!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
13617 applications should use <span
13618 class="cmtt-12">application/ogg</span>, while visual media should use <span
13619 class="cmtt-12">video/ogg</span>, and audio
13621 class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP
13622 encapsulated Vorbis should use <span
13623 class="cmtt-12">audio/vorbis </span>+ <span
13624 class="cmtt-12">audio/vorbis-config</span>.
13625 <!--l. 65--><p class="noindent" >
13626 <h4 class="subsectionHead"><span class="titlemark">A.2. </span> <a
13627 id="x1-130000A.2"></a>Encapsulation</h4>
13628 <!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
13629 <ul class="itemize1">
13630 <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
13631 as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
13632 results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
13635 <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
13637 <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
13638 more pages beginning on the second page of the logical stream. However many pages
13639 they span, the third header packet finishes the page on which it ends. The next (first
13640 audio) packet must begin on a fresh page.
13645 <li class="itemize">The granule position of these first pages containing only headers is zero.
13647 <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
13649 <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
13651 <li class="itemize">The last page is marked ’end of stream’ in the page flags.
13653 <li class="itemize">Vorbis packets may span page boundaries.
13655 <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
13656 samples (per channel; a stereo stream’s granule position does not increment at twice
13657 the speed of a mono stream).
13659 <li class="itemize">The granule position of a page represents the end PCM sample position of the last
13661 class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
13662 returned by decode, not an internal sample awaiting lapping with a subsequent block.
13663 A page that is entirely spanned by a single packet (that completes on a subsequent
13664 page) has no granule position, and the granule position is set to ’-1’.
13665 <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
13666 necessarily the middle sample from that block. If, eg, the current Vorbis packet
13667 encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
13668 decodable sample from the current packet be at position (3*long_block_length/4) -
13669 (short_block_length/4).
13671 <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
13672 started at position zero. Although the granule position belongs to the last completed
13673 packet on the page and a valid granule position must be positive, by inference it may
13674 indicate that the PCM position of the beginning of audio is positive or negative.
13675 <ul class="itemize2">
13676 <li class="itemize">A positive starting value simply indicates that this stream begins at some
13677 positive time offset, potentially within a larger program. This is a common case
13678 when connecting to the middle of broadcast stream.
13680 <li class="itemize">A negative value indicates that output samples preceeding time zero should be
13684 discarded during decoding; this technique is used to allow sample-granularity
13685 editing of the stream start time of already-encoded Vorbis streams. The number
13686 of samples to be discarded must not exceed the overlap-add span of the first two
13689 <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
13690 second finished audio packet must flush the page on which it appears and the
13691 third packet begin a fresh page. This allows the decoder to always be able to
13692 perform PCM position adjustments before needing to return any PCM data from
13693 synthesis, resulting in correct positioning information without any aditional seeking
13695 <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
13696 id="x1-131000A.2"></a><span
13697 class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return
13698 incorrect positioning information for seeking operations at the very beginning of the
13701 <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the
13702 final packet would normally return is used to end the stream on other than even frame
13703 boundaries. The difference between the actual available data returned and the
13704 declared amount indicates how many trailing samples to discard from the decoding
13710 <h3 class="sectionHead"><span class="titlemark">B. </span> <a
13711 id="x1-132000B"></a>Vorbis encapsulation in RTP</h3>
13712 <!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
13713 class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
13714 how to embed Vorbis audio in an RTP stream.
13721 <h3 class="likesectionHead"><a
13722 id="x1-133000B"></a>Colophon</h3>
13723 <!--l. 6--><p class="noindent" ><img
13724 src="Vorbis_I_spec13x.png" alt="PIC" class="graphics"><!--tex4ht:graphics
13725 name="Vorbis_I_spec13x.png" src="xifish.pdf"
13727 <!--l. 10--><p class="noindent" >Ogg is a <a
13728 href="http://www.xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from
13729 corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
13731 href="http://www.xiph.org/about.html" >About the Xiph.Org Foundation</a> for details.
13732 <!--l. 17--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
13733 Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.Org
13734 Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification
13735 and certify specification compliance.
13736 <!--l. 23--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
13737 does not restrict third parties from distributing independent implementations of Vorbis software
13738 under other licenses.
13739 <!--l. 28--><p class="noindent" >Ogg, Vorbis, Xiph.Org Foundation and their logos are trademarks (tm) of the <a
13740 href="http://www.xiph.org/" >Xiph.Org
13741 Foundation</a>. These pages are copyright (C) 1994-2007 Xiph.Org Foundation. All rights
13743 <!--l. 33--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
13744 class="E">E</span>X</span></span>.
13748 <h3 class="likesectionHead"><a
13749 id="x1-134000B"></a>References</h3>
13750 <!--l. 125--><p class="noindent" >
13751 <div class="thebibliography">
13752 <p class="bibitem" ><span class="biblabel">
13753 [1]<span class="bibsp">   </span></span><a
13754 id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
13755 B. Edler, The use of multirate filter banks for coding of high quality digital audio,
13757 href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span
13758 class="cmtt-12">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.
projects / platform / upstream / libvorbis.git / blob