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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 27, 2015</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="#x1-580003.3" id="QQ2-1-63">Use of the codebook abstraction</a></span>
104 <br /> <span class="sectionToc" >4 <a
105 href="#x1-590004" id="QQ2-1-64">Codec Setup and Packet Decode</a></span>
106 <br />  <span class="subsectionToc" >4.1 <a
107 href="#x1-600004.1" id="QQ2-1-65">Overview</a></span>
108 <br />  <span class="subsectionToc" >4.2 <a
109 href="#x1-610004.2" id="QQ2-1-66">Header decode and decode setup</a></span>
110 <br />   <span class="subsubsectionToc" >4.2.1 <a
111 href="#x1-620004.2.1" id="QQ2-1-67">Common header decode</a></span>
112 <br />   <span class="subsubsectionToc" >4.2.2 <a
113 href="#x1-630004.2.2" id="QQ2-1-68">Identification header</a></span>
114 <br />   <span class="subsubsectionToc" >4.2.3 <a
115 href="#x1-640004.2.3" id="QQ2-1-69">Comment header</a></span>
119 <br />   <span class="subsubsectionToc" >4.2.4 <a
120 href="#x1-650004.2.4" id="QQ2-1-70">Setup header</a></span>
121 <br />  <span class="subsectionToc" >4.3 <a
122 href="#x1-720004.3" id="QQ2-1-78">Audio packet decode and synthesis</a></span>
123 <br />   <span class="subsubsectionToc" >4.3.1 <a
124 href="#x1-730004.3.1" id="QQ2-1-79">packet type, mode and window decode</a></span>
125 <br />   <span class="subsubsectionToc" >4.3.2 <a
126 href="#x1-740004.3.2" id="QQ2-1-80">floor curve decode</a></span>
127 <br />   <span class="subsubsectionToc" >4.3.3 <a
128 href="#x1-750004.3.3" id="QQ2-1-81">nonzero vector propagate</a></span>
129 <br />   <span class="subsubsectionToc" >4.3.4 <a
130 href="#x1-760004.3.4" id="QQ2-1-82">residue decode</a></span>
131 <br />   <span class="subsubsectionToc" >4.3.5 <a
132 href="#x1-770004.3.5" id="QQ2-1-83">inverse coupling</a></span>
133 <br />   <span class="subsubsectionToc" >4.3.6 <a
134 href="#x1-780004.3.6" id="QQ2-1-84">dot product</a></span>
135 <br />   <span class="subsubsectionToc" >4.3.7 <a
136 href="#x1-790004.3.7" id="QQ2-1-85">inverse MDCT</a></span>
137 <br />   <span class="subsubsectionToc" >4.3.8 <a
138 href="#x1-800004.3.8" id="QQ2-1-86">overlap_add</a></span>
139 <br />   <span class="subsubsectionToc" >4.3.9 <a
140 href="#x1-810004.3.9" id="QQ2-1-87">output channel order</a></span>
141 <br /> <span class="sectionToc" >5 <a
142 href="#x1-820005" id="QQ2-1-88">comment field and header specification</a></span>
143 <br />  <span class="subsectionToc" >5.1 <a
144 href="#x1-830005.1" id="QQ2-1-89">Overview</a></span>
145 <br />  <span class="subsectionToc" >5.2 <a
146 href="#x1-840005.2" id="QQ2-1-90">Comment encoding</a></span>
147 <br />   <span class="subsubsectionToc" >5.2.1 <a
148 href="#x1-850005.2.1" id="QQ2-1-91">Structure</a></span>
149 <br />   <span class="subsubsectionToc" >5.2.2 <a
150 href="#x1-860005.2.2" id="QQ2-1-92">Content vector format</a></span>
151 <br />   <span class="subsubsectionToc" >5.2.3 <a
152 href="#x1-890005.2.3" id="QQ2-1-95">Encoding</a></span>
153 <br /> <span class="sectionToc" >6 <a
154 href="#x1-900006" id="QQ2-1-96">Floor type 0 setup and decode</a></span>
155 <br />  <span class="subsectionToc" >6.1 <a
156 href="#x1-910006.1" id="QQ2-1-97">Overview</a></span>
157 <br />  <span class="subsectionToc" >6.2 <a
158 href="#x1-920006.2" id="QQ2-1-98">Floor 0 format</a></span>
159 <br />   <span class="subsubsectionToc" >6.2.1 <a
160 href="#x1-930006.2.1" id="QQ2-1-99">header decode</a></span>
161 <br />   <span class="subsubsectionToc" >6.2.2 <a
162 href="#x1-940006.2.2" id="QQ2-1-100">packet decode</a></span>
163 <br />   <span class="subsubsectionToc" >6.2.3 <a
164 href="#x1-950006.2.3" id="QQ2-1-101">curve computation</a></span>
165 <br /> <span class="sectionToc" >7 <a
166 href="#x1-970007" id="QQ2-1-103">Floor type 1 setup and decode</a></span>
167 <br />  <span class="subsectionToc" >7.1 <a
168 href="#x1-980007.1" id="QQ2-1-104">Overview</a></span>
169 <br />  <span class="subsectionToc" >7.2 <a
170 href="#x1-990007.2" id="QQ2-1-105">Floor 1 format</a></span>
171 <br />   <span class="subsubsectionToc" >7.2.1 <a
172 href="#x1-1000007.2.1" id="QQ2-1-106">model</a></span>
173 <br />   <span class="subsubsectionToc" >7.2.2 <a
174 href="#x1-1010007.2.2" id="QQ2-1-111">header decode</a></span>
175 <br />   <span class="subsubsectionToc" >7.2.3 <a
176 href="#x1-1020007.2.3" id="QQ2-1-112">packet decode</a></span>
180 <br />   <span class="subsubsectionToc" >7.2.4 <a
181 href="#x1-1030007.2.4" id="QQ2-1-113">curve computation</a></span>
182 <br /> <span class="sectionToc" >8 <a
183 href="#x1-1040008" id="QQ2-1-114">Residue setup and decode</a></span>
184 <br />  <span class="subsectionToc" >8.1 <a
185 href="#x1-1050008.1" id="QQ2-1-115">Overview</a></span>
186 <br />  <span class="subsectionToc" >8.2 <a
187 href="#x1-1060008.2" id="QQ2-1-116">Residue format</a></span>
188 <br />  <span class="subsectionToc" >8.3 <a
189 href="#x1-1070008.3" id="QQ2-1-118">residue 0</a></span>
190 <br />  <span class="subsectionToc" >8.4 <a
191 href="#x1-1080008.4" id="QQ2-1-119">residue 1</a></span>
192 <br />  <span class="subsectionToc" >8.5 <a
193 href="#x1-1090008.5" id="QQ2-1-120">residue 2</a></span>
194 <br />  <span class="subsectionToc" >8.6 <a
195 href="#x1-1100008.6" id="QQ2-1-122">Residue decode</a></span>
196 <br />   <span class="subsubsectionToc" >8.6.1 <a
197 href="#x1-1110008.6.1" id="QQ2-1-123">header decode</a></span>
198 <br />   <span class="subsubsectionToc" >8.6.2 <a
199 href="#x1-1120008.6.2" id="QQ2-1-124">packet decode</a></span>
200 <br />   <span class="subsubsectionToc" >8.6.3 <a
201 href="#x1-1130008.6.3" id="QQ2-1-125">format 0 specifics</a></span>
202 <br />   <span class="subsubsectionToc" >8.6.4 <a
203 href="#x1-1140008.6.4" id="QQ2-1-126">format 1 specifics</a></span>
204 <br />   <span class="subsubsectionToc" >8.6.5 <a
205 href="#x1-1150008.6.5" id="QQ2-1-127">format 2 specifics</a></span>
206 <br /> <span class="sectionToc" >9 <a
207 href="#x1-1160009" id="QQ2-1-128">Helper equations</a></span>
208 <br />  <span class="subsectionToc" >9.1 <a
209 href="#x1-1170009.1" id="QQ2-1-129">Overview</a></span>
210 <br />  <span class="subsectionToc" >9.2 <a
211 href="#x1-1180009.2" id="QQ2-1-130">Functions</a></span>
212 <br />   <span class="subsubsectionToc" >9.2.1 <a
213 href="#x1-1190009.2.1" id="QQ2-1-131">ilog</a></span>
214 <br />   <span class="subsubsectionToc" >9.2.2 <a
215 href="#x1-1200009.2.2" id="QQ2-1-132">float32_unpack</a></span>
216 <br />   <span class="subsubsectionToc" >9.2.3 <a
217 href="#x1-1210009.2.3" id="QQ2-1-133">lookup1_values</a></span>
218 <br />   <span class="subsubsectionToc" >9.2.4 <a
219 href="#x1-1220009.2.4" id="QQ2-1-134">low_neighbor</a></span>
220 <br />   <span class="subsubsectionToc" >9.2.5 <a
221 href="#x1-1230009.2.5" id="QQ2-1-135">high_neighbor</a></span>
222 <br />   <span class="subsubsectionToc" >9.2.6 <a
223 href="#x1-1240009.2.6" id="QQ2-1-136">render_point</a></span>
224 <br />   <span class="subsubsectionToc" >9.2.7 <a
225 href="#x1-1250009.2.7" id="QQ2-1-137">render_line</a></span>
226 <br /> <span class="sectionToc" >10 <a
227 href="#x1-12600010" id="QQ2-1-138">Tables</a></span>
228 <br />  <span class="subsectionToc" >10.1 <a
229 href="#x1-12700010.1" id="QQ2-1-139">floor1_inverse_dB_table</a></span>
230 <br /> <span class="sectionToc" >A <a
231 href="#x1-128000A" id="QQ2-1-140">Embedding Vorbis into an Ogg stream</a></span>
232 <br />  <span class="subsectionToc" >A.1 <a
233 href="#x1-129000A.1" id="QQ2-1-141">Overview</a></span>
234 <br />   <span class="subsubsectionToc" >A.1.1 <a
235 href="#x1-130000A.1.1" id="QQ2-1-142">Restrictions</a></span>
236 <br />   <span class="subsubsectionToc" >A.1.2 <a
237 href="#x1-131000A.1.2" id="QQ2-1-143">MIME type</a></span>
241 <br />  <span class="subsectionToc" >A.2 <a
242 href="#x1-132000A.2" id="QQ2-1-144">Encapsulation</a></span>
243 <br /> <span class="sectionToc" >B <a
244 href="#x1-134000B" id="QQ2-1-146">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="#x1-590004">section 4</a>, “<a
257 href="#x1-590004">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="#x1-128000A">section A</a>,
311 href="#x1-128000A">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="#x1-820005">section 5</a>, “<a
500 href="#x1-820005">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"><a
746 id="x1-35002r1"></a><span
747 class="cmr-6">1</span><span
748 class="cmtt-8"> </span><span
749 class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span></div>
750 <!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
751 <!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
752 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
753 PCM output offset is ’0’ (as no data has been returned yet).
760 <h3 class="sectionHead"><span class="titlemark">2. </span> <a
761 id="x1-360002"></a>Bitpacking Convention</h3>
762 <!--l. 6--><p class="noindent" >
763 <h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a
764 id="x1-370002.1"></a>Overview</h4>
765 <!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
766 integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
767 encoder and then read one-by-one in the same monotonically increasing order by the decoder.
768 Most current binary storage arrangements group bits into a native word size of eight bits
769 (octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
770 bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
771 representation in fixed-width words.
772 <!--l. 19--><p class="noindent" >
773 <h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a
774 id="x1-380002.1.1"></a>octets, bytes and words</h5>
775 <!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
776 This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
777 For purposes of the bitpacking convention, a byte implies the native, smallest integer
778 storage representation offered by a platform. On modern platforms, this is generally
779 assumed to be eight bits (not necessarily because of the processor but because of the
780 filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
781 atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
783 <!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
784 to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
785 bitpacking convention is still well defined for any native byte size; Vorbis uses the native
786 bit-width of a given storage system. This document assumes that a byte is one octet for purposes
788 <!--l. 39--><p class="noindent" >
792 <h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a
793 id="x1-390002.1.2"></a>bit order</h5>
794 <!--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
795 storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
796 opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
797 class="cmmi-12">n </span>(<span
798 class="cmmi-12">n </span>= 7 in an
800 <!--l. 50--><p class="noindent" >
801 <h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a
802 id="x1-400002.1.3"></a>byte order</h5>
803 <!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
804 common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
805 highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
806 which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
808 <!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
809 word, level, thus host word ordering is of a concern only during optimization when writing high
810 performance code that operates on a word of storage at a time rather than by byte.
811 Logically, bytes are always coded and decoded in order from byte zero through byte
813 class="cmmi-12">n</span>.
814 <!--l. 68--><p class="noindent" >
815 <h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a
816 id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
817 <!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
818 wide, into packets. These integer fields are not aligned to the boundaries of the byte
819 representation; the next field is written at the bit position at which the previous field
821 <!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
822 bitstream first, followed by next least significant bit, etc, until the requested number of bits
823 have been coded. When packing the bits into bytes, the encoder begins by placing
824 the LSb of the integer to be written into the least significant unused bit position of
825 the destination byte, followed by the next-least significant bit of the source integer
826 and so on up to the requested number of bits. When all bits of the destination byte
827 have been filled, encoding continues by zeroing all bits of the next byte and writing
828 the next bit into the bit position 0 of that byte. Decoding follows the same process
832 as encoding, but by reading bits from the byte stream and reassembling them into
834 <!--l. 90--><p class="noindent" >
835 <h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a
836 id="x1-420002.1.5"></a>signedness</h5>
837 <!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
838 given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
839 either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
840 encoder and decoder are responsible for knowing if fields are to be treated as signed or
842 <!--l. 101--><p class="noindent" >
843 <h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a
844 id="x1-430002.1.6"></a>coding example</h5>
845 <!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
846 <!--l. 106--><p class="noindent" >
847 <div class="fancyvrb" id="fancyvrb2"><a
848 id="x1-43002r1"></a><span
849 class="cmr-6">1</span><span
850 class="cmtt-8"> </span><span
851 class="cmtt-8"> </span><span
852 class="cmtt-8"> </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><br class="fancyvrb" /><a
866 id="x1-43004r2"></a><span
867 class="cmr-6">2</span><span
868 class="cmtt-8"> </span><span
869 class="cmtt-8"> </span><span
870 class="cmtt-8"> </span><span
871 class="cmtt-8"> </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"> V</span><br class="fancyvrb" /><a
884 id="x1-43006r3"></a><span
885 class="cmr-6">3</span><span
886 class="cmtt-8"> </span><span
887 class="cmtt-8"> </span><br class="fancyvrb" /><a
888 id="x1-43008r4"></a><span
889 class="cmr-6">4</span><span
890 class="cmtt-8"> </span><span
891 class="cmtt-8"> </span><span
892 class="cmtt-8"> </span><span
893 class="cmtt-8"> </span><span
894 class="cmtt-8"> </span><span
895 class="cmtt-8"> </span><span
896 class="cmtt-8"> </span><span
897 class="cmtt-8"> </span><span
898 class="cmtt-8"> </span><span
899 class="cmtt-8"> 7</span><span
900 class="cmtt-8"> 6</span><span
901 class="cmtt-8"> 5</span><span
902 class="cmtt-8"> 4</span><span
903 class="cmtt-8"> 3</span><span
904 class="cmtt-8"> 2</span><span
905 class="cmtt-8"> 1</span><span
906 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
907 id="x1-43010r5"></a><span
908 class="cmr-6">5</span><span
909 class="cmtt-8"> </span><span
910 class="cmtt-8"> byte</span><span
911 class="cmtt-8"> 0</span><span
912 class="cmtt-8"> [0</span><span
913 class="cmtt-8"> 0</span><span
914 class="cmtt-8"> 0</span><span
915 class="cmtt-8"> 0</span><span
916 class="cmtt-8"> 1</span><span
917 class="cmtt-8"> 1</span><span
918 class="cmtt-8"> 0</span><span
919 class="cmtt-8"> 0]</span><span
920 class="cmtt-8"> </span><span
921 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
922 id="x1-43012r6"></a><span
923 class="cmr-6">6</span><span
924 class="cmtt-8"> </span><span
925 class="cmtt-8"> byte</span><span
926 class="cmtt-8"> 1</span><span
927 class="cmtt-8"> [</span><span
928 class="cmtt-8"> </span><span
929 class="cmtt-8"> </span><span
930 class="cmtt-8"> </span><span
931 class="cmtt-8"> </span><span
932 class="cmtt-8"> </span><span
933 class="cmtt-8"> </span><span
934 class="cmtt-8"> </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>
943 <br class="fancyvrb" /><a
944 id="x1-43014r7"></a><span
945 class="cmr-6">7</span><span
946 class="cmtt-8"> </span><span
947 class="cmtt-8"> byte</span><span
948 class="cmtt-8"> 2</span><span
949 class="cmtt-8"> [</span><span
950 class="cmtt-8"> </span><span
951 class="cmtt-8"> </span><span
952 class="cmtt-8"> </span><span
953 class="cmtt-8"> </span><span
954 class="cmtt-8"> </span><span
955 class="cmtt-8"> </span><span
956 class="cmtt-8"> </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><br class="fancyvrb" /><a
965 id="x1-43016r8"></a><span
966 class="cmr-6">8</span><span
967 class="cmtt-8"> </span><span
968 class="cmtt-8"> byte</span><span
969 class="cmtt-8"> 3</span><span
970 class="cmtt-8"> [</span><span
971 class="cmtt-8"> </span><span
972 class="cmtt-8"> </span><span
973 class="cmtt-8"> </span><span
974 class="cmtt-8"> </span><span
975 class="cmtt-8"> </span><span
976 class="cmtt-8"> </span><span
977 class="cmtt-8"> </span><span
978 class="cmtt-8"> </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><br class="fancyvrb" /><a
986 id="x1-43018r9"></a><span
987 class="cmr-6">9</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><span
995 class="cmtt-8"> </span><span
996 class="cmtt-8"> </span><span
997 class="cmtt-8"> </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><br class="fancyvrb" /><a
1003 id="x1-43020r10"></a><span
1004 class="cmr-6">10</span><span
1005 class="cmtt-8"> </span><span
1006 class="cmtt-8"> byte</span><span
1007 class="cmtt-8"> n</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><span
1013 class="cmtt-8"> </span><span
1014 class="cmtt-8"> </span><span
1015 class="cmtt-8"> </span><span
1016 class="cmtt-8"> </span><span
1017 class="cmtt-8"> </span><span
1018 class="cmtt-8"> </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"> bytestream</span><span
1026 class="cmtt-8"> length</span><span
1027 class="cmtt-8"> ==</span><span
1028 class="cmtt-8"> 1</span><span
1029 class="cmtt-8"> byte</span><br class="fancyvrb" /><a
1030 id="x1-43022r11"></a><span
1031 class="cmr-6">11</span><span
1032 class="cmtt-8"> </span><span
1033 class="cmtt-8"> </span></div>
1034 <!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
1035 <!--l. 123--><p class="noindent" >
1036 <div class="fancyvrb" id="fancyvrb3"><a
1037 id="x1-43024r1"></a><span
1038 class="cmr-6">1</span><span
1039 class="cmtt-8"> </span><span
1040 class="cmtt-8"> </span><span
1041 class="cmtt-8"> </span><span
1042 class="cmtt-8"> </span><span
1043 class="cmtt-8"> </span><span
1044 class="cmtt-8"> </span><span
1045 class="cmtt-8"> </span><span
1046 class="cmtt-8"> </span><span
1047 class="cmtt-8"> </span><span
1048 class="cmtt-8"> |</span><br class="fancyvrb" /><a
1049 id="x1-43026r2"></a><span
1050 class="cmr-6">2</span><span
1051 class="cmtt-8"> </span><span
1052 class="cmtt-8"> </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"> V</span><br class="fancyvrb" /><a
1061 id="x1-43028r3"></a><span
1062 class="cmr-6">3</span><span
1063 class="cmtt-8"> </span><span
1064 class="cmtt-8"> </span><br class="fancyvrb" /><a
1065 id="x1-43030r4"></a><span
1066 class="cmr-6">4</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"> </span><span
1076 class="cmtt-8"> 7</span><span
1077 class="cmtt-8"> 6</span><span
1078 class="cmtt-8"> 5</span><span
1079 class="cmtt-8"> 4</span><span
1080 class="cmtt-8"> 3</span><span
1081 class="cmtt-8"> 2</span><span
1082 class="cmtt-8"> 1</span><span
1083 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1084 id="x1-43032r5"></a><span
1085 class="cmr-6">5</span><span
1086 class="cmtt-8"> </span><span
1087 class="cmtt-8"> byte</span><span
1088 class="cmtt-8"> 0</span><span
1089 class="cmtt-8"> [0</span><span
1090 class="cmtt-8"> 1</span><span
1091 class="cmtt-8"> 1</span><span
1092 class="cmtt-8"> 1</span><span
1093 class="cmtt-8"> 1</span><span
1094 class="cmtt-8"> 1</span><span
1095 class="cmtt-8"> 0</span><span
1096 class="cmtt-8"> 0]</span><span
1097 class="cmtt-8"> </span><span
1098 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1099 id="x1-43034r6"></a><span
1100 class="cmr-6">6</span><span
1101 class="cmtt-8"> </span><span
1102 class="cmtt-8"> byte</span><span
1103 class="cmtt-8"> 1</span><span
1104 class="cmtt-8"> [</span><span
1105 class="cmtt-8"> </span><span
1106 class="cmtt-8"> </span><span
1107 class="cmtt-8"> </span><span
1108 class="cmtt-8"> </span><span
1109 class="cmtt-8"> </span><span
1110 class="cmtt-8"> </span><span
1111 class="cmtt-8"> </span><span
1112 class="cmtt-8"> </span><span
1113 class="cmtt-8"> </span><span
1114 class="cmtt-8"> </span><span
1115 class="cmtt-8"> </span><span
1116 class="cmtt-8"> </span><span
1117 class="cmtt-8"> </span><span
1118 class="cmtt-8"> </span><span
1119 class="cmtt-8"> ]</span>
1120 <br class="fancyvrb" /><a
1121 id="x1-43036r7"></a><span
1122 class="cmr-6">7</span><span
1123 class="cmtt-8"> </span><span
1124 class="cmtt-8"> byte</span><span
1125 class="cmtt-8"> 2</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><span
1139 class="cmtt-8"> </span><span
1140 class="cmtt-8"> </span><span
1141 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1142 id="x1-43038r8"></a><span
1143 class="cmr-6">8</span><span
1144 class="cmtt-8"> </span><span
1145 class="cmtt-8"> byte</span><span
1146 class="cmtt-8"> 3</span><span
1147 class="cmtt-8"> [</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><br class="fancyvrb" /><a
1163 id="x1-43040r9"></a><span
1164 class="cmr-6">9</span><span
1165 class="cmtt-8"> </span><span
1166 class="cmtt-8"> </span><span
1167 class="cmtt-8"> </span><span
1168 class="cmtt-8"> </span><span
1169 class="cmtt-8"> </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><br class="fancyvrb" /><a
1180 id="x1-43042r10"></a><span
1181 class="cmr-6">10</span><span
1182 class="cmtt-8"> </span><span
1183 class="cmtt-8"> byte</span><span
1184 class="cmtt-8"> n</span><span
1185 class="cmtt-8"> [</span><span
1186 class="cmtt-8"> </span><span
1187 class="cmtt-8"> </span><span
1188 class="cmtt-8"> </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"> bytestream</span><span
1203 class="cmtt-8"> length</span><span
1204 class="cmtt-8"> ==</span><span
1205 class="cmtt-8"> 1</span><span
1206 class="cmtt-8"> byte</span></div>
1207 <!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
1208 <!--l. 139--><p class="noindent" >
1209 <div class="fancyvrb" id="fancyvrb4"><a
1210 id="x1-43044r1"></a><span
1211 class="cmr-6">1</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><br class="fancyvrb" /><a
1224 id="x1-43046r2"></a><span
1225 class="cmr-6">2</span><span
1226 class="cmtt-8"> </span><span
1227 class="cmtt-8"> </span><span
1228 class="cmtt-8"> </span><span
1229 class="cmtt-8"> </span><span
1230 class="cmtt-8"> </span><span
1231 class="cmtt-8"> </span><span
1232 class="cmtt-8"> </span><span
1233 class="cmtt-8"> </span><span
1234 class="cmtt-8"> </span><span
1235 class="cmtt-8"> </span><span
1236 class="cmtt-8"> </span><span
1237 class="cmtt-8"> V</span><br class="fancyvrb" /><a
1238 id="x1-43048r3"></a><span
1239 class="cmr-6">3</span><span
1240 class="cmtt-8"> </span><span
1241 class="cmtt-8"> </span><br class="fancyvrb" /><a
1242 id="x1-43050r4"></a><span
1243 class="cmr-6">4</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><span
1251 class="cmtt-8"> </span><span
1252 class="cmtt-8"> </span><span
1253 class="cmtt-8"> 7</span><span
1254 class="cmtt-8"> 6</span><span
1255 class="cmtt-8"> 5</span><span
1256 class="cmtt-8"> 4</span><span
1257 class="cmtt-8"> 3</span><span
1258 class="cmtt-8"> 2</span><span
1259 class="cmtt-8"> 1</span><span
1260 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1261 id="x1-43052r5"></a><span
1262 class="cmr-6">5</span><span
1263 class="cmtt-8"> </span><span
1264 class="cmtt-8"> byte</span><span
1265 class="cmtt-8"> 0</span><span
1266 class="cmtt-8"> [1</span><span
1267 class="cmtt-8"> 1</span><span
1268 class="cmtt-8"> 1</span><span
1269 class="cmtt-8"> 1</span><span
1270 class="cmtt-8"> 1</span><span
1271 class="cmtt-8"> 1</span><span
1272 class="cmtt-8"> 0</span><span
1273 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1274 id="x1-43054r6"></a><span
1275 class="cmr-6">6</span><span
1276 class="cmtt-8"> </span><span
1277 class="cmtt-8"> byte</span><span
1278 class="cmtt-8"> 1</span><span
1279 class="cmtt-8"> [0</span><span
1280 class="cmtt-8"> 0</span><span
1281 class="cmtt-8"> 0</span><span
1282 class="cmtt-8"> 0</span><span
1283 class="cmtt-8"> 1</span><span
1284 class="cmtt-8"> 0</span><span
1285 class="cmtt-8"> 0</span><span
1286 class="cmtt-8"> 0]</span><span
1287 class="cmtt-8"> </span><span
1288 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1289 id="x1-43056r7"></a><span
1290 class="cmr-6">7</span><span
1291 class="cmtt-8"> </span><span
1292 class="cmtt-8"> byte</span><span
1293 class="cmtt-8"> 2</span><span
1294 class="cmtt-8"> [</span><span
1295 class="cmtt-8"> </span><span
1296 class="cmtt-8"> </span><span
1297 class="cmtt-8"> </span><span
1298 class="cmtt-8"> </span><span
1299 class="cmtt-8"> </span><span
1300 class="cmtt-8"> </span><span
1301 class="cmtt-8"> </span><span
1302 class="cmtt-8"> </span><span
1303 class="cmtt-8"> </span><span
1304 class="cmtt-8"> </span><span
1305 class="cmtt-8"> </span><span
1306 class="cmtt-8"> </span><span
1307 class="cmtt-8"> </span><span
1308 class="cmtt-8"> </span><span
1309 class="cmtt-8"> ]</span>
1310 <br class="fancyvrb" /><a
1311 id="x1-43058r8"></a><span
1312 class="cmr-6">8</span><span
1313 class="cmtt-8"> </span><span
1314 class="cmtt-8"> byte</span><span
1315 class="cmtt-8"> 3</span><span
1316 class="cmtt-8"> [</span><span
1317 class="cmtt-8"> </span><span
1318 class="cmtt-8"> </span><span
1319 class="cmtt-8"> </span><span
1320 class="cmtt-8"> </span><span
1321 class="cmtt-8"> </span><span
1322 class="cmtt-8"> </span><span
1323 class="cmtt-8"> </span><span
1324 class="cmtt-8"> </span><span
1325 class="cmtt-8"> </span><span
1326 class="cmtt-8"> </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><br class="fancyvrb" /><a
1332 id="x1-43060r9"></a><span
1333 class="cmr-6">9</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><span
1343 class="cmtt-8"> </span><span
1344 class="cmtt-8"> </span><span
1345 class="cmtt-8"> </span><span
1346 class="cmtt-8"> </span><span
1347 class="cmtt-8"> </span><span
1348 class="cmtt-8"> ...</span><br class="fancyvrb" /><a
1349 id="x1-43062r10"></a><span
1350 class="cmr-6">10</span><span
1351 class="cmtt-8"> </span><span
1352 class="cmtt-8"> byte</span><span
1353 class="cmtt-8"> n</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><span
1365 class="cmtt-8"> </span><span
1366 class="cmtt-8"> </span><span
1367 class="cmtt-8"> </span><span
1368 class="cmtt-8"> </span><span
1369 class="cmtt-8"> ]</span><span
1370 class="cmtt-8"> </span><span
1371 class="cmtt-8"> bytestream</span><span
1372 class="cmtt-8"> length</span><span
1373 class="cmtt-8"> ==</span><span
1374 class="cmtt-8"> 2</span><span
1375 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1376 id="x1-43064r11"></a><span
1377 class="cmr-6">11</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><span
1383 class="cmtt-8"> </span><span
1384 class="cmtt-8"> </span><span
1385 class="cmtt-8"> </span><span
1386 class="cmtt-8"> </span><span
1387 class="cmtt-8"> </span><span
1388 class="cmtt-8"> </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"> bit</span><span
1406 class="cmtt-8"> cursor</span><span
1407 class="cmtt-8"> ==</span><span
1408 class="cmtt-8"> 6</span></div>
1409 <!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
1410 <!--l. 156--><p class="noindent" >
1411 <div class="fancyvrb" id="fancyvrb5"><a
1412 id="x1-43066r1"></a><span
1413 class="cmr-6">1</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><br class="fancyvrb" /><a
1432 id="x1-43068r2"></a><span
1433 class="cmr-6">2</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"> </span><span
1442 class="cmtt-8"> </span><span
1443 class="cmtt-8"> </span><span
1444 class="cmtt-8"> </span><span
1445 class="cmtt-8"> </span><span
1446 class="cmtt-8"> </span><span
1447 class="cmtt-8"> </span><span
1448 class="cmtt-8"> </span><span
1449 class="cmtt-8"> </span><span
1450 class="cmtt-8"> </span><span
1451 class="cmtt-8"> V</span><br class="fancyvrb" /><a
1452 id="x1-43070r3"></a><span
1453 class="cmr-6">3</span><span
1454 class="cmtt-8"> </span><span
1455 class="cmtt-8"> </span><br class="fancyvrb" /><a
1456 id="x1-43072r4"></a><span
1457 class="cmr-6">4</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"> 7</span><span
1468 class="cmtt-8"> 6</span><span
1469 class="cmtt-8"> 5</span><span
1470 class="cmtt-8"> 4</span><span
1471 class="cmtt-8"> 3</span><span
1472 class="cmtt-8"> 2</span><span
1473 class="cmtt-8"> 1</span><span
1474 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1475 id="x1-43074r5"></a><span
1476 class="cmr-6">5</span><span
1477 class="cmtt-8"> </span><span
1478 class="cmtt-8"> byte</span><span
1479 class="cmtt-8"> 0</span><span
1480 class="cmtt-8"> [1</span><span
1481 class="cmtt-8"> 1</span><span
1482 class="cmtt-8"> 1</span><span
1483 class="cmtt-8"> 1</span><span
1484 class="cmtt-8"> 1</span><span
1485 class="cmtt-8"> 1</span><span
1486 class="cmtt-8"> 0</span><span
1487 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1488 id="x1-43076r6"></a><span
1489 class="cmr-6">6</span><span
1490 class="cmtt-8"> </span><span
1491 class="cmtt-8"> byte</span><span
1492 class="cmtt-8"> 1</span><span
1493 class="cmtt-8"> [0</span><span
1494 class="cmtt-8"> 1</span><span
1495 class="cmtt-8"> 0</span><span
1496 class="cmtt-8"> 0</span><span
1497 class="cmtt-8"> 1</span><span
1498 class="cmtt-8"> 0</span><span
1499 class="cmtt-8"> 0</span><span
1500 class="cmtt-8"> 0]</span>
1501 <br class="fancyvrb" /><a
1502 id="x1-43078r7"></a><span
1503 class="cmr-6">7</span><span
1504 class="cmtt-8"> </span><span
1505 class="cmtt-8"> byte</span><span
1506 class="cmtt-8"> 2</span><span
1507 class="cmtt-8"> [1</span><span
1508 class="cmtt-8"> 1</span><span
1509 class="cmtt-8"> 0</span><span
1510 class="cmtt-8"> 0</span><span
1511 class="cmtt-8"> 1</span><span
1512 class="cmtt-8"> 1</span><span
1513 class="cmtt-8"> 1</span><span
1514 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1515 id="x1-43080r8"></a><span
1516 class="cmr-6">8</span><span
1517 class="cmtt-8"> </span><span
1518 class="cmtt-8"> byte</span><span
1519 class="cmtt-8"> 3</span><span
1520 class="cmtt-8"> [0</span><span
1521 class="cmtt-8"> 0</span><span
1522 class="cmtt-8"> 0</span><span
1523 class="cmtt-8"> 0</span><span
1524 class="cmtt-8"> 0</span><span
1525 class="cmtt-8"> 1</span><span
1526 class="cmtt-8"> 1</span><span
1527 class="cmtt-8"> 0]</span><span
1528 class="cmtt-8"> </span><span
1529 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1530 id="x1-43082r9"></a><span
1531 class="cmr-6">9</span><span
1532 class="cmtt-8"> </span><span
1533 class="cmtt-8"> </span><span
1534 class="cmtt-8"> </span><span
1535 class="cmtt-8"> </span><span
1536 class="cmtt-8"> </span><span
1537 class="cmtt-8"> </span><span
1538 class="cmtt-8"> </span><span
1539 class="cmtt-8"> </span><span
1540 class="cmtt-8"> </span><span
1541 class="cmtt-8"> </span><span
1542 class="cmtt-8"> </span><span
1543 class="cmtt-8"> </span><span
1544 class="cmtt-8"> </span><span
1545 class="cmtt-8"> </span><span
1546 class="cmtt-8"> ...</span><br class="fancyvrb" /><a
1547 id="x1-43084r10"></a><span
1548 class="cmr-6">10</span><span
1549 class="cmtt-8"> </span><span
1550 class="cmtt-8"> byte</span><span
1551 class="cmtt-8"> n</span><span
1552 class="cmtt-8"> [</span><span
1553 class="cmtt-8"> </span><span
1554 class="cmtt-8"> </span><span
1555 class="cmtt-8"> </span><span
1556 class="cmtt-8"> </span><span
1557 class="cmtt-8"> </span><span
1558 class="cmtt-8"> </span><span
1559 class="cmtt-8"> </span><span
1560 class="cmtt-8"> </span><span
1561 class="cmtt-8"> </span><span
1562 class="cmtt-8"> </span><span
1563 class="cmtt-8"> </span><span
1564 class="cmtt-8"> </span><span
1565 class="cmtt-8"> </span><span
1566 class="cmtt-8"> </span><span
1567 class="cmtt-8"> ]</span><span
1568 class="cmtt-8"> </span><span
1569 class="cmtt-8"> bytestream</span><span
1570 class="cmtt-8"> length</span><span
1571 class="cmtt-8"> ==</span><span
1572 class="cmtt-8"> 4</span><span
1573 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1574 id="x1-43086r11"></a><span
1575 class="cmr-6">11</span><span
1576 class="cmtt-8"> </span><span
1577 class="cmtt-8"> </span></div>
1581 <!--l. 173--><p class="noindent" >
1582 <h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a
1583 id="x1-440002.1.7"></a>decoding example</h5>
1584 <!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
1585 <!--l. 177--><p class="noindent" >
1586 <div class="fancyvrb" id="fancyvrb6"><a
1587 id="x1-44002r1"></a><span
1588 class="cmr-6">1</span><span
1589 class="cmtt-8"> </span><span
1590 class="cmtt-8"> </span><span
1591 class="cmtt-8"> </span><span
1592 class="cmtt-8"> </span><span
1593 class="cmtt-8"> </span><span
1594 class="cmtt-8"> </span><span
1595 class="cmtt-8"> </span><span
1596 class="cmtt-8"> </span><span
1597 class="cmtt-8"> </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><br class="fancyvrb" /><a
1613 id="x1-44004r2"></a><span
1614 class="cmr-6">2</span><span
1615 class="cmtt-8"> </span><span
1616 class="cmtt-8"> </span><span
1617 class="cmtt-8"> </span><span
1618 class="cmtt-8"> </span><span
1619 class="cmtt-8"> </span><span
1620 class="cmtt-8"> </span><span
1621 class="cmtt-8"> </span><span
1622 class="cmtt-8"> </span><span
1623 class="cmtt-8"> </span><span
1624 class="cmtt-8"> </span><span
1625 class="cmtt-8"> </span><span
1626 class="cmtt-8"> </span><span
1627 class="cmtt-8"> </span><span
1628 class="cmtt-8"> </span><span
1629 class="cmtt-8"> </span><span
1630 class="cmtt-8"> </span><span
1631 class="cmtt-8"> </span><span
1632 class="cmtt-8"> </span><span
1633 class="cmtt-8"> </span><span
1634 class="cmtt-8"> </span><span
1635 class="cmtt-8"> </span><span
1636 class="cmtt-8"> </span><span
1637 class="cmtt-8"> </span><span
1638 class="cmtt-8"> V</span><br class="fancyvrb" /><a
1639 id="x1-44006r3"></a><span
1640 class="cmr-6">3</span><span
1641 class="cmtt-8"> </span><span
1642 class="cmtt-8"> </span><br class="fancyvrb" /><a
1643 id="x1-44008r4"></a><span
1644 class="cmr-6">4</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"> 7</span><span
1655 class="cmtt-8"> 6</span><span
1656 class="cmtt-8"> 5</span><span
1657 class="cmtt-8"> 4</span><span
1658 class="cmtt-8"> 3</span><span
1659 class="cmtt-8"> 2</span><span
1660 class="cmtt-8"> 1</span><span
1661 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1662 id="x1-44010r5"></a><span
1663 class="cmr-6">5</span><span
1664 class="cmtt-8"> </span><span
1665 class="cmtt-8"> byte</span><span
1666 class="cmtt-8"> 0</span><span
1667 class="cmtt-8"> [1</span><span
1668 class="cmtt-8"> 1</span><span
1669 class="cmtt-8"> 1</span><span
1670 class="cmtt-8"> 1</span><span
1671 class="cmtt-8"> 1</span><span
1672 class="cmtt-8"> 1</span><span
1673 class="cmtt-8"> 0</span><span
1674 class="cmtt-8"> 0]</span><span
1675 class="cmtt-8"> </span><span
1676 class="cmtt-8"> <-</span>
1677 <br class="fancyvrb" /><a
1678 id="x1-44012r6"></a><span
1679 class="cmr-6">6</span><span
1680 class="cmtt-8"> </span><span
1681 class="cmtt-8"> byte</span><span
1682 class="cmtt-8"> 1</span><span
1683 class="cmtt-8"> [0</span><span
1684 class="cmtt-8"> 1</span><span
1685 class="cmtt-8"> 0</span><span
1686 class="cmtt-8"> 0</span><span
1687 class="cmtt-8"> 1</span><span
1688 class="cmtt-8"> 0</span><span
1689 class="cmtt-8"> 0</span><span
1690 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1691 id="x1-44014r7"></a><span
1692 class="cmr-6">7</span><span
1693 class="cmtt-8"> </span><span
1694 class="cmtt-8"> byte</span><span
1695 class="cmtt-8"> 2</span><span
1696 class="cmtt-8"> [1</span><span
1697 class="cmtt-8"> 1</span><span
1698 class="cmtt-8"> 0</span><span
1699 class="cmtt-8"> 0</span><span
1700 class="cmtt-8"> 1</span><span
1701 class="cmtt-8"> 1</span><span
1702 class="cmtt-8"> 1</span><span
1703 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1704 id="x1-44016r8"></a><span
1705 class="cmr-6">8</span><span
1706 class="cmtt-8"> </span><span
1707 class="cmtt-8"> byte</span><span
1708 class="cmtt-8"> 3</span><span
1709 class="cmtt-8"> [0</span><span
1710 class="cmtt-8"> 0</span><span
1711 class="cmtt-8"> 0</span><span
1712 class="cmtt-8"> 0</span><span
1713 class="cmtt-8"> 0</span><span
1714 class="cmtt-8"> 1</span><span
1715 class="cmtt-8"> 1</span><span
1716 class="cmtt-8"> 0]</span><span
1717 class="cmtt-8"> </span><span
1718 class="cmtt-8"> bytestream</span><span
1719 class="cmtt-8"> length</span><span
1720 class="cmtt-8"> ==</span><span
1721 class="cmtt-8"> 4</span><span
1722 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1723 id="x1-44018r9"></a><span
1724 class="cmr-6">9</span><span
1725 class="cmtt-8"> </span><span
1726 class="cmtt-8"> </span></div>
1727 <!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
1728 are worth noting here:
1729 <ul class="itemize1">
1730 <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
1731 some other combination of bit-widths from the bitstream is well defined. There are
1732 no artificial alignment boundaries maintained in the bitstream.
1734 <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
1735 either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
1736 decode context.</li></ul>
1737 <!--l. 208--><p class="noindent" >
1738 <h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a
1739 id="x1-450002.1.8"></a>end-of-packet alignment</h5>
1740 <!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
1741 embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
1742 Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
1743 the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
1744 in the last byte of a packet.
1745 <!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
1746 should this unused space be read, it will return binary zeroes.
1747 <!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
1748 End-of-packet is not to be considered an error; it is merely a state indicating that there is
1749 insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
1753 normal mode of operation, and as such, decoders must handle reading past the end of a packet as
1754 a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
1755 also return ’end-of-packet’.
1756 <!--l. 233--><p class="noindent" >
1757 <h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a
1758 id="x1-460002.1.9"></a>reading zero bits</h5>
1759 <!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
1760 Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
1761 triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
1762 end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
1763 shall also fail with ’end-of-packet’.
1770 <h3 class="sectionHead"><span class="titlemark">3. </span> <a
1771 id="x1-470003"></a>Probability Model and Codebooks</h3>
1772 <!--l. 6--><p class="noindent" >
1773 <h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a
1774 id="x1-480003.1"></a>Overview</h4>
1775 <!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
1776 probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
1777 bitstream itself in the third header, the codec setup header. This packed configuration consists of
1778 multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
1779 compressed codewords as well as an optional lookup table of output vector values to which a
1780 decoded Huffman value is applied as an offset, generating the final decoded output corresponding
1781 to a given compressed codeword.
1782 <!--l. 18--><p class="noindent" >
1783 <h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a
1784 id="x1-490003.1.1"></a>Bitwise operation</h5>
1785 <!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
1786 and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
1787 read from the stream according to <a
1788 href="#x1-360002">section 2</a>, “<a
1789 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
1790 <!--l. 27--><p class="noindent" >
1791 <h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a
1792 id="x1-500003.2"></a>Packed codebook format</h4>
1793 <!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
1794 eight bits. This is not universally true; see <a
1795 href="#x1-360002">section 2</a>, “<a
1796 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
1797 relating to non-eight-bit bytes.
1801 <!--l. 34--><p class="noindent" >
1802 <h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a
1803 id="x1-510003.2.1"></a>codebook decode</h5>
1804 <!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
1805 <!--l. 38--><p class="noindent" >
1806 <div class="fancyvrb" id="fancyvrb7"><a
1807 id="x1-51002r1"></a><span
1808 class="cmr-6">1</span><span
1809 class="cmtt-8"> </span><span
1810 class="cmtt-8"> byte</span><span
1811 class="cmtt-8"> 0:</span><span
1812 class="cmtt-8"> [</span><span
1813 class="cmtt-8"> 0</span><span
1814 class="cmtt-8"> 1</span><span
1815 class="cmtt-8"> 0</span><span
1816 class="cmtt-8"> 0</span><span
1817 class="cmtt-8"> 0</span><span
1818 class="cmtt-8"> 0</span><span
1819 class="cmtt-8"> 1</span><span
1820 class="cmtt-8"> 0</span><span
1821 class="cmtt-8"> ]</span><span
1822 class="cmtt-8"> (0x42)</span><br class="fancyvrb" /><a
1823 id="x1-51004r2"></a><span
1824 class="cmr-6">2</span><span
1825 class="cmtt-8"> </span><span
1826 class="cmtt-8"> byte</span><span
1827 class="cmtt-8"> 1:</span><span
1828 class="cmtt-8"> [</span><span
1829 class="cmtt-8"> 0</span><span
1830 class="cmtt-8"> 1</span><span
1831 class="cmtt-8"> 0</span><span
1832 class="cmtt-8"> 0</span><span
1833 class="cmtt-8"> 0</span><span
1834 class="cmtt-8"> 0</span><span
1835 class="cmtt-8"> 1</span><span
1836 class="cmtt-8"> 1</span><span
1837 class="cmtt-8"> ]</span><span
1838 class="cmtt-8"> (0x43)</span><br class="fancyvrb" /><a
1839 id="x1-51006r3"></a><span
1840 class="cmr-6">3</span><span
1841 class="cmtt-8"> </span><span
1842 class="cmtt-8"> byte</span><span
1843 class="cmtt-8"> 2:</span><span
1844 class="cmtt-8"> [</span><span
1845 class="cmtt-8"> 0</span><span
1846 class="cmtt-8"> 1</span><span
1847 class="cmtt-8"> 0</span><span
1848 class="cmtt-8"> 1</span><span
1849 class="cmtt-8"> 0</span><span
1850 class="cmtt-8"> 1</span><span
1851 class="cmtt-8"> 1</span><span
1852 class="cmtt-8"> 0</span><span
1853 class="cmtt-8"> ]</span><span
1854 class="cmtt-8"> (0x56)</span></div>
1855 <!--l. 44--><p class="noindent" >16 bit <span
1856 class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span
1857 class="cmtt-12">[codebook_entries] </span>fields:
1858 <!--l. 46--><p class="noindent" >
1859 <div class="fancyvrb" id="fancyvrb8"><a
1860 id="x1-51008r1"></a><span
1861 class="cmr-6">1</span><span
1862 class="cmtt-8"> </span><span
1863 class="cmtt-8"> </span><br class="fancyvrb" /><a
1864 id="x1-51010r2"></a><span
1865 class="cmr-6">2</span><span
1866 class="cmtt-8"> </span><span
1867 class="cmtt-8"> byte</span><span
1868 class="cmtt-8"> 3:</span><span
1869 class="cmtt-8"> [</span><span
1870 class="cmtt-8"> X</span><span
1871 class="cmtt-8"> X</span><span
1872 class="cmtt-8"> X</span><span
1873 class="cmtt-8"> X</span><span
1874 class="cmtt-8"> X</span><span
1875 class="cmtt-8"> X</span><span
1876 class="cmtt-8"> X</span><span
1877 class="cmtt-8"> X</span><span
1878 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1879 id="x1-51012r3"></a><span
1880 class="cmr-6">3</span><span
1881 class="cmtt-8"> </span><span
1882 class="cmtt-8"> byte</span><span
1883 class="cmtt-8"> 4:</span><span
1884 class="cmtt-8"> [</span><span
1885 class="cmtt-8"> X</span><span
1886 class="cmtt-8"> X</span><span
1887 class="cmtt-8"> X</span><span
1888 class="cmtt-8"> X</span><span
1889 class="cmtt-8"> X</span><span
1890 class="cmtt-8"> X</span><span
1891 class="cmtt-8"> X</span><span
1892 class="cmtt-8"> X</span><span
1893 class="cmtt-8"> ]</span><span
1894 class="cmtt-8"> [codebook_dimensions]</span><span
1895 class="cmtt-8"> (16</span><span
1896 class="cmtt-8"> bit</span><span
1897 class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a
1898 id="x1-51014r4"></a><span
1899 class="cmr-6">4</span><span
1900 class="cmtt-8"> </span><span
1901 class="cmtt-8"> </span>
1902 <br class="fancyvrb" /><a
1903 id="x1-51016r5"></a><span
1904 class="cmr-6">5</span><span
1905 class="cmtt-8"> </span><span
1906 class="cmtt-8"> byte</span><span
1907 class="cmtt-8"> 5:</span><span
1908 class="cmtt-8"> [</span><span
1909 class="cmtt-8"> X</span><span
1910 class="cmtt-8"> X</span><span
1911 class="cmtt-8"> X</span><span
1912 class="cmtt-8"> X</span><span
1913 class="cmtt-8"> X</span><span
1914 class="cmtt-8"> X</span><span
1915 class="cmtt-8"> X</span><span
1916 class="cmtt-8"> X</span><span
1917 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1918 id="x1-51018r6"></a><span
1919 class="cmr-6">6</span><span
1920 class="cmtt-8"> </span><span
1921 class="cmtt-8"> byte</span><span
1922 class="cmtt-8"> 6:</span><span
1923 class="cmtt-8"> [</span><span
1924 class="cmtt-8"> X</span><span
1925 class="cmtt-8"> X</span><span
1926 class="cmtt-8"> X</span><span
1927 class="cmtt-8"> X</span><span
1928 class="cmtt-8"> X</span><span
1929 class="cmtt-8"> X</span><span
1930 class="cmtt-8"> X</span><span
1931 class="cmtt-8"> X</span><span
1932 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1933 id="x1-51020r7"></a><span
1934 class="cmr-6">7</span><span
1935 class="cmtt-8"> </span><span
1936 class="cmtt-8"> byte</span><span
1937 class="cmtt-8"> 7:</span><span
1938 class="cmtt-8"> [</span><span
1939 class="cmtt-8"> X</span><span
1940 class="cmtt-8"> X</span><span
1941 class="cmtt-8"> X</span><span
1942 class="cmtt-8"> X</span><span
1943 class="cmtt-8"> X</span><span
1944 class="cmtt-8"> X</span><span
1945 class="cmtt-8"> X</span><span
1946 class="cmtt-8"> X</span><span
1947 class="cmtt-8"> ]</span><span
1948 class="cmtt-8"> [codebook_entries]</span><span
1949 class="cmtt-8"> (24</span><span
1950 class="cmtt-8"> bit</span><span
1951 class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a
1952 id="x1-51022r8"></a><span
1953 class="cmr-6">8</span><span
1954 class="cmtt-8"> </span><span
1955 class="cmtt-8"> </span></div>
1956 <!--l. 57--><p class="noindent" >Next is the <span
1957 class="cmtt-12">[ordered] </span>bit flag:
1958 <!--l. 59--><p class="noindent" >
1959 <div class="fancyvrb" id="fancyvrb9"><a
1960 id="x1-51024r1"></a><span
1961 class="cmr-6">1</span><span
1962 class="cmtt-8"> </span><span
1963 class="cmtt-8"> </span><br class="fancyvrb" /><a
1964 id="x1-51026r2"></a><span
1965 class="cmr-6">2</span><span
1966 class="cmtt-8"> </span><span
1967 class="cmtt-8"> byte</span><span
1968 class="cmtt-8"> 8:</span><span
1969 class="cmtt-8"> [</span><span
1970 class="cmtt-8"> </span><span
1971 class="cmtt-8"> </span><span
1972 class="cmtt-8"> </span><span
1973 class="cmtt-8"> </span><span
1974 class="cmtt-8"> </span><span
1975 class="cmtt-8"> </span><span
1976 class="cmtt-8"> </span><span
1977 class="cmtt-8"> </span><span
1978 class="cmtt-8"> </span><span
1979 class="cmtt-8"> </span><span
1980 class="cmtt-8"> </span><span
1981 class="cmtt-8"> </span><span
1982 class="cmtt-8"> </span><span
1983 class="cmtt-8"> </span><span
1984 class="cmtt-8"> X</span><span
1985 class="cmtt-8"> ]</span><span
1986 class="cmtt-8"> [ordered]</span><span
1987 class="cmtt-8"> (1</span><span
1988 class="cmtt-8"> bit)</span><br class="fancyvrb" /><a
1989 id="x1-51028r3"></a><span
1990 class="cmr-6">3</span><span
1991 class="cmtt-8"> </span><span
1992 class="cmtt-8"> </span></div>
1993 <!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
1994 class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length.
1995 We now read the list of codeword lengths and store these lengths in the array
1997 class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span
1998 class="cmtt-12">[ordered] </span>flag
2000 <ul class="itemize1">
2001 <li class="itemize">If the <span
2002 class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
2003 needs to read each codeword length one-by-one.
2004 <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
2005 class="cmtt-12">[sparse] </span>flag. This flag determines
2006 whether or not the codebook contains unused entries that are not to be included in
2007 the codeword decode tree:
2008 <!--l. 82--><p class="noindent" >
2009 <div class="fancyvrb" id="fancyvrb10"><a
2010 id="x1-51030r1"></a><span
2011 class="cmr-6">1</span><span
2012 class="cmtt-8"> </span><span
2013 class="cmtt-8"> byte</span><span
2014 class="cmtt-8"> 8:</span><span
2015 class="cmtt-8"> [</span><span
2016 class="cmtt-8"> </span><span
2017 class="cmtt-8"> </span><span
2018 class="cmtt-8"> </span><span
2019 class="cmtt-8"> </span><span
2020 class="cmtt-8"> </span><span
2021 class="cmtt-8"> </span><span
2022 class="cmtt-8"> </span><span
2023 class="cmtt-8"> </span><span
2024 class="cmtt-8"> </span><span
2025 class="cmtt-8"> </span><span
2026 class="cmtt-8"> </span><span
2027 class="cmtt-8"> </span><span
2028 class="cmtt-8"> X</span><span
2029 class="cmtt-8"> 1</span><span
2030 class="cmtt-8"> ]</span><span
2031 class="cmtt-8"> [sparse]</span><span
2032 class="cmtt-8"> flag</span><span
2033 class="cmtt-8"> (1</span><span
2034 class="cmtt-8"> bit)</span></div>
2035 <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
2036 class="cmtt-12">[codebook_entries] </span>codebook entries:
2037 <!--l. 89--><p class="noindent" >
2038 <div class="fancyvrb" id="fancyvrb11"><a
2039 id="x1-51032r1"></a><span
2040 class="cmr-6">1</span><span
2041 class="cmtt-8"> </span><span
2042 class="cmtt-8"> </span><br class="fancyvrb" /><a
2043 id="x1-51034r2"></a><span
2044 class="cmr-6">2</span><span
2045 class="cmtt-8"> </span><span
2046 class="cmtt-8"> </span><span
2047 class="cmtt-8"> </span><span
2048 class="cmtt-8"> 1)</span><span
2049 class="cmtt-8"> if([sparse]</span><span
2050 class="cmtt-8"> is</span><span
2051 class="cmtt-8"> set)</span><span
2052 class="cmtt-8"> </span><span
2053 class="cmsy-8">{</span><br class="fancyvrb" /><a
2054 id="x1-51036r3"></a><span
2055 class="cmr-6">3</span><span
2056 class="cmtt-8"> </span><span
2057 class="cmtt-8"> </span><br class="fancyvrb" /><a
2058 id="x1-51038r4"></a><span
2059 class="cmr-6">4</span><span
2060 class="cmtt-8"> </span><span
2061 class="cmtt-8"> </span><span
2062 class="cmtt-8"> </span><span
2063 class="cmtt-8"> </span><span
2064 class="cmtt-8"> </span><span
2065 class="cmtt-8"> </span><span
2066 class="cmtt-8"> </span><span
2067 class="cmtt-8"> </span><span
2068 class="cmtt-8"> </span><span
2069 class="cmtt-8"> </span><span
2070 class="cmtt-8"> 2)</span><span
2071 class="cmtt-8"> [flag]</span><span
2072 class="cmtt-8"> =</span><span
2073 class="cmtt-8"> read</span><span
2074 class="cmtt-8"> one</span><span
2075 class="cmtt-8"> bit;</span><br class="fancyvrb" /><a
2076 id="x1-51040r5"></a><span
2077 class="cmr-6">5</span><span
2078 class="cmtt-8"> </span><span
2079 class="cmtt-8"> </span><span
2080 class="cmtt-8"> </span><span
2081 class="cmtt-8"> </span><span
2082 class="cmtt-8"> </span><span
2083 class="cmtt-8"> </span><span
2084 class="cmtt-8"> </span><span
2085 class="cmtt-8"> </span><span
2086 class="cmtt-8"> </span><span
2087 class="cmtt-8"> </span><span
2088 class="cmtt-8"> 3)</span><span
2089 class="cmtt-8"> if([flag]</span><span
2090 class="cmtt-8"> is</span><span
2091 class="cmtt-8"> set)</span><span
2092 class="cmtt-8"> </span><span
2093 class="cmsy-8">{</span><br class="fancyvrb" /><a
2094 id="x1-51042r6"></a><span
2095 class="cmr-6">6</span><span
2096 class="cmtt-8"> </span><span
2097 class="cmtt-8"> </span>
2098 <br class="fancyvrb" /><a
2099 id="x1-51044r7"></a><span
2100 class="cmr-6">7</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"> </span><span
2106 class="cmtt-8"> </span><span
2107 class="cmtt-8"> </span><span
2108 class="cmtt-8"> </span><span
2109 class="cmtt-8"> </span><span
2110 class="cmtt-8"> </span><span
2111 class="cmtt-8"> </span><span
2112 class="cmtt-8"> </span><span
2113 class="cmtt-8"> </span><span
2114 class="cmtt-8"> </span><span
2115 class="cmtt-8"> </span><span
2116 class="cmtt-8"> 4)</span><span
2117 class="cmtt-8"> [length]</span><span
2118 class="cmtt-8"> =</span><span
2119 class="cmtt-8"> read</span><span
2120 class="cmtt-8"> a</span><span
2121 class="cmtt-8"> five</span><span
2122 class="cmtt-8"> bit</span><span
2123 class="cmtt-8"> unsigned</span><span
2124 class="cmtt-8"> integer;</span><br class="fancyvrb" /><a
2125 id="x1-51046r8"></a><span
2126 class="cmr-6">8</span><span
2127 class="cmtt-8"> </span><span
2128 class="cmtt-8"> </span><span
2129 class="cmtt-8"> </span><span
2130 class="cmtt-8"> </span><span
2131 class="cmtt-8"> </span><span
2132 class="cmtt-8"> </span><span
2133 class="cmtt-8"> </span><span
2134 class="cmtt-8"> </span><span
2135 class="cmtt-8"> </span><span
2136 class="cmtt-8"> </span><span
2137 class="cmtt-8"> </span><span
2138 class="cmtt-8"> </span><span
2139 class="cmtt-8"> </span><span
2140 class="cmtt-8"> </span><span
2141 class="cmtt-8"> </span><span
2142 class="cmtt-8"> 5)</span><span
2143 class="cmtt-8"> codeword</span><span
2144 class="cmtt-8"> length</span><span
2145 class="cmtt-8"> for</span><span
2146 class="cmtt-8"> this</span><span
2147 class="cmtt-8"> entry</span><span
2148 class="cmtt-8"> is</span><span
2149 class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a
2150 id="x1-51048r9"></a><span
2151 class="cmr-6">9</span><span
2152 class="cmtt-8"> </span><span
2153 class="cmtt-8"> </span>
2154 <br class="fancyvrb" /><a
2155 id="x1-51050r10"></a><span
2156 class="cmr-6">10</span><span
2157 class="cmtt-8"> </span><span
2158 class="cmtt-8"> </span><span
2159 class="cmtt-8"> </span><span
2160 class="cmtt-8"> </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="cmsy-8">}</span><span
2172 class="cmtt-8"> else</span><span
2173 class="cmtt-8"> </span><span
2174 class="cmsy-8">{</span><br class="fancyvrb" /><a
2175 id="x1-51052r11"></a><span
2176 class="cmr-6">11</span><span
2177 class="cmtt-8"> </span><span
2178 class="cmtt-8"> </span><br class="fancyvrb" /><a
2179 id="x1-51054r12"></a><span
2180 class="cmr-6">12</span><span
2181 class="cmtt-8"> </span><span
2182 class="cmtt-8"> </span><span
2183 class="cmtt-8"> </span><span
2184 class="cmtt-8"> </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"> 6)</span><span
2197 class="cmtt-8"> this</span><span
2198 class="cmtt-8"> entry</span><span
2199 class="cmtt-8"> is</span><span
2200 class="cmtt-8"> unused.</span><span
2201 class="cmtt-8"> </span><span
2202 class="cmtt-8"> mark</span><span
2203 class="cmtt-8"> it</span><span
2204 class="cmtt-8"> as</span><span
2205 class="cmtt-8"> such.</span><br class="fancyvrb" /><a
2206 id="x1-51056r13"></a><span
2207 class="cmr-6">13</span><span
2208 class="cmtt-8"> </span><span
2209 class="cmtt-8"> </span><br class="fancyvrb" /><a
2210 id="x1-51058r14"></a><span
2211 class="cmr-6">14</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="cmsy-8">}</span><br class="fancyvrb" /><a
2227 id="x1-51060r15"></a><span
2228 class="cmr-6">15</span><span
2229 class="cmtt-8"> </span><span
2230 class="cmtt-8"> </span><br class="fancyvrb" /><a
2231 id="x1-51062r16"></a><span
2232 class="cmr-6">16</span><span
2233 class="cmtt-8"> </span><span
2234 class="cmtt-8"> </span><span
2235 class="cmtt-8"> </span><span
2236 class="cmtt-8"> </span><span
2237 class="cmtt-8"> </span><span
2238 class="cmtt-8"> </span><span
2239 class="cmtt-8"> </span><span
2240 class="cmsy-8">}</span><span
2241 class="cmtt-8"> else</span><span
2242 class="cmtt-8"> the</span><span
2243 class="cmtt-8"> sparse</span><span
2244 class="cmtt-8"> flag</span><span
2245 class="cmtt-8"> is</span><span
2246 class="cmtt-8"> not</span><span
2247 class="cmtt-8"> set</span><span
2248 class="cmtt-8"> </span><span
2249 class="cmsy-8">{</span>
2250 <br class="fancyvrb" /><a
2251 id="x1-51064r17"></a><span
2252 class="cmr-6">17</span><span
2253 class="cmtt-8"> </span><span
2254 class="cmtt-8"> </span><br class="fancyvrb" /><a
2255 id="x1-51066r18"></a><span
2256 class="cmr-6">18</span><span
2257 class="cmtt-8"> </span><span
2258 class="cmtt-8"> </span><span
2259 class="cmtt-8"> </span><span
2260 class="cmtt-8"> </span><span
2261 class="cmtt-8"> </span><span
2262 class="cmtt-8"> </span><span
2263 class="cmtt-8"> </span><span
2264 class="cmtt-8"> </span><span
2265 class="cmtt-8"> </span><span
2266 class="cmtt-8"> 7)</span><span
2267 class="cmtt-8"> [length]</span><span
2268 class="cmtt-8"> =</span><span
2269 class="cmtt-8"> read</span><span
2270 class="cmtt-8"> a</span><span
2271 class="cmtt-8"> five</span><span
2272 class="cmtt-8"> bit</span><span
2273 class="cmtt-8"> unsigned</span><span
2274 class="cmtt-8"> integer;</span><br class="fancyvrb" /><a
2275 id="x1-51068r19"></a><span
2276 class="cmr-6">19</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"> </span><span
2285 class="cmtt-8"> </span><span
2286 class="cmtt-8"> 8)</span><span
2287 class="cmtt-8"> the</span><span
2288 class="cmtt-8"> codeword</span><span
2289 class="cmtt-8"> length</span><span
2290 class="cmtt-8"> for</span><span
2291 class="cmtt-8"> this</span><span
2292 class="cmtt-8"> entry</span><span
2293 class="cmtt-8"> is</span><span
2294 class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a
2295 id="x1-51070r20"></a><span
2296 class="cmr-6">20</span><span
2297 class="cmtt-8"> </span><span
2298 class="cmtt-8"> </span><br class="fancyvrb" /><a
2299 id="x1-51072r21"></a><span
2300 class="cmr-6">21</span><span
2301 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
2309 id="x1-51074r22"></a><span
2310 class="cmr-6">22</span><span
2311 class="cmtt-8"> </span><span
2312 class="cmtt-8"> </span></div>
2317 <li class="itemize">If the <span
2318 class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
2319 ascending length order. Rather than reading a length for every codeword, the
2320 encoder reads the number of codewords per length. That is, beginning at entry
2322 <!--l. 120--><p class="noindent" >
2323 <div class="fancyvrb" id="fancyvrb12"><a
2324 id="x1-51076r1"></a><span
2325 class="cmr-6">1</span><span
2326 class="cmtt-8"> </span><span
2327 class="cmtt-8"> </span><span
2328 class="cmtt-8"> </span><span
2329 class="cmtt-8"> 1)</span><span
2330 class="cmtt-8"> [current_entry]</span><span
2331 class="cmtt-8"> =</span><span
2332 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
2333 id="x1-51078r2"></a><span
2334 class="cmr-6">2</span><span
2335 class="cmtt-8"> </span><span
2336 class="cmtt-8"> </span><span
2337 class="cmtt-8"> </span><span
2338 class="cmtt-8"> 2)</span><span
2339 class="cmtt-8"> [current_length]</span><span
2340 class="cmtt-8"> =</span><span
2341 class="cmtt-8"> read</span><span
2342 class="cmtt-8"> a</span><span
2343 class="cmtt-8"> five</span><span
2344 class="cmtt-8"> bit</span><span
2345 class="cmtt-8"> unsigned</span><span
2346 class="cmtt-8"> integer</span><span
2347 class="cmtt-8"> and</span><span
2348 class="cmtt-8"> add</span><span
2349 class="cmtt-8"> 1;</span>
2350 <br class="fancyvrb" /><a
2351 id="x1-51080r3"></a><span
2352 class="cmr-6">3</span><span
2353 class="cmtt-8"> </span><span
2354 class="cmtt-8"> </span><span
2355 class="cmtt-8"> </span><span
2356 class="cmtt-8"> 3)</span><span
2357 class="cmtt-8"> [number]</span><span
2358 class="cmtt-8"> =</span><span
2359 class="cmtt-8"> read</span><span
2360 class="cmtt-8"> </span><a
2361 href="#x1-1190009.2.1"><span
2362 class="cmtt-8">ilog</span></a><span
2363 class="cmtt-8">([codebook_entries]</span><span
2364 class="cmtt-8"> -</span><span
2365 class="cmtt-8"> [current_entry])</span><span
2366 class="cmtt-8"> bits</span><span
2367 class="cmtt-8"> as</span><span
2368 class="cmtt-8"> an</span><span
2369 class="cmtt-8"> unsigned</span><span
2370 class="cmtt-8"> integer</span>
2371 <br class="fancyvrb" /><a
2372 id="x1-51082r4"></a><span
2373 class="cmr-6">4</span><span
2374 class="cmtt-8"> </span><span
2375 class="cmtt-8"> </span><span
2376 class="cmtt-8"> </span><span
2377 class="cmtt-8"> 4)</span><span
2378 class="cmtt-8"> set</span><span
2379 class="cmtt-8"> the</span><span
2380 class="cmtt-8"> entries</span><span
2381 class="cmtt-8"> [current_entry]</span><span
2382 class="cmtt-8"> through</span><span
2383 class="cmtt-8"> [current_entry]+[number]-1,</span><span
2384 class="cmtt-8"> inclusive,</span>
2385 <br class="fancyvrb" /><a
2386 id="x1-51084r5"></a><span
2387 class="cmr-6">5</span><span
2388 class="cmtt-8"> </span><span
2389 class="cmtt-8"> </span><span
2390 class="cmtt-8"> </span><span
2391 class="cmtt-8"> </span><span
2392 class="cmtt-8"> </span><span
2393 class="cmtt-8"> of</span><span
2394 class="cmtt-8"> the</span><span
2395 class="cmtt-8"> [codebook_codeword_lengths]</span><span
2396 class="cmtt-8"> array</span><span
2397 class="cmtt-8"> to</span><span
2398 class="cmtt-8"> [current_length]</span>
2399 <br class="fancyvrb" /><a
2400 id="x1-51086r6"></a><span
2401 class="cmr-6">6</span><span
2402 class="cmtt-8"> </span><span
2403 class="cmtt-8"> </span><span
2404 class="cmtt-8"> </span><span
2405 class="cmtt-8"> 5)</span><span
2406 class="cmtt-8"> set</span><span
2407 class="cmtt-8"> [current_entry]</span><span
2408 class="cmtt-8"> to</span><span
2409 class="cmtt-8"> [number]</span><span
2410 class="cmtt-8"> +</span><span
2411 class="cmtt-8"> [current_entry]</span><br class="fancyvrb" /><a
2412 id="x1-51088r7"></a><span
2413 class="cmr-6">7</span><span
2414 class="cmtt-8"> </span><span
2415 class="cmtt-8"> </span><span
2416 class="cmtt-8"> </span><span
2417 class="cmtt-8"> 6)</span><span
2418 class="cmtt-8"> increment</span><span
2419 class="cmtt-8"> [current_length]</span><span
2420 class="cmtt-8"> by</span><span
2421 class="cmtt-8"> 1</span>
2422 <br class="fancyvrb" /><a
2423 id="x1-51090r8"></a><span
2424 class="cmr-6">8</span><span
2425 class="cmtt-8"> </span><span
2426 class="cmtt-8"> </span><span
2427 class="cmtt-8"> </span><span
2428 class="cmtt-8"> 7)</span><span
2429 class="cmtt-8"> if</span><span
2430 class="cmtt-8"> [current_entry]</span><span
2431 class="cmtt-8"> is</span><span
2432 class="cmtt-8"> greater</span><span
2433 class="cmtt-8"> than</span><span
2434 class="cmtt-8"> [codebook_entries]</span><span
2435 class="cmtt-8"> ERROR</span><span
2436 class="cmtt-8"> CONDITION;</span><br class="fancyvrb" /><a
2437 id="x1-51092r9"></a><span
2438 class="cmr-6">9</span><span
2439 class="cmtt-8"> </span><span
2440 class="cmtt-8"> </span><span
2441 class="cmtt-8"> </span><span
2442 class="cmtt-8"> </span><span
2443 class="cmtt-8"> </span><span
2444 class="cmtt-8"> the</span><span
2445 class="cmtt-8"> decoder</span><span
2446 class="cmtt-8"> will</span><span
2447 class="cmtt-8"> not</span><span
2448 class="cmtt-8"> be</span><span
2449 class="cmtt-8"> able</span><span
2450 class="cmtt-8"> to</span><span
2451 class="cmtt-8"> read</span><span
2452 class="cmtt-8"> this</span><span
2453 class="cmtt-8"> stream.</span>
2454 <br class="fancyvrb" /><a
2455 id="x1-51094r10"></a><span
2456 class="cmr-6">10</span><span
2457 class="cmtt-8"> </span><span
2458 class="cmtt-8"> </span><span
2459 class="cmtt-8"> </span><span
2460 class="cmtt-8"> 8)</span><span
2461 class="cmtt-8"> if</span><span
2462 class="cmtt-8"> [current_entry]</span><span
2463 class="cmtt-8"> is</span><span
2464 class="cmtt-8"> less</span><span
2465 class="cmtt-8"> than</span><span
2466 class="cmtt-8"> [codebook_entries],</span><span
2467 class="cmtt-8"> repeat</span><span
2468 class="cmtt-8"> process</span><span
2469 class="cmtt-8"> starting</span><span
2470 class="cmtt-8"> at</span><span
2471 class="cmtt-8"> 3)</span><br class="fancyvrb" /><a
2472 id="x1-51096r11"></a><span
2473 class="cmr-6">11</span><span
2474 class="cmtt-8"> </span><span
2475 class="cmtt-8"> </span><span
2476 class="cmtt-8"> </span><span
2477 class="cmtt-8"> 9)</span><span
2478 class="cmtt-8"> done.</span></div>
2480 <!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
2481 I supports three lookup types:
2482 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
2484 class="enumerate-enumitem">No lookup
2485 </dd><dt class="enumerate-enumitem">
2487 class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ)
2488 </dd><dt class="enumerate-enumitem">
2490 class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl>
2491 <!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
2492 <div class="fancyvrb" id="fancyvrb13"><a
2493 id="x1-51101r1"></a><span
2494 class="cmr-6">1</span><span
2495 class="cmtt-8"> </span><span
2496 class="cmtt-8"> </span><span
2497 class="cmtt-8"> </span><span
2498 class="cmtt-8"> 1)</span><span
2499 class="cmtt-8"> [codebook_lookup_type]</span><span
2500 class="cmtt-8"> =</span><span
2501 class="cmtt-8"> read</span><span
2502 class="cmtt-8"> four</span><span
2503 class="cmtt-8"> bits</span><span
2504 class="cmtt-8"> as</span><span
2505 class="cmtt-8"> an</span><span
2506 class="cmtt-8"> unsigned</span><span
2507 class="cmtt-8"> integer</span></div>
2508 <!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
2509 class="cmtt-12">[codebook_lookup_type]</span>:
2510 <ul class="itemize1">
2511 <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
2513 <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
2514 be read. Lookup type one reads a list of values that are permuted in a set pattern to
2515 build a list of vectors, each vector of order <span
2516 class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup
2517 type two builds the same vector list, but reads each scalar for each vector explicitly,
2518 rather than building vectors from a smaller list of possible scalar values. Lookup
2519 decode proceeds as follows:
2520 <!--l. 168--><p class="noindent" >
2521 <div class="fancyvrb" id="fancyvrb14"><a
2522 id="x1-51103r1"></a><span
2523 class="cmr-6">1</span><span
2524 class="cmtt-8"> </span><span
2525 class="cmtt-8"> </span><span
2526 class="cmtt-8"> </span><span
2527 class="cmtt-8"> 1)</span><span
2528 class="cmtt-8"> [codebook_minimum_value]</span><span
2529 class="cmtt-8"> =</span><span
2530 class="cmtt-8"> </span><a
2531 href="#x1-1200009.2.2"><span
2532 class="cmtt-8">float32_unpack</span></a><span
2533 class="cmtt-8">(</span><span
2534 class="cmtt-8"> read</span><span
2535 class="cmtt-8"> 32</span><span
2536 class="cmtt-8"> bits</span><span
2537 class="cmtt-8"> as</span><span
2538 class="cmtt-8"> an</span><span
2539 class="cmtt-8"> unsigned</span><span
2540 class="cmtt-8"> integer)</span>
2541 <br class="fancyvrb" /><a
2542 id="x1-51105r2"></a><span
2543 class="cmr-6">2</span><span
2544 class="cmtt-8"> </span><span
2545 class="cmtt-8"> </span><span
2546 class="cmtt-8"> </span><span
2547 class="cmtt-8"> 2)</span><span
2548 class="cmtt-8"> [codebook_delta_value]</span><span
2549 class="cmtt-8"> =</span><span
2550 class="cmtt-8"> </span><a
2551 href="#x1-1200009.2.2"><span
2552 class="cmtt-8">float32_unpack</span></a><span
2553 class="cmtt-8">(</span><span
2554 class="cmtt-8"> read</span><span
2555 class="cmtt-8"> 32</span><span
2556 class="cmtt-8"> bits</span><span
2557 class="cmtt-8"> as</span><span
2558 class="cmtt-8"> an</span><span
2559 class="cmtt-8"> unsigned</span><span
2560 class="cmtt-8"> integer)</span>
2561 <br class="fancyvrb" /><a
2562 id="x1-51107r3"></a><span
2563 class="cmr-6">3</span><span
2564 class="cmtt-8"> </span><span
2565 class="cmtt-8"> </span><span
2566 class="cmtt-8"> </span><span
2567 class="cmtt-8"> 3)</span><span
2568 class="cmtt-8"> [codebook_value_bits]</span><span
2569 class="cmtt-8"> =</span><span
2570 class="cmtt-8"> read</span><span
2571 class="cmtt-8"> 4</span><span
2572 class="cmtt-8"> bits</span><span
2573 class="cmtt-8"> as</span><span
2574 class="cmtt-8"> an</span><span
2575 class="cmtt-8"> unsigned</span><span
2576 class="cmtt-8"> integer</span><span
2577 class="cmtt-8"> and</span><span
2578 class="cmtt-8"> add</span><span
2579 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
2580 id="x1-51109r4"></a><span
2581 class="cmr-6">4</span><span
2582 class="cmtt-8"> </span><span
2583 class="cmtt-8"> </span><span
2584 class="cmtt-8"> </span><span
2585 class="cmtt-8"> 4)</span><span
2586 class="cmtt-8"> [codebook_sequence_p]</span><span
2587 class="cmtt-8"> =</span><span
2588 class="cmtt-8"> read</span><span
2589 class="cmtt-8"> 1</span><span
2590 class="cmtt-8"> bit</span><span
2591 class="cmtt-8"> as</span><span
2592 class="cmtt-8"> a</span><span
2593 class="cmtt-8"> boolean</span><span
2594 class="cmtt-8"> flag</span><br class="fancyvrb" /><a
2595 id="x1-51111r5"></a><span
2596 class="cmr-6">5</span><span
2597 class="cmtt-8"> </span><span
2598 class="cmtt-8"> </span>
2602 <br class="fancyvrb" /><a
2603 id="x1-51113r6"></a><span
2604 class="cmr-6">6</span><span
2605 class="cmtt-8"> </span><span
2606 class="cmtt-8"> </span><span
2607 class="cmtt-8"> </span><span
2608 class="cmtt-8"> if</span><span
2609 class="cmtt-8"> (</span><span
2610 class="cmtt-8"> [codebook_lookup_type]</span><span
2611 class="cmtt-8"> is</span><span
2612 class="cmtt-8"> 1</span><span
2613 class="cmtt-8"> )</span><span
2614 class="cmtt-8"> </span><span
2615 class="cmsy-8">{</span><br class="fancyvrb" /><a
2616 id="x1-51115r7"></a><span
2617 class="cmr-6">7</span><span
2618 class="cmtt-8"> </span><span
2619 class="cmtt-8"> </span><br class="fancyvrb" /><a
2620 id="x1-51117r8"></a><span
2621 class="cmr-6">8</span><span
2622 class="cmtt-8"> </span><span
2623 class="cmtt-8"> </span><span
2624 class="cmtt-8"> </span><span
2625 class="cmtt-8"> </span><span
2626 class="cmtt-8"> </span><span
2627 class="cmtt-8"> </span><span
2628 class="cmtt-8"> 5)</span><span
2629 class="cmtt-8"> [codebook_lookup_values]</span><span
2630 class="cmtt-8"> =</span><span
2631 class="cmtt-8"> </span><a
2632 href="#x1-1210009.2.3"><span
2633 class="cmtt-8">lookup1_values</span></a><span
2634 class="cmtt-8">([codebook_entries],</span><span
2635 class="cmtt-8"> [codebook_dimensions]</span><span
2636 class="cmtt-8"> )</span>
2637 <br class="fancyvrb" /><a
2638 id="x1-51119r9"></a><span
2639 class="cmr-6">9</span><span
2640 class="cmtt-8"> </span><span
2641 class="cmtt-8"> </span><br class="fancyvrb" /><a
2642 id="x1-51121r10"></a><span
2643 class="cmr-6">10</span><span
2644 class="cmtt-8"> </span><span
2645 class="cmtt-8"> </span><span
2646 class="cmtt-8"> </span><span
2647 class="cmtt-8"> </span><span
2648 class="cmsy-8">}</span><span
2649 class="cmtt-8"> else</span><span
2650 class="cmtt-8"> </span><span
2651 class="cmsy-8">{</span><br class="fancyvrb" /><a
2652 id="x1-51123r11"></a><span
2653 class="cmr-6">11</span><span
2654 class="cmtt-8"> </span><span
2655 class="cmtt-8"> </span><br class="fancyvrb" /><a
2656 id="x1-51125r12"></a><span
2657 class="cmr-6">12</span><span
2658 class="cmtt-8"> </span><span
2659 class="cmtt-8"> </span><span
2660 class="cmtt-8"> </span><span
2661 class="cmtt-8"> </span><span
2662 class="cmtt-8"> </span><span
2663 class="cmtt-8"> </span><span
2664 class="cmtt-8"> 6)</span><span
2665 class="cmtt-8"> [codebook_lookup_values]</span><span
2666 class="cmtt-8"> =</span><span
2667 class="cmtt-8"> [codebook_entries]</span><span
2668 class="cmtt-8"> *</span><span
2669 class="cmtt-8"> [codebook_dimensions]</span><br class="fancyvrb" /><a
2670 id="x1-51127r13"></a><span
2671 class="cmr-6">13</span><span
2672 class="cmtt-8"> </span><span
2673 class="cmtt-8"> </span><br class="fancyvrb" /><a
2674 id="x1-51129r14"></a><span
2675 class="cmr-6">14</span><span
2676 class="cmtt-8"> </span><span
2677 class="cmtt-8"> </span><span
2678 class="cmtt-8"> </span><span
2679 class="cmtt-8"> </span><span
2680 class="cmsy-8">}</span><br class="fancyvrb" /><a
2681 id="x1-51131r15"></a><span
2682 class="cmr-6">15</span><span
2683 class="cmtt-8"> </span><span
2684 class="cmtt-8"> </span>
2685 <br class="fancyvrb" /><a
2686 id="x1-51133r16"></a><span
2687 class="cmr-6">16</span><span
2688 class="cmtt-8"> </span><span
2689 class="cmtt-8"> </span><span
2690 class="cmtt-8"> </span><span
2691 class="cmtt-8"> 7)</span><span
2692 class="cmtt-8"> read</span><span
2693 class="cmtt-8"> a</span><span
2694 class="cmtt-8"> total</span><span
2695 class="cmtt-8"> of</span><span
2696 class="cmtt-8"> [codebook_lookup_values]</span><span
2697 class="cmtt-8"> unsigned</span><span
2698 class="cmtt-8"> integers</span><span
2699 class="cmtt-8"> of</span><span
2700 class="cmtt-8"> [codebook_value_bits]</span><span
2701 class="cmtt-8"> each;</span>
2702 <br class="fancyvrb" /><a
2703 id="x1-51135r17"></a><span
2704 class="cmr-6">17</span><span
2705 class="cmtt-8"> </span><span
2706 class="cmtt-8"> </span><span
2707 class="cmtt-8"> </span><span
2708 class="cmtt-8"> </span><span
2709 class="cmtt-8"> </span><span
2710 class="cmtt-8"> </span><span
2711 class="cmtt-8"> store</span><span
2712 class="cmtt-8"> these</span><span
2713 class="cmtt-8"> in</span><span
2714 class="cmtt-8"> order</span><span
2715 class="cmtt-8"> in</span><span
2716 class="cmtt-8"> the</span><span
2717 class="cmtt-8"> array</span><span
2718 class="cmtt-8"> [codebook_multiplicands]</span></div>
2720 <li class="itemize">A <span
2721 class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is
2722 not decodable by the specification in this document.
2724 <!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
2725 rendering the stream undecodable.
2726 <!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
2727 id="x1-520003.2.1"></a><span
2728 class="cmbx-12">Huffman decision tree representation</span></span>
2730 class="cmtt-12">[codebook_codeword_lengths] </span>array and <span
2731 class="cmtt-12">[codebook_entries] </span>value uniquely define the
2732 Huffman decision tree used for entropy decoding.
2733 <!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
2734 codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
2735 possible. Assume the following codeword length list:
2736 <!--l. 209--><p class="noindent" >
2737 <div class="fancyvrb" id="fancyvrb15"><a
2738 id="x1-52002r1"></a><span
2739 class="cmr-6">1</span><span
2740 class="cmtt-8"> </span><span
2741 class="cmtt-8"> entry</span><span
2742 class="cmtt-8"> 0:</span><span
2743 class="cmtt-8"> length</span><span
2744 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
2745 id="x1-52004r2"></a><span
2746 class="cmr-6">2</span><span
2747 class="cmtt-8"> </span><span
2748 class="cmtt-8"> entry</span><span
2749 class="cmtt-8"> 1:</span><span
2750 class="cmtt-8"> length</span><span
2751 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2752 id="x1-52006r3"></a><span
2753 class="cmr-6">3</span><span
2754 class="cmtt-8"> </span><span
2755 class="cmtt-8"> entry</span><span
2756 class="cmtt-8"> 2:</span><span
2757 class="cmtt-8"> length</span><span
2758 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2759 id="x1-52008r4"></a><span
2760 class="cmr-6">4</span><span
2761 class="cmtt-8"> </span><span
2762 class="cmtt-8"> entry</span><span
2763 class="cmtt-8"> 3:</span><span
2764 class="cmtt-8"> length</span><span
2765 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2766 id="x1-52010r5"></a><span
2767 class="cmr-6">5</span><span
2768 class="cmtt-8"> </span><span
2769 class="cmtt-8"> entry</span><span
2770 class="cmtt-8"> 4:</span><span
2771 class="cmtt-8"> length</span><span
2772 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2773 id="x1-52012r6"></a><span
2774 class="cmr-6">6</span><span
2775 class="cmtt-8"> </span><span
2776 class="cmtt-8"> entry</span><span
2777 class="cmtt-8"> 5:</span><span
2778 class="cmtt-8"> length</span><span
2779 class="cmtt-8"> 2</span>
2780 <br class="fancyvrb" /><a
2781 id="x1-52014r7"></a><span
2782 class="cmr-6">7</span><span
2783 class="cmtt-8"> </span><span
2784 class="cmtt-8"> entry</span><span
2785 class="cmtt-8"> 6:</span><span
2786 class="cmtt-8"> length</span><span
2787 class="cmtt-8"> 3</span><br class="fancyvrb" /><a
2788 id="x1-52016r8"></a><span
2789 class="cmr-6">8</span><span
2790 class="cmtt-8"> </span><span
2791 class="cmtt-8"> entry</span><span
2792 class="cmtt-8"> 7:</span><span
2793 class="cmtt-8"> length</span><span
2794 class="cmtt-8"> 3</span></div>
2795 <!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
2796 in the following codeword list:
2797 <!--l. 223--><p class="noindent" >
2798 <div class="fancyvrb" id="fancyvrb16"><a
2799 id="x1-52018r1"></a><span
2800 class="cmr-6">1</span><span
2801 class="cmtt-8"> </span><span
2802 class="cmtt-8"> entry</span><span
2803 class="cmtt-8"> 0:</span><span
2804 class="cmtt-8"> length</span><span
2805 class="cmtt-8"> 2</span><span
2806 class="cmtt-8"> codeword</span><span
2807 class="cmtt-8"> 00</span><br class="fancyvrb" /><a
2808 id="x1-52020r2"></a><span
2809 class="cmr-6">2</span><span
2810 class="cmtt-8"> </span><span
2811 class="cmtt-8"> entry</span><span
2812 class="cmtt-8"> 1:</span><span
2813 class="cmtt-8"> length</span><span
2814 class="cmtt-8"> 4</span><span
2815 class="cmtt-8"> codeword</span><span
2816 class="cmtt-8"> 0100</span><br class="fancyvrb" /><a
2817 id="x1-52022r3"></a><span
2818 class="cmr-6">3</span><span
2819 class="cmtt-8"> </span><span
2820 class="cmtt-8"> entry</span><span
2821 class="cmtt-8"> 2:</span><span
2822 class="cmtt-8"> length</span><span
2823 class="cmtt-8"> 4</span><span
2824 class="cmtt-8"> codeword</span><span
2825 class="cmtt-8"> 0101</span><br class="fancyvrb" /><a
2826 id="x1-52024r4"></a><span
2827 class="cmr-6">4</span><span
2828 class="cmtt-8"> </span><span
2829 class="cmtt-8"> entry</span><span
2830 class="cmtt-8"> 3:</span><span
2831 class="cmtt-8"> length</span><span
2832 class="cmtt-8"> 4</span><span
2833 class="cmtt-8"> codeword</span><span
2834 class="cmtt-8"> 0110</span>
2835 <br class="fancyvrb" /><a
2836 id="x1-52026r5"></a><span
2837 class="cmr-6">5</span><span
2838 class="cmtt-8"> </span><span
2839 class="cmtt-8"> entry</span><span
2840 class="cmtt-8"> 4:</span><span
2841 class="cmtt-8"> length</span><span
2842 class="cmtt-8"> 4</span><span
2843 class="cmtt-8"> codeword</span><span
2844 class="cmtt-8"> 0111</span><br class="fancyvrb" /><a
2845 id="x1-52028r6"></a><span
2846 class="cmr-6">6</span><span
2847 class="cmtt-8"> </span><span
2848 class="cmtt-8"> entry</span><span
2849 class="cmtt-8"> 5:</span><span
2850 class="cmtt-8"> length</span><span
2851 class="cmtt-8"> 2</span><span
2852 class="cmtt-8"> codeword</span><span
2853 class="cmtt-8"> 10</span><br class="fancyvrb" /><a
2854 id="x1-52030r7"></a><span
2855 class="cmr-6">7</span><span
2856 class="cmtt-8"> </span><span
2857 class="cmtt-8"> entry</span><span
2858 class="cmtt-8"> 6:</span><span
2859 class="cmtt-8"> length</span><span
2860 class="cmtt-8"> 3</span><span
2861 class="cmtt-8"> codeword</span><span
2862 class="cmtt-8"> 110</span><br class="fancyvrb" /><a
2863 id="x1-52032r8"></a><span
2864 class="cmr-6">8</span><span
2865 class="cmtt-8"> </span><span
2866 class="cmtt-8"> entry</span><span
2867 class="cmtt-8"> 7:</span><span
2868 class="cmtt-8"> length</span><span
2869 class="cmtt-8"> 3</span><span
2870 class="cmtt-8"> codeword</span><span
2871 class="cmtt-8"> 111</span></div>
2872 <!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
2873 id="x1-530003.2.1"></a><span
2874 class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
2875 be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
2876 one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
2878 <!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
2879 numbers equivalent to the leaves numbered left-to-right:
2885 <!--l. 247--><p class="noindent" >
2887 <!--l. 248--><p class="noindent" ><img
2888 src="hufftree.png" alt="PIC"
2890 <br /> <div class="caption"
2891 ><span class="id">Figure 4: </span><span
2892 class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 -->
2894 <!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
2896 <!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
2897 In the above example, if codeword seven were eliminated, it’s clear that the tree is
2901 <!--l. 260--><p class="noindent" >
2903 <!--l. 261--><p class="noindent" ><img
2904 src="hufftree-under.png" alt="PIC"
2906 <br /> <div class="caption"
2907 ><span class="id">Figure 5: </span><span
2908 class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 -->
2910 <!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
2911 codeword is impossible. Both underspecified and overspecified trees are an error condition
2912 rendering the stream undecodable.
2913 <!--l. 271--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
2914 codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
2915 from the stream to decode to that entry number.
2916 <!--l. 276--><p class="noindent" ><span class="paragraphHead"><a
2917 id="x1-540003.2.1"></a><span
2918 class="cmbx-12">Errata 20150226: Single entry codebooks</span></span>
2919 A ’single-entry codebook’ is a codebook with one active codeword entry. A single-entry codebook
2920 may be either a fully populated codebook with only one declared entry, or a sparse codebook
2921 with only one entry marked used. The Vorbis I spec provides no means to specify a codeword
2922 length of zero, and as a result, a single-entry codebook is inherently malformed because it is
2923 underpopulated. The original specification did not address directly the matter of single-entry
2924 codebooks; they were implicitly illegal as it was not possible to write such a codebook with a
2925 valid tree structure.
2929 <!--l. 288--><p class="noindent" >In r14811 of the libvorbis reference implementation, Xiph added an additional check to the
2930 codebook implementation to reject underpopulated Huffman trees. This change led to the
2931 discovery of single-entry books used ’in the wild’ when the new, stricter checks rejected a number
2932 of apparently working streams.
2933 <!--l. 294--><p class="noindent" >In order to minimize breakage of deployed (if technically erroneous) streams, r16073 of the
2934 reference implementation explicitly special-cased single-entry codebooks to tolerate the
2935 single-entry case. Commit r16073 also added the following to the specification:
2936 <!--l. 303--><p class="noindent" >“<span class="sout">Take special care that a codebook with a single used entry is handled properly; it consists of a
2937 single codework of zero bits and reading a value out of such a codebook always returns the single
2938 used value and sinks zero bits. </span>”
2939 <!--l. 305--><p class="noindent" >The intent was to clarify the spec and codify current practice. However, this addition is
2940 erroneously at odds with the intent of preserving usability of existing streams using single-entry
2941 codebooks, disagrees with the code changes that reinstated decoding, and does not address how
2942 single-entry codebooks should be encoded.
2943 <!--l. 311--><p class="noindent" >As such, the above addition made in r16037 is struck from the specification and replaced by the
2945 <!--l. 330--><p class="noindent" >
2947 <!--l. 330--><p class="noindent" >It is possible to declare a Vorbis codebook containing a single codework
2948 entry. A single-entry codebook may be either a fully populated codebook with
2950 class="cmtt-12">[codebook_entries] </span>set to 1, or a sparse codebook marking only one entry
2951 used. Note that it is not possible to also encode a <span
2952 class="cmtt-12">[codeword_length] </span>of zero
2953 for the single used codeword, as the unsigned value written to the stream
2955 class="cmtt-12">[codeword_length]-1</span>. Instead, encoder implementations should indicate a
2957 class="cmtt-12">[codeword_length] </span>of 1 and ’write’ the codeword to a stream during audio
2958 encoding by writing a single zero bit.
2959 <!--l. 330--><p class="noindent" >Decoder implementations shall reject a codebook if it contains only one used
2960 entry and the encoded <span
2961 class="cmtt-12">[codeword_length] </span>of that entry is not 1. ’Reading’ a
2962 value from single-entry codebook always returns the single used codeword value
2963 and sinks one bit. Decoders should tolerate that the bit read from the stream
2964 be ’1’ instead of ’0’; both values shall return the single used codeword.</div>
2965 <!--l. 332--><p class="noindent" ><span class="paragraphHead"><a
2966 id="x1-550003.2.1"></a><span
2967 class="cmbx-12">VQ lookup table vector representation</span></span>
2968 Unpacking the VQ lookup table vectors relies on the following values:
2972 <div class="fancyvrb" id="fancyvrb17"><a
2973 id="x1-55002r1"></a><span
2974 class="cmr-6">1</span><span
2975 class="cmtt-8"> </span><span
2976 class="cmtt-8"> the</span><span
2977 class="cmtt-8"> [codebook\_multiplicands]</span><span
2978 class="cmtt-8"> array</span><br class="fancyvrb" /><a
2979 id="x1-55004r2"></a><span
2980 class="cmr-6">2</span><span
2981 class="cmtt-8"> </span><span
2982 class="cmtt-8"> [codebook\_minimum\_value]</span><br class="fancyvrb" /><a
2983 id="x1-55006r3"></a><span
2984 class="cmr-6">3</span><span
2985 class="cmtt-8"> </span><span
2986 class="cmtt-8"> [codebook\_delta\_value]</span><br class="fancyvrb" /><a
2987 id="x1-55008r4"></a><span
2988 class="cmr-6">4</span><span
2989 class="cmtt-8"> </span><span
2990 class="cmtt-8"> [codebook\_sequence\_p]</span>
2991 <br class="fancyvrb" /><a
2992 id="x1-55010r5"></a><span
2993 class="cmr-6">5</span><span
2994 class="cmtt-8"> </span><span
2995 class="cmtt-8"> [codebook\_lookup\_type]</span><br class="fancyvrb" /><a
2996 id="x1-55012r6"></a><span
2997 class="cmr-6">6</span><span
2998 class="cmtt-8"> </span><span
2999 class="cmtt-8"> [codebook\_entries]</span><br class="fancyvrb" /><a
3000 id="x1-55014r7"></a><span
3001 class="cmr-6">7</span><span
3002 class="cmtt-8"> </span><span
3003 class="cmtt-8"> [codebook\_dimensions]</span><br class="fancyvrb" /><a
3004 id="x1-55016r8"></a><span
3005 class="cmr-6">8</span><span
3006 class="cmtt-8"> </span><span
3007 class="cmtt-8"> [codebook\_lookup\_values]</span></div>
3008 <!--l. 348--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
3010 class="cmtt-12">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return
3011 during audio packet decode in a VQ context.
3012 <!--l. 353--><p class="noindent" ><span class="paragraphHead"><a
3013 id="x1-560003.2.1"></a><span
3014 class="cmbx-12">Vector value decode: Lookup type 1</span></span>
3015 Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of
3016 scalar values. Calculate (unpack) the final values of a codebook entry vector from
3017 the entries in <span
3018 class="cmtt-12">[codebook_multiplicands] </span>as follows (<span
3019 class="cmtt-12">[value_vector] </span>is the output
3020 vector representing the vector of values for entry number <span
3021 class="cmtt-12">[lookup_offset] </span>in this
3023 <!--l. 362--><p class="noindent" >
3024 <div class="fancyvrb" id="fancyvrb18"><a
3025 id="x1-56002r1"></a><span
3026 class="cmr-6">1</span><span
3027 class="cmtt-8"> </span><span
3028 class="cmtt-8"> </span><span
3029 class="cmtt-8"> </span><span
3030 class="cmtt-8"> 1)</span><span
3031 class="cmtt-8"> [last]</span><span
3032 class="cmtt-8"> =</span><span
3033 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
3034 id="x1-56004r2"></a><span
3035 class="cmr-6">2</span><span
3036 class="cmtt-8"> </span><span
3037 class="cmtt-8"> </span><span
3038 class="cmtt-8"> </span><span
3039 class="cmtt-8"> 2)</span><span
3040 class="cmtt-8"> [index_divisor]</span><span
3041 class="cmtt-8"> =</span><span
3042 class="cmtt-8"> 1;</span><br class="fancyvrb" /><a
3043 id="x1-56006r3"></a><span
3044 class="cmr-6">3</span><span
3045 class="cmtt-8"> </span><span
3046 class="cmtt-8"> </span><span
3047 class="cmtt-8"> </span><span
3048 class="cmtt-8"> 3)</span><span
3049 class="cmtt-8"> iterate</span><span
3050 class="cmtt-8"> [i]</span><span
3051 class="cmtt-8"> over</span><span
3052 class="cmtt-8"> the</span><span
3053 class="cmtt-8"> range</span><span
3054 class="cmtt-8"> 0</span><span
3055 class="cmtt-8"> ...</span><span
3056 class="cmtt-8"> [codebook_dimensions]-1</span><span
3057 class="cmtt-8"> (once</span><span
3058 class="cmtt-8"> for</span><span
3059 class="cmtt-8"> each</span><span
3060 class="cmtt-8"> scalar</span><span
3061 class="cmtt-8"> value</span><span
3062 class="cmtt-8"> in</span><span
3063 class="cmtt-8"> the</span><span
3064 class="cmtt-8"> value</span><span
3065 class="cmtt-8"> vector)</span><span
3066 class="cmtt-8"> </span><span
3067 class="cmsy-8">{</span>
3068 <br class="fancyvrb" /><a
3069 id="x1-56008r4"></a><span
3070 class="cmr-6">4</span><span
3071 class="cmtt-8"> </span><span
3072 class="cmtt-8"> </span><br class="fancyvrb" /><a
3073 id="x1-56010r5"></a><span
3074 class="cmr-6">5</span><span
3075 class="cmtt-8"> </span><span
3076 class="cmtt-8"> </span><span
3077 class="cmtt-8"> </span><span
3078 class="cmtt-8"> </span><span
3079 class="cmtt-8"> </span><span
3080 class="cmtt-8"> </span><span
3081 class="cmtt-8"> </span><span
3082 class="cmtt-8"> </span><span
3083 class="cmtt-8"> 4)</span><span
3084 class="cmtt-8"> [multiplicand_offset]</span><span
3085 class="cmtt-8"> =</span><span
3086 class="cmtt-8"> (</span><span
3087 class="cmtt-8"> [lookup_offset]</span><span
3088 class="cmtt-8"> divided</span><span
3089 class="cmtt-8"> by</span><span
3090 class="cmtt-8"> [index_divisor]</span><span
3091 class="cmtt-8"> using</span><span
3092 class="cmtt-8"> integer</span>
3093 <br class="fancyvrb" /><a
3094 id="x1-56012r6"></a><span
3095 class="cmr-6">6</span><span
3096 class="cmtt-8"> </span><span
3097 class="cmtt-8"> </span><span
3098 class="cmtt-8"> </span><span
3099 class="cmtt-8"> </span><span
3100 class="cmtt-8"> </span><span
3101 class="cmtt-8"> </span><span
3102 class="cmtt-8"> </span><span
3103 class="cmtt-8"> </span><span
3104 class="cmtt-8"> </span><span
3105 class="cmtt-8"> </span><span
3106 class="cmtt-8"> </span><span
3107 class="cmtt-8"> division</span><span
3108 class="cmtt-8"> )</span><span
3109 class="cmtt-8"> integer</span><span
3110 class="cmtt-8"> modulo</span><span
3111 class="cmtt-8"> [codebook_lookup_values]</span><br class="fancyvrb" /><a
3112 id="x1-56014r7"></a><span
3113 class="cmr-6">7</span><span
3114 class="cmtt-8"> </span><span
3115 class="cmtt-8"> </span><br class="fancyvrb" /><a
3116 id="x1-56016r8"></a><span
3117 class="cmr-6">8</span><span
3118 class="cmtt-8"> </span><span
3119 class="cmtt-8"> </span><span
3120 class="cmtt-8"> </span><span
3121 class="cmtt-8"> </span><span
3122 class="cmtt-8"> </span><span
3123 class="cmtt-8"> </span><span
3124 class="cmtt-8"> </span><span
3125 class="cmtt-8"> </span><span
3126 class="cmtt-8"> 5)</span><span
3127 class="cmtt-8"> vector</span><span
3128 class="cmtt-8"> [value_vector]</span><span
3129 class="cmtt-8"> element</span><span
3130 class="cmtt-8"> [i]</span><span
3131 class="cmtt-8"> =</span>
3132 <br class="fancyvrb" /><a
3133 id="x1-56018r9"></a><span
3134 class="cmr-6">9</span><span
3135 class="cmtt-8"> </span><span
3136 class="cmtt-8"> </span><span
3137 class="cmtt-8"> </span><span
3138 class="cmtt-8"> </span><span
3139 class="cmtt-8"> </span><span
3140 class="cmtt-8"> </span><span
3141 class="cmtt-8"> </span><span
3142 class="cmtt-8"> </span><span
3143 class="cmtt-8"> </span><span
3144 class="cmtt-8"> </span><span
3145 class="cmtt-8"> </span><span
3146 class="cmtt-8"> </span><span
3147 class="cmtt-8"> </span><span
3148 class="cmtt-8"> (</span><span
3149 class="cmtt-8"> [codebook_multiplicands]</span><span
3150 class="cmtt-8"> array</span><span
3151 class="cmtt-8"> element</span><span
3152 class="cmtt-8"> number</span><span
3153 class="cmtt-8"> [multiplicand_offset]</span><span
3154 class="cmtt-8"> )</span><span
3155 class="cmtt-8"> *</span>
3156 <br class="fancyvrb" /><a
3157 id="x1-56020r10"></a><span
3158 class="cmr-6">10</span><span
3159 class="cmtt-8"> </span><span
3160 class="cmtt-8"> </span><span
3161 class="cmtt-8"> </span><span
3162 class="cmtt-8"> </span><span
3163 class="cmtt-8"> </span><span
3164 class="cmtt-8"> </span><span
3165 class="cmtt-8"> </span><span
3166 class="cmtt-8"> </span><span
3167 class="cmtt-8"> </span><span
3168 class="cmtt-8"> </span><span
3169 class="cmtt-8"> </span><span
3170 class="cmtt-8"> </span><span
3171 class="cmtt-8"> </span><span
3172 class="cmtt-8"> [codebook_delta_value]</span><span
3173 class="cmtt-8"> +</span><span
3174 class="cmtt-8"> [codebook_minimum_value]</span><span
3175 class="cmtt-8"> +</span><span
3176 class="cmtt-8"> [last];</span><br class="fancyvrb" /><a
3177 id="x1-56022r11"></a><span
3178 class="cmr-6">11</span><span
3179 class="cmtt-8"> </span><span
3180 class="cmtt-8"> </span>
3181 <br class="fancyvrb" /><a
3182 id="x1-56024r12"></a><span
3183 class="cmr-6">12</span><span
3184 class="cmtt-8"> </span><span
3185 class="cmtt-8"> </span><span
3186 class="cmtt-8"> </span><span
3187 class="cmtt-8"> </span><span
3188 class="cmtt-8"> </span><span
3189 class="cmtt-8"> </span><span
3190 class="cmtt-8"> </span><span
3191 class="cmtt-8"> </span><span
3192 class="cmtt-8"> 6)</span><span
3193 class="cmtt-8"> if</span><span
3194 class="cmtt-8"> (</span><span
3195 class="cmtt-8"> [codebook_sequence_p]</span><span
3196 class="cmtt-8"> is</span><span
3197 class="cmtt-8"> set</span><span
3198 class="cmtt-8"> )</span><span
3199 class="cmtt-8"> then</span><span
3200 class="cmtt-8"> set</span><span
3201 class="cmtt-8"> [last]</span><span
3202 class="cmtt-8"> =</span><span
3203 class="cmtt-8"> vector</span><span
3204 class="cmtt-8"> [value_vector]</span><span
3205 class="cmtt-8"> element</span><span
3206 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
3207 id="x1-56026r13"></a><span
3208 class="cmr-6">13</span><span
3209 class="cmtt-8"> </span><span
3210 class="cmtt-8"> </span>
3211 <br class="fancyvrb" /><a
3212 id="x1-56028r14"></a><span
3213 class="cmr-6">14</span><span
3214 class="cmtt-8"> </span><span
3215 class="cmtt-8"> </span><span
3216 class="cmtt-8"> </span><span
3217 class="cmtt-8"> </span><span
3218 class="cmtt-8"> </span><span
3219 class="cmtt-8"> </span><span
3220 class="cmtt-8"> </span><span
3221 class="cmtt-8"> </span><span
3222 class="cmtt-8"> 7)</span><span
3223 class="cmtt-8"> [index_divisor]</span><span
3224 class="cmtt-8"> =</span><span
3225 class="cmtt-8"> [index_divisor]</span><span
3226 class="cmtt-8"> *</span><span
3227 class="cmtt-8"> [codebook_lookup_values]</span><br class="fancyvrb" /><a
3228 id="x1-56030r15"></a><span
3229 class="cmr-6">15</span><span
3230 class="cmtt-8"> </span><span
3231 class="cmtt-8"> </span><br class="fancyvrb" /><a
3232 id="x1-56032r16"></a><span
3233 class="cmr-6">16</span><span
3234 class="cmtt-8"> </span><span
3235 class="cmtt-8"> </span><span
3236 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
3242 id="x1-56034r17"></a><span
3243 class="cmr-6">17</span><span
3244 class="cmtt-8"> </span><span
3245 class="cmtt-8"> </span><br class="fancyvrb" /><a
3246 id="x1-56036r18"></a><span
3247 class="cmr-6">18</span><span
3248 class="cmtt-8"> </span><span
3249 class="cmtt-8"> </span><span
3250 class="cmtt-8"> </span><span
3251 class="cmtt-8"> 8)</span><span
3252 class="cmtt-8"> vector</span><span
3253 class="cmtt-8"> calculation</span><span
3254 class="cmtt-8"> completed.</span></div>
3255 <!--l. 385--><p class="noindent" ><span class="paragraphHead"><a
3256 id="x1-570003.2.1"></a><span
3257 class="cmbx-12">Vector value decode: Lookup type 2</span></span>
3258 Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set
3260 class="cmtt-12">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final
3261 values of a codebook entry vector from the entries in <span
3262 class="cmtt-12">[codebook_multiplicands] </span>as follows
3264 class="cmtt-12">[value_vector] </span>is the output vector representing the vector of values for entry number
3266 class="cmtt-12">[lookup_offset] </span>in this codebook):
3267 <!--l. 395--><p class="noindent" >
3268 <div class="fancyvrb" id="fancyvrb19"><a
3269 id="x1-57002r1"></a><span
3270 class="cmr-6">1</span><span
3271 class="cmtt-8"> </span><span
3272 class="cmtt-8"> </span><span
3273 class="cmtt-8"> </span><span
3274 class="cmtt-8"> 1)</span><span
3275 class="cmtt-8"> [last]</span><span
3276 class="cmtt-8"> =</span><span
3277 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
3278 id="x1-57004r2"></a><span
3279 class="cmr-6">2</span><span
3280 class="cmtt-8"> </span><span
3281 class="cmtt-8"> </span><span
3282 class="cmtt-8"> </span><span
3283 class="cmtt-8"> 2)</span><span
3284 class="cmtt-8"> [multiplicand_offset]</span><span
3285 class="cmtt-8"> =</span><span
3286 class="cmtt-8"> [lookup_offset]</span><span
3287 class="cmtt-8"> *</span><span
3288 class="cmtt-8"> [codebook_dimensions]</span>
3289 <br class="fancyvrb" /><a
3290 id="x1-57006r3"></a><span
3291 class="cmr-6">3</span><span
3292 class="cmtt-8"> </span><span
3293 class="cmtt-8"> </span><span
3294 class="cmtt-8"> </span><span
3295 class="cmtt-8"> 3)</span><span
3296 class="cmtt-8"> iterate</span><span
3297 class="cmtt-8"> [i]</span><span
3298 class="cmtt-8"> over</span><span
3299 class="cmtt-8"> the</span><span
3300 class="cmtt-8"> range</span><span
3301 class="cmtt-8"> 0</span><span
3302 class="cmtt-8"> ...</span><span
3303 class="cmtt-8"> [codebook_dimensions]-1</span><span
3304 class="cmtt-8"> (once</span><span
3305 class="cmtt-8"> for</span><span
3306 class="cmtt-8"> each</span><span
3307 class="cmtt-8"> scalar</span><span
3308 class="cmtt-8"> value</span><span
3309 class="cmtt-8"> in</span><span
3310 class="cmtt-8"> the</span><span
3311 class="cmtt-8"> value</span><span
3312 class="cmtt-8"> vector)</span><span
3313 class="cmtt-8"> </span><span
3314 class="cmsy-8">{</span><br class="fancyvrb" /><a
3315 id="x1-57008r4"></a><span
3316 class="cmr-6">4</span><span
3317 class="cmtt-8"> </span><span
3318 class="cmtt-8"> </span>
3319 <br class="fancyvrb" /><a
3320 id="x1-57010r5"></a><span
3321 class="cmr-6">5</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"> </span><span
3327 class="cmtt-8"> </span><span
3328 class="cmtt-8"> </span><span
3329 class="cmtt-8"> </span><span
3330 class="cmtt-8"> 4)</span><span
3331 class="cmtt-8"> vector</span><span
3332 class="cmtt-8"> [value_vector]</span><span
3333 class="cmtt-8"> element</span><span
3334 class="cmtt-8"> [i]</span><span
3335 class="cmtt-8"> =</span><br class="fancyvrb" /><a
3336 id="x1-57012r6"></a><span
3337 class="cmr-6">6</span><span
3338 class="cmtt-8"> </span><span
3339 class="cmtt-8"> </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="cmtt-8"> </span><span
3348 class="cmtt-8"> </span><span
3349 class="cmtt-8"> </span><span
3350 class="cmtt-8"> </span><span
3351 class="cmtt-8"> (</span><span
3352 class="cmtt-8"> [codebook_multiplicands]</span><span
3353 class="cmtt-8"> array</span><span
3354 class="cmtt-8"> element</span><span
3355 class="cmtt-8"> number</span><span
3356 class="cmtt-8"> [multiplicand_offset]</span><span
3357 class="cmtt-8"> )</span><span
3358 class="cmtt-8"> *</span>
3359 <br class="fancyvrb" /><a
3360 id="x1-57014r7"></a><span
3361 class="cmr-6">7</span><span
3362 class="cmtt-8"> </span><span
3363 class="cmtt-8"> </span><span
3364 class="cmtt-8"> </span><span
3365 class="cmtt-8"> </span><span
3366 class="cmtt-8"> </span><span
3367 class="cmtt-8"> </span><span
3368 class="cmtt-8"> </span><span
3369 class="cmtt-8"> </span><span
3370 class="cmtt-8"> </span><span
3371 class="cmtt-8"> </span><span
3372 class="cmtt-8"> </span><span
3373 class="cmtt-8"> </span><span
3374 class="cmtt-8"> </span><span
3375 class="cmtt-8"> [codebook_delta_value]</span><span
3376 class="cmtt-8"> +</span><span
3377 class="cmtt-8"> [codebook_minimum_value]</span><span
3378 class="cmtt-8"> +</span><span
3379 class="cmtt-8"> [last];</span><br class="fancyvrb" /><a
3380 id="x1-57016r8"></a><span
3381 class="cmr-6">8</span><span
3382 class="cmtt-8"> </span><span
3383 class="cmtt-8"> </span>
3384 <br class="fancyvrb" /><a
3385 id="x1-57018r9"></a><span
3386 class="cmr-6">9</span><span
3387 class="cmtt-8"> </span><span
3388 class="cmtt-8"> </span><span
3389 class="cmtt-8"> </span><span
3390 class="cmtt-8"> </span><span
3391 class="cmtt-8"> </span><span
3392 class="cmtt-8"> </span><span
3393 class="cmtt-8"> </span><span
3394 class="cmtt-8"> </span><span
3395 class="cmtt-8"> 5)</span><span
3396 class="cmtt-8"> if</span><span
3397 class="cmtt-8"> (</span><span
3398 class="cmtt-8"> [codebook_sequence_p]</span><span
3399 class="cmtt-8"> is</span><span
3400 class="cmtt-8"> set</span><span
3401 class="cmtt-8"> )</span><span
3402 class="cmtt-8"> then</span><span
3403 class="cmtt-8"> set</span><span
3404 class="cmtt-8"> [last]</span><span
3405 class="cmtt-8"> =</span><span
3406 class="cmtt-8"> vector</span><span
3407 class="cmtt-8"> [value_vector]</span><span
3408 class="cmtt-8"> element</span><span
3409 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
3410 id="x1-57020r10"></a><span
3411 class="cmr-6">10</span><span
3412 class="cmtt-8"> </span><span
3413 class="cmtt-8"> </span>
3414 <br class="fancyvrb" /><a
3415 id="x1-57022r11"></a><span
3416 class="cmr-6">11</span><span
3417 class="cmtt-8"> </span><span
3418 class="cmtt-8"> </span><span
3419 class="cmtt-8"> </span><span
3420 class="cmtt-8"> </span><span
3421 class="cmtt-8"> </span><span
3422 class="cmtt-8"> </span><span
3423 class="cmtt-8"> </span><span
3424 class="cmtt-8"> </span><span
3425 class="cmtt-8"> 6)</span><span
3426 class="cmtt-8"> increment</span><span
3427 class="cmtt-8"> [multiplicand_offset]</span><br class="fancyvrb" /><a
3428 id="x1-57024r12"></a><span
3429 class="cmr-6">12</span><span
3430 class="cmtt-8"> </span><span
3431 class="cmtt-8"> </span><br class="fancyvrb" /><a
3432 id="x1-57026r13"></a><span
3433 class="cmr-6">13</span><span
3434 class="cmtt-8"> </span><span
3435 class="cmtt-8"> </span><span
3436 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
3442 id="x1-57028r14"></a><span
3443 class="cmr-6">14</span><span
3444 class="cmtt-8"> </span><span
3445 class="cmtt-8"> </span><br class="fancyvrb" /><a
3446 id="x1-57030r15"></a><span
3447 class="cmr-6">15</span><span
3448 class="cmtt-8"> </span><span
3449 class="cmtt-8"> </span><span
3450 class="cmtt-8"> </span><span
3451 class="cmtt-8"> 7)</span><span
3452 class="cmtt-8"> vector</span><span
3453 class="cmtt-8"> calculation</span><span
3454 class="cmtt-8"> completed.</span></div>
3458 <!--l. 421--><p class="noindent" >
3459 <h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a
3460 id="x1-580003.3"></a>Use of the codebook abstraction</h4>
3461 <!--l. 423--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a
3462 specific codebook reads a codeword from the bitstream, decoding it into an entry number, and
3463 then returns that entry number to the decoder (when used in a scalar entropy coding context), or
3464 uses that entry number as an offset into the VQ lookup table, returning a vector of values (when
3465 used in a context desiring a VQ value). Scalar or VQ context is always explicit; any
3466 call to the codebook mechanism requests either a scalar entry number or a lookup
3468 <!--l. 433--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting
3469 decode using a codebook of lookup type 0 in any context expecting a vector return
3470 value (even in a case where a vector of dimension one) is forbidden. If decoder setup
3471 or decode requests such an action, that is an error condition rendering the packet
3473 <!--l. 440--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
3474 next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
3475 codeword in the codebook. This process can be though of as logically walking the
3476 Huffman decode tree by reading one bit at a time from the bitstream, and using the
3477 bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
3478 branch (right in the above examples). Walking the tree finishes when the decode process
3479 hits a leaf in the decision tree; the result is the entry number corresponding to that
3480 leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
3482 <!--l. 452--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
3484 <!--l. 455--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
3485 table. The value returned to the decoder is the vector of scalars corresponding to this
3493 <h3 class="sectionHead"><span class="titlemark">4. </span> <a
3494 id="x1-590004"></a>Codec Setup and Packet Decode</h3>
3495 <!--l. 7--><p class="noindent" >
3496 <h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a
3497 id="x1-600004.1"></a>Overview</h4>
3498 <!--l. 9--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
3499 of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
3500 process, which is provided in <a
3501 href="#x1-20001">section 1</a>, “<a
3502 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
3503 href="#x1-360002">section 2</a>,
3505 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
3507 <!--l. 17--><p class="noindent" >
3508 <h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a
3509 id="x1-610004.2"></a>Header decode and decode setup</h4>
3510 <!--l. 19--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
3511 identification header, the comments header, and the setup header. All are required for decode
3512 compliance. An end-of-packet condition during decoding the first or third header packet renders
3513 the stream undecodable. End-of-packet decoding the comment header is a non-fatal error
3515 <!--l. 26--><p class="noindent" >
3516 <h5 class="subsubsectionHead"><span class="titlemark">4.2.1. </span> <a
3517 id="x1-620004.2.1"></a>Common header decode</h5>
3518 <!--l. 28--><p class="noindent" >Each header packet begins with the same header fields.
3519 <!--l. 31--><p class="noindent" >
3520 <div class="fancyvrb" id="fancyvrb20"><a
3521 id="x1-62002r1"></a><span
3522 class="cmr-6">1</span><span
3523 class="cmtt-8"> </span><span
3524 class="cmtt-8"> </span><span
3525 class="cmtt-8"> </span><span
3526 class="cmtt-8"> 1)</span><span
3527 class="cmtt-8"> [packet_type]</span><span
3528 class="cmtt-8"> :</span><span
3529 class="cmtt-8"> 8</span><span
3530 class="cmtt-8"> bit</span><span
3531 class="cmtt-8"> value</span><br class="fancyvrb" /><a
3532 id="x1-62004r2"></a><span
3533 class="cmr-6">2</span><span
3534 class="cmtt-8"> </span><span
3535 class="cmtt-8"> </span><span
3536 class="cmtt-8"> </span><span
3537 class="cmtt-8"> 2)</span><span
3538 class="cmtt-8"> 0x76,</span><span
3539 class="cmtt-8"> 0x6f,</span><span
3540 class="cmtt-8"> 0x72,</span><span
3541 class="cmtt-8"> 0x62,</span><span
3542 class="cmtt-8"> 0x69,</span><span
3543 class="cmtt-8"> 0x73:</span><span
3544 class="cmtt-8"> the</span><span
3545 class="cmtt-8"> characters</span><span
3546 class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
3547 class="cmtt-8"> as</span><span
3548 class="cmtt-8"> six</span><span
3549 class="cmtt-8"> octets</span></div>
3550 <!--l. 36--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
3551 header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
3552 single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
3557 <!--l. 44--><p class="noindent" >
3558 <h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a
3559 id="x1-630004.2.2"></a>Identification header</h5>
3560 <!--l. 46--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream
3561 definitively as Vorbis, and provide a few externally relevant pieces of information about the audio
3562 stream. The identification header is coded as follows:
3563 <!--l. 51--><p class="noindent" >
3564 <div class="fancyvrb" id="fancyvrb21"><a
3565 id="x1-63002r1"></a><span
3566 class="cmr-6">1</span><span
3567 class="cmtt-8"> </span><span
3568 class="cmtt-8"> </span><span
3569 class="cmtt-8"> 1)</span><span
3570 class="cmtt-8"> [vorbis_version]</span><span
3571 class="cmtt-8"> =</span><span
3572 class="cmtt-8"> read</span><span
3573 class="cmtt-8"> 32</span><span
3574 class="cmtt-8"> bits</span><span
3575 class="cmtt-8"> as</span><span
3576 class="cmtt-8"> unsigned</span><span
3577 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3578 id="x1-63004r2"></a><span
3579 class="cmr-6">2</span><span
3580 class="cmtt-8"> </span><span
3581 class="cmtt-8"> </span><span
3582 class="cmtt-8"> 2)</span><span
3583 class="cmtt-8"> [audio_channels]</span><span
3584 class="cmtt-8"> =</span><span
3585 class="cmtt-8"> read</span><span
3586 class="cmtt-8"> 8</span><span
3587 class="cmtt-8"> bit</span><span
3588 class="cmtt-8"> integer</span><span
3589 class="cmtt-8"> as</span><span
3590 class="cmtt-8"> unsigned</span>
3591 <br class="fancyvrb" /><a
3592 id="x1-63006r3"></a><span
3593 class="cmr-6">3</span><span
3594 class="cmtt-8"> </span><span
3595 class="cmtt-8"> </span><span
3596 class="cmtt-8"> 3)</span><span
3597 class="cmtt-8"> [audio_sample_rate]</span><span
3598 class="cmtt-8"> =</span><span
3599 class="cmtt-8"> read</span><span
3600 class="cmtt-8"> 32</span><span
3601 class="cmtt-8"> bits</span><span
3602 class="cmtt-8"> as</span><span
3603 class="cmtt-8"> unsigned</span><span
3604 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3605 id="x1-63008r4"></a><span
3606 class="cmr-6">4</span><span
3607 class="cmtt-8"> </span><span
3608 class="cmtt-8"> </span><span
3609 class="cmtt-8"> 4)</span><span
3610 class="cmtt-8"> [bitrate_maximum]</span><span
3611 class="cmtt-8"> =</span><span
3612 class="cmtt-8"> read</span><span
3613 class="cmtt-8"> 32</span><span
3614 class="cmtt-8"> bits</span><span
3615 class="cmtt-8"> as</span><span
3616 class="cmtt-8"> signed</span><span
3617 class="cmtt-8"> integer</span>
3618 <br class="fancyvrb" /><a
3619 id="x1-63010r5"></a><span
3620 class="cmr-6">5</span><span
3621 class="cmtt-8"> </span><span
3622 class="cmtt-8"> </span><span
3623 class="cmtt-8"> 5)</span><span
3624 class="cmtt-8"> [bitrate_nominal]</span><span
3625 class="cmtt-8"> =</span><span
3626 class="cmtt-8"> read</span><span
3627 class="cmtt-8"> 32</span><span
3628 class="cmtt-8"> bits</span><span
3629 class="cmtt-8"> as</span><span
3630 class="cmtt-8"> signed</span><span
3631 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3632 id="x1-63012r6"></a><span
3633 class="cmr-6">6</span><span
3634 class="cmtt-8"> </span><span
3635 class="cmtt-8"> </span><span
3636 class="cmtt-8"> 6)</span><span
3637 class="cmtt-8"> [bitrate_minimum]</span><span
3638 class="cmtt-8"> =</span><span
3639 class="cmtt-8"> read</span><span
3640 class="cmtt-8"> 32</span><span
3641 class="cmtt-8"> bits</span><span
3642 class="cmtt-8"> as</span><span
3643 class="cmtt-8"> signed</span><span
3644 class="cmtt-8"> integer</span>
3645 <br class="fancyvrb" /><a
3646 id="x1-63014r7"></a><span
3647 class="cmr-6">7</span><span
3648 class="cmtt-8"> </span><span
3649 class="cmtt-8"> </span><span
3650 class="cmtt-8"> 7)</span><span
3651 class="cmtt-8"> [blocksize_0]</span><span
3652 class="cmtt-8"> =</span><span
3653 class="cmtt-8"> 2</span><span
3654 class="cmtt-8"> exponent</span><span
3655 class="cmtt-8"> (read</span><span
3656 class="cmtt-8"> 4</span><span
3657 class="cmtt-8"> bits</span><span
3658 class="cmtt-8"> as</span><span
3659 class="cmtt-8"> unsigned</span><span
3660 class="cmtt-8"> integer)</span><br class="fancyvrb" /><a
3661 id="x1-63016r8"></a><span
3662 class="cmr-6">8</span><span
3663 class="cmtt-8"> </span><span
3664 class="cmtt-8"> </span><span
3665 class="cmtt-8"> 8)</span><span
3666 class="cmtt-8"> [blocksize_1]</span><span
3667 class="cmtt-8"> =</span><span
3668 class="cmtt-8"> 2</span><span
3669 class="cmtt-8"> exponent</span><span
3670 class="cmtt-8"> (read</span><span
3671 class="cmtt-8"> 4</span><span
3672 class="cmtt-8"> bits</span><span
3673 class="cmtt-8"> as</span><span
3674 class="cmtt-8"> unsigned</span><span
3675 class="cmtt-8"> integer)</span>
3676 <br class="fancyvrb" /><a
3677 id="x1-63018r9"></a><span
3678 class="cmr-6">9</span><span
3679 class="cmtt-8"> </span><span
3680 class="cmtt-8"> </span><span
3681 class="cmtt-8"> 9)</span><span
3682 class="cmtt-8"> [framing_flag]</span><span
3683 class="cmtt-8"> =</span><span
3684 class="cmtt-8"> read</span><span
3685 class="cmtt-8"> one</span><span
3686 class="cmtt-8"> bit</span></div>
3687 <!--l. 63--><p class="noindent" ><span
3688 class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
3690 class="cmtt-12">[audio_channels] </span>and <span
3691 class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final
3692 blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
3693 class="cmtt-12">[blocksize_0]</span>
3694 must be less than or equal to <span
3695 class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet
3696 any of these conditions renders a stream undecodable.
3697 <!--l. 71--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
3698 considerably off in purely VBR streams. The fields are meaningful only when greater than
3700 <ul class="itemize1">
3701 <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
3702 fixed-rate bitstream
3704 <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
3706 <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
3708 <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
3712 <!--l. 85--><p class="noindent" >
3713 <h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a
3714 id="x1-640004.2.3"></a>Comment header</h5>
3715 <!--l. 86--><p class="noindent" >Comment header decode and data specification is covered in <a
3716 href="#x1-820005">section 5</a>, “<a
3717 href="#x1-820005">comment field and
3718 header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
3719 <!--l. 90--><p class="noindent" >
3720 <h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a
3721 id="x1-650004.2.4"></a>Setup header</h5>
3722 <!--l. 92--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
3725 <!--l. 94--><p class="noindent" >
3727 <!--l. 95--><p class="noindent" ><img
3728 src="components.png" alt="PIC"
3730 <br /> <div class="caption"
3731 ><span class="id">Figure 6: </span><span
3732 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-650016 -->
3734 <!--l. 100--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
3735 header contains, in order, the lists of codebook configurations, time-domain transform
3736 configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
3737 mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
3738 decode proceeds in the following order:
3739 <!--l. 108--><p class="noindent" ><span class="paragraphHead"><a
3740 id="x1-660004.2.4"></a><span
3741 class="cmbx-12">Codebooks</span></span>
3742 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3744 class="enumerate-enumitem"><span
3745 class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
3746 </dd><dt class="enumerate-enumitem">
3748 class="enumerate-enumitem">Decode <span
3749 class="cmtt-12">[vorbis_codebook_count] </span>codebooks in order as defined in <a
3750 href="#x1-470003">section 3</a>,
3752 href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
3753 of codebook configurations <span
3754 class="cmtt-12">[vorbis_codebook_configurations]</span>.</dd></dl>
3758 <!--l. 120--><p class="noindent" ><span class="paragraphHead"><a
3759 id="x1-670004.2.4"></a><span
3760 class="cmbx-12">Time domain transforms</span></span>
3761 These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must
3762 be read to maintain bitstream sync.
3763 <!--l. 127--><p class="noindent" >
3764 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3766 class="enumerate-enumitem"><span
3767 class="cmtt-12">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
3768 </dd><dt class="enumerate-enumitem">
3770 class="enumerate-enumitem">read <span
3771 class="cmtt-12">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
3772 nonzero, this is an error condition and the stream is undecodable.</dd></dl>
3773 <!--l. 133--><p class="noindent" ><span class="paragraphHead"><a
3774 id="x1-680004.2.4"></a><span
3775 class="cmbx-12">Floors</span></span>
3776 Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
3778 <!--l. 139--><p class="noindent" >
3779 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3781 class="enumerate-enumitem"><span
3782 class="cmtt-12">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
3783 </dd><dt class="enumerate-enumitem">
3785 class="enumerate-enumitem">For each <span
3786 class="cmtt-12">[i] </span>of <span
3787 class="cmtt-12">[vorbis_floor_count] </span>floor numbers:
3788 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3790 class="enumerate-enumitem">read the floor type: vector <span
3791 class="cmtt-12">[vorbis_floor_types] </span>element <span
3792 class="cmtt-12">[i] </span>= read 16 bits
3794 </dd><dt class="enumerate-enumitem">
3796 class="enumerate-enumitem">If the floor type is zero, decode the floor configuration as defined in <a
3797 href="#x1-900006">section 6</a>,
3799 href="#x1-900006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
3800 class="cmtt-12">[i] </span>of the floor
3801 configuration array <span
3802 class="cmtt-12">[vorbis_floor_configurations]</span>.
3803 </dd><dt class="enumerate-enumitem">
3805 class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a
3806 href="#x1-970007">section 7</a>,
3808 href="#x1-970007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
3809 class="cmtt-12">[i] </span>of the floor
3810 configuration array <span
3811 class="cmtt-12">[vorbis_floor_configurations]</span>.
3812 </dd><dt class="enumerate-enumitem">
3814 class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR
3820 <!--l. 157--><p class="noindent" ><span class="paragraphHead"><a
3821 id="x1-690004.2.4"></a><span
3822 class="cmbx-12">Residues</span></span>
3823 Vorbis uses three residue types; header decode of each type is identical.
3824 <!--l. 163--><p class="noindent" >
3825 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3827 class="enumerate-enumitem"><span
3828 class="cmtt-12">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
3829 </dd><dt class="enumerate-enumitem">
3831 class="enumerate-enumitem">For each of <span
3832 class="cmtt-12">[vorbis_residue_count] </span>residue numbers:
3833 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3835 class="enumerate-enumitem">read the residue type; vector <span
3836 class="cmtt-12">[vorbis_residue_types] </span>element <span
3837 class="cmtt-12">[i] </span>= read 16
3838 bits as unsigned integer
3839 </dd><dt class="enumerate-enumitem">
3841 class="enumerate-enumitem">If the residue type is zero, one or two, decode the residue configuration as defined
3843 href="#x1-1040008">section 8</a>, “<a
3844 href="#x1-1040008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
3845 class="cmtt-12">[i] </span>of
3846 the residue configuration array <span
3847 class="cmtt-12">[vorbis_residue_configurations]</span>.
3848 </dd><dt class="enumerate-enumitem">
3850 class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR
3853 <!--l. 177--><p class="noindent" ><span class="paragraphHead"><a
3854 id="x1-700004.2.4"></a><span
3855 class="cmbx-12">Mappings</span></span>
3856 Mappings are used to set up specific pipelines for encoding multichannel audio with varying
3857 channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
3859 <!--l. 188--><p class="noindent" >
3860 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3862 class="enumerate-enumitem"><span
3863 class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
3864 </dd><dt class="enumerate-enumitem">
3866 class="enumerate-enumitem">For each <span
3867 class="cmtt-12">[i] </span>of <span
3868 class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers:
3872 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3874 class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
3875 the mapping type in Vorbis I.
3876 </dd><dt class="enumerate-enumitem">
3878 class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable
3879 </dd><dt class="enumerate-enumitem">
3881 class="enumerate-enumitem">If the mapping type is zero:
3882 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3884 class="enumerate-enumitem">read 1 bit as a boolean flag
3885 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3887 class="enumerate-enumitem">if set, <span
3888 class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer
3890 </dd><dt class="enumerate-enumitem">
3892 class="enumerate-enumitem">if unset, <span
3893 class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</dd></dl>
3894 </dd><dt class="enumerate-enumitem">
3896 class="enumerate-enumitem">read 1 bit as a boolean flag
3897 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3899 class="enumerate-enumitem">if set, square polar channel mapping is in use:
3900 <ul class="itemize1">
3901 <li class="itemize"><span
3902 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned
3905 <li class="itemize">for <span
3906 class="cmtt-12">[j] </span>each of <span
3907 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps:
3908 <ul class="itemize2">
3909 <li class="itemize">vector <span
3910 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
3911 class="cmtt-12">[j]</span>= read
3913 href="#x1-1190009.2.1">ilog</a>(<span
3914 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
3916 <li class="itemize">vector <span
3917 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
3918 class="cmtt-12">[j]</span>= read
3920 href="#x1-1190009.2.1">ilog</a>(<span
3921 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
3923 <li class="itemize">the numbers read in the above two steps are channel numbers
3924 representing the channel to treat as magnitude and the channel
3925 to treat as angle, respectively. If for any coupling step the
3926 angle channel number equals the magnitude channel number, the
3927 magnitude channel number is greater than <span
3928 class="cmtt-12">[audio_channels]</span>-1, or
3929 the angle channel is greater than <span
3930 class="cmtt-12">[audio_channels]</span>-1, the stream
3931 is undecodable.</li></ul>
3936 </dd><dt class="enumerate-enumitem">
3938 class="enumerate-enumitem">if unset, <span
3939 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= 0</dd></dl>
3940 </dd><dt class="enumerate-enumitem">
3942 class="enumerate-enumitem">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
3943 </dd><dt class="enumerate-enumitem">
3945 class="enumerate-enumitem">if <span
3946 class="cmtt-12">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
3947 settings. For each <span
3948 class="cmtt-12">[j] </span>of <span
3949 class="cmtt-12">[audio_channels] </span>channels:
3950 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3952 class="enumerate-enumitem">vector <span
3953 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
3954 class="cmtt-12">[j] </span>= read 4 bits as unsigned
3956 </dd><dt class="enumerate-enumitem">
3958 class="enumerate-enumitem">if the value is greater than the highest numbered submap
3960 class="cmtt-12">[vorbis_mapping_submaps] </span>- 1), this in an error condition rendering
3961 the stream undecodable</dd></dl>
3962 </dd><dt class="enumerate-enumitem">
3964 class="enumerate-enumitem">for each submap <span
3965 class="cmtt-12">[j] </span>of <span
3966 class="cmtt-12">[vorbis_mapping_submaps] </span>submaps, read the floor and
3967 residue numbers for use in decoding that submap:
3968 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3970 class="enumerate-enumitem">read and discard 8 bits (the unused time configuration placeholder)
3971 </dd><dt class="enumerate-enumitem">
3973 class="enumerate-enumitem">read 8 bits as unsigned integer for the floor number; save in vector
3975 class="cmtt-12">[vorbis_mapping_submap_floor] </span>element <span
3976 class="cmtt-12">[j]</span>
3977 </dd><dt class="enumerate-enumitem">
3979 class="enumerate-enumitem">verify the floor number is not greater than the highest number floor
3980 configured for the bitstream. If it is, the bitstream is undecodable
3981 </dd><dt class="enumerate-enumitem">
3983 class="enumerate-enumitem">read 8 bits as unsigned integer for the residue number; save in vector
3985 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
3986 class="cmtt-12">[j]</span>
3987 </dd><dt class="enumerate-enumitem">
3989 class="enumerate-enumitem">verify the residue number is not greater than the highest number residue
3990 configured for the bitstream. If it is, the bitstream is undecodable</dd></dl>
3991 </dd><dt class="enumerate-enumitem">
3993 class="enumerate-enumitem">save this mapping configuration in slot <span
3994 class="cmtt-12">[i] </span>of the mapping configuration array
3996 class="cmtt-12">[vorbis_mapping_configurations]</span>.</dd></dl>
4002 <!--l. 247--><p class="noindent" ><span class="paragraphHead"><a
4003 id="x1-710004.2.4"></a><span
4004 class="cmbx-12">Modes</span></span>
4005 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4007 class="enumerate-enumitem"><span
4008 class="cmtt-12">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
4009 </dd><dt class="enumerate-enumitem">
4011 class="enumerate-enumitem">For each of <span
4012 class="cmtt-12">[vorbis_mode_count] </span>mode numbers:
4013 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4015 class="enumerate-enumitem"><span
4016 class="cmtt-12">[vorbis_mode_blockflag] </span>= read 1 bit
4017 </dd><dt class="enumerate-enumitem">
4019 class="enumerate-enumitem"><span
4020 class="cmtt-12">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
4021 </dd><dt class="enumerate-enumitem">
4023 class="enumerate-enumitem"><span
4024 class="cmtt-12">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
4025 </dd><dt class="enumerate-enumitem">
4027 class="enumerate-enumitem"><span
4028 class="cmtt-12">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
4029 </dd><dt class="enumerate-enumitem">
4031 class="enumerate-enumitem">verify ranges; zero is the only legal value in
4033 class="cmtt-12">[vorbis_mode_windowtype] </span>and <span
4034 class="cmtt-12">[vorbis_mode_transformtype]</span>.
4036 class="cmtt-12">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
4037 in use. Any illegal values render the stream undecodable.
4038 </dd><dt class="enumerate-enumitem">
4040 class="enumerate-enumitem">save this mode configuration in slot <span
4041 class="cmtt-12">[i] </span>of the mode configuration array
4043 class="cmtt-12">[vorbis_mode_configurations]</span>.</dd></dl>
4044 </dd><dt class="enumerate-enumitem">
4046 class="enumerate-enumitem">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
4047 decodable.</dd></dl>
4048 <!--l. 268--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
4049 <!--l. 277--><p class="noindent" >
4050 <h4 class="subsectionHead"><span class="titlemark">4.3. </span> <a
4051 id="x1-720004.3"></a>Audio packet decode and synthesis</h4>
4055 <!--l. 279--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
4056 audio packet decode is to read and verify the packet type. <span
4057 class="cmti-12">A non-audio packet when audio is</span>
4059 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
4061 class="cmti-12">packet and not attempt decoding it to audio</span>.
4062 <!--l. 286--><p class="noindent" >
4063 <h5 class="subsubsectionHead"><span class="titlemark">4.3.1. </span> <a
4064 id="x1-730004.3.1"></a>packet type, mode and window decode</h5>
4065 <!--l. 289--><p class="noindent" >
4066 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4068 class="enumerate-enumitem">read 1 bit <span
4069 class="cmtt-12">[packet_type]</span>; check that packet type is 0 (audio)
4070 </dd><dt class="enumerate-enumitem">
4072 class="enumerate-enumitem">read <a
4073 href="#x1-1190009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span
4074 class="cmtt-12">[mode_number]</span>
4075 </dd><dt class="enumerate-enumitem">
4077 class="enumerate-enumitem">decode blocksize <span
4078 class="cmtt-12">[n] </span>is equal to <span
4079 class="cmtt-12">[blocksize_0] </span>if <span
4080 class="cmtt-12">[vorbis_mode_blockflag] </span>is 0,
4082 class="cmtt-12">[n] </span>is equal to <span
4083 class="cmtt-12">[blocksize_1]</span>.
4084 </dd><dt class="enumerate-enumitem">
4086 class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse
4088 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4090 class="enumerate-enumitem">if this is a long window (the <span
4091 class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is
4093 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4095 class="enumerate-enumitem">read 1 bit for <span
4096 class="cmtt-12">[previous_window_flag]</span>
4097 </dd><dt class="enumerate-enumitem">
4099 class="enumerate-enumitem">read 1 bit for <span
4100 class="cmtt-12">[next_window_flag]</span>
4101 </dd><dt class="enumerate-enumitem">
4103 class="enumerate-enumitem">if <span
4104 class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will
4105 be a hybrid window for lapping with a short block. See <a
4106 href="#paragraph.1" >paragraph <a
4107 href="#x1-260001.3.2">1.3.2</a></a>,
4109 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4110 overlapping dissimilar windows. Else, the left half window will have normal
4112 </dd><dt class="enumerate-enumitem">
4114 class="enumerate-enumitem">if <span
4115 class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be
4116 a hybrid window for lapping with a short block. See <a
4117 href="#x1-260001.3.2">paragraph 1.3.2</a>,
4122 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4123 overlapping dissimilar windows. Else, the left right window will have normal
4124 long shape.</dd></dl>
4125 </dd><dt class="enumerate-enumitem">
4127 class="enumerate-enumitem">if this is a short window, the window is always the same short-window
4130 <!--l. 321--><p class="noindent" >Vorbis windows all use the slope function <span
4131 class="cmmi-12">y </span>= sin(<img
4132 src="Vorbis_I_spec1x.png" alt="π
4133 2" class="frac" align="middle"> <span
4134 class="cmsy-10x-x-120">*</span> sin <sup><span
4135 class="cmr-8">2</span></sup>((<span
4136 class="cmmi-12">x </span>+ 0<span
4137 class="cmmi-12">.</span>5)<span
4138 class="cmmi-12">∕n </span><span
4139 class="cmsy-10x-x-120">* </span><span
4140 class="cmmi-12">π</span>)), where <span
4141 class="cmmi-12">n </span>is window
4143 class="cmmi-12">x </span>ranges 0<span
4144 class="cmmi-12">…</span><span
4145 class="cmmi-12">n</span><span
4146 class="cmsy-10x-x-120">- </span>1, but dissimilar lapping requirements can affect overall shape. Window
4147 generation proceeds as follows:
4148 <!--l. 327--><p class="noindent" >
4149 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4151 class="enumerate-enumitem"><span
4152 class="cmtt-12">[window_center] </span>= <span
4153 class="cmtt-12">[n] </span>/ 2
4154 </dd><dt class="enumerate-enumitem">
4156 class="enumerate-enumitem">if (<span
4157 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4158 class="cmtt-12">[previous_window_flag] </span>is not set)
4160 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4162 class="enumerate-enumitem"><span
4163 class="cmtt-12">[left_window_start] </span>= <span
4164 class="cmtt-12">[n]</span>/4 - <span
4165 class="cmtt-12">[blocksize_0]</span>/4
4166 </dd><dt class="enumerate-enumitem">
4168 class="enumerate-enumitem"><span
4169 class="cmtt-12">[left_window_end] </span>= <span
4170 class="cmtt-12">[n]</span>/4 + <span
4171 class="cmtt-12">[blocksize_0]</span>/4
4172 </dd><dt class="enumerate-enumitem">
4174 class="enumerate-enumitem"><span
4175 class="cmtt-12">[left_n] </span>= <span
4176 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4177 <!--l. 336--><p class="noindent" >else
4178 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4180 class="enumerate-enumitem"><span
4181 class="cmtt-12">[left_window_start] </span>= 0
4182 </dd><dt class="enumerate-enumitem">
4184 class="enumerate-enumitem"><span
4185 class="cmtt-12">[left_window_end] </span>= <span
4186 class="cmtt-12">[window_center]</span>
4187 </dd><dt class="enumerate-enumitem">
4189 class="enumerate-enumitem"><span
4190 class="cmtt-12">[left_n] </span>= <span
4191 class="cmtt-12">[n]</span>/2</dd></dl>
4192 </dd><dt class="enumerate-enumitem">
4194 class="enumerate-enumitem">if (<span
4195 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4196 class="cmtt-12">[next_window_flag] </span>is not set) then
4197 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4199 class="enumerate-enumitem"><span
4200 class="cmtt-12">[right_window_start] </span>= <span
4201 class="cmtt-12">[n]*3</span>/4 - <span
4202 class="cmtt-12">[blocksize_0]</span>/4
4203 </dd><dt class="enumerate-enumitem">
4205 class="enumerate-enumitem"><span
4206 class="cmtt-12">[right_window_end] </span>= <span
4207 class="cmtt-12">[n]*3</span>/4 + <span
4208 class="cmtt-12">[blocksize_0]</span>/4
4212 </dd><dt class="enumerate-enumitem">
4214 class="enumerate-enumitem"><span
4215 class="cmtt-12">[right_n] </span>= <span
4216 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4217 <!--l. 352--><p class="noindent" >else
4218 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4220 class="enumerate-enumitem"><span
4221 class="cmtt-12">[right_window_start] </span>= <span
4222 class="cmtt-12">[window_center]</span>
4223 </dd><dt class="enumerate-enumitem">
4225 class="enumerate-enumitem"><span
4226 class="cmtt-12">[right_window_end] </span>= <span
4227 class="cmtt-12">[n]</span>
4228 </dd><dt class="enumerate-enumitem">
4230 class="enumerate-enumitem"><span
4231 class="cmtt-12">[right_n] </span>= <span
4232 class="cmtt-12">[n]</span>/2</dd></dl>
4233 </dd><dt class="enumerate-enumitem">
4235 class="enumerate-enumitem">window from range 0 ... <span
4236 class="cmtt-12">[left_window_start]</span>-1 inclusive is zero
4237 </dd><dt class="enumerate-enumitem">
4239 class="enumerate-enumitem">for <span
4240 class="cmtt-12">[i] </span>in range <span
4241 class="cmtt-12">[left_window_start] </span>... <span
4242 class="cmtt-12">[left_window_end]</span>-1, window(<span
4243 class="cmtt-12">[i]</span>) =
4245 src="Vorbis_I_spec2x.png" alt="π
4246 2" class="frac" align="middle"> <span
4247 class="cmsy-10x-x-120">*</span> sin <sup><span
4248 class="cmr-8">2</span></sup>( (<span
4249 class="cmtt-12">[i]</span>-<span
4250 class="cmtt-12">[left_window_start]</span>+0.5) / <span
4251 class="cmtt-12">[left_n] </span><span
4252 class="cmsy-10x-x-120">*</span><img
4253 src="Vorbis_I_spec3x.png" alt="π
4254 2" class="frac" align="middle">) )
4255 </dd><dt class="enumerate-enumitem">
4257 class="enumerate-enumitem">window from range <span
4258 class="cmtt-12">[left_window_end] </span>... <span
4259 class="cmtt-12">[right_window_start]</span>-1 inclusive is
4261 </dd><dt class="enumerate-enumitem">
4263 class="enumerate-enumitem">for <span
4264 class="cmtt-12">[i] </span>in range <span
4265 class="cmtt-12">[right_window_start] </span>... <span
4266 class="cmtt-12">[right_window_end]</span>-1, window(<span
4267 class="cmtt-12">[i]</span>) =
4269 src="Vorbis_I_spec4x.png" alt="π2" class="frac" align="middle"> <span
4270 class="cmsy-10x-x-120">*</span> sin <sup><span
4271 class="cmr-8">2</span></sup>( (<span
4272 class="cmtt-12">[i]</span>-<span
4273 class="cmtt-12">[right_window_start]</span>+0.5) / <span
4274 class="cmtt-12">[right_n] </span><span
4275 class="cmsy-10x-x-120">*</span><img
4276 src="Vorbis_I_spec5x.png" alt="π2" class="frac" align="middle"> + <img
4277 src="Vorbis_I_spec6x.png" alt="π2" class="frac" align="middle">) )
4278 </dd><dt class="enumerate-enumitem">
4280 class="enumerate-enumitem">window from range <span
4281 class="cmtt-12">[right_window_start] </span>... <span
4282 class="cmtt-12">[n]</span>-1 is zero</dd></dl>
4283 <!--l. 368--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this
4284 packet from the stream. An end of packet condition past this point is to be considered a possible
4286 <!--l. 375--><p class="noindent" >
4287 <h5 class="subsubsectionHead"><span class="titlemark">4.3.2. </span> <a
4288 id="x1-740004.3.2"></a>floor curve decode</h5>
4289 <!--l. 377--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
4290 class="cmtt-12">[mode_number]</span>
4291 from configuration array <span
4292 class="cmtt-12">[vorbis_mode_configurations] </span>and the map number
4294 class="cmtt-12">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
4296 class="cmtt-12">[vorbis_mapping_configurations]</span>.
4297 <!--l. 384--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
4301 <!--l. 386--><p class="noindent" >For each floor <span
4302 class="cmtt-12">[i] </span>of <span
4303 class="cmtt-12">[audio_channels]</span>
4304 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4306 class="enumerate-enumitem"><span
4307 class="cmtt-12">[submap_number] </span>= element <span
4308 class="cmtt-12">[i] </span>of vector [vorbis_mapping_mux]
4309 </dd><dt class="enumerate-enumitem">
4311 class="enumerate-enumitem"><span
4312 class="cmtt-12">[floor_number] </span>= element <span
4313 class="cmtt-12">[submap_number] </span>of vector [vorbis_submap_floor]
4314 </dd><dt class="enumerate-enumitem">
4316 class="enumerate-enumitem">if the floor type of this floor (vector
4318 class="cmtt-12">[vorbis_floor_types] </span>element <span
4319 class="cmtt-12">[floor_number]</span>) is zero then decode the floor for
4321 class="cmtt-12">[i] </span>according to the <a
4322 href="#x1-940006.2.2">subsubsection 6.2.2</a>, “<a
4323 href="#x1-940006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
4324 </dd><dt class="enumerate-enumitem">
4326 class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span
4327 class="cmtt-12">[i] </span>according to the
4329 href="#x1-1020007.2.3">subsubsection 7.2.3</a>, “<a
4330 href="#x1-1020007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
4331 </dd><dt class="enumerate-enumitem">
4333 class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis
4334 </dd><dt class="enumerate-enumitem">
4336 class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span
4337 class="cmtt-12">[no_residue] </span>element <span
4338 class="cmtt-12">[i] </span>to true,
4339 else set vector <span
4340 class="cmtt-12">[no_residue] </span>element <span
4341 class="cmtt-12">[i] </span>to false</dd></dl>
4342 <!--l. 406--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
4343 output vectors and skipping to the add/overlap output stage.
4344 <!--l. 412--><p class="noindent" >
4345 <h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a
4346 id="x1-750004.3.3"></a>nonzero vector propagate</h5>
4347 <!--l. 414--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
4348 that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
4349 coded in the stream, save for one complication. If some vectors are used and some are not,
4350 channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
4352 <!--l. 421--><p class="noindent" >for each <span
4353 class="cmtt-12">[i] </span>from 0 ... <span
4354 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1
4355 <!--l. 424--><p class="noindent" >
4356 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4358 class="enumerate-enumitem">if either <span
4359 class="cmtt-12">[no_residue] </span>entry for channel (<span
4360 class="cmtt-12">[vorbis_mapping_magnitude] </span>element
4362 class="cmtt-12">[i]</span>) or channel (<span
4363 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
4364 class="cmtt-12">[i]</span>) are set to false, then both
4365 must be set to false. Note that an ’unused’ floor has no decoded floor information; it
4369 is important that this is remembered at floor curve synthesis time.</dd></dl>
4370 <!--l. 436--><p class="noindent" >
4371 <h5 class="subsubsectionHead"><span class="titlemark">4.3.4. </span> <a
4372 id="x1-760004.3.4"></a>residue decode</h5>
4373 <!--l. 438--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
4375 <!--l. 441--><p class="noindent" >for each submap <span
4376 class="cmtt-12">[i] </span>in order from 0 ... <span
4377 class="cmtt-12">[vorbis_mapping_submaps]</span>-1
4378 <!--l. 444--><p class="noindent" >
4379 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4381 class="enumerate-enumitem"><span
4382 class="cmtt-12">[ch] </span>= 0
4383 </dd><dt class="enumerate-enumitem">
4385 class="enumerate-enumitem">for each channel <span
4386 class="cmtt-12">[j] </span>in order from 0 ... <span
4387 class="cmtt-12">[audio_channels] </span>- 1
4388 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4390 class="enumerate-enumitem">if channel <span
4391 class="cmtt-12">[j] </span>in submap <span
4392 class="cmtt-12">[i] </span>(vector <span
4393 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4394 class="cmtt-12">[j] </span>is equal to
4396 class="cmtt-12">[i]</span>)
4397 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4399 class="enumerate-enumitem">if vector <span
4400 class="cmtt-12">[no_residue] </span>element <span
4401 class="cmtt-12">[j] </span>is true
4402 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4404 class="enumerate-enumitem">vector <span
4405 class="cmtt-12">[do_not_decode_flag] </span>element <span
4406 class="cmtt-12">[ch] </span>is set</dd></dl>
4407 <!--l. 453--><p class="noindent" >else
4408 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4410 class="enumerate-enumitem">vector <span
4411 class="cmtt-12">[do_not_decode_flag] </span>element <span
4412 class="cmtt-12">[ch] </span>is unset</dd></dl>
4413 </dd><dt class="enumerate-enumitem">
4415 class="enumerate-enumitem">increment <span
4416 class="cmtt-12">[ch]</span></dd></dl>
4418 </dd><dt class="enumerate-enumitem">
4420 class="enumerate-enumitem"><span
4421 class="cmtt-12">[residue_number] </span>= vector <span
4422 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
4423 class="cmtt-12">[i]</span>
4424 </dd><dt class="enumerate-enumitem">
4426 class="enumerate-enumitem"><span
4427 class="cmtt-12">[residue_type] </span>= vector <span
4428 class="cmtt-12">[vorbis_residue_types] </span>element <span
4429 class="cmtt-12">[residue_number]</span>
4430 </dd><dt class="enumerate-enumitem">
4432 class="enumerate-enumitem">decode <span
4433 class="cmtt-12">[ch] </span>vectors using residue <span
4434 class="cmtt-12">[residue_number]</span>, according to type <span
4435 class="cmtt-12">[residue_type]</span>,
4439 also passing vector <span
4440 class="cmtt-12">[do_not_decode_flag] </span>to indicate which vectors in the bundle should
4441 not be decoded. Correct per-vector decode length is <span
4442 class="cmtt-12">[n]</span>/2.
4443 </dd><dt class="enumerate-enumitem">
4445 class="enumerate-enumitem"><span
4446 class="cmtt-12">[ch] </span>= 0
4447 </dd><dt class="enumerate-enumitem">
4449 class="enumerate-enumitem">for each channel <span
4450 class="cmtt-12">[j] </span>in order from 0 ... <span
4451 class="cmtt-12">[audio_channels]</span>
4452 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4454 class="enumerate-enumitem">if channel <span
4455 class="cmtt-12">[j] </span>is in submap <span
4456 class="cmtt-12">[i] </span>(vector <span
4457 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4458 class="cmtt-12">[j] </span>is equal
4460 class="cmtt-12">[i]</span>)
4461 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4463 class="enumerate-enumitem">residue vector for channel <span
4464 class="cmtt-12">[j] </span>is set to decoded residue vector <span
4465 class="cmtt-12">[ch]</span>
4466 </dd><dt class="enumerate-enumitem">
4468 class="enumerate-enumitem">increment <span
4469 class="cmtt-12">[ch]</span></dd></dl>
4472 <!--l. 480--><p class="noindent" >
4473 <h5 class="subsubsectionHead"><span class="titlemark">4.3.5. </span> <a
4474 id="x1-770004.3.5"></a>inverse coupling</h5>
4475 <!--l. 482--><p class="noindent" >for each <span
4476 class="cmtt-12">[i] </span>from <span
4477 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
4478 <!--l. 485--><p class="noindent" >
4479 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4481 class="enumerate-enumitem"><span
4482 class="cmtt-12">[magnitude_vector] </span>= the residue vector for channel (vector
4484 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
4485 class="cmtt-12">[i]</span>)
4486 </dd><dt class="enumerate-enumitem">
4488 class="enumerate-enumitem"><span
4489 class="cmtt-12">[angle_vector] </span>= the residue vector for channel (vector <span
4490 class="cmtt-12">[vorbis_mapping_angle]</span>
4492 class="cmtt-12">[i]</span>)
4493 </dd><dt class="enumerate-enumitem">
4495 class="enumerate-enumitem">for each scalar value <span
4496 class="cmtt-12">[M] </span>in vector <span
4497 class="cmtt-12">[magnitude_vector] </span>and the corresponding scalar value
4499 class="cmtt-12">[A] </span>in vector <span
4500 class="cmtt-12">[angle_vector]</span>:
4501 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4503 class="enumerate-enumitem">if (<span
4504 class="cmtt-12">[M] </span>is greater than zero)
4508 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4510 class="enumerate-enumitem">if (<span
4511 class="cmtt-12">[A] </span>is greater than zero)
4512 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4514 class="enumerate-enumitem"><span
4515 class="cmtt-12">[new_M] </span>= <span
4516 class="cmtt-12">[M]</span>
4517 </dd><dt class="enumerate-enumitem">
4519 class="enumerate-enumitem"><span
4520 class="cmtt-12">[new_A] </span>= <span
4521 class="cmtt-12">[M]</span>-<span
4522 class="cmtt-12">[A]</span></dd></dl>
4523 <!--l. 498--><p class="noindent" >else
4524 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4526 class="enumerate-enumitem"><span
4527 class="cmtt-12">[new_A] </span>= <span
4528 class="cmtt-12">[M]</span>
4529 </dd><dt class="enumerate-enumitem">
4531 class="enumerate-enumitem"><span
4532 class="cmtt-12">[new_M] </span>= <span
4533 class="cmtt-12">[M]</span>+<span
4534 class="cmtt-12">[A]</span></dd></dl>
4536 <!--l. 505--><p class="noindent" >else
4537 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4539 class="enumerate-enumitem">if (<span
4540 class="cmtt-12">[A] </span>is greater than zero)
4541 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4543 class="enumerate-enumitem"><span
4544 class="cmtt-12">[new_M] </span>= <span
4545 class="cmtt-12">[M]</span>
4546 </dd><dt class="enumerate-enumitem">
4548 class="enumerate-enumitem"><span
4549 class="cmtt-12">[new_A] </span>= <span
4550 class="cmtt-12">[M]</span>+<span
4551 class="cmtt-12">[A]</span></dd></dl>
4552 <!--l. 512--><p class="noindent" >else
4553 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4555 class="enumerate-enumitem"><span
4556 class="cmtt-12">[new_A] </span>= <span
4557 class="cmtt-12">[M]</span>
4558 </dd><dt class="enumerate-enumitem">
4560 class="enumerate-enumitem"><span
4561 class="cmtt-12">[new_M] </span>= <span
4562 class="cmtt-12">[M]</span>-<span
4563 class="cmtt-12">[A]</span></dd></dl>
4565 </dd><dt class="enumerate-enumitem">
4567 class="enumerate-enumitem">set scalar value <span
4568 class="cmtt-12">[M] </span>in vector <span
4569 class="cmtt-12">[magnitude_vector] </span>to <span
4570 class="cmtt-12">[new_M]</span>
4571 </dd><dt class="enumerate-enumitem">
4573 class="enumerate-enumitem">set scalar value <span
4574 class="cmtt-12">[A] </span>in vector <span
4575 class="cmtt-12">[angle_vector] </span>to <span
4576 class="cmtt-12">[new_A]</span></dd></dl>
4581 <!--l. 529--><p class="noindent" >
4582 <h5 class="subsubsectionHead"><span class="titlemark">4.3.6. </span> <a
4583 id="x1-780004.3.6"></a>dot product</h5>
4584 <!--l. 531--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
4585 packet type. Note that the vector synthesis length for floor computation is <span
4586 class="cmtt-12">[n]</span>/2.
4587 <!--l. 535--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
4588 channel’s residue vector. The result is the dot product of the floor and residue vectors for
4589 each channel; the produced vectors are the length <span
4590 class="cmtt-12">[n]</span>/2 audio spectrum for each
4592 <!--l. 543--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
4593 implementation might be to assume that a 32 bit fixed-point representation for floor and
4594 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
4595 in all cases because it happens to mostly work with the current Xiph.Org reference
4597 <!--l. 550--><p class="noindent" >However, floor vector values can span <span
4598 class="cmsy-10x-x-120">~</span>140dB (<span
4599 class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum
4600 vector should represent a minimum of 120dB (<span
4601 class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16
4602 bit PCM device. For the residue vector to represent full scale if the floor is nailed
4604 class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
4605 full scale if the floor is nailed at 0dB, it must be able to represent <span
4606 class="cmsy-10x-x-120">-</span>140dB to +0dB.
4607 Thus, in order to handle full range dynamics, a residue vector may span <span
4608 class="cmsy-10x-x-120">-</span>140dB to
4609 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
4610 residue vector must be able to represent a 48 bit range and the dot product must
4611 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
4612 achieved using large (64 bit or larger) integers, or implementing a movable binary point
4614 <!--l. 567--><p class="noindent" >
4615 <h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a
4616 id="x1-790004.3.7"></a>inverse MDCT</h5>
4617 <!--l. 569--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
4618 inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is
4619 available in <span class="cite">[<a
4620 href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
4625 <!--l. 576--><p class="noindent" >
4626 <h5 class="subsubsectionHead"><span class="titlemark">4.3.8. </span> <a
4627 id="x1-800004.3.8"></a>overlap_add</h5>
4628 <!--l. 578--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
4629 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
4630 current window (as illustrated in <a
4631 href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a
4632 href="#x1-260001.3.2">Window shape decode (long windows
4633 only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
4634 is finished data to be returned by the decoder. This data spans from the center of
4635 the previous window to the center of the current window. In the case of same-sized
4636 windows, the amount of data to return is one-half block consisting of and only of the
4637 overlapped portions. When overlapping a short and long window, much of the returned
4638 range does not actually overlap. This does not damage transform orthogonality. Pay
4639 attention however to returning the correct data range; the amount of data to be returned
4641 <!--l. 592--><p class="noindent" >
4642 <div class="fancyvrb" id="fancyvrb22"><a
4643 id="x1-80002r1"></a><span
4644 class="cmr-6">1</span><span
4645 class="cmtt-8"> </span><span
4646 class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span></div>
4647 <!--l. 596--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
4648 windowsize/2-1, inclusive) of the current window.
4649 <!--l. 599--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
4650 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
4651 PCM output offset is ’0’ (as no data has been returned yet).
4652 <!--l. 606--><p class="noindent" >
4653 <h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a
4654 id="x1-810004.3.9"></a>output channel order</h5>
4655 <!--l. 608--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
4656 implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the
4657 specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for
4658 greater-than-eight channels remains ’left to the implementation’.
4659 <!--l. 614--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a
4660 decoder to produce output with channels in any order. Any such decoder should explicitly
4661 document channel reordering behavior.
4662 <!--l. 620--><p class="noindent" >
4663 <dl class="description"><dt class="description">
4665 class="cmssbx-10x-x-120">one channel</span> </dt><dd
4666 class="description">the stream is monophonic
4670 </dd><dt class="description">
4672 class="cmssbx-10x-x-120">two channels</span> </dt><dd
4673 class="description">the stream is stereo. channel order: left, right
4674 </dd><dt class="description">
4676 class="cmssbx-10x-x-120">three channels</span> </dt><dd
4677 class="description">the stream is a 1d-surround encoding. channel order: left, center, right
4678 </dd><dt class="description">
4680 class="cmssbx-10x-x-120">four channels</span> </dt><dd
4681 class="description">the stream is quadraphonic surround. channel order: front left, front right,
4682 rear left, rear right
4683 </dd><dt class="description">
4685 class="cmssbx-10x-x-120">five channels</span> </dt><dd
4686 class="description">the stream is five-channel surround. channel order: front left, center, front
4687 right, rear left, rear right
4688 </dd><dt class="description">
4690 class="cmssbx-10x-x-120">six channels</span> </dt><dd
4691 class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear
4692 left, rear right, LFE
4693 </dd><dt class="description">
4695 class="cmssbx-10x-x-120">seven channels</span> </dt><dd
4696 class="description">the stream is 6.1 surround. channel order: front left, center, front right,
4697 side left, side right, rear center, LFE
4698 </dd><dt class="description">
4700 class="cmssbx-10x-x-120">eight channels</span> </dt><dd
4701 class="description">the stream is 7.1 surround. channel order: front left, center, front right,
4702 side left, side right, rear left, rear right, LFE
4703 </dd><dt class="description">
4705 class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd
4706 class="description">channel use and order is defined by the application
4708 <!--l. 656--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
4709 channel mappings (such as three and four channel <a
4710 href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
4711 mappings other than mapping 0.
4718 <h3 class="sectionHead"><span class="titlemark">5. </span> <a
4719 id="x1-820005"></a>comment field and header specification</h3>
4720 <!--l. 6--><p class="noindent" >
4721 <h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a
4722 id="x1-830005.1"></a>Overview</h4>
4723 <!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
4724 bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
4725 belongs in a separate logical bitstream (usually an XML stream type) that provides greater
4726 structure and machine parseability.
4727 <!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
4728 a CDR. It should be a little information to remember the disc by and explain it to others; a
4729 short, to-the-point text note that need not only be a couple words, but isn’t going to be more
4730 than a short paragraph. The essentials, in other words, whatever they turn out to be,
4732 <!--l. 21--><p class="noindent" >
4734 <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
4735 class="cmti-12">“I’m Still Around”</span>, opening
4736 for Moxy Früvous, 1997.</div>
4737 <!--l. 29--><p class="noindent" >
4738 <h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a
4739 id="x1-840005.2"></a>Comment encoding</h4>
4740 <!--l. 31--><p class="noindent" >
4741 <h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a
4742 id="x1-850005.2.1"></a>Structure</h5>
4743 <!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
4744 bounded to 2<sup><span
4745 class="cmr-8">32</span></sup> <span
4746 class="cmsy-10x-x-120">- </span>1 and the length of each vector is limited to 2<sup><span
4747 class="cmr-8">32</span></sup> <span
4748 class="cmsy-10x-x-120">- </span>1 bytes. The vector length is
4752 encoded; the vector contents themselves are not null terminated. In addition to the vector list,
4753 there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
4754 example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
4756 <!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
4757 packing conventions of the vorbis codec. However, since data in the comment header
4758 is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
4760 <!--l. 46--><p class="noindent" >The comment header is decoded as follows:
4761 <!--l. 48--><p class="noindent" >
4762 <div class="fancyvrb" id="fancyvrb23"><a
4763 id="x1-85002r1"></a><span
4764 class="cmr-6">1</span><span
4765 class="cmtt-8"> </span><span
4766 class="cmtt-8"> </span><span
4767 class="cmtt-8"> </span><span
4768 class="cmtt-8"> 1)</span><span
4769 class="cmtt-8"> [vendor\_length]</span><span
4770 class="cmtt-8"> =</span><span
4771 class="cmtt-8"> read</span><span
4772 class="cmtt-8"> an</span><span
4773 class="cmtt-8"> unsigned</span><span
4774 class="cmtt-8"> integer</span><span
4775 class="cmtt-8"> of</span><span
4776 class="cmtt-8"> 32</span><span
4777 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4778 id="x1-85004r2"></a><span
4779 class="cmr-6">2</span><span
4780 class="cmtt-8"> </span><span
4781 class="cmtt-8"> </span><span
4782 class="cmtt-8"> </span><span
4783 class="cmtt-8"> 2)</span><span
4784 class="cmtt-8"> [vendor\_string]</span><span
4785 class="cmtt-8"> =</span><span
4786 class="cmtt-8"> read</span><span
4787 class="cmtt-8"> a</span><span
4788 class="cmtt-8"> UTF-8</span><span
4789 class="cmtt-8"> vector</span><span
4790 class="cmtt-8"> as</span><span
4791 class="cmtt-8"> [vendor\_length]</span><span
4792 class="cmtt-8"> octets</span>
4793 <br class="fancyvrb" /><a
4794 id="x1-85006r3"></a><span
4795 class="cmr-6">3</span><span
4796 class="cmtt-8"> </span><span
4797 class="cmtt-8"> </span><span
4798 class="cmtt-8"> </span><span
4799 class="cmtt-8"> 3)</span><span
4800 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4801 class="cmtt-8"> =</span><span
4802 class="cmtt-8"> read</span><span
4803 class="cmtt-8"> an</span><span
4804 class="cmtt-8"> unsigned</span><span
4805 class="cmtt-8"> integer</span><span
4806 class="cmtt-8"> of</span><span
4807 class="cmtt-8"> 32</span><span
4808 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4809 id="x1-85008r4"></a><span
4810 class="cmr-6">4</span><span
4811 class="cmtt-8"> </span><span
4812 class="cmtt-8"> </span><span
4813 class="cmtt-8"> </span><span
4814 class="cmtt-8"> 4)</span><span
4815 class="cmtt-8"> iterate</span><span
4816 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4817 class="cmtt-8"> times</span><span
4818 class="cmtt-8"> {</span>
4819 <br class="fancyvrb" /><a
4820 id="x1-85010r5"></a><span
4821 class="cmr-6">5</span><span
4822 class="cmtt-8"> </span><span
4823 class="cmtt-8"> </span><span
4824 class="cmtt-8"> </span><span
4825 class="cmtt-8"> </span><span
4826 class="cmtt-8"> </span><span
4827 class="cmtt-8"> </span><span
4828 class="cmtt-8"> </span><span
4829 class="cmtt-8"> </span><span
4830 class="cmtt-8"> 5)</span><span
4831 class="cmtt-8"> [length]</span><span
4832 class="cmtt-8"> =</span><span
4833 class="cmtt-8"> read</span><span
4834 class="cmtt-8"> an</span><span
4835 class="cmtt-8"> unsigned</span><span
4836 class="cmtt-8"> integer</span><span
4837 class="cmtt-8"> of</span><span
4838 class="cmtt-8"> 32</span><span
4839 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4840 id="x1-85012r6"></a><span
4841 class="cmr-6">6</span><span
4842 class="cmtt-8"> </span><span
4843 class="cmtt-8"> </span><span
4844 class="cmtt-8"> </span><span
4845 class="cmtt-8"> </span><span
4846 class="cmtt-8"> </span><span
4847 class="cmtt-8"> </span><span
4848 class="cmtt-8"> </span><span
4849 class="cmtt-8"> </span><span
4850 class="cmtt-8"> 6)</span><span
4851 class="cmtt-8"> this</span><span
4852 class="cmtt-8"> iteration’s</span><span
4853 class="cmtt-8"> user</span><span
4854 class="cmtt-8"> comment</span><span
4855 class="cmtt-8"> =</span><span
4856 class="cmtt-8"> read</span><span
4857 class="cmtt-8"> a</span><span
4858 class="cmtt-8"> UTF-8</span><span
4859 class="cmtt-8"> vector</span><span
4860 class="cmtt-8"> as</span><span
4861 class="cmtt-8"> [length]</span><span
4862 class="cmtt-8"> octets</span>
4863 <br class="fancyvrb" /><a
4864 id="x1-85014r7"></a><span
4865 class="cmr-6">7</span><span
4866 class="cmtt-8"> </span><span
4867 class="cmtt-8"> </span><span
4868 class="cmtt-8"> </span><span
4869 class="cmtt-8"> </span><span
4870 class="cmtt-8"> </span><span
4871 class="cmtt-8"> </span><span
4872 class="cmtt-8"> }</span><br class="fancyvrb" /><a
4873 id="x1-85016r8"></a><span
4874 class="cmr-6">8</span><span
4875 class="cmtt-8"> </span><span
4876 class="cmtt-8"> </span><span
4877 class="cmtt-8"> </span><span
4878 class="cmtt-8"> 7)</span><span
4879 class="cmtt-8"> [framing\_bit]</span><span
4880 class="cmtt-8"> =</span><span
4881 class="cmtt-8"> read</span><span
4882 class="cmtt-8"> a</span><span
4883 class="cmtt-8"> single</span><span
4884 class="cmtt-8"> bit</span><span
4885 class="cmtt-8"> as</span><span
4886 class="cmtt-8"> boolean</span><br class="fancyvrb" /><a
4887 id="x1-85018r9"></a><span
4888 class="cmr-6">9</span><span
4889 class="cmtt-8"> </span><span
4890 class="cmtt-8"> </span><span
4891 class="cmtt-8"> </span><span
4892 class="cmtt-8"> 8)</span><span
4893 class="cmtt-8"> if</span><span
4894 class="cmtt-8"> (</span><span
4895 class="cmtt-8"> [framing\_bit]</span><span
4896 class="cmtt-8"> unset</span><span
4897 class="cmtt-8"> or</span><span
4898 class="cmtt-8"> end-of-packet</span><span
4899 class="cmtt-8"> )</span><span
4900 class="cmtt-8"> then</span><span
4901 class="cmtt-8"> ERROR</span><br class="fancyvrb" /><a
4902 id="x1-85020r10"></a><span
4903 class="cmr-6">10</span><span
4904 class="cmtt-8"> </span><span
4905 class="cmtt-8"> </span><span
4906 class="cmtt-8"> </span><span
4907 class="cmtt-8"> 9)</span><span
4908 class="cmtt-8"> done.</span></div>
4909 <!--l. 64--><p class="noindent" >
4910 <h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a
4911 id="x1-860005.2.2"></a>Content vector format</h5>
4912 <!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is,
4913 comment fields consist of a field name and a corresponding value and look like:
4914 <!--l. 70--><p class="noindent" >
4916 <!--l. 71--><p class="noindent" >
4917 <div class="fancyvrb" id="fancyvrb24"><a
4918 id="x1-86002r1"></a><span
4919 class="cmr-6">1</span><span
4920 class="cmtt-8"> </span><span
4921 class="cmtt-8"> comment[0]="ARTIST=me";</span><br class="fancyvrb" /><a
4922 id="x1-86004r2"></a><span
4923 class="cmr-6">2</span><span
4924 class="cmtt-8"> </span><span
4925 class="cmtt-8"> comment[1]="TITLE=the</span><span
4926 class="cmtt-8"> sound</span><span
4927 class="cmtt-8"> of</span><span
4928 class="cmtt-8"> Vorbis";</span></div>
4930 <!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
4931 excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
4932 ASCII 0x61 through 0x7A inclusive (characters a-z).
4933 <!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
4934 terminate the field name.
4935 <!--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
4940 <!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
4941 id="x1-870005.2.2"></a><span
4942 class="cmbx-12">Field names</span></span>
4943 Below is a proposed, minimal list of standard field names with a description of intended use. No
4944 single or group of field names is mandatory; a comment header may contain one, all or none of
4945 the names in this list.
4946 <!--l. 99--><p class="noindent" >
4947 <dl class="description"><dt class="description">
4949 class="cmssbx-10x-x-120">TITLE</span> </dt><dd
4950 class="description">Track/Work name
4951 </dd><dt class="description">
4953 class="cmssbx-10x-x-120">VERSION</span> </dt><dd
4954 class="description">The version field may be used to differentiate multiple versions of the same
4955 track title in a single collection. (e.g. remix info)
4956 </dd><dt class="description">
4958 class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
4959 class="description">The collection name to which this track belongs
4960 </dd><dt class="description">
4962 class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
4963 class="description">The track number of this piece if part of a specific larger collection or
4965 </dd><dt class="description">
4967 class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
4968 class="description">The artist generally considered responsible for the work. In popular music this is
4969 usually the performing band or singer. For classical music it would be the composer.
4970 For an audio book it would be the author of the original text.
4971 </dd><dt class="description">
4973 class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
4974 class="description">The artist(s) who performed the work. In classical music this would be the
4975 conductor, orchestra, soloists. In an audio book it would be the actor who did the
4976 reading. In popular music this is typically the same as the ARTIST and is omitted.
4977 </dd><dt class="description">
4979 class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
4980 class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
4981 </dd><dt class="description">
4983 class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
4984 class="description">License information, for example, ’All Rights Reserved’, ’Any Use Permitted’, a URL to
4985 a license such as a Creative
4986 Commons license (e.g. ”creativecommons.org/license/by/4.0/l”)
4988 </dd><dt class="description">
4990 class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
4991 class="description">Name of the organization producing the track (i.e. the ’record label’)
4992 </dd><dt class="description">
4994 class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
4995 class="description">A short text description of the contents
4996 </dd><dt class="description">
5001 class="cmssbx-10x-x-120">GENRE</span> </dt><dd
5002 class="description">A short text indication of music genre
5003 </dd><dt class="description">
5005 class="cmssbx-10x-x-120">DATE</span> </dt><dd
5006 class="description">Date the track was recorded
5007 </dd><dt class="description">
5009 class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
5010 class="description">Location where track was recorded
5011 </dd><dt class="description">
5013 class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
5014 class="description">Contact information for the creators or distributors of the track. This could
5015 be a URL, an email address, the physical address of the producing label.
5016 </dd><dt class="description">
5018 class="cmssbx-10x-x-120">ISRC</span> </dt><dd
5019 class="description">International Standard Recording Code for the track; see <a
5020 href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for
5021 more information on ISRC numbers.
5023 <!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
5024 id="x1-880005.2.2"></a><span
5025 class="cmbx-12">Implications</span></span>
5026 Field names should not be ’internationalized’; this is a concession to simplicity not
5027 an attempt to exclude the majority of the world that doesn’t speak English. Field
5029 class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
5031 <!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
5032 the field name is bounded in a known way. Thus we also have the length of the field
5034 <!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
5035 use of comment fields should be clear through context at this point. Abuse will be
5037 <!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
5038 to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
5039 tags here to help with standardization.
5040 <!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
5041 example, assume a track was recorded by three well know artists; the following is permissible,
5043 <!--l. 183--><p class="noindent" >
5045 <!--l. 184--><p class="noindent" >
5049 <div class="fancyvrb" id="fancyvrb25"><a
5050 id="x1-88002r1"></a><span
5051 class="cmr-6">1</span><span
5052 class="cmtt-8"> </span><span
5053 class="cmtt-8"> ARTIST=Dizzy</span><span
5054 class="cmtt-8"> Gillespie</span><br class="fancyvrb" /><a
5055 id="x1-88004r2"></a><span
5056 class="cmr-6">2</span><span
5057 class="cmtt-8"> </span><span
5058 class="cmtt-8"> ARTIST=Sonny</span><span
5059 class="cmtt-8"> Rollins</span><br class="fancyvrb" /><a
5060 id="x1-88006r3"></a><span
5061 class="cmr-6">3</span><span
5062 class="cmtt-8"> </span><span
5063 class="cmtt-8"> ARTIST=Sonny</span><span
5064 class="cmtt-8"> Stitt</span></div>
5066 <!--l. 197--><p class="noindent" >
5067 <h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a
5068 id="x1-890005.2.3"></a>Encoding</h5>
5069 <!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
5070 first bitstream header packet, it is not generally the only packet on the second page and may not
5071 be restricted to within the second bitstream page. The length of the comment header packet is
5072 (practically) unbounded. The comment header packet is not optional; it must be present in the
5073 bitstream even if it is effectively empty.
5074 <!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
5075 renders least-significant-bit of the word to be coded into the least significant available bit of the
5076 current bitstream octet first):
5077 <!--l. 213--><p class="noindent" >
5078 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5080 class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets)
5081 </dd><dt class="enumerate-enumitem">
5083 class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of
5084 string, not null terminated)
5085 </dd><dt class="enumerate-enumitem">
5087 class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields)
5088 </dd><dt class="enumerate-enumitem">
5090 class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span
5091 class="cmmi-12">> </span>0; 32 bit unsigned quantity
5092 specifying number of octets)
5093 </dd><dt class="enumerate-enumitem">
5095 class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
5096 end of string, not null terminated)
5097 </dd><dt class="enumerate-enumitem">
5099 class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span
5100 class="cmmi-12">> </span>1...)...
5102 <!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
5104 class="cmtt-12">vorbis/lib/info.c</span>, <span
5105 class="cmtt-12">_vorbis_pack_comment() </span>and <span
5106 class="cmtt-12">_vorbis_unpack_comment()</span>.
5116 <h3 class="sectionHead"><span class="titlemark">6. </span> <a
5117 id="x1-900006"></a>Floor type 0 setup and decode</h3>
5118 <!--l. 6--><p class="noindent" >
5119 <h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a
5120 id="x1-910006.1"></a>Overview</h4>
5121 <!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
5122 Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
5123 response of the LSP filter. This representation is equivalent to a traditional all-pole infinite
5124 impulse response filter as would be used in linear predictive coding; LSP representation may be
5125 converted to LPC representation and vice-versa.
5126 <!--l. 18--><p class="noindent" >
5127 <h4 class="subsectionHead"><span class="titlemark">6.2. </span> <a
5128 id="x1-920006.2"></a>Floor 0 format</h4>
5129 <!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
5130 coding/decoding the LSP filter coefficient values used by each frame.
5131 <!--l. 24--><p class="noindent" >
5132 <h5 class="subsubsectionHead"><span class="titlemark">6.2.1. </span> <a
5133 id="x1-930006.2.1"></a>header decode</h5>
5134 <!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
5135 packet). configuration decode proceeds as follows:
5136 <!--l. 30--><p class="noindent" >
5137 <div class="fancyvrb" id="fancyvrb26"><a
5138 id="x1-93002r1"></a><span
5139 class="cmr-6">1</span><span
5140 class="cmtt-8"> </span><span
5141 class="cmtt-8"> </span><span
5142 class="cmtt-8"> </span><span
5143 class="cmtt-8"> 1)</span><span
5144 class="cmtt-8"> [floor0_order]</span><span
5145 class="cmtt-8"> =</span><span
5146 class="cmtt-8"> read</span><span
5147 class="cmtt-8"> an</span><span
5148 class="cmtt-8"> unsigned</span><span
5149 class="cmtt-8"> integer</span><span
5150 class="cmtt-8"> of</span><span
5151 class="cmtt-8"> 8</span><span
5152 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5153 id="x1-93004r2"></a><span
5154 class="cmr-6">2</span><span
5155 class="cmtt-8"> </span><span
5156 class="cmtt-8"> </span><span
5157 class="cmtt-8"> </span><span
5158 class="cmtt-8"> 2)</span><span
5159 class="cmtt-8"> [floor0_rate]</span><span
5160 class="cmtt-8"> =</span><span
5161 class="cmtt-8"> read</span><span
5162 class="cmtt-8"> an</span><span
5163 class="cmtt-8"> unsigned</span><span
5164 class="cmtt-8"> integer</span><span
5165 class="cmtt-8"> of</span><span
5166 class="cmtt-8"> 16</span><span
5167 class="cmtt-8"> bits</span>
5168 <br class="fancyvrb" /><a
5169 id="x1-93006r3"></a><span
5170 class="cmr-6">3</span><span
5171 class="cmtt-8"> </span><span
5172 class="cmtt-8"> </span><span
5173 class="cmtt-8"> </span><span
5174 class="cmtt-8"> 3)</span><span
5175 class="cmtt-8"> [floor0_bark_map_size]</span><span
5176 class="cmtt-8"> =</span><span
5177 class="cmtt-8"> read</span><span
5178 class="cmtt-8"> an</span><span
5179 class="cmtt-8"> unsigned</span><span
5180 class="cmtt-8"> integer</span><span
5181 class="cmtt-8"> of</span><span
5182 class="cmtt-8"> 16</span><span
5183 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5184 id="x1-93008r4"></a><span
5185 class="cmr-6">4</span><span
5186 class="cmtt-8"> </span><span
5187 class="cmtt-8"> </span><span
5188 class="cmtt-8"> </span><span
5189 class="cmtt-8"> 4)</span><span
5190 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5191 class="cmtt-8"> =</span><span
5192 class="cmtt-8"> read</span><span
5193 class="cmtt-8"> an</span><span
5194 class="cmtt-8"> unsigned</span><span
5195 class="cmtt-8"> integer</span><span
5196 class="cmtt-8"> of</span><span
5197 class="cmtt-8"> six</span><span
5198 class="cmtt-8"> bits</span>
5199 <br class="fancyvrb" /><a
5200 id="x1-93010r5"></a><span
5201 class="cmr-6">5</span><span
5202 class="cmtt-8"> </span><span
5203 class="cmtt-8"> </span><span
5204 class="cmtt-8"> </span><span
5205 class="cmtt-8"> 5)</span><span
5206 class="cmtt-8"> [floor0_amplitude_offset]</span><span
5207 class="cmtt-8"> =</span><span
5208 class="cmtt-8"> read</span><span
5209 class="cmtt-8"> an</span><span
5210 class="cmtt-8"> unsigned</span><span
5211 class="cmtt-8"> integer</span><span
5212 class="cmtt-8"> of</span><span
5213 class="cmtt-8"> eight</span><span
5214 class="cmtt-8"> bits</span>
5215 <br class="fancyvrb" /><a
5216 id="x1-93012r6"></a><span
5217 class="cmr-6">6</span><span
5218 class="cmtt-8"> </span><span
5219 class="cmtt-8"> </span><span
5220 class="cmtt-8"> </span><span
5221 class="cmtt-8"> 6)</span><span
5222 class="cmtt-8"> [floor0_number_of_books]</span><span
5223 class="cmtt-8"> =</span><span
5224 class="cmtt-8"> read</span><span
5225 class="cmtt-8"> an</span><span
5226 class="cmtt-8"> unsigned</span><span
5227 class="cmtt-8"> integer</span><span
5228 class="cmtt-8"> of</span><span
5229 class="cmtt-8"> four</span><span
5230 class="cmtt-8"> bits</span><span
5231 class="cmtt-8"> and</span><span
5232 class="cmtt-8"> add</span><span
5233 class="cmtt-8"> 1</span>
5234 <br class="fancyvrb" /><a
5235 id="x1-93014r7"></a><span
5236 class="cmr-6">7</span><span
5237 class="cmtt-8"> </span><span
5238 class="cmtt-8"> </span><span
5239 class="cmtt-8"> </span><span
5240 class="cmtt-8"> 7)</span><span
5241 class="cmtt-8"> array</span><span
5242 class="cmtt-8"> [floor0_book_list]</span><span
5243 class="cmtt-8"> =</span><span
5244 class="cmtt-8"> read</span><span
5245 class="cmtt-8"> a</span><span
5246 class="cmtt-8"> list</span><span
5247 class="cmtt-8"> of</span><span
5248 class="cmtt-8"> [floor0_number_of_books]</span><span
5249 class="cmtt-8"> unsigned</span><span
5250 class="cmtt-8"> integers</span><span
5251 class="cmtt-8"> of</span><span
5252 class="cmtt-8"> eight</span><span
5253 class="cmtt-8"> bits</span><span
5254 class="cmtt-8"> each;</span></div>
5258 <!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
5259 In addition, any element of the array <span
5260 class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum
5261 codebook number for this bitstream is an error condition that also renders the stream
5263 <!--l. 48--><p class="noindent" >
5264 <h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a
5265 id="x1-940006.2.2"></a>packet decode</h5>
5266 <!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve
5268 class="cmtt-12">[floor0_order] </span>LSP coefficient values from the bitstream, and then
5269 computing the floor curve, which is defined as the frequency response of the decoded LSP
5271 <!--l. 56--><p class="noindent" >Packet decode proceeds as follows:
5272 <div class="fancyvrb" id="fancyvrb27"><a
5273 id="x1-94002r1"></a><span
5274 class="cmr-6">1</span><span
5275 class="cmtt-8"> </span><span
5276 class="cmtt-8"> </span><span
5277 class="cmtt-8"> </span><span
5278 class="cmtt-8"> 1)</span><span
5279 class="cmtt-8"> [amplitude]</span><span
5280 class="cmtt-8"> =</span><span
5281 class="cmtt-8"> read</span><span
5282 class="cmtt-8"> an</span><span
5283 class="cmtt-8"> unsigned</span><span
5284 class="cmtt-8"> integer</span><span
5285 class="cmtt-8"> of</span><span
5286 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5287 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5288 id="x1-94004r2"></a><span
5289 class="cmr-6">2</span><span
5290 class="cmtt-8"> </span><span
5291 class="cmtt-8"> </span><span
5292 class="cmtt-8"> </span><span
5293 class="cmtt-8"> 2)</span><span
5294 class="cmtt-8"> if</span><span
5295 class="cmtt-8"> (</span><span
5296 class="cmtt-8"> [amplitude]</span><span
5297 class="cmtt-8"> is</span><span
5298 class="cmtt-8"> greater</span><span
5299 class="cmtt-8"> than</span><span
5300 class="cmtt-8"> zero</span><span
5301 class="cmtt-8"> )</span><span
5302 class="cmtt-8"> </span><span
5303 class="cmsy-8">{</span>
5304 <br class="fancyvrb" /><a
5305 id="x1-94006r3"></a><span
5306 class="cmr-6">3</span><span
5307 class="cmtt-8"> </span><span
5308 class="cmtt-8"> </span><span
5309 class="cmtt-8"> </span><span
5310 class="cmtt-8"> </span><span
5311 class="cmtt-8"> </span><span
5312 class="cmtt-8"> </span><span
5313 class="cmtt-8"> </span><span
5314 class="cmtt-8"> </span><span
5315 class="cmtt-8"> 3)</span><span
5316 class="cmtt-8"> [coefficients]</span><span
5317 class="cmtt-8"> is</span><span
5318 class="cmtt-8"> an</span><span
5319 class="cmtt-8"> empty,</span><span
5320 class="cmtt-8"> zero</span><span
5321 class="cmtt-8"> length</span><span
5322 class="cmtt-8"> vector</span><br class="fancyvrb" /><a
5323 id="x1-94008r4"></a><span
5324 class="cmr-6">4</span><span
5325 class="cmtt-8"> </span><span
5326 class="cmtt-8"> </span><span
5327 class="cmtt-8"> </span><span
5328 class="cmtt-8"> </span><span
5329 class="cmtt-8"> </span><span
5330 class="cmtt-8"> </span><span
5331 class="cmtt-8"> </span><span
5332 class="cmtt-8"> </span><span
5333 class="cmtt-8"> 4)</span><span
5334 class="cmtt-8"> [booknumber]</span><span
5335 class="cmtt-8"> =</span><span
5336 class="cmtt-8"> read</span><span
5337 class="cmtt-8"> an</span><span
5338 class="cmtt-8"> unsigned</span><span
5339 class="cmtt-8"> integer</span><span
5340 class="cmtt-8"> of</span><span
5341 class="cmtt-8"> </span><a
5342 href="#x1-1190009.2.1"><span
5343 class="cmtt-8">ilog</span></a><span
5344 class="cmtt-8">(</span><span
5345 class="cmtt-8"> [floor0_number_of_books]</span><span
5346 class="cmtt-8"> )</span><span
5347 class="cmtt-8"> bits</span>
5348 <br class="fancyvrb" /><a
5349 id="x1-94010r5"></a><span
5350 class="cmr-6">5</span><span
5351 class="cmtt-8"> </span><span
5352 class="cmtt-8"> </span><span
5353 class="cmtt-8"> </span><span
5354 class="cmtt-8"> </span><span
5355 class="cmtt-8"> </span><span
5356 class="cmtt-8"> </span><span
5357 class="cmtt-8"> </span><span
5358 class="cmtt-8"> </span><span
5359 class="cmtt-8"> 5)</span><span
5360 class="cmtt-8"> if</span><span
5361 class="cmtt-8"> (</span><span
5362 class="cmtt-8"> [booknumber]</span><span
5363 class="cmtt-8"> is</span><span
5364 class="cmtt-8"> greater</span><span
5365 class="cmtt-8"> than</span><span
5366 class="cmtt-8"> the</span><span
5367 class="cmtt-8"> highest</span><span
5368 class="cmtt-8"> number</span><span
5369 class="cmtt-8"> decode</span><span
5370 class="cmtt-8"> codebook</span><span
5371 class="cmtt-8"> )</span><span
5372 class="cmtt-8"> then</span><span
5373 class="cmtt-8"> packet</span><span
5374 class="cmtt-8"> is</span><span
5375 class="cmtt-8"> undecodable</span><br class="fancyvrb" /><a
5376 id="x1-94012r6"></a><span
5377 class="cmr-6">6</span><span
5378 class="cmtt-8"> </span><span
5379 class="cmtt-8"> </span><span
5380 class="cmtt-8"> </span><span
5381 class="cmtt-8"> </span><span
5382 class="cmtt-8"> </span><span
5383 class="cmtt-8"> </span><span
5384 class="cmtt-8"> </span><span
5385 class="cmtt-8"> </span><span
5386 class="cmtt-8"> 6)</span><span
5387 class="cmtt-8"> [last]</span><span
5388 class="cmtt-8"> =</span><span
5389 class="cmtt-8"> zero;</span>
5390 <br class="fancyvrb" /><a
5391 id="x1-94014r7"></a><span
5392 class="cmr-6">7</span><span
5393 class="cmtt-8"> </span><span
5394 class="cmtt-8"> </span><span
5395 class="cmtt-8"> </span><span
5396 class="cmtt-8"> </span><span
5397 class="cmtt-8"> </span><span
5398 class="cmtt-8"> </span><span
5399 class="cmtt-8"> </span><span
5400 class="cmtt-8"> </span><span
5401 class="cmtt-8"> 7)</span><span
5402 class="cmtt-8"> vector</span><span
5403 class="cmtt-8"> [temp_vector]</span><span
5404 class="cmtt-8"> =</span><span
5405 class="cmtt-8"> read</span><span
5406 class="cmtt-8"> vector</span><span
5407 class="cmtt-8"> from</span><span
5408 class="cmtt-8"> bitstream</span><span
5409 class="cmtt-8"> using</span><span
5410 class="cmtt-8"> codebook</span><span
5411 class="cmtt-8"> number</span><span
5412 class="cmtt-8"> [floor0_book_list]</span><span
5413 class="cmtt-8"> element</span><span
5414 class="cmtt-8"> [booknumber]</span><span
5415 class="cmtt-8"> in</span><span
5416 class="cmtt-8"> VQ</span><span
5417 class="cmtt-8"> context.</span>
5418 <br class="fancyvrb" /><a
5419 id="x1-94016r8"></a><span
5420 class="cmr-6">8</span><span
5421 class="cmtt-8"> </span><span
5422 class="cmtt-8"> </span><span
5423 class="cmtt-8"> </span><span
5424 class="cmtt-8"> </span><span
5425 class="cmtt-8"> </span><span
5426 class="cmtt-8"> </span><span
5427 class="cmtt-8"> </span><span
5428 class="cmtt-8"> </span><span
5429 class="cmtt-8"> 8)</span><span
5430 class="cmtt-8"> add</span><span
5431 class="cmtt-8"> the</span><span
5432 class="cmtt-8"> scalar</span><span
5433 class="cmtt-8"> value</span><span
5434 class="cmtt-8"> [last]</span><span
5435 class="cmtt-8"> to</span><span
5436 class="cmtt-8"> each</span><span
5437 class="cmtt-8"> scalar</span><span
5438 class="cmtt-8"> in</span><span
5439 class="cmtt-8"> vector</span><span
5440 class="cmtt-8"> [temp_vector]</span><br class="fancyvrb" /><a
5441 id="x1-94018r9"></a><span
5442 class="cmr-6">9</span><span
5443 class="cmtt-8"> </span><span
5444 class="cmtt-8"> </span><span
5445 class="cmtt-8"> </span><span
5446 class="cmtt-8"> </span><span
5447 class="cmtt-8"> </span><span
5448 class="cmtt-8"> </span><span
5449 class="cmtt-8"> </span><span
5450 class="cmtt-8"> </span><span
5451 class="cmtt-8"> 9)</span><span
5452 class="cmtt-8"> [last]</span><span
5453 class="cmtt-8"> =</span><span
5454 class="cmtt-8"> the</span><span
5455 class="cmtt-8"> value</span><span
5456 class="cmtt-8"> of</span><span
5457 class="cmtt-8"> the</span><span
5458 class="cmtt-8"> last</span><span
5459 class="cmtt-8"> scalar</span><span
5460 class="cmtt-8"> in</span><span
5461 class="cmtt-8"> vector</span><span
5462 class="cmtt-8"> [temp_vector]</span>
5463 <br class="fancyvrb" /><a
5464 id="x1-94020r10"></a><span
5465 class="cmr-6">10</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"> 10)</span><span
5474 class="cmtt-8"> concatenate</span><span
5475 class="cmtt-8"> [temp_vector]</span><span
5476 class="cmtt-8"> onto</span><span
5477 class="cmtt-8"> the</span><span
5478 class="cmtt-8"> end</span><span
5479 class="cmtt-8"> of</span><span
5480 class="cmtt-8"> the</span><span
5481 class="cmtt-8"> [coefficients]</span><span
5482 class="cmtt-8"> vector</span>
5483 <br class="fancyvrb" /><a
5484 id="x1-94022r11"></a><span
5485 class="cmr-6">11</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"> </span><span
5493 class="cmtt-8"> 11)</span><span
5494 class="cmtt-8"> if</span><span
5495 class="cmtt-8"> (length</span><span
5496 class="cmtt-8"> of</span><span
5497 class="cmtt-8"> vector</span><span
5498 class="cmtt-8"> [coefficients]</span><span
5499 class="cmtt-8"> is</span><span
5500 class="cmtt-8"> less</span><span
5501 class="cmtt-8"> than</span><span
5502 class="cmtt-8"> [floor0_order],</span><span
5503 class="cmtt-8"> continue</span><span
5504 class="cmtt-8"> at</span><span
5505 class="cmtt-8"> step</span><span
5506 class="cmtt-8"> 6</span><br class="fancyvrb" /><a
5507 id="x1-94024r12"></a><span
5508 class="cmr-6">12</span><span
5509 class="cmtt-8"> </span><span
5510 class="cmtt-8"> </span><br class="fancyvrb" /><a
5511 id="x1-94026r13"></a><span
5512 class="cmr-6">13</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"> </span><span
5519 class="cmtt-8"> </span><span
5520 class="cmsy-8">}</span><br class="fancyvrb" /><a
5521 id="x1-94028r14"></a><span
5522 class="cmr-6">14</span><span
5523 class="cmtt-8"> </span><span
5524 class="cmtt-8"> </span><br class="fancyvrb" /><a
5525 id="x1-94030r15"></a><span
5526 class="cmr-6">15</span><span
5527 class="cmtt-8"> </span><span
5528 class="cmtt-8"> </span><span
5529 class="cmtt-8"> 12)</span><span
5530 class="cmtt-8"> done.</span><br class="fancyvrb" /><a
5531 id="x1-94032r16"></a><span
5532 class="cmr-6">16</span><span
5533 class="cmtt-8"> </span><span
5534 class="cmtt-8"> </span></div>
5535 <!--l. 76--><p class="noindent" >Take note of the following properties of decode:
5536 <ul class="itemize1">
5537 <li class="itemize">An <span
5538 class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
5539 is unused in this frame (the output of the channel will be all-zeroes in synthesis).
5540 Several later stages of decode don’t occur for an unused channel.
5542 <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
5543 if end-of-packet is reached during any read operation above, floor decode is to return
5544 ’unused’ status as if the <span
5545 class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
5547 <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
5548 href="#x1-1190009.2.1">ilog</a>(
5550 class="cmtt-12">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
5551 and values greater than the maximum possible book value are reserved.
5553 <li class="itemize">The number of scalars read into the vector <span
5554 class="cmtt-12">[coefficients] </span>may be greater
5556 class="cmtt-12">[floor0_order]</span>, the number actually required for curve computation. For
5557 example, if the VQ codebook used for the floor currently being decoded has a
5559 class="cmtt-12">[codebook_dimensions] </span>value of three and <span
5560 class="cmtt-12">[floor0_order] </span>is ten, the only way to
5564 fill all the needed scalars in <span
5565 class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
5566 as four vectors of three scalars each. This is not an error condition, and care must
5567 be taken not to allow a buffer overflow in decode. The extra values are not used and
5568 may be ignored or discarded.</li></ul>
5569 <!--l. 104--><p class="noindent" >
5570 <h5 class="subsubsectionHead"><span class="titlemark">6.2.3. </span> <a
5571 id="x1-950006.2.3"></a>curve computation</h5>
5572 <!--l. 106--><p class="noindent" >Given an <span
5573 class="cmtt-12">[amplitude] </span>integer and <span
5574 class="cmtt-12">[coefficients] </span>vector from packet decode as well as
5575 the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and
5576 [floor0_amplitude_offset] values from floor setup, and an output vector size <span
5577 class="cmtt-12">[n] </span>specified by the
5578 decode process, we compute a floor output vector.
5579 <!--l. 113--><p class="noindent" >If the value <span
5580 class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span
5581 class="cmtt-12">[n] </span>vector with all-zero
5582 scalars. Otherwise, begin by assuming the following definitions for the given vector to be
5584 <center class="par-math-display" >
5586 src="Vorbis_I_spec7x.png" alt=" {
5587 map = min (floor0_bark_map_size - 1,f oobar) for i ∈ [0, n - 1]
5589 " class="par-math-display" ></center>
5590 <!--l. 128--><p class="nopar" >
5591 <!--l. 130--><p class="noindent" >where
5592 <center class="par-math-display" >
5594 src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋
5595 ( floor0_rate--⋅ i) floor0_bark_map_size----
5596 f oobar = bark 2n ⋅ bark(.5 ⋅ floor0_rate )
5597 " class="par-math-display" ></center>
5598 <!--l. 137--><p class="nopar" >
5599 <!--l. 139--><p class="noindent" >and
5600 <center class="par-math-display" >
5602 src="Vorbis_I_spec9x.png" alt=" 2
5603 bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x ) + .0001x
5604 " class="par-math-display" ></center>
5605 <!--l. 143--><p class="nopar" >
5606 <!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
5607 result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
5609 class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
5611 <!--l. 151--><p class="noindent" >
5612 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5614 class="enumerate-enumitem"><span
5615 class="cmtt-12">[i] </span>= 0
5616 </dd><dt class="enumerate-enumitem">
5618 class="enumerate-enumitem"><span
5619 class="cmtt-12">[</span><span
5620 class="cmmi-12">ω</span><span
5621 class="cmtt-12">] </span>= <span
5622 class="cmmi-12">π </span>* map element <span
5623 class="cmtt-12">[i] </span>/ <span
5624 class="cmtt-12">[floor0_bark_map_size]</span>
5625 </dd><dt class="enumerate-enumitem">
5627 class="enumerate-enumitem">if ( <span
5628 class="cmtt-12">[floor0_order] </span>is odd )
5629 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5631 class="enumerate-enumitem">calculate <span
5632 class="cmtt-12">[p] </span>and <span
5633 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5634 <center class="math-display" >
5636 src="Vorbis_I_spec10x.png" alt=" floor0∏_2order-3
5637 p = (1 - cos2ω) 4(cos([coefficients ]2j+1) - cosω )2
5641 q = 4- 4(cos([coefficients ]2j) - cosω )
5643 " class="math-display" ></center>
5646 <!--l. 162--><p class="noindent" >else <span
5647 class="cmtt-12">[floor0_order] </span>is even
5651 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5653 class="enumerate-enumitem">calculate <span
5654 class="cmtt-12">[p] </span>and <span
5655 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5656 <center class="math-display" >
5658 src="Vorbis_I_spec11x.png" alt=" floor0_order-2
5659 (1 - cosω ) ---∏2-----
5660 p = ----------- 4(cos([coefficients ]2j+1) - cosω)2
5663 (1-+-cosω-) ∏2 2
5664 q = 2 4(cos([coefficients ]2j) - cos ω)
5666 " class="math-display" ></center>
5669 </dd><dt class="enumerate-enumitem">
5671 class="enumerate-enumitem">calculate <span
5672 class="cmtt-12">[linear_floor_value] </span>according to:
5673 <center class="math-display" >
5675 src="Vorbis_I_spec12x.png" alt=" ( ( ))
5676 amplitude---⋅ floor0_amplitute_offset---
5677 exp .11512925 (2floor0_amplitude_bits - 1)√p--+-q - floor0_amplitude_offset
5678 " class="math-display" ></center>
5679 <!--l. 177--><p class="nopar" >
5680 </dd><dt class="enumerate-enumitem">
5682 class="enumerate-enumitem"><span
5683 class="cmtt-12">[iteration_condition] </span>= map element <span
5684 class="cmtt-12">[i]</span>
5685 </dd><dt class="enumerate-enumitem">
5687 class="enumerate-enumitem"><span
5688 class="cmtt-12">[output] </span>element <span
5689 class="cmtt-12">[i] </span>= <span
5690 class="cmtt-12">[linear_floor_value]</span>
5691 </dd><dt class="enumerate-enumitem">
5693 class="enumerate-enumitem">increment <span
5694 class="cmtt-12">[i]</span>
5695 </dd><dt class="enumerate-enumitem">
5697 class="enumerate-enumitem">if ( map element <span
5698 class="cmtt-12">[i] </span>is equal to <span
5699 class="cmtt-12">[iteration_condition] </span>) continue at step
5704 </dd><dt class="enumerate-enumitem">
5706 class="enumerate-enumitem">if ( <span
5707 class="cmtt-12">[i] </span>is less than <span
5708 class="cmtt-12">[n] </span>) continue at step 2
5709 </dd><dt class="enumerate-enumitem">
5711 class="enumerate-enumitem">done</dd></dl>
5712 <!--l. 187--><p class="noindent" ><span class="paragraphHead"><a
5713 id="x1-960006.2.3"></a><span
5714 class="cmbx-12">Errata 20150227: Bark scale computation</span></span>
5715 Due to a typo when typesetting this version of the specification from the original HTML
5716 document, the Bark scale computation previously erroneously read:
5717 <center class="par-math-display" >
5719 src="Vorbis_I_spec13x.png" alt=" 2
5720 bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x )
5721 " class="par-math-display" ></center>
5722 <!--l. 195--><p class="nopar" >
5723 <!--l. 197--><p class="noindent" >Note that the last parenthesis is misplaced. This document now uses the correct equation as it
5724 appeared in the original HTML spec document:
5725 <center class="par-math-display" >
5727 src="Vorbis_I_spec14x.png" alt="bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x2 ) + .0001x
5728 " class="par-math-display" ></center>
5729 <!--l. 201--><p class="nopar" >
5736 <h3 class="sectionHead"><span class="titlemark">7. </span> <a
5737 id="x1-970007"></a>Floor type 1 setup and decode</h3>
5738 <!--l. 6--><p class="noindent" >
5739 <h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a
5740 id="x1-980007.1"></a>Overview</h4>
5741 <!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
5742 curve. The representation plots this curve mechanically on a linear frequency axis and a
5743 logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
5745 <!--l. 16--><p class="noindent" >
5746 <h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a
5747 id="x1-990007.2"></a>Floor 1 format</h4>
5748 <!--l. 18--><p class="noindent" >
5749 <h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a
5750 id="x1-1000007.2.1"></a>model</h5>
5751 <!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
5752 floor curve using iterative prediction in a process roughly equivalent to the following simplified
5754 <ul class="itemize1">
5755 <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
5756 where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
5759 <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
5760 produces a y˙new value at that point computed from the existing line’s y value at
5761 x˙new (as plotted by the line) and a difference value decoded from the bitstream
5767 <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
5768 x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
5769 y˙new represents no change to the amplitude value at x˙new so that later refinement
5770 is additionally bounded at x˙new.
5772 <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
5773 at floor 1 initialization time. Computation is completed at the end of the x value list.
5775 <!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
5776 representing typical configuration:
5777 <!--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
5778 in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
5779 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
5780 example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
5781 way, beginning with the first line:
5784 <!--l. 59--><p class="noindent" >
5786 <!--l. 60--><p class="noindent" ><img
5787 src="floor1-1.png" alt="PIC"
5789 <br /> <div class="caption"
5790 ><span class="id">Figure 7: </span><span
5791 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000017 -->
5793 <!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
5797 <!--l. 67--><p class="noindent" >
5799 <!--l. 68--><p class="noindent" ><img
5800 src="floor1-2.png" alt="PIC"
5802 <br /> <div class="caption"
5803 ><span class="id">Figure 8: </span><span
5804 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000028 -->
5806 <!--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
5807 further refinement. From here on, the pattern should be clear; we complete the floor computation
5814 <!--l. 76--><p class="noindent" >
5816 <!--l. 77--><p class="noindent" ><img
5817 src="floor1-3.png" alt="PIC"
5819 <br /> <div class="caption"
5820 ><span class="id">Figure 9: </span><span
5821 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000039 -->
5825 <!--l. 81--><p class="noindent" >
5827 <!--l. 82--><p class="noindent" ><img
5828 src="floor1-4.png" alt="PIC"
5830 <br /> <div class="caption"
5831 ><span class="id">Figure 10: </span><span
5832 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-10000410 -->
5834 <!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
5835 decode, as described later. The actual algorithm splits Y value computation and line plotting
5836 into two steps with modifications to the above algorithm to eliminate noise accumulation
5837 through integer roundoff/truncation.
5838 <!--l. 94--><p class="noindent" >
5839 <h5 class="subsubsectionHead"><span class="titlemark">7.2.2. </span> <a
5840 id="x1-1010007.2.2"></a>header decode</h5>
5841 <!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
5842 during packet decode and synthesis). This list is split into partitions, and each partition is
5843 assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
5844 partition or partition class.
5845 <!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
5846 the partition class encodes at once), a ’subclass’ value representing the number of
5847 alternate entropy books the partition class may use in representing Y values, the list of
5848 [subclass] books and a master book used to encode which alternate books were chosen
5849 for representation in a given packet. The master/subclass mechanism is meant to be
5850 used as a flexible representation cascade while still using codebooks only in a scalar
5855 <!--l. 112--><p class="noindent" >
5856 <div class="fancyvrb" id="fancyvrb28"><a
5857 id="x1-101002r1"></a><span
5858 class="cmr-6">1</span><span
5859 class="cmtt-8"> </span><span
5860 class="cmtt-8"> </span><br class="fancyvrb" /><a
5861 id="x1-101004r2"></a><span
5862 class="cmr-6">2</span><span
5863 class="cmtt-8"> </span><span
5864 class="cmtt-8"> </span><span
5865 class="cmtt-8"> </span><span
5866 class="cmtt-8"> 1)</span><span
5867 class="cmtt-8"> [floor1_partitions]</span><span
5868 class="cmtt-8"> =</span><span
5869 class="cmtt-8"> read</span><span
5870 class="cmtt-8"> 5</span><span
5871 class="cmtt-8"> bits</span><span
5872 class="cmtt-8"> as</span><span
5873 class="cmtt-8"> unsigned</span><span
5874 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
5875 id="x1-101006r3"></a><span
5876 class="cmr-6">3</span><span
5877 class="cmtt-8"> </span><span
5878 class="cmtt-8"> </span><span
5879 class="cmtt-8"> </span><span
5880 class="cmtt-8"> 2)</span><span
5881 class="cmtt-8"> [maximum_class]</span><span
5882 class="cmtt-8"> =</span><span
5883 class="cmtt-8"> -1</span><br class="fancyvrb" /><a
5884 id="x1-101008r4"></a><span
5885 class="cmr-6">4</span><span
5886 class="cmtt-8"> </span><span
5887 class="cmtt-8"> </span><span
5888 class="cmtt-8"> </span><span
5889 class="cmtt-8"> 3)</span><span
5890 class="cmtt-8"> iterate</span><span
5891 class="cmtt-8"> [i]</span><span
5892 class="cmtt-8"> over</span><span
5893 class="cmtt-8"> the</span><span
5894 class="cmtt-8"> range</span><span
5895 class="cmtt-8"> 0</span><span
5896 class="cmtt-8"> ...</span><span
5897 class="cmtt-8"> [floor1_partitions]-1</span><span
5898 class="cmtt-8"> </span><span
5899 class="cmsy-8">{</span>
5900 <br class="fancyvrb" /><a
5901 id="x1-101010r5"></a><span
5902 class="cmr-6">5</span><span
5903 class="cmtt-8"> </span><span
5904 class="cmtt-8"> </span><br class="fancyvrb" /><a
5905 id="x1-101012r6"></a><span
5906 class="cmr-6">6</span><span
5907 class="cmtt-8"> </span><span
5908 class="cmtt-8"> </span><span
5909 class="cmtt-8"> </span><span
5910 class="cmtt-8"> </span><span
5911 class="cmtt-8"> </span><span
5912 class="cmtt-8"> </span><span
5913 class="cmtt-8"> </span><span
5914 class="cmtt-8"> </span><span
5915 class="cmtt-8"> </span><span
5916 class="cmtt-8"> 4)</span><span
5917 class="cmtt-8"> vector</span><span
5918 class="cmtt-8"> [floor1_partition_class_list]</span><span
5919 class="cmtt-8"> element</span><span
5920 class="cmtt-8"> [i]</span><span
5921 class="cmtt-8"> =</span><span
5922 class="cmtt-8"> read</span><span
5923 class="cmtt-8"> 4</span><span
5924 class="cmtt-8"> bits</span><span
5925 class="cmtt-8"> as</span><span
5926 class="cmtt-8"> unsigned</span><span
5927 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
5928 id="x1-101014r7"></a><span
5929 class="cmr-6">7</span><span
5930 class="cmtt-8"> </span><span
5931 class="cmtt-8"> </span><br class="fancyvrb" /><a
5932 id="x1-101016r8"></a><span
5933 class="cmr-6">8</span><span
5934 class="cmtt-8"> </span><span
5935 class="cmtt-8"> </span><span
5936 class="cmtt-8"> </span><span
5937 class="cmtt-8"> </span><span
5938 class="cmtt-8"> </span><span
5939 class="cmtt-8"> </span><span
5940 class="cmtt-8"> </span><span
5941 class="cmsy-8">}</span><br class="fancyvrb" /><a
5942 id="x1-101018r9"></a><span
5943 class="cmr-6">9</span><span
5944 class="cmtt-8"> </span><span
5945 class="cmtt-8"> </span>
5946 <br class="fancyvrb" /><a
5947 id="x1-101020r10"></a><span
5948 class="cmr-6">10</span><span
5949 class="cmtt-8"> </span><span
5950 class="cmtt-8"> </span><span
5951 class="cmtt-8"> </span><span
5952 class="cmtt-8"> 5)</span><span
5953 class="cmtt-8"> [maximum_class]</span><span
5954 class="cmtt-8"> =</span><span
5955 class="cmtt-8"> largest</span><span
5956 class="cmtt-8"> integer</span><span
5957 class="cmtt-8"> scalar</span><span
5958 class="cmtt-8"> value</span><span
5959 class="cmtt-8"> in</span><span
5960 class="cmtt-8"> vector</span><span
5961 class="cmtt-8"> [floor1_partition_class_list]</span><br class="fancyvrb" /><a
5962 id="x1-101022r11"></a><span
5963 class="cmr-6">11</span><span
5964 class="cmtt-8"> </span><span
5965 class="cmtt-8"> </span><span
5966 class="cmtt-8"> </span><span
5967 class="cmtt-8"> 6)</span><span
5968 class="cmtt-8"> iterate</span><span
5969 class="cmtt-8"> [i]</span><span
5970 class="cmtt-8"> over</span><span
5971 class="cmtt-8"> the</span><span
5972 class="cmtt-8"> range</span><span
5973 class="cmtt-8"> 0</span><span
5974 class="cmtt-8"> ...</span><span
5975 class="cmtt-8"> [maximum_class]</span><span
5976 class="cmtt-8"> </span><span
5977 class="cmsy-8">{</span>
5978 <br class="fancyvrb" /><a
5979 id="x1-101024r12"></a><span
5980 class="cmr-6">12</span><span
5981 class="cmtt-8"> </span><span
5982 class="cmtt-8"> </span><br class="fancyvrb" /><a
5983 id="x1-101026r13"></a><span
5984 class="cmr-6">13</span><span
5985 class="cmtt-8"> </span><span
5986 class="cmtt-8"> </span><span
5987 class="cmtt-8"> </span><span
5988 class="cmtt-8"> </span><span
5989 class="cmtt-8"> </span><span
5990 class="cmtt-8"> </span><span
5991 class="cmtt-8"> </span><span
5992 class="cmtt-8"> </span><span
5993 class="cmtt-8"> </span><span
5994 class="cmtt-8"> 7)</span><span
5995 class="cmtt-8"> vector</span><span
5996 class="cmtt-8"> [floor1_class_dimensions]</span><span
5997 class="cmtt-8"> element</span><span
5998 class="cmtt-8"> [i]</span><span
5999 class="cmtt-8"> =</span><span
6000 class="cmtt-8"> read</span><span
6001 class="cmtt-8"> 3</span><span
6002 class="cmtt-8"> bits</span><span
6003 class="cmtt-8"> as</span><span
6004 class="cmtt-8"> unsigned</span><span
6005 class="cmtt-8"> integer</span><span
6006 class="cmtt-8"> and</span><span
6007 class="cmtt-8"> add</span><span
6008 class="cmtt-8"> 1</span>
6009 <br class="fancyvrb" /><a
6010 id="x1-101028r14"></a><span
6011 class="cmr-6">14</span><span
6012 class="cmtt-8"> </span><span
6013 class="cmtt-8">  8)</span><span
6014 class="cmtt-8"> vector</span><span
6015 class="cmtt-8"> [floor1_class_subclasses]</span><span
6016 class="cmtt-8"> element</span><span
6017 class="cmtt-8"> [i]</span><span
6018 class="cmtt-8"> =</span><span
6019 class="cmtt-8"> read</span><span
6020 class="cmtt-8"> 2</span><span
6021 class="cmtt-8"> bits</span><span
6022 class="cmtt-8"> as</span><span
6023 class="cmtt-8"> unsigned</span><span
6024 class="cmtt-8"> integer</span>
6025 <br class="fancyvrb" /><a
6026 id="x1-101030r15"></a><span
6027 class="cmr-6">15</span><span
6028 class="cmtt-8"> </span><span
6029 class="cmtt-8"> </span><span
6030 class="cmtt-8"> </span><span
6031 class="cmtt-8"> </span><span
6032 class="cmtt-8"> </span><span
6033 class="cmtt-8"> </span><span
6034 class="cmtt-8"> </span><span
6035 class="cmtt-8"> </span><span
6036 class="cmtt-8"> </span><span
6037 class="cmtt-8"> 9)</span><span
6038 class="cmtt-8"> if</span><span
6039 class="cmtt-8"> (</span><span
6040 class="cmtt-8"> vector</span><span
6041 class="cmtt-8"> [floor1_class_subclasses]</span><span
6042 class="cmtt-8"> element</span><span
6043 class="cmtt-8"> [i]</span><span
6044 class="cmtt-8"> is</span><span
6045 class="cmtt-8"> nonzero</span><span
6046 class="cmtt-8"> )</span><span
6047 class="cmtt-8"> </span><span
6048 class="cmsy-8">{</span><br class="fancyvrb" /><a
6049 id="x1-101032r16"></a><span
6050 class="cmr-6">16</span><span
6051 class="cmtt-8"> </span><span
6052 class="cmtt-8"> </span>
6053 <br class="fancyvrb" /><a
6054 id="x1-101034r17"></a><span
6055 class="cmr-6">17</span><span
6056 class="cmtt-8"> </span><span
6057 class="cmtt-8"> </span><span
6058 class="cmtt-8"> </span><span
6059 class="cmtt-8"> </span><span
6060 class="cmtt-8"> </span><span
6061 class="cmtt-8"> </span><span
6062 class="cmtt-8"> </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"> 10)</span><span
6071 class="cmtt-8"> vector</span><span
6072 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6073 class="cmtt-8"> element</span><span
6074 class="cmtt-8"> [i]</span><span
6075 class="cmtt-8"> =</span><span
6076 class="cmtt-8"> read</span><span
6077 class="cmtt-8"> 8</span><span
6078 class="cmtt-8"> bits</span><span
6079 class="cmtt-8"> as</span><span
6080 class="cmtt-8"> unsigned</span><span
6081 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
6082 id="x1-101036r18"></a><span
6083 class="cmr-6">18</span><span
6084 class="cmtt-8"> </span><span
6085 class="cmtt-8"> </span><br class="fancyvrb" /><a
6086 id="x1-101038r19"></a><span
6087 class="cmr-6">19</span><span
6088 class="cmtt-8"> </span><span
6089 class="cmtt-8"> </span><span
6090 class="cmtt-8"> </span><span
6091 class="cmtt-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="cmtt-8"> </span><span
6100 class="cmtt-8"> </span><span
6101 class="cmsy-8">}</span><br class="fancyvrb" /><a
6102 id="x1-101040r20"></a><span
6103 class="cmr-6">20</span><span
6104 class="cmtt-8"> </span><span
6105 class="cmtt-8"> </span>
6106 <br class="fancyvrb" /><a
6107 id="x1-101042r21"></a><span
6108 class="cmr-6">21</span><span
6109 class="cmtt-8"> </span><span
6110 class="cmtt-8"> </span><span
6111 class="cmtt-8"> </span><span
6112 class="cmtt-8"> </span><span
6113 class="cmtt-8"> </span><span
6114 class="cmtt-8"> </span><span
6115 class="cmtt-8"> </span><span
6116 class="cmtt-8"> </span><span
6117 class="cmtt-8"> 11)</span><span
6118 class="cmtt-8"> iterate</span><span
6119 class="cmtt-8"> [j]</span><span
6120 class="cmtt-8"> over</span><span
6121 class="cmtt-8"> the</span><span
6122 class="cmtt-8"> range</span><span
6123 class="cmtt-8"> 0</span><span
6124 class="cmtt-8"> ...</span><span
6125 class="cmtt-8"> (2</span><span
6126 class="cmtt-8"> exponent</span><span
6127 class="cmtt-8"> [floor1_class_subclasses]</span><span
6128 class="cmtt-8"> element</span><span
6129 class="cmtt-8"> [i])</span><span
6130 class="cmtt-8"> -</span><span
6131 class="cmtt-8"> 1</span><span
6132 class="cmtt-8"> </span><span
6133 class="cmsy-8">{</span><br class="fancyvrb" /><a
6134 id="x1-101044r22"></a><span
6135 class="cmr-6">22</span><span
6136 class="cmtt-8"> </span><span
6137 class="cmtt-8"> </span>
6138 <br class="fancyvrb" /><a
6139 id="x1-101046r23"></a><span
6140 class="cmr-6">23</span><span
6141 class="cmtt-8"> </span><span
6142 class="cmtt-8"> </span><span
6143 class="cmtt-8"> </span><span
6144 class="cmtt-8"> </span><span
6145 class="cmtt-8"> </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"> 12)</span><span
6156 class="cmtt-8"> array</span><span
6157 class="cmtt-8"> [floor1_subclass_books]</span><span
6158 class="cmtt-8"> element</span><span
6159 class="cmtt-8"> [i],[j]</span><span
6160 class="cmtt-8"> =</span><br class="fancyvrb" /><a
6161 id="x1-101048r24"></a><span
6162 class="cmr-6">24</span><span
6163 class="cmtt-8"> </span><span
6164 class="cmtt-8"> </span><span
6165 class="cmtt-8"> </span><span
6166 class="cmtt-8"> </span><span
6167 class="cmtt-8"> </span><span
6168 class="cmtt-8"> </span><span
6169 class="cmtt-8"> </span><span
6170 class="cmtt-8"> </span><span
6171 class="cmtt-8"> </span><span
6172 class="cmtt-8"> </span><span
6173 class="cmtt-8"> </span><span
6174 class="cmtt-8"> </span><span
6175 class="cmtt-8"> </span><span
6176 class="cmtt-8"> </span><span
6177 class="cmtt-8"> </span><span
6178 class="cmtt-8"> </span><span
6179 class="cmtt-8"> </span><span
6180 class="cmtt-8"> </span><span
6181 class="cmtt-8"> read</span><span
6182 class="cmtt-8"> 8</span><span
6183 class="cmtt-8"> bits</span><span
6184 class="cmtt-8"> as</span><span
6185 class="cmtt-8"> unsigned</span><span
6186 class="cmtt-8"> integer</span><span
6187 class="cmtt-8"> and</span><span
6188 class="cmtt-8"> subtract</span><span
6189 class="cmtt-8"> one</span><br class="fancyvrb" /><a
6190 id="x1-101050r25"></a><span
6191 class="cmr-6">25</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"> </span><span
6199 class="cmtt-8"> </span><span
6200 class="cmtt-8"> </span><span
6201 class="cmtt-8"> </span><span
6202 class="cmtt-8"> </span><span
6203 class="cmtt-8"> </span><span
6204 class="cmtt-8"> </span><span
6205 class="cmsy-8">}</span>
6206 <br class="fancyvrb" /><a
6207 id="x1-101052r26"></a><span
6208 class="cmr-6">26</span><span
6209 class="cmtt-8"> </span><span
6210 class="cmtt-8"> </span><span
6211 class="cmtt-8"> </span><span
6212 class="cmtt-8"> </span><span
6213 class="cmtt-8"> </span><span
6214 class="cmtt-8"> </span><span
6215 class="cmtt-8"> </span><span
6216 class="cmtt-8"> </span><span
6217 class="cmsy-8">}</span><br class="fancyvrb" /><a
6218 id="x1-101054r27"></a><span
6219 class="cmr-6">27</span><span
6220 class="cmtt-8"> </span><span
6221 class="cmtt-8"> </span><br class="fancyvrb" /><a
6222 id="x1-101056r28"></a><span
6223 class="cmr-6">28</span><span
6224 class="cmtt-8"> </span><span
6225 class="cmtt-8"> </span><span
6226 class="cmtt-8"> 13)</span><span
6227 class="cmtt-8"> [floor1_multiplier]</span><span
6228 class="cmtt-8"> =</span><span
6229 class="cmtt-8"> read</span><span
6230 class="cmtt-8"> 2</span><span
6231 class="cmtt-8"> bits</span><span
6232 class="cmtt-8"> as</span><span
6233 class="cmtt-8"> unsigned</span><span
6234 class="cmtt-8"> integer</span><span
6235 class="cmtt-8"> and</span><span
6236 class="cmtt-8"> add</span><span
6237 class="cmtt-8"> one</span><br class="fancyvrb" /><a
6238 id="x1-101058r29"></a><span
6239 class="cmr-6">29</span><span
6240 class="cmtt-8"> </span><span
6241 class="cmtt-8"> </span><span
6242 class="cmtt-8"> 14)</span><span
6243 class="cmtt-8"> [rangebits]</span><span
6244 class="cmtt-8"> =</span><span
6245 class="cmtt-8"> read</span><span
6246 class="cmtt-8"> 4</span><span
6247 class="cmtt-8"> bits</span><span
6248 class="cmtt-8"> as</span><span
6249 class="cmtt-8"> unsigned</span><span
6250 class="cmtt-8"> integer</span>
6251 <br class="fancyvrb" /><a
6252 id="x1-101060r30"></a><span
6253 class="cmr-6">30</span><span
6254 class="cmtt-8"> </span><span
6255 class="cmtt-8"> </span><span
6256 class="cmtt-8"> 15)</span><span
6257 class="cmtt-8"> vector</span><span
6258 class="cmtt-8"> [floor1_X_list]</span><span
6259 class="cmtt-8"> element</span><span
6260 class="cmtt-8"> [0]</span><span
6261 class="cmtt-8"> =</span><span
6262 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
6263 id="x1-101062r31"></a><span
6264 class="cmr-6">31</span><span
6265 class="cmtt-8"> </span><span
6266 class="cmtt-8"> </span><span
6267 class="cmtt-8"> 16)</span><span
6268 class="cmtt-8"> vector</span><span
6269 class="cmtt-8"> [floor1_X_list]</span><span
6270 class="cmtt-8"> element</span><span
6271 class="cmtt-8"> [1]</span><span
6272 class="cmtt-8"> =</span><span
6273 class="cmtt-8"> 2</span><span
6274 class="cmtt-8"> exponent</span><span
6275 class="cmtt-8"> [rangebits];</span>
6276 <br class="fancyvrb" /><a
6277 id="x1-101064r32"></a><span
6278 class="cmr-6">32</span><span
6279 class="cmtt-8"> </span><span
6280 class="cmtt-8"> </span><span
6281 class="cmtt-8"> 17)</span><span
6282 class="cmtt-8"> [floor1_values]</span><span
6283 class="cmtt-8"> =</span><span
6284 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
6285 id="x1-101066r33"></a><span
6286 class="cmr-6">33</span><span
6287 class="cmtt-8"> </span><span
6288 class="cmtt-8"> </span><span
6289 class="cmtt-8"> 18)</span><span
6290 class="cmtt-8"> iterate</span><span
6291 class="cmtt-8"> [i]</span><span
6292 class="cmtt-8"> over</span><span
6293 class="cmtt-8"> the</span><span
6294 class="cmtt-8"> range</span><span
6295 class="cmtt-8"> 0</span><span
6296 class="cmtt-8"> ...</span><span
6297 class="cmtt-8"> [floor1_partitions]-1</span><span
6298 class="cmtt-8"> </span><span
6299 class="cmsy-8">{</span>
6300 <br class="fancyvrb" /><a
6301 id="x1-101068r34"></a><span
6302 class="cmr-6">34</span><span
6303 class="cmtt-8"> </span><span
6304 class="cmtt-8"> </span><br class="fancyvrb" /><a
6305 id="x1-101070r35"></a><span
6306 class="cmr-6">35</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"> 19)</span><span
6316 class="cmtt-8"> [current_class_number]</span><span
6317 class="cmtt-8"> =</span><span
6318 class="cmtt-8"> vector</span><span
6319 class="cmtt-8"> [floor1_partition_class_list]</span><span
6320 class="cmtt-8"> element</span><span
6321 class="cmtt-8"> [i]</span>
6322 <br class="fancyvrb" /><a
6323 id="x1-101072r36"></a><span
6324 class="cmr-6">36</span><span
6325 class="cmtt-8"> </span><span
6326 class="cmtt-8"> </span><span
6327 class="cmtt-8"> </span><span
6328 class="cmtt-8"> </span><span
6329 class="cmtt-8"> </span><span
6330 class="cmtt-8"> </span><span
6331 class="cmtt-8"> </span><span
6332 class="cmtt-8"> </span><span
6333 class="cmtt-8"> 20)</span><span
6334 class="cmtt-8"> iterate</span><span
6335 class="cmtt-8"> [j]</span><span
6336 class="cmtt-8"> over</span><span
6337 class="cmtt-8"> the</span><span
6338 class="cmtt-8"> range</span><span
6339 class="cmtt-8"> 0</span><span
6340 class="cmtt-8"> ...</span><span
6341 class="cmtt-8"> ([floor1_class_dimensions]</span><span
6342 class="cmtt-8"> element</span><span
6343 class="cmtt-8"> [current_class_number])-1</span><span
6344 class="cmtt-8"> </span><span
6345 class="cmsy-8">{</span>
6346 <br class="fancyvrb" /><a
6347 id="x1-101074r37"></a><span
6348 class="cmr-6">37</span><span
6349 class="cmtt-8"> </span><span
6350 class="cmtt-8"> </span><span
6351 class="cmtt-8"> </span><span
6352 class="cmtt-8"> </span><span
6353 class="cmtt-8"> </span><span
6354 class="cmtt-8"> </span><span
6355 class="cmtt-8"> </span><span
6356 class="cmtt-8"> </span><span
6357 class="cmtt-8"> </span><span
6358 class="cmtt-8"> </span><span
6359 class="cmtt-8"> </span><span
6360 class="cmtt-8"> </span><span
6361 class="cmtt-8"> </span><span
6362 class="cmtt-8"> </span><span
6363 class="cmtt-8"> 21)</span><span
6364 class="cmtt-8"> vector</span><span
6365 class="cmtt-8"> [floor1_X_list]</span><span
6366 class="cmtt-8"> element</span><span
6367 class="cmtt-8"> ([floor1_values])</span><span
6368 class="cmtt-8"> =</span><br class="fancyvrb" /><a
6369 id="x1-101076r38"></a><span
6370 class="cmr-6">38</span><span
6371 class="cmtt-8"> </span><span
6372 class="cmtt-8"> </span><span
6373 class="cmtt-8"> </span><span
6374 class="cmtt-8"> </span><span
6375 class="cmtt-8"> </span><span
6376 class="cmtt-8"> </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="cmtt-8"> </span><span
6386 class="cmtt-8"> </span><span
6387 class="cmtt-8"> </span><span
6388 class="cmtt-8"> </span><span
6389 class="cmtt-8"> read</span><span
6390 class="cmtt-8"> [rangebits]</span><span
6391 class="cmtt-8"> bits</span><span
6392 class="cmtt-8"> as</span><span
6393 class="cmtt-8"> unsigned</span><span
6394 class="cmtt-8"> integer</span>
6395 <br class="fancyvrb" /><a
6396 id="x1-101078r39"></a><span
6397 class="cmr-6">39</span><span
6398 class="cmtt-8"> </span><span
6399 class="cmtt-8"> </span><span
6400 class="cmtt-8"> </span><span
6401 class="cmtt-8"> </span><span
6402 class="cmtt-8"> </span><span
6403 class="cmtt-8"> </span><span
6404 class="cmtt-8"> </span><span
6405 class="cmtt-8"> </span><span
6406 class="cmtt-8"> </span><span
6407 class="cmtt-8"> </span><span
6408 class="cmtt-8"> </span><span
6409 class="cmtt-8"> </span><span
6410 class="cmtt-8"> </span><span
6411 class="cmtt-8"> </span><span
6412 class="cmtt-8"> 22)</span><span
6413 class="cmtt-8"> increment</span><span
6414 class="cmtt-8"> [floor1_values]</span><span
6415 class="cmtt-8"> by</span><span
6416 class="cmtt-8"> one</span><br class="fancyvrb" /><a
6417 id="x1-101080r40"></a><span
6418 class="cmr-6">40</span><span
6419 class="cmtt-8"> </span><span
6420 class="cmtt-8"> </span><span
6421 class="cmtt-8"> </span><span
6422 class="cmtt-8"> </span><span
6423 class="cmtt-8"> </span><span
6424 class="cmtt-8"> </span><span
6425 class="cmtt-8"> </span><span
6426 class="cmtt-8"> </span><span
6427 class="cmtt-8"> </span><span
6428 class="cmtt-8"> </span><span
6429 class="cmtt-8"> </span><span
6430 class="cmtt-8"> </span><span
6431 class="cmtt-8"> </span><span
6432 class="cmsy-8">}</span><br class="fancyvrb" /><a
6433 id="x1-101082r41"></a><span
6434 class="cmr-6">41</span><span
6435 class="cmtt-8"> </span><span
6436 class="cmtt-8"> </span><span
6437 class="cmtt-8"> </span><span
6438 class="cmtt-8"> </span><span
6439 class="cmtt-8"> </span><span
6440 class="cmtt-8"> </span><span
6441 class="cmtt-8"> </span><span
6442 class="cmsy-8">}</span><br class="fancyvrb" /><a
6443 id="x1-101084r42"></a><span
6444 class="cmr-6">42</span><span
6445 class="cmtt-8"> </span><span
6446 class="cmtt-8"> </span><br class="fancyvrb" /><a
6447 id="x1-101086r43"></a><span
6448 class="cmr-6">43</span><span
6449 class="cmtt-8"> </span><span
6450 class="cmtt-8"> </span><span
6451 class="cmtt-8"> 23)</span><span
6452 class="cmtt-8"> done</span></div>
6453 <!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
6454 setup renders a stream undecodable. In addition, a <span
6455 class="cmtt-12">[floor1_class_masterbooks] </span>or
6457 class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook
6458 configured in this stream is an error condition that renders the stream undecodable. Vector
6459 [floor1_x_list] is limited to a maximum length of 65 elements; a setup indicating more than 65
6460 total elements (including elements 0 and 1 set prior to the read loop) renders the stream
6461 undecodable. All vector [floor1_x_list] element values must be unique within the vector; a
6462 non-unique value renders the stream undecodable.
6463 <!--l. 170--><p class="noindent" >
6464 <h5 class="subsubsectionHead"><span class="titlemark">7.2.3. </span> <a
6465 id="x1-1020007.2.3"></a>packet decode</h5>
6466 <!--l. 172--><p class="noindent" >Packet decode begins by checking the <span
6467 class="cmtt-12">[nonzero] </span>flag:
6468 <!--l. 174--><p class="noindent" >
6469 <div class="fancyvrb" id="fancyvrb29"><a
6470 id="x1-102002r1"></a><span
6471 class="cmr-6">1</span><span
6472 class="cmtt-8"> </span><span
6473 class="cmtt-8"> </span><span
6474 class="cmtt-8"> </span><span
6475 class="cmtt-8"> 1)</span><span
6476 class="cmtt-8"> [nonzero]</span><span
6477 class="cmtt-8"> =</span><span
6478 class="cmtt-8"> read</span><span
6479 class="cmtt-8"> 1</span><span
6480 class="cmtt-8"> bit</span><span
6481 class="cmtt-8"> as</span><span
6482 class="cmtt-8"> boolean</span></div>
6483 <!--l. 178--><p class="noindent" >If <span
6484 class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
6485 Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
6486 this frame. (A return status of ’unused’ is different from decoding a floor that has all
6487 points set to minimum representation amplitude, which happens to be approximately
6489 <!--l. 186--><p class="noindent" >Assuming <span
6490 class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
6491 <!--l. 188--><p class="noindent" >
6492 <div class="fancyvrb" id="fancyvrb30"><a
6493 id="x1-102004r1"></a><span
6494 class="cmr-6">1</span><span
6495 class="cmtt-8"> </span><span
6496 class="cmtt-8"> </span><span
6497 class="cmtt-8"> </span><span
6498 class="cmtt-8"> 1)</span><span
6499 class="cmtt-8"> [range]</span><span
6500 class="cmtt-8"> =</span><span
6501 class="cmtt-8"> vector</span><span
6502 class="cmtt-8"> </span><span
6503 class="cmsy-8">{</span><span
6504 class="cmtt-8"> 256,</span><span
6505 class="cmtt-8"> 128,</span><span
6506 class="cmtt-8"> 86,</span><span
6507 class="cmtt-8"> 64</span><span
6508 class="cmtt-8"> </span><span
6509 class="cmsy-8">}</span><span
6510 class="cmtt-8"> element</span><span
6511 class="cmtt-8"> ([floor1_multiplier]-1)</span>
6515 <br class="fancyvrb" /><a
6516 id="x1-102006r2"></a><span
6517 class="cmr-6">2</span><span
6518 class="cmtt-8"> </span><span
6519 class="cmtt-8"> </span><span
6520 class="cmtt-8"> </span><span
6521 class="cmtt-8"> 2)</span><span
6522 class="cmtt-8"> vector</span><span
6523 class="cmtt-8"> [floor1_Y]</span><span
6524 class="cmtt-8"> element</span><span
6525 class="cmtt-8"> [0]</span><span
6526 class="cmtt-8"> =</span><span
6527 class="cmtt-8"> read</span><span
6528 class="cmtt-8"> </span><a
6529 href="#x1-1190009.2.1"><span
6530 class="cmtt-8">ilog</span></a><span
6531 class="cmtt-8">([range]-1)</span><span
6532 class="cmtt-8"> bits</span><span
6533 class="cmtt-8"> as</span><span
6534 class="cmtt-8"> unsigned</span><span
6535 class="cmtt-8"> integer</span>
6536 <br class="fancyvrb" /><a
6537 id="x1-102008r3"></a><span
6538 class="cmr-6">3</span><span
6539 class="cmtt-8"> </span><span
6540 class="cmtt-8"> </span><span
6541 class="cmtt-8"> </span><span
6542 class="cmtt-8"> 3)</span><span
6543 class="cmtt-8"> vector</span><span
6544 class="cmtt-8"> [floor1_Y]</span><span
6545 class="cmtt-8"> element</span><span
6546 class="cmtt-8"> [1]</span><span
6547 class="cmtt-8"> =</span><span
6548 class="cmtt-8"> read</span><span
6549 class="cmtt-8"> </span><a
6550 href="#x1-1190009.2.1"><span
6551 class="cmtt-8">ilog</span></a><span
6552 class="cmtt-8">([range]-1)</span><span
6553 class="cmtt-8"> bits</span><span
6554 class="cmtt-8"> as</span><span
6555 class="cmtt-8"> unsigned</span><span
6556 class="cmtt-8"> integer</span>
6557 <br class="fancyvrb" /><a
6558 id="x1-102010r4"></a><span
6559 class="cmr-6">4</span><span
6560 class="cmtt-8"> </span><span
6561 class="cmtt-8"> </span><span
6562 class="cmtt-8"> </span><span
6563 class="cmtt-8"> 4)</span><span
6564 class="cmtt-8"> [offset]</span><span
6565 class="cmtt-8"> =</span><span
6566 class="cmtt-8"> 2;</span><br class="fancyvrb" /><a
6567 id="x1-102012r5"></a><span
6568 class="cmr-6">5</span><span
6569 class="cmtt-8"> </span><span
6570 class="cmtt-8"> </span><span
6571 class="cmtt-8"> </span><span
6572 class="cmtt-8"> 5)</span><span
6573 class="cmtt-8"> iterate</span><span
6574 class="cmtt-8"> [i]</span><span
6575 class="cmtt-8"> over</span><span
6576 class="cmtt-8"> the</span><span
6577 class="cmtt-8"> range</span><span
6578 class="cmtt-8"> 0</span><span
6579 class="cmtt-8"> ...</span><span
6580 class="cmtt-8"> [floor1_partitions]-1</span><span
6581 class="cmtt-8"> </span><span
6582 class="cmsy-8">{</span><br class="fancyvrb" /><a
6583 id="x1-102014r6"></a><span
6584 class="cmr-6">6</span><span
6585 class="cmtt-8"> </span><span
6586 class="cmtt-8"> </span>
6587 <br class="fancyvrb" /><a
6588 id="x1-102016r7"></a><span
6589 class="cmr-6">7</span><span
6590 class="cmtt-8"> </span><span
6591 class="cmtt-8"> </span><span
6592 class="cmtt-8"> </span><span
6593 class="cmtt-8"> </span><span
6594 class="cmtt-8"> </span><span
6595 class="cmtt-8"> </span><span
6596 class="cmtt-8"> </span><span
6597 class="cmtt-8"> </span><span
6598 class="cmtt-8"> 6)</span><span
6599 class="cmtt-8"> [class]</span><span
6600 class="cmtt-8"> =</span><span
6601 class="cmtt-8"> vector</span><span
6602 class="cmtt-8"> [floor1_partition_class]</span><span
6603 class="cmtt-8"> </span><span
6604 class="cmtt-8"> element</span><span
6605 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
6606 id="x1-102018r8"></a><span
6607 class="cmr-6">8</span><span
6608 class="cmtt-8"> </span><span
6609 class="cmtt-8"> </span><span
6610 class="cmtt-8"> </span><span
6611 class="cmtt-8"> </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"> 7)</span><span
6617 class="cmtt-8"> [cdim]</span><span
6618 class="cmtt-8"> </span><span
6619 class="cmtt-8"> =</span><span
6620 class="cmtt-8"> vector</span><span
6621 class="cmtt-8"> [floor1_class_dimensions]</span><span
6622 class="cmtt-8"> element</span><span
6623 class="cmtt-8"> [class]</span>
6624 <br class="fancyvrb" /><a
6625 id="x1-102020r9"></a><span
6626 class="cmr-6">9</span><span
6627 class="cmtt-8"> </span><span
6628 class="cmtt-8"> </span><span
6629 class="cmtt-8"> </span><span
6630 class="cmtt-8"> </span><span
6631 class="cmtt-8"> </span><span
6632 class="cmtt-8"> </span><span
6633 class="cmtt-8"> </span><span
6634 class="cmtt-8"> </span><span
6635 class="cmtt-8"> 8)</span><span
6636 class="cmtt-8"> [cbits]</span><span
6637 class="cmtt-8"> =</span><span
6638 class="cmtt-8"> vector</span><span
6639 class="cmtt-8"> [floor1_class_subclasses]</span><span
6640 class="cmtt-8"> element</span><span
6641 class="cmtt-8"> [class]</span><br class="fancyvrb" /><a
6642 id="x1-102022r10"></a><span
6643 class="cmr-6">10</span><span
6644 class="cmtt-8"> </span><span
6645 class="cmtt-8"> </span><span
6646 class="cmtt-8"> </span><span
6647 class="cmtt-8"> </span><span
6648 class="cmtt-8"> </span><span
6649 class="cmtt-8"> </span><span
6650 class="cmtt-8"> </span><span
6651 class="cmtt-8"> </span><span
6652 class="cmtt-8"> 9)</span><span
6653 class="cmtt-8"> [csub]</span><span
6654 class="cmtt-8"> </span><span
6655 class="cmtt-8"> =</span><span
6656 class="cmtt-8"> (2</span><span
6657 class="cmtt-8"> exponent</span><span
6658 class="cmtt-8"> [cbits])-1</span><br class="fancyvrb" /><a
6659 id="x1-102024r11"></a><span
6660 class="cmr-6">11</span><span
6661 class="cmtt-8"> </span><span
6662 class="cmtt-8"> </span><span
6663 class="cmtt-8"> </span><span
6664 class="cmtt-8"> </span><span
6665 class="cmtt-8"> </span><span
6666 class="cmtt-8"> </span><span
6667 class="cmtt-8"> </span><span
6668 class="cmtt-8"> 10)</span><span
6669 class="cmtt-8"> [cval]</span><span
6670 class="cmtt-8"> </span><span
6671 class="cmtt-8"> =</span><span
6672 class="cmtt-8"> 0</span>
6673 <br class="fancyvrb" /><a
6674 id="x1-102026r12"></a><span
6675 class="cmr-6">12</span><span
6676 class="cmtt-8"> </span><span
6677 class="cmtt-8"> </span><span
6678 class="cmtt-8"> </span><span
6679 class="cmtt-8"> </span><span
6680 class="cmtt-8"> </span><span
6681 class="cmtt-8"> </span><span
6682 class="cmtt-8"> </span><span
6683 class="cmtt-8"> 11)</span><span
6684 class="cmtt-8"> if</span><span
6685 class="cmtt-8"> (</span><span
6686 class="cmtt-8"> [cbits]</span><span
6687 class="cmtt-8"> is</span><span
6688 class="cmtt-8"> greater</span><span
6689 class="cmtt-8"> than</span><span
6690 class="cmtt-8"> zero</span><span
6691 class="cmtt-8"> )</span><span
6692 class="cmtt-8"> </span><span
6693 class="cmsy-8">{</span><br class="fancyvrb" /><a
6694 id="x1-102028r13"></a><span
6695 class="cmr-6">13</span><span
6696 class="cmtt-8"> </span><span
6697 class="cmtt-8"> </span><br class="fancyvrb" /><a
6698 id="x1-102030r14"></a><span
6699 class="cmr-6">14</span><span
6700 class="cmtt-8"> </span><span
6701 class="cmtt-8"> </span><span
6702 class="cmtt-8"> </span><span
6703 class="cmtt-8"> </span><span
6704 class="cmtt-8"> </span><span
6705 class="cmtt-8"> </span><span
6706 class="cmtt-8"> </span><span
6707 class="cmtt-8"> </span><span
6708 class="cmtt-8"> </span><span
6709 class="cmtt-8"> </span><span
6710 class="cmtt-8"> </span><span
6711 class="cmtt-8"> </span><span
6712 class="cmtt-8"> </span><span
6713 class="cmtt-8"> </span><span
6714 class="cmtt-8"> 12)</span><span
6715 class="cmtt-8"> [cval]</span><span
6716 class="cmtt-8"> =</span><span
6717 class="cmtt-8"> read</span><span
6718 class="cmtt-8"> from</span><span
6719 class="cmtt-8"> packet</span><span
6720 class="cmtt-8"> using</span><span
6721 class="cmtt-8"> codebook</span><span
6722 class="cmtt-8"> number</span>
6723 <br class="fancyvrb" /><a
6724 id="x1-102032r15"></a><span
6725 class="cmr-6">15</span><span
6726 class="cmtt-8"> </span><span
6727 class="cmtt-8"> </span><span
6728 class="cmtt-8"> </span><span
6729 class="cmtt-8"> </span><span
6730 class="cmtt-8"> </span><span
6731 class="cmtt-8"> </span><span
6732 class="cmtt-8"> </span><span
6733 class="cmtt-8"> </span><span
6734 class="cmtt-8"> </span><span
6735 class="cmtt-8"> </span><span
6736 class="cmtt-8"> </span><span
6737 class="cmtt-8"> </span><span
6738 class="cmtt-8"> </span><span
6739 class="cmtt-8"> </span><span
6740 class="cmtt-8"> </span><span
6741 class="cmtt-8"> </span><span
6742 class="cmtt-8"> </span><span
6743 class="cmtt-8"> </span><span
6744 class="cmtt-8"> (vector</span><span
6745 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6746 class="cmtt-8"> element</span><span
6747 class="cmtt-8"> [class])</span><span
6748 class="cmtt-8"> in</span><span
6749 class="cmtt-8"> scalar</span><span
6750 class="cmtt-8"> context</span>
6751 <br class="fancyvrb" /><a
6752 id="x1-102034r16"></a><span
6753 class="cmr-6">16</span><span
6754 class="cmtt-8"> </span><span
6755 class="cmtt-8"> </span><span
6756 class="cmtt-8"> </span><span
6757 class="cmtt-8"> </span><span
6758 class="cmtt-8"> </span><span
6759 class="cmtt-8"> </span><span
6760 class="cmtt-8"> </span><span
6761 class="cmtt-8"> </span><span
6762 class="cmtt-8"> </span><span
6763 class="cmtt-8"> </span><span
6764 class="cmtt-8"> </span><span
6765 class="cmtt-8"> </span><span
6766 class="cmsy-8">}</span><br class="fancyvrb" /><a
6767 id="x1-102036r17"></a><span
6768 class="cmr-6">17</span><span
6769 class="cmtt-8"> </span><span
6770 class="cmtt-8"> </span><br class="fancyvrb" /><a
6771 id="x1-102038r18"></a><span
6772 class="cmr-6">18</span><span
6773 class="cmtt-8"> </span><span
6774 class="cmtt-8"> </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"> 13)</span><span
6781 class="cmtt-8"> iterate</span><span
6782 class="cmtt-8"> [j]</span><span
6783 class="cmtt-8"> over</span><span
6784 class="cmtt-8"> the</span><span
6785 class="cmtt-8"> range</span><span
6786 class="cmtt-8"> 0</span><span
6787 class="cmtt-8"> ...</span><span
6788 class="cmtt-8"> [cdim]-1</span><span
6789 class="cmtt-8"> </span><span
6790 class="cmsy-8">{</span><br class="fancyvrb" /><a
6791 id="x1-102040r19"></a><span
6792 class="cmr-6">19</span><span
6793 class="cmtt-8"> </span><span
6794 class="cmtt-8"> </span>
6795 <br class="fancyvrb" /><a
6796 id="x1-102042r20"></a><span
6797 class="cmr-6">20</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"> </span><span
6803 class="cmtt-8"> </span><span
6804 class="cmtt-8"> </span><span
6805 class="cmtt-8"> </span><span
6806 class="cmtt-8"> </span><span
6807 class="cmtt-8"> </span><span
6808 class="cmtt-8"> </span><span
6809 class="cmtt-8"> </span><span
6810 class="cmtt-8"> </span><span
6811 class="cmtt-8"> </span><span
6812 class="cmtt-8"> 14)</span><span
6813 class="cmtt-8"> [book]</span><span
6814 class="cmtt-8"> =</span><span
6815 class="cmtt-8"> array</span><span
6816 class="cmtt-8"> [floor1_subclass_books]</span><span
6817 class="cmtt-8"> element</span><span
6818 class="cmtt-8"> [class],([cval]</span><span
6819 class="cmtt-8"> bitwise</span><span
6820 class="cmtt-8"> AND</span><span
6821 class="cmtt-8"> [csub])</span>
6822 <br class="fancyvrb" /><a
6823 id="x1-102044r21"></a><span
6824 class="cmr-6">21</span><span
6825 class="cmtt-8"> </span><span
6826 class="cmtt-8"> </span><span
6827 class="cmtt-8"> </span><span
6828 class="cmtt-8"> </span><span
6829 class="cmtt-8"> </span><span
6830 class="cmtt-8"> </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"> 15)</span><span
6840 class="cmtt-8"> [cval]</span><span
6841 class="cmtt-8"> =</span><span
6842 class="cmtt-8"> [cval]</span><span
6843 class="cmtt-8"> right</span><span
6844 class="cmtt-8"> shifted</span><span
6845 class="cmtt-8"> [cbits]</span><span
6846 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
6847 id="x1-102046r22"></a><span
6848 class="cmr-6">22</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"> 16)</span><span
6856 class="cmtt-8"> if</span><span
6857 class="cmtt-8"> (</span><span
6858 class="cmtt-8"> [book]</span><span
6859 class="cmtt-8"> is</span><span
6860 class="cmtt-8"> not</span><span
6861 class="cmtt-8"> less</span><span
6862 class="cmtt-8"> than</span><span
6863 class="cmtt-8"> zero</span><span
6864 class="cmtt-8"> )</span><span
6865 class="cmtt-8"> </span><span
6866 class="cmsy-8">{</span><br class="fancyvrb" /><a
6867 id="x1-102048r23"></a><span
6868 class="cmr-6">23</span><span
6869 class="cmtt-8"> </span><span
6870 class="cmtt-8"> </span>
6871 <br class="fancyvrb" /><a
6872 id="x1-102050r24"></a><span
6873 class="cmr-6">24</span><span
6874 class="cmtt-8"> </span><span
6875 class="cmtt-8">  </span><span
6876 class="cmtt-8"> </span><span
6877 class="cmtt-8"> </span><span
6878 class="cmtt-8"> </span><span
6879 class="cmtt-8"> </span><span
6880 class="cmtt-8"> </span><span
6881 class="cmtt-8"> </span><span
6882 class="cmtt-8"> </span><span
6883 class="cmtt-8"> </span><span
6884 class="cmtt-8"> </span><span
6885 class="cmtt-8"> </span><span
6886 class="cmtt-8"> 17)</span><span
6887 class="cmtt-8"> vector</span><span
6888 class="cmtt-8"> [floor1_Y]</span><span
6889 class="cmtt-8"> element</span><span
6890 class="cmtt-8"> ([j]+[offset])</span><span
6891 class="cmtt-8"> =</span><span
6892 class="cmtt-8"> read</span><span
6893 class="cmtt-8"> from</span><span
6894 class="cmtt-8"> packet</span><span
6895 class="cmtt-8"> using</span><span
6896 class="cmtt-8"> codebook</span><br class="fancyvrb" /><a
6897 id="x1-102052r25"></a><span
6898 class="cmr-6">25</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"> </span><span
6905 class="cmtt-8"> </span><span
6906 class="cmtt-8"> </span><span
6907 class="cmtt-8"> </span><span
6908 class="cmtt-8"> </span><span
6909 class="cmtt-8"> </span><span
6910 class="cmtt-8"> </span><span
6911 class="cmtt-8"> </span><span
6912 class="cmtt-8"> </span><span
6913 class="cmtt-8"> </span><span
6914 class="cmtt-8"> </span><span
6915 class="cmtt-8"> </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"> [book]</span><span
6924 class="cmtt-8"> in</span><span
6925 class="cmtt-8"> scalar</span><span
6926 class="cmtt-8"> context</span>
6927 <br class="fancyvrb" /><a
6928 id="x1-102054r26"></a><span
6929 class="cmr-6">26</span><span
6930 class="cmtt-8"> </span><span
6931 class="cmtt-8"> </span><br class="fancyvrb" /><a
6932 id="x1-102056r27"></a><span
6933 class="cmr-6">27</span><span
6934 class="cmtt-8"> </span><span
6935 class="cmtt-8"> </span><span
6936 class="cmtt-8"> </span><span
6937 class="cmtt-8"> </span><span
6938 class="cmtt-8"> </span><span
6939 class="cmtt-8"> </span><span
6940 class="cmtt-8"> </span><span
6941 class="cmtt-8"> </span><span
6942 class="cmtt-8"> </span><span
6943 class="cmtt-8"> </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="cmsy-8">}</span><span
6954 class="cmtt-8"> else</span><span
6955 class="cmtt-8"> [book]</span><span
6956 class="cmtt-8"> is</span><span
6957 class="cmtt-8"> less</span><span
6958 class="cmtt-8"> than</span><span
6959 class="cmtt-8"> zero</span><span
6960 class="cmtt-8"> </span><span
6961 class="cmsy-8">{</span><br class="fancyvrb" /><a
6962 id="x1-102058r28"></a><span
6963 class="cmr-6">28</span><span
6964 class="cmtt-8"> </span><span
6965 class="cmtt-8"> </span><br class="fancyvrb" /><a
6966 id="x1-102060r29"></a><span
6967 class="cmr-6">29</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"> </span><span
6973 class="cmtt-8"> </span><span
6974 class="cmtt-8"> </span><span
6975 class="cmtt-8"> </span><span
6976 class="cmtt-8"> </span><span
6977 class="cmtt-8"> </span><span
6978 class="cmtt-8"> </span><span
6979 class="cmtt-8"> </span><span
6980 class="cmtt-8"> 18)</span><span
6981 class="cmtt-8"> vector</span><span
6982 class="cmtt-8"> [floor1_Y]</span><span
6983 class="cmtt-8"> element</span><span
6984 class="cmtt-8"> ([j]+[offset])</span><span
6985 class="cmtt-8"> =</span><span
6986 class="cmtt-8"> 0</span>
6987 <br class="fancyvrb" /><a
6988 id="x1-102062r30"></a><span
6989 class="cmr-6">30</span><span
6990 class="cmtt-8"> </span><span
6991 class="cmtt-8"> </span><br class="fancyvrb" /><a
6992 id="x1-102064r31"></a><span
6993 class="cmr-6">31</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"> </span><span
7006 class="cmtt-8"> </span><span
7007 class="cmtt-8"> </span><span
7008 class="cmtt-8"> </span><span
7009 class="cmtt-8"> </span><span
7010 class="cmtt-8"> </span><span
7011 class="cmtt-8"> </span><span
7012 class="cmtt-8"> </span><span
7013 class="cmsy-8">}</span><br class="fancyvrb" /><a
7014 id="x1-102066r32"></a><span
7015 class="cmr-6">32</span><span
7016 class="cmtt-8"> </span><span
7017 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
7029 id="x1-102068r33"></a><span
7030 class="cmr-6">33</span><span
7031 class="cmtt-8"> </span><span
7032 class="cmtt-8"> </span><br class="fancyvrb" /><a
7033 id="x1-102070r34"></a><span
7034 class="cmr-6">34</span><span
7035 class="cmtt-8"> </span><span
7036 class="cmtt-8"> </span><span
7037 class="cmtt-8"> </span><span
7038 class="cmtt-8"> </span><span
7039 class="cmtt-8"> </span><span
7040 class="cmtt-8"> </span><span
7041 class="cmtt-8"> </span><span
7042 class="cmtt-8"> 19)</span><span
7043 class="cmtt-8"> [offset]</span><span
7044 class="cmtt-8"> =</span><span
7045 class="cmtt-8"> [offset]</span><span
7046 class="cmtt-8"> +</span><span
7047 class="cmtt-8"> [cdim]</span><br class="fancyvrb" /><a
7048 id="x1-102072r35"></a><span
7049 class="cmr-6">35</span><span
7050 class="cmtt-8"> </span><span
7051 class="cmtt-8"> </span><br class="fancyvrb" /><a
7052 id="x1-102074r36"></a><span
7053 class="cmr-6">36</span><span
7054 class="cmtt-8"> </span><span
7055 class="cmtt-8"> </span><span
7056 class="cmtt-8"> </span><span
7057 class="cmtt-8"> </span><span
7058 class="cmtt-8"> </span><span
7059 class="cmtt-8"> </span><span
7060 class="cmtt-8"> </span><span
7061 class="cmsy-8">}</span><br class="fancyvrb" /><a
7062 id="x1-102076r37"></a><span
7063 class="cmr-6">37</span><span
7064 class="cmtt-8"> </span><span
7065 class="cmtt-8"> </span><br class="fancyvrb" /><a
7066 id="x1-102078r38"></a><span
7067 class="cmr-6">38</span><span
7068 class="cmtt-8"> </span><span
7069 class="cmtt-8"> </span><span
7070 class="cmtt-8"> 20)</span><span
7071 class="cmtt-8"> done</span></div>
7072 <!--l. 229--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
7073 end-of-packet is reached during any read operation above, floor decode is to return ’unused’
7074 status as if the <span
7075 class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
7076 <!--l. 235--><p class="noindent" >Vector <span
7077 class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
7078 <!--l. 240--><p class="noindent" >
7079 <h5 class="subsubsectionHead"><span class="titlemark">7.2.4. </span> <a
7080 id="x1-1030007.2.4"></a>curve computation</h5>
7081 <!--l. 242--><p class="noindent" >Curve computation is split into two logical steps; the first step derives final Y amplitude values
7082 from the encoded, wrapped difference values taken from the bitstream. The second step
7083 plots the curve lines. Also, although zero-difference values are used in the iterative
7084 prediction to find final Y values, these points are conditionally skipped during final
7085 line computation in step two. Skipping zero-difference values allows a smoother line
7087 <!--l. 250--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations,
7088 implementors are warned to follow the details closely. Deviation from implementing a strictly
7089 equivalent algorithm can result in serious decoding errors.
7090 <!--l. 255--><p class="noindent" ><span
7091 class="cmti-12">Additional note: </span>Although <span
7092 class="cmtt-12">[floor1_final_Y] </span>values in the prediction loop and at the end of
7093 step 1 are inherently limited by the prediction algorithm to [0, <span
7094 class="cmtt-12">[range]</span>), it is possible to abuse
7095 the setup and codebook machinery to produce negative or over-range results. We suggest that
7096 decoder implementations guard the values in vector <span
7097 class="cmtt-12">[floor1_final_Y] </span>by clamping each
7098 element to [0, <span
7099 class="cmtt-12">[range]</span>) after step 1. Variants of this suggestion are acceptable as valid floor1
7100 setups cannot produce out of range values.
7101 <!--l. 266--><p class="noindent" >
7102 <dl class="description"><dt class="description">
7104 class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd
7105 class="description">
7106 <!--l. 268--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
7110 values, then apply to line prediction.
7111 <!--l. 271--><p class="noindent" >
7112 <div class="fancyvrb" id="fancyvrb31"><a
7113 id="x1-103002r1"></a><span
7114 class="cmr-6">1</span><span
7115 class="cmtt-8"> </span><span
7116 class="cmtt-8"> </span><span
7117 class="cmtt-8"> </span><span
7118 class="cmtt-8"> 1)</span><span
7119 class="cmtt-8"> [range]</span><span
7120 class="cmtt-8"> =</span><span
7121 class="cmtt-8"> vector</span><span
7122 class="cmtt-8"> </span><span
7123 class="cmsy-8">{</span><span
7124 class="cmtt-8"> 256,</span><span
7125 class="cmtt-8"> 128,</span><span
7126 class="cmtt-8"> 86,</span><span
7127 class="cmtt-8"> 64</span><span
7128 class="cmtt-8"> </span><span
7129 class="cmsy-8">}</span><span
7130 class="cmtt-8"> element</span><span
7131 class="cmtt-8"> ([floor1_multiplier]-1)</span><br class="fancyvrb" /><a
7132 id="x1-103004r2"></a><span
7133 class="cmr-6">2</span><span
7134 class="cmtt-8"> </span><span
7135 class="cmtt-8"> </span><span
7136 class="cmtt-8"> </span><span
7137 class="cmtt-8"> 2)</span><span
7138 class="cmtt-8"> vector</span><span
7139 class="cmtt-8"> [floor1_step2_flag]</span><span
7140 class="cmtt-8"> element</span><span
7141 class="cmtt-8"> [0]</span><span
7142 class="cmtt-8"> =</span><span
7143 class="cmtt-8"> set</span>
7144 <br class="fancyvrb" /><a
7145 id="x1-103006r3"></a><span
7146 class="cmr-6">3</span><span
7147 class="cmtt-8"> </span><span
7148 class="cmtt-8"> </span><span
7149 class="cmtt-8"> </span><span
7150 class="cmtt-8"> 3)</span><span
7151 class="cmtt-8"> vector</span><span
7152 class="cmtt-8"> [floor1_step2_flag]</span><span
7153 class="cmtt-8"> element</span><span
7154 class="cmtt-8"> [1]</span><span
7155 class="cmtt-8"> =</span><span
7156 class="cmtt-8"> set</span><br class="fancyvrb" /><a
7157 id="x1-103008r4"></a><span
7158 class="cmr-6">4</span><span
7159 class="cmtt-8"> </span><span
7160 class="cmtt-8"> </span><span
7161 class="cmtt-8"> </span><span
7162 class="cmtt-8"> 4)</span><span
7163 class="cmtt-8"> vector</span><span
7164 class="cmtt-8"> [floor1_final_Y]</span><span
7165 class="cmtt-8"> element</span><span
7166 class="cmtt-8"> [0]</span><span
7167 class="cmtt-8"> =</span><span
7168 class="cmtt-8"> vector</span><span
7169 class="cmtt-8"> [floor1_Y]</span><span
7170 class="cmtt-8"> element</span><span
7171 class="cmtt-8"> [0]</span>
7172 <br class="fancyvrb" /><a
7173 id="x1-103010r5"></a><span
7174 class="cmr-6">5</span><span
7175 class="cmtt-8"> </span><span
7176 class="cmtt-8"> </span><span
7177 class="cmtt-8"> </span><span
7178 class="cmtt-8"> 5)</span><span
7179 class="cmtt-8"> vector</span><span
7180 class="cmtt-8"> [floor1_final_Y]</span><span
7181 class="cmtt-8"> element</span><span
7182 class="cmtt-8"> [1]</span><span
7183 class="cmtt-8"> =</span><span
7184 class="cmtt-8"> vector</span><span
7185 class="cmtt-8"> [floor1_Y]</span><span
7186 class="cmtt-8"> element</span><span
7187 class="cmtt-8"> [1]</span><br class="fancyvrb" /><a
7188 id="x1-103012r6"></a><span
7189 class="cmr-6">6</span><span
7190 class="cmtt-8"> </span><span
7191 class="cmtt-8"> </span><span
7192 class="cmtt-8"> </span><span
7193 class="cmtt-8"> 6)</span><span
7194 class="cmtt-8"> iterate</span><span
7195 class="cmtt-8"> [i]</span><span
7196 class="cmtt-8"> over</span><span
7197 class="cmtt-8"> the</span><span
7198 class="cmtt-8"> range</span><span
7199 class="cmtt-8"> 2</span><span
7200 class="cmtt-8"> ...</span><span
7201 class="cmtt-8"> [floor1_values]-1</span><span
7202 class="cmtt-8"> </span><span
7203 class="cmsy-8">{</span><br class="fancyvrb" /><a
7204 id="x1-103014r7"></a><span
7205 class="cmr-6">7</span><span
7206 class="cmtt-8"> </span><span
7207 class="cmtt-8"> </span>
7208 <br class="fancyvrb" /><a
7209 id="x1-103016r8"></a><span
7210 class="cmr-6">8</span><span
7211 class="cmtt-8"> </span><span
7212 class="cmtt-8"> </span><span
7213 class="cmtt-8"> </span><span
7214 class="cmtt-8"> </span><span
7215 class="cmtt-8"> </span><span
7216 class="cmtt-8"> </span><span
7217 class="cmtt-8"> </span><span
7218 class="cmtt-8"> </span><span
7219 class="cmtt-8"> 7)</span><span
7220 class="cmtt-8"> [low_neighbor_offset]</span><span
7221 class="cmtt-8"> =</span><span
7222 class="cmtt-8"> </span><a
7223 href="#x1-1220009.2.4"><span
7224 class="cmtt-8">low_neighbor</span></a><span
7225 class="cmtt-8">([floor1_X_list],[i])</span><br class="fancyvrb" /><a
7226 id="x1-103018r9"></a><span
7227 class="cmr-6">9</span><span
7228 class="cmtt-8"> </span><span
7229 class="cmtt-8"> </span><span
7230 class="cmtt-8"> </span><span
7231 class="cmtt-8"> </span><span
7232 class="cmtt-8"> </span><span
7233 class="cmtt-8"> </span><span
7234 class="cmtt-8"> </span><span
7235 class="cmtt-8"> </span><span
7236 class="cmtt-8"> 8)</span><span
7237 class="cmtt-8"> [high_neighbor_offset]</span><span
7238 class="cmtt-8"> =</span><span
7239 class="cmtt-8"> </span><a
7240 href="#x1-1230009.2.5"><span
7241 class="cmtt-8">high_neighbor</span></a><span
7242 class="cmtt-8">([floor1_X_list],[i])</span>
7243 <br class="fancyvrb" /><a
7244 id="x1-103020r10"></a><span
7245 class="cmr-6">10</span><span
7246 class="cmtt-8"> </span><span
7247 class="cmtt-8"> </span><br class="fancyvrb" /><a
7248 id="x1-103022r11"></a><span
7249 class="cmr-6">11</span><span
7250 class="cmtt-8"> </span><span
7251 class="cmtt-8"> </span><span
7252 class="cmtt-8"> </span><span
7253 class="cmtt-8"> </span><span
7254 class="cmtt-8"> </span><span
7255 class="cmtt-8"> </span><span
7256 class="cmtt-8"> </span><span
7257 class="cmtt-8"> </span><span
7258 class="cmtt-8"> 9)</span><span
7259 class="cmtt-8"> [predicted]</span><span
7260 class="cmtt-8"> =</span><span
7261 class="cmtt-8"> </span><a
7262 href="#x1-1240009.2.6"><span
7263 class="cmtt-8">render_point</span></a><span
7264 class="cmtt-8">(</span><span
7265 class="cmtt-8"> vector</span><span
7266 class="cmtt-8"> [floor1_X_list]</span><span
7267 class="cmtt-8"> element</span><span
7268 class="cmtt-8"> [low_neighbor_offset],</span>
7269 <br class="fancyvrb" /><a
7270 id="x1-103024r12"></a><span
7271 class="cmr-6">12</span><span
7272 class="cmtt-8"> </span><span
7273 class="cmtt-8">  </span><span
7274 class="cmtt-8"> </span><span
7275 class="cmtt-8"> </span><span
7276 class="cmtt-8"> </span><span
7277 class="cmtt-8"> </span><span
7278 class="cmtt-8"> </span><span
7279 class="cmtt-8"> vector</span><span
7280 class="cmtt-8"> [floor1_final_Y]</span><span
7281 class="cmtt-8"> element</span><span
7282 class="cmtt-8"> [low_neighbor_offset],</span>
7283 <br class="fancyvrb" /><a
7284 id="x1-103026r13"></a><span
7285 class="cmr-6">13</span><span
7286 class="cmtt-8"> </span><span
7287 class="cmtt-8"> </span><span
7288 class="cmtt-8"> </span><span
7289 class="cmtt-8"> </span><span
7290 class="cmtt-8"> </span><span
7291 class="cmtt-8"> </span><span
7292 class="cmtt-8"> </span><span
7293 class="cmtt-8"> </span><span
7294 class="cmtt-8"> </span><span
7295 class="cmtt-8"> </span><span
7296 class="cmtt-8"> </span><span
7297 class="cmtt-8"> </span><span
7298 class="cmtt-8"> </span><span
7299 class="cmtt-8"> </span><span
7300 class="cmtt-8"> </span><span
7301 class="cmtt-8"> </span><span
7302 class="cmtt-8"> </span><span
7303 class="cmtt-8"> </span><span
7304 class="cmtt-8"> </span><span
7305 class="cmtt-8"> </span><span
7306 class="cmtt-8"> </span><span
7307 class="cmtt-8"> </span><span
7308 class="cmtt-8"> </span><span
7309 class="cmtt-8"> </span><span
7310 class="cmtt-8"> </span><span
7311 class="cmtt-8"> </span><span
7312 class="cmtt-8"> </span><span
7313 class="cmtt-8"> </span><span
7314 class="cmtt-8"> </span><span
7315 class="cmtt-8"> </span><span
7316 class="cmtt-8"> </span><span
7317 class="cmtt-8"> </span><span
7318 class="cmtt-8"> </span><span
7319 class="cmtt-8"> </span><span
7320 class="cmtt-8"> </span><span
7321 class="cmtt-8"> </span><span
7322 class="cmtt-8"> </span><span
7323 class="cmtt-8"> </span><span
7324 class="cmtt-8"> </span><span
7325 class="cmtt-8"> vector</span><span
7326 class="cmtt-8"> [floor1_X_list]</span><span
7327 class="cmtt-8"> element</span><span
7328 class="cmtt-8"> [high_neighbor_offset],</span>
7329 <br class="fancyvrb" /><a
7330 id="x1-103028r14"></a><span
7331 class="cmr-6">14</span><span
7332 class="cmtt-8"> </span><span
7333 class="cmtt-8">  </span><span
7334 class="cmtt-8"> </span><span
7335 class="cmtt-8"> </span><span
7336 class="cmtt-8"> </span><span
7337 class="cmtt-8"> </span><span
7338 class="cmtt-8"> </span><span
7339 class="cmtt-8"> vector</span><span
7340 class="cmtt-8"> [floor1_final_Y]</span><span
7341 class="cmtt-8"> element</span><span
7342 class="cmtt-8"> [high_neighbor_offset],</span>
7343 <br class="fancyvrb" /><a
7344 id="x1-103030r15"></a><span
7345 class="cmr-6">15</span><span
7346 class="cmtt-8"> </span><span
7347 class="cmtt-8"> </span><span
7348 class="cmtt-8"> </span><span
7349 class="cmtt-8"> </span><span
7350 class="cmtt-8"> </span><span
7351 class="cmtt-8"> </span><span
7352 class="cmtt-8"> </span><span
7353 class="cmtt-8"> </span><span
7354 class="cmtt-8"> </span><span
7355 class="cmtt-8"> </span><span
7356 class="cmtt-8"> </span><span
7357 class="cmtt-8"> </span><span
7358 class="cmtt-8"> </span><span
7359 class="cmtt-8"> </span><span
7360 class="cmtt-8"> </span><span
7361 class="cmtt-8"> </span><span
7362 class="cmtt-8"> </span><span
7363 class="cmtt-8"> </span><span
7364 class="cmtt-8"> </span><span
7365 class="cmtt-8"> </span><span
7366 class="cmtt-8"> </span><span
7367 class="cmtt-8"> </span><span
7368 class="cmtt-8"> </span><span
7369 class="cmtt-8"> </span><span
7370 class="cmtt-8"> </span><span
7371 class="cmtt-8"> </span><span
7372 class="cmtt-8"> </span><span
7373 class="cmtt-8"> </span><span
7374 class="cmtt-8"> </span><span
7375 class="cmtt-8"> </span><span
7376 class="cmtt-8"> </span><span
7377 class="cmtt-8"> </span><span
7378 class="cmtt-8"> </span><span
7379 class="cmtt-8"> </span><span
7380 class="cmtt-8"> </span><span
7381 class="cmtt-8"> </span><span
7382 class="cmtt-8"> </span><span
7383 class="cmtt-8"> </span><span
7384 class="cmtt-8"> </span><span
7385 class="cmtt-8"> vector</span><span
7386 class="cmtt-8"> [floor1_X_list]</span><span
7387 class="cmtt-8"> element</span><span
7388 class="cmtt-8"> [i]</span><span
7389 class="cmtt-8"> )</span><br class="fancyvrb" /><a
7390 id="x1-103032r16"></a><span
7391 class="cmr-6">16</span><span
7392 class="cmtt-8"> </span><span
7393 class="cmtt-8"> </span><br class="fancyvrb" /><a
7394 id="x1-103034r17"></a><span
7395 class="cmr-6">17</span><span
7396 class="cmtt-8"> </span><span
7397 class="cmtt-8"> </span><span
7398 class="cmtt-8"> </span><span
7399 class="cmtt-8"> </span><span
7400 class="cmtt-8"> </span><span
7401 class="cmtt-8"> </span><span
7402 class="cmtt-8"> </span><span
7403 class="cmtt-8"> 10)</span><span
7404 class="cmtt-8"> [val]</span><span
7405 class="cmtt-8"> =</span><span
7406 class="cmtt-8"> vector</span><span
7407 class="cmtt-8"> [floor1_Y]</span><span
7408 class="cmtt-8"> element</span><span
7409 class="cmtt-8"> [i]</span>
7410 <br class="fancyvrb" /><a
7411 id="x1-103036r18"></a><span
7412 class="cmr-6">18</span><span
7413 class="cmtt-8"> </span><span
7414 class="cmtt-8"> </span><span
7415 class="cmtt-8"> </span><span
7416 class="cmtt-8"> </span><span
7417 class="cmtt-8"> </span><span
7418 class="cmtt-8"> </span><span
7419 class="cmtt-8"> </span><span
7420 class="cmtt-8"> 11)</span><span
7421 class="cmtt-8"> [highroom]</span><span
7422 class="cmtt-8"> =</span><span
7423 class="cmtt-8"> [range]</span><span
7424 class="cmtt-8"> -</span><span
7425 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
7426 id="x1-103038r19"></a><span
7427 class="cmr-6">19</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"> 12)</span><span
7436 class="cmtt-8"> [lowroom]</span><span
7437 class="cmtt-8"> </span><span
7438 class="cmtt-8"> =</span><span
7439 class="cmtt-8"> [predicted]</span>
7440 <br class="fancyvrb" /><a
7441 id="x1-103040r20"></a><span
7442 class="cmr-6">20</span><span
7443 class="cmtt-8"> </span><span
7444 class="cmtt-8"> </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"> 13)</span><span
7451 class="cmtt-8"> if</span><span
7452 class="cmtt-8"> (</span><span
7453 class="cmtt-8"> [highroom]</span><span
7454 class="cmtt-8"> is</span><span
7455 class="cmtt-8"> less</span><span
7456 class="cmtt-8"> than</span><span
7457 class="cmtt-8"> [lowroom]</span><span
7458 class="cmtt-8"> )</span><span
7459 class="cmtt-8"> </span><span
7460 class="cmsy-8">{</span><br class="fancyvrb" /><a
7461 id="x1-103042r21"></a><span
7462 class="cmr-6">21</span><span
7463 class="cmtt-8"> </span><span
7464 class="cmtt-8"> </span><br class="fancyvrb" /><a
7465 id="x1-103044r22"></a><span
7466 class="cmr-6">22</span><span
7467 class="cmtt-8"> </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"> </span><span
7477 class="cmtt-8"> </span><span
7478 class="cmtt-8"> </span><span
7479 class="cmtt-8"> </span><span
7480 class="cmtt-8"> 14)</span><span
7481 class="cmtt-8"> [room]</span><span
7482 class="cmtt-8"> =</span><span
7483 class="cmtt-8"> [highroom]</span><span
7484 class="cmtt-8"> *</span><span
7485 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
7486 id="x1-103046r23"></a><span
7487 class="cmr-6">23</span><span
7488 class="cmtt-8"> </span><span
7489 class="cmtt-8"> </span>
7490 <br class="fancyvrb" /><a
7491 id="x1-103048r24"></a><span
7492 class="cmr-6">24</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"> </span><span
7498 class="cmtt-8"> </span><span
7499 class="cmtt-8"> </span><span
7500 class="cmtt-8"> </span><span
7501 class="cmtt-8"> </span><span
7502 class="cmtt-8"> </span><span
7503 class="cmtt-8"> </span><span
7504 class="cmtt-8"> </span><span
7505 class="cmsy-8">}</span><span
7506 class="cmtt-8"> else</span><span
7507 class="cmtt-8"> [highroom]</span><span
7508 class="cmtt-8"> is</span><span
7509 class="cmtt-8"> not</span><span
7510 class="cmtt-8"> less</span><span
7511 class="cmtt-8"> than</span><span
7512 class="cmtt-8"> [lowroom]</span><span
7513 class="cmtt-8"> </span><span
7514 class="cmsy-8">{</span><br class="fancyvrb" /><a
7515 id="x1-103050r25"></a><span
7516 class="cmr-6">25</span><span
7517 class="cmtt-8"> </span><span
7518 class="cmtt-8"> </span><br class="fancyvrb" /><a
7519 id="x1-103052r26"></a><span
7520 class="cmr-6">26</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"> 15)</span><span
7535 class="cmtt-8"> [room]</span><span
7536 class="cmtt-8"> =</span><span
7537 class="cmtt-8"> [lowroom]</span><span
7538 class="cmtt-8"> *</span><span
7539 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
7540 id="x1-103054r27"></a><span
7541 class="cmr-6">27</span><span
7542 class="cmtt-8"> </span><span
7543 class="cmtt-8"> </span><br class="fancyvrb" /><a
7544 id="x1-103056r28"></a><span
7545 class="cmr-6">28</span><span
7546 class="cmtt-8"> </span><span
7547 class="cmtt-8"> </span><span
7548 class="cmtt-8"> </span><span
7549 class="cmtt-8"> </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"> </span><span
7558 class="cmsy-8">}</span><br class="fancyvrb" /><a
7559 id="x1-103058r29"></a><span
7560 class="cmr-6">29</span><span
7561 class="cmtt-8"> </span><span
7562 class="cmtt-8"> </span>
7563 <br class="fancyvrb" /><a
7564 id="x1-103060r30"></a><span
7565 class="cmr-6">30</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"> 16)</span><span
7574 class="cmtt-8"> if</span><span
7575 class="cmtt-8"> (</span><span
7576 class="cmtt-8"> [val]</span><span
7577 class="cmtt-8"> is</span><span
7578 class="cmtt-8"> nonzero</span><span
7579 class="cmtt-8"> )</span><span
7580 class="cmtt-8"> </span><span
7581 class="cmsy-8">{</span><br class="fancyvrb" /><a
7582 id="x1-103062r31"></a><span
7583 class="cmr-6">31</span><span
7584 class="cmtt-8"> </span><span
7585 class="cmtt-8"> </span><br class="fancyvrb" /><a
7586 id="x1-103064r32"></a><span
7587 class="cmr-6">32</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"> 17)</span><span
7602 class="cmtt-8"> vector</span><span
7603 class="cmtt-8"> [floor1_step2_flag]</span><span
7604 class="cmtt-8"> element</span><span
7605 class="cmtt-8"> [low_neighbor_offset]</span><span
7606 class="cmtt-8"> =</span><span
7607 class="cmtt-8"> set</span>
7608 <br class="fancyvrb" /><a
7609 id="x1-103066r33"></a><span
7610 class="cmr-6">33</span><span
7611 class="cmtt-8"> </span><span
7612 class="cmtt-8"> </span><span
7613 class="cmtt-8"> </span><span
7614 class="cmtt-8"> </span><span
7615 class="cmtt-8"> </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"> </span><span
7624 class="cmtt-8"> 18)</span><span
7625 class="cmtt-8"> vector</span><span
7626 class="cmtt-8"> [floor1_step2_flag]</span><span
7627 class="cmtt-8"> element</span><span
7628 class="cmtt-8"> [high_neighbor_offset]</span><span
7629 class="cmtt-8"> =</span><span
7630 class="cmtt-8"> set</span>
7631 <br class="fancyvrb" /><a
7632 id="x1-103068r34"></a><span
7633 class="cmr-6">34</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"> </span><span
7641 class="cmtt-8"> </span><span
7642 class="cmtt-8"> </span><span
7643 class="cmtt-8"> </span><span
7644 class="cmtt-8"> </span><span
7645 class="cmtt-8"> </span><span
7646 class="cmtt-8"> </span><span
7647 class="cmtt-8"> 19)</span><span
7648 class="cmtt-8"> vector</span><span
7649 class="cmtt-8"> [floor1_step2_flag]</span><span
7650 class="cmtt-8"> element</span><span
7651 class="cmtt-8"> [i]</span><span
7652 class="cmtt-8"> =</span><span
7653 class="cmtt-8"> set</span><br class="fancyvrb" /><a
7654 id="x1-103070r35"></a><span
7655 class="cmr-6">35</span><span
7656 class="cmtt-8"> </span><span
7657 class="cmtt-8"> </span><span
7658 class="cmtt-8"> </span><span
7659 class="cmtt-8"> </span><span
7660 class="cmtt-8"> </span><span
7661 class="cmtt-8"> </span><span
7662 class="cmtt-8"> </span><span
7663 class="cmtt-8"> </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"> 20)</span><span
7670 class="cmtt-8"> if</span><span
7671 class="cmtt-8"> (</span><span
7672 class="cmtt-8"> [val]</span><span
7673 class="cmtt-8"> is</span><span
7674 class="cmtt-8"> greater</span><span
7675 class="cmtt-8"> than</span><span
7676 class="cmtt-8"> or</span><span
7677 class="cmtt-8"> equal</span><span
7678 class="cmtt-8"> to</span><span
7679 class="cmtt-8"> [room]</span><span
7680 class="cmtt-8"> )</span><span
7681 class="cmtt-8"> </span><span
7682 class="cmsy-8">{</span>
7683 <br class="fancyvrb" /><a
7684 id="x1-103072r36"></a><span
7685 class="cmr-6">36</span><span
7686 class="cmtt-8"> </span><span
7687 class="cmtt-8"> </span><br class="fancyvrb" /><a
7688 id="x1-103074r37"></a><span
7689 class="cmr-6">37</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"> </span><span
7704 class="cmtt-8"> </span><span
7705 class="cmtt-8"> </span><span
7706 class="cmtt-8"> </span><span
7707 class="cmtt-8"> </span><span
7708 class="cmtt-8"> </span><span
7709 class="cmtt-8"> 21)</span><span
7710 class="cmtt-8"> if</span><span
7711 class="cmtt-8"> (</span><span
7712 class="cmtt-8"> [highroom]</span><span
7713 class="cmtt-8"> is</span><span
7714 class="cmtt-8"> greater</span><span
7715 class="cmtt-8"> than</span><span
7716 class="cmtt-8"> [lowroom]</span><span
7717 class="cmtt-8"> )</span><span
7718 class="cmtt-8"> </span><span
7719 class="cmsy-8">{</span><br class="fancyvrb" /><a
7720 id="x1-103076r38"></a><span
7721 class="cmr-6">38</span><span
7722 class="cmtt-8"> </span><span
7723 class="cmtt-8"> </span>
7724 <br class="fancyvrb" /><a
7725 id="x1-103078r39"></a><span
7726 class="cmr-6">39</span><span
7727 class="cmtt-8"> </span><span
7728 class="cmtt-8"> </span><span
7729 class="cmtt-8"> </span><span
7730 class="cmtt-8"> </span><span
7731 class="cmtt-8"> </span><span
7732 class="cmtt-8"> </span><span
7733 class="cmtt-8"> </span><span
7734 class="cmtt-8"> </span><span
7735 class="cmtt-8"> </span><span
7736 class="cmtt-8"> </span><span
7737 class="cmtt-8"> </span><span
7738 class="cmtt-8"> </span><span
7739 class="cmtt-8"> </span><span
7740 class="cmtt-8"> </span><span
7741 class="cmtt-8"> </span><span
7742 class="cmtt-8"> </span><span
7743 class="cmtt-8"> </span><span
7744 class="cmtt-8"> </span><span
7745 class="cmtt-8"> </span><span
7746 class="cmtt-8"> </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"> 22)</span><span
7753 class="cmtt-8"> vector</span><span
7754 class="cmtt-8"> [floor1_final_Y]</span><span
7755 class="cmtt-8"> element</span><span
7756 class="cmtt-8"> [i]</span><span
7757 class="cmtt-8"> =</span><span
7758 class="cmtt-8"> [val]</span><span
7759 class="cmtt-8"> -</span><span
7760 class="cmtt-8"> [lowroom]</span><span
7761 class="cmtt-8"> +</span><span
7762 class="cmtt-8"> [predicted]</span>
7763 <br class="fancyvrb" /><a
7764 id="x1-103080r40"></a><span
7765 class="cmr-6">40</span><span
7766 class="cmtt-8"> </span><span
7767 class="cmtt-8"> </span><br class="fancyvrb" /><a
7768 id="x1-103082r41"></a><span
7769 class="cmr-6">41</span><span
7770 class="cmtt-8"> </span><span
7771 class="cmtt-8">  </span><span
7772 class="cmtt-8"> </span><span
7773 class="cmtt-8"> </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="cmsy-8">}</span><span
7779 class="cmtt-8"> else</span><span
7780 class="cmtt-8"> [highroom]</span><span
7781 class="cmtt-8"> is</span><span
7782 class="cmtt-8"> not</span><span
7783 class="cmtt-8"> greater</span><span
7784 class="cmtt-8"> than</span><span
7785 class="cmtt-8"> [lowroom]</span><span
7786 class="cmtt-8"> </span><span
7787 class="cmsy-8">{</span><br class="fancyvrb" /><a
7788 id="x1-103084r42"></a><span
7789 class="cmr-6">42</span><span
7790 class="cmtt-8"> </span><span
7791 class="cmtt-8"> </span>
7792 <br class="fancyvrb" /><a
7793 id="x1-103086r43"></a><span
7794 class="cmr-6">43</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"> </span><span
7803 class="cmtt-8"> </span><span
7804 class="cmtt-8"> </span><span
7805 class="cmtt-8"> </span><span
7806 class="cmtt-8"> </span><span
7807 class="cmtt-8"> </span><span
7808 class="cmtt-8"> </span><span
7809 class="cmtt-8"> </span><span
7810 class="cmtt-8"> </span><span
7811 class="cmtt-8"> </span><span
7812 class="cmtt-8"> </span><span
7813 class="cmtt-8"> </span><span
7814 class="cmtt-8"> </span><span
7815 class="cmtt-8"> </span><span
7816 class="cmtt-8"> </span><span
7817 class="cmtt-8"> </span><span
7818 class="cmtt-8"> </span><span
7819 class="cmtt-8"> </span><span
7820 class="cmtt-8"> 23)</span><span
7821 class="cmtt-8"> vector</span><span
7822 class="cmtt-8"> [floor1_final_Y]</span><span
7823 class="cmtt-8"> element</span><span
7824 class="cmtt-8"> [i]</span><span
7825 class="cmtt-8"> =</span><span
7826 class="cmtt-8"> [predicted]</span><span
7827 class="cmtt-8"> -</span><span
7828 class="cmtt-8"> [val]</span><span
7829 class="cmtt-8"> +</span><span
7830 class="cmtt-8"> [highroom]</span><span
7831 class="cmtt-8"> -</span><span
7832 class="cmtt-8"> 1</span>
7833 <br class="fancyvrb" /><a
7834 id="x1-103088r44"></a><span
7835 class="cmr-6">44</span><span
7836 class="cmtt-8"> </span><span
7837 class="cmtt-8"> </span><br class="fancyvrb" /><a
7838 id="x1-103090r45"></a><span
7839 class="cmr-6">45</span><span
7840 class="cmtt-8"> </span><span
7841 class="cmtt-8"> </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"> </span><span
7856 class="cmtt-8"> </span><span
7857 class="cmtt-8"> </span><span
7858 class="cmtt-8"> </span><span
7859 class="cmtt-8"> </span><span
7860 class="cmtt-8"> </span><span
7861 class="cmtt-8"> </span><span
7862 class="cmtt-8"> </span><span
7863 class="cmtt-8"> </span><span
7864 class="cmsy-8">}</span><br class="fancyvrb" /><a
7865 id="x1-103092r46"></a><span
7866 class="cmr-6">46</span><span
7867 class="cmtt-8"> </span><span
7868 class="cmtt-8"> </span><br class="fancyvrb" /><a
7869 id="x1-103094r47"></a><span
7870 class="cmr-6">47</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"> </span><span
7879 class="cmtt-8"> </span><span
7880 class="cmtt-8"> </span><span
7881 class="cmtt-8"> </span><span
7882 class="cmtt-8"> </span><span
7883 class="cmtt-8"> </span><span
7884 class="cmtt-8"> </span><span
7885 class="cmtt-8"> </span><span
7886 class="cmtt-8"> </span><span
7887 class="cmtt-8"> </span><span
7888 class="cmtt-8"> </span><span
7889 class="cmsy-8">}</span><span
7890 class="cmtt-8"> else</span><span
7891 class="cmtt-8"> [val]</span><span
7892 class="cmtt-8"> is</span><span
7893 class="cmtt-8"> less</span><span
7894 class="cmtt-8"> than</span><span
7895 class="cmtt-8"> [room]</span><span
7896 class="cmtt-8"> </span><span
7897 class="cmsy-8">{</span><br class="fancyvrb" /><a
7898 id="x1-103096r48"></a><span
7899 class="cmr-6">48</span><span
7900 class="cmtt-8"> </span><span
7901 class="cmtt-8"> </span>
7902 <br class="fancyvrb" /><a
7903 id="x1-103098r49"></a><span
7904 class="cmr-6">49</span><span
7905 class="cmtt-8"> </span><span
7906 class="cmtt-8"> </span><span
7907 class="cmtt-8"> </span><span
7908 class="cmtt-8"> </span><span
7909 class="cmtt-8"> </span><span
7910 class="cmtt-8"> </span><span
7911 class="cmtt-8"> </span><span
7912 class="cmtt-8"> </span><span
7913 class="cmtt-8"> </span><span
7914 class="cmtt-8"> </span><span
7915 class="cmtt-8"> </span><span
7916 class="cmtt-8"> </span><span
7917 class="cmtt-8"> </span><span
7918 class="cmtt-8"> </span><span
7919 class="cmtt-8"> </span><span
7920 class="cmtt-8"> </span><span
7921 class="cmtt-8"> </span><span
7922 class="cmtt-8"> </span><span
7923 class="cmtt-8"> </span><span
7924 class="cmtt-8"> </span><span
7925 class="cmtt-8"> </span><span
7926 class="cmtt-8"> 24)</span><span
7927 class="cmtt-8"> if</span><span
7928 class="cmtt-8"> ([val]</span><span
7929 class="cmtt-8"> is</span><span
7930 class="cmtt-8"> odd)</span><span
7931 class="cmtt-8"> </span><span
7932 class="cmsy-8">{</span><br class="fancyvrb" /><a
7933 id="x1-103100r50"></a><span
7934 class="cmr-6">50</span><span
7935 class="cmtt-8"> </span><span
7936 class="cmtt-8"> </span><br class="fancyvrb" /><a
7937 id="x1-103102r51"></a><span
7938 class="cmr-6">51</span><span
7939 class="cmtt-8"> </span><span
7940 class="cmtt-8"> </span><span
7941 class="cmtt-8"> </span><span
7942 class="cmtt-8"> </span><span
7943 class="cmtt-8"> </span><span
7944 class="cmtt-8"> </span><span
7945 class="cmtt-8"> </span><span
7946 class="cmtt-8"> </span><span
7947 class="cmtt-8"> </span><span
7948 class="cmtt-8"> </span><span
7949 class="cmtt-8"> </span><span
7950 class="cmtt-8"> </span><span
7951 class="cmtt-8"> </span><span
7952 class="cmtt-8"> </span><span
7953 class="cmtt-8"> </span><span
7954 class="cmtt-8"> </span><span
7955 class="cmtt-8"> </span><span
7956 class="cmtt-8"> </span><span
7957 class="cmtt-8"> </span><span
7958 class="cmtt-8"> </span><span
7959 class="cmtt-8"> </span><span
7960 class="cmtt-8"> </span><span
7961 class="cmtt-8"> </span><span
7962 class="cmtt-8"> </span><span
7963 class="cmtt-8"> </span><span
7964 class="cmtt-8"> 25)</span><span
7965 class="cmtt-8"> vector</span><span
7966 class="cmtt-8"> [floor1_final_Y]</span><span
7967 class="cmtt-8"> element</span><span
7968 class="cmtt-8"> [i]</span><span
7969 class="cmtt-8"> =</span>
7970 <br class="fancyvrb" /><a
7971 id="x1-103104r52"></a><span
7972 class="cmr-6">52</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"> </span><span
7987 class="cmtt-8"> </span><span
7988 class="cmtt-8"> </span><span
7989 class="cmtt-8"> </span><span
7990 class="cmtt-8"> </span><span
7991 class="cmtt-8"> </span><span
7992 class="cmtt-8"> </span><span
7993 class="cmtt-8"> </span><span
7994 class="cmtt-8"> </span><span
7995 class="cmtt-8"> </span><span
7996 class="cmtt-8"> </span><span
7997 class="cmtt-8"> </span><span
7998 class="cmtt-8"> </span><span
7999 class="cmtt-8"> </span><span
8000 class="cmtt-8"> </span><span
8001 class="cmtt-8"> </span><span
8002 class="cmtt-8"> [predicted]</span><span
8003 class="cmtt-8"> -</span><span
8004 class="cmtt-8"> (([val]</span><span
8005 class="cmtt-8"> +</span><span
8006 class="cmtt-8"> 1)</span><span
8007 class="cmtt-8"> divided</span><span
8008 class="cmtt-8"> by</span><span
8009 class="cmtt-8"> </span><span
8010 class="cmtt-8"> 2</span><span
8011 class="cmtt-8"> using</span><span
8012 class="cmtt-8"> integer</span><span
8013 class="cmtt-8"> division)</span><br class="fancyvrb" /><a
8014 id="x1-103106r53"></a><span
8015 class="cmr-6">53</span><span
8016 class="cmtt-8"> </span><span
8017 class="cmtt-8"> </span>
8018 <br class="fancyvrb" /><a
8019 id="x1-103108r54"></a><span
8020 class="cmr-6">54</span><span
8021 class="cmtt-8"> </span><span
8022 class="cmtt-8"> </span><span
8023 class="cmtt-8"> </span><span
8024 class="cmtt-8"> </span><span
8025 class="cmtt-8"> </span><span
8026 class="cmtt-8"> </span><span
8027 class="cmtt-8"> </span><span
8028 class="cmtt-8"> </span><span
8029 class="cmtt-8"> </span><span
8030 class="cmtt-8"> </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="cmsy-8">}</span><span
8046 class="cmtt-8"> else</span><span
8047 class="cmtt-8"> [val]</span><span
8048 class="cmtt-8"> is</span><span
8049 class="cmtt-8"> even</span><span
8050 class="cmtt-8"> </span><span
8051 class="cmsy-8">{</span><br class="fancyvrb" /><a
8052 id="x1-103110r55"></a><span
8053 class="cmr-6">55</span><span
8054 class="cmtt-8"> </span><span
8055 class="cmtt-8"> </span><br class="fancyvrb" /><a
8056 id="x1-103112r56"></a><span
8057 class="cmr-6">56</span><span
8058 class="cmtt-8"> </span><span
8059 class="cmtt-8"> </span><span
8060 class="cmtt-8"> </span><span
8061 class="cmtt-8"> </span><span
8062 class="cmtt-8"> </span><span
8063 class="cmtt-8"> </span><span
8064 class="cmtt-8"> </span><span
8065 class="cmtt-8"> </span><span
8066 class="cmtt-8"> </span><span
8067 class="cmtt-8"> </span><span
8068 class="cmtt-8"> </span><span
8069 class="cmtt-8"> </span><span
8070 class="cmtt-8"> </span><span
8071 class="cmtt-8"> </span><span
8072 class="cmtt-8"> </span><span
8073 class="cmtt-8"> </span><span
8074 class="cmtt-8"> </span><span
8075 class="cmtt-8"> </span><span
8076 class="cmtt-8"> </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"> 26)</span><span
8084 class="cmtt-8"> vector</span><span
8085 class="cmtt-8"> [floor1_final_Y]</span><span
8086 class="cmtt-8"> element</span><span
8087 class="cmtt-8"> [i]</span><span
8088 class="cmtt-8"> =</span>
8089 <br class="fancyvrb" /><a
8090 id="x1-103114r57"></a><span
8091 class="cmr-6">57</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="cmtt-8"> </span><span
8102 class="cmtt-8"> </span><span
8103 class="cmtt-8"> </span><span
8104 class="cmtt-8"> </span><span
8105 class="cmtt-8"> </span><span
8106 class="cmtt-8"> </span><span
8107 class="cmtt-8"> </span><span
8108 class="cmtt-8"> </span><span
8109 class="cmtt-8"> </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"> [predicted]</span><span
8122 class="cmtt-8"> +</span><span
8123 class="cmtt-8"> ([val]</span><span
8124 class="cmtt-8"> /</span><span
8125 class="cmtt-8"> 2</span><span
8126 class="cmtt-8"> using</span><span
8127 class="cmtt-8"> integer</span><span
8128 class="cmtt-8"> division)</span><br class="fancyvrb" /><a
8129 id="x1-103116r58"></a><span
8130 class="cmr-6">58</span><span
8131 class="cmtt-8"> </span><span
8132 class="cmtt-8"> </span><br class="fancyvrb" /><a
8133 id="x1-103118r59"></a><span
8134 class="cmr-6">59</span><span
8135 class="cmtt-8"> </span><span
8136 class="cmtt-8"> </span><span
8137 class="cmtt-8"> </span><span
8138 class="cmtt-8"> </span><span
8139 class="cmtt-8"> </span><span
8140 class="cmtt-8"> </span><span
8141 class="cmtt-8"> </span><span
8142 class="cmtt-8"> </span><span
8143 class="cmtt-8"> </span><span
8144 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
8160 id="x1-103120r60"></a><span
8161 class="cmr-6">60</span><span
8162 class="cmtt-8"> </span><span
8163 class="cmtt-8"> </span>
8164 <br class="fancyvrb" /><a
8165 id="x1-103122r61"></a><span
8166 class="cmr-6">61</span><span
8167 class="cmtt-8"> </span><span
8168 class="cmtt-8"> </span><span
8169 class="cmtt-8"> </span><span
8170 class="cmtt-8"> </span><span
8171 class="cmtt-8"> </span><span
8172 class="cmtt-8"> </span><span
8173 class="cmtt-8"> </span><span
8174 class="cmtt-8"> </span><span
8175 class="cmtt-8"> </span><span
8176 class="cmtt-8"> </span><span
8177 class="cmtt-8"> </span><span
8178 class="cmtt-8"> </span><span
8179 class="cmtt-8"> </span><span
8180 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
8186 id="x1-103124r62"></a><span
8187 class="cmr-6">62</span><span
8188 class="cmtt-8"> </span><span
8189 class="cmtt-8"> </span><br class="fancyvrb" /><a
8190 id="x1-103126r63"></a><span
8191 class="cmr-6">63</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="cmsy-8">}</span><span
8205 class="cmtt-8"> else</span><span
8206 class="cmtt-8"> [val]</span><span
8207 class="cmtt-8"> is</span><span
8208 class="cmtt-8"> zero</span><span
8209 class="cmtt-8"> </span><span
8210 class="cmsy-8">{</span><br class="fancyvrb" /><a
8211 id="x1-103128r64"></a><span
8212 class="cmr-6">64</span><span
8213 class="cmtt-8"> </span><span
8214 class="cmtt-8"> </span><br class="fancyvrb" /><a
8215 id="x1-103130r65"></a><span
8216 class="cmr-6">65</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"> 27)</span><span
8231 class="cmtt-8"> vector</span><span
8232 class="cmtt-8"> [floor1_step2_flag]</span><span
8233 class="cmtt-8"> element</span><span
8234 class="cmtt-8"> [i]</span><span
8235 class="cmtt-8"> =</span><span
8236 class="cmtt-8"> unset</span>
8237 <br class="fancyvrb" /><a
8238 id="x1-103132r66"></a><span
8239 class="cmr-6">66</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"> </span><span
8245 class="cmtt-8"> </span><span
8246 class="cmtt-8"> </span><span
8247 class="cmtt-8"> </span><span
8248 class="cmtt-8"> </span><span
8249 class="cmtt-8"> </span><span
8250 class="cmtt-8"> </span><span
8251 class="cmtt-8"> </span><span
8252 class="cmtt-8"> </span><span
8253 class="cmtt-8"> 28)</span><span
8254 class="cmtt-8"> vector</span><span
8255 class="cmtt-8"> [floor1_final_Y]</span><span
8256 class="cmtt-8"> element</span><span
8257 class="cmtt-8"> [i]</span><span
8258 class="cmtt-8"> =</span><span
8259 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
8260 id="x1-103134r67"></a><span
8261 class="cmr-6">67</span><span
8262 class="cmtt-8"> </span><span
8263 class="cmtt-8"> </span><br class="fancyvrb" /><a
8264 id="x1-103136r68"></a><span
8265 class="cmr-6">68</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="cmsy-8">}</span><br class="fancyvrb" /><a
8279 id="x1-103138r69"></a><span
8280 class="cmr-6">69</span><span
8281 class="cmtt-8"> </span><span
8282 class="cmtt-8"> </span><br class="fancyvrb" /><a
8283 id="x1-103140r70"></a><span
8284 class="cmr-6">70</span><span
8285 class="cmtt-8"> </span><span
8286 class="cmtt-8"> </span><span
8287 class="cmtt-8"> </span><span
8288 class="cmtt-8"> </span><span
8289 class="cmtt-8"> </span><span
8290 class="cmtt-8"> </span><span
8291 class="cmtt-8"> </span><span
8292 class="cmsy-8">}</span><br class="fancyvrb" /><a
8293 id="x1-103142r71"></a><span
8294 class="cmr-6">71</span><span
8295 class="cmtt-8"> </span><span
8296 class="cmtt-8"> </span><br class="fancyvrb" /><a
8297 id="x1-103144r72"></a><span
8298 class="cmr-6">72</span><span
8299 class="cmtt-8"> </span><span
8300 class="cmtt-8"> </span><span
8301 class="cmtt-8"> 29)</span><span
8302 class="cmtt-8"> done</span><br class="fancyvrb" /><a
8303 id="x1-103146r73"></a><span
8304 class="cmr-6">73</span><span
8305 class="cmtt-8"> </span><span
8306 class="cmtt-8"> </span></div>
8307 </dd><dt class="description">
8309 class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
8310 class="description">
8311 <!--l. 351--><p class="noindent" >Curve synthesis generates a return vector <span
8312 class="cmtt-12">[floor] </span>of length <span
8313 class="cmtt-12">[n] </span>(where <span
8314 class="cmtt-12">[n] </span>is provided by
8315 the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
8317 class="cmtt-12">[floor1_X_list]</span>, <span
8318 class="cmtt-12">[floor1_final_Y] </span>and <span
8319 class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as
8320 [floor1_multiplier] and [floor1_values] values.
8321 <!--l. 358--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
8322 class="cmtt-12">[floor1_X_list]</span>, <span
8323 class="cmtt-12">[floor1_final_Y] </span>and
8325 class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span
8326 class="cmtt-12">[floor1_X_list]’</span>, <span
8327 class="cmtt-12">[floor1_final_Y]’</span>
8329 class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
8331 class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span
8332 class="cmtt-12">[floor1_X_list] </span>and then apply the same
8333 permutation to elements of the other two vectors so that the X, Y and step2_flag values
8335 <!--l. 368--><p class="noindent" >Then compute the final curve in one pass:
8336 <!--l. 370--><p class="noindent" >
8337 <div class="fancyvrb" id="fancyvrb32"><a
8338 id="x1-103148r1"></a><span
8339 class="cmr-6">1</span><span
8340 class="cmtt-8"> </span><span
8341 class="cmtt-8"> </span><span
8342 class="cmtt-8"> </span><span
8343 class="cmtt-8"> 1)</span><span
8344 class="cmtt-8"> [hx]</span><span
8345 class="cmtt-8"> =</span><span
8346 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
8347 id="x1-103150r2"></a><span
8348 class="cmr-6">2</span><span
8349 class="cmtt-8"> </span><span
8350 class="cmtt-8"> </span><span
8351 class="cmtt-8"> </span><span
8352 class="cmtt-8"> 2)</span><span
8353 class="cmtt-8"> [lx]</span><span
8354 class="cmtt-8"> =</span><span
8355 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
8356 id="x1-103152r3"></a><span
8357 class="cmr-6">3</span><span
8358 class="cmtt-8"> </span><span
8359 class="cmtt-8"> </span><span
8360 class="cmtt-8"> </span><span
8361 class="cmtt-8"> 3)</span><span
8362 class="cmtt-8"> [ly]</span><span
8363 class="cmtt-8"> =</span><span
8364 class="cmtt-8"> vector</span><span
8365 class="cmtt-8"> [floor1_final_Y]’</span><span
8366 class="cmtt-8"> element</span><span
8367 class="cmtt-8"> [0]</span><span
8368 class="cmtt-8"> *</span><span
8369 class="cmtt-8"> [floor1_multiplier]</span>
8370 <br class="fancyvrb" /><a
8371 id="x1-103154r4"></a><span
8372 class="cmr-6">4</span><span
8373 class="cmtt-8"> </span><span
8374 class="cmtt-8"> </span><span
8375 class="cmtt-8"> </span><span
8376 class="cmtt-8"> 4)</span><span
8377 class="cmtt-8"> iterate</span><span
8378 class="cmtt-8"> [i]</span><span
8379 class="cmtt-8"> over</span><span
8380 class="cmtt-8"> the</span><span
8381 class="cmtt-8"> range</span><span
8382 class="cmtt-8"> 1</span><span
8383 class="cmtt-8"> ...</span><span
8384 class="cmtt-8"> [floor1_values]-1</span><span
8385 class="cmtt-8"> </span><span
8386 class="cmsy-8">{</span><br class="fancyvrb" /><a
8387 id="x1-103156r5"></a><span
8388 class="cmr-6">5</span><span
8389 class="cmtt-8"> </span><span
8390 class="cmtt-8"> </span><br class="fancyvrb" /><a
8391 id="x1-103158r6"></a><span
8392 class="cmr-6">6</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"> 5)</span><span
8402 class="cmtt-8"> if</span><span
8403 class="cmtt-8"> (</span><span
8404 class="cmtt-8"> [floor1_step2_flag]’</span><span
8405 class="cmtt-8"> element</span><span
8406 class="cmtt-8"> [i]</span><span
8407 class="cmtt-8"> is</span><span
8408 class="cmtt-8"> set</span><span
8409 class="cmtt-8"> )</span><span
8410 class="cmtt-8"> </span><span
8411 class="cmsy-8">{</span><br class="fancyvrb" /><a
8412 id="x1-103160r7"></a><span
8413 class="cmr-6">7</span><span
8414 class="cmtt-8"> </span><span
8415 class="cmtt-8"> </span>
8416 <br class="fancyvrb" /><a
8417 id="x1-103162r8"></a><span
8418 class="cmr-6">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="cmtt-8"> 6)</span><span
8434 class="cmtt-8"> [hy]</span><span
8435 class="cmtt-8"> =</span><span
8436 class="cmtt-8"> [floor1_final_Y]’</span><span
8437 class="cmtt-8"> element</span><span
8438 class="cmtt-8"> [i]</span><span
8439 class="cmtt-8"> *</span><span
8440 class="cmtt-8"> [floor1_multiplier]</span><br class="fancyvrb" /><a
8441 id="x1-103164r9"></a><span
8442 class="cmr-6">9</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"> 7)</span><span
8451 class="cmtt-8"> [hx]</span><span
8452 class="cmtt-8"> =</span><span
8453 class="cmtt-8"> [floor1_X_list]’</span><span
8454 class="cmtt-8"> element</span><span
8455 class="cmtt-8"> [i]</span>
8456 <br class="fancyvrb" /><a
8457 id="x1-103166r10"></a><span
8458 class="cmr-6">10</span><span
8459 class="cmtt-8"> </span><span
8460 class="cmtt-8"> </span><span
8461 class="cmtt-8"> </span><span
8462 class="cmtt-8"> </span><span
8463 class="cmtt-8"> </span><span
8464 class="cmtt-8"> </span><span
8465 class="cmtt-8"> </span><span
8466 class="cmtt-8"> </span><span
8467 class="cmtt-8"> </span><span
8468 class="cmtt-8"> </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"> 8)</span><span
8474 class="cmtt-8"> </span><a
8475 href="#x1-1250009.2.7"><span
8476 class="cmtt-8">render_line</span></a><span
8477 class="cmtt-8">(</span><span
8478 class="cmtt-8"> [lx],</span><span
8479 class="cmtt-8"> [ly],</span><span
8480 class="cmtt-8"> [hx],</span><span
8481 class="cmtt-8"> [hy],</span><span
8482 class="cmtt-8"> [floor]</span><span
8483 class="cmtt-8"> )</span><br class="fancyvrb" /><a
8484 id="x1-103168r11"></a><span
8485 class="cmr-6">11</span><span
8486 class="cmtt-8"> </span><span
8487 class="cmtt-8"> </span><span
8488 class="cmtt-8"> </span><span
8489 class="cmtt-8"> </span><span
8490 class="cmtt-8"> </span><span
8491 class="cmtt-8"> </span><span
8492 class="cmtt-8"> </span><span
8493 class="cmtt-8"> </span><span
8494 class="cmtt-8"> </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"> 9)</span><span
8501 class="cmtt-8"> [lx]</span><span
8502 class="cmtt-8"> =</span><span
8503 class="cmtt-8"> [hx]</span><br class="fancyvrb" /><a
8504 id="x1-103170r12"></a><span
8505 class="cmr-6">12</span><span
8506 class="cmtt-8"> </span><span
8507 class="cmtt-8">  </span><span
8508 class="cmtt-8"> </span><span
8509 class="cmtt-8"> </span><span
8510 class="cmtt-8"> </span><span
8511 class="cmtt-8"> 10)</span><span
8512 class="cmtt-8"> [ly]</span><span
8513 class="cmtt-8"> =</span><span
8514 class="cmtt-8"> [hy]</span>
8515 <br class="fancyvrb" /><a
8516 id="x1-103172r13"></a><span
8517 class="cmr-6">13</span><span
8518 class="cmtt-8"> </span><span
8519 class="cmtt-8"> </span><span
8520 class="cmtt-8"> </span><span
8521 class="cmtt-8"> </span><span
8522 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
8531 id="x1-103174r14"></a><span
8532 class="cmr-6">14</span><span
8533 class="cmtt-8"> </span><span
8534 class="cmtt-8"> </span><span
8535 class="cmtt-8"> </span><span
8536 class="cmtt-8"> </span><span
8537 class="cmtt-8"> </span><span
8538 class="cmtt-8"> </span><span
8539 class="cmtt-8"> </span><span
8540 class="cmsy-8">}</span><br class="fancyvrb" /><a
8541 id="x1-103176r15"></a><span
8542 class="cmr-6">15</span><span
8543 class="cmtt-8"> </span><span
8544 class="cmtt-8"> </span><br class="fancyvrb" /><a
8545 id="x1-103178r16"></a><span
8546 class="cmr-6">16</span><span
8547 class="cmtt-8"> </span><span
8548 class="cmtt-8"> </span><span
8549 class="cmtt-8"> 11)</span><span
8550 class="cmtt-8"> if</span><span
8551 class="cmtt-8"> (</span><span
8552 class="cmtt-8"> [hx]</span><span
8553 class="cmtt-8"> is</span><span
8554 class="cmtt-8"> less</span><span
8555 class="cmtt-8"> than</span><span
8556 class="cmtt-8"> [n]</span><span
8557 class="cmtt-8"> )</span><span
8558 class="cmtt-8"> </span><span
8559 class="cmsy-8">{</span><br class="fancyvrb" /><a
8560 id="x1-103180r17"></a><span
8561 class="cmr-6">17</span><span
8562 class="cmtt-8"> </span><span
8563 class="cmtt-8"> </span><br class="fancyvrb" /><a
8564 id="x1-103182r18"></a><span
8565 class="cmr-6">18</span><span
8566 class="cmtt-8"> </span><span
8567 class="cmtt-8"> </span><span
8568 class="cmtt-8"> </span><span
8569 class="cmtt-8"> </span><span
8570 class="cmtt-8"> </span><span
8571 class="cmtt-8"> </span><span
8572 class="cmtt-8"> </span><span
8573 class="cmtt-8"> </span><span
8574 class="cmtt-8"> </span><span
8575 class="cmtt-8"> 12)</span><span
8576 class="cmtt-8"> </span><a
8577 href="#x1-1250009.2.7"><span
8578 class="cmtt-8">render_line</span></a><span
8579 class="cmtt-8">(</span><span
8580 class="cmtt-8"> [hx],</span><span
8581 class="cmtt-8"> [hy],</span><span
8582 class="cmtt-8"> [n],</span><span
8583 class="cmtt-8"> [hy],</span><span
8584 class="cmtt-8"> [floor]</span><span
8585 class="cmtt-8"> )</span>
8586 <br class="fancyvrb" /><a
8587 id="x1-103184r19"></a><span
8588 class="cmr-6">19</span><span
8589 class="cmtt-8"> </span><span
8590 class="cmtt-8"> </span><br class="fancyvrb" /><a
8591 id="x1-103186r20"></a><span
8592 class="cmr-6">20</span><span
8593 class="cmtt-8"> </span><span
8594 class="cmtt-8"> </span><span
8595 class="cmtt-8"> </span><span
8596 class="cmtt-8"> </span><span
8597 class="cmtt-8"> </span><span
8598 class="cmtt-8"> </span><span
8599 class="cmtt-8"> </span><span
8600 class="cmsy-8">}</span><br class="fancyvrb" /><a
8601 id="x1-103188r21"></a><span
8602 class="cmr-6">21</span><span
8603 class="cmtt-8"> </span><span
8604 class="cmtt-8"> </span><br class="fancyvrb" /><a
8605 id="x1-103190r22"></a><span
8606 class="cmr-6">22</span><span
8607 class="cmtt-8"> </span><span
8608 class="cmtt-8"> </span><span
8609 class="cmtt-8"> 13)</span><span
8610 class="cmtt-8"> if</span><span
8611 class="cmtt-8"> (</span><span
8612 class="cmtt-8"> [hx]</span><span
8613 class="cmtt-8"> is</span><span
8614 class="cmtt-8"> greater</span><span
8615 class="cmtt-8"> than</span><span
8616 class="cmtt-8"> [n]</span><span
8617 class="cmtt-8"> )</span><span
8618 class="cmtt-8"> </span><span
8619 class="cmsy-8">{</span><br class="fancyvrb" /><a
8620 id="x1-103192r23"></a><span
8621 class="cmr-6">23</span><span
8622 class="cmtt-8"> </span><span
8623 class="cmtt-8"> </span><br class="fancyvrb" /><a
8624 id="x1-103194r24"></a><span
8625 class="cmr-6">24</span><span
8626 class="cmtt-8"> </span><span
8627 class="cmtt-8"> </span><span
8628 class="cmtt-8"> </span><span
8629 class="cmtt-8"> </span><span
8630 class="cmtt-8"> </span><span
8631 class="cmtt-8"> </span><span
8632 class="cmtt-8"> </span><span
8633 class="cmtt-8"> </span><span
8634 class="cmtt-8"> </span><span
8635 class="cmtt-8"> </span><span
8636 class="cmtt-8"> </span><span
8637 class="cmtt-8"> </span><span
8638 class="cmtt-8"> </span><span
8639 class="cmtt-8"> 14)</span><span
8640 class="cmtt-8"> truncate</span><span
8641 class="cmtt-8"> vector</span><span
8642 class="cmtt-8"> [floor]</span><span
8643 class="cmtt-8"> to</span><span
8644 class="cmtt-8"> [n]</span><span
8645 class="cmtt-8"> elements</span>
8646 <br class="fancyvrb" /><a
8647 id="x1-103196r25"></a><span
8648 class="cmr-6">25</span><span
8649 class="cmtt-8"> </span><span
8650 class="cmtt-8"> </span><br class="fancyvrb" /><a
8651 id="x1-103198r26"></a><span
8652 class="cmr-6">26</span><span
8653 class="cmtt-8"> </span><span
8654 class="cmtt-8"> </span><span
8655 class="cmtt-8"> </span><span
8656 class="cmtt-8"> </span><span
8657 class="cmtt-8"> </span><span
8658 class="cmtt-8"> </span><span
8659 class="cmtt-8"> </span><span
8660 class="cmsy-8">}</span><br class="fancyvrb" /><a
8661 id="x1-103200r27"></a><span
8662 class="cmr-6">27</span><span
8663 class="cmtt-8"> </span><span
8664 class="cmtt-8"> </span><br class="fancyvrb" /><a
8665 id="x1-103202r28"></a><span
8666 class="cmr-6">28</span><span
8667 class="cmtt-8"> </span><span
8668 class="cmtt-8"> </span><span
8669 class="cmtt-8"> 15)</span><span
8670 class="cmtt-8"> for</span><span
8671 class="cmtt-8"> each</span><span
8672 class="cmtt-8"> scalar</span><span
8673 class="cmtt-8"> in</span><span
8674 class="cmtt-8"> vector</span><span
8675 class="cmtt-8"> [floor],</span><span
8676 class="cmtt-8"> perform</span><span
8677 class="cmtt-8"> a</span><span
8678 class="cmtt-8"> lookup</span><span
8679 class="cmtt-8"> substitution</span><span
8680 class="cmtt-8"> using</span>
8684 <br class="fancyvrb" /><a
8685 id="x1-103204r29"></a><span
8686 class="cmr-6">29</span><span
8687 class="cmtt-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"> the</span><span
8694 class="cmtt-8"> scalar</span><span
8695 class="cmtt-8"> value</span><span
8696 class="cmtt-8"> from</span><span
8697 class="cmtt-8"> [floor]</span><span
8698 class="cmtt-8"> as</span><span
8699 class="cmtt-8"> an</span><span
8700 class="cmtt-8"> offset</span><span
8701 class="cmtt-8"> into</span><span
8702 class="cmtt-8"> the</span><span
8703 class="cmtt-8"> vector</span><span
8704 class="cmtt-8"> </span><a
8705 href="#x1-12700010.1"><span
8706 class="cmtt-8">[floor1_inverse_dB_static_table]</span></a><br class="fancyvrb" /><a
8707 id="x1-103206r30"></a><span
8708 class="cmr-6">30</span><span
8709 class="cmtt-8"> </span><span
8710 class="cmtt-8"> </span><br class="fancyvrb" /><a
8711 id="x1-103208r31"></a><span
8712 class="cmr-6">31</span><span
8713 class="cmtt-8"> </span><span
8714 class="cmtt-8"> </span><span
8715 class="cmtt-8"> 16)</span><span
8716 class="cmtt-8"> done</span><br class="fancyvrb" /><a
8717 id="x1-103210r32"></a><span
8718 class="cmr-6">32</span><span
8719 class="cmtt-8"> </span><span
8720 class="cmtt-8"> </span></div>
8725 <h3 class="sectionHead"><span class="titlemark">8. </span> <a
8726 id="x1-1040008"></a>Residue setup and decode</h3>
8727 <!--l. 6--><p class="noindent" >
8728 <h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a
8729 id="x1-1050008.1"></a>Overview</h4>
8730 <!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
8731 after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
8732 may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel
8733 coupling. The exact semantic content of the vector does not matter to the residue
8735 <!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
8736 bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
8737 different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
8739 <!--l. 23--><p class="noindent" >
8740 <h4 class="subsectionHead"><span class="titlemark">8.2. </span> <a
8741 id="x1-1060008.2"></a>Residue format</h4>
8742 <!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
8743 chunk, encodes the chunk classifications and finally encodes the chunks themselves
8744 using the the specific VQ arrangement defined for each selected classification. The
8745 exact interleaving and partitioning vary by residue encoding number, however the
8746 high-level process used to classify and encode the residue vector is the same in all three
8748 <!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
8749 the moment exactly how a partition is encoded and simply trusting that it is, is as
8751 <ul class="itemize1">
8752 <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
8753 specified. If we have a vector size of <span
8754 class="cmti-12">n</span>, a partition size <span
8755 class="cmti-12">residue</span><span
8756 class="cmti-12">_partition</span><span
8757 class="cmti-12">_size</span>,
8758 and a total of <span
8759 class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded
8764 class="cmti-12">n</span>/<span
8765 class="cmti-12">residue</span><span
8766 class="cmti-12">_partition</span><span
8767 class="cmti-12">_size</span>*<span
8768 class="cmti-12">ch</span>. It is important to note that the integer division
8769 truncates. In the below example, we assume an example <span
8770 class="cmti-12">residue</span><span
8771 class="cmti-12">_partition</span><span
8772 class="cmti-12">_size </span>of 8.
8774 <li class="itemize">Each partition in each vector has a classification number that specifies which of
8775 multiple configured VQ codebook setups are used to decode that partition. The
8776 classification numbers of each partition can be thought of as forming a vector in
8777 their own right, as in the illustration below. Just as the residue vectors are coded
8778 in grouped partitions to increase encoding efficiency, the classification vector is also
8779 partitioned into chunks. The integer elements of each scalar in a classification chunk
8780 are built into a single scalar that represents the classification numbers in that chunk.
8781 In the below example, the classification codeword encodes two classification numbers.
8783 <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
8784 the residue vector, but more often efficient codebook design dictates that each vector
8785 is encoded as the additive sum of several passes through the residue vector using
8786 more than one VQ codebook. Thus, each residue value potentially accumulates values
8787 from multiple decode passes. The classification value associated with a partition is
8788 the same in each pass, thus the classification codeword is coded only in the first pass.
8792 <!--l. 70--><p class="noindent" >
8794 <!--l. 71--><p class="noindent" ><img
8795 src="residue-pack.png" alt="PIC"
8797 <br /> <div class="caption"
8798 ><span class="id">Figure 11: </span><span
8799 class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10600111 -->
8801 <!--l. 77--><p class="noindent" >
8802 <h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a
8803 id="x1-1070008.3"></a>residue 0</h4>
8804 <!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
8805 partition encoding (visually treated as a black box–or cyan box or brown box–in the above
8807 <!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
8811 encode a partition in a specific pass. The dimension of the codebook need not be the same in
8812 multiple passes, however the partition size must be an even multiple of the codebook
8814 <!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
8815 codebook sizes of 8, 4, 2 and 1:
8816 <!--l. 92--><p class="noindent" >
8817 <div class="fancyvrb" id="fancyvrb33"><a
8818 id="x1-107002r1"></a><span
8819 class="cmr-6">1</span><span
8820 class="cmtt-8"> </span><span
8821 class="cmtt-8"> </span><br class="fancyvrb" /><a
8822 id="x1-107004r2"></a><span
8823 class="cmr-6">2</span><span
8824 class="cmtt-8"> </span><span
8825 class="cmtt-8"> </span><span
8826 class="cmtt-8"> </span><span
8827 class="cmtt-8"> </span><span
8828 class="cmtt-8"> </span><span
8829 class="cmtt-8"> </span><span
8830 class="cmtt-8"> </span><span
8831 class="cmtt-8"> </span><span
8832 class="cmtt-8"> </span><span
8833 class="cmtt-8"> </span><span
8834 class="cmtt-8"> </span><span
8835 class="cmtt-8"> </span><span
8836 class="cmtt-8"> </span><span
8837 class="cmtt-8"> original</span><span
8838 class="cmtt-8"> residue</span><span
8839 class="cmtt-8"> vector:</span><span
8840 class="cmtt-8"> [</span><span
8841 class="cmtt-8"> 0</span><span
8842 class="cmtt-8"> 1</span><span
8843 class="cmtt-8"> 2</span><span
8844 class="cmtt-8"> 3</span><span
8845 class="cmtt-8"> 4</span><span
8846 class="cmtt-8"> 5</span><span
8847 class="cmtt-8"> 6</span><span
8848 class="cmtt-8"> 7</span><span
8849 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8850 id="x1-107006r3"></a><span
8851 class="cmr-6">3</span><span
8852 class="cmtt-8"> </span><span
8853 class="cmtt-8"> </span><br class="fancyvrb" /><a
8854 id="x1-107008r4"></a><span
8855 class="cmr-6">4</span><span
8856 class="cmtt-8"> </span><span
8857 class="cmtt-8"> codebook</span><span
8858 class="cmtt-8"> dimensions</span><span
8859 class="cmtt-8"> =</span><span
8860 class="cmtt-8"> 8</span><span
8861 class="cmtt-8"> </span><span
8862 class="cmtt-8"> encoded</span><span
8863 class="cmtt-8"> as:</span><span
8864 class="cmtt-8"> [</span><span
8865 class="cmtt-8"> 0</span><span
8866 class="cmtt-8"> 1</span><span
8867 class="cmtt-8"> 2</span><span
8868 class="cmtt-8"> 3</span><span
8869 class="cmtt-8"> 4</span><span
8870 class="cmtt-8"> 5</span><span
8871 class="cmtt-8"> 6</span><span
8872 class="cmtt-8"> 7</span><span
8873 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8874 id="x1-107010r5"></a><span
8875 class="cmr-6">5</span><span
8876 class="cmtt-8"> </span><span
8877 class="cmtt-8"> </span>
8878 <br class="fancyvrb" /><a
8879 id="x1-107012r6"></a><span
8880 class="cmr-6">6</span><span
8881 class="cmtt-8"> </span><span
8882 class="cmtt-8"> codebook</span><span
8883 class="cmtt-8"> dimensions</span><span
8884 class="cmtt-8"> =</span><span
8885 class="cmtt-8"> 4</span><span
8886 class="cmtt-8"> </span><span
8887 class="cmtt-8"> encoded</span><span
8888 class="cmtt-8"> as:</span><span
8889 class="cmtt-8"> [</span><span
8890 class="cmtt-8"> 0</span><span
8891 class="cmtt-8"> 2</span><span
8892 class="cmtt-8"> 4</span><span
8893 class="cmtt-8"> 6</span><span
8894 class="cmtt-8"> ],</span><span
8895 class="cmtt-8"> [</span><span
8896 class="cmtt-8"> 1</span><span
8897 class="cmtt-8"> 3</span><span
8898 class="cmtt-8"> 5</span><span
8899 class="cmtt-8"> 7</span><span
8900 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8901 id="x1-107014r7"></a><span
8902 class="cmr-6">7</span><span
8903 class="cmtt-8"> </span><span
8904 class="cmtt-8"> </span><br class="fancyvrb" /><a
8905 id="x1-107016r8"></a><span
8906 class="cmr-6">8</span><span
8907 class="cmtt-8"> </span><span
8908 class="cmtt-8"> codebook</span><span
8909 class="cmtt-8"> dimensions</span><span
8910 class="cmtt-8"> =</span><span
8911 class="cmtt-8"> 2</span><span
8912 class="cmtt-8"> </span><span
8913 class="cmtt-8"> encoded</span><span
8914 class="cmtt-8"> as:</span><span
8915 class="cmtt-8"> [</span><span
8916 class="cmtt-8"> 0</span><span
8917 class="cmtt-8"> 4</span><span
8918 class="cmtt-8"> ],</span><span
8919 class="cmtt-8"> [</span><span
8920 class="cmtt-8"> 1</span><span
8921 class="cmtt-8"> 5</span><span
8922 class="cmtt-8"> ],</span><span
8923 class="cmtt-8"> [</span><span
8924 class="cmtt-8"> 2</span><span
8925 class="cmtt-8"> 6</span><span
8926 class="cmtt-8"> ],</span><span
8927 class="cmtt-8"> [</span><span
8928 class="cmtt-8"> 3</span><span
8929 class="cmtt-8"> 7</span><span
8930 class="cmtt-8"> ]</span>
8931 <br class="fancyvrb" /><a
8932 id="x1-107018r9"></a><span
8933 class="cmr-6">9</span><span
8934 class="cmtt-8"> </span><span
8935 class="cmtt-8"> </span><br class="fancyvrb" /><a
8936 id="x1-107020r10"></a><span
8937 class="cmr-6">10</span><span
8938 class="cmtt-8"> </span><span
8939 class="cmtt-8"> codebook</span><span
8940 class="cmtt-8"> dimensions</span><span
8941 class="cmtt-8"> =</span><span
8942 class="cmtt-8"> 1</span><span
8943 class="cmtt-8"> </span><span
8944 class="cmtt-8"> encoded</span><span
8945 class="cmtt-8"> as:</span><span
8946 class="cmtt-8"> [</span><span
8947 class="cmtt-8"> 0</span><span
8948 class="cmtt-8"> ],</span><span
8949 class="cmtt-8"> [</span><span
8950 class="cmtt-8"> 1</span><span
8951 class="cmtt-8"> ],</span><span
8952 class="cmtt-8"> [</span><span
8953 class="cmtt-8"> 2</span><span
8954 class="cmtt-8"> ],</span><span
8955 class="cmtt-8"> [</span><span
8956 class="cmtt-8"> 3</span><span
8957 class="cmtt-8"> ],</span><span
8958 class="cmtt-8"> [</span><span
8959 class="cmtt-8"> 4</span><span
8960 class="cmtt-8"> ],</span><span
8961 class="cmtt-8"> [</span><span
8962 class="cmtt-8"> 5</span><span
8963 class="cmtt-8"> ],</span><span
8964 class="cmtt-8"> [</span><span
8965 class="cmtt-8"> 6</span><span
8966 class="cmtt-8"> ],</span><span
8967 class="cmtt-8"> [</span><span
8968 class="cmtt-8"> 7</span><span
8969 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8970 id="x1-107022r11"></a><span
8971 class="cmr-6">11</span><span
8972 class="cmtt-8"> </span><span
8973 class="cmtt-8"> </span></div>
8974 <!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
8975 restricted to a power of two.
8976 <!--l. 111--><p class="noindent" >
8977 <h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a
8978 id="x1-1080008.4"></a>residue 1</h4>
8979 <!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As
8980 with residue 0, however, partition length must be an integer multiple of the codebook dimension,
8981 although dimension may vary from pass to pass.
8982 <!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
8983 codebook sizes of 8, 4, 2 and 1:
8984 <!--l. 121--><p class="noindent" >
8985 <div class="fancyvrb" id="fancyvrb34"><a
8986 id="x1-108002r1"></a><span
8987 class="cmr-6">1</span><span
8988 class="cmtt-8"> </span><span
8989 class="cmtt-8"> </span><br class="fancyvrb" /><a
8990 id="x1-108004r2"></a><span
8991 class="cmr-6">2</span><span
8992 class="cmtt-8"> </span><span
8993 class="cmtt-8"> </span><span
8994 class="cmtt-8"> </span><span
8995 class="cmtt-8"> </span><span
8996 class="cmtt-8"> </span><span
8997 class="cmtt-8"> </span><span
8998 class="cmtt-8"> </span><span
8999 class="cmtt-8"> </span><span
9000 class="cmtt-8"> </span><span
9001 class="cmtt-8"> </span><span
9002 class="cmtt-8"> </span><span
9003 class="cmtt-8"> </span><span
9004 class="cmtt-8"> </span><span
9005 class="cmtt-8"> original</span><span
9006 class="cmtt-8"> residue</span><span
9007 class="cmtt-8"> vector:</span><span
9008 class="cmtt-8"> [</span><span
9009 class="cmtt-8"> 0</span><span
9010 class="cmtt-8"> 1</span><span
9011 class="cmtt-8"> 2</span><span
9012 class="cmtt-8"> 3</span><span
9013 class="cmtt-8"> 4</span><span
9014 class="cmtt-8"> 5</span><span
9015 class="cmtt-8"> 6</span><span
9016 class="cmtt-8"> 7</span><span
9017 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
9018 id="x1-108006r3"></a><span
9019 class="cmr-6">3</span><span
9020 class="cmtt-8"> </span><span
9021 class="cmtt-8"> </span><br class="fancyvrb" /><a
9022 id="x1-108008r4"></a><span
9023 class="cmr-6">4</span><span
9024 class="cmtt-8"> </span><span
9025 class="cmtt-8"> codebook</span><span
9026 class="cmtt-8"> dimensions</span><span
9027 class="cmtt-8"> =</span><span
9028 class="cmtt-8"> 8</span><span
9029 class="cmtt-8"> </span><span
9030 class="cmtt-8"> encoded</span><span
9031 class="cmtt-8"> as:</span><span
9032 class="cmtt-8"> [</span><span
9033 class="cmtt-8"> 0</span><span
9034 class="cmtt-8"> 1</span><span
9035 class="cmtt-8"> 2</span><span
9036 class="cmtt-8"> 3</span><span
9037 class="cmtt-8"> 4</span><span
9038 class="cmtt-8"> 5</span><span
9039 class="cmtt-8"> 6</span><span
9040 class="cmtt-8"> 7</span><span
9041 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
9042 id="x1-108010r5"></a><span
9043 class="cmr-6">5</span><span
9044 class="cmtt-8"> </span><span
9045 class="cmtt-8"> </span>
9046 <br class="fancyvrb" /><a
9047 id="x1-108012r6"></a><span
9048 class="cmr-6">6</span><span
9049 class="cmtt-8"> </span><span
9050 class="cmtt-8"> codebook</span><span
9051 class="cmtt-8"> dimensions</span><span
9052 class="cmtt-8"> =</span><span
9053 class="cmtt-8"> 4</span><span
9054 class="cmtt-8"> </span><span
9055 class="cmtt-8"> encoded</span><span
9056 class="cmtt-8"> as:</span><span
9057 class="cmtt-8"> [</span><span
9058 class="cmtt-8"> 0</span><span
9059 class="cmtt-8"> 1</span><span
9060 class="cmtt-8"> 2</span><span
9061 class="cmtt-8"> 3</span><span
9062 class="cmtt-8"> ],</span><span
9063 class="cmtt-8"> [</span><span
9064 class="cmtt-8"> 4</span><span
9065 class="cmtt-8"> 5</span><span
9066 class="cmtt-8"> 6</span><span
9067 class="cmtt-8"> 7</span><span
9068 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
9069 id="x1-108014r7"></a><span
9070 class="cmr-6">7</span><span
9071 class="cmtt-8"> </span><span
9072 class="cmtt-8"> </span><br class="fancyvrb" /><a
9073 id="x1-108016r8"></a><span
9074 class="cmr-6">8</span><span
9075 class="cmtt-8"> </span><span
9076 class="cmtt-8"> codebook</span><span
9077 class="cmtt-8"> dimensions</span><span
9078 class="cmtt-8"> =</span><span
9079 class="cmtt-8"> 2</span><span
9080 class="cmtt-8"> </span><span
9081 class="cmtt-8"> encoded</span><span
9082 class="cmtt-8"> as:</span><span
9083 class="cmtt-8"> [</span><span
9084 class="cmtt-8"> 0</span><span
9085 class="cmtt-8"> 1</span><span
9086 class="cmtt-8"> ],</span><span
9087 class="cmtt-8"> [</span><span
9088 class="cmtt-8"> 2</span><span
9089 class="cmtt-8"> 3</span><span
9090 class="cmtt-8"> ],</span><span
9091 class="cmtt-8"> [</span><span
9092 class="cmtt-8"> 4</span><span
9093 class="cmtt-8"> 5</span><span
9094 class="cmtt-8"> ],</span><span
9095 class="cmtt-8"> [</span><span
9096 class="cmtt-8"> 6</span><span
9097 class="cmtt-8"> 7</span><span
9098 class="cmtt-8"> ]</span>
9099 <br class="fancyvrb" /><a
9100 id="x1-108018r9"></a><span
9101 class="cmr-6">9</span><span
9102 class="cmtt-8"> </span><span
9103 class="cmtt-8"> </span><br class="fancyvrb" /><a
9104 id="x1-108020r10"></a><span
9105 class="cmr-6">10</span><span
9106 class="cmtt-8"> </span><span
9107 class="cmtt-8"> codebook</span><span
9108 class="cmtt-8"> dimensions</span><span
9109 class="cmtt-8"> =</span><span
9110 class="cmtt-8"> 1</span><span
9111 class="cmtt-8"> </span><span
9112 class="cmtt-8"> encoded</span><span
9113 class="cmtt-8"> as:</span><span
9114 class="cmtt-8"> [</span><span
9115 class="cmtt-8"> 0</span><span
9116 class="cmtt-8"> ],</span><span
9117 class="cmtt-8"> [</span><span
9118 class="cmtt-8"> 1</span><span
9119 class="cmtt-8"> ],</span><span
9120 class="cmtt-8"> [</span><span
9121 class="cmtt-8"> 2</span><span
9122 class="cmtt-8"> ],</span><span
9123 class="cmtt-8"> [</span><span
9124 class="cmtt-8"> 3</span><span
9125 class="cmtt-8"> ],</span><span
9126 class="cmtt-8"> [</span><span
9127 class="cmtt-8"> 4</span><span
9128 class="cmtt-8"> ],</span><span
9129 class="cmtt-8"> [</span><span
9130 class="cmtt-8"> 5</span><span
9131 class="cmtt-8"> ],</span><span
9132 class="cmtt-8"> [</span><span
9133 class="cmtt-8"> 6</span><span
9134 class="cmtt-8"> ],</span><span
9135 class="cmtt-8"> [</span><span
9136 class="cmtt-8"> 7</span><span
9137 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
9138 id="x1-108022r11"></a><span
9139 class="cmr-6">11</span><span
9140 class="cmtt-8"> </span><span
9141 class="cmtt-8"> </span></div>
9142 <!--l. 137--><p class="noindent" >
9143 <h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a
9144 id="x1-1090008.5"></a>residue 2</h4>
9145 <!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
9146 passed-in vectors as in residue type 1, the <span
9147 class="cmti-12">ch </span>passed in vectors of length <span
9148 class="cmti-12">n </span>are first interleaved
9149 and flattened into a single vector of length <span
9150 class="cmti-12">ch</span>*<span
9151 class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
9152 is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
9153 residue type 1 and type 2 are equivalent.
9159 <!--l. 147--><p class="noindent" >
9161 <!--l. 148--><p class="noindent" ><img
9162 src="residue2.png" alt="PIC"
9164 <br /> <div class="caption"
9165 ><span class="id">Figure 12: </span><span
9166 class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10900112 -->
9168 <!--l. 153--><p class="noindent" >
9169 <h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a
9170 id="x1-1100008.6"></a>Residue decode</h4>
9171 <!--l. 155--><p class="noindent" >
9172 <h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a
9173 id="x1-1110008.6.1"></a>header decode</h5>
9174 <!--l. 157--><p class="noindent" >Header decode for all three residue types is identical.
9175 <div class="fancyvrb" id="fancyvrb35"><a
9176 id="x1-111002r1"></a><span
9177 class="cmr-6">1</span><span
9178 class="cmtt-8"> </span><span
9179 class="cmtt-8"> </span><span
9180 class="cmtt-8"> </span><span
9181 class="cmtt-8"> 1)</span><span
9182 class="cmtt-8"> [residue\_begin]</span><span
9183 class="cmtt-8"> =</span><span
9184 class="cmtt-8"> read</span><span
9185 class="cmtt-8"> 24</span><span
9186 class="cmtt-8"> bits</span><span
9187 class="cmtt-8"> as</span><span
9188 class="cmtt-8"> unsigned</span><span
9189 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
9190 id="x1-111004r2"></a><span
9191 class="cmr-6">2</span><span
9192 class="cmtt-8"> </span><span
9193 class="cmtt-8"> </span><span
9194 class="cmtt-8"> </span><span
9195 class="cmtt-8"> 2)</span><span
9196 class="cmtt-8"> [residue\_end]</span><span
9197 class="cmtt-8"> =</span><span
9198 class="cmtt-8"> read</span><span
9199 class="cmtt-8"> 24</span><span
9200 class="cmtt-8"> bits</span><span
9201 class="cmtt-8"> as</span><span
9202 class="cmtt-8"> unsigned</span><span
9203 class="cmtt-8"> integer</span>
9204 <br class="fancyvrb" /><a
9205 id="x1-111006r3"></a><span
9206 class="cmr-6">3</span><span
9207 class="cmtt-8"> </span><span
9208 class="cmtt-8"> </span><span
9209 class="cmtt-8"> </span><span
9210 class="cmtt-8"> 3)</span><span
9211 class="cmtt-8"> [residue\_partition\_size]</span><span
9212 class="cmtt-8"> =</span><span
9213 class="cmtt-8"> read</span><span
9214 class="cmtt-8"> 24</span><span
9215 class="cmtt-8"> bits</span><span
9216 class="cmtt-8"> as</span><span
9217 class="cmtt-8"> unsigned</span><span
9218 class="cmtt-8"> integer</span><span
9219 class="cmtt-8"> and</span><span
9220 class="cmtt-8"> add</span><span
9221 class="cmtt-8"> one</span>
9222 <br class="fancyvrb" /><a
9223 id="x1-111008r4"></a><span
9224 class="cmr-6">4</span><span
9225 class="cmtt-8"> </span><span
9226 class="cmtt-8"> </span><span
9227 class="cmtt-8"> </span><span
9228 class="cmtt-8"> 4)</span><span
9229 class="cmtt-8"> [residue\_classifications]</span><span
9230 class="cmtt-8"> =</span><span
9231 class="cmtt-8"> read</span><span
9232 class="cmtt-8"> 6</span><span
9233 class="cmtt-8"> bits</span><span
9234 class="cmtt-8"> as</span><span
9235 class="cmtt-8"> unsigned</span><span
9236 class="cmtt-8"> integer</span><span
9237 class="cmtt-8"> and</span><span
9238 class="cmtt-8"> add</span><span
9239 class="cmtt-8"> one</span><br class="fancyvrb" /><a
9240 id="x1-111010r5"></a><span
9241 class="cmr-6">5</span><span
9242 class="cmtt-8"> </span><span
9243 class="cmtt-8"> </span><span
9244 class="cmtt-8"> </span><span
9245 class="cmtt-8"> 5)</span><span
9246 class="cmtt-8"> [residue\_classbook]</span><span
9247 class="cmtt-8"> =</span><span
9248 class="cmtt-8"> read</span><span
9249 class="cmtt-8"> 8</span><span
9250 class="cmtt-8"> bits</span><span
9251 class="cmtt-8"> as</span><span
9252 class="cmtt-8"> unsigned</span><span
9253 class="cmtt-8"> integer</span></div>
9254 <!--l. 166--><p class="noindent" ><span
9255 class="cmtt-12">[residue_begin] </span>and <span
9256 class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is
9257 actually coded; it implements akin to a bandpass where, for coding purposes, the vector
9258 effectively begins at element <span
9259 class="cmtt-12">[residue_begin] </span>and ends at <span
9260 class="cmtt-12">[residue_end]</span>. Preceding and
9261 following values in the unpacked vectors are zeroed. Note that for residue type 2, these
9262 values as well as <span
9263 class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the
9264 individual vectors before interleave. <span
9265 class="cmtt-12">[residue_partition_size] </span>is as explained above,
9267 class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can
9269 class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification
9270 codewords. The number of dimensions in book <span
9271 class="cmtt-12">[residue_classbook] </span>determines how
9272 many classification values are grouped into a single classification codeword. Note that
9273 the number of entries and dimensions in book <span
9274 class="cmtt-12">[residue_classbook]</span>, along with
9276 class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification
9278 class="cmtt-12">[residue_classifications]</span>ˆ<span
9279 class="cmtt-12">[residue_classbook]</span>.dimensions exceeds
9281 class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
9285 <!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
9287 <!--l. 193--><p class="noindent" >
9288 <div class="fancyvrb" id="fancyvrb36"><a
9289 id="x1-111012r1"></a><span
9290 class="cmr-6">1</span><span
9291 class="cmtt-8"> </span><span
9292 class="cmtt-8"> </span><span
9293 class="cmtt-8"> </span><span
9294 class="cmtt-8"> 1)</span><span
9295 class="cmtt-8"> iterate</span><span
9296 class="cmtt-8"> [i]</span><span
9297 class="cmtt-8"> over</span><span
9298 class="cmtt-8"> the</span><span
9299 class="cmtt-8"> range</span><span
9300 class="cmtt-8"> 0</span><span
9301 class="cmtt-8"> ...</span><span
9302 class="cmtt-8"> [residue\_classifications]-1</span><span
9303 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9304 id="x1-111014r2"></a><span
9305 class="cmr-6">2</span><span
9306 class="cmtt-8"> </span><span
9307 class="cmtt-8"> </span><br class="fancyvrb" /><a
9308 id="x1-111016r3"></a><span
9309 class="cmr-6">3</span><span
9310 class="cmtt-8"> </span><span
9311 class="cmtt-8"> </span><span
9312 class="cmtt-8"> </span><span
9313 class="cmtt-8"> </span><span
9314 class="cmtt-8"> </span><span
9315 class="cmtt-8"> </span><span
9316 class="cmtt-8"> </span><span
9317 class="cmtt-8"> </span><span
9318 class="cmtt-8"> 2)</span><span
9319 class="cmtt-8"> [high\_bits]</span><span
9320 class="cmtt-8"> =</span><span
9321 class="cmtt-8"> 0</span>
9322 <br class="fancyvrb" /><a
9323 id="x1-111018r4"></a><span
9324 class="cmr-6">4</span><span
9325 class="cmtt-8"> </span><span
9326 class="cmtt-8"> </span><span
9327 class="cmtt-8"> </span><span
9328 class="cmtt-8"> </span><span
9329 class="cmtt-8"> </span><span
9330 class="cmtt-8"> </span><span
9331 class="cmtt-8"> </span><span
9332 class="cmtt-8"> </span><span
9333 class="cmtt-8"> 3)</span><span
9334 class="cmtt-8"> [low\_bits]</span><span
9335 class="cmtt-8"> =</span><span
9336 class="cmtt-8"> read</span><span
9337 class="cmtt-8"> 3</span><span
9338 class="cmtt-8"> bits</span><span
9339 class="cmtt-8"> as</span><span
9340 class="cmtt-8"> unsigned</span><span
9341 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
9342 id="x1-111020r5"></a><span
9343 class="cmr-6">5</span><span
9344 class="cmtt-8"> </span><span
9345 class="cmtt-8"> </span><span
9346 class="cmtt-8"> </span><span
9347 class="cmtt-8"> </span><span
9348 class="cmtt-8"> </span><span
9349 class="cmtt-8"> </span><span
9350 class="cmtt-8"> </span><span
9351 class="cmtt-8"> </span><span
9352 class="cmtt-8"> 4)</span><span
9353 class="cmtt-8"> [bitflag]</span><span
9354 class="cmtt-8"> =</span><span
9355 class="cmtt-8"> read</span><span
9356 class="cmtt-8"> one</span><span
9357 class="cmtt-8"> bit</span><span
9358 class="cmtt-8"> as</span><span
9359 class="cmtt-8"> boolean</span>
9360 <br class="fancyvrb" /><a
9361 id="x1-111022r6"></a><span
9362 class="cmr-6">6</span><span
9363 class="cmtt-8"> </span><span
9364 class="cmtt-8"> </span><span
9365 class="cmtt-8"> </span><span
9366 class="cmtt-8"> </span><span
9367 class="cmtt-8"> </span><span
9368 class="cmtt-8"> </span><span
9369 class="cmtt-8"> </span><span
9370 class="cmtt-8"> </span><span
9371 class="cmtt-8"> 5)</span><span
9372 class="cmtt-8"> if</span><span
9373 class="cmtt-8"> (</span><span
9374 class="cmtt-8"> [bitflag]</span><span
9375 class="cmtt-8"> is</span><span
9376 class="cmtt-8"> set</span><span
9377 class="cmtt-8"> )</span><span
9378 class="cmtt-8"> then</span><span
9379 class="cmtt-8"> [high\_bits]</span><span
9380 class="cmtt-8"> =</span><span
9381 class="cmtt-8"> read</span><span
9382 class="cmtt-8"> five</span><span
9383 class="cmtt-8"> bits</span><span
9384 class="cmtt-8"> as</span><span
9385 class="cmtt-8"> unsigned</span><span
9386 class="cmtt-8"> integer</span>
9387 <br class="fancyvrb" /><a
9388 id="x1-111024r7"></a><span
9389 class="cmr-6">7</span><span
9390 class="cmtt-8"> </span><span
9391 class="cmtt-8"> </span><span
9392 class="cmtt-8"> </span><span
9393 class="cmtt-8"> </span><span
9394 class="cmtt-8"> </span><span
9395 class="cmtt-8"> </span><span
9396 class="cmtt-8"> </span><span
9397 class="cmtt-8"> </span><span
9398 class="cmtt-8"> 6)</span><span
9399 class="cmtt-8"> vector</span><span
9400 class="cmtt-8"> [residue\_cascade]</span><span
9401 class="cmtt-8"> element</span><span
9402 class="cmtt-8"> [i]</span><span
9403 class="cmtt-8"> =</span><span
9404 class="cmtt-8"> [high\_bits]</span><span
9405 class="cmtt-8"> *</span><span
9406 class="cmtt-8"> 8</span><span
9407 class="cmtt-8"> +</span><span
9408 class="cmtt-8"> [low\_bits]</span><br class="fancyvrb" /><a
9409 id="x1-111026r8"></a><span
9410 class="cmr-6">8</span><span
9411 class="cmtt-8"> </span><span
9412 class="cmtt-8"> </span><span
9413 class="cmtt-8"> </span><span
9414 class="cmtt-8"> </span><span
9415 class="cmtt-8"> </span><span
9416 class="cmtt-8"> </span><span
9417 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9418 id="x1-111028r9"></a><span
9419 class="cmr-6">9</span><span
9420 class="cmtt-8"> </span><span
9421 class="cmtt-8"> </span><span
9422 class="cmtt-8"> </span><span
9423 class="cmtt-8"> 7)</span><span
9424 class="cmtt-8"> done</span></div>
9425 <!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
9426 bitmap. We loop over the possible codebook classifications and the maximum possible number of
9427 encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
9429 <!--l. 211--><p class="noindent" >
9430 <div class="fancyvrb" id="fancyvrb37"><a
9431 id="x1-111030r1"></a><span
9432 class="cmr-6">1</span><span
9433 class="cmtt-8"> </span><span
9434 class="cmtt-8"> </span><span
9435 class="cmtt-8"> </span><span
9436 class="cmtt-8"> 1)</span><span
9437 class="cmtt-8"> iterate</span><span
9438 class="cmtt-8"> [i]</span><span
9439 class="cmtt-8"> over</span><span
9440 class="cmtt-8"> the</span><span
9441 class="cmtt-8"> range</span><span
9442 class="cmtt-8"> 0</span><span
9443 class="cmtt-8"> ...</span><span
9444 class="cmtt-8"> [residue\_classifications]-1</span><span
9445 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9446 id="x1-111032r2"></a><span
9447 class="cmr-6">2</span><span
9448 class="cmtt-8"> </span><span
9449 class="cmtt-8"> </span><br class="fancyvrb" /><a
9450 id="x1-111034r3"></a><span
9451 class="cmr-6">3</span><span
9452 class="cmtt-8"> </span><span
9453 class="cmtt-8"> </span><span
9454 class="cmtt-8"> </span><span
9455 class="cmtt-8"> </span><span
9456 class="cmtt-8"> </span><span
9457 class="cmtt-8"> </span><span
9458 class="cmtt-8"> </span><span
9459 class="cmtt-8"> </span><span
9460 class="cmtt-8"> 2)</span><span
9461 class="cmtt-8"> iterate</span><span
9462 class="cmtt-8"> [j]</span><span
9463 class="cmtt-8"> over</span><span
9464 class="cmtt-8"> the</span><span
9465 class="cmtt-8"> range</span><span
9466 class="cmtt-8"> 0</span><span
9467 class="cmtt-8"> ...</span><span
9468 class="cmtt-8"> 7</span><span
9469 class="cmtt-8"> {</span>
9470 <br class="fancyvrb" /><a
9471 id="x1-111036r4"></a><span
9472 class="cmr-6">4</span><span
9473 class="cmtt-8"> </span><span
9474 class="cmtt-8"> </span><br class="fancyvrb" /><a
9475 id="x1-111038r5"></a><span
9476 class="cmr-6">5</span><span
9477 class="cmtt-8"> </span><span
9478 class="cmtt-8"> </span><span
9479 class="cmtt-8"> </span><span
9480 class="cmtt-8"> </span><span
9481 class="cmtt-8"> </span><span
9482 class="cmtt-8"> </span><span
9483 class="cmtt-8"> </span><span
9484 class="cmtt-8"> </span><span
9485 class="cmtt-8"> </span><span
9486 class="cmtt-8"> </span><span
9487 class="cmtt-8"> </span><span
9488 class="cmtt-8"> </span><span
9489 class="cmtt-8"> </span><span
9490 class="cmtt-8"> 3)</span><span
9491 class="cmtt-8"> if</span><span
9492 class="cmtt-8"> (</span><span
9493 class="cmtt-8"> vector</span><span
9494 class="cmtt-8"> [residue\_cascade]</span><span
9495 class="cmtt-8"> element</span><span
9496 class="cmtt-8"> [i]</span><span
9497 class="cmtt-8"> bit</span><span
9498 class="cmtt-8"> [j]</span><span
9499 class="cmtt-8"> is</span><span
9500 class="cmtt-8"> set</span><span
9501 class="cmtt-8"> )</span><span
9502 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9503 id="x1-111040r6"></a><span
9504 class="cmr-6">6</span><span
9505 class="cmtt-8"> </span><span
9506 class="cmtt-8"> </span>
9507 <br class="fancyvrb" /><a
9508 id="x1-111042r7"></a><span
9509 class="cmr-6">7</span><span
9510 class="cmtt-8"> </span><span
9511 class="cmtt-8"> </span><span
9512 class="cmtt-8"> </span><span
9513 class="cmtt-8"> </span><span
9514 class="cmtt-8"> </span><span
9515 class="cmtt-8"> </span><span
9516 class="cmtt-8"> </span><span
9517 class="cmtt-8"> </span><span
9518 class="cmtt-8"> </span><span
9519 class="cmtt-8"> </span><span
9520 class="cmtt-8"> </span><span
9521 class="cmtt-8"> </span><span
9522 class="cmtt-8"> </span><span
9523 class="cmtt-8"> </span><span
9524 class="cmtt-8"> </span><span
9525 class="cmtt-8"> </span><span
9526 class="cmtt-8"> </span><span
9527 class="cmtt-8"> </span><span
9528 class="cmtt-8"> 4)</span><span
9529 class="cmtt-8"> array</span><span
9530 class="cmtt-8"> [residue\_books]</span><span
9531 class="cmtt-8"> element</span><span
9532 class="cmtt-8"> [i][j]</span><span
9533 class="cmtt-8"> =</span><span
9534 class="cmtt-8"> read</span><span
9535 class="cmtt-8"> 8</span><span
9536 class="cmtt-8"> bits</span><span
9537 class="cmtt-8"> as</span><span
9538 class="cmtt-8"> unsigned</span><span
9539 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
9540 id="x1-111044r8"></a><span
9541 class="cmr-6">8</span><span
9542 class="cmtt-8"> </span><span
9543 class="cmtt-8"> </span><br class="fancyvrb" /><a
9544 id="x1-111046r9"></a><span
9545 class="cmr-6">9</span><span
9546 class="cmtt-8"> </span><span
9547 class="cmtt-8"> </span><span
9548 class="cmtt-8"> </span><span
9549 class="cmtt-8"> </span><span
9550 class="cmtt-8"> </span><span
9551 class="cmtt-8"> </span><span
9552 class="cmtt-8"> </span><span
9553 class="cmtt-8"> </span><span
9554 class="cmtt-8"> </span><span
9555 class="cmtt-8"> </span><span
9556 class="cmtt-8"> </span><span
9557 class="cmtt-8"> </span><span
9558 class="cmtt-8"> </span><span
9559 class="cmtt-8"> </span><span
9560 class="cmtt-8"> </span><span
9561 class="cmtt-8"> </span><span
9562 class="cmtt-8"> }</span><span
9563 class="cmtt-8"> else</span><span
9564 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9565 id="x1-111048r10"></a><span
9566 class="cmr-6">10</span><span
9567 class="cmtt-8"> </span><span
9568 class="cmtt-8"> </span>
9569 <br class="fancyvrb" /><a
9570 id="x1-111050r11"></a><span
9571 class="cmr-6">11</span><span
9572 class="cmtt-8"> </span><span
9573 class="cmtt-8"> </span><span
9574 class="cmtt-8"> </span><span
9575 class="cmtt-8"> </span><span
9576 class="cmtt-8"> </span><span
9577 class="cmtt-8"> </span><span
9578 class="cmtt-8"> </span><span
9579 class="cmtt-8"> </span><span
9580 class="cmtt-8"> </span><span
9581 class="cmtt-8"> </span><span
9582 class="cmtt-8"> </span><span
9583 class="cmtt-8"> </span><span
9584 class="cmtt-8"> </span><span
9585 class="cmtt-8"> </span><span
9586 class="cmtt-8"> </span><span
9587 class="cmtt-8"> </span><span
9588 class="cmtt-8"> </span><span
9589 class="cmtt-8"> </span><span
9590 class="cmtt-8"> 5)</span><span
9591 class="cmtt-8"> array</span><span
9592 class="cmtt-8"> [residue\_books]</span><span
9593 class="cmtt-8"> element</span><span
9594 class="cmtt-8"> [i][j]</span><span
9595 class="cmtt-8"> =</span><span
9596 class="cmtt-8"> unused</span><br class="fancyvrb" /><a
9597 id="x1-111052r12"></a><span
9598 class="cmr-6">12</span><span
9599 class="cmtt-8"> </span><span
9600 class="cmtt-8"> </span><br class="fancyvrb" /><a
9601 id="x1-111054r13"></a><span
9602 class="cmr-6">13</span><span
9603 class="cmtt-8"> </span><span
9604 class="cmtt-8"> </span><span
9605 class="cmtt-8"> </span><span
9606 class="cmtt-8"> </span><span
9607 class="cmtt-8"> </span><span
9608 class="cmtt-8"> </span><span
9609 class="cmtt-8"> </span><span
9610 class="cmtt-8"> </span><span
9611 class="cmtt-8"> </span><span
9612 class="cmtt-8"> </span><span
9613 class="cmtt-8"> </span><span
9614 class="cmtt-8"> </span><span
9615 class="cmtt-8"> </span><span
9616 class="cmtt-8"> </span><span
9617 class="cmtt-8"> </span><span
9618 class="cmtt-8"> </span><span
9619 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9620 id="x1-111056r14"></a><span
9621 class="cmr-6">14</span><span
9622 class="cmtt-8"> </span><span
9623 class="cmtt-8"> </span><span
9624 class="cmtt-8"> </span><span
9625 class="cmtt-8"> </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><br class="fancyvrb" /><a
9634 id="x1-111058r15"></a><span
9635 class="cmr-6">15</span><span
9636 class="cmtt-8"> </span><span
9637 class="cmtt-8"> </span><span
9638 class="cmtt-8"> </span><span
9639 class="cmtt-8"> </span><span
9640 class="cmtt-8"> </span><span
9641 class="cmtt-8"> </span><span
9642 class="cmtt-8"> </span><span
9643 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9644 id="x1-111060r16"></a><span
9645 class="cmr-6">16</span><span
9646 class="cmtt-8"> </span><span
9647 class="cmtt-8"> </span><br class="fancyvrb" /><a
9648 id="x1-111062r17"></a><span
9649 class="cmr-6">17</span><span
9650 class="cmtt-8"> </span><span
9651 class="cmtt-8"> </span><span
9652 class="cmtt-8"> </span><span
9653 class="cmtt-8"> 6)</span><span
9654 class="cmtt-8"> done</span></div>
9655 <!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable.
9656 In addition, any codebook number greater than the maximum numbered codebook
9657 set up in this stream also renders the stream undecodable. All codebooks in array
9658 [residue_books] are required to have a value mapping. The presence of codebook in array
9659 [residue_books] without a value mapping (maptype equals zero) renders the stream
9661 <!--l. 241--><p class="noindent" >
9662 <h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a
9663 id="x1-1120008.6.2"></a>packet decode</h5>
9664 <!--l. 243--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
9665 decode can be built out of the format 1 decode process. Thus we describe first the decode
9666 infrastructure identical to all three formats.
9667 <!--l. 248--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
9668 vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
9669 decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
9670 decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
9671 allocated and zeroed.
9672 <!--l. 255--><p class="noindent" >Depending on the values of <span
9673 class="cmtt-12">[residue_begin] </span>and <span
9674 class="cmtt-12">[residue_end]</span>, it is obvious that the
9675 encoded portion of a residue vector may be the entire possible residue vector or some other strict
9676 subset of the actual residue vector size with zero padding at either uncoded end. However, it is
9680 also possible to set <span
9681 class="cmtt-12">[residue_begin] </span>and <span
9682 class="cmtt-12">[residue_end] </span>to specify a range partially or wholly
9683 beyond the maximum vector size. Before beginning residue decode, limit <span
9684 class="cmtt-12">[residue_begin]</span>
9686 class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that
9687 the number of vectors being encoded, <span
9688 class="cmtt-12">[ch] </span>is provided by the higher level decoding
9690 <!--l. 269--><p class="noindent" >
9691 <div class="fancyvrb" id="fancyvrb38"><a
9692 id="x1-112002r1"></a><span
9693 class="cmr-6">1</span><span
9694 class="cmtt-8"> </span><span
9695 class="cmtt-8"> </span><span
9696 class="cmtt-8"> </span><span
9697 class="cmtt-8"> 1)</span><span
9698 class="cmtt-8"> [actual\_size]</span><span
9699 class="cmtt-8"> =</span><span
9700 class="cmtt-8"> current</span><span
9701 class="cmtt-8"> blocksize/2;</span><br class="fancyvrb" /><a
9702 id="x1-112004r2"></a><span
9703 class="cmr-6">2</span><span
9704 class="cmtt-8"> </span><span
9705 class="cmtt-8"> </span><span
9706 class="cmtt-8"> </span><span
9707 class="cmtt-8"> 2)</span><span
9708 class="cmtt-8"> if</span><span
9709 class="cmtt-8"> residue</span><span
9710 class="cmtt-8"> encoding</span><span
9711 class="cmtt-8"> is</span><span
9712 class="cmtt-8"> format</span><span
9713 class="cmtt-8"> 2</span>
9714 <br class="fancyvrb" /><a
9715 id="x1-112006r3"></a><span
9716 class="cmr-6">3</span><span
9717 class="cmtt-8"> </span><span
9718 class="cmtt-8"> </span><span
9719 class="cmtt-8"> </span><span
9720 class="cmtt-8"> </span><span
9721 class="cmtt-8"> </span><span
9722 class="cmtt-8"> </span><span
9723 class="cmtt-8"> </span><span
9724 class="cmtt-8"> </span><span
9725 class="cmtt-8"> 3)</span><span
9726 class="cmtt-8"> [actual\_size]</span><span
9727 class="cmtt-8"> =</span><span
9728 class="cmtt-8"> [actual\_size]</span><span
9729 class="cmtt-8"> *</span><span
9730 class="cmtt-8"> [ch];</span><br class="fancyvrb" /><a
9731 id="x1-112008r4"></a><span
9732 class="cmr-6">4</span><span
9733 class="cmtt-8"> </span><span
9734 class="cmtt-8"> </span><span
9735 class="cmtt-8"> </span><span
9736 class="cmtt-8"> 4)</span><span
9737 class="cmtt-8"> [limit\_residue\_begin]</span><span
9738 class="cmtt-8"> =</span><span
9739 class="cmtt-8"> minimum</span><span
9740 class="cmtt-8"> of</span><span
9741 class="cmtt-8"> ([residue\_begin],[actual\_size]);</span>
9742 <br class="fancyvrb" /><a
9743 id="x1-112010r5"></a><span
9744 class="cmr-6">5</span><span
9745 class="cmtt-8"> </span><span
9746 class="cmtt-8"> </span><span
9747 class="cmtt-8"> </span><span
9748 class="cmtt-8"> 5)</span><span
9749 class="cmtt-8"> [limit\_residue\_end]</span><span
9750 class="cmtt-8"> =</span><span
9751 class="cmtt-8"> minimum</span><span
9752 class="cmtt-8"> of</span><span
9753 class="cmtt-8"> ([residue\_end],[actual\_size]);</span></div>
9754 <!--l. 277--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
9755 <!--l. 280--><p class="noindent" >
9756 <div class="fancyvrb" id="fancyvrb39"><a
9757 id="x1-112012r1"></a><span
9758 class="cmr-6">1</span><span
9759 class="cmtt-8"> </span><span
9760 class="cmtt-8"> </span><span
9761 class="cmtt-8"> </span><span
9762 class="cmtt-8"> 1)</span><span
9763 class="cmtt-8"> [classwords\_per\_codeword]</span><span
9764 class="cmtt-8"> =</span><span
9765 class="cmtt-8"> [codebook\_dimensions]</span><span
9766 class="cmtt-8"> value</span><span
9767 class="cmtt-8"> of</span><span
9768 class="cmtt-8"> codebook</span><span
9769 class="cmtt-8"> [residue\_classbook]</span>
9770 <br class="fancyvrb" /><a
9771 id="x1-112014r2"></a><span
9772 class="cmr-6">2</span><span
9773 class="cmtt-8"> </span><span
9774 class="cmtt-8"> </span><span
9775 class="cmtt-8"> </span><span
9776 class="cmtt-8"> 2)</span><span
9777 class="cmtt-8"> [n\_to\_read]</span><span
9778 class="cmtt-8"> =</span><span
9779 class="cmtt-8"> [limit\_residue\_end]</span><span
9780 class="cmtt-8"> -</span><span
9781 class="cmtt-8"> [limit\_residue\_begin]</span><br class="fancyvrb" /><a
9782 id="x1-112016r3"></a><span
9783 class="cmr-6">3</span><span
9784 class="cmtt-8"> </span><span
9785 class="cmtt-8"> </span><span
9786 class="cmtt-8"> </span><span
9787 class="cmtt-8"> 3)</span><span
9788 class="cmtt-8"> [partitions\_to\_read]</span><span
9789 class="cmtt-8"> =</span><span
9790 class="cmtt-8"> [n\_to\_read]</span><span
9791 class="cmtt-8"> /</span><span
9792 class="cmtt-8"> [residue\_partition\_size]</span></div>
9793 <!--l. 286--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
9794 <div class="fancyvrb" id="fancyvrb40"><a
9795 id="x1-112018r1"></a><span
9796 class="cmr-6">1</span><span
9797 class="cmtt-8"> </span><span
9798 class="cmtt-8"> </span><span
9799 class="cmtt-8"> </span><span
9800 class="cmtt-8"> 1)</span><span
9801 class="cmtt-8"> allocate</span><span
9802 class="cmtt-8"> and</span><span
9803 class="cmtt-8"> zero</span><span
9804 class="cmtt-8"> all</span><span
9805 class="cmtt-8"> vectors</span><span
9806 class="cmtt-8"> that</span><span
9807 class="cmtt-8"> will</span><span
9808 class="cmtt-8"> be</span><span
9809 class="cmtt-8"> returned.</span><br class="fancyvrb" /><a
9810 id="x1-112020r2"></a><span
9811 class="cmr-6">2</span><span
9812 class="cmtt-8"> </span><span
9813 class="cmtt-8"> </span><span
9814 class="cmtt-8"> </span><span
9815 class="cmtt-8"> 2)</span><span
9816 class="cmtt-8"> if</span><span
9817 class="cmtt-8"> ([n\_to\_read]</span><span
9818 class="cmtt-8"> is</span><span
9819 class="cmtt-8"> zero),</span><span
9820 class="cmtt-8"> stop;</span><span
9821 class="cmtt-8"> there</span><span
9822 class="cmtt-8"> is</span><span
9823 class="cmtt-8"> no</span><span
9824 class="cmtt-8"> residue</span><span
9825 class="cmtt-8"> to</span><span
9826 class="cmtt-8"> decode.</span>
9827 <br class="fancyvrb" /><a
9828 id="x1-112022r3"></a><span
9829 class="cmr-6">3</span><span
9830 class="cmtt-8"> </span><span
9831 class="cmtt-8"> </span><span
9832 class="cmtt-8"> </span><span
9833 class="cmtt-8"> 3)</span><span
9834 class="cmtt-8"> iterate</span><span
9835 class="cmtt-8"> [pass]</span><span
9836 class="cmtt-8"> over</span><span
9837 class="cmtt-8"> the</span><span
9838 class="cmtt-8"> range</span><span
9839 class="cmtt-8"> 0</span><span
9840 class="cmtt-8"> ...</span><span
9841 class="cmtt-8"> 7</span><span
9842 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9843 id="x1-112024r4"></a><span
9844 class="cmr-6">4</span><span
9845 class="cmtt-8"> </span><span
9846 class="cmtt-8"> </span><br class="fancyvrb" /><a
9847 id="x1-112026r5"></a><span
9848 class="cmr-6">5</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"> </span><span
9854 class="cmtt-8"> </span><span
9855 class="cmtt-8"> </span><span
9856 class="cmtt-8"> </span><span
9857 class="cmtt-8"> 4)</span><span
9858 class="cmtt-8"> [partition\_count]</span><span
9859 class="cmtt-8"> =</span><span
9860 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
9861 id="x1-112028r6"></a><span
9862 class="cmr-6">6</span><span
9863 class="cmtt-8"> </span><span
9864 class="cmtt-8"> </span>
9865 <br class="fancyvrb" /><a
9866 id="x1-112030r7"></a><span
9867 class="cmr-6">7</span><span
9868 class="cmtt-8"> </span><span
9869 class="cmtt-8"> </span><span
9870 class="cmtt-8"> </span><span
9871 class="cmtt-8"> </span><span
9872 class="cmtt-8"> </span><span
9873 class="cmtt-8"> </span><span
9874 class="cmtt-8"> </span><span
9875 class="cmtt-8"> </span><span
9876 class="cmtt-8"> 5)</span><span
9877 class="cmtt-8"> while</span><span
9878 class="cmtt-8"> [partition\_count]</span><span
9879 class="cmtt-8"> is</span><span
9880 class="cmtt-8"> less</span><span
9881 class="cmtt-8"> than</span><span
9882 class="cmtt-8"> [partitions\_to\_read]</span><br class="fancyvrb" /><a
9883 id="x1-112032r8"></a><span
9884 class="cmr-6">8</span><span
9885 class="cmtt-8"> </span><span
9886 class="cmtt-8"> </span><br class="fancyvrb" /><a
9887 id="x1-112034r9"></a><span
9888 class="cmr-6">9</span><span
9889 class="cmtt-8"> </span><span
9890 class="cmtt-8"> </span><span
9891 class="cmtt-8"> </span><span
9892 class="cmtt-8"> </span><span
9893 class="cmtt-8"> </span><span
9894 class="cmtt-8"> </span><span
9895 class="cmtt-8"> </span><span
9896 class="cmtt-8"> </span><span
9897 class="cmtt-8"> </span><span
9898 class="cmtt-8"> </span><span
9899 class="cmtt-8"> </span><span
9900 class="cmtt-8"> </span><span
9901 class="cmtt-8"> </span><span
9902 class="cmtt-8"> 6)</span><span
9903 class="cmtt-8"> if</span><span
9904 class="cmtt-8"> ([pass]</span><span
9905 class="cmtt-8"> is</span><span
9906 class="cmtt-8"> zero)</span><span
9907 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9908 id="x1-112036r10"></a><span
9909 class="cmr-6">10</span><span
9910 class="cmtt-8"> </span><span
9911 class="cmtt-8"> </span>
9912 <br class="fancyvrb" /><a
9913 id="x1-112038r11"></a><span
9914 class="cmr-6">11</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"> </span><span
9922 class="cmtt-8"> </span><span
9923 class="cmtt-8"> </span><span
9924 class="cmtt-8"> </span><span
9925 class="cmtt-8"> </span><span
9926 class="cmtt-8"> </span><span
9927 class="cmtt-8"> </span><span
9928 class="cmtt-8"> </span><span
9929 class="cmtt-8"> </span><span
9930 class="cmtt-8"> </span><span
9931 class="cmtt-8"> </span><span
9932 class="cmtt-8"> </span><span
9933 class="cmtt-8"> 7)</span><span
9934 class="cmtt-8"> iterate</span><span
9935 class="cmtt-8"> [j]</span><span
9936 class="cmtt-8"> over</span><span
9937 class="cmtt-8"> the</span><span
9938 class="cmtt-8"> range</span><span
9939 class="cmtt-8"> 0</span><span
9940 class="cmtt-8"> ..</span><span
9941 class="cmtt-8"> [ch]-1</span><span
9942 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9943 id="x1-112040r12"></a><span
9944 class="cmr-6">12</span><span
9945 class="cmtt-8"> </span><span
9946 class="cmtt-8"> </span><br class="fancyvrb" /><a
9947 id="x1-112042r13"></a><span
9948 class="cmr-6">13</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><span
9953 class="cmtt-8"> </span><span
9954 class="cmtt-8"> </span><span
9955 class="cmtt-8"> </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><span
9968 class="cmtt-8"> </span><span
9969 class="cmtt-8"> </span><span
9970 class="cmtt-8"> </span><span
9971 class="cmtt-8"> </span><span
9972 class="cmtt-8"> 8)</span><span
9973 class="cmtt-8"> if</span><span
9974 class="cmtt-8"> vector</span><span
9975 class="cmtt-8"> [j]</span><span
9976 class="cmtt-8"> is</span><span
9977 class="cmtt-8"> not</span><span
9978 class="cmtt-8"> marked</span><span
9979 class="cmtt-8"> ’do</span><span
9980 class="cmtt-8"> not</span><span
9981 class="cmtt-8"> decode’</span><span
9982 class="cmtt-8"> {</span>
9983 <br class="fancyvrb" /><a
9984 id="x1-112044r14"></a><span
9985 class="cmr-6">14</span><span
9986 class="cmtt-8"> </span><span
9987 class="cmtt-8"> </span><br class="fancyvrb" /><a
9988 id="x1-112046r15"></a><span
9989 class="cmr-6">15</span><span
9990 class="cmtt-8"> </span><span
9991 class="cmtt-8"> </span><span
9992 class="cmtt-8"> </span><span
9993 class="cmtt-8"> </span><span
9994 class="cmtt-8"> </span><span
9995 class="cmtt-8"> </span><span
9996 class="cmtt-8"> </span><span
9997 class="cmtt-8"> </span><span
9998 class="cmtt-8"> </span><span
9999 class="cmtt-8"> </span><span
10000 class="cmtt-8"> </span><span
10001 class="cmtt-8"> </span><span
10002 class="cmtt-8"> </span><span
10003 class="cmtt-8"> </span><span
10004 class="cmtt-8"> </span><span
10005 class="cmtt-8"> </span><span
10006 class="cmtt-8"> </span><span
10007 class="cmtt-8"> </span><span
10008 class="cmtt-8"> </span><span
10009 class="cmtt-8"> </span><span
10010 class="cmtt-8"> </span><span
10011 class="cmtt-8"> </span><span
10012 class="cmtt-8"> </span><span
10013 class="cmtt-8"> </span><span
10014 class="cmtt-8"> </span><span
10015 class="cmtt-8"> </span><span
10016 class="cmtt-8"> </span><span
10017 class="cmtt-8"> </span><span
10018 class="cmtt-8"> 9)</span><span
10019 class="cmtt-8"> [temp]</span><span
10020 class="cmtt-8"> =</span><span
10021 class="cmtt-8"> read</span><span
10022 class="cmtt-8"> from</span><span
10023 class="cmtt-8"> packet</span><span
10024 class="cmtt-8"> using</span><span
10025 class="cmtt-8"> codebook</span><span
10026 class="cmtt-8"> [residue\_classbook]</span><span
10027 class="cmtt-8"> in</span><span
10028 class="cmtt-8"> scalar</span><span
10029 class="cmtt-8"> context</span>
10030 <br class="fancyvrb" /><a
10031 id="x1-112048r16"></a><span
10032 class="cmr-6">16</span><span
10033 class="cmtt-8"> </span><span
10034 class="cmtt-8"> </span><span
10035 class="cmtt-8"> </span><span
10036 class="cmtt-8"> </span><span
10037 class="cmtt-8"> </span><span
10038 class="cmtt-8"> </span><span
10039 class="cmtt-8"> </span><span
10040 class="cmtt-8"> </span><span
10041 class="cmtt-8"> </span><span
10042 class="cmtt-8"> </span><span
10043 class="cmtt-8"> </span><span
10044 class="cmtt-8"> </span><span
10045 class="cmtt-8"> </span><span
10046 class="cmtt-8"> </span><span
10047 class="cmtt-8"> </span><span
10048 class="cmtt-8"> </span><span
10049 class="cmtt-8"> </span><span
10050 class="cmtt-8"> </span><span
10051 class="cmtt-8"> </span><span
10052 class="cmtt-8"> </span><span
10053 class="cmtt-8"> </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"> 10)</span><span
10061 class="cmtt-8"> iterate</span><span
10062 class="cmtt-8"> [i]</span><span
10063 class="cmtt-8"> descending</span><span
10064 class="cmtt-8"> over</span><span
10065 class="cmtt-8"> the</span><span
10066 class="cmtt-8"> range</span><span
10067 class="cmtt-8"> [classwords\_per\_codeword]-1</span><span
10068 class="cmtt-8"> ...</span><span
10069 class="cmtt-8"> 0</span><span
10070 class="cmtt-8"> {</span>
10071 <br class="fancyvrb" /><a
10072 id="x1-112050r17"></a><span
10073 class="cmr-6">17</span><span
10074 class="cmtt-8"> </span><span
10075 class="cmtt-8"> </span><br class="fancyvrb" /><a
10076 id="x1-112052r18"></a><span
10077 class="cmr-6">18</span><span
10078 class="cmtt-8"> </span><span
10079 class="cmtt-8"> </span><span
10080 class="cmtt-8"> </span><span
10081 class="cmtt-8"> </span><span
10082 class="cmtt-8"> </span><span
10083 class="cmtt-8"> </span><span
10084 class="cmtt-8"> </span><span
10085 class="cmtt-8"> </span><span
10086 class="cmtt-8"> </span><span
10087 class="cmtt-8"> </span><span
10088 class="cmtt-8"> </span><span
10089 class="cmtt-8"> </span><span
10090 class="cmtt-8"> </span><span
10091 class="cmtt-8"> </span><span
10092 class="cmtt-8"> </span><span
10093 class="cmtt-8"> </span><span
10094 class="cmtt-8"> </span><span
10095 class="cmtt-8"> </span><span
10096 class="cmtt-8"> </span><span
10097 class="cmtt-8"> </span><span
10098 class="cmtt-8"> </span><span
10099 class="cmtt-8"> </span><span
10100 class="cmtt-8"> </span><span
10101 class="cmtt-8"> </span><span
10102 class="cmtt-8"> </span><span
10103 class="cmtt-8"> </span><span
10104 class="cmtt-8"> </span><span
10105 class="cmtt-8"> </span><span
10106 class="cmtt-8"> </span><span
10107 class="cmtt-8"> </span><span
10108 class="cmtt-8"> </span><span
10109 class="cmtt-8"> </span><span
10110 class="cmtt-8"> 11)</span><span
10111 class="cmtt-8"> array</span><span
10112 class="cmtt-8"> [classifications]</span><span
10113 class="cmtt-8"> element</span><span
10114 class="cmtt-8"> [j],([i]+[partition\_count])</span><span
10115 class="cmtt-8"> =</span>
10116 <br class="fancyvrb" /><a
10117 id="x1-112054r19"></a><span
10118 class="cmr-6">19</span><span
10119 class="cmtt-8"> </span><span
10120 class="cmtt-8"> </span><span
10121 class="cmtt-8"> </span><span
10122 class="cmtt-8"> </span><span
10123 class="cmtt-8"> </span><span
10124 class="cmtt-8"> </span><span
10125 class="cmtt-8"> </span><span
10126 class="cmtt-8"> </span><span
10127 class="cmtt-8"> </span><span
10128 class="cmtt-8"> </span><span
10129 class="cmtt-8"> </span><span
10130 class="cmtt-8"> </span><span
10131 class="cmtt-8"> </span><span
10132 class="cmtt-8"> </span><span
10133 class="cmtt-8"> </span><span
10134 class="cmtt-8"> </span><span
10135 class="cmtt-8"> </span><span
10136 class="cmtt-8"> </span><span
10137 class="cmtt-8"> </span><span
10138 class="cmtt-8"> </span><span
10139 class="cmtt-8"> </span><span
10140 class="cmtt-8"> </span><span
10141 class="cmtt-8"> </span><span
10142 class="cmtt-8"> </span><span
10143 class="cmtt-8"> </span><span
10144 class="cmtt-8"> </span><span
10145 class="cmtt-8"> </span><span
10146 class="cmtt-8"> </span><span
10147 class="cmtt-8"> </span><span
10148 class="cmtt-8"> </span><span
10149 class="cmtt-8"> </span><span
10150 class="cmtt-8"> </span><span
10151 class="cmtt-8"> </span><span
10152 class="cmtt-8"> </span><span
10153 class="cmtt-8"> </span><span
10154 class="cmtt-8"> </span><span
10155 class="cmtt-8"> [temp]</span><span
10156 class="cmtt-8"> integer</span><span
10157 class="cmtt-8"> modulo</span><span
10158 class="cmtt-8"> [residue\_classifications]</span>
10159 <br class="fancyvrb" /><a
10160 id="x1-112056r20"></a><span
10161 class="cmr-6">20</span><span
10162 class="cmtt-8"> </span><span
10163 class="cmtt-8"> </span><span
10164 class="cmtt-8"> </span><span
10165 class="cmtt-8"> </span><span
10166 class="cmtt-8"> </span><span
10167 class="cmtt-8"> </span><span
10168 class="cmtt-8"> </span><span
10169 class="cmtt-8"> </span><span
10170 class="cmtt-8"> </span><span
10171 class="cmtt-8"> </span><span
10172 class="cmtt-8"> </span><span
10173 class="cmtt-8"> </span><span
10174 class="cmtt-8"> </span><span
10175 class="cmtt-8"> </span><span
10176 class="cmtt-8"> </span><span
10177 class="cmtt-8"> </span><span
10178 class="cmtt-8"> </span><span
10179 class="cmtt-8"> </span><span
10180 class="cmtt-8"> </span><span
10181 class="cmtt-8"> </span><span
10182 class="cmtt-8"> </span><span
10183 class="cmtt-8"> </span><span
10184 class="cmtt-8"> </span><span
10185 class="cmtt-8"> </span><span
10186 class="cmtt-8"> </span><span
10187 class="cmtt-8"> </span><span
10188 class="cmtt-8"> </span><span
10189 class="cmtt-8"> </span><span
10190 class="cmtt-8"> </span><span
10191 class="cmtt-8"> </span><span
10192 class="cmtt-8"> </span><span
10193 class="cmtt-8"> </span><span
10194 class="cmtt-8"> 12)</span><span
10195 class="cmtt-8"> [temp]</span><span
10196 class="cmtt-8"> =</span><span
10197 class="cmtt-8"> [temp]</span><span
10198 class="cmtt-8"> /</span><span
10199 class="cmtt-8"> [residue\_classifications]</span><span
10200 class="cmtt-8"> using</span><span
10201 class="cmtt-8"> integer</span><span
10202 class="cmtt-8"> division</span><br class="fancyvrb" /><a
10203 id="x1-112058r21"></a><span
10204 class="cmr-6">21</span><span
10205 class="cmtt-8"> </span><span
10206 class="cmtt-8"> </span>
10207 <br class="fancyvrb" /><a
10208 id="x1-112060r22"></a><span
10209 class="cmr-6">22</span><span
10210 class="cmtt-8"> </span><span
10211 class="cmtt-8"> </span><span
10212 class="cmtt-8"> </span><span
10213 class="cmtt-8"> </span><span
10214 class="cmtt-8"> </span><span
10215 class="cmtt-8"> </span><span
10216 class="cmtt-8"> </span><span
10217 class="cmtt-8"> </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"> </span><span
10227 class="cmtt-8"> </span><span
10228 class="cmtt-8"> </span><span
10229 class="cmtt-8"> </span><span
10230 class="cmtt-8"> </span><span
10231 class="cmtt-8"> </span><span
10232 class="cmtt-8"> </span><span
10233 class="cmtt-8"> </span><span
10234 class="cmtt-8"> </span><span
10235 class="cmtt-8"> </span><span
10236 class="cmtt-8"> </span><span
10237 class="cmtt-8"> </span><span
10238 class="cmtt-8"> </span><span
10239 class="cmtt-8"> </span><span
10240 class="cmtt-8"> </span><span
10241 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10242 id="x1-112062r23"></a><span
10243 class="cmr-6">23</span><span
10244 class="cmtt-8"> </span><span
10245 class="cmtt-8"> </span><br class="fancyvrb" /><a
10246 id="x1-112064r24"></a><span
10247 class="cmr-6">24</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"> </span><span
10255 class="cmtt-8"> </span><span
10256 class="cmtt-8"> </span><span
10257 class="cmtt-8"> </span><span
10258 class="cmtt-8"> </span><span
10259 class="cmtt-8"> </span><span
10260 class="cmtt-8"> </span><span
10261 class="cmtt-8"> </span><span
10262 class="cmtt-8"> </span><span
10263 class="cmtt-8"> </span><span
10264 class="cmtt-8"> </span><span
10265 class="cmtt-8"> </span><span
10266 class="cmtt-8"> </span><span
10267 class="cmtt-8"> </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><br class="fancyvrb" /><a
10275 id="x1-112066r25"></a><span
10276 class="cmr-6">25</span><span
10277 class="cmtt-8"> </span><span
10278 class="cmtt-8"> </span><br class="fancyvrb" /><a
10279 id="x1-112068r26"></a><span
10280 class="cmr-6">26</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"> </span><span
10287 class="cmtt-8"> </span><span
10288 class="cmtt-8"> </span><span
10289 class="cmtt-8"> </span><span
10290 class="cmtt-8"> </span><span
10291 class="cmtt-8"> </span><span
10292 class="cmtt-8"> </span><span
10293 class="cmtt-8"> </span><span
10294 class="cmtt-8"> </span><span
10295 class="cmtt-8"> </span><span
10296 class="cmtt-8"> </span><span
10297 class="cmtt-8"> </span><span
10298 class="cmtt-8"> </span><span
10299 class="cmtt-8"> </span><span
10300 class="cmtt-8"> </span><span
10301 class="cmtt-8"> </span><span
10302 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10303 id="x1-112070r27"></a><span
10304 class="cmr-6">27</span><span
10305 class="cmtt-8"> </span><span
10306 class="cmtt-8"> </span><br class="fancyvrb" /><a
10307 id="x1-112072r28"></a><span
10308 class="cmr-6">28</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><br class="fancyvrb" /><a
10326 id="x1-112074r29"></a><span
10327 class="cmr-6">29</span><span
10328 class="cmtt-8"> </span><span
10329 class="cmtt-8"> </span>
10330 <br class="fancyvrb" /><a
10331 id="x1-112076r30"></a><span
10332 class="cmr-6">30</span><span
10333 class="cmtt-8"> </span><span
10334 class="cmtt-8"> </span><span
10335 class="cmtt-8"> </span><span
10336 class="cmtt-8"> </span><span
10337 class="cmtt-8"> </span><span
10338 class="cmtt-8"> </span><span
10339 class="cmtt-8"> </span><span
10340 class="cmtt-8"> </span><span
10341 class="cmtt-8"> </span><span
10342 class="cmtt-8"> </span><span
10343 class="cmtt-8"> </span><span
10344 class="cmtt-8"> </span><span
10345 class="cmtt-8"> 13)</span><span
10346 class="cmtt-8"> iterate</span><span
10347 class="cmtt-8"> [i]</span><span
10348 class="cmtt-8"> over</span><span
10349 class="cmtt-8"> the</span><span
10350 class="cmtt-8"> range</span><span
10351 class="cmtt-8"> 0</span><span
10352 class="cmtt-8"> ..</span><span
10353 class="cmtt-8"> ([classwords\_per\_codeword]</span><span
10354 class="cmtt-8"> -</span><span
10355 class="cmtt-8"> 1)</span><span
10356 class="cmtt-8"> while</span><span
10357 class="cmtt-8"> [partition\_count]</span>
10358 <br class="fancyvrb" /><a
10359 id="x1-112078r31"></a><span
10360 class="cmr-6">31</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"> </span><span
10375 class="cmtt-8"> </span><span
10376 class="cmtt-8"> </span><span
10377 class="cmtt-8"> is</span><span
10378 class="cmtt-8"> also</span><span
10379 class="cmtt-8"> less</span><span
10380 class="cmtt-8"> than</span><span
10381 class="cmtt-8"> [partitions\_to\_read]</span><span
10382 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10383 id="x1-112080r32"></a><span
10384 class="cmr-6">32</span><span
10385 class="cmtt-8"> </span><span
10386 class="cmtt-8"> </span><br class="fancyvrb" /><a
10387 id="x1-112082r33"></a><span
10388 class="cmr-6">33</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"> 14)</span><span
10408 class="cmtt-8"> iterate</span><span
10409 class="cmtt-8"> [j]</span><span
10410 class="cmtt-8"> over</span><span
10411 class="cmtt-8"> the</span><span
10412 class="cmtt-8"> range</span><span
10413 class="cmtt-8"> 0</span><span
10414 class="cmtt-8"> ..</span><span
10415 class="cmtt-8"> [ch]-1</span><span
10416 class="cmtt-8"> {</span>
10417 <br class="fancyvrb" /><a
10418 id="x1-112084r34"></a><span
10419 class="cmr-6">34</span><span
10420 class="cmtt-8"> </span><span
10421 class="cmtt-8"> </span><br class="fancyvrb" /><a
10422 id="x1-112086r35"></a><span
10423 class="cmr-6">35</span><span
10424 class="cmtt-8"> </span><span
10425 class="cmtt-8"> </span><span
10426 class="cmtt-8"> </span><span
10427 class="cmtt-8"> </span><span
10428 class="cmtt-8"> </span><span
10429 class="cmtt-8"> </span><span
10430 class="cmtt-8"> </span><span
10431 class="cmtt-8"> </span><span
10432 class="cmtt-8"> </span><span
10433 class="cmtt-8"> </span><span
10434 class="cmtt-8"> </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"> 15)</span><span
10448 class="cmtt-8"> if</span><span
10449 class="cmtt-8"> vector</span><span
10450 class="cmtt-8"> [j]</span><span
10451 class="cmtt-8"> is</span><span
10452 class="cmtt-8"> not</span><span
10453 class="cmtt-8"> marked</span><span
10454 class="cmtt-8"> ’do</span><span
10455 class="cmtt-8"> not</span><span
10456 class="cmtt-8"> decode’</span><span
10457 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10458 id="x1-112088r36"></a><span
10459 class="cmr-6">36</span><span
10460 class="cmtt-8"> </span><span
10461 class="cmtt-8"> </span>
10462 <br class="fancyvrb" /><a
10463 id="x1-112090r37"></a><span
10464 class="cmr-6">37</span><span
10465 class="cmtt-8"> </span><span
10466 class="cmtt-8"> </span><span
10467 class="cmtt-8"> </span><span
10468 class="cmtt-8"> </span><span
10469 class="cmtt-8"> </span><span
10470 class="cmtt-8"> </span><span
10471 class="cmtt-8"> </span><span
10472 class="cmtt-8"> </span><span
10473 class="cmtt-8"> </span><span
10474 class="cmtt-8"> </span><span
10475 class="cmtt-8"> </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"> 16)</span><span
10494 class="cmtt-8"> [vqclass]</span><span
10495 class="cmtt-8"> =</span><span
10496 class="cmtt-8"> array</span><span
10497 class="cmtt-8"> [classifications]</span><span
10498 class="cmtt-8"> element</span><span
10499 class="cmtt-8"> [j],[partition\_count]</span>
10500 <br class="fancyvrb" /><a
10501 id="x1-112092r38"></a><span
10502 class="cmr-6">38</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"> </span><span
10513 class="cmtt-8"> </span><span
10514 class="cmtt-8"> </span><span
10515 class="cmtt-8"> </span><span
10516 class="cmtt-8"> </span><span
10517 class="cmtt-8"> </span><span
10518 class="cmtt-8"> </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"> 17)</span><span
10532 class="cmtt-8"> [vqbook]</span><span
10533 class="cmtt-8"> =</span><span
10534 class="cmtt-8"> array</span><span
10535 class="cmtt-8"> [residue\_books]</span><span
10536 class="cmtt-8"> element</span><span
10537 class="cmtt-8"> [vqclass],[pass]</span><br class="fancyvrb" /><a
10538 id="x1-112094r39"></a><span
10539 class="cmr-6">39</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"> </span><span
10552 class="cmtt-8"> </span><span
10553 class="cmtt-8"> </span><span
10554 class="cmtt-8"> </span><span
10555 class="cmtt-8"> </span><span
10556 class="cmtt-8"> </span><span
10557 class="cmtt-8"> </span><span
10558 class="cmtt-8"> </span><span
10559 class="cmtt-8"> </span><span
10560 class="cmtt-8"> </span><span
10561 class="cmtt-8"> </span><span
10562 class="cmtt-8"> </span><span
10563 class="cmtt-8"> </span><span
10564 class="cmtt-8"> </span><span
10565 class="cmtt-8"> </span><span
10566 class="cmtt-8"> </span><span
10567 class="cmtt-8"> </span><span
10568 class="cmtt-8"> 18)</span><span
10569 class="cmtt-8"> if</span><span
10570 class="cmtt-8"> ([vqbook]</span><span
10571 class="cmtt-8"> is</span><span
10572 class="cmtt-8"> not</span><span
10573 class="cmtt-8"> ’unused’)</span><span
10574 class="cmtt-8"> {</span>
10575 <br class="fancyvrb" /><a
10576 id="x1-112096r40"></a><span
10577 class="cmr-6">40</span><span
10578 class="cmtt-8"> </span><span
10579 class="cmtt-8"> </span><br class="fancyvrb" /><a
10580 id="x1-112098r41"></a><span
10581 class="cmr-6">41</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><span
10600 class="cmtt-8"> </span><span
10601 class="cmtt-8"> </span><span
10602 class="cmtt-8"> </span><span
10603 class="cmtt-8"> </span><span
10604 class="cmtt-8"> </span><span
10605 class="cmtt-8"> </span><span
10606 class="cmtt-8"> </span><span
10607 class="cmtt-8"> </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"> 19)</span><span
10616 class="cmtt-8"> decode</span><span
10617 class="cmtt-8"> partition</span><span
10618 class="cmtt-8"> into</span><span
10619 class="cmtt-8"> output</span><span
10620 class="cmtt-8"> vector</span><span
10621 class="cmtt-8"> number</span><span
10622 class="cmtt-8"> [j],</span><span
10623 class="cmtt-8"> starting</span><span
10624 class="cmtt-8"> at</span><span
10625 class="cmtt-8"> scalar</span>
10626 <br class="fancyvrb" /><a
10627 id="x1-112100r42"></a><span
10628 class="cmr-6">42</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><span
10635 class="cmtt-8"> </span><span
10636 class="cmtt-8"> </span><span
10637 class="cmtt-8"> </span><span
10638 class="cmtt-8"> </span><span
10639 class="cmtt-8"> </span><span
10640 class="cmtt-8"> </span><span
10641 class="cmtt-8"> </span><span
10642 class="cmtt-8"> </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><span
10665 class="cmtt-8"> </span><span
10666 class="cmtt-8"> offset</span><span
10667 class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span
10668 class="cmtt-8"> using</span>
10669 <br class="fancyvrb" /><a
10670 id="x1-112102r43"></a><span
10671 class="cmr-6">43</span><span
10672 class="cmtt-8"> </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><span
10690 class="cmtt-8"> </span><span
10691 class="cmtt-8"> </span><span
10692 class="cmtt-8"> </span><span
10693 class="cmtt-8"> </span><span
10694 class="cmtt-8"> </span><span
10695 class="cmtt-8"> </span><span
10696 class="cmtt-8"> </span><span
10697 class="cmtt-8"> </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"> codebook</span><span
10710 class="cmtt-8"> number</span><span
10711 class="cmtt-8"> [vqbook]</span><span
10712 class="cmtt-8"> in</span><span
10713 class="cmtt-8"> VQ</span><span
10714 class="cmtt-8"> context</span><br class="fancyvrb" /><a
10715 id="x1-112104r44"></a><span
10716 class="cmr-6">44</span><span
10717 class="cmtt-8"> </span><span
10718 class="cmtt-8"> </span><span
10719 class="cmtt-8"> </span><span
10720 class="cmtt-8"> </span><span
10721 class="cmtt-8"> </span><span
10722 class="cmtt-8"> </span><span
10723 class="cmtt-8"> </span><span
10724 class="cmtt-8"> </span><span
10725 class="cmtt-8"> </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"> </span><span
10743 class="cmtt-8"> </span><span
10744 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10745 id="x1-112106r45"></a><span
10746 class="cmr-6">45</span><span
10747 class="cmtt-8"> </span><span
10748 class="cmtt-8"> </span><span
10749 class="cmtt-8"> </span><span
10750 class="cmtt-8"> </span><span
10751 class="cmtt-8"> </span><span
10752 class="cmtt-8"> </span><span
10753 class="cmtt-8"> </span><span
10754 class="cmtt-8"> </span><span
10755 class="cmtt-8"> </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>
10770 <br class="fancyvrb" /><a
10771 id="x1-112108r46"></a><span
10772 class="cmr-6">46</span><span
10773 class="cmtt-8"> </span><span
10774 class="cmtt-8"> </span><br class="fancyvrb" /><a
10775 id="x1-112110r47"></a><span
10776 class="cmr-6">47</span><span
10777 class="cmtt-8"> </span><span
10778 class="cmtt-8"> </span><span
10779 class="cmtt-8"> </span><span
10780 class="cmtt-8"> </span><span
10781 class="cmtt-8"> </span><span
10782 class="cmtt-8"> </span><span
10783 class="cmtt-8"> </span><span
10784 class="cmtt-8"> </span><span
10785 class="cmtt-8"> </span><span
10786 class="cmtt-8"> </span><span
10787 class="cmtt-8"> </span><span
10788 class="cmtt-8"> </span><span
10789 class="cmtt-8"> </span><span
10790 class="cmtt-8"> </span><span
10791 class="cmtt-8"> </span><span
10792 class="cmtt-8"> </span><span
10793 class="cmtt-8"> </span><span
10794 class="cmtt-8"> </span><span
10795 class="cmtt-8"> 20)</span><span
10796 class="cmtt-8"> increment</span><span
10797 class="cmtt-8"> [partition\_count]</span><span
10798 class="cmtt-8"> by</span><span
10799 class="cmtt-8"> one</span><br class="fancyvrb" /><a
10800 id="x1-112112r48"></a><span
10801 class="cmr-6">48</span><span
10802 class="cmtt-8"> </span><span
10803 class="cmtt-8"> </span><br class="fancyvrb" /><a
10804 id="x1-112114r49"></a><span
10805 class="cmr-6">49</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"> </span><span
10816 class="cmtt-8"> </span><span
10817 class="cmtt-8"> </span><span
10818 class="cmtt-8"> </span><span
10819 class="cmtt-8"> </span><span
10820 class="cmtt-8"> </span><span
10821 class="cmtt-8"> </span><span
10822 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10823 id="x1-112116r50"></a><span
10824 class="cmr-6">50</span><span
10825 class="cmtt-8"> </span><span
10826 class="cmtt-8"> </span><span
10827 class="cmtt-8"> </span><span
10828 class="cmtt-8"> </span><span
10829 class="cmtt-8"> </span><span
10830 class="cmtt-8"> </span><span
10831 class="cmtt-8"> </span><span
10832 class="cmtt-8"> </span><span
10833 class="cmtt-8"> </span><span
10834 class="cmtt-8"> </span><span
10835 class="cmtt-8"> </span><span
10836 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10837 id="x1-112118r51"></a><span
10838 class="cmr-6">51</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><br class="fancyvrb" /><a
10846 id="x1-112120r52"></a><span
10847 class="cmr-6">52</span><span
10848 class="cmtt-8"> </span><span
10849 class="cmtt-8"> </span><br class="fancyvrb" /><a
10850 id="x1-112122r53"></a><span
10851 class="cmr-6">53</span><span
10852 class="cmtt-8"> </span><span
10853 class="cmtt-8"> </span><span
10854 class="cmtt-8"> 21)</span><span
10855 class="cmtt-8"> done</span><br class="fancyvrb" /><a
10856 id="x1-112124r54"></a><span
10857 class="cmr-6">54</span><span
10858 class="cmtt-8"> </span><span
10859 class="cmtt-8"> </span></div>
10860 <!--l. 344--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
10861 Decode returns the result of vector decode up to that point.
10862 <!--l. 350--><p class="noindent" >
10863 <h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a
10864 id="x1-1130008.6.3"></a>format 0 specifics</h5>
10865 <!--l. 352--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
10866 section. The following pseudocode presents the same algorithm. Assume:
10870 <ul class="itemize1">
10871 <li class="itemize"><span
10872 class="cmtt-12">[n] </span>is the value in <span
10873 class="cmtt-12">[residue_partition_size]</span>
10875 <li class="itemize"><span
10876 class="cmtt-12">[v] </span>is the residue vector
10878 <li class="itemize"><span
10879 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
10880 <!--l. 363--><p class="noindent" >
10881 <div class="fancyvrb" id="fancyvrb41"><a
10882 id="x1-113002r1"></a><span
10883 class="cmr-6">1</span><span
10884 class="cmtt-8"> </span><span
10885 class="cmtt-8"> </span><span
10886 class="cmtt-8"> 1)</span><span
10887 class="cmtt-8"> [step]</span><span
10888 class="cmtt-8"> =</span><span
10889 class="cmtt-8"> [n]</span><span
10890 class="cmtt-8"> /</span><span
10891 class="cmtt-8"> [codebook\_dimensions]</span><br class="fancyvrb" /><a
10892 id="x1-113004r2"></a><span
10893 class="cmr-6">2</span><span
10894 class="cmtt-8"> </span><span
10895 class="cmtt-8"> </span><span
10896 class="cmtt-8"> 2)</span><span
10897 class="cmtt-8"> iterate</span><span
10898 class="cmtt-8"> [i]</span><span
10899 class="cmtt-8"> over</span><span
10900 class="cmtt-8"> the</span><span
10901 class="cmtt-8"> range</span><span
10902 class="cmtt-8"> 0</span><span
10903 class="cmtt-8"> ...</span><span
10904 class="cmtt-8"> [step]-1</span><span
10905 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10906 id="x1-113006r3"></a><span
10907 class="cmr-6">3</span><span
10908 class="cmtt-8"> </span><span
10909 class="cmtt-8"> </span>
10910 <br class="fancyvrb" /><a
10911 id="x1-113008r4"></a><span
10912 class="cmr-6">4</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"> 3)</span><span
10921 class="cmtt-8"> vector</span><span
10922 class="cmtt-8"> [entry\_temp]</span><span
10923 class="cmtt-8"> =</span><span
10924 class="cmtt-8"> read</span><span
10925 class="cmtt-8"> vector</span><span
10926 class="cmtt-8"> from</span><span
10927 class="cmtt-8"> packet</span><span
10928 class="cmtt-8"> using</span><span
10929 class="cmtt-8"> current</span><span
10930 class="cmtt-8"> codebook</span><span
10931 class="cmtt-8"> in</span><span
10932 class="cmtt-8"> VQ</span><span
10933 class="cmtt-8"> context</span>
10934 <br class="fancyvrb" /><a
10935 id="x1-113010r5"></a><span
10936 class="cmr-6">5</span><span
10937 class="cmtt-8"> </span><span
10938 class="cmtt-8"> </span><span
10939 class="cmtt-8"> </span><span
10940 class="cmtt-8"> </span><span
10941 class="cmtt-8"> </span><span
10942 class="cmtt-8"> </span><span
10943 class="cmtt-8"> </span><span
10944 class="cmtt-8"> 4)</span><span
10945 class="cmtt-8"> iterate</span><span
10946 class="cmtt-8"> [j]</span><span
10947 class="cmtt-8"> over</span><span
10948 class="cmtt-8"> the</span><span
10949 class="cmtt-8"> range</span><span
10950 class="cmtt-8"> 0</span><span
10951 class="cmtt-8"> ...</span><span
10952 class="cmtt-8"> [codebook\_dimensions]-1</span><span
10953 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10954 id="x1-113012r6"></a><span
10955 class="cmr-6">6</span><span
10956 class="cmtt-8"> </span><span
10957 class="cmtt-8"> </span><br class="fancyvrb" /><a
10958 id="x1-113014r7"></a><span
10959 class="cmr-6">7</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"> 5)</span><span
10973 class="cmtt-8"> vector</span><span
10974 class="cmtt-8"> [v]</span><span
10975 class="cmtt-8"> element</span><span
10976 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
10977 class="cmtt-8"> =</span>
10978 <br class="fancyvrb" /><a
10979 id="x1-113016r8"></a><span
10980 class="cmr-6">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"> </span><span
10987 class="cmtt-8"> </span><span
10988 class="cmtt-8"> </span><span
10989 class="cmtt-8"> </span><span
10990 class="cmtt-8"> vector</span><span
10991 class="cmtt-8"> [v]</span><span
10992 class="cmtt-8"> element</span><span
10993 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
10994 class="cmtt-8"> +</span><br class="fancyvrb" /><a
10995 id="x1-113018r9"></a><span
10996 class="cmr-6">9</span><span
10997 class="cmtt-8"> </span><span
10998 class="cmtt-8"> </span><span
10999 class="cmtt-8"> </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"> vector</span><span
11015 class="cmtt-8"> [entry\_temp]</span><span
11016 class="cmtt-8"> element</span><span
11017 class="cmtt-8"> [j]</span><br class="fancyvrb" /><a
11018 id="x1-113020r10"></a><span
11019 class="cmr-6">10</span><span
11020 class="cmtt-8"> </span><span
11021 class="cmtt-8"> </span><br class="fancyvrb" /><a
11022 id="x1-113022r11"></a><span
11023 class="cmr-6">11</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><br class="fancyvrb" /><a
11035 id="x1-113024r12"></a><span
11036 class="cmr-6">12</span><span
11037 class="cmtt-8"> </span><span
11038 class="cmtt-8"> </span><br class="fancyvrb" /><a
11039 id="x1-113026r13"></a><span
11040 class="cmr-6">13</span><span
11041 class="cmtt-8"> </span><span
11042 class="cmtt-8"> </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><br class="fancyvrb" /><a
11047 id="x1-113028r14"></a><span
11048 class="cmr-6">14</span><span
11049 class="cmtt-8"> </span><span
11050 class="cmtt-8"> </span><br class="fancyvrb" /><a
11051 id="x1-113030r15"></a><span
11052 class="cmr-6">15</span><span
11053 class="cmtt-8"> </span><span
11054 class="cmtt-8"> </span><span
11055 class="cmtt-8"> </span><span
11056 class="cmtt-8"> 6)</span><span
11057 class="cmtt-8"> done</span><br class="fancyvrb" /><a
11058 id="x1-113032r16"></a><span
11059 class="cmr-6">16</span><span
11060 class="cmtt-8"> </span><span
11061 class="cmtt-8"> </span></div>
11062 <!--l. 384--><p class="noindent" >
11063 <h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a
11064 id="x1-1140008.6.4"></a>format 1 specifics</h5>
11065 <!--l. 386--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
11066 section. The following pseudocode presents the same algorithm. Assume:
11067 <ul class="itemize1">
11068 <li class="itemize"><span
11069 class="cmtt-12">[n] </span>is the value in <span
11070 class="cmtt-12">[residue_partition_size]</span>
11072 <li class="itemize"><span
11073 class="cmtt-12">[v] </span>is the residue vector
11075 <li class="itemize"><span
11076 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
11077 <!--l. 398--><p class="noindent" >
11078 <div class="fancyvrb" id="fancyvrb42"><a
11079 id="x1-114002r1"></a><span
11080 class="cmr-6">1</span><span
11081 class="cmtt-8"> </span><span
11082 class="cmtt-8"> </span><span
11083 class="cmtt-8"> 1)</span><span
11084 class="cmtt-8"> [i]</span><span
11085 class="cmtt-8"> =</span><span
11086 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
11087 id="x1-114004r2"></a><span
11088 class="cmr-6">2</span><span
11089 class="cmtt-8"> </span><span
11090 class="cmtt-8"> </span><span
11091 class="cmtt-8"> 2)</span><span
11092 class="cmtt-8"> vector</span><span
11093 class="cmtt-8"> [entry\_temp]</span><span
11094 class="cmtt-8"> =</span><span
11095 class="cmtt-8"> read</span><span
11096 class="cmtt-8"> vector</span><span
11097 class="cmtt-8"> from</span><span
11098 class="cmtt-8"> packet</span><span
11099 class="cmtt-8"> using</span><span
11100 class="cmtt-8"> current</span><span
11101 class="cmtt-8"> codebook</span><span
11102 class="cmtt-8"> in</span><span
11103 class="cmtt-8"> VQ</span><span
11104 class="cmtt-8"> context</span>
11105 <br class="fancyvrb" /><a
11106 id="x1-114006r3"></a><span
11107 class="cmr-6">3</span><span
11108 class="cmtt-8"> </span><span
11109 class="cmtt-8"> </span><span
11110 class="cmtt-8"> 3)</span><span
11111 class="cmtt-8"> iterate</span><span
11112 class="cmtt-8"> [j]</span><span
11113 class="cmtt-8"> over</span><span
11114 class="cmtt-8"> the</span><span
11115 class="cmtt-8"> range</span><span
11116 class="cmtt-8"> 0</span><span
11117 class="cmtt-8"> ...</span><span
11118 class="cmtt-8"> [codebook\_dimensions]-1</span><span
11119 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11120 id="x1-114008r4"></a><span
11121 class="cmr-6">4</span><span
11122 class="cmtt-8"> </span><span
11123 class="cmtt-8"> </span><br class="fancyvrb" /><a
11124 id="x1-114010r5"></a><span
11125 class="cmr-6">5</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"> 4)</span><span
11134 class="cmtt-8"> vector</span><span
11135 class="cmtt-8"> [v]</span><span
11136 class="cmtt-8"> element</span><span
11137 class="cmtt-8"> ([offset]+[i])</span><span
11138 class="cmtt-8"> =</span>
11139 <br class="fancyvrb" /><a
11140 id="x1-114012r6"></a><span
11141 class="cmr-6">6</span><span
11142 class="cmtt-8"> </span><span
11143 class="cmtt-8">  </span><span
11144 class="cmtt-8"> </span><span
11145 class="cmtt-8"> vector</span><span
11146 class="cmtt-8"> [v]</span><span
11147 class="cmtt-8"> element</span><span
11148 class="cmtt-8"> ([offset]+[i])</span><span
11149 class="cmtt-8"> +</span><br class="fancyvrb" /><a
11150 id="x1-114014r7"></a><span
11151 class="cmr-6">7</span><span
11152 class="cmtt-8"> </span><span
11153 class="cmtt-8"> </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"> vector</span><span
11164 class="cmtt-8"> [entry\_temp]</span><span
11165 class="cmtt-8"> element</span><span
11166 class="cmtt-8"> [j]</span><br class="fancyvrb" /><a
11167 id="x1-114016r8"></a><span
11168 class="cmr-6">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"> </span><span
11173 class="cmtt-8"> </span><span
11174 class="cmtt-8"> </span><span
11175 class="cmtt-8"> </span><span
11176 class="cmtt-8"> 5)</span><span
11177 class="cmtt-8"> increment</span><span
11178 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
11179 id="x1-114018r9"></a><span
11180 class="cmr-6">9</span><span
11181 class="cmtt-8"> </span><span
11182 class="cmtt-8"> </span>
11183 <br class="fancyvrb" /><a
11184 id="x1-114020r10"></a><span
11185 class="cmr-6">10</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><br class="fancyvrb" /><a
11192 id="x1-114022r11"></a><span
11193 class="cmr-6">11</span><span
11194 class="cmtt-8"> </span><span
11195 class="cmtt-8"> </span><br class="fancyvrb" /><a
11196 id="x1-114024r12"></a><span
11197 class="cmr-6">12</span><span
11198 class="cmtt-8"> </span><span
11199 class="cmtt-8"> </span><span
11200 class="cmtt-8"> </span><span
11201 class="cmtt-8"> 6)</span><span
11202 class="cmtt-8"> if</span><span
11203 class="cmtt-8"> (</span><span
11204 class="cmtt-8"> [i]</span><span
11205 class="cmtt-8"> is</span><span
11206 class="cmtt-8"> less</span><span
11207 class="cmtt-8"> than</span><span
11208 class="cmtt-8"> [n]</span><span
11209 class="cmtt-8"> )</span><span
11210 class="cmtt-8"> continue</span><span
11211 class="cmtt-8"> at</span><span
11212 class="cmtt-8"> step</span><span
11213 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
11214 id="x1-114026r13"></a><span
11215 class="cmr-6">13</span><span
11216 class="cmtt-8"> </span><span
11217 class="cmtt-8"> </span><span
11218 class="cmtt-8"> </span><span
11219 class="cmtt-8"> 7)</span><span
11220 class="cmtt-8"> done</span></div>
11221 <!--l. 416--><p class="noindent" >
11222 <h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a
11223 id="x1-1150008.6.5"></a>format 2 specifics</h5>
11227 <!--l. 418--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
11228 additional post-decode step after a normal format 1 decode.
11229 <!--l. 421--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
11230 ’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
11231 the vectors are decoded. We then request normal format 1 to decode a single vector
11232 representing all output channels, rather than a vector for each channel. After decode,
11233 deinterleave the vector into independent vectors, one for each output channel. That
11235 <!--l. 429--><p class="noindent" >
11236 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
11238 class="enumerate-enumitem">If all vectors 0 through <span
11239 class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
11241 class="cmtt-12">[v]</span>of length <span
11242 class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
11244 </dd><dt class="enumerate-enumitem">
11246 class="enumerate-enumitem">Rather than performing format 1 decode to produce <span
11247 class="cmti-12">ch </span>vectors of length <span
11248 class="cmti-12">n </span>each, call
11249 format 1 decode to produce a single vector <span
11250 class="cmtt-12">[v] </span>of length <span
11251 class="cmti-12">ch*n</span>.
11252 </dd><dt class="enumerate-enumitem">
11254 class="enumerate-enumitem">Post decode: Deinterleave the single vector <span
11255 class="cmtt-12">[v] </span>returned by format 1 decode as
11256 described above into <span
11257 class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
11259 <div class="fancyvrb" id="fancyvrb43"><a
11260 id="x1-115005r1"></a><span
11261 class="cmr-6">1</span><span
11262 class="cmtt-8"> </span><span
11263 class="cmtt-8"> </span><span
11264 class="cmtt-8"> </span><span
11265 class="cmtt-8"> 1)</span><span
11266 class="cmtt-8"> iterate</span><span
11267 class="cmtt-8"> [i]</span><span
11268 class="cmtt-8"> over</span><span
11269 class="cmtt-8"> the</span><span
11270 class="cmtt-8"> range</span><span
11271 class="cmtt-8"> 0</span><span
11272 class="cmtt-8"> ...</span><span
11273 class="cmtt-8"> [n]-1</span><span
11274 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11275 id="x1-115007r2"></a><span
11276 class="cmr-6">2</span><span
11277 class="cmtt-8"> </span><span
11278 class="cmtt-8"> </span><br class="fancyvrb" /><a
11279 id="x1-115009r3"></a><span
11280 class="cmr-6">3</span><span
11281 class="cmtt-8"> </span><span
11282 class="cmtt-8"> </span><span
11283 class="cmtt-8"> </span><span
11284 class="cmtt-8"> </span><span
11285 class="cmtt-8"> </span><span
11286 class="cmtt-8"> </span><span
11287 class="cmtt-8"> </span><span
11288 class="cmtt-8"> </span><span
11289 class="cmtt-8"> 2)</span><span
11290 class="cmtt-8"> iterate</span><span
11291 class="cmtt-8"> [j]</span><span
11292 class="cmtt-8"> over</span><span
11293 class="cmtt-8"> the</span><span
11294 class="cmtt-8"> range</span><span
11295 class="cmtt-8"> 0</span><span
11296 class="cmtt-8"> ...</span><span
11297 class="cmtt-8"> [ch]-1</span><span
11298 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11299 id="x1-115011r4"></a><span
11300 class="cmr-6">4</span><span
11301 class="cmtt-8"> </span><span
11302 class="cmtt-8"> </span>
11303 <br class="fancyvrb" /><a
11304 id="x1-115013r5"></a><span
11305 class="cmr-6">5</span><span
11306 class="cmtt-8"> </span><span
11307 class="cmtt-8"> </span><span
11308 class="cmtt-8"> </span><span
11309 class="cmtt-8"> </span><span
11310 class="cmtt-8"> </span><span
11311 class="cmtt-8"> </span><span
11312 class="cmtt-8"> </span><span
11313 class="cmtt-8"> </span><span
11314 class="cmtt-8"> </span><span
11315 class="cmtt-8"> </span><span
11316 class="cmtt-8"> </span><span
11317 class="cmtt-8"> </span><span
11318 class="cmtt-8"> </span><span
11319 class="cmtt-8"> 3)</span><span
11320 class="cmtt-8"> output</span><span
11321 class="cmtt-8"> vector</span><span
11322 class="cmtt-8"> number</span><span
11323 class="cmtt-8"> [j]</span><span
11324 class="cmtt-8"> element</span><span
11325 class="cmtt-8"> [i]</span><span
11326 class="cmtt-8"> =</span><span
11327 class="cmtt-8"> vector</span><span
11328 class="cmtt-8"> [v]</span><span
11329 class="cmtt-8"> element</span><span
11330 class="cmtt-8"> ([i]</span><span
11331 class="cmtt-8"> *</span><span
11332 class="cmtt-8"> [ch]</span><span
11333 class="cmtt-8"> +</span><span
11334 class="cmtt-8"> [j])</span><br class="fancyvrb" /><a
11335 id="x1-115015r6"></a><span
11336 class="cmr-6">6</span><span
11337 class="cmtt-8"> </span><span
11338 class="cmtt-8"> </span><br class="fancyvrb" /><a
11339 id="x1-115017r7"></a><span
11340 class="cmr-6">7</span><span
11341 class="cmtt-8"> </span><span
11342 class="cmtt-8"> </span><span
11343 class="cmtt-8"> </span><span
11344 class="cmtt-8"> </span><span
11345 class="cmtt-8"> </span><span
11346 class="cmtt-8"> </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><br class="fancyvrb" /><a
11353 id="x1-115019r8"></a><span
11354 class="cmr-6">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"> </span><span
11360 class="cmtt-8"> </span><span
11361 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11362 id="x1-115021r9"></a><span
11363 class="cmr-6">9</span><span
11364 class="cmtt-8"> </span><span
11365 class="cmtt-8"> </span><br class="fancyvrb" /><a
11366 id="x1-115023r10"></a><span
11367 class="cmr-6">10</span><span
11368 class="cmtt-8"> </span><span
11369 class="cmtt-8"> </span><span
11370 class="cmtt-8"> </span><span
11371 class="cmtt-8"> 4)</span><span
11372 class="cmtt-8"> done</span></div>
11380 <h3 class="sectionHead"><span class="titlemark">9. </span> <a
11381 id="x1-1160009"></a>Helper equations</h3>
11382 <!--l. 6--><p class="noindent" >
11383 <h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a
11384 id="x1-1170009.1"></a>Overview</h4>
11385 <!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
11386 cluttering up the main specification documents, they are defined here and referenced where
11388 <!--l. 13--><p class="noindent" >
11389 <h4 class="subsectionHead"><span class="titlemark">9.2. </span> <a
11390 id="x1-1180009.2"></a>Functions</h4>
11391 <!--l. 15--><p class="noindent" >
11392 <h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a
11393 id="x1-1190009.2.1"></a>ilog</h5>
11394 <!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
11395 two’s complement integer value <span
11396 class="cmtt-12">[x]</span>. Values of <span
11397 class="cmtt-12">[x] </span>less than zero are defined to return
11399 <!--l. 20--><p class="noindent" >
11400 <div class="fancyvrb" id="fancyvrb44"><a
11401 id="x1-119002r1"></a><span
11402 class="cmr-6">1</span><span
11403 class="cmtt-8"> </span><span
11404 class="cmtt-8"> </span><span
11405 class="cmtt-8"> </span><span
11406 class="cmtt-8"> 1)</span><span
11407 class="cmtt-8"> [return\_value]</span><span
11408 class="cmtt-8"> =</span><span
11409 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
11410 id="x1-119004r2"></a><span
11411 class="cmr-6">2</span><span
11412 class="cmtt-8"> </span><span
11413 class="cmtt-8"> </span><span
11414 class="cmtt-8"> </span><span
11415 class="cmtt-8"> 2)</span><span
11416 class="cmtt-8"> if</span><span
11417 class="cmtt-8"> (</span><span
11418 class="cmtt-8"> [x]</span><span
11419 class="cmtt-8"> is</span><span
11420 class="cmtt-8"> greater</span><span
11421 class="cmtt-8"> than</span><span
11422 class="cmtt-8"> zero</span><span
11423 class="cmtt-8"> )</span><span
11424 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11425 id="x1-119006r3"></a><span
11426 class="cmr-6">3</span><span
11427 class="cmtt-8"> </span><span
11428 class="cmtt-8"> </span><br class="fancyvrb" /><a
11429 id="x1-119008r4"></a><span
11430 class="cmr-6">4</span><span
11431 class="cmtt-8"> </span><span
11432 class="cmtt-8"> </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><span
11439 class="cmtt-8"> 3)</span><span
11440 class="cmtt-8"> increment</span><span
11441 class="cmtt-8"> [return\_value];</span>
11442 <br class="fancyvrb" /><a
11443 id="x1-119010r5"></a><span
11444 class="cmr-6">5</span><span
11445 class="cmtt-8"> </span><span
11446 class="cmtt-8"> </span><span
11447 class="cmtt-8"> </span><span
11448 class="cmtt-8"> </span><span
11449 class="cmtt-8"> </span><span
11450 class="cmtt-8"> </span><span
11451 class="cmtt-8"> </span><span
11452 class="cmtt-8"> </span><span
11453 class="cmtt-8"> 4)</span><span
11454 class="cmtt-8"> logical</span><span
11455 class="cmtt-8"> shift</span><span
11456 class="cmtt-8"> [x]</span><span
11457 class="cmtt-8"> one</span><span
11458 class="cmtt-8"> bit</span><span
11459 class="cmtt-8"> to</span><span
11460 class="cmtt-8"> the</span><span
11461 class="cmtt-8"> right,</span><span
11462 class="cmtt-8"> padding</span><span
11463 class="cmtt-8"> the</span><span
11464 class="cmtt-8"> MSb</span><span
11465 class="cmtt-8"> with</span><span
11466 class="cmtt-8"> zero</span><br class="fancyvrb" /><a
11467 id="x1-119012r6"></a><span
11468 class="cmr-6">6</span><span
11469 class="cmtt-8"> </span><span
11470 class="cmtt-8"> </span><span
11471 class="cmtt-8"> </span><span
11472 class="cmtt-8"> </span><span
11473 class="cmtt-8"> </span><span
11474 class="cmtt-8"> </span><span
11475 class="cmtt-8"> </span><span
11476 class="cmtt-8"> </span><span
11477 class="cmtt-8"> 5)</span><span
11478 class="cmtt-8"> repeat</span><span
11479 class="cmtt-8"> at</span><span
11480 class="cmtt-8"> step</span><span
11481 class="cmtt-8"> 2)</span><br class="fancyvrb" /><a
11482 id="x1-119014r7"></a><span
11483 class="cmr-6">7</span><span
11484 class="cmtt-8"> </span><span
11485 class="cmtt-8"> </span><br class="fancyvrb" /><a
11486 id="x1-119016r8"></a><span
11487 class="cmr-6">8</span><span
11488 class="cmtt-8"> </span><span
11489 class="cmtt-8"> </span><span
11490 class="cmtt-8"> </span><span
11491 class="cmtt-8"> </span><span
11492 class="cmtt-8"> </span><span
11493 class="cmtt-8"> </span><span
11494 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11495 id="x1-119018r9"></a><span
11496 class="cmr-6">9</span><span
11497 class="cmtt-8"> </span><span
11498 class="cmtt-8"> </span><br class="fancyvrb" /><a
11499 id="x1-119020r10"></a><span
11500 class="cmr-6">10</span><span
11501 class="cmtt-8"> </span><span
11502 class="cmtt-8"> </span><span
11503 class="cmtt-8"> </span><span
11504 class="cmtt-8"> </span><span
11505 class="cmtt-8"> 6)</span><span
11506 class="cmtt-8"> done</span></div>
11507 <!--l. 33--><p class="noindent" >Examples:
11508 <ul class="itemize1">
11509 <li class="itemize">ilog(0) = 0;
11511 <li class="itemize">ilog(1) = 1;
11516 <li class="itemize">ilog(2) = 2;
11518 <li class="itemize">ilog(3) = 2;
11520 <li class="itemize">ilog(4) = 3;
11522 <li class="itemize">ilog(7) = 3;
11524 <li class="itemize">ilog(negative number) = 0;</li></ul>
11525 <!--l. 48--><p class="noindent" >
11526 <h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a
11527 id="x1-1200009.2.2"></a>float32_unpack</h5>
11528 <!--l. 50--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis
11529 codebook float value into the representation used by the decoder for floating point numbers. For
11530 purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
11532 <!--l. 56--><p class="noindent" >
11533 <div class="fancyvrb" id="fancyvrb45"><a
11534 id="x1-120002r1"></a><span
11535 class="cmr-6">1</span><span
11536 class="cmtt-8"> </span><span
11537 class="cmtt-8"> </span><span
11538 class="cmtt-8"> </span><span
11539 class="cmtt-8"> 1)</span><span
11540 class="cmtt-8"> [mantissa]</span><span
11541 class="cmtt-8"> =</span><span
11542 class="cmtt-8"> [x]</span><span
11543 class="cmtt-8"> bitwise</span><span
11544 class="cmtt-8"> AND</span><span
11545 class="cmtt-8"> 0x1fffff</span><span
11546 class="cmtt-8"> (unsigned</span><span
11547 class="cmtt-8"> result)</span><br class="fancyvrb" /><a
11548 id="x1-120004r2"></a><span
11549 class="cmr-6">2</span><span
11550 class="cmtt-8"> </span><span
11551 class="cmtt-8"> </span><span
11552 class="cmtt-8"> </span><span
11553 class="cmtt-8"> 2)</span><span
11554 class="cmtt-8"> [sign]</span><span
11555 class="cmtt-8"> =</span><span
11556 class="cmtt-8"> [x]</span><span
11557 class="cmtt-8"> bitwise</span><span
11558 class="cmtt-8"> AND</span><span
11559 class="cmtt-8"> 0x80000000</span><span
11560 class="cmtt-8"> (unsigned</span><span
11561 class="cmtt-8"> result)</span>
11562 <br class="fancyvrb" /><a
11563 id="x1-120006r3"></a><span
11564 class="cmr-6">3</span><span
11565 class="cmtt-8"> </span><span
11566 class="cmtt-8"> </span><span
11567 class="cmtt-8"> </span><span
11568 class="cmtt-8"> 3)</span><span
11569 class="cmtt-8"> [exponent]</span><span
11570 class="cmtt-8"> =</span><span
11571 class="cmtt-8"> (</span><span
11572 class="cmtt-8"> [x]</span><span
11573 class="cmtt-8"> bitwise</span><span
11574 class="cmtt-8"> AND</span><span
11575 class="cmtt-8"> 0x7fe00000)</span><span
11576 class="cmtt-8"> shifted</span><span
11577 class="cmtt-8"> right</span><span
11578 class="cmtt-8"> 21</span><span
11579 class="cmtt-8"> bits</span><span
11580 class="cmtt-8"> (unsigned</span><span
11581 class="cmtt-8"> result)</span>
11582 <br class="fancyvrb" /><a
11583 id="x1-120008r4"></a><span
11584 class="cmr-6">4</span><span
11585 class="cmtt-8"> </span><span
11586 class="cmtt-8"> </span><span
11587 class="cmtt-8"> </span><span
11588 class="cmtt-8"> 4)</span><span
11589 class="cmtt-8"> if</span><span
11590 class="cmtt-8"> (</span><span
11591 class="cmtt-8"> [sign]</span><span
11592 class="cmtt-8"> is</span><span
11593 class="cmtt-8"> nonzero</span><span
11594 class="cmtt-8"> )</span><span
11595 class="cmtt-8"> then</span><span
11596 class="cmtt-8"> negate</span><span
11597 class="cmtt-8"> [mantissa]</span><br class="fancyvrb" /><a
11598 id="x1-120010r5"></a><span
11599 class="cmr-6">5</span><span
11600 class="cmtt-8"> </span><span
11601 class="cmtt-8"> </span><span
11602 class="cmtt-8"> </span><span
11603 class="cmtt-8"> 5)</span><span
11604 class="cmtt-8"> return</span><span
11605 class="cmtt-8"> [mantissa]</span><span
11606 class="cmtt-8"> *</span><span
11607 class="cmtt-8"> (</span><span
11608 class="cmtt-8"> 2</span><span
11609 class="cmtt-8"> ^</span><span
11610 class="cmtt-8"> (</span><span
11611 class="cmtt-8"> [exponent]</span><span
11612 class="cmtt-8"> -</span><span
11613 class="cmtt-8"> 788</span><span
11614 class="cmtt-8"> )</span><span
11615 class="cmtt-8"> )</span></div>
11616 <!--l. 66--><p class="noindent" >
11617 <h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a
11618 id="x1-1210009.2.3"></a>lookup1_values</h5>
11619 <!--l. 68--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the
11620 correct length of the value index for a codebook VQ lookup table of lookup type 1.
11621 The values on this list are permuted to construct the VQ vector lookup table of size
11623 class="cmtt-12">[codebook_entries]</span>.
11624 <!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
11626 class="cmtt-12">[return_value] </span>to the power of <span
11627 class="cmtt-12">[codebook_dimensions] </span>is less than or equal to
11629 class="cmtt-12">[codebook_entries]</span>’.
11633 <!--l. 81--><p class="noindent" >
11634 <h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a
11635 id="x1-1220009.2.4"></a>low_neighbor</h5>
11636 <!--l. 83--><p class="noindent" >”low_neighbor(v,x)” finds the position <span
11637 class="cmtt-12">n </span>in vector <span
11638 class="cmtt-12">[v] </span>of the greatest value scalar element for
11640 class="cmtt-12">n </span>is less than <span
11641 class="cmtt-12">[x] </span>and vector <span
11642 class="cmtt-12">[v] </span>element <span
11643 class="cmtt-12">n </span>is less than vector <span
11644 class="cmtt-12">[v] </span>element
11646 class="cmtt-12">[x]</span>.
11647 <!--l. 88--><p class="noindent" >
11648 <h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a
11649 id="x1-1230009.2.5"></a>high_neighbor</h5>
11650 <!--l. 90--><p class="noindent" >”high_neighbor(v,x)” finds the position <span
11651 class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
11653 class="cmtt-12">n </span>is less than <span
11654 class="cmtt-12">[x] </span>and vector <span
11655 class="cmtt-12">[v] </span>element <span
11656 class="cmtt-12">n </span>is greater than vector <span
11657 class="cmtt-12">[v] </span>element
11659 class="cmtt-12">[x]</span>.
11660 <!--l. 97--><p class="noindent" >
11661 <h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a
11662 id="x1-1240009.2.6"></a>render_point</h5>
11663 <!--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
11664 x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
11665 calculating intervening values along the line.
11666 <!--l. 104--><p class="noindent" >
11667 <div class="fancyvrb" id="fancyvrb46"><a
11668 id="x1-124002r1"></a><span
11669 class="cmr-6">1</span><span
11670 class="cmtt-8"> </span><span
11671 class="cmtt-8"> </span><span
11672 class="cmtt-8"> </span><span
11673 class="cmtt-8"> 1)</span><span
11674 class="cmtt-8"> </span><span
11675 class="cmtt-8"> [dy]</span><span
11676 class="cmtt-8"> =</span><span
11677 class="cmtt-8"> [y1]</span><span
11678 class="cmtt-8"> -</span><span
11679 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11680 id="x1-124004r2"></a><span
11681 class="cmr-6">2</span><span
11682 class="cmtt-8"> </span><span
11683 class="cmtt-8"> </span><span
11684 class="cmtt-8"> </span><span
11685 class="cmtt-8"> 2)</span><span
11686 class="cmtt-8"> [adx]</span><span
11687 class="cmtt-8"> =</span><span
11688 class="cmtt-8"> [x1]</span><span
11689 class="cmtt-8"> -</span><span
11690 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11691 id="x1-124006r3"></a><span
11692 class="cmr-6">3</span><span
11693 class="cmtt-8"> </span><span
11694 class="cmtt-8"> </span><span
11695 class="cmtt-8"> </span><span
11696 class="cmtt-8"> 3)</span><span
11697 class="cmtt-8"> [ady]</span><span
11698 class="cmtt-8"> =</span><span
11699 class="cmtt-8"> absolute</span><span
11700 class="cmtt-8"> value</span><span
11701 class="cmtt-8"> of</span><span
11702 class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a
11703 id="x1-124008r4"></a><span
11704 class="cmr-6">4</span><span
11705 class="cmtt-8"> </span><span
11706 class="cmtt-8"> </span><span
11707 class="cmtt-8"> </span><span
11708 class="cmtt-8"> 4)</span><span
11709 class="cmtt-8"> [err]</span><span
11710 class="cmtt-8"> =</span><span
11711 class="cmtt-8"> [ady]</span><span
11712 class="cmtt-8"> *</span><span
11713 class="cmtt-8"> ([X]</span><span
11714 class="cmtt-8"> -</span><span
11715 class="cmtt-8"> [x0])</span>
11716 <br class="fancyvrb" /><a
11717 id="x1-124010r5"></a><span
11718 class="cmr-6">5</span><span
11719 class="cmtt-8"> </span><span
11720 class="cmtt-8"> </span><span
11721 class="cmtt-8"> </span><span
11722 class="cmtt-8"> 5)</span><span
11723 class="cmtt-8"> [off]</span><span
11724 class="cmtt-8"> =</span><span
11725 class="cmtt-8"> [err]</span><span
11726 class="cmtt-8"> /</span><span
11727 class="cmtt-8"> [adx]</span><span
11728 class="cmtt-8"> using</span><span
11729 class="cmtt-8"> integer</span><span
11730 class="cmtt-8"> division</span><br class="fancyvrb" /><a
11731 id="x1-124012r6"></a><span
11732 class="cmr-6">6</span><span
11733 class="cmtt-8"> </span><span
11734 class="cmtt-8"> </span><span
11735 class="cmtt-8"> </span><span
11736 class="cmtt-8"> 6)</span><span
11737 class="cmtt-8"> if</span><span
11738 class="cmtt-8"> (</span><span
11739 class="cmtt-8"> [dy]</span><span
11740 class="cmtt-8"> is</span><span
11741 class="cmtt-8"> less</span><span
11742 class="cmtt-8"> than</span><span
11743 class="cmtt-8"> zero</span><span
11744 class="cmtt-8"> )</span><span
11745 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11746 id="x1-124014r7"></a><span
11747 class="cmr-6">7</span><span
11748 class="cmtt-8"> </span><span
11749 class="cmtt-8"> </span><br class="fancyvrb" /><a
11750 id="x1-124016r8"></a><span
11751 class="cmr-6">8</span><span
11752 class="cmtt-8"> </span><span
11753 class="cmtt-8"> </span><span
11754 class="cmtt-8"> </span><span
11755 class="cmtt-8"> </span><span
11756 class="cmtt-8"> </span><span
11757 class="cmtt-8"> </span><span
11758 class="cmtt-8"> </span><span
11759 class="cmtt-8"> </span><span
11760 class="cmtt-8"> 7)</span><span
11761 class="cmtt-8"> [Y]</span><span
11762 class="cmtt-8"> =</span><span
11763 class="cmtt-8"> [y0]</span><span
11764 class="cmtt-8"> -</span><span
11765 class="cmtt-8"> [off]</span>
11766 <br class="fancyvrb" /><a
11767 id="x1-124018r9"></a><span
11768 class="cmr-6">9</span><span
11769 class="cmtt-8"> </span><span
11770 class="cmtt-8"> </span><br class="fancyvrb" /><a
11771 id="x1-124020r10"></a><span
11772 class="cmr-6">10</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><span
11779 class="cmtt-8"> }</span><span
11780 class="cmtt-8"> else</span><span
11781 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11782 id="x1-124022r11"></a><span
11783 class="cmr-6">11</span><span
11784 class="cmtt-8"> </span><span
11785 class="cmtt-8"> </span><br class="fancyvrb" /><a
11786 id="x1-124024r12"></a><span
11787 class="cmr-6">12</span><span
11788 class="cmtt-8"> </span><span
11789 class="cmtt-8"> </span><span
11790 class="cmtt-8"> </span><span
11791 class="cmtt-8"> </span><span
11792 class="cmtt-8"> </span><span
11793 class="cmtt-8"> </span><span
11794 class="cmtt-8"> </span><span
11795 class="cmtt-8"> </span><span
11796 class="cmtt-8"> 8)</span><span
11797 class="cmtt-8"> [Y]</span><span
11798 class="cmtt-8"> =</span><span
11799 class="cmtt-8"> [y0]</span><span
11800 class="cmtt-8"> +</span><span
11801 class="cmtt-8"> [off]</span><br class="fancyvrb" /><a
11802 id="x1-124026r13"></a><span
11803 class="cmr-6">13</span><span
11804 class="cmtt-8"> </span><span
11805 class="cmtt-8"> </span><br class="fancyvrb" /><a
11806 id="x1-124028r14"></a><span
11807 class="cmr-6">14</span><span
11808 class="cmtt-8"> </span><span
11809 class="cmtt-8"> </span><span
11810 class="cmtt-8"> </span><span
11811 class="cmtt-8"> </span><span
11812 class="cmtt-8"> </span><span
11813 class="cmtt-8"> </span><span
11814 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11815 id="x1-124030r15"></a><span
11816 class="cmr-6">15</span><span
11817 class="cmtt-8"> </span><span
11818 class="cmtt-8"> </span><br class="fancyvrb" /><a
11819 id="x1-124032r16"></a><span
11820 class="cmr-6">16</span><span
11821 class="cmtt-8"> </span><span
11822 class="cmtt-8"> </span><span
11823 class="cmtt-8"> </span><span
11824 class="cmtt-8"> 9)</span><span
11825 class="cmtt-8"> done</span></div>
11826 <!--l. 125--><p class="noindent" >
11827 <h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a
11828 id="x1-1250009.2.7"></a>render_line</h5>
11832 <!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)”
11833 to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
11834 been relevant elsewhere, but here we must define integer division as rounding division of both
11835 positive and negative numbers toward zero.
11836 <!--l. 134--><p class="noindent" >
11837 <div class="fancyvrb" id="fancyvrb47"><a
11838 id="x1-125002r1"></a><span
11839 class="cmr-6">1</span><span
11840 class="cmtt-8"> </span><span
11841 class="cmtt-8"> </span><span
11842 class="cmtt-8"> </span><span
11843 class="cmtt-8"> 1)</span><span
11844 class="cmtt-8"> </span><span
11845 class="cmtt-8"> </span><span
11846 class="cmtt-8"> [dy]</span><span
11847 class="cmtt-8"> =</span><span
11848 class="cmtt-8"> [y1]</span><span
11849 class="cmtt-8"> -</span><span
11850 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11851 id="x1-125004r2"></a><span
11852 class="cmr-6">2</span><span
11853 class="cmtt-8"> </span><span
11854 class="cmtt-8"> </span><span
11855 class="cmtt-8"> </span><span
11856 class="cmtt-8"> 2)</span><span
11857 class="cmtt-8"> </span><span
11858 class="cmtt-8"> [adx]</span><span
11859 class="cmtt-8"> =</span><span
11860 class="cmtt-8"> [x1]</span><span
11861 class="cmtt-8"> -</span><span
11862 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11863 id="x1-125006r3"></a><span
11864 class="cmr-6">3</span><span
11865 class="cmtt-8"> </span><span
11866 class="cmtt-8"> </span><span
11867 class="cmtt-8"> </span><span
11868 class="cmtt-8"> 3)</span><span
11869 class="cmtt-8"> </span><span
11870 class="cmtt-8"> [ady]</span><span
11871 class="cmtt-8"> =</span><span
11872 class="cmtt-8"> absolute</span><span
11873 class="cmtt-8"> value</span><span
11874 class="cmtt-8"> of</span><span
11875 class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a
11876 id="x1-125008r4"></a><span
11877 class="cmr-6">4</span><span
11878 class="cmtt-8"> </span><span
11879 class="cmtt-8"> </span><span
11880 class="cmtt-8"> </span><span
11881 class="cmtt-8"> 4)</span><span
11882 class="cmtt-8"> [base]</span><span
11883 class="cmtt-8"> =</span><span
11884 class="cmtt-8"> [dy]</span><span
11885 class="cmtt-8"> /</span><span
11886 class="cmtt-8"> [adx]</span><span
11887 class="cmtt-8"> using</span><span
11888 class="cmtt-8"> integer</span><span
11889 class="cmtt-8"> division</span>
11890 <br class="fancyvrb" /><a
11891 id="x1-125010r5"></a><span
11892 class="cmr-6">5</span><span
11893 class="cmtt-8"> </span><span
11894 class="cmtt-8"> </span><span
11895 class="cmtt-8"> </span><span
11896 class="cmtt-8"> 5)</span><span
11897 class="cmtt-8"> </span><span
11898 class="cmtt-8"> </span><span
11899 class="cmtt-8"> </span><span
11900 class="cmtt-8"> [x]</span><span
11901 class="cmtt-8"> =</span><span
11902 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11903 id="x1-125012r6"></a><span
11904 class="cmr-6">6</span><span
11905 class="cmtt-8"> </span><span
11906 class="cmtt-8"> </span><span
11907 class="cmtt-8"> </span><span
11908 class="cmtt-8"> 6)</span><span
11909 class="cmtt-8"> </span><span
11910 class="cmtt-8"> </span><span
11911 class="cmtt-8"> </span><span
11912 class="cmtt-8"> [y]</span><span
11913 class="cmtt-8"> =</span><span
11914 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11915 id="x1-125014r7"></a><span
11916 class="cmr-6">7</span><span
11917 class="cmtt-8"> </span><span
11918 class="cmtt-8"> </span><span
11919 class="cmtt-8"> </span><span
11920 class="cmtt-8"> 7)</span><span
11921 class="cmtt-8"> </span><span
11922 class="cmtt-8"> [err]</span><span
11923 class="cmtt-8"> =</span><span
11924 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
11925 id="x1-125016r8"></a><span
11926 class="cmr-6">8</span><span
11927 class="cmtt-8"> </span><span
11928 class="cmtt-8"> </span><br class="fancyvrb" /><a
11929 id="x1-125018r9"></a><span
11930 class="cmr-6">9</span><span
11931 class="cmtt-8"> </span><span
11932 class="cmtt-8"> </span><span
11933 class="cmtt-8"> </span><span
11934 class="cmtt-8"> 8)</span><span
11935 class="cmtt-8"> if</span><span
11936 class="cmtt-8"> (</span><span
11937 class="cmtt-8"> [dy]</span><span
11938 class="cmtt-8"> is</span><span
11939 class="cmtt-8"> less</span><span
11940 class="cmtt-8"> than</span><span
11941 class="cmtt-8"> 0</span><span
11942 class="cmtt-8"> )</span><span
11943 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11944 id="x1-125020r10"></a><span
11945 class="cmr-6">10</span><span
11946 class="cmtt-8"> </span><span
11947 class="cmtt-8"> </span><br class="fancyvrb" /><a
11948 id="x1-125022r11"></a><span
11949 class="cmr-6">11</span><span
11950 class="cmtt-8"> </span><span
11951 class="cmtt-8"> </span><span
11952 class="cmtt-8"> </span><span
11953 class="cmtt-8"> </span><span
11954 class="cmtt-8"> </span><span
11955 class="cmtt-8"> </span><span
11956 class="cmtt-8"> </span><span
11957 class="cmtt-8"> </span><span
11958 class="cmtt-8"> </span><span
11959 class="cmtt-8"> 9)</span><span
11960 class="cmtt-8"> [sy]</span><span
11961 class="cmtt-8"> =</span><span
11962 class="cmtt-8"> [base]</span><span
11963 class="cmtt-8"> -</span><span
11964 class="cmtt-8"> 1</span>
11965 <br class="fancyvrb" /><a
11966 id="x1-125024r12"></a><span
11967 class="cmr-6">12</span><span
11968 class="cmtt-8"> </span><span
11969 class="cmtt-8"> </span><br class="fancyvrb" /><a
11970 id="x1-125026r13"></a><span
11971 class="cmr-6">13</span><span
11972 class="cmtt-8"> </span><span
11973 class="cmtt-8"> </span><span
11974 class="cmtt-8"> </span><span
11975 class="cmtt-8"> </span><span
11976 class="cmtt-8"> </span><span
11977 class="cmtt-8"> </span><span
11978 class="cmtt-8"> }</span><span
11979 class="cmtt-8"> else</span><span
11980 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11981 id="x1-125028r14"></a><span
11982 class="cmr-6">14</span><span
11983 class="cmtt-8"> </span><span
11984 class="cmtt-8"> </span><br class="fancyvrb" /><a
11985 id="x1-125030r15"></a><span
11986 class="cmr-6">15</span><span
11987 class="cmtt-8"> </span><span
11988 class="cmtt-8"> </span><span
11989 class="cmtt-8"> </span><span
11990 class="cmtt-8"> </span><span
11991 class="cmtt-8"> </span><span
11992 class="cmtt-8"> </span><span
11993 class="cmtt-8"> </span><span
11994 class="cmtt-8"> </span><span
11995 class="cmtt-8"> 10)</span><span
11996 class="cmtt-8"> [sy]</span><span
11997 class="cmtt-8"> =</span><span
11998 class="cmtt-8"> [base]</span><span
11999 class="cmtt-8"> +</span><span
12000 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
12001 id="x1-125032r16"></a><span
12002 class="cmr-6">16</span><span
12003 class="cmtt-8"> </span><span
12004 class="cmtt-8"> </span><br class="fancyvrb" /><a
12005 id="x1-125034r17"></a><span
12006 class="cmr-6">17</span><span
12007 class="cmtt-8"> </span><span
12008 class="cmtt-8"> </span><span
12009 class="cmtt-8"> </span><span
12010 class="cmtt-8"> </span><span
12011 class="cmtt-8"> </span><span
12012 class="cmtt-8"> </span><span
12013 class="cmtt-8"> }</span><br class="fancyvrb" /><a
12014 id="x1-125036r18"></a><span
12015 class="cmr-6">18</span><span
12016 class="cmtt-8"> </span><span
12017 class="cmtt-8"> </span><br class="fancyvrb" /><a
12018 id="x1-125038r19"></a><span
12019 class="cmr-6">19</span><span
12020 class="cmtt-8"> </span><span
12021 class="cmtt-8"> </span><span
12022 class="cmtt-8"> 11)</span><span
12023 class="cmtt-8"> [ady]</span><span
12024 class="cmtt-8"> =</span><span
12025 class="cmtt-8"> [ady]</span><span
12026 class="cmtt-8"> -</span><span
12027 class="cmtt-8"> (absolute</span><span
12028 class="cmtt-8"> value</span><span
12029 class="cmtt-8"> of</span><span
12030 class="cmtt-8"> [base])</span><span
12031 class="cmtt-8"> *</span><span
12032 class="cmtt-8"> [adx]</span>
12033 <br class="fancyvrb" /><a
12034 id="x1-125040r20"></a><span
12035 class="cmr-6">20</span><span
12036 class="cmtt-8"> </span><span
12037 class="cmtt-8"> </span><span
12038 class="cmtt-8"> 12)</span><span
12039 class="cmtt-8"> vector</span><span
12040 class="cmtt-8"> [v]</span><span
12041 class="cmtt-8"> element</span><span
12042 class="cmtt-8"> [x]</span><span
12043 class="cmtt-8"> =</span><span
12044 class="cmtt-8"> [y]</span><br class="fancyvrb" /><a
12045 id="x1-125042r21"></a><span
12046 class="cmr-6">21</span><span
12047 class="cmtt-8"> </span><span
12048 class="cmtt-8"> </span><br class="fancyvrb" /><a
12049 id="x1-125044r22"></a><span
12050 class="cmr-6">22</span><span
12051 class="cmtt-8"> </span><span
12052 class="cmtt-8"> </span><span
12053 class="cmtt-8"> 13)</span><span
12054 class="cmtt-8"> iterate</span><span
12055 class="cmtt-8"> [x]</span><span
12056 class="cmtt-8"> over</span><span
12057 class="cmtt-8"> the</span><span
12058 class="cmtt-8"> range</span><span
12059 class="cmtt-8"> [x0]+1</span><span
12060 class="cmtt-8"> ...</span><span
12061 class="cmtt-8"> [x1]-1</span><span
12062 class="cmtt-8"> {</span><br class="fancyvrb" /><a
12063 id="x1-125046r23"></a><span
12064 class="cmr-6">23</span><span
12065 class="cmtt-8"> </span><span
12066 class="cmtt-8"> </span><br class="fancyvrb" /><a
12067 id="x1-125048r24"></a><span
12068 class="cmr-6">24</span><span
12069 class="cmtt-8"> </span><span
12070 class="cmtt-8"> </span><span
12071 class="cmtt-8"> </span><span
12072 class="cmtt-8"> </span><span
12073 class="cmtt-8"> </span><span
12074 class="cmtt-8"> </span><span
12075 class="cmtt-8"> </span><span
12076 class="cmtt-8"> </span><span
12077 class="cmtt-8"> 14)</span><span
12078 class="cmtt-8"> [err]</span><span
12079 class="cmtt-8"> =</span><span
12080 class="cmtt-8"> [err]</span><span
12081 class="cmtt-8"> +</span><span
12082 class="cmtt-8"> [ady];</span>
12083 <br class="fancyvrb" /><a
12084 id="x1-125050r25"></a><span
12085 class="cmr-6">25</span><span
12086 class="cmtt-8"> </span><span
12087 class="cmtt-8"> </span><span
12088 class="cmtt-8"> </span><span
12089 class="cmtt-8"> </span><span
12090 class="cmtt-8"> </span><span
12091 class="cmtt-8"> </span><span
12092 class="cmtt-8"> </span><span
12093 class="cmtt-8"> </span><span
12094 class="cmtt-8"> 15)</span><span
12095 class="cmtt-8"> if</span><span
12096 class="cmtt-8"> (</span><span
12097 class="cmtt-8"> [err]</span><span
12098 class="cmtt-8"> >=</span><span
12099 class="cmtt-8"> [adx]</span><span
12100 class="cmtt-8"> )</span><span
12101 class="cmtt-8"> {</span><br class="fancyvrb" /><a
12102 id="x1-125052r26"></a><span
12103 class="cmr-6">26</span><span
12104 class="cmtt-8"> </span><span
12105 class="cmtt-8"> </span><br class="fancyvrb" /><a
12106 id="x1-125054r27"></a><span
12107 class="cmr-6">27</span><span
12108 class="cmtt-8"> </span><span
12109 class="cmtt-8"> </span><span
12110 class="cmtt-8"> </span><span
12111 class="cmtt-8"> </span><span
12112 class="cmtt-8"> </span><span
12113 class="cmtt-8"> </span><span
12114 class="cmtt-8"> </span><span
12115 class="cmtt-8"> </span><span
12116 class="cmtt-8"> </span><span
12117 class="cmtt-8"> </span><span
12118 class="cmtt-8"> </span><span
12119 class="cmtt-8"> </span><span
12120 class="cmtt-8"> </span><span
12121 class="cmtt-8"> </span><span
12122 class="cmtt-8"> 16)</span><span
12123 class="cmtt-8"> [err]</span><span
12124 class="cmtt-8"> =</span><span
12125 class="cmtt-8"> [err]</span><span
12126 class="cmtt-8"> -</span><span
12127 class="cmtt-8"> [adx]</span><br class="fancyvrb" /><a
12128 id="x1-125056r28"></a><span
12129 class="cmr-6">28</span><span
12130 class="cmtt-8"> </span><span
12131 class="cmtt-8"> </span><span
12132 class="cmtt-8"> </span><span
12133 class="cmtt-8"> </span><span
12134 class="cmtt-8"> </span><span
12135 class="cmtt-8"> </span><span
12136 class="cmtt-8"> </span><span
12137 class="cmtt-8"> </span><span
12138 class="cmtt-8"> </span><span
12139 class="cmtt-8"> </span><span
12140 class="cmtt-8"> </span><span
12141 class="cmtt-8"> </span><span
12142 class="cmtt-8"> </span><span
12143 class="cmtt-8"> </span><span
12144 class="cmtt-8"> 17)</span><span
12145 class="cmtt-8"> </span><span
12146 class="cmtt-8"> </span><span
12147 class="cmtt-8"> [y]</span><span
12148 class="cmtt-8"> =</span><span
12149 class="cmtt-8"> [y]</span><span
12150 class="cmtt-8"> +</span><span
12151 class="cmtt-8"> [sy]</span><br class="fancyvrb" /><a
12152 id="x1-125058r29"></a><span
12153 class="cmr-6">29</span><span
12154 class="cmtt-8"> </span><span
12155 class="cmtt-8"> </span>
12156 <br class="fancyvrb" /><a
12157 id="x1-125060r30"></a><span
12158 class="cmr-6">30</span><span
12159 class="cmtt-8"> </span><span
12160 class="cmtt-8"> </span><span
12161 class="cmtt-8"> </span><span
12162 class="cmtt-8"> </span><span
12163 class="cmtt-8"> </span><span
12164 class="cmtt-8"> </span><span
12165 class="cmtt-8"> </span><span
12166 class="cmtt-8"> </span><span
12167 class="cmtt-8"> </span><span
12168 class="cmtt-8"> </span><span
12169 class="cmtt-8"> </span><span
12170 class="cmtt-8"> </span><span
12171 class="cmtt-8"> }</span><span
12172 class="cmtt-8"> else</span><span
12173 class="cmtt-8"> {</span><br class="fancyvrb" /><a
12174 id="x1-125062r31"></a><span
12175 class="cmr-6">31</span><span
12176 class="cmtt-8"> </span><span
12177 class="cmtt-8"> </span><br class="fancyvrb" /><a
12178 id="x1-125064r32"></a><span
12179 class="cmr-6">32</span><span
12180 class="cmtt-8"> </span><span
12181 class="cmtt-8"> </span><span
12182 class="cmtt-8"> </span><span
12183 class="cmtt-8"> </span><span
12184 class="cmtt-8"> </span><span
12185 class="cmtt-8"> </span><span
12186 class="cmtt-8"> </span><span
12187 class="cmtt-8"> </span><span
12188 class="cmtt-8"> </span><span
12189 class="cmtt-8"> </span><span
12190 class="cmtt-8"> </span><span
12191 class="cmtt-8"> </span><span
12192 class="cmtt-8"> </span><span
12193 class="cmtt-8"> </span><span
12194 class="cmtt-8"> 18)</span><span
12195 class="cmtt-8"> [y]</span><span
12196 class="cmtt-8"> =</span><span
12197 class="cmtt-8"> [y]</span><span
12198 class="cmtt-8"> +</span><span
12199 class="cmtt-8"> [base]</span><br class="fancyvrb" /><a
12200 id="x1-125066r33"></a><span
12201 class="cmr-6">33</span><span
12202 class="cmtt-8"> </span><span
12203 class="cmtt-8"> </span><br class="fancyvrb" /><a
12204 id="x1-125068r34"></a><span
12205 class="cmr-6">34</span><span
12206 class="cmtt-8"> </span><span
12207 class="cmtt-8"> </span><span
12208 class="cmtt-8"> </span><span
12209 class="cmtt-8"> </span><span
12210 class="cmtt-8"> </span><span
12211 class="cmtt-8"> </span><span
12212 class="cmtt-8"> </span><span
12213 class="cmtt-8"> </span><span
12214 class="cmtt-8"> </span><span
12215 class="cmtt-8"> </span><span
12216 class="cmtt-8"> </span><span
12217 class="cmtt-8"> </span><span
12218 class="cmtt-8"> }</span><br class="fancyvrb" /><a
12219 id="x1-125070r35"></a><span
12220 class="cmr-6">35</span><span
12221 class="cmtt-8"> </span><span
12222 class="cmtt-8"> </span><br class="fancyvrb" /><a
12223 id="x1-125072r36"></a><span
12224 class="cmr-6">36</span><span
12225 class="cmtt-8"> </span><span
12226 class="cmtt-8"> </span><span
12227 class="cmtt-8"> </span><span
12228 class="cmtt-8"> </span><span
12229 class="cmtt-8"> </span><span
12230 class="cmtt-8"> </span><span
12231 class="cmtt-8"> </span><span
12232 class="cmtt-8"> </span><span
12233 class="cmtt-8"> 19)</span><span
12234 class="cmtt-8"> vector</span><span
12235 class="cmtt-8"> [v]</span><span
12236 class="cmtt-8"> element</span><span
12237 class="cmtt-8"> [x]</span><span
12238 class="cmtt-8"> =</span><span
12239 class="cmtt-8"> [y]</span><br class="fancyvrb" /><a
12240 id="x1-125074r37"></a><span
12241 class="cmr-6">37</span><span
12242 class="cmtt-8"> </span><span
12243 class="cmtt-8"> </span><br class="fancyvrb" /><a
12244 id="x1-125076r38"></a><span
12245 class="cmr-6">38</span><span
12246 class="cmtt-8"> </span><span
12247 class="cmtt-8"> </span><span
12248 class="cmtt-8"> </span><span
12249 class="cmtt-8"> </span><span
12250 class="cmtt-8"> </span><span
12251 class="cmtt-8"> </span><span
12252 class="cmtt-8"> }</span></div>
12259 <h3 class="sectionHead"><span class="titlemark">10. </span> <a
12260 id="x1-12600010"></a>Tables</h3>
12261 <!--l. 6--><p class="noindent" >
12262 <h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a
12263 id="x1-12700010.1"></a>floor1_inverse_dB_table</h4>
12264 <!--l. 8--><p class="noindent" >The vector <span
12265 class="cmtt-12">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consisting of the
12266 following values (read left to right then top to bottom):
12267 <!--l. 12--><p class="noindent" >
12268 <div class="fancyvrb" id="fancyvrb48"><a
12269 id="x1-127002r1"></a><span
12270 class="cmr-6">1</span><span
12271 class="cmtt-8"> </span><span
12272 class="cmtt-8"> </span><span
12273 class="cmtt-8"> </span><span
12274 class="cmtt-8"> 1.0649863e-07,</span><span
12275 class="cmtt-8"> 1.1341951e-07,</span><span
12276 class="cmtt-8"> 1.2079015e-07,</span><span
12277 class="cmtt-8"> 1.2863978e-07,</span><br class="fancyvrb" /><a
12278 id="x1-127004r2"></a><span
12279 class="cmr-6">2</span><span
12280 class="cmtt-8"> </span><span
12281 class="cmtt-8"> </span><span
12282 class="cmtt-8"> </span><span
12283 class="cmtt-8"> 1.3699951e-07,</span><span
12284 class="cmtt-8"> 1.4590251e-07,</span><span
12285 class="cmtt-8"> 1.5538408e-07,</span><span
12286 class="cmtt-8"> 1.6548181e-07,</span>
12287 <br class="fancyvrb" /><a
12288 id="x1-127006r3"></a><span
12289 class="cmr-6">3</span><span
12290 class="cmtt-8"> </span><span
12291 class="cmtt-8"> </span><span
12292 class="cmtt-8"> </span><span
12293 class="cmtt-8"> 1.7623575e-07,</span><span
12294 class="cmtt-8"> 1.8768855e-07,</span><span
12295 class="cmtt-8"> 1.9988561e-07,</span><span
12296 class="cmtt-8"> 2.1287530e-07,</span><br class="fancyvrb" /><a
12297 id="x1-127008r4"></a><span
12298 class="cmr-6">4</span><span
12299 class="cmtt-8"> </span><span
12300 class="cmtt-8"> </span><span
12301 class="cmtt-8"> </span><span
12302 class="cmtt-8"> 2.2670913e-07,</span><span
12303 class="cmtt-8"> 2.4144197e-07,</span><span
12304 class="cmtt-8"> 2.5713223e-07,</span><span
12305 class="cmtt-8"> 2.7384213e-07,</span>
12306 <br class="fancyvrb" /><a
12307 id="x1-127010r5"></a><span
12308 class="cmr-6">5</span><span
12309 class="cmtt-8"> </span><span
12310 class="cmtt-8"> </span><span
12311 class="cmtt-8"> </span><span
12312 class="cmtt-8"> 2.9163793e-07,</span><span
12313 class="cmtt-8"> 3.1059021e-07,</span><span
12314 class="cmtt-8"> 3.3077411e-07,</span><span
12315 class="cmtt-8"> 3.5226968e-07,</span><br class="fancyvrb" /><a
12316 id="x1-127012r6"></a><span
12317 class="cmr-6">6</span><span
12318 class="cmtt-8"> </span><span
12319 class="cmtt-8"> </span><span
12320 class="cmtt-8"> </span><span
12321 class="cmtt-8"> 3.7516214e-07,</span><span
12322 class="cmtt-8"> 3.9954229e-07,</span><span
12323 class="cmtt-8"> 4.2550680e-07,</span><span
12324 class="cmtt-8"> 4.5315863e-07,</span>
12325 <br class="fancyvrb" /><a
12326 id="x1-127014r7"></a><span
12327 class="cmr-6">7</span><span
12328 class="cmtt-8"> </span><span
12329 class="cmtt-8"> </span><span
12330 class="cmtt-8"> </span><span
12331 class="cmtt-8"> 4.8260743e-07,</span><span
12332 class="cmtt-8"> 5.1396998e-07,</span><span
12333 class="cmtt-8"> 5.4737065e-07,</span><span
12334 class="cmtt-8"> 5.8294187e-07,</span><br class="fancyvrb" /><a
12335 id="x1-127016r8"></a><span
12336 class="cmr-6">8</span><span
12337 class="cmtt-8"> </span><span
12338 class="cmtt-8"> </span><span
12339 class="cmtt-8"> </span><span
12340 class="cmtt-8"> 6.2082472e-07,</span><span
12341 class="cmtt-8"> 6.6116941e-07,</span><span
12342 class="cmtt-8"> 7.0413592e-07,</span><span
12343 class="cmtt-8"> 7.4989464e-07,</span>
12344 <br class="fancyvrb" /><a
12345 id="x1-127018r9"></a><span
12346 class="cmr-6">9</span><span
12347 class="cmtt-8"> </span><span
12348 class="cmtt-8"> </span><span
12349 class="cmtt-8"> </span><span
12350 class="cmtt-8"> 7.9862701e-07,</span><span
12351 class="cmtt-8"> 8.5052630e-07,</span><span
12352 class="cmtt-8"> 9.0579828e-07,</span><span
12353 class="cmtt-8"> 9.6466216e-07,</span><br class="fancyvrb" /><a
12354 id="x1-127020r10"></a><span
12355 class="cmr-6">10</span><span
12356 class="cmtt-8"> </span><span
12357 class="cmtt-8"> </span><span
12358 class="cmtt-8"> </span><span
12359 class="cmtt-8"> 1.0273513e-06,</span><span
12360 class="cmtt-8"> 1.0941144e-06,</span><span
12361 class="cmtt-8"> 1.1652161e-06,</span><span
12362 class="cmtt-8"> 1.2409384e-06,</span>
12363 <br class="fancyvrb" /><a
12364 id="x1-127022r11"></a><span
12365 class="cmr-6">11</span><span
12366 class="cmtt-8"> </span><span
12367 class="cmtt-8"> </span><span
12368 class="cmtt-8"> </span><span
12369 class="cmtt-8"> 1.3215816e-06,</span><span
12370 class="cmtt-8"> 1.4074654e-06,</span><span
12371 class="cmtt-8"> 1.4989305e-06,</span><span
12372 class="cmtt-8"> 1.5963394e-06,</span><br class="fancyvrb" /><a
12373 id="x1-127024r12"></a><span
12374 class="cmr-6">12</span><span
12375 class="cmtt-8"> </span><span
12376 class="cmtt-8"> </span><span
12377 class="cmtt-8"> </span><span
12378 class="cmtt-8"> 1.7000785e-06,</span><span
12379 class="cmtt-8"> 1.8105592e-06,</span><span
12380 class="cmtt-8"> 1.9282195e-06,</span><span
12381 class="cmtt-8"> 2.0535261e-06,</span>
12382 <br class="fancyvrb" /><a
12383 id="x1-127026r13"></a><span
12384 class="cmr-6">13</span><span
12385 class="cmtt-8"> </span><span
12386 class="cmtt-8"> </span><span
12387 class="cmtt-8"> </span><span
12388 class="cmtt-8"> 2.1869758e-06,</span><span
12389 class="cmtt-8"> 2.3290978e-06,</span><span
12390 class="cmtt-8"> 2.4804557e-06,</span><span
12391 class="cmtt-8"> 2.6416497e-06,</span><br class="fancyvrb" /><a
12392 id="x1-127028r14"></a><span
12393 class="cmr-6">14</span><span
12394 class="cmtt-8"> </span><span
12395 class="cmtt-8"> </span><span
12396 class="cmtt-8"> </span><span
12397 class="cmtt-8"> 2.8133190e-06,</span><span
12398 class="cmtt-8"> 2.9961443e-06,</span><span
12399 class="cmtt-8"> 3.1908506e-06,</span><span
12400 class="cmtt-8"> 3.3982101e-06,</span>
12401 <br class="fancyvrb" /><a
12402 id="x1-127030r15"></a><span
12403 class="cmr-6">15</span><span
12404 class="cmtt-8"> </span><span
12405 class="cmtt-8"> </span><span
12406 class="cmtt-8"> </span><span
12407 class="cmtt-8"> 3.6190449e-06,</span><span
12408 class="cmtt-8"> 3.8542308e-06,</span><span
12409 class="cmtt-8"> 4.1047004e-06,</span><span
12410 class="cmtt-8"> 4.3714470e-06,</span><br class="fancyvrb" /><a
12411 id="x1-127032r16"></a><span
12412 class="cmr-6">16</span><span
12413 class="cmtt-8"> </span><span
12414 class="cmtt-8"> </span><span
12415 class="cmtt-8"> </span><span
12416 class="cmtt-8"> 4.6555282e-06,</span><span
12417 class="cmtt-8"> 4.9580707e-06,</span><span
12418 class="cmtt-8"> 5.2802740e-06,</span><span
12419 class="cmtt-8"> 5.6234160e-06,</span>
12420 <br class="fancyvrb" /><a
12421 id="x1-127034r17"></a><span
12422 class="cmr-6">17</span><span
12423 class="cmtt-8"> </span><span
12424 class="cmtt-8"> </span><span
12425 class="cmtt-8"> </span><span
12426 class="cmtt-8"> 5.9888572e-06,</span><span
12427 class="cmtt-8"> 6.3780469e-06,</span><span
12428 class="cmtt-8"> 6.7925283e-06,</span><span
12429 class="cmtt-8"> 7.2339451e-06,</span><br class="fancyvrb" /><a
12430 id="x1-127036r18"></a><span
12431 class="cmr-6">18</span><span
12432 class="cmtt-8"> </span><span
12433 class="cmtt-8"> </span><span
12434 class="cmtt-8"> </span><span
12435 class="cmtt-8"> 7.7040476e-06,</span><span
12436 class="cmtt-8"> 8.2047000e-06,</span><span
12437 class="cmtt-8"> 8.7378876e-06,</span><span
12438 class="cmtt-8"> 9.3057248e-06,</span>
12439 <br class="fancyvrb" /><a
12440 id="x1-127038r19"></a><span
12441 class="cmr-6">19</span><span
12442 class="cmtt-8"> </span><span
12443 class="cmtt-8"> </span><span
12444 class="cmtt-8"> </span><span
12445 class="cmtt-8"> 9.9104632e-06,</span><span
12446 class="cmtt-8"> 1.0554501e-05,</span><span
12447 class="cmtt-8"> 1.1240392e-05,</span><span
12448 class="cmtt-8"> 1.1970856e-05,</span><br class="fancyvrb" /><a
12449 id="x1-127040r20"></a><span
12450 class="cmr-6">20</span><span
12451 class="cmtt-8"> </span><span
12452 class="cmtt-8"> </span><span
12453 class="cmtt-8"> </span><span
12454 class="cmtt-8"> 1.2748789e-05,</span><span
12455 class="cmtt-8"> 1.3577278e-05,</span><span
12456 class="cmtt-8"> 1.4459606e-05,</span><span
12457 class="cmtt-8"> 1.5399272e-05,</span>
12458 <br class="fancyvrb" /><a
12459 id="x1-127042r21"></a><span
12460 class="cmr-6">21</span><span
12461 class="cmtt-8"> </span><span
12462 class="cmtt-8"> </span><span
12463 class="cmtt-8"> </span><span
12464 class="cmtt-8"> 1.6400004e-05,</span><span
12465 class="cmtt-8"> 1.7465768e-05,</span><span
12466 class="cmtt-8"> 1.8600792e-05,</span><span
12467 class="cmtt-8"> 1.9809576e-05,</span><br class="fancyvrb" /><a
12468 id="x1-127044r22"></a><span
12469 class="cmr-6">22</span><span
12470 class="cmtt-8"> </span><span
12471 class="cmtt-8"> </span><span
12472 class="cmtt-8"> </span><span
12473 class="cmtt-8"> 2.1096914e-05,</span><span
12474 class="cmtt-8"> 2.2467911e-05,</span><span
12475 class="cmtt-8"> 2.3928002e-05,</span><span
12476 class="cmtt-8"> 2.5482978e-05,</span>
12477 <br class="fancyvrb" /><a
12478 id="x1-127046r23"></a><span
12479 class="cmr-6">23</span><span
12480 class="cmtt-8"> </span><span
12481 class="cmtt-8"> </span><span
12482 class="cmtt-8"> </span><span
12483 class="cmtt-8"> 2.7139006e-05,</span><span
12484 class="cmtt-8"> 2.8902651e-05,</span><span
12485 class="cmtt-8"> 3.0780908e-05,</span><span
12486 class="cmtt-8"> 3.2781225e-05,</span><br class="fancyvrb" /><a
12487 id="x1-127048r24"></a><span
12488 class="cmr-6">24</span><span
12489 class="cmtt-8"> </span><span
12490 class="cmtt-8"> </span><span
12491 class="cmtt-8"> </span><span
12492 class="cmtt-8"> 3.4911534e-05,</span><span
12493 class="cmtt-8"> 3.7180282e-05,</span><span
12494 class="cmtt-8"> 3.9596466e-05,</span><span
12495 class="cmtt-8"> 4.2169667e-05,</span>
12496 <br class="fancyvrb" /><a
12497 id="x1-127050r25"></a><span
12498 class="cmr-6">25</span><span
12499 class="cmtt-8"> </span><span
12500 class="cmtt-8"> </span><span
12501 class="cmtt-8"> </span><span
12502 class="cmtt-8"> 4.4910090e-05,</span><span
12503 class="cmtt-8"> 4.7828601e-05,</span><span
12504 class="cmtt-8"> 5.0936773e-05,</span><span
12505 class="cmtt-8"> 5.4246931e-05,</span><br class="fancyvrb" /><a
12506 id="x1-127052r26"></a><span
12507 class="cmr-6">26</span><span
12508 class="cmtt-8"> </span><span
12509 class="cmtt-8"> </span><span
12510 class="cmtt-8"> </span><span
12511 class="cmtt-8"> 5.7772202e-05,</span><span
12512 class="cmtt-8"> 6.1526565e-05,</span><span
12513 class="cmtt-8"> 6.5524908e-05,</span><span
12514 class="cmtt-8"> 6.9783085e-05,</span>
12515 <br class="fancyvrb" /><a
12516 id="x1-127054r27"></a><span
12517 class="cmr-6">27</span><span
12518 class="cmtt-8"> </span><span
12519 class="cmtt-8"> </span><span
12520 class="cmtt-8"> </span><span
12521 class="cmtt-8"> 7.4317983e-05,</span><span
12522 class="cmtt-8"> 7.9147585e-05,</span><span
12523 class="cmtt-8"> 8.4291040e-05,</span><span
12524 class="cmtt-8"> 8.9768747e-05,</span><br class="fancyvrb" /><a
12525 id="x1-127056r28"></a><span
12526 class="cmr-6">28</span><span
12527 class="cmtt-8"> </span><span
12528 class="cmtt-8"> </span><span
12529 class="cmtt-8"> </span><span
12530 class="cmtt-8"> 9.5602426e-05,</span><span
12531 class="cmtt-8"> 0.00010181521,</span><span
12532 class="cmtt-8"> 0.00010843174,</span><span
12533 class="cmtt-8"> 0.00011547824,</span>
12534 <br class="fancyvrb" /><a
12535 id="x1-127058r29"></a><span
12536 class="cmr-6">29</span><span
12537 class="cmtt-8"> </span><span
12538 class="cmtt-8"> </span><span
12539 class="cmtt-8"> </span><span
12540 class="cmtt-8"> 0.00012298267,</span><span
12541 class="cmtt-8"> 0.00013097477,</span><span
12542 class="cmtt-8"> 0.00013948625,</span><span
12543 class="cmtt-8"> 0.00014855085,</span><br class="fancyvrb" /><a
12544 id="x1-127060r30"></a><span
12545 class="cmr-6">30</span><span
12546 class="cmtt-8"> </span><span
12547 class="cmtt-8"> </span><span
12548 class="cmtt-8"> </span><span
12549 class="cmtt-8"> 0.00015820453,</span><span
12550 class="cmtt-8"> 0.00016848555,</span><span
12551 class="cmtt-8"> 0.00017943469,</span><span
12552 class="cmtt-8"> 0.00019109536,</span>
12553 <br class="fancyvrb" /><a
12554 id="x1-127062r31"></a><span
12555 class="cmr-6">31</span><span
12556 class="cmtt-8"> </span><span
12557 class="cmtt-8"> </span><span
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12559 class="cmtt-8"> 0.00020351382,</span><span
12560 class="cmtt-8"> 0.00021673929,</span><span
12561 class="cmtt-8"> 0.00023082423,</span><span
12562 class="cmtt-8"> 0.00024582449,</span><br class="fancyvrb" /><a
12563 id="x1-127064r32"></a><span
12564 class="cmr-6">32</span><span
12565 class="cmtt-8"> </span><span
12566 class="cmtt-8"> </span><span
12567 class="cmtt-8"> </span><span
12568 class="cmtt-8"> 0.00026179955,</span><span
12569 class="cmtt-8"> 0.00027881276,</span><span
12570 class="cmtt-8"> 0.00029693158,</span><span
12571 class="cmtt-8"> 0.00031622787,</span>
12572 <br class="fancyvrb" /><a
12573 id="x1-127066r33"></a><span
12574 class="cmr-6">33</span><span
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12579 class="cmtt-8"> 0.00035866388,</span><span
12580 class="cmtt-8"> 0.00038197188,</span><span
12581 class="cmtt-8"> 0.00040679456,</span><br class="fancyvrb" /><a
12582 id="x1-127068r34"></a><span
12583 class="cmr-6">34</span><span
12584 class="cmtt-8"> </span><span
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12586 class="cmtt-8"> </span><span
12587 class="cmtt-8"> 0.00043323036,</span><span
12588 class="cmtt-8"> 0.00046138411,</span><span
12589 class="cmtt-8"> 0.00049136745,</span><span
12590 class="cmtt-8"> 0.00052329927,</span>
12591 <br class="fancyvrb" /><a
12592 id="x1-127070r35"></a><span
12593 class="cmr-6">35</span><span
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12598 class="cmtt-8"> 0.00059352311,</span><span
12599 class="cmtt-8"> 0.00063209358,</span><span
12600 class="cmtt-8"> 0.00067317058,</span><br class="fancyvrb" /><a
12601 id="x1-127072r36"></a><span
12602 class="cmr-6">36</span><span
12603 class="cmtt-8"> </span><span
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12606 class="cmtt-8"> 0.00071691700,</span><span
12607 class="cmtt-8"> 0.00076350630,</span><span
12608 class="cmtt-8"> 0.00081312324,</span><span
12609 class="cmtt-8"> 0.00086596457,</span>
12610 <br class="fancyvrb" /><a
12611 id="x1-127074r37"></a><span
12612 class="cmr-6">37</span><span
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12614 class="cmtt-8"> </span><span
12615 class="cmtt-8"> </span><span
12616 class="cmtt-8"> 0.00092223983,</span><span
12617 class="cmtt-8"> 0.00098217216,</span><span
12618 class="cmtt-8"> 0.0010459992,</span><span
12619 class="cmtt-8"> </span><span
12620 class="cmtt-8"> 0.0011139742,</span><br class="fancyvrb" /><a
12621 id="x1-127076r38"></a><span
12622 class="cmr-6">38</span><span
12623 class="cmtt-8"> </span><span
12624 class="cmtt-8"> </span><span
12625 class="cmtt-8"> </span><span
12626 class="cmtt-8"> 0.0011863665,</span><span
12627 class="cmtt-8"> </span><span
12628 class="cmtt-8"> 0.0012634633,</span><span
12629 class="cmtt-8"> </span><span
12630 class="cmtt-8"> 0.0013455702,</span><span
12631 class="cmtt-8"> </span><span
12632 class="cmtt-8"> 0.0014330129,</span>
12633 <br class="fancyvrb" /><a
12634 id="x1-127078r39"></a><span
12635 class="cmr-6">39</span><span
12636 class="cmtt-8"> </span><span
12637 class="cmtt-8"> </span><span
12638 class="cmtt-8"> </span><span
12639 class="cmtt-8"> 0.0015261382,</span><span
12640 class="cmtt-8"> </span><span
12641 class="cmtt-8"> 0.0016253153,</span><span
12642 class="cmtt-8"> </span><span
12643 class="cmtt-8"> 0.0017309374,</span><span
12644 class="cmtt-8"> </span><span
12645 class="cmtt-8"> 0.0018434235,</span><br class="fancyvrb" /><a
12646 id="x1-127080r40"></a><span
12647 class="cmr-6">40</span><span
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12650 class="cmtt-8"> </span><span
12651 class="cmtt-8"> 0.0019632195,</span><span
12652 class="cmtt-8"> </span><span
12653 class="cmtt-8"> 0.0020908006,</span><span
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12655 class="cmtt-8"> 0.0022266726,</span><span
12656 class="cmtt-8"> </span><span
12657 class="cmtt-8"> 0.0023713743,</span>
12658 <br class="fancyvrb" /><a
12659 id="x1-127082r41"></a><span
12660 class="cmr-6">41</span><span
12661 class="cmtt-8"> </span><span
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12663 class="cmtt-8"> </span><span
12664 class="cmtt-8"> 0.0025254795,</span><span
12665 class="cmtt-8"> </span><span
12666 class="cmtt-8"> 0.0026895994,</span><span
12667 class="cmtt-8"> </span><span
12668 class="cmtt-8"> 0.0028643847,</span><span
12669 class="cmtt-8"> </span><span
12670 class="cmtt-8"> 0.0030505286,</span><br class="fancyvrb" /><a
12671 id="x1-127084r42"></a><span
12672 class="cmr-6">42</span><span
12673 class="cmtt-8"> </span><span
12674 class="cmtt-8"> </span><span
12675 class="cmtt-8"> </span><span
12676 class="cmtt-8"> 0.0032487691,</span><span
12677 class="cmtt-8"> </span><span
12678 class="cmtt-8"> 0.0034598925,</span><span
12679 class="cmtt-8"> </span><span
12680 class="cmtt-8"> 0.0036847358,</span><span
12681 class="cmtt-8"> </span><span
12682 class="cmtt-8"> 0.0039241906,</span>
12683 <br class="fancyvrb" /><a
12684 id="x1-127086r43"></a><span
12685 class="cmr-6">43</span><span
12686 class="cmtt-8"> </span><span
12687 class="cmtt-8"> </span><span
12688 class="cmtt-8"> </span><span
12689 class="cmtt-8"> 0.0041792066,</span><span
12690 class="cmtt-8"> </span><span
12691 class="cmtt-8"> 0.0044507950,</span><span
12692 class="cmtt-8"> </span><span
12693 class="cmtt-8"> 0.0047400328,</span><span
12694 class="cmtt-8"> </span><span
12695 class="cmtt-8"> 0.0050480668,</span><br class="fancyvrb" /><a
12696 id="x1-127088r44"></a><span
12697 class="cmr-6">44</span><span
12698 class="cmtt-8"> </span><span
12699 class="cmtt-8"> </span><span
12700 class="cmtt-8"> </span><span
12701 class="cmtt-8"> 0.0053761186,</span><span
12702 class="cmtt-8"> </span><span
12703 class="cmtt-8"> 0.0057254891,</span><span
12704 class="cmtt-8"> </span><span
12705 class="cmtt-8"> 0.0060975636,</span><span
12706 class="cmtt-8"> </span><span
12707 class="cmtt-8"> 0.0064938176,</span>
12708 <br class="fancyvrb" /><a
12709 id="x1-127090r45"></a><span
12710 class="cmr-6">45</span><span
12711 class="cmtt-8"> </span><span
12712 class="cmtt-8"> </span><span
12713 class="cmtt-8"> </span><span
12714 class="cmtt-8"> 0.0069158225,</span><span
12715 class="cmtt-8"> </span><span
12716 class="cmtt-8"> 0.0073652516,</span><span
12717 class="cmtt-8"> </span><span
12718 class="cmtt-8"> 0.0078438871,</span><span
12719 class="cmtt-8"> </span><span
12720 class="cmtt-8"> 0.0083536271,</span><br class="fancyvrb" /><a
12721 id="x1-127092r46"></a><span
12722 class="cmr-6">46</span><span
12723 class="cmtt-8"> </span><span
12724 class="cmtt-8"> </span><span
12725 class="cmtt-8"> </span><span
12726 class="cmtt-8"> 0.0088964928,</span><span
12727 class="cmtt-8"> </span><span
12728 class="cmtt-8"> 0.009474637,</span><span
12729 class="cmtt-8"> </span><span
12730 class="cmtt-8"> </span><span
12731 class="cmtt-8"> 0.010090352,</span><span
12732 class="cmtt-8"> </span><span
12733 class="cmtt-8"> </span><span
12734 class="cmtt-8"> 0.010746080,</span>
12735 <br class="fancyvrb" /><a
12736 id="x1-127094r47"></a><span
12737 class="cmr-6">47</span><span
12738 class="cmtt-8"> </span><span
12739 class="cmtt-8"> </span><span
12740 class="cmtt-8"> </span><span
12741 class="cmtt-8"> 0.011444421,</span><span
12742 class="cmtt-8"> </span><span
12743 class="cmtt-8"> </span><span
12744 class="cmtt-8"> 0.012188144,</span><span
12745 class="cmtt-8"> </span><span
12746 class="cmtt-8"> </span><span
12747 class="cmtt-8"> 0.012980198,</span><span
12748 class="cmtt-8"> </span><span
12749 class="cmtt-8"> </span><span
12750 class="cmtt-8"> 0.013823725,</span><br class="fancyvrb" /><a
12751 id="x1-127096r48"></a><span
12752 class="cmr-6">48</span><span
12753 class="cmtt-8"> </span><span
12754 class="cmtt-8"> </span><span
12755 class="cmtt-8"> </span><span
12756 class="cmtt-8"> 0.014722068,</span><span
12757 class="cmtt-8"> </span><span
12758 class="cmtt-8"> </span><span
12759 class="cmtt-8"> 0.015678791,</span><span
12760 class="cmtt-8"> </span><span
12761 class="cmtt-8"> </span><span
12762 class="cmtt-8"> 0.016697687,</span><span
12763 class="cmtt-8"> </span><span
12764 class="cmtt-8"> </span><span
12765 class="cmtt-8"> 0.017782797,</span>
12766 <br class="fancyvrb" /><a
12767 id="x1-127098r49"></a><span
12768 class="cmr-6">49</span><span
12769 class="cmtt-8"> </span><span
12770 class="cmtt-8"> </span><span
12771 class="cmtt-8"> </span><span
12772 class="cmtt-8"> 0.018938423,</span><span
12773 class="cmtt-8"> </span><span
12774 class="cmtt-8"> </span><span
12775 class="cmtt-8"> 0.020169149,</span><span
12776 class="cmtt-8"> </span><span
12777 class="cmtt-8"> </span><span
12778 class="cmtt-8"> 0.021479854,</span><span
12779 class="cmtt-8"> </span><span
12780 class="cmtt-8"> </span><span
12781 class="cmtt-8"> 0.022875735,</span><br class="fancyvrb" /><a
12782 id="x1-127100r50"></a><span
12783 class="cmr-6">50</span><span
12784 class="cmtt-8"> </span><span
12785 class="cmtt-8"> </span><span
12786 class="cmtt-8"> </span><span
12787 class="cmtt-8"> 0.024362330,</span><span
12788 class="cmtt-8"> </span><span
12789 class="cmtt-8"> </span><span
12790 class="cmtt-8"> 0.025945531,</span><span
12791 class="cmtt-8"> </span><span
12792 class="cmtt-8"> </span><span
12793 class="cmtt-8"> 0.027631618,</span><span
12794 class="cmtt-8"> </span><span
12795 class="cmtt-8"> </span><span
12796 class="cmtt-8"> 0.029427276,</span>
12797 <br class="fancyvrb" /><a
12798 id="x1-127102r51"></a><span
12799 class="cmr-6">51</span><span
12800 class="cmtt-8"> </span><span
12801 class="cmtt-8"> </span><span
12802 class="cmtt-8"> </span><span
12803 class="cmtt-8"> 0.031339626,</span><span
12804 class="cmtt-8"> </span><span
12805 class="cmtt-8"> </span><span
12806 class="cmtt-8"> 0.033376252,</span><span
12807 class="cmtt-8"> </span><span
12808 class="cmtt-8"> </span><span
12809 class="cmtt-8"> 0.035545228,</span><span
12810 class="cmtt-8"> </span><span
12811 class="cmtt-8"> </span><span
12812 class="cmtt-8"> 0.037855157,</span><br class="fancyvrb" /><a
12813 id="x1-127104r52"></a><span
12814 class="cmr-6">52</span><span
12815 class="cmtt-8"> </span><span
12816 class="cmtt-8"> </span><span
12817 class="cmtt-8"> </span><span
12818 class="cmtt-8"> 0.040315199,</span><span
12819 class="cmtt-8"> </span><span
12820 class="cmtt-8"> </span><span
12821 class="cmtt-8"> 0.042935108,</span><span
12822 class="cmtt-8"> </span><span
12823 class="cmtt-8"> </span><span
12824 class="cmtt-8"> 0.045725273,</span><span
12825 class="cmtt-8"> </span><span
12826 class="cmtt-8"> </span><span
12827 class="cmtt-8"> 0.048696758,</span>
12828 <br class="fancyvrb" /><a
12829 id="x1-127106r53"></a><span
12830 class="cmr-6">53</span><span
12831 class="cmtt-8"> </span><span
12832 class="cmtt-8"> </span><span
12833 class="cmtt-8"> </span><span
12834 class="cmtt-8"> 0.051861348,</span><span
12835 class="cmtt-8"> </span><span
12836 class="cmtt-8"> </span><span
12837 class="cmtt-8"> 0.055231591,</span><span
12838 class="cmtt-8"> </span><span
12839 class="cmtt-8"> </span><span
12840 class="cmtt-8"> 0.058820850,</span><span
12841 class="cmtt-8"> </span><span
12842 class="cmtt-8"> </span><span
12843 class="cmtt-8"> 0.062643361,</span><br class="fancyvrb" /><a
12844 id="x1-127108r54"></a><span
12845 class="cmr-6">54</span><span
12846 class="cmtt-8"> </span><span
12847 class="cmtt-8"> </span><span
12848 class="cmtt-8"> </span><span
12849 class="cmtt-8"> 0.066714279,</span><span
12850 class="cmtt-8"> </span><span
12851 class="cmtt-8"> </span><span
12852 class="cmtt-8"> 0.071049749,</span><span
12853 class="cmtt-8"> </span><span
12854 class="cmtt-8"> </span><span
12855 class="cmtt-8"> 0.075666962,</span><span
12856 class="cmtt-8"> </span><span
12857 class="cmtt-8"> </span><span
12858 class="cmtt-8"> 0.080584227,</span>
12859 <br class="fancyvrb" /><a
12860 id="x1-127110r55"></a><span
12861 class="cmr-6">55</span><span
12862 class="cmtt-8"> </span><span
12863 class="cmtt-8"> </span><span
12864 class="cmtt-8"> </span><span
12865 class="cmtt-8"> 0.085821044,</span><span
12866 class="cmtt-8"> </span><span
12867 class="cmtt-8"> </span><span
12868 class="cmtt-8"> 0.091398179,</span><span
12869 class="cmtt-8"> </span><span
12870 class="cmtt-8"> </span><span
12871 class="cmtt-8"> 0.097337747,</span><span
12872 class="cmtt-8"> </span><span
12873 class="cmtt-8"> </span><span
12874 class="cmtt-8"> 0.10366330,</span><br class="fancyvrb" /><a
12875 id="x1-127112r56"></a><span
12876 class="cmr-6">56</span><span
12877 class="cmtt-8"> </span><span
12878 class="cmtt-8"> </span><span
12879 class="cmtt-8"> </span><span
12880 class="cmtt-8"> 0.11039993,</span><span
12881 class="cmtt-8"> </span><span
12882 class="cmtt-8"> </span><span
12883 class="cmtt-8"> </span><span
12884 class="cmtt-8"> 0.11757434,</span><span
12885 class="cmtt-8"> </span><span
12886 class="cmtt-8"> </span><span
12887 class="cmtt-8"> </span><span
12888 class="cmtt-8"> 0.12521498,</span><span
12889 class="cmtt-8"> </span><span
12890 class="cmtt-8"> </span><span
12891 class="cmtt-8"> </span><span
12892 class="cmtt-8"> 0.13335215,</span>
12893 <br class="fancyvrb" /><a
12894 id="x1-127114r57"></a><span
12895 class="cmr-6">57</span><span
12896 class="cmtt-8"> </span><span
12897 class="cmtt-8"> </span><span
12898 class="cmtt-8"> </span><span
12899 class="cmtt-8"> 0.14201813,</span><span
12900 class="cmtt-8"> </span><span
12901 class="cmtt-8"> </span><span
12902 class="cmtt-8"> </span><span
12903 class="cmtt-8"> 0.15124727,</span><span
12904 class="cmtt-8"> </span><span
12905 class="cmtt-8"> </span><span
12906 class="cmtt-8"> </span><span
12907 class="cmtt-8"> 0.16107617,</span><span
12908 class="cmtt-8"> </span><span
12909 class="cmtt-8"> </span><span
12910 class="cmtt-8"> </span><span
12911 class="cmtt-8"> 0.17154380,</span><br class="fancyvrb" /><a
12912 id="x1-127116r58"></a><span
12913 class="cmr-6">58</span><span
12914 class="cmtt-8"> </span><span
12915 class="cmtt-8"> </span><span
12916 class="cmtt-8"> </span><span
12917 class="cmtt-8"> 0.18269168,</span><span
12918 class="cmtt-8"> </span><span
12919 class="cmtt-8"> </span><span
12920 class="cmtt-8"> </span><span
12921 class="cmtt-8"> 0.19456402,</span><span
12922 class="cmtt-8"> </span><span
12923 class="cmtt-8"> </span><span
12924 class="cmtt-8"> </span><span
12925 class="cmtt-8"> 0.20720788,</span><span
12926 class="cmtt-8"> </span><span
12927 class="cmtt-8"> </span><span
12928 class="cmtt-8"> </span><span
12929 class="cmtt-8"> 0.22067342,</span>
12930 <br class="fancyvrb" /><a
12931 id="x1-127118r59"></a><span
12932 class="cmr-6">59</span><span
12933 class="cmtt-8"> </span><span
12934 class="cmtt-8"> </span><span
12935 class="cmtt-8"> </span><span
12936 class="cmtt-8"> 0.23501402,</span><span
12937 class="cmtt-8"> </span><span
12938 class="cmtt-8"> </span><span
12939 class="cmtt-8"> </span><span
12940 class="cmtt-8"> 0.25028656,</span><span
12941 class="cmtt-8"> </span><span
12942 class="cmtt-8"> </span><span
12943 class="cmtt-8"> </span><span
12944 class="cmtt-8"> 0.26655159,</span><span
12945 class="cmtt-8"> </span><span
12946 class="cmtt-8"> </span><span
12947 class="cmtt-8"> </span><span
12948 class="cmtt-8"> 0.28387361,</span><br class="fancyvrb" /><a
12949 id="x1-127120r60"></a><span
12950 class="cmr-6">60</span><span
12951 class="cmtt-8"> </span><span
12952 class="cmtt-8"> </span><span
12953 class="cmtt-8"> </span><span
12954 class="cmtt-8"> 0.30232132,</span><span
12955 class="cmtt-8"> </span><span
12956 class="cmtt-8"> </span><span
12957 class="cmtt-8"> </span><span
12958 class="cmtt-8"> 0.32196786,</span><span
12959 class="cmtt-8"> </span><span
12960 class="cmtt-8"> </span><span
12961 class="cmtt-8"> </span><span
12962 class="cmtt-8"> 0.34289114,</span><span
12963 class="cmtt-8"> </span><span
12964 class="cmtt-8"> </span><span
12965 class="cmtt-8"> </span><span
12966 class="cmtt-8"> 0.36517414,</span>
12967 <br class="fancyvrb" /><a
12968 id="x1-127122r61"></a><span
12969 class="cmr-6">61</span><span
12970 class="cmtt-8"> </span><span
12971 class="cmtt-8"> </span><span
12972 class="cmtt-8"> </span><span
12973 class="cmtt-8"> 0.38890521,</span><span
12974 class="cmtt-8"> </span><span
12975 class="cmtt-8"> </span><span
12976 class="cmtt-8"> </span><span
12977 class="cmtt-8"> 0.41417847,</span><span
12978 class="cmtt-8"> </span><span
12979 class="cmtt-8"> </span><span
12980 class="cmtt-8"> </span><span
12981 class="cmtt-8"> 0.44109412,</span><span
12982 class="cmtt-8"> </span><span
12983 class="cmtt-8"> </span><span
12984 class="cmtt-8"> </span><span
12985 class="cmtt-8"> 0.46975890,</span><br class="fancyvrb" /><a
12986 id="x1-127124r62"></a><span
12987 class="cmr-6">62</span><span
12988 class="cmtt-8"> </span><span
12989 class="cmtt-8"> </span><span
12990 class="cmtt-8"> </span><span
12991 class="cmtt-8"> 0.50028648,</span><span
12992 class="cmtt-8"> </span><span
12993 class="cmtt-8"> </span><span
12994 class="cmtt-8"> </span><span
12995 class="cmtt-8"> 0.53279791,</span><span
12996 class="cmtt-8"> </span><span
12997 class="cmtt-8"> </span><span
12998 class="cmtt-8"> </span><span
12999 class="cmtt-8"> 0.56742212,</span><span
13000 class="cmtt-8"> </span><span
13001 class="cmtt-8"> </span><span
13002 class="cmtt-8"> </span><span
13003 class="cmtt-8"> 0.60429640,</span>
13004 <br class="fancyvrb" /><a
13005 id="x1-127126r63"></a><span
13006 class="cmr-6">63</span><span
13007 class="cmtt-8"> </span><span
13008 class="cmtt-8"> </span><span
13009 class="cmtt-8"> </span><span
13010 class="cmtt-8"> 0.64356699,</span><span
13011 class="cmtt-8"> </span><span
13012 class="cmtt-8"> </span><span
13013 class="cmtt-8"> </span><span
13014 class="cmtt-8"> 0.68538959,</span><span
13015 class="cmtt-8"> </span><span
13016 class="cmtt-8"> </span><span
13017 class="cmtt-8"> </span><span
13018 class="cmtt-8"> 0.72993007,</span><span
13019 class="cmtt-8"> </span><span
13020 class="cmtt-8"> </span><span
13021 class="cmtt-8"> </span><span
13022 class="cmtt-8"> 0.77736504,</span><br class="fancyvrb" /><a
13023 id="x1-127128r64"></a><span
13024 class="cmr-6">64</span><span
13025 class="cmtt-8"> </span><span
13026 class="cmtt-8"> </span><span
13027 class="cmtt-8"> </span><span
13028 class="cmtt-8"> 0.82788260,</span><span
13029 class="cmtt-8"> </span><span
13030 class="cmtt-8"> </span><span
13031 class="cmtt-8"> </span><span
13032 class="cmtt-8"> 0.88168307,</span><span
13033 class="cmtt-8"> </span><span
13034 class="cmtt-8"> </span><span
13035 class="cmtt-8"> </span><span
13036 class="cmtt-8"> 0.9389798,</span><span
13037 class="cmtt-8"> </span><span
13038 class="cmtt-8"> </span><span
13039 class="cmtt-8"> </span><span
13040 class="cmtt-8"> </span><span
13041 class="cmtt-8"> 1.</span></div>
13048 <h3 class="sectionHead"><span class="titlemark">A. </span> <a
13049 id="x1-128000A"></a>Embedding Vorbis into an Ogg stream</h3>
13050 <!--l. 6--><p class="noindent" >
13051 <h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a
13052 id="x1-129000A.1"></a>Overview</h4>
13053 <!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
13054 compressed audio packet data into file form.
13055 <!--l. 12--><p class="noindent" >The <a
13056 href="#x1-20001">section 1</a>, “<a
13057 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of Vorbis
13059 <!--l. 15--><p class="noindent" >The <a
13060 href="oggstream.html" >Ogg bitstream overview</a> and <a
13061 href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
13062 descriptions of Ogg transport streams. This specification document assumes a working
13063 knowledge of the concepts covered in these named backround documents. Please read them
13065 <!--l. 22--><p class="noindent" >
13066 <h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a
13067 id="x1-130000A.1.1"></a>Restrictions</h5>
13068 <!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
13069 streams in degenerate, unmultiplexed form only. That is:
13070 <ul class="itemize1">
13071 <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
13073 <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
13076 <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
13082 <!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
13083 types into a multi-stream Ogg file. At the time this document was written, Ogg was
13084 becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
13085 audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
13086 within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
13087 implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
13088 stream (naturally, application authors are encouraged to support full multiplexed Ogg
13090 <!--l. 55--><p class="noindent" >
13091 <h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a
13092 id="x1-131000A.1.2"></a>MIME type</h5>
13093 <!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
13094 applications should use <span
13095 class="cmtt-12">application/ogg</span>, while visual media should use <span
13096 class="cmtt-12">video/ogg</span>, and audio
13098 class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP
13099 encapsulated Vorbis should use <span
13100 class="cmtt-12">audio/vorbis </span>+ <span
13101 class="cmtt-12">audio/vorbis-config</span>.
13102 <!--l. 65--><p class="noindent" >
13103 <h4 class="subsectionHead"><span class="titlemark">A.2. </span> <a
13104 id="x1-132000A.2"></a>Encapsulation</h4>
13105 <!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
13106 <ul class="itemize1">
13107 <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
13108 as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
13109 results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
13112 <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
13114 <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
13115 more pages beginning on the second page of the logical stream. However many pages
13116 they span, the third header packet finishes the page on which it ends. The next (first
13117 audio) packet must begin on a fresh page.
13122 <li class="itemize">The granule position of these first pages containing only headers is zero.
13124 <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
13126 <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
13128 <li class="itemize">The last page is marked ’end of stream’ in the page flags.
13130 <li class="itemize">Vorbis packets may span page boundaries.
13132 <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
13133 samples (per channel; a stereo stream’s granule position does not increment at twice
13134 the speed of a mono stream).
13136 <li class="itemize">The granule position of a page represents the end PCM sample position of the last
13138 class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
13139 returned by decode, not an internal sample awaiting lapping with a subsequent block.
13140 A page that is entirely spanned by a single packet (that completes on a subsequent
13141 page) has no granule position, and the granule position is set to ’-1’.
13142 <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
13143 necessarily the middle sample from that block. If, eg, the current Vorbis packet
13144 encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
13145 decodable sample from the current packet be at position (3*long_block_length/4) -
13146 (short_block_length/4).
13148 <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
13149 started at position zero. Although the granule position belongs to the last completed
13150 packet on the page and a valid granule position must be positive, by inference it may
13151 indicate that the PCM position of the beginning of audio is positive or negative.
13152 <ul class="itemize2">
13153 <li class="itemize">A positive starting value simply indicates that this stream begins at some
13154 positive time offset, potentially within a larger program. This is a common case
13155 when connecting to the middle of broadcast stream.
13157 <li class="itemize">A negative value indicates that output samples preceeding time zero should be
13161 discarded during decoding; this technique is used to allow sample-granularity
13162 editing of the stream start time of already-encoded Vorbis streams. The number
13163 of samples to be discarded must not exceed the overlap-add span of the first two
13166 <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
13167 second finished audio packet must flush the page on which it appears and the
13168 third packet begin a fresh page. This allows the decoder to always be able to
13169 perform PCM position adjustments before needing to return any PCM data from
13170 synthesis, resulting in correct positioning information without any aditional seeking
13172 <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
13173 id="x1-133000A.2"></a><span
13174 class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return
13175 incorrect positioning information for seeking operations at the very beginning of the
13178 <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the
13179 final packet would normally return is used to end the stream on other than even frame
13180 boundaries. The difference between the actual available data returned and the
13181 declared amount indicates how many trailing samples to discard from the decoding
13187 <h3 class="sectionHead"><span class="titlemark">B. </span> <a
13188 id="x1-134000B"></a>Vorbis encapsulation in RTP</h3>
13189 <!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
13190 class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
13191 how to embed Vorbis audio in an RTP stream.
13198 <h3 class="likesectionHead"><a
13199 id="x1-135000B"></a>Colophon</h3>
13200 <!--l. 6--><p class="noindent" ><img
13201 src="fish_xiph_org.png" alt="PIC"
13203 <!--l. 9--><p class="noindent" >Ogg is a <a
13204 href="http://www.xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from
13205 corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
13207 href="http://www.xiph.org/about.html" >About the Xiph.Org Foundation</a> for details.
13208 <!--l. 16--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
13209 Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.Org
13210 Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification
13211 and certify specification compliance.
13212 <!--l. 22--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
13213 does not restrict third parties from distributing independent implementations of Vorbis software
13214 under other licenses.
13215 <!--l. 27--><p class="noindent" >Ogg, Vorbis, Xiph.Org Foundation and their logos are trademarks (tm) of the <a
13216 href="http://www.xiph.org/" >Xiph.Org
13217 Foundation</a>. These pages are copyright (C) 1994-2015 Xiph.Org Foundation. All rights
13219 <!--l. 32--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
13220 class="E">E</span>X</span></span>.
13224 <h3 class="likesectionHead"><a
13225 id="x1-136000B"></a>References</h3>
13226 <!--l. 133--><p class="noindent" >
13227 <div class="thebibliography">
13228 <p class="bibitem" ><span class="biblabel">
13229 [1]<span class="bibsp">   </span></span><a
13230 id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
13231 B. Edler, The use of multirate filter banks for coding of high quality digital audio,
13233 href="https://media.taricorp.net/eusipco_corrected.pdf" class="url" ><span
13234 class="cmtt-12">https://media.taricorp.net/eusipco_corrected.pdf</span></a>.
projects / platform / upstream / libvorbis.git / blob