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18 <h2 class="titleHead">Vorbis I specification</h2>
19 <div class="author" ><span
20 class="cmr-17">Xiph.Org Foundation</span></div><br />
21 <div class="date" ><span
22 class="cmr-17">July 4, 2020</span></div>
24 <h3 class="likesectionHead"><a
25 id="x1-1000"></a>Contents</h3>
26 <div class="tableofcontents">
27  <span class="sectionToc" >1 <a
28 href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
29 <br />  <span class="subsectionToc" >1.1 <a
30 href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
31 <br />   <span class="subsubsectionToc" >1.1.1 <a
32 href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
33 <br />   <span class="subsubsectionToc" >1.1.2 <a
34 href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
35 <br />   <span class="subsubsectionToc" >1.1.3 <a
36 href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
37 <br />   <span class="subsubsectionToc" >1.1.4 <a
38 href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
39 <br />   <span class="subsubsectionToc" >1.1.5 <a
40 href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
41 <br />   <span class="subsubsectionToc" >1.1.6 <a
42 href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
43 <br />  <span class="subsectionToc" >1.2 <a
44 href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
45 <br />   <span class="subsubsectionToc" >1.2.1 <a
46 href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
47 <br />   <span class="subsubsectionToc" >1.2.2 <a
48 href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
49 <br />   <span class="subsubsectionToc" >1.2.3 <a
50 href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
54 <br />   <span class="subsubsectionToc" >1.2.4 <a
55 href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
56 <br />   <span class="subsubsectionToc" >1.2.5 <a
57 href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
58 <br />   <span class="subsubsectionToc" >1.2.6 <a
59 href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
60 <br />  <span class="subsectionToc" >1.3 <a
61 href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
62 <br />   <span class="subsubsectionToc" >1.3.1 <a
63 href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
64 <br />   <span class="subsubsectionToc" >1.3.2 <a
65 href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
66 <br /> <span class="sectionToc" >2 <a
67 href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
68 <br />  <span class="subsectionToc" >2.1 <a
69 href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
70 <br />   <span class="subsubsectionToc" >2.1.1 <a
71 href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
72 <br />   <span class="subsubsectionToc" >2.1.2 <a
73 href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
74 <br />   <span class="subsubsectionToc" >2.1.3 <a
75 href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
76 <br />   <span class="subsubsectionToc" >2.1.4 <a
77 href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
78 <br />   <span class="subsubsectionToc" >2.1.5 <a
79 href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
80 <br />   <span class="subsubsectionToc" >2.1.6 <a
81 href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
82 <br />   <span class="subsubsectionToc" >2.1.7 <a
83 href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
84 <br />   <span class="subsubsectionToc" >2.1.8 <a
85 href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
86 <br />   <span class="subsubsectionToc" >2.1.9 <a
87 href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
88 <br /> <span class="sectionToc" >3 <a
89 href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
90 <br />  <span class="subsectionToc" >3.1 <a
91 href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
92 <br />   <span class="subsubsectionToc" >3.1.1 <a
93 href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
94 <br />  <span class="subsectionToc" >3.2 <a
95 href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
96 <br />   <span class="subsubsectionToc" >3.2.1 <a
97 href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
98 <br />  <span class="subsectionToc" >3.3 <a
99 href="#x1-580003.3" id="QQ2-1-63">Use of the codebook abstraction</a></span>
100 <br /> <span class="sectionToc" >4 <a
101 href="#x1-590004" id="QQ2-1-64">Codec Setup and Packet Decode</a></span>
102 <br />  <span class="subsectionToc" >4.1 <a
103 href="#x1-600004.1" id="QQ2-1-65">Overview</a></span>
104 <br />  <span class="subsectionToc" >4.2 <a
105 href="#x1-610004.2" id="QQ2-1-66">Header decode and decode setup</a></span>
106 <br />   <span class="subsubsectionToc" >4.2.1 <a
107 href="#x1-620004.2.1" id="QQ2-1-67">Common header decode</a></span>
108 <br />   <span class="subsubsectionToc" >4.2.2 <a
109 href="#x1-630004.2.2" id="QQ2-1-68">Identification header</a></span>
110 <br />   <span class="subsubsectionToc" >4.2.3 <a
111 href="#x1-640004.2.3" id="QQ2-1-69">Comment header</a></span>
115 <br />   <span class="subsubsectionToc" >4.2.4 <a
116 href="#x1-650004.2.4" id="QQ2-1-70">Setup header</a></span>
117 <br />  <span class="subsectionToc" >4.3 <a
118 href="#x1-720004.3" id="QQ2-1-78">Audio packet decode and synthesis</a></span>
119 <br />   <span class="subsubsectionToc" >4.3.1 <a
120 href="#x1-730004.3.1" id="QQ2-1-79">packet type, mode and window decode</a></span>
121 <br />   <span class="subsubsectionToc" >4.3.2 <a
122 href="#x1-740004.3.2" id="QQ2-1-80">floor curve decode</a></span>
123 <br />   <span class="subsubsectionToc" >4.3.3 <a
124 href="#x1-750004.3.3" id="QQ2-1-81">nonzero vector propagate</a></span>
125 <br />   <span class="subsubsectionToc" >4.3.4 <a
126 href="#x1-760004.3.4" id="QQ2-1-82">residue decode</a></span>
127 <br />   <span class="subsubsectionToc" >4.3.5 <a
128 href="#x1-770004.3.5" id="QQ2-1-83">inverse coupling</a></span>
129 <br />   <span class="subsubsectionToc" >4.3.6 <a
130 href="#x1-780004.3.6" id="QQ2-1-84">dot product</a></span>
131 <br />   <span class="subsubsectionToc" >4.3.7 <a
132 href="#x1-790004.3.7" id="QQ2-1-85">inverse MDCT</a></span>
133 <br />   <span class="subsubsectionToc" >4.3.8 <a
134 href="#x1-800004.3.8" id="QQ2-1-86">overlap_add</a></span>
135 <br />   <span class="subsubsectionToc" >4.3.9 <a
136 href="#x1-810004.3.9" id="QQ2-1-87">output channel order</a></span>
137 <br /> <span class="sectionToc" >5 <a
138 href="#x1-820005" id="QQ2-1-88">comment field and header specification</a></span>
139 <br />  <span class="subsectionToc" >5.1 <a
140 href="#x1-830005.1" id="QQ2-1-89">Overview</a></span>
141 <br />  <span class="subsectionToc" >5.2 <a
142 href="#x1-840005.2" id="QQ2-1-90">Comment encoding</a></span>
143 <br />   <span class="subsubsectionToc" >5.2.1 <a
144 href="#x1-850005.2.1" id="QQ2-1-91">Structure</a></span>
145 <br />   <span class="subsubsectionToc" >5.2.2 <a
146 href="#x1-860005.2.2" id="QQ2-1-92">Content vector format</a></span>
147 <br />   <span class="subsubsectionToc" >5.2.3 <a
148 href="#x1-890005.2.3" id="QQ2-1-95">Encoding</a></span>
149 <br /> <span class="sectionToc" >6 <a
150 href="#x1-900006" id="QQ2-1-96">Floor type 0 setup and decode</a></span>
151 <br />  <span class="subsectionToc" >6.1 <a
152 href="#x1-910006.1" id="QQ2-1-97">Overview</a></span>
153 <br />  <span class="subsectionToc" >6.2 <a
154 href="#x1-920006.2" id="QQ2-1-98">Floor 0 format</a></span>
155 <br />   <span class="subsubsectionToc" >6.2.1 <a
156 href="#x1-930006.2.1" id="QQ2-1-99">header decode</a></span>
157 <br />   <span class="subsubsectionToc" >6.2.2 <a
158 href="#x1-940006.2.2" id="QQ2-1-100">packet decode</a></span>
159 <br />   <span class="subsubsectionToc" >6.2.3 <a
160 href="#x1-950006.2.3" id="QQ2-1-101">curve computation</a></span>
161 <br /> <span class="sectionToc" >7 <a
162 href="#x1-970007" id="QQ2-1-103">Floor type 1 setup and decode</a></span>
163 <br />  <span class="subsectionToc" >7.1 <a
164 href="#x1-980007.1" id="QQ2-1-104">Overview</a></span>
165 <br />  <span class="subsectionToc" >7.2 <a
166 href="#x1-990007.2" id="QQ2-1-105">Floor 1 format</a></span>
167 <br />   <span class="subsubsectionToc" >7.2.1 <a
168 href="#x1-1000007.2.1" id="QQ2-1-106">model</a></span>
169 <br />   <span class="subsubsectionToc" >7.2.2 <a
170 href="#x1-1010007.2.2" id="QQ2-1-111">header decode</a></span>
171 <br />   <span class="subsubsectionToc" >7.2.3 <a
172 href="#x1-1020007.2.3" id="QQ2-1-112">packet decode</a></span>
176 <br />   <span class="subsubsectionToc" >7.2.4 <a
177 href="#x1-1030007.2.4" id="QQ2-1-113">curve computation</a></span>
178 <br /> <span class="sectionToc" >8 <a
179 href="#x1-1040008" id="QQ2-1-114">Residue setup and decode</a></span>
180 <br />  <span class="subsectionToc" >8.1 <a
181 href="#x1-1050008.1" id="QQ2-1-115">Overview</a></span>
182 <br />  <span class="subsectionToc" >8.2 <a
183 href="#x1-1060008.2" id="QQ2-1-116">Residue format</a></span>
184 <br />  <span class="subsectionToc" >8.3 <a
185 href="#x1-1070008.3" id="QQ2-1-118">residue 0</a></span>
186 <br />  <span class="subsectionToc" >8.4 <a
187 href="#x1-1080008.4" id="QQ2-1-119">residue 1</a></span>
188 <br />  <span class="subsectionToc" >8.5 <a
189 href="#x1-1090008.5" id="QQ2-1-120">residue 2</a></span>
190 <br />  <span class="subsectionToc" >8.6 <a
191 href="#x1-1100008.6" id="QQ2-1-122">Residue decode</a></span>
192 <br />   <span class="subsubsectionToc" >8.6.1 <a
193 href="#x1-1110008.6.1" id="QQ2-1-123">header decode</a></span>
194 <br />   <span class="subsubsectionToc" >8.6.2 <a
195 href="#x1-1120008.6.2" id="QQ2-1-124">packet decode</a></span>
196 <br />   <span class="subsubsectionToc" >8.6.3 <a
197 href="#x1-1130008.6.3" id="QQ2-1-125">format 0 specifics</a></span>
198 <br />   <span class="subsubsectionToc" >8.6.4 <a
199 href="#x1-1140008.6.4" id="QQ2-1-126">format 1 specifics</a></span>
200 <br />   <span class="subsubsectionToc" >8.6.5 <a
201 href="#x1-1150008.6.5" id="QQ2-1-127">format 2 specifics</a></span>
202 <br /> <span class="sectionToc" >9 <a
203 href="#x1-1160009" id="QQ2-1-128">Helper equations</a></span>
204 <br />  <span class="subsectionToc" >9.1 <a
205 href="#x1-1170009.1" id="QQ2-1-129">Overview</a></span>
206 <br />  <span class="subsectionToc" >9.2 <a
207 href="#x1-1180009.2" id="QQ2-1-130">Functions</a></span>
208 <br />   <span class="subsubsectionToc" >9.2.1 <a
209 href="#x1-1190009.2.1" id="QQ2-1-131">ilog</a></span>
210 <br />   <span class="subsubsectionToc" >9.2.2 <a
211 href="#x1-1200009.2.2" id="QQ2-1-132">float32_unpack</a></span>
212 <br />   <span class="subsubsectionToc" >9.2.3 <a
213 href="#x1-1210009.2.3" id="QQ2-1-133">lookup1_values</a></span>
214 <br />   <span class="subsubsectionToc" >9.2.4 <a
215 href="#x1-1220009.2.4" id="QQ2-1-134">low_neighbor</a></span>
216 <br />   <span class="subsubsectionToc" >9.2.5 <a
217 href="#x1-1230009.2.5" id="QQ2-1-135">high_neighbor</a></span>
218 <br />   <span class="subsubsectionToc" >9.2.6 <a
219 href="#x1-1240009.2.6" id="QQ2-1-136">render_point</a></span>
220 <br />   <span class="subsubsectionToc" >9.2.7 <a
221 href="#x1-1250009.2.7" id="QQ2-1-137">render_line</a></span>
222 <br /> <span class="sectionToc" >10 <a
223 href="#x1-12600010" id="QQ2-1-138">Tables</a></span>
224 <br />  <span class="subsectionToc" >10.1 <a
225 href="#x1-12700010.1" id="QQ2-1-139">floor1_inverse_dB_table</a></span>
226 <br /> <span class="sectionToc" >A <a
227 href="#x1-128000A" id="QQ2-1-140">Embedding Vorbis into an Ogg stream</a></span>
228 <br />  <span class="subsectionToc" >A.1 <a
229 href="#x1-129000A.1" id="QQ2-1-141">Overview</a></span>
230 <br />   <span class="subsubsectionToc" >A.1.1 <a
231 href="#x1-130000A.1.1" id="QQ2-1-142">Restrictions</a></span>
232 <br />   <span class="subsubsectionToc" >A.1.2 <a
233 href="#x1-131000A.1.2" id="QQ2-1-143">MIME type</a></span>
237 <br />  <span class="subsectionToc" >A.2 <a
238 href="#x1-132000A.2" id="QQ2-1-144">Encapsulation</a></span>
239 <br /> <span class="sectionToc" >B <a
240 href="#x1-134000B" id="QQ2-1-146">Vorbis encapsulation in RTP</a></span>
245 <h3 class="sectionHead"><span class="titlemark">1. </span> <a
246 id="x1-20001"></a>Introduction and Description</h3>
247 <!--l. 5--><p class="noindent" >
248 <h4 class="subsectionHead"><span class="titlemark">1.1. </span> <a
249 id="x1-30001.1"></a>Overview</h4>
250 <!--l. 7--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
251 specification appears beginning in <a
252 href="#x1-590004">section 4</a>, “<a
253 href="#x1-590004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later
254 sections assume a high-level understanding of the Vorbis decode process, which is provided
256 <!--l. 14--><p class="noindent" >
257 <h5 class="subsubsectionHead"><span class="titlemark">1.1.1. </span> <a
258 id="x1-40001.1.1"></a>Application</h5>
259 <!--l. 15--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
260 flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At
261 the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same
262 league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT
263 rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower
264 and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
265 representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
267 <!--l. 28--><p class="noindent" >
268 <h5 class="subsubsectionHead"><span class="titlemark">1.1.2. </span> <a
269 id="x1-50001.1.2"></a>Classification</h5>
270 <!--l. 29--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete
271 Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in
272 Vorbis II to offer better transient response and reproduction using a transform better suited to
273 localized time events.
277 <!--l. 36--><p class="noindent" >
278 <h5 class="subsubsectionHead"><span class="titlemark">1.1.3. </span> <a
279 id="x1-60001.1.3"></a>Assumptions</h5>
280 <!--l. 38--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
281 low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
282 require more working memory as Vorbis has no static probability model; the vector codebooks
283 used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
284 bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to
285 which they are pre-decoded into a cache is the dominant factor in decoder memory
287 <!--l. 49--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it
288 is solely a method of accepting input audio, dividing it into individual frames and
289 compressing these frames into raw, unformatted ’packets’. The decoder then accepts
290 these raw packets in sequence, decodes them, synthesizes audio frames from them, and
291 reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form
292 variable bit rate (VBR) codec and packets have no minimum size, maximum size, or
293 fixed/expected size. Packets are designed that they may be truncated (or padded)
294 and remain decodable; this is not to be considered an error condition and is used
295 extensively in bitrate management in peeling. Both the transport mechanism and
296 decoder must allow that a packet may be any size, or end before or after packet decode
298 <!--l. 63--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
299 framing, sync, positioning and error correction in accordance with these design assumptions, such
300 as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
301 document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
302 although this is by no means a requirement or fundamental assumption in the Vorbis
304 <!--l. 71--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
305 href="#x1-128000A">section A</a>,
307 href="#x1-128000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
308 <!--l. 76--><p class="noindent" >
309 <h5 class="subsubsectionHead"><span class="titlemark">1.1.4. </span> <a
310 id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
311 <!--l. 78--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
312 decades of continuous encoder improvement before running out of room within the codec
313 specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
314 extreme of forward adaptive.
318 <!--l. 84--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis
319 developer to keep in mind) is that the entire probability model of the codec, the Huffman and
320 VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
321 parameters (often several hundred fields). This makes it impossible, as it would be with
322 MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
323 decode at any frame in the stream without having previously fetched the codec setup
325 <!--l. 94--><p class="noindent" ><span class="likesubparagraphHead"><a
326 id="x1-80001.1.4"></a><span
327 class="cmbx-12">Note:</span></span> Vorbis <span
328 class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
329 has been initialized/setup with the setup headers.
330 <!--l. 100--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream
331 headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less
332 is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
333 <!--l. 105--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is
334 an unusual design and thus causes some amount of complaint among engineers as this runs
335 against current design trends (and also points out limitations in some existing software/interface
336 designs, such as Windows’ ACM codec framework). However, we find that it does not
337 fundamentally limit Vorbis’ suitable application space.
338 <!--l. 114--><p class="noindent" >
339 <h5 class="subsubsectionHead"><span class="titlemark">1.1.5. </span> <a
340 id="x1-90001.1.5"></a>Format Specification</h5>
341 <!--l. 115--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets
342 that are correctly decoded by the reference Vorbis decoder described below may be considered
343 a proper Vorbis encoder. A decoder must faithfully and completely implement the
344 specification defined below (except where noted) to be considered a proper Vorbis
346 <!--l. 122--><p class="noindent" >
347 <h5 class="subsubsectionHead"><span class="titlemark">1.1.6. </span> <a
348 id="x1-100001.1.6"></a>Hardware Profile</h5>
352 <!--l. 123--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
353 embedded design. For this reason, embedded designs are allowed to deviate in limited ways from
354 the ‘full’ decode specification yet still be certified compliant. These optional omissions are
355 labelled in the spec where relevant.
356 <!--l. 130--><p class="noindent" >
357 <h4 class="subsectionHead"><span class="titlemark">1.2. </span> <a
358 id="x1-110001.2"></a>Decoder Configuration</h4>
359 <!--l. 132--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
360 perform specific functions in the decode pipeline. Each different component instance of a specific
361 type is semantically interchangeable; decoder configuration consists both of internal component
362 configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
363 arrangement is roughly as follows:
366 <!--l. 140--><p class="noindent" >
368 <!--l. 141--><p class="noindent" ><img
369 src="components.png" alt="PIC"
371 <br /> <div class="caption"
372 ><span class="id">Figure 1: </span><span
373 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-110011 -->
375 <!--l. 145--><p class="noindent" >
376 <h5 class="subsubsectionHead"><span class="titlemark">1.2.1. </span> <a
377 id="x1-120001.2.1"></a>Global Config</h5>
378 <!--l. 146--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
379 version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
380 configuration is in the context of specific components.
381 <!--l. 151--><p class="noindent" >
382 <h5 class="subsubsectionHead"><span class="titlemark">1.2.2. </span> <a
383 id="x1-130001.2.2"></a>Mode</h5>
387 <!--l. 153--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
389 <!--l. 156--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
390 methods with the intention of choosing a method best suited to that frame. Different
391 modes are, e.g. how frame size is changed from frame to frame. The mode number of a
392 frame serves as a top level configuration switch for all other specific aspects of frame
394 <!--l. 163--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis
395 window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping
396 number. The mapping number specifies which mapping configuration instance to use for low-level
397 packet decode and synthesis.
398 <!--l. 170--><p class="noindent" >
399 <h5 class="subsubsectionHead"><span class="titlemark">1.2.3. </span> <a
400 id="x1-140001.2.3"></a>Mapping</h5>
401 <!--l. 172--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets
402 of channel vectors together for grouped encoding and decoding. These submaps are
403 not references to external components; the submap list is internal and specific to a
405 <!--l. 177--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors
406 within a mapping. The submap functions as a last layer of indirection such that specific special
407 floor or residue settings can be applied not only to all the vectors in a given mode, but also
408 specific vectors in a specific mode. Each submap specifies the proper floor and residue
409 instance number to use for decoding that submap’s spectral floor and spectral residue
411 <!--l. 185--><p class="noindent" >As an example:
412 <!--l. 187--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth
413 channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a
414 full-spectrum version of it as with the other channels. The submapping mechanism can be used
415 to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only
416 representation to the bass channel, thus saving space. In this example, channels 0-4 belong to
417 submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which
418 uses a bass-only representation.
422 <!--l. 198--><p class="noindent" >
423 <h5 class="subsubsectionHead"><span class="titlemark">1.2.4. </span> <a
424 id="x1-150001.2.4"></a>Floor</h5>
425 <!--l. 200--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
426 representation of the audio spectrum for the given channel in the current frame, generally used
427 akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has
428 historically used it as a unit-baseline for spectral resolution.
429 <!--l. 207--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
430 amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
431 interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
432 are semantically interchangeable in encoding/decoding. However, floor type 1 provides more
433 stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and
434 high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
436 <!--l. 217--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
437 encoder past Xiph.Org’s own beta 4 makes use of floor 0.
438 <!--l. 221--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy
439 coding to save space. For this reason, a floor configuration generally refers to multiple
440 codebooks in the codebook component list. Entropy coding is thus provided as an
441 abstraction, and each floor instance may choose from any and all available codebooks when
443 <!--l. 229--><p class="noindent" >
444 <h5 class="subsubsectionHead"><span class="titlemark">1.2.5. </span> <a
445 id="x1-160001.2.5"></a>Residue</h5>
446 <!--l. 230--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been
447 subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector
448 quantization according to one of three specific packing/coding algorithms numbered
449 0 through 2. The packing algorithm details are configured by residue instance. As
450 with the floor components, the final VQ/entropy encoding is provided by external
451 codebook instances and each residue instance may choose from any and all available
453 <!--l. 240--><p class="noindent" >
457 <h5 class="subsubsectionHead"><span class="titlemark">1.2.6. </span> <a
458 id="x1-170001.2.6"></a>Codebooks</h5>
459 <!--l. 242--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use
460 the entropy-decoded integer value as an offset into an index of output value vectors, returning
461 the indicated vector of values.
462 <!--l. 247--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
463 representation. This tree is tightly packed using one of several methods, depending on whether
464 codeword lengths are ordered or unordered, or the tree is sparse.
465 <!--l. 252--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
466 the vector index is encoded as a single list of values of possible values that are then permuted
467 into a list of n-dimensional rows (lattice VQ).
468 <!--l. 259--><p class="noindent" >
469 <h4 class="subsectionHead"><span class="titlemark">1.3. </span> <a
470 id="x1-180001.3"></a>High-level Decode Process</h4>
471 <!--l. 261--><p class="noindent" >
472 <h5 class="subsubsectionHead"><span class="titlemark">1.3.1. </span> <a
473 id="x1-190001.3.1"></a>Decode Setup</h5>
474 <!--l. 263--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
475 stream to be decoded. Vorbis uses three header packets; all are required, in-order, by
476 this specification. Once set up, decode may begin at any audio packet belonging to
477 the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio
479 <!--l. 270--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
481 <!--l. 273--><p class="noindent" ><span class="paragraphHead"><a
482 id="x1-200001.3.1"></a><span
483 class="cmbx-12">Identification Header</span></span>
484 The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
485 characteristics of the stream such as sample rate and number of channels.
489 <!--l. 278--><p class="noindent" ><span class="paragraphHead"><a
490 id="x1-210001.3.1"></a><span
491 class="cmbx-12">Comment Header</span></span>
492 The comment header includes user text comments (“tags”) and a vendor string for the
493 application/library that produced the bitstream. The encoding and proper use of the comment
494 header is described in <a
495 href="#x1-820005">section 5</a>, “<a
496 href="#x1-820005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
497 <!--l. 283--><p class="noindent" ><span class="paragraphHead"><a
498 id="x1-220001.3.1"></a><span
499 class="cmbx-12">Setup Header</span></span>
500 The setup header includes extensive CODEC setup information as well as the complete VQ and
501 Huffman codebooks needed for decode.
502 <!--l. 288--><p class="noindent" >
503 <h5 class="subsubsectionHead"><span class="titlemark">1.3.2. </span> <a
504 id="x1-230001.3.2"></a>Decode Procedure</h5>
505 <!--l. 290--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
506 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
508 class="enumerate-enumitem">decode packet type flag
509 </dd><dt class="enumerate-enumitem">
511 class="enumerate-enumitem">decode mode number
512 </dd><dt class="enumerate-enumitem">
514 class="enumerate-enumitem">decode window shape (long windows only)
515 </dd><dt class="enumerate-enumitem">
517 class="enumerate-enumitem">decode floor
518 </dd><dt class="enumerate-enumitem">
520 class="enumerate-enumitem">decode residue into residue vectors
521 </dd><dt class="enumerate-enumitem">
523 class="enumerate-enumitem">inverse channel coupling of residue vectors
524 </dd><dt class="enumerate-enumitem">
526 class="enumerate-enumitem">generate floor curve from decoded floor data
527 </dd><dt class="enumerate-enumitem">
529 class="enumerate-enumitem">compute dot product of floor and residue, producing audio spectrum vector
530 </dd><dt class="enumerate-enumitem">
532 class="enumerate-enumitem">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis
537 </dd><dt class="enumerate-enumitem">
539 class="enumerate-enumitem">overlap/add left-hand output of transform with right-hand output of previous frame
540 </dd><dt class="enumerate-enumitem">
542 class="enumerate-enumitem">store right hand-data from transform of current frame for future lapping
543 </dd><dt class="enumerate-enumitem">
545 class="enumerate-enumitem">if not first frame, return results of overlap/add as audio result of current frame</dd></dl>
546 <!--l. 307--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can
547 take advantage of symmetries in the MDCT to store the right-hand transform data of a partial
548 MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before
549 overlap/add with the next frame. This optimization produces entirely equivalent output and is
550 naturally perfectly legal. The decoder must be <span
551 class="cmti-12">entirely mathematically equivalent </span>to the
552 specification, it need not be a literal semantic implementation.
553 <!--l. 316--><p class="noindent" ><span class="paragraphHead"><a
554 id="x1-240001.3.2"></a><span
555 class="cmbx-12">Packet type decode</span></span>
556 Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis
557 headers described above. The fourth packet type marks an audio packet. All other packet types
558 are reserved; packets marked with a reserved type should be ignored.
559 <!--l. 323--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
560 audio packet decode is to read and verify the packet type; <span
561 class="cmti-12">a non-audio packet when audio is</span>
563 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
565 class="cmti-12">packet and not attempt decoding it to audio</span>.
566 <!--l. 333--><p class="noindent" ><span class="paragraphHead"><a
567 id="x1-250001.3.2"></a><span
568 class="cmbx-12">Mode decode</span></span>
569 Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
570 which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
571 offset into the mode instance index.
572 <!--l. 340--><p class="noindent" ><span class="paragraphHead"><a
573 id="x1-260001.3.2"></a><span
574 class="cmbx-12">Window shape decode (long windows only)</span></span>
575 Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I,
576 legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis
577 handles channels as independent vectors and these frame sizes are in samples per
582 <!--l. 347--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
583 avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
584 according to MDCT requirements, overlapped 50% with the output of the previous frame and
585 added. The window shape assures seamless reconstruction.
586 <!--l. 353--><p class="noindent" >This is easy to visualize in the case of equal sized-windows:
589 <!--l. 355--><p class="noindent" >
591 <!--l. 356--><p class="noindent" ><img
592 src="window1.png" alt="PIC"
594 <br /> <div class="caption"
595 ><span class="id">Figure 2: </span><span
596 class="content">overlap of two equal-sized windows</span></div><!--tex4ht:label?: x1-260012 -->
598 <!--l. 360--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows:
601 <!--l. 363--><p class="noindent" >
603 <!--l. 364--><p class="noindent" ><img
604 src="window2.png" alt="PIC"
606 <br /> <div class="caption"
607 ><span class="id">Figure 3: </span><span
608 class="content">overlap of a long and a short window</span></div><!--tex4ht:label?: x1-260023 -->
610 <!--l. 368--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
611 seamless lapping as above. It is possible to correctly infer window shape to be applied to the
612 current window from knowing the sizes of the current, previous and next window. It is legal for a
613 decoder to use this method. However, in the case of a long window (short windows require no
614 modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although
615 not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to
616 the point of lapping entirely independently of any other packet, allowing easier abstraction of
617 decode layers as well as allowing a greater level of easy parallelism in encode and
619 <!--l. 381--><p class="noindent" >A description of valid window functions for use with an inverse MDCT can be found in <span class="cite">[<a
620 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
621 Vorbis windows all use the slope function
622 <center class="math-display" >
624 src="Vorbis_I_spec0x.png" alt="y = sin (.5 * π sin2((x + .5)∕n * π)).
628 " class="math-display" ></center>
629 <!--l. 384--><p class="nopar" >
630 <!--l. 388--><p class="noindent" ><span class="paragraphHead"><a
631 id="x1-270001.3.2"></a><span
632 class="cmbx-12">floor decode</span></span>
633 Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
634 specifies which floor configuration to use. All floors are decoded before residue decode
636 <!--l. 394--><p class="noindent" ><span class="paragraphHead"><a
637 id="x1-280001.3.2"></a><span
638 class="cmbx-12">residue decode</span></span>
639 Although the number of residue vectors equals the number of channels, channel coupling may
640 mean that the raw residue vectors extracted during decode do not map directly to specific
641 channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or
642 angle. The coupling relationships are described in the codec setup and may differ from frame to
643 frame, due to different mode numbers.
644 <!--l. 403--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from
645 submap 0 through n-1. This differs from floors which are coded using a configuration provided by
646 submap number, but are coded individually in channel order.
647 <!--l. 410--><p class="noindent" ><span class="paragraphHead"><a
648 id="x1-290001.3.2"></a><span
649 class="cmbx-12">inverse channel coupling</span></span>
650 A detailed discussion of stereo in the Vorbis codec can be found in the document
652 href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo
653 coupling, but the stereo document also gives a good overview of the generic coupling
655 <!--l. 418--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a
656 pair at a time in the order and using the vectors specified in the current mapping
657 configuration. The decoupling operation is the same for all pairs, converting square polar
658 representation (where one vector is magnitude and the second angle) back to Cartesian
660 <!--l. 425--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
661 represent the fine spectral detail of each output channel.
665 <!--l. 431--><p class="noindent" ><span class="paragraphHead"><a
666 id="x1-300001.3.2"></a><span
667 class="cmbx-12">generate floor curve</span></span>
668 The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to
669 generate the output curve when the floor data is decoded from the raw packet, or it
670 can be generated after inverse coupling and applied to the spectral residue directly,
671 combining generation and the dot product into one step and eliminating some working
673 <!--l. 440--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied
674 (dot product) by the linear-range, linear-domain spectral residue.
675 <!--l. 446--><p class="noindent" ><span class="paragraphHead"><a
676 id="x1-310001.3.2"></a><span
677 class="cmbx-12">compute floor/residue dot product</span></span>
678 This step is straightforward; for each output channel, the decoder multiplies the floor curve and
679 residue vectors element by element, producing the finished audio spectrum of each
681 <!--l. 454--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
682 implementation might be to assume that a 32 bit fixed-point representation for floor and
683 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
684 in all cases because it happens to mostly work with the current Xiph.Org reference
686 <!--l. 461--><p class="noindent" >However, floor vector values can span <span
687 class="cmsy-10x-x-120">~</span>140dB (<span
688 class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum
689 vector should represent a minimum of 120dB (<span
690 class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16
691 bit PCM device. For the residue vector to represent full scale if the floor is nailed
693 class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
694 full scale if the floor is nailed at 0dB, it must be able to represent <span
695 class="cmsy-10x-x-120">-</span>140dB to +0dB.
696 Thus, in order to handle full range dynamics, a residue vector may span <span
697 class="cmsy-10x-x-120">-</span>140dB to
698 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
699 residue vector must be able to represent a 48 bit range and the dot product must
700 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
701 achieved using large (64 bit or larger) integers, or implementing a movable binary point
703 <!--l. 478--><p class="noindent" ><span class="paragraphHead"><a
704 id="x1-320001.3.2"></a><span
705 class="cmbx-12">inverse monolithic transform (MDCT)</span></span>
706 The audio spectrum is converted back into time domain PCM audio via an inverse Modified
707 Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
708 <span class="cite">[<a
709 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
710 <!--l. 484--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be
714 lapped with surrounding frames using an appropriate window (such as the Vorbis window) before
715 the MDCT can be considered orthogonal.
716 <!--l. 491--><p class="noindent" ><span class="paragraphHead"><a
717 id="x1-330001.3.2"></a><span
718 class="cmbx-12">overlap/add data</span></span>
719 Windowed MDCT output is overlapped and added with the right hand data of the previous
720 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
721 current window (as illustrated in the window overlap diagram). At this point, the audio data
722 between the center of the previous frame and the center of the current frame is now finished and
723 ready to be returned.
724 <!--l. 500--><p class="noindent" ><span class="paragraphHead"><a
725 id="x1-340001.3.2"></a><span
726 class="cmbx-12">cache right hand data</span></span>
727 The decoder must cache the right hand portion of the current frame to be lapped with the left
728 hand portion of the next frame.
729 <!--l. 506--><p class="noindent" ><span class="paragraphHead"><a
730 id="x1-350001.3.2"></a><span
731 class="cmbx-12">return finished audio data</span></span>
732 The overlapped portion produced from overlapping the previous and current frame data
733 is finished data to be returned by the decoder. This data spans from the center of
734 the previous window to the center of the current window. In the case of same-sized
735 windows, the amount of data to return is one-half block consisting of and only of the
736 overlapped portions. When overlapping a short and long window, much of the returned
737 range is not actually overlap. This does not damage transform orthogonality. Pay
738 attention however to returning the correct data range; the amount of data to be returned
740 <!--l. 518--><p class="noindent" >
741 <div class="fancyvrb" id="fancyvrb1"><a
742 id="x1-35002r1"></a><span
743 class="cmr-6">1</span><span
744 class="cmtt-8">window</span><span
745 class="cmtt-8">_blocksize(previous</span><span
746 class="cmtt-8">_window)/4+window</span><span
747 class="cmtt-8">_blocksize(current</span><span
748 class="cmtt-8">_window)/4</span></div>
749 <!--l. 522--><p class="noindent" >from the center of the previous window to the center of the current window.
750 <!--l. 525--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
751 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
752 PCM output offset is ’0’ (as no data has been returned yet).
759 <h3 class="sectionHead"><span class="titlemark">2. </span> <a
760 id="x1-360002"></a>Bitpacking Convention</h3>
761 <!--l. 5--><p class="noindent" >
762 <h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a
763 id="x1-370002.1"></a>Overview</h4>
764 <!--l. 7--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
765 integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
766 encoder and then read one-by-one in the same monotonically increasing order by the decoder.
767 Most current binary storage arrangements group bits into a native word size of eight bits
768 (octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
769 bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
770 representation in fixed-width words.
771 <!--l. 18--><p class="noindent" >
772 <h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a
773 id="x1-380002.1.1"></a>octets, bytes and words</h5>
774 <!--l. 20--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
775 This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
776 For purposes of the bitpacking convention, a byte implies the native, smallest integer
777 storage representation offered by a platform. On modern platforms, this is generally
778 assumed to be eight bits (not necessarily because of the processor but because of the
779 filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
780 atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
782 <!--l. 31--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
783 to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
784 bitpacking convention is still well defined for any native byte size; Vorbis uses the native
785 bit-width of a given storage system. This document assumes that a byte is one octet for purposes
787 <!--l. 38--><p class="noindent" >
791 <h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a
792 id="x1-390002.1.2"></a>bit order</h5>
793 <!--l. 40--><p class="noindent" >A byte has a well-defined ’least significant’ bit (LSb), which is the only bit set when the byte is
794 storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
795 opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
796 class="cmmi-12">n </span>(<span
797 class="cmmi-12">n </span>= 7 in an
799 <!--l. 49--><p class="noindent" >
800 <h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a
801 id="x1-400002.1.3"></a>byte order</h5>
802 <!--l. 51--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
803 common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
804 highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
805 which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
807 <!--l. 58--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
808 word, level, thus host word ordering is of a concern only during optimization when writing high
809 performance code that operates on a word of storage at a time rather than by byte.
810 Logically, bytes are always coded and decoded in order from byte zero through byte
812 class="cmmi-12">n</span>.
813 <!--l. 67--><p class="noindent" >
814 <h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a
815 id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
816 <!--l. 69--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
817 wide, into packets. These integer fields are not aligned to the boundaries of the byte
818 representation; the next field is written at the bit position at which the previous field
820 <!--l. 74--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
821 bitstream first, followed by next least significant bit, etc, until the requested number of bits
822 have been coded. When packing the bits into bytes, the encoder begins by placing
823 the LSb of the integer to be written into the least significant unused bit position of
824 the destination byte, followed by the next-least significant bit of the source integer
825 and so on up to the requested number of bits. When all bits of the destination byte
826 have been filled, encoding continues by zeroing all bits of the next byte and writing
827 the next bit into the bit position 0 of that byte. Decoding follows the same process
831 as encoding, but by reading bits from the byte stream and reassembling them into
833 <!--l. 89--><p class="noindent" >
834 <h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a
835 id="x1-420002.1.5"></a>signedness</h5>
836 <!--l. 91--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
837 given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
838 either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
839 encoder and decoder are responsible for knowing if fields are to be treated as signed or
841 <!--l. 100--><p class="noindent" >
842 <h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a
843 id="x1-430002.1.6"></a>coding example</h5>
844 <!--l. 102--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
845 <!--l. 105--><p class="noindent" >
846 <div class="fancyvrb" id="fancyvrb2"><a
847 id="x1-43002r1"></a><span
848 class="cmr-6">1</span><span
849 class="cmtt-8"> </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><br class="fancyvrb" /><a
863 id="x1-43004r2"></a><span
864 class="cmr-6">2</span><span
865 class="cmtt-8"> </span><span
866 class="cmtt-8"> </span><span
867 class="cmtt-8"> </span><span
868 class="cmtt-8"> </span><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"> V</span><br class="fancyvrb" /><a
879 id="x1-43006r3"></a><span
880 class="cmr-6">3</span><br class="fancyvrb" /><a
881 id="x1-43008r4"></a><span
882 class="cmr-6">4</span><span
883 class="cmtt-8"> </span><span
884 class="cmtt-8"> </span><span
885 class="cmtt-8"> </span><span
886 class="cmtt-8"> </span><span
887 class="cmtt-8"> </span><span
888 class="cmtt-8"> </span><span
889 class="cmtt-8"> </span><span
890 class="cmtt-8"> 7</span><span
891 class="cmtt-8"> 6</span><span
892 class="cmtt-8"> 5</span><span
893 class="cmtt-8"> 4</span><span
894 class="cmtt-8"> 3</span><span
895 class="cmtt-8"> 2</span><span
896 class="cmtt-8"> 1</span><span
897 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
898 id="x1-43010r5"></a><span
899 class="cmr-6">5</span><span
900 class="cmtt-8">byte</span><span
901 class="cmtt-8"> 0</span><span
902 class="cmtt-8"> [0</span><span
903 class="cmtt-8"> 0</span><span
904 class="cmtt-8"> 0</span><span
905 class="cmtt-8"> 0</span><span
906 class="cmtt-8"> 1</span><span
907 class="cmtt-8"> 1</span><span
908 class="cmtt-8"> 0</span><span
909 class="cmtt-8"> 0]</span><span
910 class="cmtt-8"> </span><span
911 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
912 id="x1-43012r6"></a><span
913 class="cmr-6">6</span><span
914 class="cmtt-8">byte</span><span
915 class="cmtt-8"> 1</span><span
916 class="cmtt-8"> [</span><span
917 class="cmtt-8"> </span><span
918 class="cmtt-8"> </span><span
919 class="cmtt-8"> </span><span
920 class="cmtt-8"> </span><span
921 class="cmtt-8"> </span><span
922 class="cmtt-8"> </span><span
923 class="cmtt-8"> </span><span
924 class="cmtt-8"> </span><span
925 class="cmtt-8"> </span><span
926 class="cmtt-8"> </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>
932 <br class="fancyvrb" /><a
933 id="x1-43014r7"></a><span
934 class="cmr-6">7</span><span
935 class="cmtt-8">byte</span><span
936 class="cmtt-8"> 2</span><span
937 class="cmtt-8"> [</span><span
938 class="cmtt-8"> </span><span
939 class="cmtt-8"> </span><span
940 class="cmtt-8"> </span><span
941 class="cmtt-8"> </span><span
942 class="cmtt-8"> </span><span
943 class="cmtt-8"> </span><span
944 class="cmtt-8"> </span><span
945 class="cmtt-8"> </span><span
946 class="cmtt-8"> </span><span
947 class="cmtt-8"> </span><span
948 class="cmtt-8"> </span><span
949 class="cmtt-8"> </span><span
950 class="cmtt-8"> </span><span
951 class="cmtt-8"> </span><span
952 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
953 id="x1-43016r8"></a><span
954 class="cmr-6">8</span><span
955 class="cmtt-8">byte</span><span
956 class="cmtt-8"> 3</span><span
957 class="cmtt-8"> [</span><span
958 class="cmtt-8"> </span><span
959 class="cmtt-8"> </span><span
960 class="cmtt-8"> </span><span
961 class="cmtt-8"> </span><span
962 class="cmtt-8"> </span><span
963 class="cmtt-8"> </span><span
964 class="cmtt-8"> </span><span
965 class="cmtt-8"> </span><span
966 class="cmtt-8"> </span><span
967 class="cmtt-8"> </span><span
968 class="cmtt-8"> </span><span
969 class="cmtt-8"> </span><span
970 class="cmtt-8"> </span><span
971 class="cmtt-8"> </span><span
972 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
973 id="x1-43018r9"></a><span
974 class="cmr-6">9</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><span
986 class="cmtt-8"> </span><span
987 class="cmtt-8"> ...</span><br class="fancyvrb" /><a
988 id="x1-43020r10"></a><span
989 class="cmr-6">10</span><span
990 class="cmtt-8">byte</span><span
991 class="cmtt-8"> n</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><span
1003 class="cmtt-8"> </span><span
1004 class="cmtt-8"> </span><span
1005 class="cmtt-8"> </span><span
1006 class="cmtt-8"> </span><span
1007 class="cmtt-8"> ]</span><span
1008 class="cmtt-8"> </span><span
1009 class="cmtt-8"> bytestream</span><span
1010 class="cmtt-8"> length</span><span
1011 class="cmtt-8"> ==</span><span
1012 class="cmtt-8"> 1</span><span
1013 class="cmtt-8"> byte</span><br class="fancyvrb" /><a
1014 id="x1-43022r11"></a><span
1015 class="cmr-6">11</span></div>
1016 <!--l. 120--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
1017 <!--l. 122--><p class="noindent" >
1018 <div class="fancyvrb" id="fancyvrb3"><a
1019 id="x1-43024r1"></a><span
1020 class="cmr-6">1</span><span
1021 class="cmtt-8"> </span><span
1022 class="cmtt-8"> </span><span
1023 class="cmtt-8"> </span><span
1024 class="cmtt-8"> </span><span
1025 class="cmtt-8"> </span><span
1026 class="cmtt-8"> </span><span
1027 class="cmtt-8"> </span><span
1028 class="cmtt-8"> |</span><br class="fancyvrb" /><a
1029 id="x1-43026r2"></a><span
1030 class="cmr-6">2</span><span
1031 class="cmtt-8"> </span><span
1032 class="cmtt-8"> </span><span
1033 class="cmtt-8"> </span><span
1034 class="cmtt-8"> </span><span
1035 class="cmtt-8"> </span><span
1036 class="cmtt-8"> </span><span
1037 class="cmtt-8"> </span><span
1038 class="cmtt-8"> V</span><br class="fancyvrb" /><a
1039 id="x1-43028r3"></a><span
1040 class="cmr-6">3</span><br class="fancyvrb" /><a
1041 id="x1-43030r4"></a><span
1042 class="cmr-6">4</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><span
1049 class="cmtt-8"> </span><span
1050 class="cmtt-8"> 7</span><span
1051 class="cmtt-8"> 6</span><span
1052 class="cmtt-8"> 5</span><span
1053 class="cmtt-8"> 4</span><span
1054 class="cmtt-8"> 3</span><span
1055 class="cmtt-8"> 2</span><span
1056 class="cmtt-8"> 1</span><span
1057 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1058 id="x1-43032r5"></a><span
1059 class="cmr-6">5</span><span
1060 class="cmtt-8">byte</span><span
1061 class="cmtt-8"> 0</span><span
1062 class="cmtt-8"> [0</span><span
1063 class="cmtt-8"> 1</span><span
1064 class="cmtt-8"> 1</span><span
1065 class="cmtt-8"> 1</span><span
1066 class="cmtt-8"> 1</span><span
1067 class="cmtt-8"> 1</span><span
1068 class="cmtt-8"> 0</span><span
1069 class="cmtt-8"> 0]</span><span
1070 class="cmtt-8"> </span><span
1071 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1072 id="x1-43034r6"></a><span
1073 class="cmr-6">6</span><span
1074 class="cmtt-8">byte</span><span
1075 class="cmtt-8"> 1</span><span
1076 class="cmtt-8"> [</span><span
1077 class="cmtt-8"> </span><span
1078 class="cmtt-8"> </span><span
1079 class="cmtt-8"> </span><span
1080 class="cmtt-8"> </span><span
1081 class="cmtt-8"> </span><span
1082 class="cmtt-8"> </span><span
1083 class="cmtt-8"> </span><span
1084 class="cmtt-8"> </span><span
1085 class="cmtt-8"> </span><span
1086 class="cmtt-8"> </span><span
1087 class="cmtt-8"> </span><span
1088 class="cmtt-8"> </span><span
1089 class="cmtt-8"> </span><span
1090 class="cmtt-8"> </span><span
1091 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1092 id="x1-43036r7"></a><span
1093 class="cmr-6">7</span><span
1094 class="cmtt-8">byte</span><span
1095 class="cmtt-8"> 2</span><span
1096 class="cmtt-8"> [</span><span
1097 class="cmtt-8"> </span><span
1098 class="cmtt-8"> </span><span
1099 class="cmtt-8"> </span><span
1100 class="cmtt-8"> </span><span
1101 class="cmtt-8"> </span><span
1102 class="cmtt-8"> </span><span
1103 class="cmtt-8"> </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>
1112 <br class="fancyvrb" /><a
1113 id="x1-43038r8"></a><span
1114 class="cmr-6">8</span><span
1115 class="cmtt-8">byte</span><span
1116 class="cmtt-8"> 3</span><span
1117 class="cmtt-8"> [</span><span
1118 class="cmtt-8"> </span><span
1119 class="cmtt-8"> </span><span
1120 class="cmtt-8"> </span><span
1121 class="cmtt-8"> </span><span
1122 class="cmtt-8"> </span><span
1123 class="cmtt-8"> </span><span
1124 class="cmtt-8"> </span><span
1125 class="cmtt-8"> </span><span
1126 class="cmtt-8"> </span><span
1127 class="cmtt-8"> </span><span
1128 class="cmtt-8"> </span><span
1129 class="cmtt-8"> </span><span
1130 class="cmtt-8"> </span><span
1131 class="cmtt-8"> </span><span
1132 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1133 id="x1-43040r9"></a><span
1134 class="cmr-6">9</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><span
1142 class="cmtt-8"> </span><span
1143 class="cmtt-8"> </span><span
1144 class="cmtt-8"> </span><span
1145 class="cmtt-8"> </span><span
1146 class="cmtt-8"> </span><span
1147 class="cmtt-8"> ...</span><br class="fancyvrb" /><a
1148 id="x1-43042r10"></a><span
1149 class="cmr-6">10</span><span
1150 class="cmtt-8">byte</span><span
1151 class="cmtt-8"> n</span><span
1152 class="cmtt-8"> [</span><span
1153 class="cmtt-8"> </span><span
1154 class="cmtt-8"> </span><span
1155 class="cmtt-8"> </span><span
1156 class="cmtt-8"> </span><span
1157 class="cmtt-8"> </span><span
1158 class="cmtt-8"> </span><span
1159 class="cmtt-8"> </span><span
1160 class="cmtt-8"> </span><span
1161 class="cmtt-8"> </span><span
1162 class="cmtt-8"> </span><span
1163 class="cmtt-8"> </span><span
1164 class="cmtt-8"> </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"> bytestream</span><span
1170 class="cmtt-8"> length</span><span
1171 class="cmtt-8"> ==</span><span
1172 class="cmtt-8"> 1</span><span
1173 class="cmtt-8"> byte</span></div>
1174 <!--l. 136--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
1175 <!--l. 138--><p class="noindent" >
1176 <div class="fancyvrb" id="fancyvrb4"><a
1177 id="x1-43044r1"></a><span
1178 class="cmr-6">1</span><span
1179 class="cmtt-8"> </span><span
1180 class="cmtt-8"> </span><span
1181 class="cmtt-8"> </span><span
1182 class="cmtt-8"> </span><span
1183 class="cmtt-8"> </span><span
1184 class="cmtt-8"> </span><span
1185 class="cmtt-8"> </span><span
1186 class="cmtt-8"> </span><span
1187 class="cmtt-8"> </span><span
1188 class="cmtt-8"> |</span><br class="fancyvrb" /><a
1189 id="x1-43046r2"></a><span
1190 class="cmr-6">2</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"> V</span><br class="fancyvrb" /><a
1201 id="x1-43048r3"></a><span
1202 class="cmr-6">3</span><br class="fancyvrb" /><a
1203 id="x1-43050r4"></a><span
1204 class="cmr-6">4</span><span
1205 class="cmtt-8"> </span><span
1206 class="cmtt-8"> </span><span
1207 class="cmtt-8"> </span><span
1208 class="cmtt-8"> </span><span
1209 class="cmtt-8"> </span><span
1210 class="cmtt-8"> </span><span
1211 class="cmtt-8"> </span><span
1212 class="cmtt-8"> 7</span><span
1213 class="cmtt-8"> 6</span><span
1214 class="cmtt-8"> 5</span><span
1215 class="cmtt-8"> 4</span><span
1216 class="cmtt-8"> 3</span><span
1217 class="cmtt-8"> 2</span><span
1218 class="cmtt-8"> 1</span><span
1219 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1220 id="x1-43052r5"></a><span
1221 class="cmr-6">5</span><span
1222 class="cmtt-8">byte</span><span
1223 class="cmtt-8"> 0</span><span
1224 class="cmtt-8"> [1</span><span
1225 class="cmtt-8"> 1</span><span
1226 class="cmtt-8"> 1</span><span
1227 class="cmtt-8"> 1</span><span
1228 class="cmtt-8"> 1</span><span
1229 class="cmtt-8"> 1</span><span
1230 class="cmtt-8"> 0</span><span
1231 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1232 id="x1-43054r6"></a><span
1233 class="cmr-6">6</span><span
1234 class="cmtt-8">byte</span><span
1235 class="cmtt-8"> 1</span><span
1236 class="cmtt-8"> [0</span><span
1237 class="cmtt-8"> 0</span><span
1238 class="cmtt-8"> 0</span><span
1239 class="cmtt-8"> 0</span><span
1240 class="cmtt-8"> 1</span><span
1241 class="cmtt-8"> 0</span><span
1242 class="cmtt-8"> 0</span><span
1243 class="cmtt-8"> 0]</span><span
1244 class="cmtt-8"> </span><span
1245 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1246 id="x1-43056r7"></a><span
1247 class="cmr-6">7</span><span
1248 class="cmtt-8">byte</span><span
1249 class="cmtt-8"> 2</span><span
1250 class="cmtt-8"> [</span><span
1251 class="cmtt-8"> </span><span
1252 class="cmtt-8"> </span><span
1253 class="cmtt-8"> </span><span
1254 class="cmtt-8"> </span><span
1255 class="cmtt-8"> </span><span
1256 class="cmtt-8"> </span><span
1257 class="cmtt-8"> </span><span
1258 class="cmtt-8"> </span><span
1259 class="cmtt-8"> </span><span
1260 class="cmtt-8"> </span><span
1261 class="cmtt-8"> </span><span
1262 class="cmtt-8"> </span><span
1263 class="cmtt-8"> </span><span
1264 class="cmtt-8"> </span><span
1265 class="cmtt-8"> ]</span>
1266 <br class="fancyvrb" /><a
1267 id="x1-43058r8"></a><span
1268 class="cmr-6">8</span><span
1269 class="cmtt-8">byte</span><span
1270 class="cmtt-8"> 3</span><span
1271 class="cmtt-8"> [</span><span
1272 class="cmtt-8"> </span><span
1273 class="cmtt-8"> </span><span
1274 class="cmtt-8"> </span><span
1275 class="cmtt-8"> </span><span
1276 class="cmtt-8"> </span><span
1277 class="cmtt-8"> </span><span
1278 class="cmtt-8"> </span><span
1279 class="cmtt-8"> </span><span
1280 class="cmtt-8"> </span><span
1281 class="cmtt-8"> </span><span
1282 class="cmtt-8"> </span><span
1283 class="cmtt-8"> </span><span
1284 class="cmtt-8"> </span><span
1285 class="cmtt-8"> </span><span
1286 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1287 id="x1-43060r9"></a><span
1288 class="cmr-6">9</span><span
1289 class="cmtt-8"> </span><span
1290 class="cmtt-8"> </span><span
1291 class="cmtt-8"> </span><span
1292 class="cmtt-8"> </span><span
1293 class="cmtt-8"> </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><br class="fancyvrb" /><a
1302 id="x1-43062r10"></a><span
1303 class="cmr-6">10</span><span
1304 class="cmtt-8">byte</span><span
1305 class="cmtt-8"> n</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><span
1310 class="cmtt-8"> </span><span
1311 class="cmtt-8"> </span><span
1312 class="cmtt-8"> </span><span
1313 class="cmtt-8"> </span><span
1314 class="cmtt-8"> </span><span
1315 class="cmtt-8"> </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"> bytestream</span><span
1324 class="cmtt-8"> length</span><span
1325 class="cmtt-8"> ==</span><span
1326 class="cmtt-8"> 2</span><span
1327 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1328 id="x1-43064r11"></a><span
1329 class="cmr-6">11</span><span
1330 class="cmtt-8"> </span><span
1331 class="cmtt-8"> </span><span
1332 class="cmtt-8"> </span><span
1333 class="cmtt-8"> </span><span
1334 class="cmtt-8"> </span><span
1335 class="cmtt-8"> </span><span
1336 class="cmtt-8"> </span><span
1337 class="cmtt-8"> </span><span
1338 class="cmtt-8"> </span><span
1339 class="cmtt-8"> </span><span
1340 class="cmtt-8"> </span><span
1341 class="cmtt-8"> </span><span
1342 class="cmtt-8"> </span><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><span
1349 class="cmtt-8"> </span><span
1350 class="cmtt-8"> </span><span
1351 class="cmtt-8"> </span><span
1352 class="cmtt-8"> </span><span
1353 class="cmtt-8"> </span><span
1354 class="cmtt-8"> </span><span
1355 class="cmtt-8"> bit</span><span
1356 class="cmtt-8"> cursor</span><span
1357 class="cmtt-8"> ==</span><span
1358 class="cmtt-8"> 6</span></div>
1359 <!--l. 153--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
1360 <!--l. 155--><p class="noindent" >
1361 <div class="fancyvrb" id="fancyvrb5"><a
1362 id="x1-43066r1"></a><span
1363 class="cmr-6">1</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"> </span><span
1372 class="cmtt-8"> </span><span
1373 class="cmtt-8"> </span><span
1374 class="cmtt-8"> </span><span
1375 class="cmtt-8"> </span><span
1376 class="cmtt-8"> </span><span
1377 class="cmtt-8"> </span><span
1378 class="cmtt-8"> </span><span
1379 class="cmtt-8"> |</span><br class="fancyvrb" /><a
1380 id="x1-43068r2"></a><span
1381 class="cmr-6">2</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"> V</span><br class="fancyvrb" /><a
1398 id="x1-43070r3"></a><span
1399 class="cmr-6">3</span><br class="fancyvrb" /><a
1400 id="x1-43072r4"></a><span
1401 class="cmr-6">4</span><span
1402 class="cmtt-8"> </span><span
1403 class="cmtt-8"> </span><span
1404 class="cmtt-8"> </span><span
1405 class="cmtt-8"> </span><span
1406 class="cmtt-8"> </span><span
1407 class="cmtt-8"> </span><span
1408 class="cmtt-8"> </span><span
1409 class="cmtt-8"> 7</span><span
1410 class="cmtt-8"> 6</span><span
1411 class="cmtt-8"> 5</span><span
1412 class="cmtt-8"> 4</span><span
1413 class="cmtt-8"> 3</span><span
1414 class="cmtt-8"> 2</span><span
1415 class="cmtt-8"> 1</span><span
1416 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1417 id="x1-43074r5"></a><span
1418 class="cmr-6">5</span><span
1419 class="cmtt-8">byte</span><span
1420 class="cmtt-8"> 0</span><span
1421 class="cmtt-8"> [1</span><span
1422 class="cmtt-8"> 1</span><span
1423 class="cmtt-8"> 1</span><span
1424 class="cmtt-8"> 1</span><span
1425 class="cmtt-8"> 1</span><span
1426 class="cmtt-8"> 1</span><span
1427 class="cmtt-8"> 0</span><span
1428 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1429 id="x1-43076r6"></a><span
1430 class="cmr-6">6</span><span
1431 class="cmtt-8">byte</span><span
1432 class="cmtt-8"> 1</span><span
1433 class="cmtt-8"> [0</span><span
1434 class="cmtt-8"> 1</span><span
1435 class="cmtt-8"> 0</span><span
1436 class="cmtt-8"> 0</span><span
1437 class="cmtt-8"> 1</span><span
1438 class="cmtt-8"> 0</span><span
1439 class="cmtt-8"> 0</span><span
1440 class="cmtt-8"> 0]</span>
1441 <br class="fancyvrb" /><a
1442 id="x1-43078r7"></a><span
1443 class="cmr-6">7</span><span
1444 class="cmtt-8">byte</span><span
1445 class="cmtt-8"> 2</span><span
1446 class="cmtt-8"> [1</span><span
1447 class="cmtt-8"> 1</span><span
1448 class="cmtt-8"> 0</span><span
1449 class="cmtt-8"> 0</span><span
1450 class="cmtt-8"> 1</span><span
1451 class="cmtt-8"> 1</span><span
1452 class="cmtt-8"> 1</span><span
1453 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1454 id="x1-43080r8"></a><span
1455 class="cmr-6">8</span><span
1456 class="cmtt-8">byte</span><span
1457 class="cmtt-8"> 3</span><span
1458 class="cmtt-8"> [0</span><span
1459 class="cmtt-8"> 0</span><span
1460 class="cmtt-8"> 0</span><span
1461 class="cmtt-8"> 0</span><span
1462 class="cmtt-8"> 0</span><span
1463 class="cmtt-8"> 1</span><span
1464 class="cmtt-8"> 1</span><span
1465 class="cmtt-8"> 0]</span><span
1466 class="cmtt-8"> </span><span
1467 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1468 id="x1-43082r9"></a><span
1469 class="cmr-6">9</span><span
1470 class="cmtt-8"> </span><span
1471 class="cmtt-8"> </span><span
1472 class="cmtt-8"> </span><span
1473 class="cmtt-8"> </span><span
1474 class="cmtt-8"> </span><span
1475 class="cmtt-8"> </span><span
1476 class="cmtt-8"> </span><span
1477 class="cmtt-8"> </span><span
1478 class="cmtt-8"> </span><span
1479 class="cmtt-8"> </span><span
1480 class="cmtt-8"> </span><span
1481 class="cmtt-8"> </span><span
1482 class="cmtt-8"> ...</span><br class="fancyvrb" /><a
1483 id="x1-43084r10"></a><span
1484 class="cmr-6">10</span><span
1485 class="cmtt-8">byte</span><span
1486 class="cmtt-8"> n</span><span
1487 class="cmtt-8"> [</span><span
1488 class="cmtt-8"> </span><span
1489 class="cmtt-8"> </span><span
1490 class="cmtt-8"> </span><span
1491 class="cmtt-8"> </span><span
1492 class="cmtt-8"> </span><span
1493 class="cmtt-8"> </span><span
1494 class="cmtt-8"> </span><span
1495 class="cmtt-8"> </span><span
1496 class="cmtt-8"> </span><span
1497 class="cmtt-8"> </span><span
1498 class="cmtt-8"> </span><span
1499 class="cmtt-8"> </span><span
1500 class="cmtt-8"> </span><span
1501 class="cmtt-8"> </span><span
1502 class="cmtt-8"> ]</span><span
1503 class="cmtt-8"> </span><span
1504 class="cmtt-8"> bytestream</span><span
1505 class="cmtt-8"> length</span><span
1506 class="cmtt-8"> ==</span><span
1507 class="cmtt-8"> 4</span><span
1508 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1509 id="x1-43086r11"></a><span
1510 class="cmr-6">11</span></div>
1514 <!--l. 172--><p class="noindent" >
1515 <h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a
1516 id="x1-440002.1.7"></a>decoding example</h5>
1517 <!--l. 174--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
1518 <!--l. 176--><p class="noindent" >
1519 <div class="fancyvrb" id="fancyvrb6"><a
1520 id="x1-44002r1"></a><span
1521 class="cmr-6">1</span><span
1522 class="cmtt-8"> </span><span
1523 class="cmtt-8"> </span><span
1524 class="cmtt-8"> </span><span
1525 class="cmtt-8"> </span><span
1526 class="cmtt-8"> </span><span
1527 class="cmtt-8"> </span><span
1528 class="cmtt-8"> </span><span
1529 class="cmtt-8"> </span><span
1530 class="cmtt-8"> </span><span
1531 class="cmtt-8"> </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><br class="fancyvrb" /><a
1544 id="x1-44004r2"></a><span
1545 class="cmr-6">2</span><span
1546 class="cmtt-8"> </span><span
1547 class="cmtt-8"> </span><span
1548 class="cmtt-8"> </span><span
1549 class="cmtt-8"> </span><span
1550 class="cmtt-8"> </span><span
1551 class="cmtt-8"> </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"> V</span><br class="fancyvrb" /><a
1568 id="x1-44006r3"></a><span
1569 class="cmr-6">3</span><br class="fancyvrb" /><a
1570 id="x1-44008r4"></a><span
1571 class="cmr-6">4</span><span
1572 class="cmtt-8"> </span><span
1573 class="cmtt-8"> </span><span
1574 class="cmtt-8"> </span><span
1575 class="cmtt-8"> </span><span
1576 class="cmtt-8"> </span><span
1577 class="cmtt-8"> </span><span
1578 class="cmtt-8"> </span><span
1579 class="cmtt-8"> 7</span><span
1580 class="cmtt-8"> 6</span><span
1581 class="cmtt-8"> 5</span><span
1582 class="cmtt-8"> 4</span><span
1583 class="cmtt-8"> 3</span><span
1584 class="cmtt-8"> 2</span><span
1585 class="cmtt-8"> 1</span><span
1586 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
1587 id="x1-44010r5"></a><span
1588 class="cmr-6">5</span><span
1589 class="cmtt-8">byte</span><span
1590 class="cmtt-8"> 0</span><span
1591 class="cmtt-8"> [1</span><span
1592 class="cmtt-8"> 1</span><span
1593 class="cmtt-8"> 1</span><span
1594 class="cmtt-8"> 1</span><span
1595 class="cmtt-8"> 1</span><span
1596 class="cmtt-8"> 1</span><span
1597 class="cmtt-8"> 0</span><span
1598 class="cmtt-8"> 0]</span><span
1599 class="cmtt-8"> </span><span
1600 class="cmtt-8"> <-</span><br class="fancyvrb" /><a
1601 id="x1-44012r6"></a><span
1602 class="cmr-6">6</span><span
1603 class="cmtt-8">byte</span><span
1604 class="cmtt-8"> 1</span><span
1605 class="cmtt-8"> [0</span><span
1606 class="cmtt-8"> 1</span><span
1607 class="cmtt-8"> 0</span><span
1608 class="cmtt-8"> 0</span><span
1609 class="cmtt-8"> 1</span><span
1610 class="cmtt-8"> 0</span><span
1611 class="cmtt-8"> 0</span><span
1612 class="cmtt-8"> 0]</span>
1613 <br class="fancyvrb" /><a
1614 id="x1-44014r7"></a><span
1615 class="cmr-6">7</span><span
1616 class="cmtt-8">byte</span><span
1617 class="cmtt-8"> 2</span><span
1618 class="cmtt-8"> [1</span><span
1619 class="cmtt-8"> 1</span><span
1620 class="cmtt-8"> 0</span><span
1621 class="cmtt-8"> 0</span><span
1622 class="cmtt-8"> 1</span><span
1623 class="cmtt-8"> 1</span><span
1624 class="cmtt-8"> 1</span><span
1625 class="cmtt-8"> 0]</span><br class="fancyvrb" /><a
1626 id="x1-44016r8"></a><span
1627 class="cmr-6">8</span><span
1628 class="cmtt-8">byte</span><span
1629 class="cmtt-8"> 3</span><span
1630 class="cmtt-8"> [0</span><span
1631 class="cmtt-8"> 0</span><span
1632 class="cmtt-8"> 0</span><span
1633 class="cmtt-8"> 0</span><span
1634 class="cmtt-8"> 0</span><span
1635 class="cmtt-8"> 1</span><span
1636 class="cmtt-8"> 1</span><span
1637 class="cmtt-8"> 0]</span><span
1638 class="cmtt-8"> </span><span
1639 class="cmtt-8"> bytestream</span><span
1640 class="cmtt-8"> length</span><span
1641 class="cmtt-8"> ==</span><span
1642 class="cmtt-8"> 4</span><span
1643 class="cmtt-8"> bytes</span><br class="fancyvrb" /><a
1644 id="x1-44018r9"></a><span
1645 class="cmr-6">9</span></div>
1646 <!--l. 189--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
1647 are worth noting here:
1648 <ul class="itemize1">
1649 <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
1650 some other combination of bit-widths from the bitstream is well defined. There are
1651 no artificial alignment boundaries maintained in the bitstream.
1653 <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
1654 either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
1655 decode context.</li></ul>
1656 <!--l. 207--><p class="noindent" >
1657 <h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a
1658 id="x1-450002.1.8"></a>end-of-packet alignment</h5>
1659 <!--l. 209--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
1660 embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
1661 Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
1662 the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
1663 in the last byte of a packet.
1664 <!--l. 217--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
1665 should this unused space be read, it will return binary zeroes.
1666 <!--l. 221--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
1667 End-of-packet is not to be considered an error; it is merely a state indicating that there is
1668 insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
1672 normal mode of operation, and as such, decoders must handle reading past the end of a packet as
1673 a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
1674 also return ’end-of-packet’.
1675 <!--l. 232--><p class="noindent" >
1676 <h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a
1677 id="x1-460002.1.9"></a>reading zero bits</h5>
1678 <!--l. 234--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
1679 Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
1680 triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
1681 end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
1682 shall also fail with ’end-of-packet’.
1689 <h3 class="sectionHead"><span class="titlemark">3. </span> <a
1690 id="x1-470003"></a>Probability Model and Codebooks</h3>
1691 <!--l. 5--><p class="noindent" >
1692 <h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a
1693 id="x1-480003.1"></a>Overview</h4>
1694 <!--l. 7--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
1695 probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
1696 bitstream itself in the third header, the codec setup header. This packed configuration consists of
1697 multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
1698 compressed codewords as well as an optional lookup table of output vector values to which a
1699 decoded Huffman value is applied as an offset, generating the final decoded output corresponding
1700 to a given compressed codeword.
1701 <!--l. 17--><p class="noindent" >
1702 <h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a
1703 id="x1-490003.1.1"></a>Bitwise operation</h5>
1704 <!--l. 18--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
1705 and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
1706 read from the stream according to <a
1707 href="#x1-360002">section 2</a>, “<a
1708 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
1709 <!--l. 26--><p class="noindent" >
1710 <h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a
1711 id="x1-500003.2"></a>Packed codebook format</h4>
1712 <!--l. 28--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
1713 eight bits. This is not universally true; see <a
1714 href="#x1-360002">section 2</a>, “<a
1715 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
1716 relating to non-eight-bit bytes.
1720 <!--l. 33--><p class="noindent" >
1721 <h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a
1722 id="x1-510003.2.1"></a>codebook decode</h5>
1723 <!--l. 35--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
1724 <!--l. 37--><p class="noindent" >
1725 <div class="fancyvrb" id="fancyvrb7"><a
1726 id="x1-51002r1"></a><span
1727 class="cmr-6">1</span><span
1728 class="cmtt-8">byte</span><span
1729 class="cmtt-8"> 0:</span><span
1730 class="cmtt-8"> [</span><span
1731 class="cmtt-8"> 0</span><span
1732 class="cmtt-8"> 1</span><span
1733 class="cmtt-8"> 0</span><span
1734 class="cmtt-8"> 0</span><span
1735 class="cmtt-8"> 0</span><span
1736 class="cmtt-8"> 0</span><span
1737 class="cmtt-8"> 1</span><span
1738 class="cmtt-8"> 0</span><span
1739 class="cmtt-8"> ]</span><span
1740 class="cmtt-8"> (0x42)</span><br class="fancyvrb" /><a
1741 id="x1-51004r2"></a><span
1742 class="cmr-6">2</span><span
1743 class="cmtt-8">byte</span><span
1744 class="cmtt-8"> 1:</span><span
1745 class="cmtt-8"> [</span><span
1746 class="cmtt-8"> 0</span><span
1747 class="cmtt-8"> 1</span><span
1748 class="cmtt-8"> 0</span><span
1749 class="cmtt-8"> 0</span><span
1750 class="cmtt-8"> 0</span><span
1751 class="cmtt-8"> 0</span><span
1752 class="cmtt-8"> 1</span><span
1753 class="cmtt-8"> 1</span><span
1754 class="cmtt-8"> ]</span><span
1755 class="cmtt-8"> (0x43)</span><br class="fancyvrb" /><a
1756 id="x1-51006r3"></a><span
1757 class="cmr-6">3</span><span
1758 class="cmtt-8">byte</span><span
1759 class="cmtt-8"> 2:</span><span
1760 class="cmtt-8"> [</span><span
1761 class="cmtt-8"> 0</span><span
1762 class="cmtt-8"> 1</span><span
1763 class="cmtt-8"> 0</span><span
1764 class="cmtt-8"> 1</span><span
1765 class="cmtt-8"> 0</span><span
1766 class="cmtt-8"> 1</span><span
1767 class="cmtt-8"> 1</span><span
1768 class="cmtt-8"> 0</span><span
1769 class="cmtt-8"> ]</span><span
1770 class="cmtt-8"> (0x56)</span></div>
1771 <!--l. 43--><p class="noindent" >16 bit <span
1772 class="cmtt-12">[codebook</span><span
1773 class="cmtt-12">_dimensions] </span>and 24 bit <span
1774 class="cmtt-12">[codebook</span><span
1775 class="cmtt-12">_entries] </span>fields:
1776 <!--l. 45--><p class="noindent" >
1777 <div class="fancyvrb" id="fancyvrb8"><a
1778 id="x1-51008r1"></a><span
1779 class="cmr-6">1</span><br class="fancyvrb" /><a
1780 id="x1-51010r2"></a><span
1781 class="cmr-6">2</span><span
1782 class="cmtt-8">byte</span><span
1783 class="cmtt-8"> 3:</span><span
1784 class="cmtt-8"> [</span><span
1785 class="cmtt-8"> X</span><span
1786 class="cmtt-8"> X</span><span
1787 class="cmtt-8"> X</span><span
1788 class="cmtt-8"> X</span><span
1789 class="cmtt-8"> X</span><span
1790 class="cmtt-8"> X</span><span
1791 class="cmtt-8"> X</span><span
1792 class="cmtt-8"> X</span><span
1793 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1794 id="x1-51012r3"></a><span
1795 class="cmr-6">3</span><span
1796 class="cmtt-8">byte</span><span
1797 class="cmtt-8"> 4:</span><span
1798 class="cmtt-8"> [</span><span
1799 class="cmtt-8"> X</span><span
1800 class="cmtt-8"> X</span><span
1801 class="cmtt-8"> X</span><span
1802 class="cmtt-8"> X</span><span
1803 class="cmtt-8"> X</span><span
1804 class="cmtt-8"> X</span><span
1805 class="cmtt-8"> X</span><span
1806 class="cmtt-8"> X</span><span
1807 class="cmtt-8"> ]</span><span
1808 class="cmtt-8"> [codebook</span><span
1809 class="cmtt-8">_dimensions]</span><span
1810 class="cmtt-8"> (16</span><span
1811 class="cmtt-8"> bit</span><span
1812 class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a
1813 id="x1-51014r4"></a><span
1814 class="cmr-6">4</span><br class="fancyvrb" /><a
1815 id="x1-51016r5"></a><span
1816 class="cmr-6">5</span><span
1817 class="cmtt-8">byte</span><span
1818 class="cmtt-8"> 5:</span><span
1819 class="cmtt-8"> [</span><span
1820 class="cmtt-8"> X</span><span
1821 class="cmtt-8"> X</span><span
1822 class="cmtt-8"> X</span><span
1823 class="cmtt-8"> X</span><span
1824 class="cmtt-8"> X</span><span
1825 class="cmtt-8"> X</span><span
1826 class="cmtt-8"> X</span><span
1827 class="cmtt-8"> X</span><span
1828 class="cmtt-8"> ]</span>
1829 <br class="fancyvrb" /><a
1830 id="x1-51018r6"></a><span
1831 class="cmr-6">6</span><span
1832 class="cmtt-8">byte</span><span
1833 class="cmtt-8"> 6:</span><span
1834 class="cmtt-8"> [</span><span
1835 class="cmtt-8"> X</span><span
1836 class="cmtt-8"> X</span><span
1837 class="cmtt-8"> X</span><span
1838 class="cmtt-8"> X</span><span
1839 class="cmtt-8"> X</span><span
1840 class="cmtt-8"> X</span><span
1841 class="cmtt-8"> X</span><span
1842 class="cmtt-8"> X</span><span
1843 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
1844 id="x1-51020r7"></a><span
1845 class="cmr-6">7</span><span
1846 class="cmtt-8">byte</span><span
1847 class="cmtt-8"> 7:</span><span
1848 class="cmtt-8"> [</span><span
1849 class="cmtt-8"> X</span><span
1850 class="cmtt-8"> X</span><span
1851 class="cmtt-8"> X</span><span
1852 class="cmtt-8"> X</span><span
1853 class="cmtt-8"> X</span><span
1854 class="cmtt-8"> X</span><span
1855 class="cmtt-8"> X</span><span
1856 class="cmtt-8"> X</span><span
1857 class="cmtt-8"> ]</span><span
1858 class="cmtt-8"> [codebook</span><span
1859 class="cmtt-8">_entries]</span><span
1860 class="cmtt-8"> (24</span><span
1861 class="cmtt-8"> bit</span><span
1862 class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a
1863 id="x1-51022r8"></a><span
1864 class="cmr-6">8</span></div>
1865 <!--l. 56--><p class="noindent" >Next is the <span
1866 class="cmtt-12">[ordered] </span>bit flag:
1867 <!--l. 58--><p class="noindent" >
1868 <div class="fancyvrb" id="fancyvrb9"><a
1869 id="x1-51024r1"></a><span
1870 class="cmr-6">1</span><br class="fancyvrb" /><a
1871 id="x1-51026r2"></a><span
1872 class="cmr-6">2</span><span
1873 class="cmtt-8">byte</span><span
1874 class="cmtt-8"> 8:</span><span
1875 class="cmtt-8"> [</span><span
1876 class="cmtt-8"> </span><span
1877 class="cmtt-8"> </span><span
1878 class="cmtt-8"> </span><span
1879 class="cmtt-8"> </span><span
1880 class="cmtt-8"> </span><span
1881 class="cmtt-8"> </span><span
1882 class="cmtt-8"> </span><span
1883 class="cmtt-8"> </span><span
1884 class="cmtt-8"> </span><span
1885 class="cmtt-8"> </span><span
1886 class="cmtt-8"> </span><span
1887 class="cmtt-8"> </span><span
1888 class="cmtt-8"> </span><span
1889 class="cmtt-8"> </span><span
1890 class="cmtt-8"> X</span><span
1891 class="cmtt-8"> ]</span><span
1892 class="cmtt-8"> [ordered]</span><span
1893 class="cmtt-8"> (1</span><span
1894 class="cmtt-8"> bit)</span><br class="fancyvrb" /><a
1895 id="x1-51028r3"></a><span
1896 class="cmr-6">3</span></div>
1897 <!--l. 64--><p class="noindent" >Each entry, numbering a total of <span
1898 class="cmtt-12">[codebook</span><span
1899 class="cmtt-12">_entries]</span>, is assigned a codeword length.
1900 We now read the list of codeword lengths and store these lengths in the array
1902 class="cmtt-12">[codebook</span><span
1903 class="cmtt-12">_codeword</span><span
1904 class="cmtt-12">_lengths]</span>. Decode of lengths is according to whether the <span
1905 class="cmtt-12">[ordered] </span>flag
1907 <ul class="itemize1">
1908 <li class="itemize">If the <span
1909 class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
1910 needs to read each codeword length one-by-one.
1911 <!--l. 76--><p class="noindent" >The decoder first reads one additional bit flag, the <span
1912 class="cmtt-12">[sparse] </span>flag. This flag determines
1913 whether or not the codebook contains unused entries that are not to be included in
1914 the codeword decode tree:
1915 <!--l. 81--><p class="noindent" >
1916 <div class="fancyvrb" id="fancyvrb10"><a
1917 id="x1-51030r1"></a><span
1918 class="cmr-6">1</span><span
1919 class="cmtt-8">byte</span><span
1920 class="cmtt-8"> 8:</span><span
1921 class="cmtt-8"> [</span><span
1922 class="cmtt-8"> </span><span
1923 class="cmtt-8"> </span><span
1924 class="cmtt-8"> </span><span
1925 class="cmtt-8"> </span><span
1926 class="cmtt-8"> </span><span
1927 class="cmtt-8"> </span><span
1928 class="cmtt-8"> </span><span
1929 class="cmtt-8"> </span><span
1930 class="cmtt-8"> </span><span
1931 class="cmtt-8"> </span><span
1932 class="cmtt-8"> </span><span
1933 class="cmtt-8"> </span><span
1934 class="cmtt-8"> X</span><span
1935 class="cmtt-8"> 1</span><span
1936 class="cmtt-8"> ]</span><span
1937 class="cmtt-8"> [sparse]</span><span
1938 class="cmtt-8"> flag</span><span
1939 class="cmtt-8"> (1</span><span
1940 class="cmtt-8"> bit)</span></div>
1941 <!--l. 85--><p class="noindent" >The decoder now performs for each of the <span
1942 class="cmtt-12">[codebook</span><span
1943 class="cmtt-12">_entries] </span>codebook entries:
1944 <!--l. 88--><p class="noindent" >
1945 <div class="fancyvrb" id="fancyvrb11"><a
1946 id="x1-51032r1"></a><span
1947 class="cmr-6">1</span><br class="fancyvrb" /><a
1948 id="x1-51034r2"></a><span
1949 class="cmr-6">2</span><span
1950 class="cmtt-8"> </span><span
1951 class="cmtt-8"> 1)</span><span
1952 class="cmtt-8"> if([sparse]</span><span
1953 class="cmtt-8"> is</span><span
1954 class="cmtt-8"> set)</span><span
1955 class="cmtt-8"> </span><span
1956 class="cmsy-8">{</span><br class="fancyvrb" /><a
1957 id="x1-51036r3"></a><span
1958 class="cmr-6">3</span><br class="fancyvrb" /><a
1959 id="x1-51038r4"></a><span
1960 class="cmr-6">4</span><span
1961 class="cmtt-8"> </span><span
1962 class="cmtt-8"> </span><span
1963 class="cmtt-8"> </span><span
1964 class="cmtt-8"> </span><span
1965 class="cmtt-8"> </span><span
1966 class="cmtt-8"> </span><span
1967 class="cmtt-8"> </span><span
1968 class="cmtt-8"> </span><span
1969 class="cmtt-8"> 2)</span><span
1970 class="cmtt-8"> [flag]</span><span
1971 class="cmtt-8"> =</span><span
1972 class="cmtt-8"> read</span><span
1973 class="cmtt-8"> one</span><span
1974 class="cmtt-8"> bit;</span><br class="fancyvrb" /><a
1975 id="x1-51040r5"></a><span
1976 class="cmr-6">5</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"> </span><span
1985 class="cmtt-8"> 3)</span><span
1986 class="cmtt-8"> if([flag]</span><span
1987 class="cmtt-8"> is</span><span
1988 class="cmtt-8"> set)</span><span
1989 class="cmtt-8"> </span><span
1990 class="cmsy-8">{</span><br class="fancyvrb" /><a
1991 id="x1-51042r6"></a><span
1992 class="cmr-6">6</span>
1993 <br class="fancyvrb" /><a
1994 id="x1-51044r7"></a><span
1995 class="cmr-6">7</span><span
1996 class="cmtt-8"> </span><span
1997 class="cmtt-8"> </span><span
1998 class="cmtt-8"> </span><span
1999 class="cmtt-8"> </span><span
2000 class="cmtt-8"> </span><span
2001 class="cmtt-8"> </span><span
2002 class="cmtt-8"> </span><span
2003 class="cmtt-8"> </span><span
2004 class="cmtt-8"> </span><span
2005 class="cmtt-8"> </span><span
2006 class="cmtt-8"> </span><span
2007 class="cmtt-8"> </span><span
2008 class="cmtt-8"> </span><span
2009 class="cmtt-8"> 4)</span><span
2010 class="cmtt-8"> [length]</span><span
2011 class="cmtt-8"> =</span><span
2012 class="cmtt-8"> read</span><span
2013 class="cmtt-8"> a</span><span
2014 class="cmtt-8"> five</span><span
2015 class="cmtt-8"> bit</span><span
2016 class="cmtt-8"> unsigned</span><span
2017 class="cmtt-8"> integer;</span><br class="fancyvrb" /><a
2018 id="x1-51046r8"></a><span
2019 class="cmr-6">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"> </span><span
2029 class="cmtt-8"> </span><span
2030 class="cmtt-8"> </span><span
2031 class="cmtt-8"> </span><span
2032 class="cmtt-8"> </span><span
2033 class="cmtt-8"> 5)</span><span
2034 class="cmtt-8"> codeword</span><span
2035 class="cmtt-8"> length</span><span
2036 class="cmtt-8"> for</span><span
2037 class="cmtt-8"> this</span><span
2038 class="cmtt-8"> entry</span><span
2039 class="cmtt-8"> is</span><span
2040 class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a
2041 id="x1-51048r9"></a><span
2042 class="cmr-6">9</span>
2043 <br class="fancyvrb" /><a
2044 id="x1-51050r10"></a><span
2045 class="cmr-6">10</span><span
2046 class="cmtt-8"> </span><span
2047 class="cmtt-8"> </span><span
2048 class="cmtt-8"> </span><span
2049 class="cmtt-8"> </span><span
2050 class="cmtt-8"> </span><span
2051 class="cmtt-8"> </span><span
2052 class="cmtt-8"> </span><span
2053 class="cmtt-8"> </span><span
2054 class="cmtt-8"> </span><span
2055 class="cmtt-8"> </span><span
2056 class="cmtt-8"> </span><span
2057 class="cmtt-8"> </span><span
2058 class="cmsy-8">}</span><span
2059 class="cmtt-8"> else</span><span
2060 class="cmtt-8"> </span><span
2061 class="cmsy-8">{</span><br class="fancyvrb" /><a
2062 id="x1-51052r11"></a><span
2063 class="cmr-6">11</span><br class="fancyvrb" /><a
2064 id="x1-51054r12"></a><span
2065 class="cmr-6">12</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"> </span><span
2071 class="cmtt-8"> </span><span
2072 class="cmtt-8"> </span><span
2073 class="cmtt-8"> </span><span
2074 class="cmtt-8"> </span><span
2075 class="cmtt-8"> </span><span
2076 class="cmtt-8"> </span><span
2077 class="cmtt-8"> </span><span
2078 class="cmtt-8"> </span><span
2079 class="cmtt-8"> 6)</span><span
2080 class="cmtt-8"> this</span><span
2081 class="cmtt-8"> entry</span><span
2082 class="cmtt-8"> is</span><span
2083 class="cmtt-8"> unused.</span><span
2084 class="cmtt-8"> </span><span
2085 class="cmtt-8"> mark</span><span
2086 class="cmtt-8"> it</span><span
2087 class="cmtt-8"> as</span><span
2088 class="cmtt-8"> such.</span><br class="fancyvrb" /><a
2089 id="x1-51056r13"></a><span
2090 class="cmr-6">13</span><br class="fancyvrb" /><a
2091 id="x1-51058r14"></a><span
2092 class="cmr-6">14</span><span
2093 class="cmtt-8"> </span><span
2094 class="cmtt-8"> </span><span
2095 class="cmtt-8"> </span><span
2096 class="cmtt-8"> </span><span
2097 class="cmtt-8"> </span><span
2098 class="cmtt-8"> </span><span
2099 class="cmtt-8"> </span><span
2100 class="cmtt-8"> </span><span
2101 class="cmtt-8"> </span><span
2102 class="cmtt-8"> </span><span
2103 class="cmtt-8"> </span><span
2104 class="cmtt-8"> </span><span
2105 class="cmsy-8">}</span><br class="fancyvrb" /><a
2106 id="x1-51060r15"></a><span
2107 class="cmr-6">15</span><br class="fancyvrb" /><a
2108 id="x1-51062r16"></a><span
2109 class="cmr-6">16</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="cmsy-8">}</span><span
2116 class="cmtt-8"> else</span><span
2117 class="cmtt-8"> the</span><span
2118 class="cmtt-8"> sparse</span><span
2119 class="cmtt-8"> flag</span><span
2120 class="cmtt-8"> is</span><span
2121 class="cmtt-8"> not</span><span
2122 class="cmtt-8"> set</span><span
2123 class="cmtt-8"> </span><span
2124 class="cmsy-8">{</span><br class="fancyvrb" /><a
2125 id="x1-51064r17"></a><span
2126 class="cmr-6">17</span>
2127 <br class="fancyvrb" /><a
2128 id="x1-51066r18"></a><span
2129 class="cmr-6">18</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"> 7)</span><span
2138 class="cmtt-8"> [length]</span><span
2139 class="cmtt-8"> =</span><span
2140 class="cmtt-8"> read</span><span
2141 class="cmtt-8"> a</span><span
2142 class="cmtt-8"> five</span><span
2143 class="cmtt-8"> bit</span><span
2144 class="cmtt-8"> unsigned</span><span
2145 class="cmtt-8"> integer;</span><br class="fancyvrb" /><a
2146 id="x1-51068r19"></a><span
2147 class="cmr-6">19</span><span
2148 class="cmtt-8"> </span><span
2149 class="cmtt-8"> </span><span
2150 class="cmtt-8"> </span><span
2151 class="cmtt-8"> </span><span
2152 class="cmtt-8"> </span><span
2153 class="cmtt-8"> </span><span
2154 class="cmtt-8"> </span><span
2155 class="cmtt-8"> 8)</span><span
2156 class="cmtt-8"> the</span><span
2157 class="cmtt-8"> codeword</span><span
2158 class="cmtt-8"> length</span><span
2159 class="cmtt-8"> for</span><span
2160 class="cmtt-8"> this</span><span
2161 class="cmtt-8"> entry</span><span
2162 class="cmtt-8"> is</span><span
2163 class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a
2164 id="x1-51070r20"></a><span
2165 class="cmr-6">20</span><br class="fancyvrb" /><a
2166 id="x1-51072r21"></a><span
2167 class="cmr-6">21</span><span
2168 class="cmtt-8"> </span><span
2169 class="cmtt-8"> </span><span
2170 class="cmtt-8"> </span><span
2171 class="cmtt-8"> </span><span
2172 class="cmtt-8"> </span><span
2173 class="cmsy-8">}</span><br class="fancyvrb" /><a
2174 id="x1-51074r22"></a><span
2175 class="cmr-6">22</span></div>
2180 <li class="itemize">If the <span
2181 class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
2182 ascending length order. Rather than reading a length for every codeword, the
2183 encoder reads the number of codewords per length. That is, beginning at entry
2185 <!--l. 119--><p class="noindent" >
2186 <div class="fancyvrb" id="fancyvrb12"><a
2187 id="x1-51076r1"></a><span
2188 class="cmr-6">1</span><span
2189 class="cmtt-8"> </span><span
2190 class="cmtt-8"> 1)</span><span
2191 class="cmtt-8"> [current</span><span
2192 class="cmtt-8">_entry]</span><span
2193 class="cmtt-8"> =</span><span
2194 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
2195 id="x1-51078r2"></a><span
2196 class="cmr-6">2</span><span
2197 class="cmtt-8"> </span><span
2198 class="cmtt-8"> 2)</span><span
2199 class="cmtt-8"> [current</span><span
2200 class="cmtt-8">_length]</span><span
2201 class="cmtt-8"> =</span><span
2202 class="cmtt-8"> read</span><span
2203 class="cmtt-8"> a</span><span
2204 class="cmtt-8"> five</span><span
2205 class="cmtt-8"> bit</span><span
2206 class="cmtt-8"> unsigned</span><span
2207 class="cmtt-8"> integer</span><span
2208 class="cmtt-8"> and</span><span
2209 class="cmtt-8"> add</span><span
2210 class="cmtt-8"> 1;</span>
2211 <br class="fancyvrb" /><a
2212 id="x1-51080r3"></a><span
2213 class="cmr-6">3</span><span
2214 class="cmtt-8"> </span><span
2215 class="cmtt-8"> 3)</span><span
2216 class="cmtt-8"> [number]</span><span
2217 class="cmtt-8"> =</span><span
2218 class="cmtt-8"> read</span><span
2219 class="cmtt-8"> </span><a
2220 href="#x1-1190009.2.1"><span
2221 class="cmtt-8">ilog</span></a><span
2222 class="cmtt-8">([codebook</span><span
2223 class="cmtt-8">_entries]</span><span
2224 class="cmtt-8"> -</span><span
2225 class="cmtt-8"> [current</span><span
2226 class="cmtt-8">_entry])</span><span
2227 class="cmtt-8"> bits</span><span
2228 class="cmtt-8"> as</span><span
2229 class="cmtt-8"> an</span><span
2230 class="cmtt-8"> unsigned</span><span
2231 class="cmtt-8"> integer</span>
2232 <br class="fancyvrb" /><a
2233 id="x1-51082r4"></a><span
2234 class="cmr-6">4</span><span
2235 class="cmtt-8"> </span><span
2236 class="cmtt-8"> 4)</span><span
2237 class="cmtt-8"> set</span><span
2238 class="cmtt-8"> the</span><span
2239 class="cmtt-8"> entries</span><span
2240 class="cmtt-8"> [current</span><span
2241 class="cmtt-8">_entry]</span><span
2242 class="cmtt-8"> through</span><span
2243 class="cmtt-8"> [current</span><span
2244 class="cmtt-8">_entry]+[number]-1,</span><span
2245 class="cmtt-8"> inclusive,</span>
2246 <br class="fancyvrb" /><a
2247 id="x1-51084r5"></a><span
2248 class="cmr-6">5</span><span
2249 class="cmtt-8"> </span><span
2250 class="cmtt-8"> </span><span
2251 class="cmtt-8"> </span><span
2252 class="cmtt-8"> of</span><span
2253 class="cmtt-8"> the</span><span
2254 class="cmtt-8"> [codebook</span><span
2255 class="cmtt-8">_codeword</span><span
2256 class="cmtt-8">_lengths]</span><span
2257 class="cmtt-8"> array</span><span
2258 class="cmtt-8"> to</span><span
2259 class="cmtt-8"> [current</span><span
2260 class="cmtt-8">_length]</span><br class="fancyvrb" /><a
2261 id="x1-51086r6"></a><span
2262 class="cmr-6">6</span><span
2263 class="cmtt-8"> </span><span
2264 class="cmtt-8"> 5)</span><span
2265 class="cmtt-8"> set</span><span
2266 class="cmtt-8"> [current</span><span
2267 class="cmtt-8">_entry]</span><span
2268 class="cmtt-8"> to</span><span
2269 class="cmtt-8"> [number]</span><span
2270 class="cmtt-8"> +</span><span
2271 class="cmtt-8"> [current</span><span
2272 class="cmtt-8">_entry]</span>
2273 <br class="fancyvrb" /><a
2274 id="x1-51088r7"></a><span
2275 class="cmr-6">7</span><span
2276 class="cmtt-8"> </span><span
2277 class="cmtt-8"> 6)</span><span
2278 class="cmtt-8"> increment</span><span
2279 class="cmtt-8"> [current</span><span
2280 class="cmtt-8">_length]</span><span
2281 class="cmtt-8"> by</span><span
2282 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
2283 id="x1-51090r8"></a><span
2284 class="cmr-6">8</span><span
2285 class="cmtt-8"> </span><span
2286 class="cmtt-8"> 7)</span><span
2287 class="cmtt-8"> if</span><span
2288 class="cmtt-8"> [current</span><span
2289 class="cmtt-8">_entry]</span><span
2290 class="cmtt-8"> is</span><span
2291 class="cmtt-8"> greater</span><span
2292 class="cmtt-8"> than</span><span
2293 class="cmtt-8"> [codebook</span><span
2294 class="cmtt-8">_entries]</span><span
2295 class="cmtt-8"> ERROR</span><span
2296 class="cmtt-8"> CONDITION;</span>
2297 <br class="fancyvrb" /><a
2298 id="x1-51092r9"></a><span
2299 class="cmr-6">9</span><span
2300 class="cmtt-8"> </span><span
2301 class="cmtt-8"> </span><span
2302 class="cmtt-8"> </span><span
2303 class="cmtt-8"> the</span><span
2304 class="cmtt-8"> decoder</span><span
2305 class="cmtt-8"> will</span><span
2306 class="cmtt-8"> not</span><span
2307 class="cmtt-8"> be</span><span
2308 class="cmtt-8"> able</span><span
2309 class="cmtt-8"> to</span><span
2310 class="cmtt-8"> read</span><span
2311 class="cmtt-8"> this</span><span
2312 class="cmtt-8"> stream.</span><br class="fancyvrb" /><a
2313 id="x1-51094r10"></a><span
2314 class="cmr-6">10</span><span
2315 class="cmtt-8"> </span><span
2316 class="cmtt-8"> 8)</span><span
2317 class="cmtt-8"> if</span><span
2318 class="cmtt-8"> [current</span><span
2319 class="cmtt-8">_entry]</span><span
2320 class="cmtt-8"> is</span><span
2321 class="cmtt-8"> less</span><span
2322 class="cmtt-8"> than</span><span
2323 class="cmtt-8"> [codebook</span><span
2324 class="cmtt-8">_entries],</span><span
2325 class="cmtt-8"> repeat</span><span
2326 class="cmtt-8"> process</span><span
2327 class="cmtt-8"> starting</span><span
2328 class="cmtt-8"> at</span><span
2329 class="cmtt-8"> 3)</span>
2330 <br class="fancyvrb" /><a
2331 id="x1-51096r11"></a><span
2332 class="cmr-6">11</span><span
2333 class="cmtt-8"> </span><span
2334 class="cmtt-8"> 9)</span><span
2335 class="cmtt-8"> done.</span></div>
2337 <!--l. 135--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
2338 I supports three lookup types:
2339 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
2341 class="enumerate-enumitem">No lookup
2342 </dd><dt class="enumerate-enumitem">
2344 class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ)
2345 </dd><dt class="enumerate-enumitem">
2347 class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl>
2348 <!--l. 148--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
2349 <div class="fancyvrb" id="fancyvrb13"><a
2350 id="x1-51101r1"></a><span
2351 class="cmr-6">1</span><span
2352 class="cmtt-8"> </span><span
2353 class="cmtt-8"> 1)</span><span
2354 class="cmtt-8"> [codebook</span><span
2355 class="cmtt-8">_lookup</span><span
2356 class="cmtt-8">_type]</span><span
2357 class="cmtt-8"> =</span><span
2358 class="cmtt-8"> read</span><span
2359 class="cmtt-8"> four</span><span
2360 class="cmtt-8"> bits</span><span
2361 class="cmtt-8"> as</span><span
2362 class="cmtt-8"> an</span><span
2363 class="cmtt-8"> unsigned</span><span
2364 class="cmtt-8"> integer</span></div>
2365 <!--l. 153--><p class="noindent" >Codebook decode precedes according to <span
2366 class="cmtt-12">[codebook</span><span
2367 class="cmtt-12">_lookup</span><span
2368 class="cmtt-12">_type]</span>:
2369 <ul class="itemize1">
2370 <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
2372 <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
2373 be read. Lookup type one reads a list of values that are permuted in a set pattern to
2374 build a list of vectors, each vector of order <span
2375 class="cmtt-12">[codebook</span><span
2376 class="cmtt-12">_dimensions] </span>scalars. Lookup
2377 type two builds the same vector list, but reads each scalar for each vector explicitly,
2378 rather than building vectors from a smaller list of possible scalar values. Lookup
2379 decode proceeds as follows:
2380 <!--l. 167--><p class="noindent" >
2381 <div class="fancyvrb" id="fancyvrb14"><a
2382 id="x1-51103r1"></a><span
2383 class="cmr-6">1</span><span
2384 class="cmtt-8"> </span><span
2385 class="cmtt-8"> 1)</span><span
2386 class="cmtt-8"> [codebook</span><span
2387 class="cmtt-8">_minimum</span><span
2388 class="cmtt-8">_value]</span><span
2389 class="cmtt-8"> =</span><span
2390 class="cmtt-8"> </span><a
2391 href="#x1-1200009.2.2"><span
2392 class="cmtt-8">float32</span><span
2393 class="cmtt-8">_unpack</span></a><span
2394 class="cmtt-8">(</span><span
2395 class="cmtt-8"> read</span><span
2396 class="cmtt-8"> 32</span><span
2397 class="cmtt-8"> bits</span><span
2398 class="cmtt-8"> as</span><span
2399 class="cmtt-8"> an</span><span
2400 class="cmtt-8"> unsigned</span><span
2401 class="cmtt-8"> integer)</span>
2402 <br class="fancyvrb" /><a
2403 id="x1-51105r2"></a><span
2404 class="cmr-6">2</span><span
2405 class="cmtt-8"> </span><span
2406 class="cmtt-8"> 2)</span><span
2407 class="cmtt-8"> [codebook</span><span
2408 class="cmtt-8">_delta</span><span
2409 class="cmtt-8">_value]</span><span
2410 class="cmtt-8"> =</span><span
2411 class="cmtt-8"> </span><a
2412 href="#x1-1200009.2.2"><span
2413 class="cmtt-8">float32</span><span
2414 class="cmtt-8">_unpack</span></a><span
2415 class="cmtt-8">(</span><span
2416 class="cmtt-8"> read</span><span
2417 class="cmtt-8"> 32</span><span
2418 class="cmtt-8"> bits</span><span
2419 class="cmtt-8"> as</span><span
2420 class="cmtt-8"> an</span><span
2421 class="cmtt-8"> unsigned</span><span
2422 class="cmtt-8"> integer)</span>
2423 <br class="fancyvrb" /><a
2424 id="x1-51107r3"></a><span
2425 class="cmr-6">3</span><span
2426 class="cmtt-8"> </span><span
2427 class="cmtt-8"> 3)</span><span
2428 class="cmtt-8"> [codebook</span><span
2429 class="cmtt-8">_value</span><span
2430 class="cmtt-8">_bits]</span><span
2431 class="cmtt-8"> =</span><span
2432 class="cmtt-8"> read</span><span
2433 class="cmtt-8"> 4</span><span
2434 class="cmtt-8"> bits</span><span
2435 class="cmtt-8"> as</span><span
2436 class="cmtt-8"> an</span><span
2437 class="cmtt-8"> unsigned</span><span
2438 class="cmtt-8"> integer</span><span
2439 class="cmtt-8"> and</span><span
2440 class="cmtt-8"> add</span><span
2441 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
2442 id="x1-51109r4"></a><span
2443 class="cmr-6">4</span><span
2444 class="cmtt-8"> </span><span
2445 class="cmtt-8"> 4)</span><span
2446 class="cmtt-8"> [codebook</span><span
2447 class="cmtt-8">_sequence</span><span
2448 class="cmtt-8">_p]</span><span
2449 class="cmtt-8"> =</span><span
2450 class="cmtt-8"> read</span><span
2451 class="cmtt-8"> 1</span><span
2452 class="cmtt-8"> bit</span><span
2453 class="cmtt-8"> as</span><span
2454 class="cmtt-8"> a</span><span
2455 class="cmtt-8"> boolean</span><span
2456 class="cmtt-8"> flag</span><br class="fancyvrb" /><a
2457 id="x1-51111r5"></a><span
2458 class="cmr-6">5</span>
2462 <br class="fancyvrb" /><a
2463 id="x1-51113r6"></a><span
2464 class="cmr-6">6</span><span
2465 class="cmtt-8"> </span><span
2466 class="cmtt-8"> if</span><span
2467 class="cmtt-8"> (</span><span
2468 class="cmtt-8"> [codebook</span><span
2469 class="cmtt-8">_lookup</span><span
2470 class="cmtt-8">_type]</span><span
2471 class="cmtt-8"> is</span><span
2472 class="cmtt-8"> 1</span><span
2473 class="cmtt-8"> )</span><span
2474 class="cmtt-8"> </span><span
2475 class="cmsy-8">{</span><br class="fancyvrb" /><a
2476 id="x1-51115r7"></a><span
2477 class="cmr-6">7</span><br class="fancyvrb" /><a
2478 id="x1-51117r8"></a><span
2479 class="cmr-6">8</span><span
2480 class="cmtt-8"> </span><span
2481 class="cmtt-8"> </span><span
2482 class="cmtt-8"> </span><span
2483 class="cmtt-8"> </span><span
2484 class="cmtt-8"> 5)</span><span
2485 class="cmtt-8"> [codebook</span><span
2486 class="cmtt-8">_lookup</span><span
2487 class="cmtt-8">_values]</span><span
2488 class="cmtt-8"> =</span><span
2489 class="cmtt-8"> </span><a
2490 href="#x1-1210009.2.3"><span
2491 class="cmtt-8">lookup1</span><span
2492 class="cmtt-8">_values</span></a><span
2493 class="cmtt-8">([codebook</span><span
2494 class="cmtt-8">_entries],</span><span
2495 class="cmtt-8"> [codebook</span><span
2496 class="cmtt-8">_dimensions]</span><span
2497 class="cmtt-8"> )</span><br class="fancyvrb" /><a
2498 id="x1-51119r9"></a><span
2499 class="cmr-6">9</span>
2500 <br class="fancyvrb" /><a
2501 id="x1-51121r10"></a><span
2502 class="cmr-6">10</span><span
2503 class="cmtt-8"> </span><span
2504 class="cmtt-8"> </span><span
2505 class="cmsy-8">}</span><span
2506 class="cmtt-8"> else</span><span
2507 class="cmtt-8"> </span><span
2508 class="cmsy-8">{</span><br class="fancyvrb" /><a
2509 id="x1-51123r11"></a><span
2510 class="cmr-6">11</span><br class="fancyvrb" /><a
2511 id="x1-51125r12"></a><span
2512 class="cmr-6">12</span><span
2513 class="cmtt-8"> </span><span
2514 class="cmtt-8"> </span><span
2515 class="cmtt-8"> </span><span
2516 class="cmtt-8"> </span><span
2517 class="cmtt-8"> 6)</span><span
2518 class="cmtt-8"> [codebook</span><span
2519 class="cmtt-8">_lookup</span><span
2520 class="cmtt-8">_values]</span><span
2521 class="cmtt-8"> =</span><span
2522 class="cmtt-8"> [codebook</span><span
2523 class="cmtt-8">_entries]</span><span
2524 class="cmtt-8"> *</span><span
2525 class="cmtt-8"> [codebook</span><span
2526 class="cmtt-8">_dimensions]</span><br class="fancyvrb" /><a
2527 id="x1-51127r13"></a><span
2528 class="cmr-6">13</span><br class="fancyvrb" /><a
2529 id="x1-51129r14"></a><span
2530 class="cmr-6">14</span><span
2531 class="cmtt-8"> </span><span
2532 class="cmtt-8"> </span><span
2533 class="cmsy-8">}</span><br class="fancyvrb" /><a
2534 id="x1-51131r15"></a><span
2535 class="cmr-6">15</span>
2536 <br class="fancyvrb" /><a
2537 id="x1-51133r16"></a><span
2538 class="cmr-6">16</span><span
2539 class="cmtt-8"> </span><span
2540 class="cmtt-8"> 7)</span><span
2541 class="cmtt-8"> read</span><span
2542 class="cmtt-8"> a</span><span
2543 class="cmtt-8"> total</span><span
2544 class="cmtt-8"> of</span><span
2545 class="cmtt-8"> [codebook</span><span
2546 class="cmtt-8">_lookup</span><span
2547 class="cmtt-8">_values]</span><span
2548 class="cmtt-8"> unsigned</span><span
2549 class="cmtt-8"> integers</span><span
2550 class="cmtt-8"> of</span><span
2551 class="cmtt-8"> [codebook</span><span
2552 class="cmtt-8">_value</span><span
2553 class="cmtt-8">_bits]</span><span
2554 class="cmtt-8"> each;</span>
2555 <br class="fancyvrb" /><a
2556 id="x1-51135r17"></a><span
2557 class="cmr-6">17</span><span
2558 class="cmtt-8"> </span><span
2559 class="cmtt-8"> </span><span
2560 class="cmtt-8"> </span><span
2561 class="cmtt-8"> </span><span
2562 class="cmtt-8"> store</span><span
2563 class="cmtt-8"> these</span><span
2564 class="cmtt-8"> in</span><span
2565 class="cmtt-8"> order</span><span
2566 class="cmtt-8"> in</span><span
2567 class="cmtt-8"> the</span><span
2568 class="cmtt-8"> array</span><span
2569 class="cmtt-8"> [codebook</span><span
2570 class="cmtt-8">_multiplicands]</span></div>
2572 <li class="itemize">A <span
2573 class="cmtt-12">[codebook</span><span
2574 class="cmtt-12">_lookup</span><span
2575 class="cmtt-12">_type] </span>of greater than two is reserved and indicates a stream that is
2576 not decodable by the specification in this document.
2578 <!--l. 194--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
2579 rendering the stream undecodable.
2580 <!--l. 197--><p class="noindent" ><span class="paragraphHead"><a
2581 id="x1-520003.2.1"></a><span
2582 class="cmbx-12">Huffman decision tree representation</span></span>
2584 class="cmtt-12">[codebook</span><span
2585 class="cmtt-12">_codeword</span><span
2586 class="cmtt-12">_lengths] </span>array and <span
2587 class="cmtt-12">[codebook</span><span
2588 class="cmtt-12">_entries] </span>value uniquely define the
2589 Huffman decision tree used for entropy decoding.
2590 <!--l. 203--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
2591 codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
2592 possible. Assume the following codeword length list:
2593 <!--l. 208--><p class="noindent" >
2594 <div class="fancyvrb" id="fancyvrb15"><a
2595 id="x1-52002r1"></a><span
2596 class="cmr-6">1</span><span
2597 class="cmtt-8">entry</span><span
2598 class="cmtt-8"> 0:</span><span
2599 class="cmtt-8"> length</span><span
2600 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
2601 id="x1-52004r2"></a><span
2602 class="cmr-6">2</span><span
2603 class="cmtt-8">entry</span><span
2604 class="cmtt-8"> 1:</span><span
2605 class="cmtt-8"> length</span><span
2606 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2607 id="x1-52006r3"></a><span
2608 class="cmr-6">3</span><span
2609 class="cmtt-8">entry</span><span
2610 class="cmtt-8"> 2:</span><span
2611 class="cmtt-8"> length</span><span
2612 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2613 id="x1-52008r4"></a><span
2614 class="cmr-6">4</span><span
2615 class="cmtt-8">entry</span><span
2616 class="cmtt-8"> 3:</span><span
2617 class="cmtt-8"> length</span><span
2618 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2619 id="x1-52010r5"></a><span
2620 class="cmr-6">5</span><span
2621 class="cmtt-8">entry</span><span
2622 class="cmtt-8"> 4:</span><span
2623 class="cmtt-8"> length</span><span
2624 class="cmtt-8"> 4</span><br class="fancyvrb" /><a
2625 id="x1-52012r6"></a><span
2626 class="cmr-6">6</span><span
2627 class="cmtt-8">entry</span><span
2628 class="cmtt-8"> 5:</span><span
2629 class="cmtt-8"> length</span><span
2630 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
2631 id="x1-52014r7"></a><span
2632 class="cmr-6">7</span><span
2633 class="cmtt-8">entry</span><span
2634 class="cmtt-8"> 6:</span><span
2635 class="cmtt-8"> length</span><span
2636 class="cmtt-8"> 3</span><br class="fancyvrb" /><a
2637 id="x1-52016r8"></a><span
2638 class="cmr-6">8</span><span
2639 class="cmtt-8">entry</span><span
2640 class="cmtt-8"> 7:</span><span
2641 class="cmtt-8"> length</span><span
2642 class="cmtt-8"> 3</span></div>
2643 <!--l. 219--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
2644 in the following codeword list:
2645 <!--l. 222--><p class="noindent" >
2646 <div class="fancyvrb" id="fancyvrb16"><a
2647 id="x1-52018r1"></a><span
2648 class="cmr-6">1</span><span
2649 class="cmtt-8">entry</span><span
2650 class="cmtt-8"> 0:</span><span
2651 class="cmtt-8"> length</span><span
2652 class="cmtt-8"> 2</span><span
2653 class="cmtt-8"> codeword</span><span
2654 class="cmtt-8"> 00</span><br class="fancyvrb" /><a
2655 id="x1-52020r2"></a><span
2656 class="cmr-6">2</span><span
2657 class="cmtt-8">entry</span><span
2658 class="cmtt-8"> 1:</span><span
2659 class="cmtt-8"> length</span><span
2660 class="cmtt-8"> 4</span><span
2661 class="cmtt-8"> codeword</span><span
2662 class="cmtt-8"> 0100</span><br class="fancyvrb" /><a
2663 id="x1-52022r3"></a><span
2664 class="cmr-6">3</span><span
2665 class="cmtt-8">entry</span><span
2666 class="cmtt-8"> 2:</span><span
2667 class="cmtt-8"> length</span><span
2668 class="cmtt-8"> 4</span><span
2669 class="cmtt-8"> codeword</span><span
2670 class="cmtt-8"> 0101</span><br class="fancyvrb" /><a
2671 id="x1-52024r4"></a><span
2672 class="cmr-6">4</span><span
2673 class="cmtt-8">entry</span><span
2674 class="cmtt-8"> 3:</span><span
2675 class="cmtt-8"> length</span><span
2676 class="cmtt-8"> 4</span><span
2677 class="cmtt-8"> codeword</span><span
2678 class="cmtt-8"> 0110</span>
2679 <br class="fancyvrb" /><a
2680 id="x1-52026r5"></a><span
2681 class="cmr-6">5</span><span
2682 class="cmtt-8">entry</span><span
2683 class="cmtt-8"> 4:</span><span
2684 class="cmtt-8"> length</span><span
2685 class="cmtt-8"> 4</span><span
2686 class="cmtt-8"> codeword</span><span
2687 class="cmtt-8"> 0111</span><br class="fancyvrb" /><a
2688 id="x1-52028r6"></a><span
2689 class="cmr-6">6</span><span
2690 class="cmtt-8">entry</span><span
2691 class="cmtt-8"> 5:</span><span
2692 class="cmtt-8"> length</span><span
2693 class="cmtt-8"> 2</span><span
2694 class="cmtt-8"> codeword</span><span
2695 class="cmtt-8"> 10</span><br class="fancyvrb" /><a
2696 id="x1-52030r7"></a><span
2697 class="cmr-6">7</span><span
2698 class="cmtt-8">entry</span><span
2699 class="cmtt-8"> 6:</span><span
2700 class="cmtt-8"> length</span><span
2701 class="cmtt-8"> 3</span><span
2702 class="cmtt-8"> codeword</span><span
2703 class="cmtt-8"> 110</span><br class="fancyvrb" /><a
2704 id="x1-52032r8"></a><span
2705 class="cmr-6">8</span><span
2706 class="cmtt-8">entry</span><span
2707 class="cmtt-8"> 7:</span><span
2708 class="cmtt-8"> length</span><span
2709 class="cmtt-8"> 3</span><span
2710 class="cmtt-8"> codeword</span><span
2711 class="cmtt-8"> 111</span></div>
2712 <!--l. 234--><p class="noindent" ><span class="likesubparagraphHead"><a
2713 id="x1-530003.2.1"></a><span
2714 class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
2715 be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
2716 one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
2718 <!--l. 242--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
2719 numbers equivalent to the leaves numbered left-to-right:
2725 <!--l. 246--><p class="noindent" >
2727 <!--l. 247--><p class="noindent" ><img
2728 src="hufftree.png" alt="PIC"
2730 <br /> <div class="caption"
2731 ><span class="id">Figure 4: </span><span
2732 class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 -->
2734 <!--l. 252--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
2736 <!--l. 255--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
2737 In the above example, if codeword seven were eliminated, it’s clear that the tree is
2741 <!--l. 259--><p class="noindent" >
2743 <!--l. 260--><p class="noindent" ><img
2744 src="hufftree-under.png" alt="PIC"
2746 <br /> <div class="caption"
2747 ><span class="id">Figure 5: </span><span
2748 class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 -->
2750 <!--l. 265--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
2751 codeword is impossible. Both underspecified and overspecified trees are an error condition
2752 rendering the stream undecodable.
2753 <!--l. 270--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
2754 codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
2755 from the stream to decode to that entry number.
2756 <!--l. 275--><p class="noindent" ><span class="paragraphHead"><a
2757 id="x1-540003.2.1"></a><span
2758 class="cmbx-12">Errata 20150226: Single entry codebooks</span></span>
2759 A ’single-entry codebook’ is a codebook with one active codeword entry. A single-entry codebook
2760 may be either a fully populated codebook with only one declared entry, or a sparse codebook
2761 with only one entry marked used. The Vorbis I spec provides no means to specify a codeword
2762 length of zero, and as a result, a single-entry codebook is inherently malformed because it is
2763 underpopulated. The original specification did not address directly the matter of single-entry
2764 codebooks; they were implicitly illegal as it was not possible to write such a codebook with a
2765 valid tree structure.
2769 <!--l. 287--><p class="noindent" >In r14811 of the libvorbis reference implementation, Xiph added an additional check to the
2770 codebook implementation to reject underpopulated Huffman trees. This change led to the
2771 discovery of single-entry books used ’in the wild’ when the new, stricter checks rejected a number
2772 of apparently working streams.
2773 <!--l. 293--><p class="noindent" >In order to minimize breakage of deployed (if technically erroneous) streams, r16073 of the
2774 reference implementation explicitly special-cased single-entry codebooks to tolerate the
2775 single-entry case. Commit r16073 also added the following to the specification:
2776 <!--l. 302--><p class="noindent" >“<span class="sout">Take special care that a codebook with a single used entry is handled properly; it consists of a
2777 single codework of zero bits and reading a value out of such a codebook always returns the single
2778 used value and sinks zero bits. </span>”
2779 <!--l. 304--><p class="noindent" >The intent was to clarify the spec and codify current practice. However, this addition is
2780 erroneously at odds with the intent of preserving usability of existing streams using single-entry
2781 codebooks, disagrees with the code changes that reinstated decoding, and does not address how
2782 single-entry codebooks should be encoded.
2783 <!--l. 310--><p class="noindent" >As such, the above addition made in r16037 is struck from the specification and replaced by the
2785 <!--l. 329--><p class="noindent" >
2787 <!--l. 329--><p class="noindent" >It is possible to declare a Vorbis codebook containing a single codework
2788 entry. A single-entry codebook may be either a fully populated codebook with
2790 class="cmtt-12">[codebook</span><span
2791 class="cmtt-12">_entries] </span>set to 1, or a sparse codebook marking only one entry
2792 used. Note that it is not possible to also encode a <span
2793 class="cmtt-12">[codeword</span><span
2794 class="cmtt-12">_length] </span>of zero
2795 for the single used codeword, as the unsigned value written to the stream
2797 class="cmtt-12">[codeword</span><span
2798 class="cmtt-12">_length]-1</span>. Instead, encoder implementations should indicate a
2800 class="cmtt-12">[codeword</span><span
2801 class="cmtt-12">_length] </span>of 1 and ’write’ the codeword to a stream during audio
2802 encoding by writing a single zero bit.
2803 <!--l. 329--><p class="noindent" >Decoder implementations shall reject a codebook if it contains only one used
2804 entry and the encoded <span
2805 class="cmtt-12">[codeword</span><span
2806 class="cmtt-12">_length] </span>of that entry is not 1. ’Reading’ a
2807 value from single-entry codebook always returns the single used codeword value
2808 and sinks one bit. Decoders should tolerate that the bit read from the stream
2809 be ’1’ instead of ’0’; both values shall return the single used codeword.</div>
2810 <!--l. 331--><p class="noindent" ><span class="paragraphHead"><a
2811 id="x1-550003.2.1"></a><span
2812 class="cmbx-12">VQ lookup table vector representation</span></span>
2813 Unpacking the VQ lookup table vectors relies on the following values:
2817 <div class="fancyvrb" id="fancyvrb17"><a
2818 id="x1-55002r1"></a><span
2819 class="cmr-6">1</span><span
2820 class="cmtt-8">the</span><span
2821 class="cmtt-8"> [codebook\_multiplicands]</span><span
2822 class="cmtt-8"> array</span><br class="fancyvrb" /><a
2823 id="x1-55004r2"></a><span
2824 class="cmr-6">2</span><span
2825 class="cmtt-8">[codebook\_minimum\_value]</span><br class="fancyvrb" /><a
2826 id="x1-55006r3"></a><span
2827 class="cmr-6">3</span><span
2828 class="cmtt-8">[codebook\_delta\_value]</span><br class="fancyvrb" /><a
2829 id="x1-55008r4"></a><span
2830 class="cmr-6">4</span><span
2831 class="cmtt-8">[codebook\_sequence\_p]</span>
2832 <br class="fancyvrb" /><a
2833 id="x1-55010r5"></a><span
2834 class="cmr-6">5</span><span
2835 class="cmtt-8">[codebook\_lookup\_type]</span><br class="fancyvrb" /><a
2836 id="x1-55012r6"></a><span
2837 class="cmr-6">6</span><span
2838 class="cmtt-8">[codebook\_entries]</span><br class="fancyvrb" /><a
2839 id="x1-55014r7"></a><span
2840 class="cmr-6">7</span><span
2841 class="cmtt-8">[codebook\_dimensions]</span><br class="fancyvrb" /><a
2842 id="x1-55016r8"></a><span
2843 class="cmr-6">8</span><span
2844 class="cmtt-8">[codebook\_lookup\_values]</span></div>
2845 <!--l. 347--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
2847 class="cmtt-12">[codebook</span><span
2848 class="cmtt-12">_lookup</span><span
2849 class="cmtt-12">_type]</span>. The unpacked vector values are what a codebook would return
2850 during audio packet decode in a VQ context.
2851 <!--l. 352--><p class="noindent" ><span class="paragraphHead"><a
2852 id="x1-560003.2.1"></a><span
2853 class="cmbx-12">Vector value decode: Lookup type 1</span></span>
2854 Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of
2855 scalar values. Calculate (unpack) the final values of a codebook entry vector from
2856 the entries in <span
2857 class="cmtt-12">[codebook</span><span
2858 class="cmtt-12">_multiplicands] </span>as follows (<span
2859 class="cmtt-12">[value</span><span
2860 class="cmtt-12">_vector] </span>is the output
2861 vector representing the vector of values for entry number <span
2862 class="cmtt-12">[lookup</span><span
2863 class="cmtt-12">_offset] </span>in this
2865 <!--l. 361--><p class="noindent" >
2866 <div class="fancyvrb" id="fancyvrb18"><a
2867 id="x1-56002r1"></a><span
2868 class="cmr-6">1</span><span
2869 class="cmtt-8"> </span><span
2870 class="cmtt-8"> 1)</span><span
2871 class="cmtt-8"> [last]</span><span
2872 class="cmtt-8"> =</span><span
2873 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
2874 id="x1-56004r2"></a><span
2875 class="cmr-6">2</span><span
2876 class="cmtt-8"> </span><span
2877 class="cmtt-8"> 2)</span><span
2878 class="cmtt-8"> [index</span><span
2879 class="cmtt-8">_divisor]</span><span
2880 class="cmtt-8"> =</span><span
2881 class="cmtt-8"> 1;</span><br class="fancyvrb" /><a
2882 id="x1-56006r3"></a><span
2883 class="cmr-6">3</span><span
2884 class="cmtt-8"> </span><span
2885 class="cmtt-8"> 3)</span><span
2886 class="cmtt-8"> iterate</span><span
2887 class="cmtt-8"> [i]</span><span
2888 class="cmtt-8"> over</span><span
2889 class="cmtt-8"> the</span><span
2890 class="cmtt-8"> range</span><span
2891 class="cmtt-8"> 0</span><span
2892 class="cmtt-8"> ...</span><span
2893 class="cmtt-8"> [codebook</span><span
2894 class="cmtt-8">_dimensions]-1</span><span
2895 class="cmtt-8"> (once</span><span
2896 class="cmtt-8"> for</span><span
2897 class="cmtt-8"> each</span><span
2898 class="cmtt-8"> scalar</span><span
2899 class="cmtt-8"> value</span><span
2900 class="cmtt-8"> in</span><span
2901 class="cmtt-8"> the</span><span
2902 class="cmtt-8"> value</span><span
2903 class="cmtt-8"> vector)</span><span
2904 class="cmtt-8"> </span><span
2905 class="cmsy-8">{</span><br class="fancyvrb" /><a
2906 id="x1-56008r4"></a><span
2907 class="cmr-6">4</span>
2908 <br class="fancyvrb" /><a
2909 id="x1-56010r5"></a><span
2910 class="cmr-6">5</span><span
2911 class="cmtt-8"> </span><span
2912 class="cmtt-8"> </span><span
2913 class="cmtt-8"> </span><span
2914 class="cmtt-8"> </span><span
2915 class="cmtt-8"> </span><span
2916 class="cmtt-8"> </span><span
2917 class="cmtt-8"> 4)</span><span
2918 class="cmtt-8"> [multiplicand</span><span
2919 class="cmtt-8">_offset]</span><span
2920 class="cmtt-8"> =</span><span
2921 class="cmtt-8"> (</span><span
2922 class="cmtt-8"> [lookup</span><span
2923 class="cmtt-8">_offset]</span><span
2924 class="cmtt-8"> divided</span><span
2925 class="cmtt-8"> by</span><span
2926 class="cmtt-8"> [index</span><span
2927 class="cmtt-8">_divisor]</span><span
2928 class="cmtt-8"> using</span><span
2929 class="cmtt-8"> integer</span>
2930 <br class="fancyvrb" /><a
2931 id="x1-56012r6"></a><span
2932 class="cmr-6">6</span><span
2933 class="cmtt-8"> </span><span
2934 class="cmtt-8"> </span><span
2935 class="cmtt-8"> </span><span
2936 class="cmtt-8"> </span><span
2937 class="cmtt-8"> </span><span
2938 class="cmtt-8"> </span><span
2939 class="cmtt-8"> </span><span
2940 class="cmtt-8"> </span><span
2941 class="cmtt-8"> </span><span
2942 class="cmtt-8"> division</span><span
2943 class="cmtt-8"> )</span><span
2944 class="cmtt-8"> integer</span><span
2945 class="cmtt-8"> modulo</span><span
2946 class="cmtt-8"> [codebook</span><span
2947 class="cmtt-8">_lookup</span><span
2948 class="cmtt-8">_values]</span><br class="fancyvrb" /><a
2949 id="x1-56014r7"></a><span
2950 class="cmr-6">7</span><br class="fancyvrb" /><a
2951 id="x1-56016r8"></a><span
2952 class="cmr-6">8</span><span
2953 class="cmtt-8"> </span><span
2954 class="cmtt-8"> </span><span
2955 class="cmtt-8"> </span><span
2956 class="cmtt-8"> </span><span
2957 class="cmtt-8"> </span><span
2958 class="cmtt-8"> </span><span
2959 class="cmtt-8"> 5)</span><span
2960 class="cmtt-8"> vector</span><span
2961 class="cmtt-8"> [value</span><span
2962 class="cmtt-8">_vector]</span><span
2963 class="cmtt-8"> element</span><span
2964 class="cmtt-8"> [i]</span><span
2965 class="cmtt-8"> =</span>
2966 <br class="fancyvrb" /><a
2967 id="x1-56018r9"></a><span
2968 class="cmr-6">9</span><span
2969 class="cmtt-8"> </span><span
2970 class="cmtt-8"> </span><span
2971 class="cmtt-8"> </span><span
2972 class="cmtt-8"> </span><span
2973 class="cmtt-8"> </span><span
2974 class="cmtt-8"> </span><span
2975 class="cmtt-8"> </span><span
2976 class="cmtt-8"> </span><span
2977 class="cmtt-8"> </span><span
2978 class="cmtt-8"> </span><span
2979 class="cmtt-8"> </span><span
2980 class="cmtt-8"> (</span><span
2981 class="cmtt-8"> [codebook</span><span
2982 class="cmtt-8">_multiplicands]</span><span
2983 class="cmtt-8"> array</span><span
2984 class="cmtt-8"> element</span><span
2985 class="cmtt-8"> number</span><span
2986 class="cmtt-8"> [multiplicand</span><span
2987 class="cmtt-8">_offset]</span><span
2988 class="cmtt-8"> )</span><span
2989 class="cmtt-8"> *</span>
2990 <br class="fancyvrb" /><a
2991 id="x1-56020r10"></a><span
2992 class="cmr-6">10</span><span
2993 class="cmtt-8"> </span><span
2994 class="cmtt-8"> </span><span
2995 class="cmtt-8"> </span><span
2996 class="cmtt-8"> </span><span
2997 class="cmtt-8"> </span><span
2998 class="cmtt-8"> </span><span
2999 class="cmtt-8"> </span><span
3000 class="cmtt-8"> </span><span
3001 class="cmtt-8"> </span><span
3002 class="cmtt-8"> </span><span
3003 class="cmtt-8"> </span><span
3004 class="cmtt-8"> [codebook</span><span
3005 class="cmtt-8">_delta</span><span
3006 class="cmtt-8">_value]</span><span
3007 class="cmtt-8"> +</span><span
3008 class="cmtt-8"> [codebook</span><span
3009 class="cmtt-8">_minimum</span><span
3010 class="cmtt-8">_value]</span><span
3011 class="cmtt-8"> +</span><span
3012 class="cmtt-8"> [last];</span><br class="fancyvrb" /><a
3013 id="x1-56022r11"></a><span
3014 class="cmr-6">11</span>
3015 <br class="fancyvrb" /><a
3016 id="x1-56024r12"></a><span
3017 class="cmr-6">12</span><span
3018 class="cmtt-8"> </span><span
3019 class="cmtt-8"> </span><span
3020 class="cmtt-8"> </span><span
3021 class="cmtt-8"> </span><span
3022 class="cmtt-8"> </span><span
3023 class="cmtt-8"> </span><span
3024 class="cmtt-8"> 6)</span><span
3025 class="cmtt-8"> if</span><span
3026 class="cmtt-8"> (</span><span
3027 class="cmtt-8"> [codebook</span><span
3028 class="cmtt-8">_sequence</span><span
3029 class="cmtt-8">_p]</span><span
3030 class="cmtt-8"> is</span><span
3031 class="cmtt-8"> set</span><span
3032 class="cmtt-8"> )</span><span
3033 class="cmtt-8"> then</span><span
3034 class="cmtt-8"> set</span><span
3035 class="cmtt-8"> [last]</span><span
3036 class="cmtt-8"> =</span><span
3037 class="cmtt-8"> vector</span><span
3038 class="cmtt-8"> [value</span><span
3039 class="cmtt-8">_vector]</span><span
3040 class="cmtt-8"> element</span><span
3041 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
3042 id="x1-56026r13"></a><span
3043 class="cmr-6">13</span>
3044 <br class="fancyvrb" /><a
3045 id="x1-56028r14"></a><span
3046 class="cmr-6">14</span><span
3047 class="cmtt-8"> </span><span
3048 class="cmtt-8"> </span><span
3049 class="cmtt-8"> </span><span
3050 class="cmtt-8"> </span><span
3051 class="cmtt-8"> </span><span
3052 class="cmtt-8"> </span><span
3053 class="cmtt-8"> 7)</span><span
3054 class="cmtt-8"> [index</span><span
3055 class="cmtt-8">_divisor]</span><span
3056 class="cmtt-8"> =</span><span
3057 class="cmtt-8"> [index</span><span
3058 class="cmtt-8">_divisor]</span><span
3059 class="cmtt-8"> *</span><span
3060 class="cmtt-8"> [codebook</span><span
3061 class="cmtt-8">_lookup</span><span
3062 class="cmtt-8">_values]</span><br class="fancyvrb" /><a
3063 id="x1-56030r15"></a><span
3064 class="cmr-6">15</span><br class="fancyvrb" /><a
3065 id="x1-56032r16"></a><span
3066 class="cmr-6">16</span><span
3067 class="cmtt-8"> </span><span
3068 class="cmtt-8"> </span><span
3069 class="cmtt-8"> </span><span
3070 class="cmtt-8"> </span><span
3071 class="cmtt-8"> </span><span
3072 class="cmsy-8">}</span><br class="fancyvrb" /><a
3073 id="x1-56034r17"></a><span
3074 class="cmr-6">17</span><br class="fancyvrb" /><a
3075 id="x1-56036r18"></a><span
3076 class="cmr-6">18</span><span
3077 class="cmtt-8"> </span><span
3078 class="cmtt-8"> 8)</span><span
3079 class="cmtt-8"> vector</span><span
3080 class="cmtt-8"> calculation</span><span
3081 class="cmtt-8"> completed.</span></div>
3082 <!--l. 384--><p class="noindent" ><span class="paragraphHead"><a
3083 id="x1-570003.2.1"></a><span
3084 class="cmbx-12">Vector value decode: Lookup type 2</span></span>
3085 Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set
3087 class="cmtt-12">[codebook</span><span
3088 class="cmtt-12">_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final
3089 values of a codebook entry vector from the entries in <span
3090 class="cmtt-12">[codebook</span><span
3091 class="cmtt-12">_multiplicands] </span>as follows
3093 class="cmtt-12">[value</span><span
3094 class="cmtt-12">_vector] </span>is the output vector representing the vector of values for entry number
3096 class="cmtt-12">[lookup</span><span
3097 class="cmtt-12">_offset] </span>in this codebook):
3098 <!--l. 394--><p class="noindent" >
3099 <div class="fancyvrb" id="fancyvrb19"><a
3100 id="x1-57002r1"></a><span
3101 class="cmr-6">1</span><span
3102 class="cmtt-8"> </span><span
3103 class="cmtt-8"> 1)</span><span
3104 class="cmtt-8"> [last]</span><span
3105 class="cmtt-8"> =</span><span
3106 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
3107 id="x1-57004r2"></a><span
3108 class="cmr-6">2</span><span
3109 class="cmtt-8"> </span><span
3110 class="cmtt-8"> 2)</span><span
3111 class="cmtt-8"> [multiplicand</span><span
3112 class="cmtt-8">_offset]</span><span
3113 class="cmtt-8"> =</span><span
3114 class="cmtt-8"> [lookup</span><span
3115 class="cmtt-8">_offset]</span><span
3116 class="cmtt-8"> *</span><span
3117 class="cmtt-8"> [codebook</span><span
3118 class="cmtt-8">_dimensions]</span>
3119 <br class="fancyvrb" /><a
3120 id="x1-57006r3"></a><span
3121 class="cmr-6">3</span><span
3122 class="cmtt-8"> </span><span
3123 class="cmtt-8"> 3)</span><span
3124 class="cmtt-8"> iterate</span><span
3125 class="cmtt-8"> [i]</span><span
3126 class="cmtt-8"> over</span><span
3127 class="cmtt-8"> the</span><span
3128 class="cmtt-8"> range</span><span
3129 class="cmtt-8"> 0</span><span
3130 class="cmtt-8"> ...</span><span
3131 class="cmtt-8"> [codebook</span><span
3132 class="cmtt-8">_dimensions]-1</span><span
3133 class="cmtt-8"> (once</span><span
3134 class="cmtt-8"> for</span><span
3135 class="cmtt-8"> each</span><span
3136 class="cmtt-8"> scalar</span><span
3137 class="cmtt-8"> value</span><span
3138 class="cmtt-8"> in</span><span
3139 class="cmtt-8"> the</span><span
3140 class="cmtt-8"> value</span><span
3141 class="cmtt-8"> vector)</span><span
3142 class="cmtt-8"> </span><span
3143 class="cmsy-8">{</span><br class="fancyvrb" /><a
3144 id="x1-57008r4"></a><span
3145 class="cmr-6">4</span>
3146 <br class="fancyvrb" /><a
3147 id="x1-57010r5"></a><span
3148 class="cmr-6">5</span><span
3149 class="cmtt-8"> </span><span
3150 class="cmtt-8"> </span><span
3151 class="cmtt-8"> </span><span
3152 class="cmtt-8"> </span><span
3153 class="cmtt-8"> </span><span
3154 class="cmtt-8"> </span><span
3155 class="cmtt-8"> 4)</span><span
3156 class="cmtt-8"> vector</span><span
3157 class="cmtt-8"> [value</span><span
3158 class="cmtt-8">_vector]</span><span
3159 class="cmtt-8"> element</span><span
3160 class="cmtt-8"> [i]</span><span
3161 class="cmtt-8"> =</span><br class="fancyvrb" /><a
3162 id="x1-57012r6"></a><span
3163 class="cmr-6">6</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"> </span><span
3173 class="cmtt-8"> </span><span
3174 class="cmtt-8"> </span><span
3175 class="cmtt-8"> (</span><span
3176 class="cmtt-8"> [codebook</span><span
3177 class="cmtt-8">_multiplicands]</span><span
3178 class="cmtt-8"> array</span><span
3179 class="cmtt-8"> element</span><span
3180 class="cmtt-8"> number</span><span
3181 class="cmtt-8"> [multiplicand</span><span
3182 class="cmtt-8">_offset]</span><span
3183 class="cmtt-8"> )</span><span
3184 class="cmtt-8"> *</span>
3185 <br class="fancyvrb" /><a
3186 id="x1-57014r7"></a><span
3187 class="cmr-6">7</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"> </span><span
3193 class="cmtt-8"> </span><span
3194 class="cmtt-8"> </span><span
3195 class="cmtt-8"> </span><span
3196 class="cmtt-8"> </span><span
3197 class="cmtt-8"> </span><span
3198 class="cmtt-8"> </span><span
3199 class="cmtt-8"> [codebook</span><span
3200 class="cmtt-8">_delta</span><span
3201 class="cmtt-8">_value]</span><span
3202 class="cmtt-8"> +</span><span
3203 class="cmtt-8"> [codebook</span><span
3204 class="cmtt-8">_minimum</span><span
3205 class="cmtt-8">_value]</span><span
3206 class="cmtt-8"> +</span><span
3207 class="cmtt-8"> [last];</span><br class="fancyvrb" /><a
3208 id="x1-57016r8"></a><span
3209 class="cmr-6">8</span>
3210 <br class="fancyvrb" /><a
3211 id="x1-57018r9"></a><span
3212 class="cmr-6">9</span><span
3213 class="cmtt-8"> </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"> 5)</span><span
3220 class="cmtt-8"> if</span><span
3221 class="cmtt-8"> (</span><span
3222 class="cmtt-8"> [codebook</span><span
3223 class="cmtt-8">_sequence</span><span
3224 class="cmtt-8">_p]</span><span
3225 class="cmtt-8"> is</span><span
3226 class="cmtt-8"> set</span><span
3227 class="cmtt-8"> )</span><span
3228 class="cmtt-8"> then</span><span
3229 class="cmtt-8"> set</span><span
3230 class="cmtt-8"> [last]</span><span
3231 class="cmtt-8"> =</span><span
3232 class="cmtt-8"> vector</span><span
3233 class="cmtt-8"> [value</span><span
3234 class="cmtt-8">_vector]</span><span
3235 class="cmtt-8"> element</span><span
3236 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
3237 id="x1-57020r10"></a><span
3238 class="cmr-6">10</span>
3239 <br class="fancyvrb" /><a
3240 id="x1-57022r11"></a><span
3241 class="cmr-6">11</span><span
3242 class="cmtt-8"> </span><span
3243 class="cmtt-8"> </span><span
3244 class="cmtt-8"> </span><span
3245 class="cmtt-8"> </span><span
3246 class="cmtt-8"> </span><span
3247 class="cmtt-8"> </span><span
3248 class="cmtt-8"> 6)</span><span
3249 class="cmtt-8"> increment</span><span
3250 class="cmtt-8"> [multiplicand</span><span
3251 class="cmtt-8">_offset]</span><br class="fancyvrb" /><a
3252 id="x1-57024r12"></a><span
3253 class="cmr-6">12</span><br class="fancyvrb" /><a
3254 id="x1-57026r13"></a><span
3255 class="cmr-6">13</span><span
3256 class="cmtt-8"> </span><span
3257 class="cmtt-8"> </span><span
3258 class="cmtt-8"> </span><span
3259 class="cmtt-8"> </span><span
3260 class="cmtt-8"> </span><span
3261 class="cmsy-8">}</span><br class="fancyvrb" /><a
3262 id="x1-57028r14"></a><span
3263 class="cmr-6">14</span><br class="fancyvrb" /><a
3264 id="x1-57030r15"></a><span
3265 class="cmr-6">15</span><span
3266 class="cmtt-8"> </span><span
3267 class="cmtt-8"> 7)</span><span
3268 class="cmtt-8"> vector</span><span
3269 class="cmtt-8"> calculation</span><span
3270 class="cmtt-8"> completed.</span></div>
3274 <!--l. 420--><p class="noindent" >
3275 <h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a
3276 id="x1-580003.3"></a>Use of the codebook abstraction</h4>
3277 <!--l. 422--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a
3278 specific codebook reads a codeword from the bitstream, decoding it into an entry number, and
3279 then returns that entry number to the decoder (when used in a scalar entropy coding context), or
3280 uses that entry number as an offset into the VQ lookup table, returning a vector of values (when
3281 used in a context desiring a VQ value). Scalar or VQ context is always explicit; any
3282 call to the codebook mechanism requests either a scalar entry number or a lookup
3284 <!--l. 432--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting
3285 decode using a codebook of lookup type 0 in any context expecting a vector return
3286 value (even in a case where a vector of dimension one) is forbidden. If decoder setup
3287 or decode requests such an action, that is an error condition rendering the packet
3289 <!--l. 439--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
3290 next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
3291 codeword in the codebook. This process can be though of as logically walking the
3292 Huffman decode tree by reading one bit at a time from the bitstream, and using the
3293 bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
3294 branch (right in the above examples). Walking the tree finishes when the decode process
3295 hits a leaf in the decision tree; the result is the entry number corresponding to that
3296 leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
3298 <!--l. 451--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
3300 <!--l. 454--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
3301 table. The value returned to the decoder is the vector of scalars corresponding to this
3309 <h3 class="sectionHead"><span class="titlemark">4. </span> <a
3310 id="x1-590004"></a>Codec Setup and Packet Decode</h3>
3311 <!--l. 6--><p class="noindent" >
3312 <h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a
3313 id="x1-600004.1"></a>Overview</h4>
3314 <!--l. 8--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
3315 of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
3316 process, which is provided in <a
3317 href="#x1-20001">section 1</a>, “<a
3318 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
3319 href="#x1-360002">section 2</a>,
3321 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
3323 <!--l. 16--><p class="noindent" >
3324 <h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a
3325 id="x1-610004.2"></a>Header decode and decode setup</h4>
3326 <!--l. 18--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
3327 identification header, the comments header, and the setup header. All are required for decode
3328 compliance. An end-of-packet condition during decoding the first or third header packet renders
3329 the stream undecodable. End-of-packet decoding the comment header is a non-fatal error
3331 <!--l. 25--><p class="noindent" >
3332 <h5 class="subsubsectionHead"><span class="titlemark">4.2.1. </span> <a
3333 id="x1-620004.2.1"></a>Common header decode</h5>
3334 <!--l. 27--><p class="noindent" >Each header packet begins with the same header fields.
3335 <!--l. 30--><p class="noindent" >
3336 <div class="fancyvrb" id="fancyvrb20"><a
3337 id="x1-62002r1"></a><span
3338 class="cmr-6">1</span><span
3339 class="cmtt-8"> </span><span
3340 class="cmtt-8"> 1)</span><span
3341 class="cmtt-8"> [packet</span><span
3342 class="cmtt-8">_type]</span><span
3343 class="cmtt-8"> :</span><span
3344 class="cmtt-8"> 8</span><span
3345 class="cmtt-8"> bit</span><span
3346 class="cmtt-8"> value</span><br class="fancyvrb" /><a
3347 id="x1-62004r2"></a><span
3348 class="cmr-6">2</span><span
3349 class="cmtt-8"> </span><span
3350 class="cmtt-8"> 2)</span><span
3351 class="cmtt-8"> 0x76,</span><span
3352 class="cmtt-8"> 0x6f,</span><span
3353 class="cmtt-8"> 0x72,</span><span
3354 class="cmtt-8"> 0x62,</span><span
3355 class="cmtt-8"> 0x69,</span><span
3356 class="cmtt-8"> 0x73:</span><span
3357 class="cmtt-8"> the</span><span
3358 class="cmtt-8"> characters</span><span
3359 class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
3360 class="cmtt-8"> as</span><span
3361 class="cmtt-8"> six</span><span
3362 class="cmtt-8"> octets</span></div>
3363 <!--l. 35--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
3364 header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
3365 single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
3370 <!--l. 43--><p class="noindent" >
3371 <h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a
3372 id="x1-630004.2.2"></a>Identification header</h5>
3373 <!--l. 45--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream
3374 definitively as Vorbis, and provide a few externally relevant pieces of information about the audio
3375 stream. The identification header is coded as follows:
3376 <!--l. 50--><p class="noindent" >
3377 <div class="fancyvrb" id="fancyvrb21"><a
3378 id="x1-63002r1"></a><span
3379 class="cmr-6">1</span><span
3380 class="cmtt-8"> 1)</span><span
3381 class="cmtt-8"> [vorbis</span><span
3382 class="cmtt-8">_version]</span><span
3383 class="cmtt-8"> =</span><span
3384 class="cmtt-8"> read</span><span
3385 class="cmtt-8"> 32</span><span
3386 class="cmtt-8"> bits</span><span
3387 class="cmtt-8"> as</span><span
3388 class="cmtt-8"> unsigned</span><span
3389 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3390 id="x1-63004r2"></a><span
3391 class="cmr-6">2</span><span
3392 class="cmtt-8"> 2)</span><span
3393 class="cmtt-8"> [audio</span><span
3394 class="cmtt-8">_channels]</span><span
3395 class="cmtt-8"> =</span><span
3396 class="cmtt-8"> read</span><span
3397 class="cmtt-8"> 8</span><span
3398 class="cmtt-8"> bit</span><span
3399 class="cmtt-8"> integer</span><span
3400 class="cmtt-8"> as</span><span
3401 class="cmtt-8"> unsigned</span>
3402 <br class="fancyvrb" /><a
3403 id="x1-63006r3"></a><span
3404 class="cmr-6">3</span><span
3405 class="cmtt-8"> 3)</span><span
3406 class="cmtt-8"> [audio</span><span
3407 class="cmtt-8">_sample</span><span
3408 class="cmtt-8">_rate]</span><span
3409 class="cmtt-8"> =</span><span
3410 class="cmtt-8"> read</span><span
3411 class="cmtt-8"> 32</span><span
3412 class="cmtt-8"> bits</span><span
3413 class="cmtt-8"> as</span><span
3414 class="cmtt-8"> unsigned</span><span
3415 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3416 id="x1-63008r4"></a><span
3417 class="cmr-6">4</span><span
3418 class="cmtt-8"> 4)</span><span
3419 class="cmtt-8"> [bitrate</span><span
3420 class="cmtt-8">_maximum]</span><span
3421 class="cmtt-8"> =</span><span
3422 class="cmtt-8"> read</span><span
3423 class="cmtt-8"> 32</span><span
3424 class="cmtt-8"> bits</span><span
3425 class="cmtt-8"> as</span><span
3426 class="cmtt-8"> signed</span><span
3427 class="cmtt-8"> integer</span>
3428 <br class="fancyvrb" /><a
3429 id="x1-63010r5"></a><span
3430 class="cmr-6">5</span><span
3431 class="cmtt-8"> 5)</span><span
3432 class="cmtt-8"> [bitrate</span><span
3433 class="cmtt-8">_nominal]</span><span
3434 class="cmtt-8"> =</span><span
3435 class="cmtt-8"> read</span><span
3436 class="cmtt-8"> 32</span><span
3437 class="cmtt-8"> bits</span><span
3438 class="cmtt-8"> as</span><span
3439 class="cmtt-8"> signed</span><span
3440 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
3441 id="x1-63012r6"></a><span
3442 class="cmr-6">6</span><span
3443 class="cmtt-8"> 6)</span><span
3444 class="cmtt-8"> [bitrate</span><span
3445 class="cmtt-8">_minimum]</span><span
3446 class="cmtt-8"> =</span><span
3447 class="cmtt-8"> read</span><span
3448 class="cmtt-8"> 32</span><span
3449 class="cmtt-8"> bits</span><span
3450 class="cmtt-8"> as</span><span
3451 class="cmtt-8"> signed</span><span
3452 class="cmtt-8"> integer</span>
3453 <br class="fancyvrb" /><a
3454 id="x1-63014r7"></a><span
3455 class="cmr-6">7</span><span
3456 class="cmtt-8"> 7)</span><span
3457 class="cmtt-8"> [blocksize</span><span
3458 class="cmtt-8">_0]</span><span
3459 class="cmtt-8"> =</span><span
3460 class="cmtt-8"> 2</span><span
3461 class="cmtt-8"> exponent</span><span
3462 class="cmtt-8"> (read</span><span
3463 class="cmtt-8"> 4</span><span
3464 class="cmtt-8"> bits</span><span
3465 class="cmtt-8"> as</span><span
3466 class="cmtt-8"> unsigned</span><span
3467 class="cmtt-8"> integer)</span><br class="fancyvrb" /><a
3468 id="x1-63016r8"></a><span
3469 class="cmr-6">8</span><span
3470 class="cmtt-8"> 8)</span><span
3471 class="cmtt-8"> [blocksize</span><span
3472 class="cmtt-8">_1]</span><span
3473 class="cmtt-8"> =</span><span
3474 class="cmtt-8"> 2</span><span
3475 class="cmtt-8"> exponent</span><span
3476 class="cmtt-8"> (read</span><span
3477 class="cmtt-8"> 4</span><span
3478 class="cmtt-8"> bits</span><span
3479 class="cmtt-8"> as</span><span
3480 class="cmtt-8"> unsigned</span><span
3481 class="cmtt-8"> integer)</span>
3482 <br class="fancyvrb" /><a
3483 id="x1-63018r9"></a><span
3484 class="cmr-6">9</span><span
3485 class="cmtt-8"> 9)</span><span
3486 class="cmtt-8"> [framing</span><span
3487 class="cmtt-8">_flag]</span><span
3488 class="cmtt-8"> =</span><span
3489 class="cmtt-8"> read</span><span
3490 class="cmtt-8"> one</span><span
3491 class="cmtt-8"> bit</span></div>
3492 <!--l. 62--><p class="noindent" ><span
3493 class="cmtt-12">[vorbis</span><span
3494 class="cmtt-12">_version] </span>is to read ’0’ in order to be compatible with this document. Both
3496 class="cmtt-12">[audio</span><span
3497 class="cmtt-12">_channels] </span>and <span
3498 class="cmtt-12">[audio</span><span
3499 class="cmtt-12">_sample</span><span
3500 class="cmtt-12">_rate] </span>must read greater than zero. Allowed final
3501 blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
3502 class="cmtt-12">[blocksize</span><span
3503 class="cmtt-12">_0]</span>
3504 must be less than or equal to <span
3505 class="cmtt-12">[blocksize</span><span
3506 class="cmtt-12">_1]</span>. The framing bit must be nonzero. Failure to meet
3507 any of these conditions renders a stream undecodable.
3508 <!--l. 70--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
3509 considerably off in purely VBR streams. The fields are meaningful only when greater than
3511 <ul class="itemize1">
3512 <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
3513 fixed-rate bitstream
3515 <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
3517 <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
3519 <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
3523 <!--l. 84--><p class="noindent" >
3524 <h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a
3525 id="x1-640004.2.3"></a>Comment header</h5>
3526 <!--l. 85--><p class="noindent" >Comment header decode and data specification is covered in <a
3527 href="#x1-820005">section 5</a>, “<a
3528 href="#x1-820005">comment field and
3529 header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
3530 <!--l. 89--><p class="noindent" >
3531 <h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a
3532 id="x1-650004.2.4"></a>Setup header</h5>
3533 <!--l. 91--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
3536 <!--l. 93--><p class="noindent" >
3538 <!--l. 94--><p class="noindent" ><img
3539 src="components.png" alt="PIC"
3541 <br /> <div class="caption"
3542 ><span class="id">Figure 6: </span><span
3543 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-650016 -->
3545 <!--l. 99--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
3546 header contains, in order, the lists of codebook configurations, time-domain transform
3547 configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
3548 mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
3549 decode proceeds in the following order:
3550 <!--l. 107--><p class="noindent" ><span class="paragraphHead"><a
3551 id="x1-660004.2.4"></a><span
3552 class="cmbx-12">Codebooks</span></span>
3553 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3555 class="enumerate-enumitem"><span
3556 class="cmtt-12">[vorbis</span><span
3557 class="cmtt-12">_codebook</span><span
3558 class="cmtt-12">_count] </span>= read eight bits as unsigned integer and add one
3559 </dd><dt class="enumerate-enumitem">
3561 class="enumerate-enumitem">Decode <span
3562 class="cmtt-12">[vorbis</span><span
3563 class="cmtt-12">_codebook</span><span
3564 class="cmtt-12">_count] </span>codebooks in order as defined in <a
3565 href="#x1-470003">section 3</a>,
3567 href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
3568 of codebook configurations <span
3569 class="cmtt-12">[vorbis</span><span
3570 class="cmtt-12">_codebook</span><span
3571 class="cmtt-12">_configurations]</span>.</dd></dl>
3575 <!--l. 119--><p class="noindent" ><span class="paragraphHead"><a
3576 id="x1-670004.2.4"></a><span
3577 class="cmbx-12">Time domain transforms</span></span>
3578 These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must
3579 be read to maintain bitstream sync.
3580 <!--l. 126--><p class="noindent" >
3581 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3583 class="enumerate-enumitem"><span
3584 class="cmtt-12">[vorbis</span><span
3585 class="cmtt-12">_time</span><span
3586 class="cmtt-12">_count] </span>= read 6 bits as unsigned integer and add one
3587 </dd><dt class="enumerate-enumitem">
3589 class="enumerate-enumitem">read <span
3590 class="cmtt-12">[vorbis</span><span
3591 class="cmtt-12">_time</span><span
3592 class="cmtt-12">_count] </span>16 bit values; each value should be zero. If any value is
3593 nonzero, this is an error condition and the stream is undecodable.</dd></dl>
3594 <!--l. 132--><p class="noindent" ><span class="paragraphHead"><a
3595 id="x1-680004.2.4"></a><span
3596 class="cmbx-12">Floors</span></span>
3597 Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
3599 <!--l. 138--><p class="noindent" >
3600 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3602 class="enumerate-enumitem"><span
3603 class="cmtt-12">[vorbis</span><span
3604 class="cmtt-12">_floor</span><span
3605 class="cmtt-12">_count] </span>= read 6 bits as unsigned integer and add one
3606 </dd><dt class="enumerate-enumitem">
3608 class="enumerate-enumitem">For each <span
3609 class="cmtt-12">[i] </span>of <span
3610 class="cmtt-12">[vorbis</span><span
3611 class="cmtt-12">_floor</span><span
3612 class="cmtt-12">_count] </span>floor numbers:
3613 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3615 class="enumerate-enumitem">read the floor type: vector <span
3616 class="cmtt-12">[vorbis</span><span
3617 class="cmtt-12">_floor</span><span
3618 class="cmtt-12">_types] </span>element <span
3619 class="cmtt-12">[i] </span>= read 16 bits
3621 </dd><dt class="enumerate-enumitem">
3623 class="enumerate-enumitem">If the floor type is zero, decode the floor configuration as defined in <a
3624 href="#x1-900006">section 6</a>,
3626 href="#x1-900006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
3627 class="cmtt-12">[i] </span>of the floor
3628 configuration array <span
3629 class="cmtt-12">[vorbis</span><span
3630 class="cmtt-12">_floor</span><span
3631 class="cmtt-12">_configurations]</span>.
3632 </dd><dt class="enumerate-enumitem">
3634 class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a
3635 href="#x1-970007">section 7</a>,
3637 href="#x1-970007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
3638 class="cmtt-12">[i] </span>of the floor
3639 configuration array <span
3640 class="cmtt-12">[vorbis</span><span
3641 class="cmtt-12">_floor</span><span
3642 class="cmtt-12">_configurations]</span>.
3643 </dd><dt class="enumerate-enumitem">
3645 class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR
3651 <!--l. 156--><p class="noindent" ><span class="paragraphHead"><a
3652 id="x1-690004.2.4"></a><span
3653 class="cmbx-12">Residues</span></span>
3654 Vorbis uses three residue types; header decode of each type is identical.
3655 <!--l. 162--><p class="noindent" >
3656 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3658 class="enumerate-enumitem"><span
3659 class="cmtt-12">[vorbis</span><span
3660 class="cmtt-12">_residue</span><span
3661 class="cmtt-12">_count] </span>= read 6 bits as unsigned integer and add one
3662 </dd><dt class="enumerate-enumitem">
3664 class="enumerate-enumitem">For each of <span
3665 class="cmtt-12">[vorbis</span><span
3666 class="cmtt-12">_residue</span><span
3667 class="cmtt-12">_count] </span>residue numbers:
3668 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3670 class="enumerate-enumitem">read the residue type; vector <span
3671 class="cmtt-12">[vorbis</span><span
3672 class="cmtt-12">_residue</span><span
3673 class="cmtt-12">_types] </span>element <span
3674 class="cmtt-12">[i] </span>= read 16
3675 bits as unsigned integer
3676 </dd><dt class="enumerate-enumitem">
3678 class="enumerate-enumitem">If the residue type is zero, one or two, decode the residue configuration as defined
3680 href="#x1-1040008">section 8</a>, “<a
3681 href="#x1-1040008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
3682 class="cmtt-12">[i] </span>of
3683 the residue configuration array <span
3684 class="cmtt-12">[vorbis</span><span
3685 class="cmtt-12">_residue</span><span
3686 class="cmtt-12">_configurations]</span>.
3687 </dd><dt class="enumerate-enumitem">
3689 class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR
3692 <!--l. 176--><p class="noindent" ><span class="paragraphHead"><a
3693 id="x1-700004.2.4"></a><span
3694 class="cmbx-12">Mappings</span></span>
3695 Mappings are used to set up specific pipelines for encoding multichannel audio with varying
3696 channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
3698 <!--l. 187--><p class="noindent" >
3699 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3701 class="enumerate-enumitem"><span
3702 class="cmtt-12">[vorbis</span><span
3703 class="cmtt-12">_mapping</span><span
3704 class="cmtt-12">_count] </span>= read 6 bits as unsigned integer and add one
3705 </dd><dt class="enumerate-enumitem">
3707 class="enumerate-enumitem">For each <span
3708 class="cmtt-12">[i] </span>of <span
3709 class="cmtt-12">[vorbis</span><span
3710 class="cmtt-12">_mapping</span><span
3711 class="cmtt-12">_count] </span>mapping numbers:
3715 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3717 class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
3718 the mapping type in Vorbis I.
3719 </dd><dt class="enumerate-enumitem">
3721 class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable
3722 </dd><dt class="enumerate-enumitem">
3724 class="enumerate-enumitem">If the mapping type is zero:
3725 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3727 class="enumerate-enumitem">read 1 bit as a boolean flag
3728 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3730 class="enumerate-enumitem">if set, <span
3731 class="cmtt-12">[vorbis</span><span
3732 class="cmtt-12">_mapping</span><span
3733 class="cmtt-12">_submaps] </span>= read 4 bits as unsigned integer
3735 </dd><dt class="enumerate-enumitem">
3737 class="enumerate-enumitem">if unset, <span
3738 class="cmtt-12">[vorbis</span><span
3739 class="cmtt-12">_mapping</span><span
3740 class="cmtt-12">_submaps] </span>= 1</dd></dl>
3741 </dd><dt class="enumerate-enumitem">
3743 class="enumerate-enumitem">read 1 bit as a boolean flag
3744 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3746 class="enumerate-enumitem">if set, square polar channel mapping is in use:
3747 <ul class="itemize1">
3748 <li class="itemize"><span
3749 class="cmtt-12">[vorbis</span><span
3750 class="cmtt-12">_mapping</span><span
3751 class="cmtt-12">_coupling</span><span
3752 class="cmtt-12">_steps] </span>= read 8 bits as unsigned
3755 <li class="itemize">for <span
3756 class="cmtt-12">[j] </span>each of <span
3757 class="cmtt-12">[vorbis</span><span
3758 class="cmtt-12">_mapping</span><span
3759 class="cmtt-12">_coupling</span><span
3760 class="cmtt-12">_steps] </span>steps:
3761 <ul class="itemize2">
3762 <li class="itemize">vector <span
3763 class="cmtt-12">[vorbis</span><span
3764 class="cmtt-12">_mapping</span><span
3765 class="cmtt-12">_magnitude] </span>element <span
3766 class="cmtt-12">[j]</span>= read
3768 href="#x1-1190009.2.1">ilog</a>(<span
3769 class="cmtt-12">[audio</span><span
3770 class="cmtt-12">_channels] </span>- 1) bits as unsigned integer
3772 <li class="itemize">vector <span
3773 class="cmtt-12">[vorbis</span><span
3774 class="cmtt-12">_mapping</span><span
3775 class="cmtt-12">_angle] </span>element <span
3776 class="cmtt-12">[j]</span>= read
3778 href="#x1-1190009.2.1">ilog</a>(<span
3779 class="cmtt-12">[audio</span><span
3780 class="cmtt-12">_channels] </span>- 1) bits as unsigned integer
3782 <li class="itemize">the numbers read in the above two steps are channel numbers
3783 representing the channel to treat as magnitude and the channel
3784 to treat as angle, respectively. If for any coupling step the
3785 angle channel number equals the magnitude channel number, the
3786 magnitude channel number is greater than <span
3787 class="cmtt-12">[audio</span><span
3788 class="cmtt-12">_channels]</span>-1, or
3789 the angle channel is greater than <span
3790 class="cmtt-12">[audio</span><span
3791 class="cmtt-12">_channels]</span>-1, the stream
3792 is undecodable.</li></ul>
3797 </dd><dt class="enumerate-enumitem">
3799 class="enumerate-enumitem">if unset, <span
3800 class="cmtt-12">[vorbis</span><span
3801 class="cmtt-12">_mapping</span><span
3802 class="cmtt-12">_coupling</span><span
3803 class="cmtt-12">_steps] </span>= 0</dd></dl>
3804 </dd><dt class="enumerate-enumitem">
3806 class="enumerate-enumitem">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
3807 </dd><dt class="enumerate-enumitem">
3809 class="enumerate-enumitem">if <span
3810 class="cmtt-12">[vorbis</span><span
3811 class="cmtt-12">_mapping</span><span
3812 class="cmtt-12">_submaps] </span>is greater than one, we read channel multiplex
3813 settings. For each <span
3814 class="cmtt-12">[j] </span>of <span
3815 class="cmtt-12">[audio</span><span
3816 class="cmtt-12">_channels] </span>channels:
3817 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3819 class="enumerate-enumitem">vector <span
3820 class="cmtt-12">[vorbis</span><span
3821 class="cmtt-12">_mapping</span><span
3822 class="cmtt-12">_mux] </span>element <span
3823 class="cmtt-12">[j] </span>= read 4 bits as unsigned
3825 </dd><dt class="enumerate-enumitem">
3827 class="enumerate-enumitem">if the value is greater than the highest numbered submap
3829 class="cmtt-12">[vorbis</span><span
3830 class="cmtt-12">_mapping</span><span
3831 class="cmtt-12">_submaps] </span>- 1), this in an error condition rendering
3832 the stream undecodable</dd></dl>
3833 </dd><dt class="enumerate-enumitem">
3835 class="enumerate-enumitem">for each submap <span
3836 class="cmtt-12">[j] </span>of <span
3837 class="cmtt-12">[vorbis</span><span
3838 class="cmtt-12">_mapping</span><span
3839 class="cmtt-12">_submaps] </span>submaps, read the floor and
3840 residue numbers for use in decoding that submap:
3841 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3843 class="enumerate-enumitem">read and discard 8 bits (the unused time configuration placeholder)
3844 </dd><dt class="enumerate-enumitem">
3846 class="enumerate-enumitem">read 8 bits as unsigned integer for the floor number; save in vector
3848 class="cmtt-12">[vorbis</span><span
3849 class="cmtt-12">_mapping</span><span
3850 class="cmtt-12">_submap</span><span
3851 class="cmtt-12">_floor] </span>element <span
3852 class="cmtt-12">[j]</span>
3853 </dd><dt class="enumerate-enumitem">
3855 class="enumerate-enumitem">verify the floor number is not greater than the highest number floor
3856 configured for the bitstream. If it is, the bitstream is undecodable
3857 </dd><dt class="enumerate-enumitem">
3859 class="enumerate-enumitem">read 8 bits as unsigned integer for the residue number; save in vector
3861 class="cmtt-12">[vorbis</span><span
3862 class="cmtt-12">_mapping</span><span
3863 class="cmtt-12">_submap</span><span
3864 class="cmtt-12">_residue] </span>element <span
3865 class="cmtt-12">[j]</span>
3866 </dd><dt class="enumerate-enumitem">
3868 class="enumerate-enumitem">verify the residue number is not greater than the highest number residue
3869 configured for the bitstream. If it is, the bitstream is undecodable</dd></dl>
3870 </dd><dt class="enumerate-enumitem">
3872 class="enumerate-enumitem">save this mapping configuration in slot <span
3873 class="cmtt-12">[i] </span>of the mapping configuration array
3875 class="cmtt-12">[vorbis</span><span
3876 class="cmtt-12">_mapping</span><span
3877 class="cmtt-12">_configurations]</span>.</dd></dl>
3883 <!--l. 246--><p class="noindent" ><span class="paragraphHead"><a
3884 id="x1-710004.2.4"></a><span
3885 class="cmbx-12">Modes</span></span>
3886 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3888 class="enumerate-enumitem"><span
3889 class="cmtt-12">[vorbis</span><span
3890 class="cmtt-12">_mode</span><span
3891 class="cmtt-12">_count] </span>= read 6 bits as unsigned integer and add one
3892 </dd><dt class="enumerate-enumitem">
3894 class="enumerate-enumitem">For each of <span
3895 class="cmtt-12">[vorbis</span><span
3896 class="cmtt-12">_mode</span><span
3897 class="cmtt-12">_count] </span>mode numbers:
3898 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3900 class="enumerate-enumitem"><span
3901 class="cmtt-12">[vorbis</span><span
3902 class="cmtt-12">_mode</span><span
3903 class="cmtt-12">_blockflag] </span>= read 1 bit
3904 </dd><dt class="enumerate-enumitem">
3906 class="enumerate-enumitem"><span
3907 class="cmtt-12">[vorbis</span><span
3908 class="cmtt-12">_mode</span><span
3909 class="cmtt-12">_windowtype] </span>= read 16 bits as unsigned integer
3910 </dd><dt class="enumerate-enumitem">
3912 class="enumerate-enumitem"><span
3913 class="cmtt-12">[vorbis</span><span
3914 class="cmtt-12">_mode</span><span
3915 class="cmtt-12">_transformtype] </span>= read 16 bits as unsigned integer
3916 </dd><dt class="enumerate-enumitem">
3918 class="enumerate-enumitem"><span
3919 class="cmtt-12">[vorbis</span><span
3920 class="cmtt-12">_mode</span><span
3921 class="cmtt-12">_mapping] </span>= read 8 bits as unsigned integer
3922 </dd><dt class="enumerate-enumitem">
3924 class="enumerate-enumitem">verify ranges; zero is the only legal value in
3926 class="cmtt-12">[vorbis</span><span
3927 class="cmtt-12">_mode</span><span
3928 class="cmtt-12">_windowtype] </span>and <span
3929 class="cmtt-12">[vorbis</span><span
3930 class="cmtt-12">_mode</span><span
3931 class="cmtt-12">_transformtype]</span>.
3933 class="cmtt-12">[vorbis</span><span
3934 class="cmtt-12">_mode</span><span
3935 class="cmtt-12">_mapping] </span>must not be greater than the highest number mapping
3936 in use. Any illegal values render the stream undecodable.
3937 </dd><dt class="enumerate-enumitem">
3939 class="enumerate-enumitem">save this mode configuration in slot <span
3940 class="cmtt-12">[i] </span>of the mode configuration array
3942 class="cmtt-12">[vorbis</span><span
3943 class="cmtt-12">_mode</span><span
3944 class="cmtt-12">_configurations]</span>.</dd></dl>
3945 </dd><dt class="enumerate-enumitem">
3947 class="enumerate-enumitem">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
3948 decodable.</dd></dl>
3949 <!--l. 267--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
3950 <!--l. 276--><p class="noindent" >
3951 <h4 class="subsectionHead"><span class="titlemark">4.3. </span> <a
3952 id="x1-720004.3"></a>Audio packet decode and synthesis</h4>
3956 <!--l. 278--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
3957 audio packet decode is to read and verify the packet type. <span
3958 class="cmti-12">A non-audio packet when audio is</span>
3960 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
3962 class="cmti-12">packet and not attempt decoding it to audio</span>.
3963 <!--l. 285--><p class="noindent" >
3964 <h5 class="subsubsectionHead"><span class="titlemark">4.3.1. </span> <a
3965 id="x1-730004.3.1"></a>packet type, mode and window decode</h5>
3966 <!--l. 288--><p class="noindent" >
3967 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3969 class="enumerate-enumitem">read 1 bit <span
3970 class="cmtt-12">[packet</span><span
3971 class="cmtt-12">_type]</span>; check that packet type is 0 (audio)
3972 </dd><dt class="enumerate-enumitem">
3974 class="enumerate-enumitem">read <a
3975 href="#x1-1190009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span
3976 class="cmtt-12">[mode</span><span
3977 class="cmtt-12">_number]</span>
3978 </dd><dt class="enumerate-enumitem">
3980 class="enumerate-enumitem">decode blocksize <span
3981 class="cmtt-12">[n] </span>is equal to <span
3982 class="cmtt-12">[blocksize</span><span
3983 class="cmtt-12">_0] </span>if <span
3984 class="cmtt-12">[vorbis</span><span
3985 class="cmtt-12">_mode</span><span
3986 class="cmtt-12">_blockflag] </span>is 0,
3988 class="cmtt-12">[n] </span>is equal to <span
3989 class="cmtt-12">[blocksize</span><span
3990 class="cmtt-12">_1]</span>.
3991 </dd><dt class="enumerate-enumitem">
3993 class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse
3995 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3997 class="enumerate-enumitem">if this is a long window (the <span
3998 class="cmtt-12">[vorbis</span><span
3999 class="cmtt-12">_mode</span><span
4000 class="cmtt-12">_blockflag] </span>flag of this mode is
4002 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4004 class="enumerate-enumitem">read 1 bit for <span
4005 class="cmtt-12">[previous</span><span
4006 class="cmtt-12">_window</span><span
4007 class="cmtt-12">_flag]</span>
4008 </dd><dt class="enumerate-enumitem">
4010 class="enumerate-enumitem">read 1 bit for <span
4011 class="cmtt-12">[next</span><span
4012 class="cmtt-12">_window</span><span
4013 class="cmtt-12">_flag]</span>
4014 </dd><dt class="enumerate-enumitem">
4016 class="enumerate-enumitem">if <span
4017 class="cmtt-12">[previous</span><span
4018 class="cmtt-12">_window</span><span
4019 class="cmtt-12">_flag] </span>is not set, the left half of the window will
4020 be a hybrid window for lapping with a short block. See <a
4021 href="#paragraph.1" >paragraph <a
4022 href="#x1-260001.3.2">1.3.2</a></a>,
4024 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4025 overlapping dissimilar windows. Else, the left half window will have normal
4027 </dd><dt class="enumerate-enumitem">
4029 class="enumerate-enumitem">if <span
4030 class="cmtt-12">[next</span><span
4031 class="cmtt-12">_window</span><span
4032 class="cmtt-12">_flag] </span>is not set, the right half of the window will be
4033 a hybrid window for lapping with a short block. See <a
4034 href="#x1-260001.3.2">paragraph 1.3.2</a>,
4039 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4040 overlapping dissimilar windows. Else, the left right window will have normal
4041 long shape.</dd></dl>
4042 </dd><dt class="enumerate-enumitem">
4044 class="enumerate-enumitem">if this is a short window, the window is always the same short-window
4047 <!--l. 320--><p class="noindent" >Vorbis windows all use the slope function <span
4048 class="cmmi-12">y </span>= sin(<img
4049 src="Vorbis_I_spec1x.png" alt="π
4050 2" class="frac" align="middle"> <span
4051 class="cmsy-10x-x-120">*</span> sin <sup><span
4052 class="cmr-8">2</span></sup>((<span
4053 class="cmmi-12">x </span>+ 0<span
4054 class="cmmi-12">.</span>5)<span
4055 class="cmmi-12">∕n </span><span
4056 class="cmsy-10x-x-120">* </span><span
4057 class="cmmi-12">π</span>)), where <span
4058 class="cmmi-12">n </span>is window
4060 class="cmmi-12">x </span>ranges 0<span
4061 class="cmmi-12">…</span><span
4062 class="cmmi-12">n</span><span
4063 class="cmsy-10x-x-120">- </span>1, but dissimilar lapping requirements can affect overall shape. Window
4064 generation proceeds as follows:
4065 <!--l. 326--><p class="noindent" >
4066 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4068 class="enumerate-enumitem"><span
4069 class="cmtt-12">[window</span><span
4070 class="cmtt-12">_center] </span>= <span
4071 class="cmtt-12">[n] </span>/ 2
4072 </dd><dt class="enumerate-enumitem">
4074 class="enumerate-enumitem">if (<span
4075 class="cmtt-12">[vorbis</span><span
4076 class="cmtt-12">_mode</span><span
4077 class="cmtt-12">_blockflag] </span>is set and <span
4078 class="cmtt-12">[previous</span><span
4079 class="cmtt-12">_window</span><span
4080 class="cmtt-12">_flag] </span>is not set)
4082 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4084 class="enumerate-enumitem"><span
4085 class="cmtt-12">[left</span><span
4086 class="cmtt-12">_window</span><span
4087 class="cmtt-12">_start] </span>= <span
4088 class="cmtt-12">[n]</span>/4 - <span
4089 class="cmtt-12">[blocksize</span><span
4090 class="cmtt-12">_0]</span>/4
4091 </dd><dt class="enumerate-enumitem">
4093 class="enumerate-enumitem"><span
4094 class="cmtt-12">[left</span><span
4095 class="cmtt-12">_window</span><span
4096 class="cmtt-12">_end] </span>= <span
4097 class="cmtt-12">[n]</span>/4 + <span
4098 class="cmtt-12">[blocksize</span><span
4099 class="cmtt-12">_0]</span>/4
4100 </dd><dt class="enumerate-enumitem">
4102 class="enumerate-enumitem"><span
4103 class="cmtt-12">[left</span><span
4104 class="cmtt-12">_n] </span>= <span
4105 class="cmtt-12">[blocksize</span><span
4106 class="cmtt-12">_0]</span>/2</dd></dl>
4107 <!--l. 335--><p class="noindent" >else
4108 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4110 class="enumerate-enumitem"><span
4111 class="cmtt-12">[left</span><span
4112 class="cmtt-12">_window</span><span
4113 class="cmtt-12">_start] </span>= 0
4114 </dd><dt class="enumerate-enumitem">
4116 class="enumerate-enumitem"><span
4117 class="cmtt-12">[left</span><span
4118 class="cmtt-12">_window</span><span
4119 class="cmtt-12">_end] </span>= <span
4120 class="cmtt-12">[window</span><span
4121 class="cmtt-12">_center]</span>
4122 </dd><dt class="enumerate-enumitem">
4124 class="enumerate-enumitem"><span
4125 class="cmtt-12">[left</span><span
4126 class="cmtt-12">_n] </span>= <span
4127 class="cmtt-12">[n]</span>/2</dd></dl>
4128 </dd><dt class="enumerate-enumitem">
4130 class="enumerate-enumitem">if (<span
4131 class="cmtt-12">[vorbis</span><span
4132 class="cmtt-12">_mode</span><span
4133 class="cmtt-12">_blockflag] </span>is set and <span
4134 class="cmtt-12">[next</span><span
4135 class="cmtt-12">_window</span><span
4136 class="cmtt-12">_flag] </span>is not set) then
4137 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4139 class="enumerate-enumitem"><span
4140 class="cmtt-12">[right</span><span
4141 class="cmtt-12">_window</span><span
4142 class="cmtt-12">_start] </span>= <span
4143 class="cmtt-12">[n]*3</span>/4 - <span
4144 class="cmtt-12">[blocksize</span><span
4145 class="cmtt-12">_0]</span>/4
4146 </dd><dt class="enumerate-enumitem">
4148 class="enumerate-enumitem"><span
4149 class="cmtt-12">[right</span><span
4150 class="cmtt-12">_window</span><span
4151 class="cmtt-12">_end] </span>= <span
4152 class="cmtt-12">[n]*3</span>/4 + <span
4153 class="cmtt-12">[blocksize</span><span
4154 class="cmtt-12">_0]</span>/4
4158 </dd><dt class="enumerate-enumitem">
4160 class="enumerate-enumitem"><span
4161 class="cmtt-12">[right</span><span
4162 class="cmtt-12">_n] </span>= <span
4163 class="cmtt-12">[blocksize</span><span
4164 class="cmtt-12">_0]</span>/2</dd></dl>
4165 <!--l. 351--><p class="noindent" >else
4166 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4168 class="enumerate-enumitem"><span
4169 class="cmtt-12">[right</span><span
4170 class="cmtt-12">_window</span><span
4171 class="cmtt-12">_start] </span>= <span
4172 class="cmtt-12">[window</span><span
4173 class="cmtt-12">_center]</span>
4174 </dd><dt class="enumerate-enumitem">
4176 class="enumerate-enumitem"><span
4177 class="cmtt-12">[right</span><span
4178 class="cmtt-12">_window</span><span
4179 class="cmtt-12">_end] </span>= <span
4180 class="cmtt-12">[n]</span>
4181 </dd><dt class="enumerate-enumitem">
4183 class="enumerate-enumitem"><span
4184 class="cmtt-12">[right</span><span
4185 class="cmtt-12">_n] </span>= <span
4186 class="cmtt-12">[n]</span>/2</dd></dl>
4187 </dd><dt class="enumerate-enumitem">
4189 class="enumerate-enumitem">window from range 0 ... <span
4190 class="cmtt-12">[left</span><span
4191 class="cmtt-12">_window</span><span
4192 class="cmtt-12">_start]</span>-1 inclusive is zero
4193 </dd><dt class="enumerate-enumitem">
4195 class="enumerate-enumitem">for <span
4196 class="cmtt-12">[i] </span>in range <span
4197 class="cmtt-12">[left</span><span
4198 class="cmtt-12">_window</span><span
4199 class="cmtt-12">_start] </span>... <span
4200 class="cmtt-12">[left</span><span
4201 class="cmtt-12">_window</span><span
4202 class="cmtt-12">_end]</span>-1, window(<span
4203 class="cmtt-12">[i]</span>) =
4205 src="Vorbis_I_spec2x.png" alt="π
4206 2" class="frac" align="middle"> <span
4207 class="cmsy-10x-x-120">*</span> sin <sup><span
4208 class="cmr-8">2</span></sup>( (<span
4209 class="cmtt-12">[i]</span>-<span
4210 class="cmtt-12">[left</span><span
4211 class="cmtt-12">_window</span><span
4212 class="cmtt-12">_start]</span>+0.5) / <span
4213 class="cmtt-12">[left</span><span
4214 class="cmtt-12">_n] </span><span
4215 class="cmsy-10x-x-120">*</span><img
4216 src="Vorbis_I_spec3x.png" alt="π
4217 2" class="frac" align="middle">) )
4218 </dd><dt class="enumerate-enumitem">
4220 class="enumerate-enumitem">window from range <span
4221 class="cmtt-12">[left</span><span
4222 class="cmtt-12">_window</span><span
4223 class="cmtt-12">_end] </span>... <span
4224 class="cmtt-12">[right</span><span
4225 class="cmtt-12">_window</span><span
4226 class="cmtt-12">_start]</span>-1 inclusive is
4228 </dd><dt class="enumerate-enumitem">
4230 class="enumerate-enumitem">for <span
4231 class="cmtt-12">[i] </span>in range <span
4232 class="cmtt-12">[right</span><span
4233 class="cmtt-12">_window</span><span
4234 class="cmtt-12">_start] </span>... <span
4235 class="cmtt-12">[right</span><span
4236 class="cmtt-12">_window</span><span
4237 class="cmtt-12">_end]</span>-1, window(<span
4238 class="cmtt-12">[i]</span>) =
4240 src="Vorbis_I_spec4x.png" alt="π2" class="frac" align="middle"> <span
4241 class="cmsy-10x-x-120">*</span> sin <sup><span
4242 class="cmr-8">2</span></sup>( (<span
4243 class="cmtt-12">[i]</span>-<span
4244 class="cmtt-12">[right</span><span
4245 class="cmtt-12">_window</span><span
4246 class="cmtt-12">_start]</span>+0.5) / <span
4247 class="cmtt-12">[right</span><span
4248 class="cmtt-12">_n] </span><span
4249 class="cmsy-10x-x-120">*</span><img
4250 src="Vorbis_I_spec5x.png" alt="π2" class="frac" align="middle"> + <img
4251 src="Vorbis_I_spec6x.png" alt="π2" class="frac" align="middle">) )
4252 </dd><dt class="enumerate-enumitem">
4254 class="enumerate-enumitem">window from range <span
4255 class="cmtt-12">[right</span><span
4256 class="cmtt-12">_window</span><span
4257 class="cmtt-12">_start] </span>... <span
4258 class="cmtt-12">[n]</span>-1 is zero</dd></dl>
4259 <!--l. 367--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this
4260 packet from the stream. An end of packet condition past this point is to be considered a possible
4262 <!--l. 374--><p class="noindent" >
4263 <h5 class="subsubsectionHead"><span class="titlemark">4.3.2. </span> <a
4264 id="x1-740004.3.2"></a>floor curve decode</h5>
4265 <!--l. 376--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
4266 class="cmtt-12">[mode</span><span
4267 class="cmtt-12">_number]</span>
4268 from configuration array <span
4269 class="cmtt-12">[vorbis</span><span
4270 class="cmtt-12">_mode</span><span
4271 class="cmtt-12">_configurations] </span>and the map number
4273 class="cmtt-12">[vorbis</span><span
4274 class="cmtt-12">_mode</span><span
4275 class="cmtt-12">_mapping] </span>(specified by the current mode) taken from the mapping configuration
4277 class="cmtt-12">[vorbis</span><span
4278 class="cmtt-12">_mapping</span><span
4279 class="cmtt-12">_configurations]</span>.
4280 <!--l. 383--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
4284 <!--l. 385--><p class="noindent" >For each floor <span
4285 class="cmtt-12">[i] </span>of <span
4286 class="cmtt-12">[audio</span><span
4287 class="cmtt-12">_channels]</span>
4288 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4290 class="enumerate-enumitem"><span
4291 class="cmtt-12">[submap</span><span
4292 class="cmtt-12">_number] </span>= element <span
4293 class="cmtt-12">[i] </span>of vector [vorbis_mapping_mux]
4294 </dd><dt class="enumerate-enumitem">
4296 class="enumerate-enumitem"><span
4297 class="cmtt-12">[floor</span><span
4298 class="cmtt-12">_number] </span>= element <span
4299 class="cmtt-12">[submap</span><span
4300 class="cmtt-12">_number] </span>of vector [vorbis_submap_floor]
4301 </dd><dt class="enumerate-enumitem">
4303 class="enumerate-enumitem">if the floor type of this floor (vector
4305 class="cmtt-12">[vorbis</span><span
4306 class="cmtt-12">_floor</span><span
4307 class="cmtt-12">_types] </span>element <span
4308 class="cmtt-12">[floor</span><span
4309 class="cmtt-12">_number]</span>) is zero then decode the floor for
4311 class="cmtt-12">[i] </span>according to the <a
4312 href="#x1-940006.2.2">subsubsection 6.2.2</a>, “<a
4313 href="#x1-940006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
4314 </dd><dt class="enumerate-enumitem">
4316 class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span
4317 class="cmtt-12">[i] </span>according to the
4319 href="#x1-1020007.2.3">subsubsection 7.2.3</a>, “<a
4320 href="#x1-1020007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
4321 </dd><dt class="enumerate-enumitem">
4323 class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis
4324 </dd><dt class="enumerate-enumitem">
4326 class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span
4327 class="cmtt-12">[no</span><span
4328 class="cmtt-12">_residue] </span>element <span
4329 class="cmtt-12">[i] </span>to true,
4330 else set vector <span
4331 class="cmtt-12">[no</span><span
4332 class="cmtt-12">_residue] </span>element <span
4333 class="cmtt-12">[i] </span>to false</dd></dl>
4334 <!--l. 405--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
4335 output vectors and skipping to the add/overlap output stage.
4336 <!--l. 411--><p class="noindent" >
4337 <h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a
4338 id="x1-750004.3.3"></a>nonzero vector propagate</h5>
4339 <!--l. 413--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
4340 that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
4341 coded in the stream, save for one complication. If some vectors are used and some are not,
4342 channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
4344 <!--l. 420--><p class="noindent" >for each <span
4345 class="cmtt-12">[i] </span>from 0 ... <span
4346 class="cmtt-12">[vorbis</span><span
4347 class="cmtt-12">_mapping</span><span
4348 class="cmtt-12">_coupling</span><span
4349 class="cmtt-12">_steps]</span>-1
4350 <!--l. 423--><p class="noindent" >
4351 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4353 class="enumerate-enumitem">if either <span
4354 class="cmtt-12">[no</span><span
4355 class="cmtt-12">_residue] </span>entry for channel (<span
4356 class="cmtt-12">[vorbis</span><span
4357 class="cmtt-12">_mapping</span><span
4358 class="cmtt-12">_magnitude] </span>element
4360 class="cmtt-12">[i]</span>) or channel (<span
4361 class="cmtt-12">[vorbis</span><span
4362 class="cmtt-12">_mapping</span><span
4363 class="cmtt-12">_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. 435--><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. 437--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
4375 <!--l. 440--><p class="noindent" >for each submap <span
4376 class="cmtt-12">[i] </span>in order from 0 ... <span
4377 class="cmtt-12">[vorbis</span><span
4378 class="cmtt-12">_mapping</span><span
4379 class="cmtt-12">_submaps]</span>-1
4380 <!--l. 443--><p class="noindent" >
4381 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4383 class="enumerate-enumitem"><span
4384 class="cmtt-12">[ch] </span>= 0
4385 </dd><dt class="enumerate-enumitem">
4387 class="enumerate-enumitem">for each channel <span
4388 class="cmtt-12">[j] </span>in order from 0 ... <span
4389 class="cmtt-12">[audio</span><span
4390 class="cmtt-12">_channels] </span>- 1
4391 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4393 class="enumerate-enumitem">if channel <span
4394 class="cmtt-12">[j] </span>in submap <span
4395 class="cmtt-12">[i] </span>(vector <span
4396 class="cmtt-12">[vorbis</span><span
4397 class="cmtt-12">_mapping</span><span
4398 class="cmtt-12">_mux] </span>element <span
4399 class="cmtt-12">[j] </span>is equal to
4401 class="cmtt-12">[i]</span>)
4402 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4404 class="enumerate-enumitem">if vector <span
4405 class="cmtt-12">[no</span><span
4406 class="cmtt-12">_residue] </span>element <span
4407 class="cmtt-12">[j] </span>is true
4408 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4410 class="enumerate-enumitem">vector <span
4411 class="cmtt-12">[do</span><span
4412 class="cmtt-12">_not</span><span
4413 class="cmtt-12">_decode</span><span
4414 class="cmtt-12">_flag] </span>element <span
4415 class="cmtt-12">[ch] </span>is set</dd></dl>
4416 <!--l. 452--><p class="noindent" >else
4417 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4419 class="enumerate-enumitem">vector <span
4420 class="cmtt-12">[do</span><span
4421 class="cmtt-12">_not</span><span
4422 class="cmtt-12">_decode</span><span
4423 class="cmtt-12">_flag] </span>element <span
4424 class="cmtt-12">[ch] </span>is unset</dd></dl>
4425 </dd><dt class="enumerate-enumitem">
4427 class="enumerate-enumitem">increment <span
4428 class="cmtt-12">[ch]</span></dd></dl>
4430 </dd><dt class="enumerate-enumitem">
4432 class="enumerate-enumitem"><span
4433 class="cmtt-12">[residue</span><span
4434 class="cmtt-12">_number] </span>= vector <span
4435 class="cmtt-12">[vorbis</span><span
4436 class="cmtt-12">_mapping</span><span
4437 class="cmtt-12">_submap</span><span
4438 class="cmtt-12">_residue] </span>element <span
4439 class="cmtt-12">[i]</span>
4440 </dd><dt class="enumerate-enumitem">
4442 class="enumerate-enumitem"><span
4443 class="cmtt-12">[residue</span><span
4444 class="cmtt-12">_type] </span>= vector <span
4445 class="cmtt-12">[vorbis</span><span
4446 class="cmtt-12">_residue</span><span
4447 class="cmtt-12">_types] </span>element <span
4448 class="cmtt-12">[residue</span><span
4449 class="cmtt-12">_number]</span>
4450 </dd><dt class="enumerate-enumitem">
4452 class="enumerate-enumitem">decode <span
4453 class="cmtt-12">[ch] </span>vectors using residue <span
4454 class="cmtt-12">[residue</span><span
4455 class="cmtt-12">_number]</span>, according to type <span
4456 class="cmtt-12">[residue</span><span
4457 class="cmtt-12">_type]</span>,
4461 also passing vector <span
4462 class="cmtt-12">[do</span><span
4463 class="cmtt-12">_not</span><span
4464 class="cmtt-12">_decode</span><span
4465 class="cmtt-12">_flag] </span>to indicate which vectors in the bundle should
4466 not be decoded. Correct per-vector decode length is <span
4467 class="cmtt-12">[n]</span>/2.
4468 </dd><dt class="enumerate-enumitem">
4470 class="enumerate-enumitem"><span
4471 class="cmtt-12">[ch] </span>= 0
4472 </dd><dt class="enumerate-enumitem">
4474 class="enumerate-enumitem">for each channel <span
4475 class="cmtt-12">[j] </span>in order from 0 ... <span
4476 class="cmtt-12">[audio</span><span
4477 class="cmtt-12">_channels]</span>
4478 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4480 class="enumerate-enumitem">if channel <span
4481 class="cmtt-12">[j] </span>is in submap <span
4482 class="cmtt-12">[i] </span>(vector <span
4483 class="cmtt-12">[vorbis</span><span
4484 class="cmtt-12">_mapping</span><span
4485 class="cmtt-12">_mux] </span>element <span
4486 class="cmtt-12">[j] </span>is equal
4488 class="cmtt-12">[i]</span>)
4489 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4491 class="enumerate-enumitem">residue vector for channel <span
4492 class="cmtt-12">[j] </span>is set to decoded residue vector <span
4493 class="cmtt-12">[ch]</span>
4494 </dd><dt class="enumerate-enumitem">
4496 class="enumerate-enumitem">increment <span
4497 class="cmtt-12">[ch]</span></dd></dl>
4500 <!--l. 479--><p class="noindent" >
4501 <h5 class="subsubsectionHead"><span class="titlemark">4.3.5. </span> <a
4502 id="x1-770004.3.5"></a>inverse coupling</h5>
4503 <!--l. 481--><p class="noindent" >for each <span
4504 class="cmtt-12">[i] </span>from <span
4505 class="cmtt-12">[vorbis</span><span
4506 class="cmtt-12">_mapping</span><span
4507 class="cmtt-12">_coupling</span><span
4508 class="cmtt-12">_steps]</span>-1 descending to 0
4509 <!--l. 484--><p class="noindent" >
4510 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4512 class="enumerate-enumitem"><span
4513 class="cmtt-12">[magnitude</span><span
4514 class="cmtt-12">_vector] </span>= the residue vector for channel (vector
4516 class="cmtt-12">[vorbis</span><span
4517 class="cmtt-12">_mapping</span><span
4518 class="cmtt-12">_magnitude] </span>element <span
4519 class="cmtt-12">[i]</span>)
4520 </dd><dt class="enumerate-enumitem">
4522 class="enumerate-enumitem"><span
4523 class="cmtt-12">[angle</span><span
4524 class="cmtt-12">_vector] </span>= the residue vector for channel (vector <span
4525 class="cmtt-12">[vorbis</span><span
4526 class="cmtt-12">_mapping</span><span
4527 class="cmtt-12">_angle]</span>
4529 class="cmtt-12">[i]</span>)
4530 </dd><dt class="enumerate-enumitem">
4532 class="enumerate-enumitem">for each scalar value <span
4533 class="cmtt-12">[M] </span>in vector <span
4534 class="cmtt-12">[magnitude</span><span
4535 class="cmtt-12">_vector] </span>and the corresponding scalar value
4537 class="cmtt-12">[A] </span>in vector <span
4538 class="cmtt-12">[angle</span><span
4539 class="cmtt-12">_vector]</span>:
4540 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4542 class="enumerate-enumitem">if (<span
4543 class="cmtt-12">[M] </span>is greater than zero)
4547 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4549 class="enumerate-enumitem">if (<span
4550 class="cmtt-12">[A] </span>is greater than zero)
4551 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4553 class="enumerate-enumitem"><span
4554 class="cmtt-12">[new</span><span
4555 class="cmtt-12">_M] </span>= <span
4556 class="cmtt-12">[M]</span>
4557 </dd><dt class="enumerate-enumitem">
4559 class="enumerate-enumitem"><span
4560 class="cmtt-12">[new</span><span
4561 class="cmtt-12">_A] </span>= <span
4562 class="cmtt-12">[M]</span>-<span
4563 class="cmtt-12">[A]</span></dd></dl>
4564 <!--l. 497--><p class="noindent" >else
4565 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4567 class="enumerate-enumitem"><span
4568 class="cmtt-12">[new</span><span
4569 class="cmtt-12">_A] </span>= <span
4570 class="cmtt-12">[M]</span>
4571 </dd><dt class="enumerate-enumitem">
4573 class="enumerate-enumitem"><span
4574 class="cmtt-12">[new</span><span
4575 class="cmtt-12">_M] </span>= <span
4576 class="cmtt-12">[M]</span>+<span
4577 class="cmtt-12">[A]</span></dd></dl>
4579 <!--l. 504--><p class="noindent" >else
4580 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4582 class="enumerate-enumitem">if (<span
4583 class="cmtt-12">[A] </span>is greater than zero)
4584 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4586 class="enumerate-enumitem"><span
4587 class="cmtt-12">[new</span><span
4588 class="cmtt-12">_M] </span>= <span
4589 class="cmtt-12">[M]</span>
4590 </dd><dt class="enumerate-enumitem">
4592 class="enumerate-enumitem"><span
4593 class="cmtt-12">[new</span><span
4594 class="cmtt-12">_A] </span>= <span
4595 class="cmtt-12">[M]</span>+<span
4596 class="cmtt-12">[A]</span></dd></dl>
4597 <!--l. 511--><p class="noindent" >else
4598 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4600 class="enumerate-enumitem"><span
4601 class="cmtt-12">[new</span><span
4602 class="cmtt-12">_A] </span>= <span
4603 class="cmtt-12">[M]</span>
4604 </dd><dt class="enumerate-enumitem">
4606 class="enumerate-enumitem"><span
4607 class="cmtt-12">[new</span><span
4608 class="cmtt-12">_M] </span>= <span
4609 class="cmtt-12">[M]</span>-<span
4610 class="cmtt-12">[A]</span></dd></dl>
4612 </dd><dt class="enumerate-enumitem">
4614 class="enumerate-enumitem">set scalar value <span
4615 class="cmtt-12">[M] </span>in vector <span
4616 class="cmtt-12">[magnitude</span><span
4617 class="cmtt-12">_vector] </span>to <span
4618 class="cmtt-12">[new</span><span
4619 class="cmtt-12">_M]</span>
4620 </dd><dt class="enumerate-enumitem">
4622 class="enumerate-enumitem">set scalar value <span
4623 class="cmtt-12">[A] </span>in vector <span
4624 class="cmtt-12">[angle</span><span
4625 class="cmtt-12">_vector] </span>to <span
4626 class="cmtt-12">[new</span><span
4627 class="cmtt-12">_A]</span></dd></dl>
4632 <!--l. 528--><p class="noindent" >
4633 <h5 class="subsubsectionHead"><span class="titlemark">4.3.6. </span> <a
4634 id="x1-780004.3.6"></a>dot product</h5>
4635 <!--l. 530--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
4636 packet type. Note that the vector synthesis length for floor computation is <span
4637 class="cmtt-12">[n]</span>/2.
4638 <!--l. 534--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
4639 channel’s residue vector. The result is the dot product of the floor and residue vectors for
4640 each channel; the produced vectors are the length <span
4641 class="cmtt-12">[n]</span>/2 audio spectrum for each
4643 <!--l. 542--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
4644 implementation might be to assume that a 32 bit fixed-point representation for floor and
4645 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
4646 in all cases because it happens to mostly work with the current Xiph.Org reference
4648 <!--l. 549--><p class="noindent" >However, floor vector values can span <span
4649 class="cmsy-10x-x-120">~</span>140dB (<span
4650 class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum
4651 vector should represent a minimum of 120dB (<span
4652 class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16
4653 bit PCM device. For the residue vector to represent full scale if the floor is nailed
4655 class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
4656 full scale if the floor is nailed at 0dB, it must be able to represent <span
4657 class="cmsy-10x-x-120">-</span>140dB to +0dB.
4658 Thus, in order to handle full range dynamics, a residue vector may span <span
4659 class="cmsy-10x-x-120">-</span>140dB to
4660 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
4661 residue vector must be able to represent a 48 bit range and the dot product must
4662 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
4663 achieved using large (64 bit or larger) integers, or implementing a movable binary point
4665 <!--l. 566--><p class="noindent" >
4666 <h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a
4667 id="x1-790004.3.7"></a>inverse MDCT</h5>
4668 <!--l. 568--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
4669 inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is
4670 available in <span class="cite">[<a
4671 href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
4676 <!--l. 575--><p class="noindent" >
4677 <h5 class="subsubsectionHead"><span class="titlemark">4.3.8. </span> <a
4678 id="x1-800004.3.8"></a>overlap_add</h5>
4679 <!--l. 577--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
4680 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
4681 current window (as illustrated in <a
4682 href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a
4683 href="#x1-260001.3.2">Window shape decode (long windows
4684 only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
4685 is finished data to be returned by the decoder. This data spans from the center of
4686 the previous window to the center of the current window. In the case of same-sized
4687 windows, the amount of data to return is one-half block consisting of and only of the
4688 overlapped portions. When overlapping a short and long window, much of the returned
4689 range does not actually overlap. This does not damage transform orthogonality. Pay
4690 attention however to returning the correct data range; the amount of data to be returned
4692 <!--l. 591--><p class="noindent" >
4693 <div class="fancyvrb" id="fancyvrb22"><a
4694 id="x1-80002r1"></a><span
4695 class="cmr-6">1</span><span
4696 class="cmtt-8">window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span></div>
4697 <!--l. 595--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
4698 windowsize/2-1, inclusive) of the current window.
4699 <!--l. 598--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
4700 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
4701 PCM output offset is ’0’ (as no data has been returned yet).
4702 <!--l. 605--><p class="noindent" >
4703 <h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a
4704 id="x1-810004.3.9"></a>output channel order</h5>
4705 <!--l. 607--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
4706 implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the
4707 specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for
4708 greater-than-eight channels remains ’left to the implementation’.
4709 <!--l. 613--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a
4710 decoder to produce output with channels in any order. Any such decoder should explicitly
4711 document channel reordering behavior.
4712 <!--l. 619--><p class="noindent" >
4713 <dl class="description"><dt class="description">
4715 class="cmssbx-10x-x-120">one channel</span> </dt><dd
4716 class="description">the stream is monophonic
4720 </dd><dt class="description">
4722 class="cmssbx-10x-x-120">two channels</span> </dt><dd
4723 class="description">the stream is stereo. channel order: left, right
4724 </dd><dt class="description">
4726 class="cmssbx-10x-x-120">three channels</span> </dt><dd
4727 class="description">the stream is a 1d-surround encoding. channel order: left, center, right
4728 </dd><dt class="description">
4730 class="cmssbx-10x-x-120">four channels</span> </dt><dd
4731 class="description">the stream is quadraphonic surround. channel order: front left, front right,
4732 rear left, rear right
4733 </dd><dt class="description">
4735 class="cmssbx-10x-x-120">five channels</span> </dt><dd
4736 class="description">the stream is five-channel surround. channel order: front left, center, front
4737 right, rear left, rear right
4738 </dd><dt class="description">
4740 class="cmssbx-10x-x-120">six channels</span> </dt><dd
4741 class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear
4742 left, rear right, LFE
4743 </dd><dt class="description">
4745 class="cmssbx-10x-x-120">seven channels</span> </dt><dd
4746 class="description">the stream is 6.1 surround. channel order: front left, center, front right,
4747 side left, side right, rear center, LFE
4748 </dd><dt class="description">
4750 class="cmssbx-10x-x-120">eight channels</span> </dt><dd
4751 class="description">the stream is 7.1 surround. channel order: front left, center, front right,
4752 side left, side right, rear left, rear right, LFE
4753 </dd><dt class="description">
4755 class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd
4756 class="description">channel use and order is defined by the application
4758 <!--l. 655--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
4759 channel mappings (such as three and four channel <a
4760 href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
4761 mappings other than mapping 0.
4768 <h3 class="sectionHead"><span class="titlemark">5. </span> <a
4769 id="x1-820005"></a>comment field and header specification</h3>
4770 <!--l. 5--><p class="noindent" >
4771 <h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a
4772 id="x1-830005.1"></a>Overview</h4>
4773 <!--l. 7--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
4774 bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
4775 belongs in a separate logical bitstream (usually an XML stream type) that provides greater
4776 structure and machine parseability.
4777 <!--l. 13--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
4778 a CDR. It should be a little information to remember the disc by and explain it to others; a
4779 short, to-the-point text note that need not only be a couple words, but isn’t going to be more
4780 than a short paragraph. The essentials, in other words, whatever they turn out to be,
4782 <!--l. 20--><p class="noindent" >
4784 <!--l. 21--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
4785 class="cmti-12">“I’m Still Around”</span>, opening
4786 for Moxy Früvous, 1997.</div>
4787 <!--l. 28--><p class="noindent" >
4788 <h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a
4789 id="x1-840005.2"></a>Comment encoding</h4>
4790 <!--l. 30--><p class="noindent" >
4791 <h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a
4792 id="x1-850005.2.1"></a>Structure</h5>
4793 <!--l. 32--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
4794 bounded to 2<sup><span
4795 class="cmr-8">32</span></sup> <span
4796 class="cmsy-10x-x-120">- </span>1 and the length of each vector is limited to 2<sup><span
4797 class="cmr-8">32</span></sup> <span
4798 class="cmsy-10x-x-120">- </span>1 bytes. The vector length is
4802 encoded; the vector contents themselves are not null terminated. In addition to the vector list,
4803 there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
4804 example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
4806 <!--l. 40--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
4807 packing conventions of the vorbis codec. However, since data in the comment header
4808 is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
4810 <!--l. 45--><p class="noindent" >The comment header is decoded as follows:
4811 <!--l. 47--><p class="noindent" >
4812 <div class="fancyvrb" id="fancyvrb23"><a
4813 id="x1-85002r1"></a><span
4814 class="cmr-6">1</span><span
4815 class="cmtt-8"> </span><span
4816 class="cmtt-8"> 1)</span><span
4817 class="cmtt-8"> [vendor\_length]</span><span
4818 class="cmtt-8"> =</span><span
4819 class="cmtt-8"> read</span><span
4820 class="cmtt-8"> an</span><span
4821 class="cmtt-8"> unsigned</span><span
4822 class="cmtt-8"> integer</span><span
4823 class="cmtt-8"> of</span><span
4824 class="cmtt-8"> 32</span><span
4825 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4826 id="x1-85004r2"></a><span
4827 class="cmr-6">2</span><span
4828 class="cmtt-8"> </span><span
4829 class="cmtt-8"> 2)</span><span
4830 class="cmtt-8"> [vendor\_string]</span><span
4831 class="cmtt-8"> =</span><span
4832 class="cmtt-8"> read</span><span
4833 class="cmtt-8"> a</span><span
4834 class="cmtt-8"> UTF-8</span><span
4835 class="cmtt-8"> vector</span><span
4836 class="cmtt-8"> as</span><span
4837 class="cmtt-8"> [vendor\_length]</span><span
4838 class="cmtt-8"> octets</span>
4839 <br class="fancyvrb" /><a
4840 id="x1-85006r3"></a><span
4841 class="cmr-6">3</span><span
4842 class="cmtt-8"> </span><span
4843 class="cmtt-8"> 3)</span><span
4844 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4845 class="cmtt-8"> =</span><span
4846 class="cmtt-8"> read</span><span
4847 class="cmtt-8"> an</span><span
4848 class="cmtt-8"> unsigned</span><span
4849 class="cmtt-8"> integer</span><span
4850 class="cmtt-8"> of</span><span
4851 class="cmtt-8"> 32</span><span
4852 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4853 id="x1-85008r4"></a><span
4854 class="cmr-6">4</span><span
4855 class="cmtt-8"> </span><span
4856 class="cmtt-8"> 4)</span><span
4857 class="cmtt-8"> iterate</span><span
4858 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4859 class="cmtt-8"> times</span><span
4860 class="cmtt-8"> {</span>
4861 <br class="fancyvrb" /><a
4862 id="x1-85010r5"></a><span
4863 class="cmr-6">5</span><span
4864 class="cmtt-8"> </span><span
4865 class="cmtt-8"> </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"> 5)</span><span
4871 class="cmtt-8"> [length]</span><span
4872 class="cmtt-8"> =</span><span
4873 class="cmtt-8"> read</span><span
4874 class="cmtt-8"> an</span><span
4875 class="cmtt-8"> unsigned</span><span
4876 class="cmtt-8"> integer</span><span
4877 class="cmtt-8"> of</span><span
4878 class="cmtt-8"> 32</span><span
4879 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
4880 id="x1-85012r6"></a><span
4881 class="cmr-6">6</span><span
4882 class="cmtt-8"> </span><span
4883 class="cmtt-8"> </span><span
4884 class="cmtt-8"> </span><span
4885 class="cmtt-8"> </span><span
4886 class="cmtt-8"> </span><span
4887 class="cmtt-8"> </span><span
4888 class="cmtt-8"> 6)</span><span
4889 class="cmtt-8"> this</span><span
4890 class="cmtt-8"> iteration’s</span><span
4891 class="cmtt-8"> user</span><span
4892 class="cmtt-8"> comment</span><span
4893 class="cmtt-8"> =</span><span
4894 class="cmtt-8"> read</span><span
4895 class="cmtt-8"> a</span><span
4896 class="cmtt-8"> UTF-8</span><span
4897 class="cmtt-8"> vector</span><span
4898 class="cmtt-8"> as</span><span
4899 class="cmtt-8"> [length]</span><span
4900 class="cmtt-8"> octets</span>
4901 <br class="fancyvrb" /><a
4902 id="x1-85014r7"></a><span
4903 class="cmr-6">7</span><span
4904 class="cmtt-8"> </span><span
4905 class="cmtt-8"> </span><span
4906 class="cmtt-8"> </span><span
4907 class="cmtt-8"> </span><span
4908 class="cmtt-8"> }</span><br class="fancyvrb" /><a
4909 id="x1-85016r8"></a><span
4910 class="cmr-6">8</span><span
4911 class="cmtt-8"> </span><span
4912 class="cmtt-8"> 7)</span><span
4913 class="cmtt-8"> [framing\_bit]</span><span
4914 class="cmtt-8"> =</span><span
4915 class="cmtt-8"> read</span><span
4916 class="cmtt-8"> a</span><span
4917 class="cmtt-8"> single</span><span
4918 class="cmtt-8"> bit</span><span
4919 class="cmtt-8"> as</span><span
4920 class="cmtt-8"> boolean</span><br class="fancyvrb" /><a
4921 id="x1-85018r9"></a><span
4922 class="cmr-6">9</span><span
4923 class="cmtt-8"> </span><span
4924 class="cmtt-8"> 8)</span><span
4925 class="cmtt-8"> if</span><span
4926 class="cmtt-8"> (</span><span
4927 class="cmtt-8"> [framing\_bit]</span><span
4928 class="cmtt-8"> unset</span><span
4929 class="cmtt-8"> or</span><span
4930 class="cmtt-8"> end-of-packet</span><span
4931 class="cmtt-8"> )</span><span
4932 class="cmtt-8"> then</span><span
4933 class="cmtt-8"> ERROR</span><br class="fancyvrb" /><a
4934 id="x1-85020r10"></a><span
4935 class="cmr-6">10</span><span
4936 class="cmtt-8"> </span><span
4937 class="cmtt-8"> 9)</span><span
4938 class="cmtt-8"> done.</span></div>
4939 <!--l. 63--><p class="noindent" >
4940 <h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a
4941 id="x1-860005.2.2"></a>Content vector format</h5>
4942 <!--l. 65--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is,
4943 comment fields consist of a field name and a corresponding value and look like:
4944 <!--l. 69--><p class="noindent" >
4946 <!--l. 70--><p class="noindent" >
4947 <div class="fancyvrb" id="fancyvrb24"><a
4948 id="x1-86002r1"></a><span
4949 class="cmr-6">1</span><span
4950 class="cmtt-8">comment[0]="ARTIST=me";</span><br class="fancyvrb" /><a
4951 id="x1-86004r2"></a><span
4952 class="cmr-6">2</span><span
4953 class="cmtt-8">comment[1]="TITLE=the</span><span
4954 class="cmtt-8"> sound</span><span
4955 class="cmtt-8"> of</span><span
4956 class="cmtt-8"> Vorbis";</span></div>
4958 <!--l. 76--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
4959 excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
4960 ASCII 0x61 through 0x7A inclusive (characters a-z).
4961 <!--l. 82--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
4962 terminate the field name.
4963 <!--l. 86--><p class="noindent" >0x3D is followed by 8 bit clean UTF-8 encoded value of the field contents to the end of the
4968 <!--l. 90--><p class="noindent" ><span class="paragraphHead"><a
4969 id="x1-870005.2.2"></a><span
4970 class="cmbx-12">Field names</span></span>
4971 Below is a proposed, minimal list of standard field names with a description of intended use. No
4972 single or group of field names is mandatory; a comment header may contain one, all or none of
4973 the names in this list.
4974 <!--l. 98--><p class="noindent" >
4975 <dl class="description"><dt class="description">
4977 class="cmssbx-10x-x-120">TITLE</span> </dt><dd
4978 class="description">Track/Work name
4979 </dd><dt class="description">
4981 class="cmssbx-10x-x-120">VERSION</span> </dt><dd
4982 class="description">The version field may be used to differentiate multiple versions of the same
4983 track title in a single collection. (e.g. remix info)
4984 </dd><dt class="description">
4986 class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
4987 class="description">The collection name to which this track belongs
4988 </dd><dt class="description">
4990 class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
4991 class="description">The track number of this piece if part of a specific larger collection or
4993 </dd><dt class="description">
4995 class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
4996 class="description">The artist generally considered responsible for the work. In popular music this is
4997 usually the performing band or singer. For classical music it would be the composer.
4998 For an audio book it would be the author of the original text.
4999 </dd><dt class="description">
5001 class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
5002 class="description">The artist(s) who performed the work. In classical music this would be the
5003 conductor, orchestra, soloists. In an audio book it would be the actor who did the
5004 reading. In popular music this is typically the same as the ARTIST and is omitted.
5005 </dd><dt class="description">
5007 class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
5008 class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
5009 </dd><dt class="description">
5011 class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
5012 class="description">License information, for example, ’All Rights Reserved’, ’Any Use
5013 Permitted’, a URL to a license such as a Creative Commons license (e.g.
5014 ”creativecommons.org/license/by/4.0/”) or similar.
5015 </dd><dt class="description">
5017 class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
5018 class="description">Name of the organization producing the track (i.e. the ’record label’)
5019 </dd><dt class="description">
5021 class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
5022 class="description">A short text description of the contents
5023 </dd><dt class="description">
5025 class="cmssbx-10x-x-120">GENRE</span> </dt><dd
5026 class="description">A short text indication of music genre
5030 </dd><dt class="description">
5032 class="cmssbx-10x-x-120">DATE</span> </dt><dd
5033 class="description">Date the track was recorded
5034 </dd><dt class="description">
5036 class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
5037 class="description">Location where track was recorded
5038 </dd><dt class="description">
5040 class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
5041 class="description">Contact information for the creators or distributors of the track. This could
5042 be a URL, an email address, the physical address of the producing label.
5043 </dd><dt class="description">
5045 class="cmssbx-10x-x-120">ISRC</span> </dt><dd
5046 class="description">International Standard Recording Code for the track; see <a
5047 href="https://isrc.ifpi.org/" >the ISRC intro page</a> for
5048 more information on ISRC numbers.
5050 <!--l. 154--><p class="noindent" ><span class="paragraphHead"><a
5051 id="x1-880005.2.2"></a><span
5052 class="cmbx-12">Implications</span></span>
5053 Field names should not be ’internationalized’; this is a concession to simplicity not
5054 an attempt to exclude the majority of the world that doesn’t speak English. Field
5056 class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
5058 <!--l. 162--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
5059 the field name is bounded in a known way. Thus we also have the length of the field
5061 <!--l. 166--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
5062 use of comment fields should be clear through context at this point. Abuse will be
5064 <!--l. 170--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
5065 to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
5066 tags here to help with standardization.
5067 <!--l. 175--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
5068 example, assume a track was recorded by three well know artists; the following is permissible,
5070 <!--l. 179--><p class="noindent" >
5072 <!--l. 180--><p class="noindent" >
5073 <div class="fancyvrb" id="fancyvrb25"><a
5074 id="x1-88002r1"></a><span
5075 class="cmr-6">1</span><span
5076 class="cmtt-8">ARTIST=Dizzy</span><span
5077 class="cmtt-8"> Gillespie</span><br class="fancyvrb" /><a
5078 id="x1-88004r2"></a><span
5079 class="cmr-6">2</span><span
5080 class="cmtt-8">ARTIST=Sonny</span><span
5081 class="cmtt-8"> Rollins</span><br class="fancyvrb" /><a
5082 id="x1-88006r3"></a><span
5083 class="cmr-6">3</span><span
5084 class="cmtt-8">ARTIST=Sonny</span><span
5085 class="cmtt-8"> Stitt</span></div>
5090 <!--l. 193--><p class="noindent" >
5091 <h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a
5092 id="x1-890005.2.3"></a>Encoding</h5>
5093 <!--l. 195--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
5094 first bitstream header packet, it is not generally the only packet on the second page and may not
5095 be restricted to within the second bitstream page. The length of the comment header packet is
5096 (practically) unbounded. The comment header packet is not optional; it must be present in the
5097 bitstream even if it is effectively empty.
5098 <!--l. 203--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
5099 renders least-significant-bit of the word to be coded into the least significant available bit of the
5100 current bitstream octet first):
5101 <!--l. 209--><p class="noindent" >
5102 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5104 class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets)
5105 </dd><dt class="enumerate-enumitem">
5107 class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of
5108 string, not null terminated)
5109 </dd><dt class="enumerate-enumitem">
5111 class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields)
5112 </dd><dt class="enumerate-enumitem">
5114 class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span
5115 class="cmmi-12">> </span>0; 32 bit unsigned quantity
5116 specifying number of octets)
5117 </dd><dt class="enumerate-enumitem">
5119 class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
5120 end of string, not null terminated)
5121 </dd><dt class="enumerate-enumitem">
5123 class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span
5124 class="cmmi-12">> </span>1...)...
5126 <!--l. 230--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
5128 class="cmtt-12">vorbis/lib/info.c</span>, <span
5129 class="cmtt-12">_vorbis</span><span
5130 class="cmtt-12">_pack</span><span
5131 class="cmtt-12">_comment() </span>and <span
5132 class="cmtt-12">_vorbis</span><span
5133 class="cmtt-12">_unpack</span><span
5134 class="cmtt-12">_comment()</span>.
5141 <h3 class="sectionHead"><span class="titlemark">6. </span> <a
5142 id="x1-900006"></a>Floor type 0 setup and decode</h3>
5143 <!--l. 5--><p class="noindent" >
5144 <h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a
5145 id="x1-910006.1"></a>Overview</h4>
5146 <!--l. 7--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
5147 Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
5148 response of the LSP filter. This representation is equivalent to a traditional all-pole infinite
5149 impulse response filter as would be used in linear predictive coding; LSP representation may be
5150 converted to LPC representation and vice-versa.
5151 <!--l. 17--><p class="noindent" >
5152 <h4 class="subsectionHead"><span class="titlemark">6.2. </span> <a
5153 id="x1-920006.2"></a>Floor 0 format</h4>
5154 <!--l. 19--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
5155 coding/decoding the LSP filter coefficient values used by each frame.
5156 <!--l. 23--><p class="noindent" >
5157 <h5 class="subsubsectionHead"><span class="titlemark">6.2.1. </span> <a
5158 id="x1-930006.2.1"></a>header decode</h5>
5159 <!--l. 25--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
5160 packet). configuration decode proceeds as follows:
5161 <!--l. 29--><p class="noindent" >
5162 <div class="fancyvrb" id="fancyvrb26"><a
5163 id="x1-93002r1"></a><span
5164 class="cmr-6">1</span><span
5165 class="cmtt-8"> </span><span
5166 class="cmtt-8"> 1)</span><span
5167 class="cmtt-8"> [floor0</span><span
5168 class="cmtt-8">_order]</span><span
5169 class="cmtt-8"> =</span><span
5170 class="cmtt-8"> read</span><span
5171 class="cmtt-8"> an</span><span
5172 class="cmtt-8"> unsigned</span><span
5173 class="cmtt-8"> integer</span><span
5174 class="cmtt-8"> of</span><span
5175 class="cmtt-8"> 8</span><span
5176 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5177 id="x1-93004r2"></a><span
5178 class="cmr-6">2</span><span
5179 class="cmtt-8"> </span><span
5180 class="cmtt-8"> 2)</span><span
5181 class="cmtt-8"> [floor0</span><span
5182 class="cmtt-8">_rate]</span><span
5183 class="cmtt-8"> =</span><span
5184 class="cmtt-8"> read</span><span
5185 class="cmtt-8"> an</span><span
5186 class="cmtt-8"> unsigned</span><span
5187 class="cmtt-8"> integer</span><span
5188 class="cmtt-8"> of</span><span
5189 class="cmtt-8"> 16</span><span
5190 class="cmtt-8"> bits</span>
5191 <br class="fancyvrb" /><a
5192 id="x1-93006r3"></a><span
5193 class="cmr-6">3</span><span
5194 class="cmtt-8"> </span><span
5195 class="cmtt-8"> 3)</span><span
5196 class="cmtt-8"> [floor0</span><span
5197 class="cmtt-8">_bark</span><span
5198 class="cmtt-8">_map</span><span
5199 class="cmtt-8">_size]</span><span
5200 class="cmtt-8"> =</span><span
5201 class="cmtt-8"> read</span><span
5202 class="cmtt-8"> an</span><span
5203 class="cmtt-8"> unsigned</span><span
5204 class="cmtt-8"> integer</span><span
5205 class="cmtt-8"> of</span><span
5206 class="cmtt-8"> 16</span><span
5207 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5208 id="x1-93008r4"></a><span
5209 class="cmr-6">4</span><span
5210 class="cmtt-8"> </span><span
5211 class="cmtt-8"> 4)</span><span
5212 class="cmtt-8"> [floor0</span><span
5213 class="cmtt-8">_amplitude</span><span
5214 class="cmtt-8">_bits]</span><span
5215 class="cmtt-8"> =</span><span
5216 class="cmtt-8"> read</span><span
5217 class="cmtt-8"> an</span><span
5218 class="cmtt-8"> unsigned</span><span
5219 class="cmtt-8"> integer</span><span
5220 class="cmtt-8"> of</span><span
5221 class="cmtt-8"> six</span><span
5222 class="cmtt-8"> bits</span>
5223 <br class="fancyvrb" /><a
5224 id="x1-93010r5"></a><span
5225 class="cmr-6">5</span><span
5226 class="cmtt-8"> </span><span
5227 class="cmtt-8"> 5)</span><span
5228 class="cmtt-8"> [floor0</span><span
5229 class="cmtt-8">_amplitude</span><span
5230 class="cmtt-8">_offset]</span><span
5231 class="cmtt-8"> =</span><span
5232 class="cmtt-8"> read</span><span
5233 class="cmtt-8"> an</span><span
5234 class="cmtt-8"> unsigned</span><span
5235 class="cmtt-8"> integer</span><span
5236 class="cmtt-8"> of</span><span
5237 class="cmtt-8"> eight</span><span
5238 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5239 id="x1-93012r6"></a><span
5240 class="cmr-6">6</span><span
5241 class="cmtt-8"> </span><span
5242 class="cmtt-8"> 6)</span><span
5243 class="cmtt-8"> [floor0</span><span
5244 class="cmtt-8">_number</span><span
5245 class="cmtt-8">_of</span><span
5246 class="cmtt-8">_books]</span><span
5247 class="cmtt-8"> =</span><span
5248 class="cmtt-8"> read</span><span
5249 class="cmtt-8"> an</span><span
5250 class="cmtt-8"> unsigned</span><span
5251 class="cmtt-8"> integer</span><span
5252 class="cmtt-8"> of</span><span
5253 class="cmtt-8"> four</span><span
5254 class="cmtt-8"> bits</span><span
5255 class="cmtt-8"> and</span><span
5256 class="cmtt-8"> add</span><span
5257 class="cmtt-8"> 1</span>
5258 <br class="fancyvrb" /><a
5259 id="x1-93014r7"></a><span
5260 class="cmr-6">7</span><span
5261 class="cmtt-8"> </span><span
5262 class="cmtt-8"> 7)</span><span
5263 class="cmtt-8"> array</span><span
5264 class="cmtt-8"> [floor0</span><span
5265 class="cmtt-8">_book</span><span
5266 class="cmtt-8">_list]</span><span
5267 class="cmtt-8"> =</span><span
5268 class="cmtt-8"> read</span><span
5269 class="cmtt-8"> a</span><span
5270 class="cmtt-8"> list</span><span
5271 class="cmtt-8"> of</span><span
5272 class="cmtt-8"> [floor0</span><span
5273 class="cmtt-8">_number</span><span
5274 class="cmtt-8">_of</span><span
5275 class="cmtt-8">_books]</span><span
5276 class="cmtt-8"> unsigned</span><span
5277 class="cmtt-8"> integers</span><span
5278 class="cmtt-8"> of</span><span
5279 class="cmtt-8"> eight</span><span
5280 class="cmtt-8"> bits</span><span
5281 class="cmtt-8"> each;</span></div>
5282 <!--l. 39--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
5283 In addition, any element of the array <span
5284 class="cmtt-12">[floor0</span><span
5285 class="cmtt-12">_book</span><span
5286 class="cmtt-12">_list] </span>that is greater than the maximum
5287 codebook number for this bitstream is an error condition that also renders the stream
5292 <!--l. 47--><p class="noindent" >
5293 <h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a
5294 id="x1-940006.2.2"></a>packet decode</h5>
5295 <!--l. 49--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve
5297 class="cmtt-12">[floor0</span><span
5298 class="cmtt-12">_order] </span>LSP coefficient values from the bitstream, and then
5299 computing the floor curve, which is defined as the frequency response of the decoded LSP
5301 <!--l. 55--><p class="noindent" >Packet decode proceeds as follows:
5302 <div class="fancyvrb" id="fancyvrb27"><a
5303 id="x1-94002r1"></a><span
5304 class="cmr-6">1</span><span
5305 class="cmtt-8"> </span><span
5306 class="cmtt-8"> 1)</span><span
5307 class="cmtt-8"> [amplitude]</span><span
5308 class="cmtt-8"> =</span><span
5309 class="cmtt-8"> read</span><span
5310 class="cmtt-8"> an</span><span
5311 class="cmtt-8"> unsigned</span><span
5312 class="cmtt-8"> integer</span><span
5313 class="cmtt-8"> of</span><span
5314 class="cmtt-8"> [floor0</span><span
5315 class="cmtt-8">_amplitude</span><span
5316 class="cmtt-8">_bits]</span><span
5317 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
5318 id="x1-94004r2"></a><span
5319 class="cmr-6">2</span><span
5320 class="cmtt-8"> </span><span
5321 class="cmtt-8"> 2)</span><span
5322 class="cmtt-8"> if</span><span
5323 class="cmtt-8"> (</span><span
5324 class="cmtt-8"> [amplitude]</span><span
5325 class="cmtt-8"> is</span><span
5326 class="cmtt-8"> greater</span><span
5327 class="cmtt-8"> than</span><span
5328 class="cmtt-8"> zero</span><span
5329 class="cmtt-8"> )</span><span
5330 class="cmtt-8"> </span><span
5331 class="cmsy-8">{</span>
5332 <br class="fancyvrb" /><a
5333 id="x1-94006r3"></a><span
5334 class="cmr-6">3</span><span
5335 class="cmtt-8"> </span><span
5336 class="cmtt-8"> </span><span
5337 class="cmtt-8"> </span><span
5338 class="cmtt-8"> </span><span
5339 class="cmtt-8"> </span><span
5340 class="cmtt-8"> </span><span
5341 class="cmtt-8"> 3)</span><span
5342 class="cmtt-8"> [coefficients]</span><span
5343 class="cmtt-8"> is</span><span
5344 class="cmtt-8"> an</span><span
5345 class="cmtt-8"> empty,</span><span
5346 class="cmtt-8"> zero</span><span
5347 class="cmtt-8"> length</span><span
5348 class="cmtt-8"> vector</span><br class="fancyvrb" /><a
5349 id="x1-94008r4"></a><span
5350 class="cmr-6">4</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"> 4)</span><span
5358 class="cmtt-8"> [booknumber]</span><span
5359 class="cmtt-8"> =</span><span
5360 class="cmtt-8"> read</span><span
5361 class="cmtt-8"> an</span><span
5362 class="cmtt-8"> unsigned</span><span
5363 class="cmtt-8"> integer</span><span
5364 class="cmtt-8"> of</span><span
5365 class="cmtt-8"> </span><a
5366 href="#x1-1190009.2.1"><span
5367 class="cmtt-8">ilog</span></a><span
5368 class="cmtt-8">(</span><span
5369 class="cmtt-8"> [floor0</span><span
5370 class="cmtt-8">_number</span><span
5371 class="cmtt-8">_of</span><span
5372 class="cmtt-8">_books]</span><span
5373 class="cmtt-8"> )</span><span
5374 class="cmtt-8"> bits</span>
5375 <br class="fancyvrb" /><a
5376 id="x1-94010r5"></a><span
5377 class="cmr-6">5</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"> 5)</span><span
5385 class="cmtt-8"> if</span><span
5386 class="cmtt-8"> (</span><span
5387 class="cmtt-8"> [booknumber]</span><span
5388 class="cmtt-8"> is</span><span
5389 class="cmtt-8"> greater</span><span
5390 class="cmtt-8"> than</span><span
5391 class="cmtt-8"> the</span><span
5392 class="cmtt-8"> highest</span><span
5393 class="cmtt-8"> number</span><span
5394 class="cmtt-8"> decode</span><span
5395 class="cmtt-8"> codebook</span><span
5396 class="cmtt-8"> )</span><span
5397 class="cmtt-8"> then</span><span
5398 class="cmtt-8"> packet</span><span
5399 class="cmtt-8"> is</span><span
5400 class="cmtt-8"> undecodable</span><br class="fancyvrb" /><a
5401 id="x1-94012r6"></a><span
5402 class="cmr-6">6</span><span
5403 class="cmtt-8"> </span><span
5404 class="cmtt-8"> </span><span
5405 class="cmtt-8"> </span><span
5406 class="cmtt-8"> </span><span
5407 class="cmtt-8"> </span><span
5408 class="cmtt-8"> </span><span
5409 class="cmtt-8"> 6)</span><span
5410 class="cmtt-8"> [last]</span><span
5411 class="cmtt-8"> =</span><span
5412 class="cmtt-8"> zero;</span>
5413 <br class="fancyvrb" /><a
5414 id="x1-94014r7"></a><span
5415 class="cmr-6">7</span><span
5416 class="cmtt-8"> </span><span
5417 class="cmtt-8"> </span><span
5418 class="cmtt-8"> </span><span
5419 class="cmtt-8"> </span><span
5420 class="cmtt-8"> </span><span
5421 class="cmtt-8"> </span><span
5422 class="cmtt-8"> 7)</span><span
5423 class="cmtt-8"> vector</span><span
5424 class="cmtt-8"> [temp</span><span
5425 class="cmtt-8">_vector]</span><span
5426 class="cmtt-8"> =</span><span
5427 class="cmtt-8"> read</span><span
5428 class="cmtt-8"> vector</span><span
5429 class="cmtt-8"> from</span><span
5430 class="cmtt-8"> bitstream</span><span
5431 class="cmtt-8"> using</span><span
5432 class="cmtt-8"> codebook</span><span
5433 class="cmtt-8"> number</span><span
5434 class="cmtt-8"> [floor0</span><span
5435 class="cmtt-8">_book</span><span
5436 class="cmtt-8">_list]</span><span
5437 class="cmtt-8"> element</span><span
5438 class="cmtt-8"> [booknumber]</span><span
5439 class="cmtt-8"> in</span><span
5440 class="cmtt-8"> VQ</span><span
5441 class="cmtt-8"> context.</span>
5442 <br class="fancyvrb" /><a
5443 id="x1-94016r8"></a><span
5444 class="cmr-6">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"> 8)</span><span
5452 class="cmtt-8"> add</span><span
5453 class="cmtt-8"> the</span><span
5454 class="cmtt-8"> scalar</span><span
5455 class="cmtt-8"> value</span><span
5456 class="cmtt-8"> [last]</span><span
5457 class="cmtt-8"> to</span><span
5458 class="cmtt-8"> each</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</span><span
5463 class="cmtt-8">_vector]</span><br class="fancyvrb" /><a
5464 id="x1-94018r9"></a><span
5465 class="cmr-6">9</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"> 9)</span><span
5473 class="cmtt-8"> [last]</span><span
5474 class="cmtt-8"> =</span><span
5475 class="cmtt-8"> the</span><span
5476 class="cmtt-8"> value</span><span
5477 class="cmtt-8"> of</span><span
5478 class="cmtt-8"> the</span><span
5479 class="cmtt-8"> last</span><span
5480 class="cmtt-8"> scalar</span><span
5481 class="cmtt-8"> in</span><span
5482 class="cmtt-8"> vector</span><span
5483 class="cmtt-8"> [temp</span><span
5484 class="cmtt-8">_vector]</span>
5485 <br class="fancyvrb" /><a
5486 id="x1-94020r10"></a><span
5487 class="cmr-6">10</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"> 10)</span><span
5494 class="cmtt-8"> concatenate</span><span
5495 class="cmtt-8"> [temp</span><span
5496 class="cmtt-8">_vector]</span><span
5497 class="cmtt-8"> onto</span><span
5498 class="cmtt-8"> the</span><span
5499 class="cmtt-8"> end</span><span
5500 class="cmtt-8"> of</span><span
5501 class="cmtt-8"> the</span><span
5502 class="cmtt-8"> [coefficients]</span><span
5503 class="cmtt-8"> vector</span>
5504 <br class="fancyvrb" /><a
5505 id="x1-94022r11"></a><span
5506 class="cmr-6">11</span><span
5507 class="cmtt-8"> </span><span
5508 class="cmtt-8"> </span><span
5509 class="cmtt-8"> </span><span
5510 class="cmtt-8"> </span><span
5511 class="cmtt-8"> </span><span
5512 class="cmtt-8"> 11)</span><span
5513 class="cmtt-8"> if</span><span
5514 class="cmtt-8"> (length</span><span
5515 class="cmtt-8"> of</span><span
5516 class="cmtt-8"> vector</span><span
5517 class="cmtt-8"> [coefficients]</span><span
5518 class="cmtt-8"> is</span><span
5519 class="cmtt-8"> less</span><span
5520 class="cmtt-8"> than</span><span
5521 class="cmtt-8"> [floor0</span><span
5522 class="cmtt-8">_order],</span><span
5523 class="cmtt-8"> continue</span><span
5524 class="cmtt-8"> at</span><span
5525 class="cmtt-8"> step</span><span
5526 class="cmtt-8"> 6</span><br class="fancyvrb" /><a
5527 id="x1-94024r12"></a><span
5528 class="cmr-6">12</span><br class="fancyvrb" /><a
5529 id="x1-94026r13"></a><span
5530 class="cmr-6">13</span><span
5531 class="cmtt-8"> </span><span
5532 class="cmtt-8"> </span><span
5533 class="cmtt-8"> </span><span
5534 class="cmtt-8"> </span><span
5535 class="cmtt-8"> </span><span
5536 class="cmsy-8">}</span><br class="fancyvrb" /><a
5537 id="x1-94028r14"></a><span
5538 class="cmr-6">14</span><br class="fancyvrb" /><a
5539 id="x1-94030r15"></a><span
5540 class="cmr-6">15</span><span
5541 class="cmtt-8"> 12)</span><span
5542 class="cmtt-8"> done.</span><br class="fancyvrb" /><a
5543 id="x1-94032r16"></a><span
5544 class="cmr-6">16</span></div>
5545 <!--l. 75--><p class="noindent" >Take note of the following properties of decode:
5546 <ul class="itemize1">
5547 <li class="itemize">An <span
5548 class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
5549 is unused in this frame (the output of the channel will be all-zeroes in synthesis).
5550 Several later stages of decode don’t occur for an unused channel.
5552 <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
5553 if end-of-packet is reached during any read operation above, floor decode is to return
5554 ’unused’ status as if the <span
5555 class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
5557 <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
5558 href="#x1-1190009.2.1">ilog</a>(
5560 class="cmtt-12">[floor0</span><span
5561 class="cmtt-12">_number</span><span
5562 class="cmtt-12">_of</span><span
5563 class="cmtt-12">_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
5564 and values greater than the maximum possible book value are reserved.
5566 <li class="itemize">The number of scalars read into the vector <span
5567 class="cmtt-12">[coefficients] </span>may be greater
5569 class="cmtt-12">[floor0</span><span
5570 class="cmtt-12">_order]</span>, the number actually required for curve computation. For
5571 example, if the VQ codebook used for the floor currently being decoded has a
5573 class="cmtt-12">[codebook</span><span
5574 class="cmtt-12">_dimensions] </span>value of three and <span
5575 class="cmtt-12">[floor0</span><span
5576 class="cmtt-12">_order] </span>is ten, the only way to
5577 fill all the needed scalars in <span
5578 class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
5579 as four vectors of three scalars each. This is not an error condition, and care must
5580 be taken not to allow a buffer overflow in decode. The extra values are not used and
5584 may be ignored or discarded.</li></ul>
5585 <!--l. 103--><p class="noindent" >
5586 <h5 class="subsubsectionHead"><span class="titlemark">6.2.3. </span> <a
5587 id="x1-950006.2.3"></a>curve computation</h5>
5588 <!--l. 105--><p class="noindent" >Given an <span
5589 class="cmtt-12">[amplitude] </span>integer and <span
5590 class="cmtt-12">[coefficients] </span>vector from packet decode as well as
5591 the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and
5592 [floor0_amplitude_offset] values from floor setup, and an output vector size <span
5593 class="cmtt-12">[n] </span>specified by the
5594 decode process, we compute a floor output vector.
5595 <!--l. 112--><p class="noindent" >If the value <span
5596 class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span
5597 class="cmtt-12">[n] </span>vector with all-zero
5598 scalars. Otherwise, begin by assuming the following definitions for the given vector to be
5600 <center class="par-math-display" >
5602 src="Vorbis_I_spec7x.png" alt=" {
5603 min (floor0xbarkxmapxsize - 1,f oobar) for i ∈ [0, n - 1]
5604 mapi = - 1 for i = n
5605 " class="par-math-display" ></center>
5606 <!--l. 127--><p class="nopar" >
5607 <!--l. 129--><p class="noindent" >where
5608 <center class="par-math-display" >
5610 src="Vorbis_I_spec8x.png" alt=" ⌊ ( floor0xrate ⋅ i) floor0xbarkxmapxsize ⌋
5611 f oobar = bark ---------------- ⋅------------------------
5612 2n bark(.5 ⋅ floor0xrate )
5613 " class="par-math-display" ></center>
5614 <!--l. 136--><p class="nopar" >
5615 <!--l. 138--><p class="noindent" >and
5616 <center class="par-math-display" >
5618 src="Vorbis_I_spec9x.png" alt="bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x2 ) + .0001x
5619 " class="par-math-display" ></center>
5620 <!--l. 142--><p class="nopar" >
5624 <!--l. 144--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
5625 result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
5627 class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
5629 <!--l. 150--><p class="noindent" >
5630 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5632 class="enumerate-enumitem"><span
5633 class="cmtt-12">[i] </span>= 0
5634 </dd><dt class="enumerate-enumitem">
5636 class="enumerate-enumitem"><span
5637 class="cmtt-12">[</span><span
5638 class="cmmi-12">ω</span><span
5639 class="cmtt-12">] </span>= <span
5640 class="cmmi-12">π </span>* map element <span
5641 class="cmtt-12">[i] </span>/ <span
5642 class="cmtt-12">[floor0</span><span
5643 class="cmtt-12">_bark</span><span
5644 class="cmtt-12">_map</span><span
5645 class="cmtt-12">_size]</span>
5646 </dd><dt class="enumerate-enumitem">
5648 class="enumerate-enumitem">if ( <span
5649 class="cmtt-12">[floor0</span><span
5650 class="cmtt-12">_order] </span>is odd )
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_spec10x.png" alt=" floor0∏x2order-3
5659 p = (1 - cos2ω) 4(cos([coefficients ]2j+1) - cosω )2
5663 q = -- 4(cos([coefficients ]2j) - cosω )
5665 " class="math-display" ></center>
5668 <!--l. 161--><p class="noindent" >else <span
5669 class="cmtt-12">[floor0</span><span
5670 class="cmtt-12">_order] </span>is even
5671 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5673 class="enumerate-enumitem">calculate <span
5674 class="cmtt-12">[p] </span>and <span
5675 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5679 <center class="math-display" >
5681 src="Vorbis_I_spec11x.png" alt=" floor0x∏o2rder-2
5682 p = (1---cosω-) 4(cos([coefficients ]2j+1) - cosω)2
5685 (1 + cosω ) ∏2 2
5686 q = ----------- 4(cos([coefficients ]2j) - cos ω)
5688 " class="math-display" ></center>
5691 </dd><dt class="enumerate-enumitem">
5693 class="enumerate-enumitem">calculate <span
5694 class="cmtt-12">[linear</span><span
5695 class="cmtt-12">_floor</span><span
5696 class="cmtt-12">_value] </span>according to:
5697 <center class="math-display" >
5699 src="Vorbis_I_spec12x.png" alt=" ( ( ))
5700 amplitude ⋅ floor0xamplitutexoffset
5701 exp .11512925 ------floor0xamplitudexbits-----√----------- floor0xamplitudexoffset
5703 " class="math-display" ></center>
5704 <!--l. 176--><p class="nopar" >
5705 </dd><dt class="enumerate-enumitem">
5707 class="enumerate-enumitem"><span
5708 class="cmtt-12">[iteration</span><span
5709 class="cmtt-12">_condition] </span>= map element <span
5710 class="cmtt-12">[i]</span>
5711 </dd><dt class="enumerate-enumitem">
5713 class="enumerate-enumitem"><span
5714 class="cmtt-12">[output] </span>element <span
5715 class="cmtt-12">[i] </span>= <span
5716 class="cmtt-12">[linear</span><span
5717 class="cmtt-12">_floor</span><span
5718 class="cmtt-12">_value]</span>
5719 </dd><dt class="enumerate-enumitem">
5721 class="enumerate-enumitem">increment <span
5722 class="cmtt-12">[i]</span>
5723 </dd><dt class="enumerate-enumitem">
5725 class="enumerate-enumitem">if ( map element <span
5726 class="cmtt-12">[i] </span>is equal to <span
5727 class="cmtt-12">[iteration</span><span
5728 class="cmtt-12">_condition] </span>) continue at step
5730 </dd><dt class="enumerate-enumitem">
5732 class="enumerate-enumitem">if ( <span
5733 class="cmtt-12">[i] </span>is less than <span
5734 class="cmtt-12">[n] </span>) continue at step 2
5738 </dd><dt class="enumerate-enumitem">
5740 class="enumerate-enumitem">done</dd></dl>
5741 <!--l. 186--><p class="noindent" ><span class="paragraphHead"><a
5742 id="x1-960006.2.3"></a><span
5743 class="cmbx-12">Errata 20150227: Bark scale computation</span></span>
5744 Due to a typo when typesetting this version of the specification from the original HTML
5745 document, the Bark scale computation previously erroneously read:
5746 <center class="par-math-display" >
5748 src="Vorbis_I_spec13x.png" alt="bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x2 + .0001x )
5749 " class="par-math-display" ></center>
5750 <!--l. 194--><p class="nopar" >
5751 <!--l. 196--><p class="noindent" >Note that the last parenthesis is misplaced. This document now uses the correct equation as it
5752 appeared in the original HTML spec document:
5753 <center class="par-math-display" >
5755 src="Vorbis_I_spec14x.png" alt="bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x2 ) + .0001x
5756 " class="par-math-display" ></center>
5757 <!--l. 200--><p class="nopar" >
5764 <h3 class="sectionHead"><span class="titlemark">7. </span> <a
5765 id="x1-970007"></a>Floor type 1 setup and decode</h3>
5766 <!--l. 5--><p class="noindent" >
5767 <h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a
5768 id="x1-980007.1"></a>Overview</h4>
5769 <!--l. 7--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
5770 curve. The representation plots this curve mechanically on a linear frequency axis and a
5771 logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
5773 <!--l. 15--><p class="noindent" >
5774 <h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a
5775 id="x1-990007.2"></a>Floor 1 format</h4>
5776 <!--l. 17--><p class="noindent" >
5777 <h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a
5778 id="x1-1000007.2.1"></a>model</h5>
5779 <!--l. 19--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
5780 floor curve using iterative prediction in a process roughly equivalent to the following simplified
5782 <ul class="itemize1">
5783 <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
5784 where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
5787 <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
5788 produces a y˙new value at that point computed from the existing line’s y value at
5789 x˙new (as plotted by the line) and a difference value decoded from the bitstream
5795 <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
5796 x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
5797 y˙new represents no change to the amplitude value at x˙new so that later refinement
5798 is additionally bounded at x˙new.
5800 <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
5801 at floor 1 initialization time. Computation is completed at the end of the x value list.
5803 <!--l. 47--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
5804 representing typical configuration:
5805 <!--l. 50--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values
5806 in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
5807 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
5808 example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
5809 way, beginning with the first line:
5812 <!--l. 58--><p class="noindent" >
5814 <!--l. 59--><p class="noindent" ><img
5815 src="floor1-1.png" alt="PIC"
5817 <br /> <div class="caption"
5818 ><span class="id">Figure 7: </span><span
5819 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000017 -->
5821 <!--l. 63--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
5825 <!--l. 66--><p class="noindent" >
5827 <!--l. 67--><p class="noindent" ><img
5828 src="floor1-2.png" alt="PIC"
5830 <br /> <div class="caption"
5831 ><span class="id">Figure 8: </span><span
5832 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000028 -->
5834 <!--l. 71--><p class="noindent" >Although the new Y value at X position 96 is unchanged, it is still used later as an endpoint for
5835 further refinement. From here on, the pattern should be clear; we complete the floor computation
5842 <!--l. 75--><p class="noindent" >
5844 <!--l. 76--><p class="noindent" ><img
5845 src="floor1-3.png" alt="PIC"
5847 <br /> <div class="caption"
5848 ><span class="id">Figure 9: </span><span
5849 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000039 -->
5853 <!--l. 80--><p class="noindent" >
5855 <!--l. 81--><p class="noindent" ><img
5856 src="floor1-4.png" alt="PIC"
5858 <br /> <div class="caption"
5859 ><span class="id">Figure 10: </span><span
5860 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-10000410 -->
5862 <!--l. 85--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
5863 decode, as described later. The actual algorithm splits Y value computation and line plotting
5864 into two steps with modifications to the above algorithm to eliminate noise accumulation
5865 through integer roundoff/truncation.
5866 <!--l. 93--><p class="noindent" >
5867 <h5 class="subsubsectionHead"><span class="titlemark">7.2.2. </span> <a
5868 id="x1-1010007.2.2"></a>header decode</h5>
5869 <!--l. 95--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
5870 during packet decode and synthesis). This list is split into partitions, and each partition is
5871 assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
5872 partition or partition class.
5873 <!--l. 101--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
5874 the partition class encodes at once), a ’subclass’ value representing the number of
5875 alternate entropy books the partition class may use in representing Y values, the list of
5876 [subclass] books and a master book used to encode which alternate books were chosen
5877 for representation in a given packet. The master/subclass mechanism is meant to be
5878 used as a flexible representation cascade while still using codebooks only in a scalar
5883 <!--l. 111--><p class="noindent" >
5884 <div class="fancyvrb" id="fancyvrb28"><a
5885 id="x1-101002r1"></a><span
5886 class="cmr-6">1</span><br class="fancyvrb" /><a
5887 id="x1-101004r2"></a><span
5888 class="cmr-6">2</span><span
5889 class="cmtt-8"> </span><span
5890 class="cmtt-8"> 1)</span><span
5891 class="cmtt-8"> [floor1</span><span
5892 class="cmtt-8">_partitions]</span><span
5893 class="cmtt-8"> =</span><span
5894 class="cmtt-8"> read</span><span
5895 class="cmtt-8"> 5</span><span
5896 class="cmtt-8"> bits</span><span
5897 class="cmtt-8"> as</span><span
5898 class="cmtt-8"> unsigned</span><span
5899 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
5900 id="x1-101006r3"></a><span
5901 class="cmr-6">3</span><span
5902 class="cmtt-8"> </span><span
5903 class="cmtt-8"> 2)</span><span
5904 class="cmtt-8"> [maximum</span><span
5905 class="cmtt-8">_class]</span><span
5906 class="cmtt-8"> =</span><span
5907 class="cmtt-8"> -1</span><br class="fancyvrb" /><a
5908 id="x1-101008r4"></a><span
5909 class="cmr-6">4</span><span
5910 class="cmtt-8"> </span><span
5911 class="cmtt-8"> 3)</span><span
5912 class="cmtt-8"> iterate</span><span
5913 class="cmtt-8"> [i]</span><span
5914 class="cmtt-8"> over</span><span
5915 class="cmtt-8"> the</span><span
5916 class="cmtt-8"> range</span><span
5917 class="cmtt-8"> 0</span><span
5918 class="cmtt-8"> ...</span><span
5919 class="cmtt-8"> [floor1</span><span
5920 class="cmtt-8">_partitions]-1</span><span
5921 class="cmtt-8"> </span><span
5922 class="cmsy-8">{</span><br class="fancyvrb" /><a
5923 id="x1-101010r5"></a><span
5924 class="cmr-6">5</span>
5925 <br class="fancyvrb" /><a
5926 id="x1-101012r6"></a><span
5927 class="cmr-6">6</span><span
5928 class="cmtt-8"> </span><span
5929 class="cmtt-8"> </span><span
5930 class="cmtt-8"> </span><span
5931 class="cmtt-8"> </span><span
5932 class="cmtt-8"> </span><span
5933 class="cmtt-8"> </span><span
5934 class="cmtt-8"> </span><span
5935 class="cmtt-8"> 4)</span><span
5936 class="cmtt-8"> vector</span><span
5937 class="cmtt-8"> [floor1</span><span
5938 class="cmtt-8">_partition</span><span
5939 class="cmtt-8">_class</span><span
5940 class="cmtt-8">_list]</span><span
5941 class="cmtt-8"> element</span><span
5942 class="cmtt-8"> [i]</span><span
5943 class="cmtt-8"> =</span><span
5944 class="cmtt-8"> read</span><span
5945 class="cmtt-8"> 4</span><span
5946 class="cmtt-8"> bits</span><span
5947 class="cmtt-8"> as</span><span
5948 class="cmtt-8"> unsigned</span><span
5949 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
5950 id="x1-101014r7"></a><span
5951 class="cmr-6">7</span><br class="fancyvrb" /><a
5952 id="x1-101016r8"></a><span
5953 class="cmr-6">8</span><span
5954 class="cmtt-8"> </span><span
5955 class="cmtt-8"> </span><span
5956 class="cmtt-8"> </span><span
5957 class="cmtt-8"> </span><span
5958 class="cmtt-8"> </span><span
5959 class="cmsy-8">}</span><br class="fancyvrb" /><a
5960 id="x1-101018r9"></a><span
5961 class="cmr-6">9</span>
5962 <br class="fancyvrb" /><a
5963 id="x1-101020r10"></a><span
5964 class="cmr-6">10</span><span
5965 class="cmtt-8"> </span><span
5966 class="cmtt-8"> 5)</span><span
5967 class="cmtt-8"> [maximum</span><span
5968 class="cmtt-8">_class]</span><span
5969 class="cmtt-8"> =</span><span
5970 class="cmtt-8"> largest</span><span
5971 class="cmtt-8"> integer</span><span
5972 class="cmtt-8"> scalar</span><span
5973 class="cmtt-8"> value</span><span
5974 class="cmtt-8"> in</span><span
5975 class="cmtt-8"> vector</span><span
5976 class="cmtt-8"> [floor1</span><span
5977 class="cmtt-8">_partition</span><span
5978 class="cmtt-8">_class</span><span
5979 class="cmtt-8">_list]</span><br class="fancyvrb" /><a
5980 id="x1-101022r11"></a><span
5981 class="cmr-6">11</span><span
5982 class="cmtt-8"> </span><span
5983 class="cmtt-8"> 6)</span><span
5984 class="cmtt-8"> iterate</span><span
5985 class="cmtt-8"> [i]</span><span
5986 class="cmtt-8"> over</span><span
5987 class="cmtt-8"> the</span><span
5988 class="cmtt-8"> range</span><span
5989 class="cmtt-8"> 0</span><span
5990 class="cmtt-8"> ...</span><span
5991 class="cmtt-8"> [maximum</span><span
5992 class="cmtt-8">_class]</span><span
5993 class="cmtt-8"> </span><span
5994 class="cmsy-8">{</span><br class="fancyvrb" /><a
5995 id="x1-101024r12"></a><span
5996 class="cmr-6">12</span>
5997 <br class="fancyvrb" /><a
5998 id="x1-101026r13"></a><span
5999 class="cmr-6">13</span><span
6000 class="cmtt-8"> </span><span
6001 class="cmtt-8"> </span><span
6002 class="cmtt-8"> </span><span
6003 class="cmtt-8"> </span><span
6004 class="cmtt-8"> </span><span
6005 class="cmtt-8"> </span><span
6006 class="cmtt-8"> </span><span
6007 class="cmtt-8"> 7)</span><span
6008 class="cmtt-8"> vector</span><span
6009 class="cmtt-8"> [floor1</span><span
6010 class="cmtt-8">_class</span><span
6011 class="cmtt-8">_dimensions]</span><span
6012 class="cmtt-8"> element</span><span
6013 class="cmtt-8"> [i]</span><span
6014 class="cmtt-8"> =</span><span
6015 class="cmtt-8"> read</span><span
6016 class="cmtt-8"> 3</span><span
6017 class="cmtt-8"> bits</span><span
6018 class="cmtt-8"> as</span><span
6019 class="cmtt-8"> unsigned</span><span
6020 class="cmtt-8"> integer</span><span
6021 class="cmtt-8"> and</span><span
6022 class="cmtt-8"> add</span><span
6023 class="cmtt-8"> 1</span>
6024 <br class="fancyvrb" /><a
6025 id="x1-101028r14"></a><span
6026 class="cmr-6">14</span> <span
6027 class="cmtt-8">8)</span><span
6028 class="cmtt-8"> vector</span><span
6029 class="cmtt-8"> [floor1</span><span
6030 class="cmtt-8">_class</span><span
6031 class="cmtt-8">_subclasses]</span><span
6032 class="cmtt-8"> element</span><span
6033 class="cmtt-8"> [i]</span><span
6034 class="cmtt-8"> =</span><span
6035 class="cmtt-8"> read</span><span
6036 class="cmtt-8"> 2</span><span
6037 class="cmtt-8"> bits</span><span
6038 class="cmtt-8"> as</span><span
6039 class="cmtt-8"> unsigned</span><span
6040 class="cmtt-8"> integer</span>
6041 <br class="fancyvrb" /><a
6042 id="x1-101030r15"></a><span
6043 class="cmr-6">15</span><span
6044 class="cmtt-8"> </span><span
6045 class="cmtt-8"> </span><span
6046 class="cmtt-8"> </span><span
6047 class="cmtt-8"> </span><span
6048 class="cmtt-8"> </span><span
6049 class="cmtt-8"> </span><span
6050 class="cmtt-8"> </span><span
6051 class="cmtt-8"> 9)</span><span
6052 class="cmtt-8"> if</span><span
6053 class="cmtt-8"> (</span><span
6054 class="cmtt-8"> vector</span><span
6055 class="cmtt-8"> [floor1</span><span
6056 class="cmtt-8">_class</span><span
6057 class="cmtt-8">_subclasses]</span><span
6058 class="cmtt-8"> element</span><span
6059 class="cmtt-8"> [i]</span><span
6060 class="cmtt-8"> is</span><span
6061 class="cmtt-8"> nonzero</span><span
6062 class="cmtt-8"> )</span><span
6063 class="cmtt-8"> </span><span
6064 class="cmsy-8">{</span><br class="fancyvrb" /><a
6065 id="x1-101032r16"></a><span
6066 class="cmr-6">16</span>
6067 <br class="fancyvrb" /><a
6068 id="x1-101034r17"></a><span
6069 class="cmr-6">17</span><span
6070 class="cmtt-8"> </span><span
6071 class="cmtt-8"> </span><span
6072 class="cmtt-8"> </span><span
6073 class="cmtt-8"> </span><span
6074 class="cmtt-8"> </span><span
6075 class="cmtt-8"> </span><span
6076 class="cmtt-8"> </span><span
6077 class="cmtt-8"> </span><span
6078 class="cmtt-8"> </span><span
6079 class="cmtt-8"> </span><span
6080 class="cmtt-8"> </span><span
6081 class="cmtt-8"> </span><span
6082 class="cmtt-8"> 10)</span><span
6083 class="cmtt-8"> vector</span><span
6084 class="cmtt-8"> [floor1</span><span
6085 class="cmtt-8">_class</span><span
6086 class="cmtt-8">_masterbooks]</span><span
6087 class="cmtt-8"> element</span><span
6088 class="cmtt-8"> [i]</span><span
6089 class="cmtt-8"> =</span><span
6090 class="cmtt-8"> read</span><span
6091 class="cmtt-8"> 8</span><span
6092 class="cmtt-8"> bits</span><span
6093 class="cmtt-8"> as</span><span
6094 class="cmtt-8"> unsigned</span><span
6095 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
6096 id="x1-101036r18"></a><span
6097 class="cmr-6">18</span><br class="fancyvrb" /><a
6098 id="x1-101038r19"></a><span
6099 class="cmr-6">19</span><span
6100 class="cmtt-8"> </span><span
6101 class="cmtt-8"> </span><span
6102 class="cmtt-8"> </span><span
6103 class="cmtt-8"> </span><span
6104 class="cmtt-8"> </span><span
6105 class="cmtt-8"> </span><span
6106 class="cmtt-8"> </span><span
6107 class="cmtt-8"> </span><span
6108 class="cmtt-8"> </span><span
6109 class="cmtt-8"> </span><span
6110 class="cmtt-8"> </span><span
6111 class="cmsy-8">}</span><br class="fancyvrb" /><a
6112 id="x1-101040r20"></a><span
6113 class="cmr-6">20</span>
6114 <br class="fancyvrb" /><a
6115 id="x1-101042r21"></a><span
6116 class="cmr-6">21</span><span
6117 class="cmtt-8"> </span><span
6118 class="cmtt-8"> </span><span
6119 class="cmtt-8"> </span><span
6120 class="cmtt-8"> </span><span
6121 class="cmtt-8"> </span><span
6122 class="cmtt-8"> </span><span
6123 class="cmtt-8"> 11)</span><span
6124 class="cmtt-8"> iterate</span><span
6125 class="cmtt-8"> [j]</span><span
6126 class="cmtt-8"> over</span><span
6127 class="cmtt-8"> the</span><span
6128 class="cmtt-8"> range</span><span
6129 class="cmtt-8"> 0</span><span
6130 class="cmtt-8"> ...</span><span
6131 class="cmtt-8"> (2</span><span
6132 class="cmtt-8"> exponent</span><span
6133 class="cmtt-8"> [floor1</span><span
6134 class="cmtt-8">_class</span><span
6135 class="cmtt-8">_subclasses]</span><span
6136 class="cmtt-8"> element</span><span
6137 class="cmtt-8"> [i])</span><span
6138 class="cmtt-8"> -</span><span
6139 class="cmtt-8"> 1</span><span
6140 class="cmtt-8"> </span><span
6141 class="cmsy-8">{</span><br class="fancyvrb" /><a
6142 id="x1-101044r22"></a><span
6143 class="cmr-6">22</span>
6144 <br class="fancyvrb" /><a
6145 id="x1-101046r23"></a><span
6146 class="cmr-6">23</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"> </span><span
6156 class="cmtt-8"> </span><span
6157 class="cmtt-8"> </span><span
6158 class="cmtt-8"> </span><span
6159 class="cmtt-8"> 12)</span><span
6160 class="cmtt-8"> array</span><span
6161 class="cmtt-8"> [floor1</span><span
6162 class="cmtt-8">_subclass</span><span
6163 class="cmtt-8">_books]</span><span
6164 class="cmtt-8"> element</span><span
6165 class="cmtt-8"> [i],[j]</span><span
6166 class="cmtt-8"> =</span><br class="fancyvrb" /><a
6167 id="x1-101048r24"></a><span
6168 class="cmr-6">24</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"> </span><span
6182 class="cmtt-8"> </span><span
6183 class="cmtt-8"> </span><span
6184 class="cmtt-8"> </span><span
6185 class="cmtt-8"> read</span><span
6186 class="cmtt-8"> 8</span><span
6187 class="cmtt-8"> bits</span><span
6188 class="cmtt-8"> as</span><span
6189 class="cmtt-8"> unsigned</span><span
6190 class="cmtt-8"> integer</span><span
6191 class="cmtt-8"> and</span><span
6192 class="cmtt-8"> subtract</span><span
6193 class="cmtt-8"> one</span>
6194 <br class="fancyvrb" /><a
6195 id="x1-101050r25"></a><span
6196 class="cmr-6">25</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="cmtt-8"> </span><span
6206 class="cmtt-8"> </span><span
6207 class="cmtt-8"> </span><span
6208 class="cmsy-8">}</span><br class="fancyvrb" /><a
6209 id="x1-101052r26"></a><span
6210 class="cmr-6">26</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><br class="fancyvrb" /><a
6220 id="x1-101056r28"></a><span
6221 class="cmr-6">28</span><span
6222 class="cmtt-8"> 13)</span><span
6223 class="cmtt-8"> [floor1</span><span
6224 class="cmtt-8">_multiplier]</span><span
6225 class="cmtt-8"> =</span><span
6226 class="cmtt-8"> read</span><span
6227 class="cmtt-8"> 2</span><span
6228 class="cmtt-8"> bits</span><span
6229 class="cmtt-8"> as</span><span
6230 class="cmtt-8"> unsigned</span><span
6231 class="cmtt-8"> integer</span><span
6232 class="cmtt-8"> and</span><span
6233 class="cmtt-8"> add</span><span
6234 class="cmtt-8"> one</span><br class="fancyvrb" /><a
6235 id="x1-101058r29"></a><span
6236 class="cmr-6">29</span><span
6237 class="cmtt-8"> 14)</span><span
6238 class="cmtt-8"> [rangebits]</span><span
6239 class="cmtt-8"> =</span><span
6240 class="cmtt-8"> read</span><span
6241 class="cmtt-8"> 4</span><span
6242 class="cmtt-8"> bits</span><span
6243 class="cmtt-8"> as</span><span
6244 class="cmtt-8"> unsigned</span><span
6245 class="cmtt-8"> integer</span>
6246 <br class="fancyvrb" /><a
6247 id="x1-101060r30"></a><span
6248 class="cmr-6">30</span><span
6249 class="cmtt-8"> 15)</span><span
6250 class="cmtt-8"> vector</span><span
6251 class="cmtt-8"> [floor1</span><span
6252 class="cmtt-8">_X</span><span
6253 class="cmtt-8">_list]</span><span
6254 class="cmtt-8"> element</span><span
6255 class="cmtt-8"> [0]</span><span
6256 class="cmtt-8"> =</span><span
6257 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
6258 id="x1-101062r31"></a><span
6259 class="cmr-6">31</span><span
6260 class="cmtt-8"> 16)</span><span
6261 class="cmtt-8"> vector</span><span
6262 class="cmtt-8"> [floor1</span><span
6263 class="cmtt-8">_X</span><span
6264 class="cmtt-8">_list]</span><span
6265 class="cmtt-8"> element</span><span
6266 class="cmtt-8"> [1]</span><span
6267 class="cmtt-8"> =</span><span
6268 class="cmtt-8"> 2</span><span
6269 class="cmtt-8"> exponent</span><span
6270 class="cmtt-8"> [rangebits];</span><br class="fancyvrb" /><a
6271 id="x1-101064r32"></a><span
6272 class="cmr-6">32</span><span
6273 class="cmtt-8"> 17)</span><span
6274 class="cmtt-8"> [floor1</span><span
6275 class="cmtt-8">_values]</span><span
6276 class="cmtt-8"> =</span><span
6277 class="cmtt-8"> 2</span>
6278 <br class="fancyvrb" /><a
6279 id="x1-101066r33"></a><span
6280 class="cmr-6">33</span><span
6281 class="cmtt-8"> 18)</span><span
6282 class="cmtt-8"> iterate</span><span
6283 class="cmtt-8"> [i]</span><span
6284 class="cmtt-8"> over</span><span
6285 class="cmtt-8"> the</span><span
6286 class="cmtt-8"> range</span><span
6287 class="cmtt-8"> 0</span><span
6288 class="cmtt-8"> ...</span><span
6289 class="cmtt-8"> [floor1</span><span
6290 class="cmtt-8">_partitions]-1</span><span
6291 class="cmtt-8"> </span><span
6292 class="cmsy-8">{</span><br class="fancyvrb" /><a
6293 id="x1-101068r34"></a><span
6294 class="cmr-6">34</span><br class="fancyvrb" /><a
6295 id="x1-101070r35"></a><span
6296 class="cmr-6">35</span><span
6297 class="cmtt-8"> </span><span
6298 class="cmtt-8"> </span><span
6299 class="cmtt-8"> </span><span
6300 class="cmtt-8"> </span><span
6301 class="cmtt-8"> </span><span
6302 class="cmtt-8"> </span><span
6303 class="cmtt-8"> 19)</span><span
6304 class="cmtt-8"> [current</span><span
6305 class="cmtt-8">_class</span><span
6306 class="cmtt-8">_number]</span><span
6307 class="cmtt-8"> =</span><span
6308 class="cmtt-8"> vector</span><span
6309 class="cmtt-8"> [floor1</span><span
6310 class="cmtt-8">_partition</span><span
6311 class="cmtt-8">_class</span><span
6312 class="cmtt-8">_list]</span><span
6313 class="cmtt-8"> element</span><span
6314 class="cmtt-8"> [i]</span>
6315 <br class="fancyvrb" /><a
6316 id="x1-101072r36"></a><span
6317 class="cmr-6">36</span><span
6318 class="cmtt-8"> </span><span
6319 class="cmtt-8"> </span><span
6320 class="cmtt-8"> </span><span
6321 class="cmtt-8"> </span><span
6322 class="cmtt-8"> </span><span
6323 class="cmtt-8"> </span><span
6324 class="cmtt-8"> 20)</span><span
6325 class="cmtt-8"> iterate</span><span
6326 class="cmtt-8"> [j]</span><span
6327 class="cmtt-8"> over</span><span
6328 class="cmtt-8"> the</span><span
6329 class="cmtt-8"> range</span><span
6330 class="cmtt-8"> 0</span><span
6331 class="cmtt-8"> ...</span><span
6332 class="cmtt-8"> ([floor1</span><span
6333 class="cmtt-8">_class</span><span
6334 class="cmtt-8">_dimensions]</span><span
6335 class="cmtt-8"> element</span><span
6336 class="cmtt-8"> [current</span><span
6337 class="cmtt-8">_class</span><span
6338 class="cmtt-8">_number])-1</span><span
6339 class="cmtt-8"> </span><span
6340 class="cmsy-8">{</span>
6341 <br class="fancyvrb" /><a
6342 id="x1-101074r37"></a><span
6343 class="cmr-6">37</span><span
6344 class="cmtt-8"> </span><span
6345 class="cmtt-8"> </span><span
6346 class="cmtt-8"> </span><span
6347 class="cmtt-8"> </span><span
6348 class="cmtt-8"> </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"> 21)</span><span
6357 class="cmtt-8"> vector</span><span
6358 class="cmtt-8"> [floor1</span><span
6359 class="cmtt-8">_X</span><span
6360 class="cmtt-8">_list]</span><span
6361 class="cmtt-8"> element</span><span
6362 class="cmtt-8"> ([floor1</span><span
6363 class="cmtt-8">_values])</span><span
6364 class="cmtt-8"> =</span><br class="fancyvrb" /><a
6365 id="x1-101076r38"></a><span
6366 class="cmr-6">38</span><span
6367 class="cmtt-8"> </span><span
6368 class="cmtt-8"> </span><span
6369 class="cmtt-8"> </span><span
6370 class="cmtt-8"> </span><span
6371 class="cmtt-8"> </span><span
6372 class="cmtt-8"> </span><span
6373 class="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"> read</span><span
6384 class="cmtt-8"> [rangebits]</span><span
6385 class="cmtt-8"> bits</span><span
6386 class="cmtt-8"> as</span><span
6387 class="cmtt-8"> unsigned</span><span
6388 class="cmtt-8"> integer</span>
6389 <br class="fancyvrb" /><a
6390 id="x1-101078r39"></a><span
6391 class="cmr-6">39</span><span
6392 class="cmtt-8"> </span><span
6393 class="cmtt-8"> </span><span
6394 class="cmtt-8"> </span><span
6395 class="cmtt-8"> </span><span
6396 class="cmtt-8"> </span><span
6397 class="cmtt-8"> </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"> 22)</span><span
6405 class="cmtt-8"> increment</span><span
6406 class="cmtt-8"> [floor1</span><span
6407 class="cmtt-8">_values]</span><span
6408 class="cmtt-8"> by</span><span
6409 class="cmtt-8"> one</span><br class="fancyvrb" /><a
6410 id="x1-101080r40"></a><span
6411 class="cmr-6">40</span><span
6412 class="cmtt-8"> </span><span
6413 class="cmtt-8"> </span><span
6414 class="cmtt-8"> </span><span
6415 class="cmtt-8"> </span><span
6416 class="cmtt-8"> </span><span
6417 class="cmtt-8"> </span><span
6418 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
6424 id="x1-101082r41"></a><span
6425 class="cmr-6">41</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="cmsy-8">}</span><br class="fancyvrb" /><a
6432 id="x1-101084r42"></a><span
6433 class="cmr-6">42</span><br class="fancyvrb" /><a
6434 id="x1-101086r43"></a><span
6435 class="cmr-6">43</span><span
6436 class="cmtt-8"> 23)</span><span
6437 class="cmtt-8"> done</span></div>
6438 <!--l. 157--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
6439 setup renders a stream undecodable. In addition, a <span
6440 class="cmtt-12">[floor1</span><span
6441 class="cmtt-12">_class</span><span
6442 class="cmtt-12">_masterbooks] </span>or
6444 class="cmtt-12">[floor1</span><span
6445 class="cmtt-12">_subclass</span><span
6446 class="cmtt-12">_books] </span>scalar element greater than the highest numbered codebook
6447 configured in this stream is an error condition that renders the stream undecodable. Vector
6448 [floor1_x_list] is limited to a maximum length of 65 elements; a setup indicating more than 65
6449 total elements (including elements 0 and 1 set prior to the read loop) renders the stream
6450 undecodable. All vector [floor1_x_list] element values must be unique within the vector; a
6451 non-unique value renders the stream undecodable.
6452 <!--l. 169--><p class="noindent" >
6453 <h5 class="subsubsectionHead"><span class="titlemark">7.2.3. </span> <a
6454 id="x1-1020007.2.3"></a>packet decode</h5>
6455 <!--l. 171--><p class="noindent" >Packet decode begins by checking the <span
6456 class="cmtt-12">[nonzero] </span>flag:
6457 <!--l. 173--><p class="noindent" >
6458 <div class="fancyvrb" id="fancyvrb29"><a
6459 id="x1-102002r1"></a><span
6460 class="cmr-6">1</span><span
6461 class="cmtt-8"> </span><span
6462 class="cmtt-8"> 1)</span><span
6463 class="cmtt-8"> [nonzero]</span><span
6464 class="cmtt-8"> =</span><span
6465 class="cmtt-8"> read</span><span
6466 class="cmtt-8"> 1</span><span
6467 class="cmtt-8"> bit</span><span
6468 class="cmtt-8"> as</span><span
6469 class="cmtt-8"> boolean</span></div>
6470 <!--l. 177--><p class="noindent" >If <span
6471 class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
6472 Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
6473 this frame. (A return status of ’unused’ is different from decoding a floor that has all
6474 points set to minimum representation amplitude, which happens to be approximately
6476 <!--l. 185--><p class="noindent" >Assuming <span
6477 class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
6478 <!--l. 187--><p class="noindent" >
6479 <div class="fancyvrb" id="fancyvrb30"><a
6480 id="x1-102004r1"></a><span
6481 class="cmr-6">1</span><span
6482 class="cmtt-8"> </span><span
6483 class="cmtt-8"> 1)</span><span
6484 class="cmtt-8"> [range]</span><span
6485 class="cmtt-8"> =</span><span
6486 class="cmtt-8"> vector</span><span
6487 class="cmtt-8"> </span><span
6488 class="cmsy-8">{</span><span
6489 class="cmtt-8"> 256,</span><span
6490 class="cmtt-8"> 128,</span><span
6491 class="cmtt-8"> 86,</span><span
6492 class="cmtt-8"> 64</span><span
6493 class="cmtt-8"> </span><span
6494 class="cmsy-8">}</span><span
6495 class="cmtt-8"> element</span><span
6496 class="cmtt-8"> ([floor1</span><span
6497 class="cmtt-8">_multiplier]-1)</span>
6498 <br class="fancyvrb" /><a
6499 id="x1-102006r2"></a><span
6500 class="cmr-6">2</span><span
6501 class="cmtt-8"> </span><span
6502 class="cmtt-8"> 2)</span><span
6503 class="cmtt-8"> vector</span><span
6504 class="cmtt-8"> [floor1</span><span
6505 class="cmtt-8">_Y]</span><span
6506 class="cmtt-8"> element</span><span
6507 class="cmtt-8"> [0]</span><span
6508 class="cmtt-8"> =</span><span
6509 class="cmtt-8"> read</span><span
6510 class="cmtt-8"> </span><a
6511 href="#x1-1190009.2.1"><span
6512 class="cmtt-8">ilog</span></a><span
6513 class="cmtt-8">([range]-1)</span><span
6514 class="cmtt-8"> bits</span><span
6515 class="cmtt-8"> as</span><span
6516 class="cmtt-8"> unsigned</span><span
6517 class="cmtt-8"> integer</span>
6521 <br class="fancyvrb" /><a
6522 id="x1-102008r3"></a><span
6523 class="cmr-6">3</span><span
6524 class="cmtt-8"> </span><span
6525 class="cmtt-8"> 3)</span><span
6526 class="cmtt-8"> vector</span><span
6527 class="cmtt-8"> [floor1</span><span
6528 class="cmtt-8">_Y]</span><span
6529 class="cmtt-8"> element</span><span
6530 class="cmtt-8"> [1]</span><span
6531 class="cmtt-8"> =</span><span
6532 class="cmtt-8"> read</span><span
6533 class="cmtt-8"> </span><a
6534 href="#x1-1190009.2.1"><span
6535 class="cmtt-8">ilog</span></a><span
6536 class="cmtt-8">([range]-1)</span><span
6537 class="cmtt-8"> bits</span><span
6538 class="cmtt-8"> as</span><span
6539 class="cmtt-8"> unsigned</span><span
6540 class="cmtt-8"> integer</span>
6541 <br class="fancyvrb" /><a
6542 id="x1-102010r4"></a><span
6543 class="cmr-6">4</span><span
6544 class="cmtt-8"> </span><span
6545 class="cmtt-8"> 4)</span><span
6546 class="cmtt-8"> [offset]</span><span
6547 class="cmtt-8"> =</span><span
6548 class="cmtt-8"> 2;</span><br class="fancyvrb" /><a
6549 id="x1-102012r5"></a><span
6550 class="cmr-6">5</span><span
6551 class="cmtt-8"> </span><span
6552 class="cmtt-8"> 5)</span><span
6553 class="cmtt-8"> iterate</span><span
6554 class="cmtt-8"> [i]</span><span
6555 class="cmtt-8"> over</span><span
6556 class="cmtt-8"> the</span><span
6557 class="cmtt-8"> range</span><span
6558 class="cmtt-8"> 0</span><span
6559 class="cmtt-8"> ...</span><span
6560 class="cmtt-8"> [floor1</span><span
6561 class="cmtt-8">_partitions]-1</span><span
6562 class="cmtt-8"> </span><span
6563 class="cmsy-8">{</span><br class="fancyvrb" /><a
6564 id="x1-102014r6"></a><span
6565 class="cmr-6">6</span>
6566 <br class="fancyvrb" /><a
6567 id="x1-102016r7"></a><span
6568 class="cmr-6">7</span><span
6569 class="cmtt-8"> </span><span
6570 class="cmtt-8"> </span><span
6571 class="cmtt-8"> </span><span
6572 class="cmtt-8"> </span><span
6573 class="cmtt-8"> </span><span
6574 class="cmtt-8"> </span><span
6575 class="cmtt-8"> 6)</span><span
6576 class="cmtt-8"> [class]</span><span
6577 class="cmtt-8"> =</span><span
6578 class="cmtt-8"> vector</span><span
6579 class="cmtt-8"> [floor1</span><span
6580 class="cmtt-8">_partition</span><span
6581 class="cmtt-8">_class]</span><span
6582 class="cmtt-8"> </span><span
6583 class="cmtt-8"> element</span><span
6584 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
6585 id="x1-102018r8"></a><span
6586 class="cmr-6">8</span><span
6587 class="cmtt-8"> </span><span
6588 class="cmtt-8"> </span><span
6589 class="cmtt-8"> </span><span
6590 class="cmtt-8"> </span><span
6591 class="cmtt-8"> </span><span
6592 class="cmtt-8"> </span><span
6593 class="cmtt-8"> 7)</span><span
6594 class="cmtt-8"> [cdim]</span><span
6595 class="cmtt-8"> </span><span
6596 class="cmtt-8"> =</span><span
6597 class="cmtt-8"> vector</span><span
6598 class="cmtt-8"> [floor1</span><span
6599 class="cmtt-8">_class</span><span
6600 class="cmtt-8">_dimensions]</span><span
6601 class="cmtt-8"> element</span><span
6602 class="cmtt-8"> [class]</span>
6603 <br class="fancyvrb" /><a
6604 id="x1-102020r9"></a><span
6605 class="cmr-6">9</span><span
6606 class="cmtt-8"> </span><span
6607 class="cmtt-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"> 8)</span><span
6613 class="cmtt-8"> [cbits]</span><span
6614 class="cmtt-8"> =</span><span
6615 class="cmtt-8"> vector</span><span
6616 class="cmtt-8"> [floor1</span><span
6617 class="cmtt-8">_class</span><span
6618 class="cmtt-8">_subclasses]</span><span
6619 class="cmtt-8"> element</span><span
6620 class="cmtt-8"> [class]</span><br class="fancyvrb" /><a
6621 id="x1-102022r10"></a><span
6622 class="cmr-6">10</span><span
6623 class="cmtt-8"> </span><span
6624 class="cmtt-8"> </span><span
6625 class="cmtt-8"> </span><span
6626 class="cmtt-8"> </span><span
6627 class="cmtt-8"> </span><span
6628 class="cmtt-8"> </span><span
6629 class="cmtt-8"> 9)</span><span
6630 class="cmtt-8"> [csub]</span><span
6631 class="cmtt-8"> </span><span
6632 class="cmtt-8"> =</span><span
6633 class="cmtt-8"> (2</span><span
6634 class="cmtt-8"> exponent</span><span
6635 class="cmtt-8"> [cbits])-1</span><br class="fancyvrb" /><a
6636 id="x1-102024r11"></a><span
6637 class="cmr-6">11</span><span
6638 class="cmtt-8"> </span><span
6639 class="cmtt-8"> </span><span
6640 class="cmtt-8"> </span><span
6641 class="cmtt-8"> </span><span
6642 class="cmtt-8"> </span><span
6643 class="cmtt-8"> 10)</span><span
6644 class="cmtt-8"> [cval]</span><span
6645 class="cmtt-8"> </span><span
6646 class="cmtt-8"> =</span><span
6647 class="cmtt-8"> 0</span>
6648 <br class="fancyvrb" /><a
6649 id="x1-102026r12"></a><span
6650 class="cmr-6">12</span><span
6651 class="cmtt-8"> </span><span
6652 class="cmtt-8"> </span><span
6653 class="cmtt-8"> </span><span
6654 class="cmtt-8"> </span><span
6655 class="cmtt-8"> </span><span
6656 class="cmtt-8"> 11)</span><span
6657 class="cmtt-8"> if</span><span
6658 class="cmtt-8"> (</span><span
6659 class="cmtt-8"> [cbits]</span><span
6660 class="cmtt-8"> is</span><span
6661 class="cmtt-8"> greater</span><span
6662 class="cmtt-8"> than</span><span
6663 class="cmtt-8"> zero</span><span
6664 class="cmtt-8"> )</span><span
6665 class="cmtt-8"> </span><span
6666 class="cmsy-8">{</span><br class="fancyvrb" /><a
6667 id="x1-102028r13"></a><span
6668 class="cmr-6">13</span><br class="fancyvrb" /><a
6669 id="x1-102030r14"></a><span
6670 class="cmr-6">14</span><span
6671 class="cmtt-8"> </span><span
6672 class="cmtt-8"> </span><span
6673 class="cmtt-8"> </span><span
6674 class="cmtt-8"> </span><span
6675 class="cmtt-8"> </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"> 12)</span><span
6684 class="cmtt-8"> [cval]</span><span
6685 class="cmtt-8"> =</span><span
6686 class="cmtt-8"> read</span><span
6687 class="cmtt-8"> from</span><span
6688 class="cmtt-8"> packet</span><span
6689 class="cmtt-8"> using</span><span
6690 class="cmtt-8"> codebook</span><span
6691 class="cmtt-8"> number</span>
6692 <br class="fancyvrb" /><a
6693 id="x1-102032r15"></a><span
6694 class="cmr-6">15</span><span
6695 class="cmtt-8"> </span><span
6696 class="cmtt-8"> </span><span
6697 class="cmtt-8"> </span><span
6698 class="cmtt-8"> </span><span
6699 class="cmtt-8"> </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"> (vector</span><span
6712 class="cmtt-8"> [floor1</span><span
6713 class="cmtt-8">_class</span><span
6714 class="cmtt-8">_masterbooks]</span><span
6715 class="cmtt-8"> element</span><span
6716 class="cmtt-8"> [class])</span><span
6717 class="cmtt-8"> in</span><span
6718 class="cmtt-8"> scalar</span><span
6719 class="cmtt-8"> context</span><br class="fancyvrb" /><a
6720 id="x1-102034r16"></a><span
6721 class="cmr-6">16</span><span
6722 class="cmtt-8"> </span><span
6723 class="cmtt-8"> </span><span
6724 class="cmtt-8"> </span><span
6725 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
6733 id="x1-102036r17"></a><span
6734 class="cmr-6">17</span><br class="fancyvrb" /><a
6735 id="x1-102038r18"></a><span
6736 class="cmr-6">18</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"> 13)</span><span
6743 class="cmtt-8"> iterate</span><span
6744 class="cmtt-8"> [j]</span><span
6745 class="cmtt-8"> over</span><span
6746 class="cmtt-8"> the</span><span
6747 class="cmtt-8"> range</span><span
6748 class="cmtt-8"> 0</span><span
6749 class="cmtt-8"> ...</span><span
6750 class="cmtt-8"> [cdim]-1</span><span
6751 class="cmtt-8"> </span><span
6752 class="cmsy-8">{</span><br class="fancyvrb" /><a
6753 id="x1-102040r19"></a><span
6754 class="cmr-6">19</span>
6755 <br class="fancyvrb" /><a
6756 id="x1-102042r20"></a><span
6757 class="cmr-6">20</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="cmtt-8"> </span><span
6767 class="cmtt-8"> </span><span
6768 class="cmtt-8"> </span><span
6769 class="cmtt-8"> </span><span
6770 class="cmtt-8"> 14)</span><span
6771 class="cmtt-8"> [book]</span><span
6772 class="cmtt-8"> =</span><span
6773 class="cmtt-8"> array</span><span
6774 class="cmtt-8"> [floor1</span><span
6775 class="cmtt-8">_subclass</span><span
6776 class="cmtt-8">_books]</span><span
6777 class="cmtt-8"> element</span><span
6778 class="cmtt-8"> [class],([cval]</span><span
6779 class="cmtt-8"> bitwise</span><span
6780 class="cmtt-8"> AND</span><span
6781 class="cmtt-8"> [csub])</span>
6782 <br class="fancyvrb" /><a
6783 id="x1-102044r21"></a><span
6784 class="cmr-6">21</span><span
6785 class="cmtt-8"> </span><span
6786 class="cmtt-8"> </span><span
6787 class="cmtt-8"> </span><span
6788 class="cmtt-8"> </span><span
6789 class="cmtt-8"> </span><span
6790 class="cmtt-8"> </span><span
6791 class="cmtt-8"> </span><span
6792 class="cmtt-8"> </span><span
6793 class="cmtt-8"> </span><span
6794 class="cmtt-8"> </span><span
6795 class="cmtt-8"> </span><span
6796 class="cmtt-8"> </span><span
6797 class="cmtt-8"> 15)</span><span
6798 class="cmtt-8"> [cval]</span><span
6799 class="cmtt-8"> =</span><span
6800 class="cmtt-8"> [cval]</span><span
6801 class="cmtt-8"> right</span><span
6802 class="cmtt-8"> shifted</span><span
6803 class="cmtt-8"> [cbits]</span><span
6804 class="cmtt-8"> bits</span><br class="fancyvrb" /><a
6805 id="x1-102046r22"></a><span
6806 class="cmr-6">22</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"> 16)</span><span
6812 class="cmtt-8"> if</span><span
6813 class="cmtt-8"> (</span><span
6814 class="cmtt-8"> [book]</span><span
6815 class="cmtt-8"> is</span><span
6816 class="cmtt-8"> not</span><span
6817 class="cmtt-8"> less</span><span
6818 class="cmtt-8"> than</span><span
6819 class="cmtt-8"> zero</span><span
6820 class="cmtt-8"> )</span><span
6821 class="cmtt-8"> </span><span
6822 class="cmsy-8">{</span><br class="fancyvrb" /><a
6823 id="x1-102048r23"></a><span
6824 class="cmr-6">23</span>
6825 <br class="fancyvrb" /><a
6826 id="x1-102050r24"></a><span
6827 class="cmr-6">24</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"> 17)</span><span
6839 class="cmtt-8"> vector</span><span
6840 class="cmtt-8"> [floor1</span><span
6841 class="cmtt-8">_Y]</span><span
6842 class="cmtt-8"> element</span><span
6843 class="cmtt-8"> ([j]+[offset])</span><span
6844 class="cmtt-8"> =</span><span
6845 class="cmtt-8"> read</span><span
6846 class="cmtt-8"> from</span><span
6847 class="cmtt-8"> packet</span><span
6848 class="cmtt-8"> using</span><span
6849 class="cmtt-8"> codebook</span><br class="fancyvrb" /><a
6850 id="x1-102052r25"></a><span
6851 class="cmr-6">25</span><span
6852 class="cmtt-8"> </span><span
6853 class="cmtt-8"> </span><span
6854 class="cmtt-8"> </span><span
6855 class="cmtt-8"> </span><span
6856 class="cmtt-8"> </span><span
6857 class="cmtt-8"> </span><span
6858 class="cmtt-8"> </span><span
6859 class="cmtt-8"> </span><span
6860 class="cmtt-8"> </span><span
6861 class="cmtt-8"> </span><span
6862 class="cmtt-8"> </span><span
6863 class="cmtt-8"> </span><span
6864 class="cmtt-8"> </span><span
6865 class="cmtt-8"> </span><span
6866 class="cmtt-8"> </span><span
6867 class="cmtt-8"> </span><span
6868 class="cmtt-8"> </span><span
6869 class="cmtt-8"> </span><span
6870 class="cmtt-8"> </span><span
6871 class="cmtt-8"> </span><span
6872 class="cmtt-8"> </span><span
6873 class="cmtt-8"> </span><span
6874 class="cmtt-8"> [book]</span><span
6875 class="cmtt-8"> in</span><span
6876 class="cmtt-8"> scalar</span><span
6877 class="cmtt-8"> context</span><br class="fancyvrb" /><a
6878 id="x1-102054r26"></a><span
6879 class="cmr-6">26</span>
6880 <br class="fancyvrb" /><a
6881 id="x1-102056r27"></a><span
6882 class="cmr-6">27</span><span
6883 class="cmtt-8"> </span><span
6884 class="cmtt-8"> </span><span
6885 class="cmtt-8"> </span><span
6886 class="cmtt-8"> </span><span
6887 class="cmtt-8"> </span><span
6888 class="cmtt-8"> </span><span
6889 class="cmtt-8"> </span><span
6890 class="cmtt-8"> </span><span
6891 class="cmtt-8"> </span><span
6892 class="cmtt-8"> </span><span
6893 class="cmtt-8"> </span><span
6894 class="cmtt-8"> </span><span
6895 class="cmtt-8"> </span><span
6896 class="cmtt-8"> </span><span
6897 class="cmtt-8"> </span><span
6898 class="cmtt-8"> </span><span
6899 class="cmtt-8"> </span><span
6900 class="cmsy-8">}</span><span
6901 class="cmtt-8"> else</span><span
6902 class="cmtt-8"> [book]</span><span
6903 class="cmtt-8"> is</span><span
6904 class="cmtt-8"> less</span><span
6905 class="cmtt-8"> than</span><span
6906 class="cmtt-8"> zero</span><span
6907 class="cmtt-8"> </span><span
6908 class="cmsy-8">{</span><br class="fancyvrb" /><a
6909 id="x1-102058r28"></a><span
6910 class="cmr-6">28</span><br class="fancyvrb" /><a
6911 id="x1-102060r29"></a><span
6912 class="cmr-6">29</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"> 18)</span><span
6924 class="cmtt-8"> vector</span><span
6925 class="cmtt-8"> [floor1</span><span
6926 class="cmtt-8">_Y]</span><span
6927 class="cmtt-8"> element</span><span
6928 class="cmtt-8"> ([j]+[offset])</span><span
6929 class="cmtt-8"> =</span><span
6930 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
6931 id="x1-102062r30"></a><span
6932 class="cmr-6">30</span>
6933 <br class="fancyvrb" /><a
6934 id="x1-102064r31"></a><span
6935 class="cmr-6">31</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><br class="fancyvrb" /><a
6954 id="x1-102066r32"></a><span
6955 class="cmr-6">32</span><span
6956 class="cmtt-8"> </span><span
6957 class="cmtt-8"> </span><span
6958 class="cmtt-8"> </span><span
6959 class="cmtt-8"> </span><span
6960 class="cmtt-8"> </span><span
6961 class="cmtt-8"> </span><span
6962 class="cmtt-8"> </span><span
6963 class="cmtt-8"> </span><span
6964 class="cmtt-8"> </span><span
6965 class="cmtt-8"> </span><span
6966 class="cmsy-8">}</span><br class="fancyvrb" /><a
6967 id="x1-102068r33"></a><span
6968 class="cmr-6">33</span><br class="fancyvrb" /><a
6969 id="x1-102070r34"></a><span
6970 class="cmr-6">34</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"> 19)</span><span
6977 class="cmtt-8"> [offset]</span><span
6978 class="cmtt-8"> =</span><span
6979 class="cmtt-8"> [offset]</span><span
6980 class="cmtt-8"> +</span><span
6981 class="cmtt-8"> [cdim]</span><br class="fancyvrb" /><a
6982 id="x1-102072r35"></a><span
6983 class="cmr-6">35</span><br class="fancyvrb" /><a
6984 id="x1-102074r36"></a><span
6985 class="cmr-6">36</span><span
6986 class="cmtt-8"> </span><span
6987 class="cmtt-8"> </span><span
6988 class="cmtt-8"> </span><span
6989 class="cmtt-8"> </span><span
6990 class="cmtt-8"> </span><span
6991 class="cmsy-8">}</span><br class="fancyvrb" /><a
6992 id="x1-102076r37"></a><span
6993 class="cmr-6">37</span><br class="fancyvrb" /><a
6994 id="x1-102078r38"></a><span
6995 class="cmr-6">38</span><span
6996 class="cmtt-8"> 20)</span><span
6997 class="cmtt-8"> done</span></div>
6998 <!--l. 228--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
6999 end-of-packet is reached during any read operation above, floor decode is to return ’unused’
7000 status as if the <span
7001 class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
7002 <!--l. 234--><p class="noindent" >Vector <span
7003 class="cmtt-12">[floor1</span><span
7004 class="cmtt-12">_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
7005 <!--l. 239--><p class="noindent" >
7006 <h5 class="subsubsectionHead"><span class="titlemark">7.2.4. </span> <a
7007 id="x1-1030007.2.4"></a>curve computation</h5>
7008 <!--l. 241--><p class="noindent" >Curve computation is split into two logical steps; the first step derives final Y amplitude values
7009 from the encoded, wrapped difference values taken from the bitstream. The second step
7010 plots the curve lines. Also, although zero-difference values are used in the iterative
7011 prediction to find final Y values, these points are conditionally skipped during final
7012 line computation in step two. Skipping zero-difference values allows a smoother line
7014 <!--l. 249--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations,
7015 implementors are warned to follow the details closely. Deviation from implementing a strictly
7016 equivalent algorithm can result in serious decoding errors.
7017 <!--l. 254--><p class="noindent" ><span
7018 class="cmti-12">Additional note: </span>Although <span
7019 class="cmtt-12">[floor1</span><span
7020 class="cmtt-12">_final</span><span
7021 class="cmtt-12">_Y] </span>values in the prediction loop and at the end of
7022 step 1 are inherently limited by the prediction algorithm to [0, <span
7023 class="cmtt-12">[range]</span>), it is possible to abuse
7024 the setup and codebook machinery to produce negative or over-range results. We suggest that
7025 decoder implementations guard the values in vector <span
7026 class="cmtt-12">[floor1</span><span
7027 class="cmtt-12">_final</span><span
7028 class="cmtt-12">_Y] </span>by clamping each
7029 element to [0, <span
7030 class="cmtt-12">[range]</span>) after step 1. Variants of this suggestion are acceptable as valid floor1
7031 setups cannot produce out of range values.
7032 <!--l. 265--><p class="noindent" >
7033 <dl class="description"><dt class="description">
7035 class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd
7036 class="description">
7037 <!--l. 267--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
7038 values, then apply to line prediction.
7042 <!--l. 270--><p class="noindent" >
7043 <div class="fancyvrb" id="fancyvrb31"><a
7044 id="x1-103002r1"></a><span
7045 class="cmr-6">1</span><span
7046 class="cmtt-8"> </span><span
7047 class="cmtt-8"> 1)</span><span
7048 class="cmtt-8"> [range]</span><span
7049 class="cmtt-8"> =</span><span
7050 class="cmtt-8"> vector</span><span
7051 class="cmtt-8"> </span><span
7052 class="cmsy-8">{</span><span
7053 class="cmtt-8"> 256,</span><span
7054 class="cmtt-8"> 128,</span><span
7055 class="cmtt-8"> 86,</span><span
7056 class="cmtt-8"> 64</span><span
7057 class="cmtt-8"> </span><span
7058 class="cmsy-8">}</span><span
7059 class="cmtt-8"> element</span><span
7060 class="cmtt-8"> ([floor1</span><span
7061 class="cmtt-8">_multiplier]-1)</span><br class="fancyvrb" /><a
7062 id="x1-103004r2"></a><span
7063 class="cmr-6">2</span><span
7064 class="cmtt-8"> </span><span
7065 class="cmtt-8"> 2)</span><span
7066 class="cmtt-8"> vector</span><span
7067 class="cmtt-8"> [floor1</span><span
7068 class="cmtt-8">_step2</span><span
7069 class="cmtt-8">_flag]</span><span
7070 class="cmtt-8"> element</span><span
7071 class="cmtt-8"> [0]</span><span
7072 class="cmtt-8"> =</span><span
7073 class="cmtt-8"> set</span>
7074 <br class="fancyvrb" /><a
7075 id="x1-103006r3"></a><span
7076 class="cmr-6">3</span><span
7077 class="cmtt-8"> </span><span
7078 class="cmtt-8"> 3)</span><span
7079 class="cmtt-8"> vector</span><span
7080 class="cmtt-8"> [floor1</span><span
7081 class="cmtt-8">_step2</span><span
7082 class="cmtt-8">_flag]</span><span
7083 class="cmtt-8"> element</span><span
7084 class="cmtt-8"> [1]</span><span
7085 class="cmtt-8"> =</span><span
7086 class="cmtt-8"> set</span><br class="fancyvrb" /><a
7087 id="x1-103008r4"></a><span
7088 class="cmr-6">4</span><span
7089 class="cmtt-8"> </span><span
7090 class="cmtt-8"> 4)</span><span
7091 class="cmtt-8"> vector</span><span
7092 class="cmtt-8"> [floor1</span><span
7093 class="cmtt-8">_final</span><span
7094 class="cmtt-8">_Y]</span><span
7095 class="cmtt-8"> element</span><span
7096 class="cmtt-8"> [0]</span><span
7097 class="cmtt-8"> =</span><span
7098 class="cmtt-8"> vector</span><span
7099 class="cmtt-8"> [floor1</span><span
7100 class="cmtt-8">_Y]</span><span
7101 class="cmtt-8"> element</span><span
7102 class="cmtt-8"> [0]</span>
7103 <br class="fancyvrb" /><a
7104 id="x1-103010r5"></a><span
7105 class="cmr-6">5</span><span
7106 class="cmtt-8"> </span><span
7107 class="cmtt-8"> 5)</span><span
7108 class="cmtt-8"> vector</span><span
7109 class="cmtt-8"> [floor1</span><span
7110 class="cmtt-8">_final</span><span
7111 class="cmtt-8">_Y]</span><span
7112 class="cmtt-8"> element</span><span
7113 class="cmtt-8"> [1]</span><span
7114 class="cmtt-8"> =</span><span
7115 class="cmtt-8"> vector</span><span
7116 class="cmtt-8"> [floor1</span><span
7117 class="cmtt-8">_Y]</span><span
7118 class="cmtt-8"> element</span><span
7119 class="cmtt-8"> [1]</span><br class="fancyvrb" /><a
7120 id="x1-103012r6"></a><span
7121 class="cmr-6">6</span><span
7122 class="cmtt-8"> </span><span
7123 class="cmtt-8"> 6)</span><span
7124 class="cmtt-8"> iterate</span><span
7125 class="cmtt-8"> [i]</span><span
7126 class="cmtt-8"> over</span><span
7127 class="cmtt-8"> the</span><span
7128 class="cmtt-8"> range</span><span
7129 class="cmtt-8"> 2</span><span
7130 class="cmtt-8"> ...</span><span
7131 class="cmtt-8"> [floor1</span><span
7132 class="cmtt-8">_values]-1</span><span
7133 class="cmtt-8"> </span><span
7134 class="cmsy-8">{</span><br class="fancyvrb" /><a
7135 id="x1-103014r7"></a><span
7136 class="cmr-6">7</span>
7137 <br class="fancyvrb" /><a
7138 id="x1-103016r8"></a><span
7139 class="cmr-6">8</span><span
7140 class="cmtt-8"> </span><span
7141 class="cmtt-8"> </span><span
7142 class="cmtt-8"> </span><span
7143 class="cmtt-8"> </span><span
7144 class="cmtt-8"> </span><span
7145 class="cmtt-8"> </span><span
7146 class="cmtt-8"> 7)</span><span
7147 class="cmtt-8"> [low</span><span
7148 class="cmtt-8">_neighbor</span><span
7149 class="cmtt-8">_offset]</span><span
7150 class="cmtt-8"> =</span><span
7151 class="cmtt-8"> </span><a
7152 href="#x1-1220009.2.4"><span
7153 class="cmtt-8">low</span><span
7154 class="cmtt-8">_neighbor</span></a><span
7155 class="cmtt-8">([floor1</span><span
7156 class="cmtt-8">_X</span><span
7157 class="cmtt-8">_list],[i])</span><br class="fancyvrb" /><a
7158 id="x1-103018r9"></a><span
7159 class="cmr-6">9</span><span
7160 class="cmtt-8"> </span><span
7161 class="cmtt-8"> </span><span
7162 class="cmtt-8"> </span><span
7163 class="cmtt-8"> </span><span
7164 class="cmtt-8"> </span><span
7165 class="cmtt-8"> </span><span
7166 class="cmtt-8"> 8)</span><span
7167 class="cmtt-8"> [high</span><span
7168 class="cmtt-8">_neighbor</span><span
7169 class="cmtt-8">_offset]</span><span
7170 class="cmtt-8"> =</span><span
7171 class="cmtt-8"> </span><a
7172 href="#x1-1230009.2.5"><span
7173 class="cmtt-8">high</span><span
7174 class="cmtt-8">_neighbor</span></a><span
7175 class="cmtt-8">([floor1</span><span
7176 class="cmtt-8">_X</span><span
7177 class="cmtt-8">_list],[i])</span><br class="fancyvrb" /><a
7178 id="x1-103020r10"></a><span
7179 class="cmr-6">10</span>
7180 <br class="fancyvrb" /><a
7181 id="x1-103022r11"></a><span
7182 class="cmr-6">11</span><span
7183 class="cmtt-8"> </span><span
7184 class="cmtt-8"> </span><span
7185 class="cmtt-8"> </span><span
7186 class="cmtt-8"> </span><span
7187 class="cmtt-8"> </span><span
7188 class="cmtt-8"> </span><span
7189 class="cmtt-8"> 9)</span><span
7190 class="cmtt-8"> [predicted]</span><span
7191 class="cmtt-8"> =</span><span
7192 class="cmtt-8"> </span><a
7193 href="#x1-1240009.2.6"><span
7194 class="cmtt-8">render</span><span
7195 class="cmtt-8">_point</span></a><span
7196 class="cmtt-8">(</span><span
7197 class="cmtt-8"> vector</span><span
7198 class="cmtt-8"> [floor1</span><span
7199 class="cmtt-8">_X</span><span
7200 class="cmtt-8">_list]</span><span
7201 class="cmtt-8"> element</span><span
7202 class="cmtt-8"> [low</span><span
7203 class="cmtt-8">_neighbor</span><span
7204 class="cmtt-8">_offset],</span>
7205 <br class="fancyvrb" /><a
7206 id="x1-103024r12"></a><span
7207 class="cmr-6">12</span> <span
7208 class="cmtt-8"> </span><span
7209 class="cmtt-8"> </span><span
7210 class="cmtt-8"> </span><span
7211 class="cmtt-8"> </span><span
7212 class="cmtt-8"> </span><span
7213 class="cmtt-8"> vector</span><span
7214 class="cmtt-8"> [floor1</span><span
7215 class="cmtt-8">_final</span><span
7216 class="cmtt-8">_Y]</span><span
7217 class="cmtt-8"> element</span><span
7218 class="cmtt-8"> [low</span><span
7219 class="cmtt-8">_neighbor</span><span
7220 class="cmtt-8">_offset],</span>
7221 <br class="fancyvrb" /><a
7222 id="x1-103026r13"></a><span
7223 class="cmr-6">13</span><span
7224 class="cmtt-8"> </span><span
7225 class="cmtt-8"> </span><span
7226 class="cmtt-8"> </span><span
7227 class="cmtt-8"> </span><span
7228 class="cmtt-8"> </span><span
7229 class="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"> </span><span
7237 class="cmtt-8"> </span><span
7238 class="cmtt-8"> </span><span
7239 class="cmtt-8"> </span><span
7240 class="cmtt-8"> </span><span
7241 class="cmtt-8"> </span><span
7242 class="cmtt-8"> </span><span
7243 class="cmtt-8"> </span><span
7244 class="cmtt-8"> </span><span
7245 class="cmtt-8"> </span><span
7246 class="cmtt-8"> </span><span
7247 class="cmtt-8"> </span><span
7248 class="cmtt-8"> </span><span
7249 class="cmtt-8"> </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"> </span><span
7259 class="cmtt-8"> </span><span
7260 class="cmtt-8"> </span><span
7261 class="cmtt-8"> vector</span><span
7262 class="cmtt-8"> [floor1</span><span
7263 class="cmtt-8">_X</span><span
7264 class="cmtt-8">_list]</span><span
7265 class="cmtt-8"> element</span><span
7266 class="cmtt-8"> [high</span><span
7267 class="cmtt-8">_neighbor</span><span
7268 class="cmtt-8">_offset],</span>
7269 <br class="fancyvrb" /><a
7270 id="x1-103028r14"></a><span
7271 class="cmr-6">14</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"> vector</span><span
7278 class="cmtt-8"> [floor1</span><span
7279 class="cmtt-8">_final</span><span
7280 class="cmtt-8">_Y]</span><span
7281 class="cmtt-8"> element</span><span
7282 class="cmtt-8"> [high</span><span
7283 class="cmtt-8">_neighbor</span><span
7284 class="cmtt-8">_offset],</span>
7285 <br class="fancyvrb" /><a
7286 id="x1-103030r15"></a><span
7287 class="cmr-6">15</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</span><span
7327 class="cmtt-8">_X</span><span
7328 class="cmtt-8">_list]</span><span
7329 class="cmtt-8"> element</span><span
7330 class="cmtt-8"> [i]</span><span
7331 class="cmtt-8"> )</span><br class="fancyvrb" /><a
7332 id="x1-103032r16"></a><span
7333 class="cmr-6">16</span><br class="fancyvrb" /><a
7334 id="x1-103034r17"></a><span
7335 class="cmr-6">17</span><span
7336 class="cmtt-8"> </span><span
7337 class="cmtt-8"> </span><span
7338 class="cmtt-8"> </span><span
7339 class="cmtt-8"> </span><span
7340 class="cmtt-8"> </span><span
7341 class="cmtt-8"> 10)</span><span
7342 class="cmtt-8"> [val]</span><span
7343 class="cmtt-8"> =</span><span
7344 class="cmtt-8"> vector</span><span
7345 class="cmtt-8"> [floor1</span><span
7346 class="cmtt-8">_Y]</span><span
7347 class="cmtt-8"> element</span><span
7348 class="cmtt-8"> [i]</span>
7349 <br class="fancyvrb" /><a
7350 id="x1-103036r18"></a><span
7351 class="cmr-6">18</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"> 11)</span><span
7358 class="cmtt-8"> [highroom]</span><span
7359 class="cmtt-8"> =</span><span
7360 class="cmtt-8"> [range]</span><span
7361 class="cmtt-8"> -</span><span
7362 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
7363 id="x1-103038r19"></a><span
7364 class="cmr-6">19</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"> 12)</span><span
7371 class="cmtt-8"> [lowroom]</span><span
7372 class="cmtt-8"> </span><span
7373 class="cmtt-8"> =</span><span
7374 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
7375 id="x1-103040r20"></a><span
7376 class="cmr-6">20</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"> 13)</span><span
7383 class="cmtt-8"> if</span><span
7384 class="cmtt-8"> (</span><span
7385 class="cmtt-8"> [highroom]</span><span
7386 class="cmtt-8"> is</span><span
7387 class="cmtt-8"> less</span><span
7388 class="cmtt-8"> than</span><span
7389 class="cmtt-8"> [lowroom]</span><span
7390 class="cmtt-8"> )</span><span
7391 class="cmtt-8"> </span><span
7392 class="cmsy-8">{</span><br class="fancyvrb" /><a
7393 id="x1-103042r21"></a><span
7394 class="cmr-6">21</span>
7395 <br class="fancyvrb" /><a
7396 id="x1-103044r22"></a><span
7397 class="cmr-6">22</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"> </span><span
7404 class="cmtt-8"> </span><span
7405 class="cmtt-8"> </span><span
7406 class="cmtt-8"> </span><span
7407 class="cmtt-8"> </span><span
7408 class="cmtt-8"> </span><span
7409 class="cmtt-8"> 14)</span><span
7410 class="cmtt-8"> [room]</span><span
7411 class="cmtt-8"> =</span><span
7412 class="cmtt-8"> [highroom]</span><span
7413 class="cmtt-8"> *</span><span
7414 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
7415 id="x1-103046r23"></a><span
7416 class="cmr-6">23</span><br class="fancyvrb" /><a
7417 id="x1-103048r24"></a><span
7418 class="cmr-6">24</span><span
7419 class="cmtt-8"> </span><span
7420 class="cmtt-8"> </span><span
7421 class="cmtt-8"> </span><span
7422 class="cmtt-8"> </span><span
7423 class="cmtt-8"> </span><span
7424 class="cmtt-8"> </span><span
7425 class="cmtt-8"> </span><span
7426 class="cmtt-8"> </span><span
7427 class="cmtt-8"> </span><span
7428 class="cmtt-8"> </span><span
7429 class="cmsy-8">}</span><span
7430 class="cmtt-8"> else</span><span
7431 class="cmtt-8"> [highroom]</span><span
7432 class="cmtt-8"> is</span><span
7433 class="cmtt-8"> not</span><span
7434 class="cmtt-8"> less</span><span
7435 class="cmtt-8"> than</span><span
7436 class="cmtt-8"> [lowroom]</span><span
7437 class="cmtt-8"> </span><span
7438 class="cmsy-8">{</span><br class="fancyvrb" /><a
7439 id="x1-103050r25"></a><span
7440 class="cmr-6">25</span><br class="fancyvrb" /><a
7441 id="x1-103052r26"></a><span
7442 class="cmr-6">26</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"> </span><span
7451 class="cmtt-8"> </span><span
7452 class="cmtt-8"> </span><span
7453 class="cmtt-8"> </span><span
7454 class="cmtt-8"> 15)</span><span
7455 class="cmtt-8"> [room]</span><span
7456 class="cmtt-8"> =</span><span
7457 class="cmtt-8"> [lowroom]</span><span
7458 class="cmtt-8"> *</span><span
7459 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
7460 id="x1-103054r27"></a><span
7461 class="cmr-6">27</span>
7462 <br class="fancyvrb" /><a
7463 id="x1-103056r28"></a><span
7464 class="cmr-6">28</span><span
7465 class="cmtt-8"> </span><span
7466 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
7476 id="x1-103058r29"></a><span
7477 class="cmr-6">29</span><br class="fancyvrb" /><a
7478 id="x1-103060r30"></a><span
7479 class="cmr-6">30</span><span
7480 class="cmtt-8"> </span><span
7481 class="cmtt-8"> </span><span
7482 class="cmtt-8"> </span><span
7483 class="cmtt-8"> </span><span
7484 class="cmtt-8"> </span><span
7485 class="cmtt-8"> 16)</span><span
7486 class="cmtt-8"> if</span><span
7487 class="cmtt-8"> (</span><span
7488 class="cmtt-8"> [val]</span><span
7489 class="cmtt-8"> is</span><span
7490 class="cmtt-8"> nonzero</span><span
7491 class="cmtt-8"> )</span><span
7492 class="cmtt-8"> </span><span
7493 class="cmsy-8">{</span><br class="fancyvrb" /><a
7494 id="x1-103062r31"></a><span
7495 class="cmr-6">31</span><br class="fancyvrb" /><a
7496 id="x1-103064r32"></a><span
7497 class="cmr-6">32</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="cmtt-8"> </span><span
7506 class="cmtt-8"> </span><span
7507 class="cmtt-8"> </span><span
7508 class="cmtt-8"> </span><span
7509 class="cmtt-8"> 17)</span><span
7510 class="cmtt-8"> vector</span><span
7511 class="cmtt-8"> [floor1</span><span
7512 class="cmtt-8">_step2</span><span
7513 class="cmtt-8">_flag]</span><span
7514 class="cmtt-8"> element</span><span
7515 class="cmtt-8"> [low</span><span
7516 class="cmtt-8">_neighbor</span><span
7517 class="cmtt-8">_offset]</span><span
7518 class="cmtt-8"> =</span><span
7519 class="cmtt-8"> set</span>
7520 <br class="fancyvrb" /><a
7521 id="x1-103066r33"></a><span
7522 class="cmr-6">33</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"> 18)</span><span
7535 class="cmtt-8"> vector</span><span
7536 class="cmtt-8"> [floor1</span><span
7537 class="cmtt-8">_step2</span><span
7538 class="cmtt-8">_flag]</span><span
7539 class="cmtt-8"> element</span><span
7540 class="cmtt-8"> [high</span><span
7541 class="cmtt-8">_neighbor</span><span
7542 class="cmtt-8">_offset]</span><span
7543 class="cmtt-8"> =</span><span
7544 class="cmtt-8"> set</span><br class="fancyvrb" /><a
7545 id="x1-103068r34"></a><span
7546 class="cmr-6">34</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="cmtt-8"> 19)</span><span
7559 class="cmtt-8"> vector</span><span
7560 class="cmtt-8"> [floor1</span><span
7561 class="cmtt-8">_step2</span><span
7562 class="cmtt-8">_flag]</span><span
7563 class="cmtt-8"> element</span><span
7564 class="cmtt-8"> [i]</span><span
7565 class="cmtt-8"> =</span><span
7566 class="cmtt-8"> set</span>
7567 <br class="fancyvrb" /><a
7568 id="x1-103070r35"></a><span
7569 class="cmr-6">35</span><span
7570 class="cmtt-8"> </span><span
7571 class="cmtt-8"> </span><span
7572 class="cmtt-8"> </span><span
7573 class="cmtt-8"> </span><span
7574 class="cmtt-8"> </span><span
7575 class="cmtt-8"> </span><span
7576 class="cmtt-8"> </span><span
7577 class="cmtt-8"> </span><span
7578 class="cmtt-8"> </span><span
7579 class="cmtt-8"> </span><span
7580 class="cmtt-8"> </span><span
7581 class="cmtt-8"> 20)</span><span
7582 class="cmtt-8"> if</span><span
7583 class="cmtt-8"> (</span><span
7584 class="cmtt-8"> [val]</span><span
7585 class="cmtt-8"> is</span><span
7586 class="cmtt-8"> greater</span><span
7587 class="cmtt-8"> than</span><span
7588 class="cmtt-8"> or</span><span
7589 class="cmtt-8"> equal</span><span
7590 class="cmtt-8"> to</span><span
7591 class="cmtt-8"> [room]</span><span
7592 class="cmtt-8"> )</span><span
7593 class="cmtt-8"> </span><span
7594 class="cmsy-8">{</span><br class="fancyvrb" /><a
7595 id="x1-103072r36"></a><span
7596 class="cmr-6">36</span><br class="fancyvrb" /><a
7597 id="x1-103074r37"></a><span
7598 class="cmr-6">37</span><span
7599 class="cmtt-8"> </span><span
7600 class="cmtt-8"> </span><span
7601 class="cmtt-8"> </span><span
7602 class="cmtt-8"> </span><span
7603 class="cmtt-8"> </span><span
7604 class="cmtt-8"> </span><span
7605 class="cmtt-8"> </span><span
7606 class="cmtt-8"> </span><span
7607 class="cmtt-8"> </span><span
7608 class="cmtt-8"> </span><span
7609 class="cmtt-8"> </span><span
7610 class="cmtt-8"> </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"> 21)</span><span
7617 class="cmtt-8"> if</span><span
7618 class="cmtt-8"> (</span><span
7619 class="cmtt-8"> [highroom]</span><span
7620 class="cmtt-8"> is</span><span
7621 class="cmtt-8"> greater</span><span
7622 class="cmtt-8"> than</span><span
7623 class="cmtt-8"> [lowroom]</span><span
7624 class="cmtt-8"> )</span><span
7625 class="cmtt-8"> </span><span
7626 class="cmsy-8">{</span><br class="fancyvrb" /><a
7627 id="x1-103076r38"></a><span
7628 class="cmr-6">38</span>
7629 <br class="fancyvrb" /><a
7630 id="x1-103078r39"></a><span
7631 class="cmr-6">39</span><span
7632 class="cmtt-8"> </span><span
7633 class="cmtt-8"> </span><span
7634 class="cmtt-8"> </span><span
7635 class="cmtt-8"> </span><span
7636 class="cmtt-8"> </span><span
7637 class="cmtt-8"> </span><span
7638 class="cmtt-8"> </span><span
7639 class="cmtt-8"> </span><span
7640 class="cmtt-8"> </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"> </span><span
7648 class="cmtt-8"> </span><span
7649 class="cmtt-8"> </span><span
7650 class="cmtt-8"> </span><span
7651 class="cmtt-8"> </span><span
7652 class="cmtt-8"> </span><span
7653 class="cmtt-8"> </span><span
7654 class="cmtt-8"> </span><span
7655 class="cmtt-8"> 22)</span><span
7656 class="cmtt-8"> vector</span><span
7657 class="cmtt-8"> [floor1</span><span
7658 class="cmtt-8">_final</span><span
7659 class="cmtt-8">_Y]</span><span
7660 class="cmtt-8"> element</span><span
7661 class="cmtt-8"> [i]</span><span
7662 class="cmtt-8"> =</span><span
7663 class="cmtt-8"> [val]</span><span
7664 class="cmtt-8"> -</span><span
7665 class="cmtt-8"> [lowroom]</span><span
7666 class="cmtt-8"> +</span><span
7667 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
7668 id="x1-103080r40"></a><span
7669 class="cmr-6">40</span>
7670 <br class="fancyvrb" /><a
7671 id="x1-103082r41"></a><span
7672 class="cmr-6">41</span> <span
7673 class="cmtt-8"> </span><span
7674 class="cmtt-8"> </span><span
7675 class="cmtt-8"> </span><span
7676 class="cmtt-8"> </span><span
7677 class="cmtt-8"> </span><span
7678 class="cmtt-8"> </span><span
7679 class="cmsy-8">}</span><span
7680 class="cmtt-8"> else</span><span
7681 class="cmtt-8"> [highroom]</span><span
7682 class="cmtt-8"> is</span><span
7683 class="cmtt-8"> not</span><span
7684 class="cmtt-8"> greater</span><span
7685 class="cmtt-8"> than</span><span
7686 class="cmtt-8"> [lowroom]</span><span
7687 class="cmtt-8"> </span><span
7688 class="cmsy-8">{</span><br class="fancyvrb" /><a
7689 id="x1-103084r42"></a><span
7690 class="cmr-6">42</span>
7691 <br class="fancyvrb" /><a
7692 id="x1-103086r43"></a><span
7693 class="cmr-6">43</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"> </span><span
7710 class="cmtt-8"> </span><span
7711 class="cmtt-8"> </span><span
7712 class="cmtt-8"> </span><span
7713 class="cmtt-8"> </span><span
7714 class="cmtt-8"> </span><span
7715 class="cmtt-8"> </span><span
7716 class="cmtt-8"> </span><span
7717 class="cmtt-8"> 23)</span><span
7718 class="cmtt-8"> vector</span><span
7719 class="cmtt-8"> [floor1</span><span
7720 class="cmtt-8">_final</span><span
7721 class="cmtt-8">_Y]</span><span
7722 class="cmtt-8"> element</span><span
7723 class="cmtt-8"> [i]</span><span
7724 class="cmtt-8"> =</span><span
7725 class="cmtt-8"> [predicted]</span><span
7726 class="cmtt-8"> -</span><span
7727 class="cmtt-8"> [val]</span><span
7728 class="cmtt-8"> +</span><span
7729 class="cmtt-8"> [highroom]</span><span
7730 class="cmtt-8"> -</span><span
7731 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
7732 id="x1-103088r44"></a><span
7733 class="cmr-6">44</span>
7734 <br class="fancyvrb" /><a
7735 id="x1-103090r45"></a><span
7736 class="cmr-6">45</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"> </span><span
7753 class="cmtt-8"> </span><span
7754 class="cmtt-8"> </span><span
7755 class="cmtt-8"> </span><span
7756 class="cmtt-8"> </span><span
7757 class="cmtt-8"> </span><span
7758 class="cmtt-8"> </span><span
7759 class="cmsy-8">}</span><br class="fancyvrb" /><a
7760 id="x1-103092r46"></a><span
7761 class="cmr-6">46</span><br class="fancyvrb" /><a
7762 id="x1-103094r47"></a><span
7763 class="cmr-6">47</span><span
7764 class="cmtt-8"> </span><span
7765 class="cmtt-8"> </span><span
7766 class="cmtt-8"> </span><span
7767 class="cmtt-8"> </span><span
7768 class="cmtt-8"> </span><span
7769 class="cmtt-8"> </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="cmtt-8"> </span><span
7779 class="cmtt-8"> </span><span
7780 class="cmsy-8">}</span><span
7781 class="cmtt-8"> else</span><span
7782 class="cmtt-8"> [val]</span><span
7783 class="cmtt-8"> is</span><span
7784 class="cmtt-8"> less</span><span
7785 class="cmtt-8"> than</span><span
7786 class="cmtt-8"> [room]</span><span
7787 class="cmtt-8"> </span><span
7788 class="cmsy-8">{</span><br class="fancyvrb" /><a
7789 id="x1-103096r48"></a><span
7790 class="cmr-6">48</span>
7791 <br class="fancyvrb" /><a
7792 id="x1-103098r49"></a><span
7793 class="cmr-6">49</span><span
7794 class="cmtt-8"> </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"> 24)</span><span
7814 class="cmtt-8"> if</span><span
7815 class="cmtt-8"> ([val]</span><span
7816 class="cmtt-8"> is</span><span
7817 class="cmtt-8"> odd)</span><span
7818 class="cmtt-8"> </span><span
7819 class="cmsy-8">{</span><br class="fancyvrb" /><a
7820 id="x1-103100r50"></a><span
7821 class="cmr-6">50</span><br class="fancyvrb" /><a
7822 id="x1-103102r51"></a><span
7823 class="cmr-6">51</span><span
7824 class="cmtt-8"> </span><span
7825 class="cmtt-8"> </span><span
7826 class="cmtt-8"> </span><span
7827 class="cmtt-8"> </span><span
7828 class="cmtt-8"> </span><span
7829 class="cmtt-8"> </span><span
7830 class="cmtt-8"> </span><span
7831 class="cmtt-8"> </span><span
7832 class="cmtt-8"> </span><span
7833 class="cmtt-8"> </span><span
7834 class="cmtt-8"> </span><span
7835 class="cmtt-8"> </span><span
7836 class="cmtt-8"> </span><span
7837 class="cmtt-8"> </span><span
7838 class="cmtt-8"> </span><span
7839 class="cmtt-8"> </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"> 25)</span><span
7848 class="cmtt-8"> vector</span><span
7849 class="cmtt-8"> [floor1</span><span
7850 class="cmtt-8">_final</span><span
7851 class="cmtt-8">_Y]</span><span
7852 class="cmtt-8"> element</span><span
7853 class="cmtt-8"> [i]</span><span
7854 class="cmtt-8"> =</span>
7855 <br class="fancyvrb" /><a
7856 id="x1-103104r52"></a><span
7857 class="cmr-6">52</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="cmtt-8"> </span><span
7865 class="cmtt-8"> </span><span
7866 class="cmtt-8"> </span><span
7867 class="cmtt-8"> </span><span
7868 class="cmtt-8"> </span><span
7869 class="cmtt-8"> </span><span
7870 class="cmtt-8"> </span><span
7871 class="cmtt-8"> </span><span
7872 class="cmtt-8"> </span><span
7873 class="cmtt-8"> </span><span
7874 class="cmtt-8"> </span><span
7875 class="cmtt-8"> </span><span
7876 class="cmtt-8"> </span><span
7877 class="cmtt-8"> </span><span
7878 class="cmtt-8"> </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"> [predicted]</span><span
7886 class="cmtt-8"> -</span><span
7887 class="cmtt-8"> (([val]</span><span
7888 class="cmtt-8"> +</span><span
7889 class="cmtt-8"> 1)</span><span
7890 class="cmtt-8"> divided</span><span
7891 class="cmtt-8"> by</span><span
7892 class="cmtt-8"> </span><span
7893 class="cmtt-8"> 2</span><span
7894 class="cmtt-8"> using</span><span
7895 class="cmtt-8"> integer</span><span
7896 class="cmtt-8"> division)</span><br class="fancyvrb" /><a
7897 id="x1-103106r53"></a><span
7898 class="cmr-6">53</span>
7899 <br class="fancyvrb" /><a
7900 id="x1-103108r54"></a><span
7901 class="cmr-6">54</span><span
7902 class="cmtt-8"> </span><span
7903 class="cmtt-8"> </span><span
7904 class="cmtt-8"> </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="cmsy-8">}</span><span
7925 class="cmtt-8"> else</span><span
7926 class="cmtt-8"> [val]</span><span
7927 class="cmtt-8"> is</span><span
7928 class="cmtt-8"> even</span><span
7929 class="cmtt-8"> </span><span
7930 class="cmsy-8">{</span><br class="fancyvrb" /><a
7931 id="x1-103110r55"></a><span
7932 class="cmr-6">55</span><br class="fancyvrb" /><a
7933 id="x1-103112r56"></a><span
7934 class="cmr-6">56</span><span
7935 class="cmtt-8"> </span><span
7936 class="cmtt-8"> </span><span
7937 class="cmtt-8"> </span><span
7938 class="cmtt-8"> </span><span
7939 class="cmtt-8"> </span><span
7940 class="cmtt-8"> </span><span
7941 class="cmtt-8"> </span><span
7942 class="cmtt-8"> </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"> 26)</span><span
7959 class="cmtt-8"> vector</span><span
7960 class="cmtt-8"> [floor1</span><span
7961 class="cmtt-8">_final</span><span
7962 class="cmtt-8">_Y]</span><span
7963 class="cmtt-8"> element</span><span
7964 class="cmtt-8"> [i]</span><span
7965 class="cmtt-8"> =</span>
7966 <br class="fancyvrb" /><a
7967 id="x1-103114r57"></a><span
7968 class="cmr-6">57</span><span
7969 class="cmtt-8"> </span><span
7970 class="cmtt-8"> </span><span
7971 class="cmtt-8"> </span><span
7972 class="cmtt-8"> </span><span
7973 class="cmtt-8"> </span><span
7974 class="cmtt-8"> </span><span
7975 class="cmtt-8"> </span><span
7976 class="cmtt-8"> </span><span
7977 class="cmtt-8"> </span><span
7978 class="cmtt-8"> </span><span
7979 class="cmtt-8"> </span><span
7980 class="cmtt-8"> </span><span
7981 class="cmtt-8"> </span><span
7982 class="cmtt-8"> </span><span
7983 class="cmtt-8"> </span><span
7984 class="cmtt-8"> </span><span
7985 class="cmtt-8"> </span><span
7986 class="cmtt-8"> </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"> [predicted]</span><span
7997 class="cmtt-8"> +</span><span
7998 class="cmtt-8"> ([val]</span><span
7999 class="cmtt-8"> /</span><span
8000 class="cmtt-8"> 2</span><span
8001 class="cmtt-8"> using</span><span
8002 class="cmtt-8"> integer</span><span
8003 class="cmtt-8"> division)</span><br class="fancyvrb" /><a
8004 id="x1-103116r58"></a><span
8005 class="cmr-6">58</span><br class="fancyvrb" /><a
8006 id="x1-103118r59"></a><span
8007 class="cmr-6">59</span><span
8008 class="cmtt-8"> </span><span
8009 class="cmtt-8"> </span><span
8010 class="cmtt-8"> </span><span
8011 class="cmtt-8"> </span><span
8012 class="cmtt-8"> </span><span
8013 class="cmtt-8"> </span><span
8014 class="cmtt-8"> </span><span
8015 class="cmtt-8"> </span><span
8016 class="cmtt-8"> </span><span
8017 class="cmtt-8"> </span><span
8018 class="cmtt-8"> </span><span
8019 class="cmtt-8"> </span><span
8020 class="cmtt-8"> </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="cmsy-8">}</span><br class="fancyvrb" /><a
8031 id="x1-103120r60"></a><span
8032 class="cmr-6">60</span>
8033 <br class="fancyvrb" /><a
8034 id="x1-103122r61"></a><span
8035 class="cmr-6">61</span><span
8036 class="cmtt-8"> </span><span
8037 class="cmtt-8"> </span><span
8038 class="cmtt-8"> </span><span
8039 class="cmtt-8"> </span><span
8040 class="cmtt-8"> </span><span
8041 class="cmtt-8"> </span><span
8042 class="cmtt-8"> </span><span
8043 class="cmtt-8"> </span><span
8044 class="cmtt-8"> </span><span
8045 class="cmtt-8"> </span><span
8046 class="cmtt-8"> </span><span
8047 class="cmtt-8"> </span><span
8048 class="cmtt-8"> </span><span
8049 class="cmtt-8"> </span><span
8050 class="cmtt-8"> </span><span
8051 class="cmtt-8"> </span><span
8052 class="cmsy-8">}</span><br class="fancyvrb" /><a
8053 id="x1-103124r62"></a><span
8054 class="cmr-6">62</span><br class="fancyvrb" /><a
8055 id="x1-103126r63"></a><span
8056 class="cmr-6">63</span><span
8057 class="cmtt-8"> </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="cmsy-8">}</span><span
8068 class="cmtt-8"> else</span><span
8069 class="cmtt-8"> [val]</span><span
8070 class="cmtt-8"> is</span><span
8071 class="cmtt-8"> zero</span><span
8072 class="cmtt-8"> </span><span
8073 class="cmsy-8">{</span><br class="fancyvrb" /><a
8074 id="x1-103128r64"></a><span
8075 class="cmr-6">64</span><br class="fancyvrb" /><a
8076 id="x1-103130r65"></a><span
8077 class="cmr-6">65</span><span
8078 class="cmtt-8"> </span><span
8079 class="cmtt-8"> </span><span
8080 class="cmtt-8"> </span><span
8081 class="cmtt-8"> </span><span
8082 class="cmtt-8"> </span><span
8083 class="cmtt-8"> </span><span
8084 class="cmtt-8"> </span><span
8085 class="cmtt-8"> </span><span
8086 class="cmtt-8"> </span><span
8087 class="cmtt-8"> </span><span
8088 class="cmtt-8"> </span><span
8089 class="cmtt-8"> 27)</span><span
8090 class="cmtt-8"> vector</span><span
8091 class="cmtt-8"> [floor1</span><span
8092 class="cmtt-8">_step2</span><span
8093 class="cmtt-8">_flag]</span><span
8094 class="cmtt-8"> element</span><span
8095 class="cmtt-8"> [i]</span><span
8096 class="cmtt-8"> =</span><span
8097 class="cmtt-8"> unset</span>
8098 <br class="fancyvrb" /><a
8099 id="x1-103132r66"></a><span
8100 class="cmr-6">66</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"> 28)</span><span
8113 class="cmtt-8"> vector</span><span
8114 class="cmtt-8"> [floor1</span><span
8115 class="cmtt-8">_final</span><span
8116 class="cmtt-8">_Y]</span><span
8117 class="cmtt-8"> element</span><span
8118 class="cmtt-8"> [i]</span><span
8119 class="cmtt-8"> =</span><span
8120 class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a
8121 id="x1-103134r67"></a><span
8122 class="cmr-6">67</span><br class="fancyvrb" /><a
8123 id="x1-103136r68"></a><span
8124 class="cmr-6">68</span><span
8125 class="cmtt-8"> </span><span
8126 class="cmtt-8"> </span><span
8127 class="cmtt-8"> </span><span
8128 class="cmtt-8"> </span><span
8129 class="cmtt-8"> </span><span
8130 class="cmtt-8"> </span><span
8131 class="cmtt-8"> </span><span
8132 class="cmtt-8"> </span><span
8133 class="cmtt-8"> </span><span
8134 class="cmtt-8"> </span><span
8135 class="cmsy-8">}</span><br class="fancyvrb" /><a
8136 id="x1-103138r69"></a><span
8137 class="cmr-6">69</span><br class="fancyvrb" /><a
8138 id="x1-103140r70"></a><span
8139 class="cmr-6">70</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="cmsy-8">}</span><br class="fancyvrb" /><a
8146 id="x1-103142r71"></a><span
8147 class="cmr-6">71</span><br class="fancyvrb" /><a
8148 id="x1-103144r72"></a><span
8149 class="cmr-6">72</span><span
8150 class="cmtt-8"> 29)</span><span
8151 class="cmtt-8"> done</span><br class="fancyvrb" /><a
8152 id="x1-103146r73"></a><span
8153 class="cmr-6">73</span></div>
8154 </dd><dt class="description">
8156 class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
8157 class="description">
8158 <!--l. 350--><p class="noindent" >Curve synthesis generates a return vector <span
8159 class="cmtt-12">[floor] </span>of length <span
8160 class="cmtt-12">[n] </span>(where <span
8161 class="cmtt-12">[n] </span>is provided by
8162 the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
8164 class="cmtt-12">[floor1</span><span
8165 class="cmtt-12">_X</span><span
8166 class="cmtt-12">_list]</span>, <span
8167 class="cmtt-12">[floor1</span><span
8168 class="cmtt-12">_final</span><span
8169 class="cmtt-12">_Y] </span>and <span
8170 class="cmtt-12">[floor1</span><span
8171 class="cmtt-12">_step2</span><span
8172 class="cmtt-12">_flag] </span>vectors, as well as
8173 [floor1_multiplier] and [floor1_values] values.
8174 <!--l. 357--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
8175 class="cmtt-12">[floor1</span><span
8176 class="cmtt-12">_X</span><span
8177 class="cmtt-12">_list]</span>, <span
8178 class="cmtt-12">[floor1</span><span
8179 class="cmtt-12">_final</span><span
8180 class="cmtt-12">_Y] </span>and
8182 class="cmtt-12">[floor1</span><span
8183 class="cmtt-12">_step2</span><span
8184 class="cmtt-12">_flag] </span>together into new vectors <span
8185 class="cmtt-12">[floor1</span><span
8186 class="cmtt-12">_X</span><span
8187 class="cmtt-12">_list]’</span>, <span
8188 class="cmtt-12">[floor1</span><span
8189 class="cmtt-12">_final</span><span
8190 class="cmtt-12">_Y]’</span>
8192 class="cmtt-12">[floor1</span><span
8193 class="cmtt-12">_step2</span><span
8194 class="cmtt-12">_flag]’ </span>according to ascending sort order of the values in
8196 class="cmtt-12">[floor1</span><span
8197 class="cmtt-12">_X</span><span
8198 class="cmtt-12">_list]</span>. That is, sort the values of <span
8199 class="cmtt-12">[floor1</span><span
8200 class="cmtt-12">_X</span><span
8201 class="cmtt-12">_list] </span>and then apply the same
8202 permutation to elements of the other two vectors so that the X, Y and step2_flag values
8204 <!--l. 367--><p class="noindent" >Then compute the final curve in one pass:
8205 <!--l. 369--><p class="noindent" >
8206 <div class="fancyvrb" id="fancyvrb32"><a
8207 id="x1-103148r1"></a><span
8208 class="cmr-6">1</span><span
8209 class="cmtt-8"> </span><span
8210 class="cmtt-8"> 1)</span><span
8211 class="cmtt-8"> [hx]</span><span
8212 class="cmtt-8"> =</span><span
8213 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
8214 id="x1-103150r2"></a><span
8215 class="cmr-6">2</span><span
8216 class="cmtt-8"> </span><span
8217 class="cmtt-8"> 2)</span><span
8218 class="cmtt-8"> [lx]</span><span
8219 class="cmtt-8"> =</span><span
8220 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
8221 id="x1-103152r3"></a><span
8222 class="cmr-6">3</span><span
8223 class="cmtt-8"> </span><span
8224 class="cmtt-8"> 3)</span><span
8225 class="cmtt-8"> [ly]</span><span
8226 class="cmtt-8"> =</span><span
8227 class="cmtt-8"> vector</span><span
8228 class="cmtt-8"> [floor1</span><span
8229 class="cmtt-8">_final</span><span
8230 class="cmtt-8">_Y]’</span><span
8231 class="cmtt-8"> element</span><span
8232 class="cmtt-8"> [0]</span><span
8233 class="cmtt-8"> *</span><span
8234 class="cmtt-8"> [floor1</span><span
8235 class="cmtt-8">_multiplier]</span>
8236 <br class="fancyvrb" /><a
8237 id="x1-103154r4"></a><span
8238 class="cmr-6">4</span><span
8239 class="cmtt-8"> </span><span
8240 class="cmtt-8"> 4)</span><span
8241 class="cmtt-8"> iterate</span><span
8242 class="cmtt-8"> [i]</span><span
8243 class="cmtt-8"> over</span><span
8244 class="cmtt-8"> the</span><span
8245 class="cmtt-8"> range</span><span
8246 class="cmtt-8"> 1</span><span
8247 class="cmtt-8"> ...</span><span
8248 class="cmtt-8"> [floor1</span><span
8249 class="cmtt-8">_values]-1</span><span
8250 class="cmtt-8"> </span><span
8251 class="cmsy-8">{</span><br class="fancyvrb" /><a
8252 id="x1-103156r5"></a><span
8253 class="cmr-6">5</span><br class="fancyvrb" /><a
8254 id="x1-103158r6"></a><span
8255 class="cmr-6">6</span><span
8256 class="cmtt-8"> </span><span
8257 class="cmtt-8"> </span><span
8258 class="cmtt-8"> </span><span
8259 class="cmtt-8"> </span><span
8260 class="cmtt-8"> </span><span
8261 class="cmtt-8"> </span><span
8262 class="cmtt-8"> 5)</span><span
8263 class="cmtt-8"> if</span><span
8264 class="cmtt-8"> (</span><span
8265 class="cmtt-8"> [floor1</span><span
8266 class="cmtt-8">_step2</span><span
8267 class="cmtt-8">_flag]’</span><span
8268 class="cmtt-8"> element</span><span
8269 class="cmtt-8"> [i]</span><span
8270 class="cmtt-8"> is</span><span
8271 class="cmtt-8"> set</span><span
8272 class="cmtt-8"> )</span><span
8273 class="cmtt-8"> </span><span
8274 class="cmsy-8">{</span><br class="fancyvrb" /><a
8275 id="x1-103160r7"></a><span
8276 class="cmr-6">7</span>
8277 <br class="fancyvrb" /><a
8278 id="x1-103162r8"></a><span
8279 class="cmr-6">8</span><span
8280 class="cmtt-8"> </span><span
8281 class="cmtt-8"> </span><span
8282 class="cmtt-8"> </span><span
8283 class="cmtt-8"> </span><span
8284 class="cmtt-8"> </span><span
8285 class="cmtt-8"> </span><span
8286 class="cmtt-8"> </span><span
8287 class="cmtt-8"> </span><span
8288 class="cmtt-8"> </span><span
8289 class="cmtt-8"> </span><span
8290 class="cmtt-8"> </span><span
8291 class="cmtt-8"> </span><span
8292 class="cmtt-8"> 6)</span><span
8293 class="cmtt-8"> [hy]</span><span
8294 class="cmtt-8"> =</span><span
8295 class="cmtt-8"> [floor1</span><span
8296 class="cmtt-8">_final</span><span
8297 class="cmtt-8">_Y]’</span><span
8298 class="cmtt-8"> element</span><span
8299 class="cmtt-8"> [i]</span><span
8300 class="cmtt-8"> *</span><span
8301 class="cmtt-8"> [floor1</span><span
8302 class="cmtt-8">_multiplier]</span><br class="fancyvrb" /><a
8303 id="x1-103164r9"></a><span
8304 class="cmr-6">9</span><span
8305 class="cmtt-8">  </span><span
8306 class="cmtt-8"> </span><span
8307 class="cmtt-8"> </span><span
8308 class="cmtt-8"> </span><span
8309 class="cmtt-8"> </span><span
8310 class="cmtt-8"> 7)</span><span
8311 class="cmtt-8"> [hx]</span><span
8312 class="cmtt-8"> =</span><span
8313 class="cmtt-8"> [floor1</span><span
8314 class="cmtt-8">_X</span><span
8315 class="cmtt-8">_list]’</span><span
8316 class="cmtt-8"> element</span><span
8317 class="cmtt-8"> [i]</span>
8318 <br class="fancyvrb" /><a
8319 id="x1-103166r10"></a><span
8320 class="cmr-6">10</span><span
8321 class="cmtt-8"> </span><span
8322 class="cmtt-8"> </span><span
8323 class="cmtt-8"> </span><span
8324 class="cmtt-8"> </span><span
8325 class="cmtt-8"> </span><span
8326 class="cmtt-8"> </span><span
8327 class="cmtt-8"> </span><span
8328 class="cmtt-8"> </span><span
8329 class="cmtt-8"> </span><span
8330 class="cmtt-8"> </span><span
8331 class="cmtt-8"> </span><span
8332 class="cmtt-8"> </span><span
8333 class="cmtt-8"> 8)</span><span
8334 class="cmtt-8"> </span><a
8335 href="#x1-1250009.2.7"><span
8336 class="cmtt-8">render</span><span
8337 class="cmtt-8">_line</span></a><span
8338 class="cmtt-8">(</span><span
8339 class="cmtt-8"> [lx],</span><span
8340 class="cmtt-8"> [ly],</span><span
8341 class="cmtt-8"> [hx],</span><span
8342 class="cmtt-8"> [hy],</span><span
8343 class="cmtt-8"> [floor]</span><span
8344 class="cmtt-8"> )</span><br class="fancyvrb" /><a
8345 id="x1-103168r11"></a><span
8346 class="cmr-6">11</span><span
8347 class="cmtt-8"> </span><span
8348 class="cmtt-8"> </span><span
8349 class="cmtt-8"> </span><span
8350 class="cmtt-8"> </span><span
8351 class="cmtt-8"> </span><span
8352 class="cmtt-8"> </span><span
8353 class="cmtt-8"> </span><span
8354 class="cmtt-8"> </span><span
8355 class="cmtt-8"> </span><span
8356 class="cmtt-8"> </span><span
8357 class="cmtt-8"> </span><span
8358 class="cmtt-8"> </span><span
8359 class="cmtt-8"> 9)</span><span
8360 class="cmtt-8"> [lx]</span><span
8361 class="cmtt-8"> =</span><span
8362 class="cmtt-8"> [hx]</span><br class="fancyvrb" /><a
8363 id="x1-103170r12"></a><span
8364 class="cmr-6">12</span> <span
8365 class="cmtt-8"> </span><span
8366 class="cmtt-8"> </span><span
8367 class="cmtt-8"> </span><span
8368 class="cmtt-8"> 10)</span><span
8369 class="cmtt-8"> [ly]</span><span
8370 class="cmtt-8"> =</span><span
8371 class="cmtt-8"> [hy]</span><br class="fancyvrb" /><a
8372 id="x1-103172r13"></a><span
8373 class="cmr-6">13</span><span
8374 class="cmtt-8"> </span><span
8375 class="cmtt-8"> </span><span
8376 class="cmtt-8"> </span><span
8377 class="cmtt-8"> </span><span
8378 class="cmtt-8"> </span><span
8379 class="cmtt-8"> </span><span
8380 class="cmtt-8"> </span><span
8381 class="cmtt-8"> </span><span
8382 class="cmtt-8"> </span><span
8383 class="cmtt-8"> </span><span
8384 class="cmsy-8">}</span><br class="fancyvrb" /><a
8385 id="x1-103174r14"></a><span
8386 class="cmr-6">14</span><span
8387 class="cmtt-8"> </span><span
8388 class="cmtt-8"> </span><span
8389 class="cmtt-8"> </span><span
8390 class="cmtt-8"> </span><span
8391 class="cmtt-8"> </span><span
8392 class="cmsy-8">}</span><br class="fancyvrb" /><a
8393 id="x1-103176r15"></a><span
8394 class="cmr-6">15</span>
8395 <br class="fancyvrb" /><a
8396 id="x1-103178r16"></a><span
8397 class="cmr-6">16</span><span
8398 class="cmtt-8"> 11)</span><span
8399 class="cmtt-8"> if</span><span
8400 class="cmtt-8"> (</span><span
8401 class="cmtt-8"> [hx]</span><span
8402 class="cmtt-8"> is</span><span
8403 class="cmtt-8"> less</span><span
8404 class="cmtt-8"> than</span><span
8405 class="cmtt-8"> [n]</span><span
8406 class="cmtt-8"> )</span><span
8407 class="cmtt-8"> </span><span
8408 class="cmsy-8">{</span><br class="fancyvrb" /><a
8409 id="x1-103180r17"></a><span
8410 class="cmr-6">17</span><br class="fancyvrb" /><a
8411 id="x1-103182r18"></a><span
8412 class="cmr-6">18</span><span
8413 class="cmtt-8"> </span><span
8414 class="cmtt-8"> </span><span
8415 class="cmtt-8"> </span><span
8416 class="cmtt-8"> </span><span
8417 class="cmtt-8"> </span><span
8418 class="cmtt-8"> </span><span
8419 class="cmtt-8"> </span><span
8420 class="cmtt-8"> 12)</span><span
8421 class="cmtt-8"> </span><a
8422 href="#x1-1250009.2.7"><span
8423 class="cmtt-8">render</span><span
8424 class="cmtt-8">_line</span></a><span
8425 class="cmtt-8">(</span><span
8426 class="cmtt-8"> [hx],</span><span
8427 class="cmtt-8"> [hy],</span><span
8428 class="cmtt-8"> [n],</span><span
8429 class="cmtt-8"> [hy],</span><span
8430 class="cmtt-8"> [floor]</span><span
8431 class="cmtt-8"> )</span><br class="fancyvrb" /><a
8432 id="x1-103184r19"></a><span
8433 class="cmr-6">19</span><br class="fancyvrb" /><a
8434 id="x1-103186r20"></a><span
8435 class="cmr-6">20</span><span
8436 class="cmtt-8"> </span><span
8437 class="cmtt-8"> </span><span
8438 class="cmtt-8"> </span><span
8439 class="cmtt-8"> </span><span
8440 class="cmtt-8"> </span><span
8441 class="cmsy-8">}</span><br class="fancyvrb" /><a
8442 id="x1-103188r21"></a><span
8443 class="cmr-6">21</span><br class="fancyvrb" /><a
8444 id="x1-103190r22"></a><span
8445 class="cmr-6">22</span><span
8446 class="cmtt-8"> 13)</span><span
8447 class="cmtt-8"> if</span><span
8448 class="cmtt-8"> (</span><span
8449 class="cmtt-8"> [hx]</span><span
8450 class="cmtt-8"> is</span><span
8451 class="cmtt-8"> greater</span><span
8452 class="cmtt-8"> than</span><span
8453 class="cmtt-8"> [n]</span><span
8454 class="cmtt-8"> )</span><span
8455 class="cmtt-8"> </span><span
8456 class="cmsy-8">{</span><br class="fancyvrb" /><a
8457 id="x1-103192r23"></a><span
8458 class="cmr-6">23</span>
8459 <br class="fancyvrb" /><a
8460 id="x1-103194r24"></a><span
8461 class="cmr-6">24</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"> 14)</span><span
8474 class="cmtt-8"> truncate</span><span
8475 class="cmtt-8"> vector</span><span
8476 class="cmtt-8"> [floor]</span><span
8477 class="cmtt-8"> to</span><span
8478 class="cmtt-8"> [n]</span><span
8479 class="cmtt-8"> elements</span><br class="fancyvrb" /><a
8480 id="x1-103196r25"></a><span
8481 class="cmr-6">25</span><br class="fancyvrb" /><a
8482 id="x1-103198r26"></a><span
8483 class="cmr-6">26</span><span
8484 class="cmtt-8"> </span><span
8485 class="cmtt-8"> </span><span
8486 class="cmtt-8"> </span><span
8487 class="cmtt-8"> </span><span
8488 class="cmtt-8"> </span><span
8489 class="cmsy-8">}</span><br class="fancyvrb" /><a
8490 id="x1-103200r27"></a><span
8491 class="cmr-6">27</span><br class="fancyvrb" /><a
8492 id="x1-103202r28"></a><span
8493 class="cmr-6">28</span><span
8494 class="cmtt-8"> 15)</span><span
8495 class="cmtt-8"> for</span><span
8496 class="cmtt-8"> each</span><span
8497 class="cmtt-8"> scalar</span><span
8498 class="cmtt-8"> in</span><span
8499 class="cmtt-8"> vector</span><span
8500 class="cmtt-8"> [floor],</span><span
8501 class="cmtt-8"> perform</span><span
8502 class="cmtt-8"> a</span><span
8503 class="cmtt-8"> lookup</span><span
8504 class="cmtt-8"> substitution</span><span
8505 class="cmtt-8"> using</span>
8506 <br class="fancyvrb" /><a
8507 id="x1-103204r29"></a><span
8508 class="cmr-6">29</span><span
8509 class="cmtt-8"> </span><span
8510 class="cmtt-8"> </span><span
8511 class="cmtt-8"> </span><span
8512 class="cmtt-8"> </span><span
8513 class="cmtt-8"> the</span><span
8514 class="cmtt-8"> scalar</span><span
8515 class="cmtt-8"> value</span><span
8516 class="cmtt-8"> from</span><span
8517 class="cmtt-8"> [floor]</span><span
8518 class="cmtt-8"> as</span><span
8519 class="cmtt-8"> an</span><span
8520 class="cmtt-8"> offset</span><span
8521 class="cmtt-8"> into</span><span
8522 class="cmtt-8"> the</span><span
8523 class="cmtt-8"> vector</span><span
8524 class="cmtt-8"> </span><a
8525 href="#x1-12700010.1"><span
8526 class="cmtt-8">[floor1</span><span
8527 class="cmtt-8">_inverse</span><span
8528 class="cmtt-8">_dB</span><span
8529 class="cmtt-8">_static</span><span
8530 class="cmtt-8">_table]</span></a><br class="fancyvrb" /><a
8531 id="x1-103206r30"></a><span
8532 class="cmr-6">30</span><br class="fancyvrb" /><a
8533 id="x1-103208r31"></a><span
8534 class="cmr-6">31</span><span
8535 class="cmtt-8"> 16)</span><span
8536 class="cmtt-8"> done</span><br class="fancyvrb" /><a
8537 id="x1-103210r32"></a><span
8538 class="cmr-6">32</span></div>
8543 <h3 class="sectionHead"><span class="titlemark">8. </span> <a
8544 id="x1-1040008"></a>Residue setup and decode</h3>
8545 <!--l. 5--><p class="noindent" >
8546 <h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a
8547 id="x1-1050008.1"></a>Overview</h4>
8548 <!--l. 7--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
8549 after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
8550 may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel
8551 coupling. The exact semantic content of the vector does not matter to the residue
8553 <!--l. 14--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
8554 bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
8555 different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
8557 <!--l. 22--><p class="noindent" >
8558 <h4 class="subsectionHead"><span class="titlemark">8.2. </span> <a
8559 id="x1-1060008.2"></a>Residue format</h4>
8560 <!--l. 24--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
8561 chunk, encodes the chunk classifications and finally encodes the chunks themselves
8562 using the the specific VQ arrangement defined for each selected classification. The
8563 exact interleaving and partitioning vary by residue encoding number, however the
8564 high-level process used to classify and encode the residue vector is the same in all three
8566 <!--l. 32--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
8567 the moment exactly how a partition is encoded and simply trusting that it is, is as
8569 <ul class="itemize1">
8570 <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
8571 specified. If we have a vector size of <span
8572 class="cmti-12">n</span>, a partition size <span
8573 class="cmti-12">residue</span><span
8574 class="cmti-12">_partition</span><span
8575 class="cmti-12">_size</span>,
8576 and a total of <span
8577 class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded
8582 class="cmti-12">n</span>/<span
8583 class="cmti-12">residue</span><span
8584 class="cmti-12">_partition</span><span
8585 class="cmti-12">_size</span>*<span
8586 class="cmti-12">ch</span>. It is important to note that the integer division
8587 truncates. In the below example, we assume an example <span
8588 class="cmti-12">residue</span><span
8589 class="cmti-12">_partition</span><span
8590 class="cmti-12">_size </span>of 8.
8592 <li class="itemize">Each partition in each vector has a classification number that specifies which of
8593 multiple configured VQ codebook setups are used to decode that partition. The
8594 classification numbers of each partition can be thought of as forming a vector in
8595 their own right, as in the illustration below. Just as the residue vectors are coded
8596 in grouped partitions to increase encoding efficiency, the classification vector is also
8597 partitioned into chunks. The integer elements of each scalar in a classification chunk
8598 are built into a single scalar that represents the classification numbers in that chunk.
8599 In the below example, the classification codeword encodes two classification numbers.
8601 <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
8602 the residue vector, but more often efficient codebook design dictates that each vector
8603 is encoded as the additive sum of several passes through the residue vector using
8604 more than one VQ codebook. Thus, each residue value potentially accumulates values
8605 from multiple decode passes. The classification value associated with a partition is
8606 the same in each pass, thus the classification codeword is coded only in the first pass.
8610 <!--l. 69--><p class="noindent" >
8612 <!--l. 70--><p class="noindent" ><img
8613 src="residue-pack.png" alt="PIC"
8615 <br /> <div class="caption"
8616 ><span class="id">Figure 11: </span><span
8617 class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10600111 -->
8619 <!--l. 76--><p class="noindent" >
8620 <h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a
8621 id="x1-1070008.3"></a>residue 0</h4>
8622 <!--l. 78--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
8623 partition encoding (visually treated as a black box–or cyan box or brown box–in the above
8625 <!--l. 82--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
8629 encode a partition in a specific pass. The dimension of the codebook need not be the same in
8630 multiple passes, however the partition size must be an even multiple of the codebook
8632 <!--l. 88--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
8633 codebook sizes of 8, 4, 2 and 1:
8634 <!--l. 91--><p class="noindent" >
8635 <div class="fancyvrb" id="fancyvrb33"><a
8636 id="x1-107002r1"></a><span
8637 class="cmr-6">1</span><br class="fancyvrb" /><a
8638 id="x1-107004r2"></a><span
8639 class="cmr-6">2</span><span
8640 class="cmtt-8"> </span><span
8641 class="cmtt-8"> </span><span
8642 class="cmtt-8"> </span><span
8643 class="cmtt-8"> </span><span
8644 class="cmtt-8"> </span><span
8645 class="cmtt-8"> </span><span
8646 class="cmtt-8"> </span><span
8647 class="cmtt-8"> </span><span
8648 class="cmtt-8"> </span><span
8649 class="cmtt-8"> </span><span
8650 class="cmtt-8"> </span><span
8651 class="cmtt-8"> original</span><span
8652 class="cmtt-8"> residue</span><span
8653 class="cmtt-8"> vector:</span><span
8654 class="cmtt-8"> [</span><span
8655 class="cmtt-8"> 0</span><span
8656 class="cmtt-8"> 1</span><span
8657 class="cmtt-8"> 2</span><span
8658 class="cmtt-8"> 3</span><span
8659 class="cmtt-8"> 4</span><span
8660 class="cmtt-8"> 5</span><span
8661 class="cmtt-8"> 6</span><span
8662 class="cmtt-8"> 7</span><span
8663 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8664 id="x1-107006r3"></a><span
8665 class="cmr-6">3</span><br class="fancyvrb" /><a
8666 id="x1-107008r4"></a><span
8667 class="cmr-6">4</span><span
8668 class="cmtt-8">codebook</span><span
8669 class="cmtt-8"> dimensions</span><span
8670 class="cmtt-8"> =</span><span
8671 class="cmtt-8"> 8</span><span
8672 class="cmtt-8"> </span><span
8673 class="cmtt-8"> encoded</span><span
8674 class="cmtt-8"> as:</span><span
8675 class="cmtt-8"> [</span><span
8676 class="cmtt-8"> 0</span><span
8677 class="cmtt-8"> 1</span><span
8678 class="cmtt-8"> 2</span><span
8679 class="cmtt-8"> 3</span><span
8680 class="cmtt-8"> 4</span><span
8681 class="cmtt-8"> 5</span><span
8682 class="cmtt-8"> 6</span><span
8683 class="cmtt-8"> 7</span><span
8684 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8685 id="x1-107010r5"></a><span
8686 class="cmr-6">5</span>
8687 <br class="fancyvrb" /><a
8688 id="x1-107012r6"></a><span
8689 class="cmr-6">6</span><span
8690 class="cmtt-8">codebook</span><span
8691 class="cmtt-8"> dimensions</span><span
8692 class="cmtt-8"> =</span><span
8693 class="cmtt-8"> 4</span><span
8694 class="cmtt-8"> </span><span
8695 class="cmtt-8"> encoded</span><span
8696 class="cmtt-8"> as:</span><span
8697 class="cmtt-8"> [</span><span
8698 class="cmtt-8"> 0</span><span
8699 class="cmtt-8"> 2</span><span
8700 class="cmtt-8"> 4</span><span
8701 class="cmtt-8"> 6</span><span
8702 class="cmtt-8"> ],</span><span
8703 class="cmtt-8"> [</span><span
8704 class="cmtt-8"> 1</span><span
8705 class="cmtt-8"> 3</span><span
8706 class="cmtt-8"> 5</span><span
8707 class="cmtt-8"> 7</span><span
8708 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8709 id="x1-107014r7"></a><span
8710 class="cmr-6">7</span><br class="fancyvrb" /><a
8711 id="x1-107016r8"></a><span
8712 class="cmr-6">8</span><span
8713 class="cmtt-8">codebook</span><span
8714 class="cmtt-8"> dimensions</span><span
8715 class="cmtt-8"> =</span><span
8716 class="cmtt-8"> 2</span><span
8717 class="cmtt-8"> </span><span
8718 class="cmtt-8"> encoded</span><span
8719 class="cmtt-8"> as:</span><span
8720 class="cmtt-8"> [</span><span
8721 class="cmtt-8"> 0</span><span
8722 class="cmtt-8"> 4</span><span
8723 class="cmtt-8"> ],</span><span
8724 class="cmtt-8"> [</span><span
8725 class="cmtt-8"> 1</span><span
8726 class="cmtt-8"> 5</span><span
8727 class="cmtt-8"> ],</span><span
8728 class="cmtt-8"> [</span><span
8729 class="cmtt-8"> 2</span><span
8730 class="cmtt-8"> 6</span><span
8731 class="cmtt-8"> ],</span><span
8732 class="cmtt-8"> [</span><span
8733 class="cmtt-8"> 3</span><span
8734 class="cmtt-8"> 7</span><span
8735 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8736 id="x1-107018r9"></a><span
8737 class="cmr-6">9</span>
8738 <br class="fancyvrb" /><a
8739 id="x1-107020r10"></a><span
8740 class="cmr-6">10</span><span
8741 class="cmtt-8">codebook</span><span
8742 class="cmtt-8"> dimensions</span><span
8743 class="cmtt-8"> =</span><span
8744 class="cmtt-8"> 1</span><span
8745 class="cmtt-8"> </span><span
8746 class="cmtt-8"> encoded</span><span
8747 class="cmtt-8"> as:</span><span
8748 class="cmtt-8"> [</span><span
8749 class="cmtt-8"> 0</span><span
8750 class="cmtt-8"> ],</span><span
8751 class="cmtt-8"> [</span><span
8752 class="cmtt-8"> 1</span><span
8753 class="cmtt-8"> ],</span><span
8754 class="cmtt-8"> [</span><span
8755 class="cmtt-8"> 2</span><span
8756 class="cmtt-8"> ],</span><span
8757 class="cmtt-8"> [</span><span
8758 class="cmtt-8"> 3</span><span
8759 class="cmtt-8"> ],</span><span
8760 class="cmtt-8"> [</span><span
8761 class="cmtt-8"> 4</span><span
8762 class="cmtt-8"> ],</span><span
8763 class="cmtt-8"> [</span><span
8764 class="cmtt-8"> 5</span><span
8765 class="cmtt-8"> ],</span><span
8766 class="cmtt-8"> [</span><span
8767 class="cmtt-8"> 6</span><span
8768 class="cmtt-8"> ],</span><span
8769 class="cmtt-8"> [</span><span
8770 class="cmtt-8"> 7</span><span
8771 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8772 id="x1-107022r11"></a><span
8773 class="cmr-6">11</span></div>
8774 <!--l. 105--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
8775 restricted to a power of two.
8776 <!--l. 110--><p class="noindent" >
8777 <h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a
8778 id="x1-1080008.4"></a>residue 1</h4>
8779 <!--l. 112--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As
8780 with residue 0, however, partition length must be an integer multiple of the codebook dimension,
8781 although dimension may vary from pass to pass.
8782 <!--l. 117--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
8783 codebook sizes of 8, 4, 2 and 1:
8784 <!--l. 120--><p class="noindent" >
8785 <div class="fancyvrb" id="fancyvrb34"><a
8786 id="x1-108002r1"></a><span
8787 class="cmr-6">1</span><br class="fancyvrb" /><a
8788 id="x1-108004r2"></a><span
8789 class="cmr-6">2</span><span
8790 class="cmtt-8"> </span><span
8791 class="cmtt-8"> </span><span
8792 class="cmtt-8"> </span><span
8793 class="cmtt-8"> </span><span
8794 class="cmtt-8"> </span><span
8795 class="cmtt-8"> </span><span
8796 class="cmtt-8"> </span><span
8797 class="cmtt-8"> </span><span
8798 class="cmtt-8"> </span><span
8799 class="cmtt-8"> </span><span
8800 class="cmtt-8"> </span><span
8801 class="cmtt-8"> original</span><span
8802 class="cmtt-8"> residue</span><span
8803 class="cmtt-8"> vector:</span><span
8804 class="cmtt-8"> [</span><span
8805 class="cmtt-8"> 0</span><span
8806 class="cmtt-8"> 1</span><span
8807 class="cmtt-8"> 2</span><span
8808 class="cmtt-8"> 3</span><span
8809 class="cmtt-8"> 4</span><span
8810 class="cmtt-8"> 5</span><span
8811 class="cmtt-8"> 6</span><span
8812 class="cmtt-8"> 7</span><span
8813 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8814 id="x1-108006r3"></a><span
8815 class="cmr-6">3</span><br class="fancyvrb" /><a
8816 id="x1-108008r4"></a><span
8817 class="cmr-6">4</span><span
8818 class="cmtt-8">codebook</span><span
8819 class="cmtt-8"> dimensions</span><span
8820 class="cmtt-8"> =</span><span
8821 class="cmtt-8"> 8</span><span
8822 class="cmtt-8"> </span><span
8823 class="cmtt-8"> encoded</span><span
8824 class="cmtt-8"> as:</span><span
8825 class="cmtt-8"> [</span><span
8826 class="cmtt-8"> 0</span><span
8827 class="cmtt-8"> 1</span><span
8828 class="cmtt-8"> 2</span><span
8829 class="cmtt-8"> 3</span><span
8830 class="cmtt-8"> 4</span><span
8831 class="cmtt-8"> 5</span><span
8832 class="cmtt-8"> 6</span><span
8833 class="cmtt-8"> 7</span><span
8834 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8835 id="x1-108010r5"></a><span
8836 class="cmr-6">5</span>
8837 <br class="fancyvrb" /><a
8838 id="x1-108012r6"></a><span
8839 class="cmr-6">6</span><span
8840 class="cmtt-8">codebook</span><span
8841 class="cmtt-8"> dimensions</span><span
8842 class="cmtt-8"> =</span><span
8843 class="cmtt-8"> 4</span><span
8844 class="cmtt-8"> </span><span
8845 class="cmtt-8"> encoded</span><span
8846 class="cmtt-8"> as:</span><span
8847 class="cmtt-8"> [</span><span
8848 class="cmtt-8"> 0</span><span
8849 class="cmtt-8"> 1</span><span
8850 class="cmtt-8"> 2</span><span
8851 class="cmtt-8"> 3</span><span
8852 class="cmtt-8"> ],</span><span
8853 class="cmtt-8"> [</span><span
8854 class="cmtt-8"> 4</span><span
8855 class="cmtt-8"> 5</span><span
8856 class="cmtt-8"> 6</span><span
8857 class="cmtt-8"> 7</span><span
8858 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8859 id="x1-108014r7"></a><span
8860 class="cmr-6">7</span><br class="fancyvrb" /><a
8861 id="x1-108016r8"></a><span
8862 class="cmr-6">8</span><span
8863 class="cmtt-8">codebook</span><span
8864 class="cmtt-8"> dimensions</span><span
8865 class="cmtt-8"> =</span><span
8866 class="cmtt-8"> 2</span><span
8867 class="cmtt-8"> </span><span
8868 class="cmtt-8"> encoded</span><span
8869 class="cmtt-8"> as:</span><span
8870 class="cmtt-8"> [</span><span
8871 class="cmtt-8"> 0</span><span
8872 class="cmtt-8"> 1</span><span
8873 class="cmtt-8"> ],</span><span
8874 class="cmtt-8"> [</span><span
8875 class="cmtt-8"> 2</span><span
8876 class="cmtt-8"> 3</span><span
8877 class="cmtt-8"> ],</span><span
8878 class="cmtt-8"> [</span><span
8879 class="cmtt-8"> 4</span><span
8880 class="cmtt-8"> 5</span><span
8881 class="cmtt-8"> ],</span><span
8882 class="cmtt-8"> [</span><span
8883 class="cmtt-8"> 6</span><span
8884 class="cmtt-8"> 7</span><span
8885 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8886 id="x1-108018r9"></a><span
8887 class="cmr-6">9</span>
8888 <br class="fancyvrb" /><a
8889 id="x1-108020r10"></a><span
8890 class="cmr-6">10</span><span
8891 class="cmtt-8">codebook</span><span
8892 class="cmtt-8"> dimensions</span><span
8893 class="cmtt-8"> =</span><span
8894 class="cmtt-8"> 1</span><span
8895 class="cmtt-8"> </span><span
8896 class="cmtt-8"> encoded</span><span
8897 class="cmtt-8"> as:</span><span
8898 class="cmtt-8"> [</span><span
8899 class="cmtt-8"> 0</span><span
8900 class="cmtt-8"> ],</span><span
8901 class="cmtt-8"> [</span><span
8902 class="cmtt-8"> 1</span><span
8903 class="cmtt-8"> ],</span><span
8904 class="cmtt-8"> [</span><span
8905 class="cmtt-8"> 2</span><span
8906 class="cmtt-8"> ],</span><span
8907 class="cmtt-8"> [</span><span
8908 class="cmtt-8"> 3</span><span
8909 class="cmtt-8"> ],</span><span
8910 class="cmtt-8"> [</span><span
8911 class="cmtt-8"> 4</span><span
8912 class="cmtt-8"> ],</span><span
8913 class="cmtt-8"> [</span><span
8914 class="cmtt-8"> 5</span><span
8915 class="cmtt-8"> ],</span><span
8916 class="cmtt-8"> [</span><span
8917 class="cmtt-8"> 6</span><span
8918 class="cmtt-8"> ],</span><span
8919 class="cmtt-8"> [</span><span
8920 class="cmtt-8"> 7</span><span
8921 class="cmtt-8"> ]</span><br class="fancyvrb" /><a
8922 id="x1-108022r11"></a><span
8923 class="cmr-6">11</span></div>
8924 <!--l. 136--><p class="noindent" >
8925 <h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a
8926 id="x1-1090008.5"></a>residue 2</h4>
8927 <!--l. 138--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
8928 passed-in vectors as in residue type 1, the <span
8929 class="cmti-12">ch </span>passed in vectors of length <span
8930 class="cmti-12">n </span>are first interleaved
8931 and flattened into a single vector of length <span
8932 class="cmti-12">ch</span>*<span
8933 class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
8934 is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
8935 residue type 1 and type 2 are equivalent.
8941 <!--l. 146--><p class="noindent" >
8943 <!--l. 147--><p class="noindent" ><img
8944 src="residue2.png" alt="PIC"
8946 <br /> <div class="caption"
8947 ><span class="id">Figure 12: </span><span
8948 class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10900112 -->
8950 <!--l. 152--><p class="noindent" >
8951 <h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a
8952 id="x1-1100008.6"></a>Residue decode</h4>
8953 <!--l. 154--><p class="noindent" >
8954 <h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a
8955 id="x1-1110008.6.1"></a>header decode</h5>
8956 <!--l. 156--><p class="noindent" >Header decode for all three residue types is identical.
8957 <div class="fancyvrb" id="fancyvrb35"><a
8958 id="x1-111002r1"></a><span
8959 class="cmr-6">1</span><span
8960 class="cmtt-8"> </span><span
8961 class="cmtt-8"> 1)</span><span
8962 class="cmtt-8"> [residue\_begin]</span><span
8963 class="cmtt-8"> =</span><span
8964 class="cmtt-8"> read</span><span
8965 class="cmtt-8"> 24</span><span
8966 class="cmtt-8"> bits</span><span
8967 class="cmtt-8"> as</span><span
8968 class="cmtt-8"> unsigned</span><span
8969 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
8970 id="x1-111004r2"></a><span
8971 class="cmr-6">2</span><span
8972 class="cmtt-8"> </span><span
8973 class="cmtt-8"> 2)</span><span
8974 class="cmtt-8"> [residue\_end]</span><span
8975 class="cmtt-8"> =</span><span
8976 class="cmtt-8"> read</span><span
8977 class="cmtt-8"> 24</span><span
8978 class="cmtt-8"> bits</span><span
8979 class="cmtt-8"> as</span><span
8980 class="cmtt-8"> unsigned</span><span
8981 class="cmtt-8"> integer</span>
8982 <br class="fancyvrb" /><a
8983 id="x1-111006r3"></a><span
8984 class="cmr-6">3</span><span
8985 class="cmtt-8"> </span><span
8986 class="cmtt-8"> 3)</span><span
8987 class="cmtt-8"> [residue\_partition\_size]</span><span
8988 class="cmtt-8"> =</span><span
8989 class="cmtt-8"> read</span><span
8990 class="cmtt-8"> 24</span><span
8991 class="cmtt-8"> bits</span><span
8992 class="cmtt-8"> as</span><span
8993 class="cmtt-8"> unsigned</span><span
8994 class="cmtt-8"> integer</span><span
8995 class="cmtt-8"> and</span><span
8996 class="cmtt-8"> add</span><span
8997 class="cmtt-8"> one</span>
8998 <br class="fancyvrb" /><a
8999 id="x1-111008r4"></a><span
9000 class="cmr-6">4</span><span
9001 class="cmtt-8"> </span><span
9002 class="cmtt-8"> 4)</span><span
9003 class="cmtt-8"> [residue\_classifications]</span><span
9004 class="cmtt-8"> =</span><span
9005 class="cmtt-8"> read</span><span
9006 class="cmtt-8"> 6</span><span
9007 class="cmtt-8"> bits</span><span
9008 class="cmtt-8"> as</span><span
9009 class="cmtt-8"> unsigned</span><span
9010 class="cmtt-8"> integer</span><span
9011 class="cmtt-8"> and</span><span
9012 class="cmtt-8"> add</span><span
9013 class="cmtt-8"> one</span><br class="fancyvrb" /><a
9014 id="x1-111010r5"></a><span
9015 class="cmr-6">5</span><span
9016 class="cmtt-8"> </span><span
9017 class="cmtt-8"> 5)</span><span
9018 class="cmtt-8"> [residue\_classbook]</span><span
9019 class="cmtt-8"> =</span><span
9020 class="cmtt-8"> read</span><span
9021 class="cmtt-8"> 8</span><span
9022 class="cmtt-8"> bits</span><span
9023 class="cmtt-8"> as</span><span
9024 class="cmtt-8"> unsigned</span><span
9025 class="cmtt-8"> integer</span></div>
9026 <!--l. 165--><p class="noindent" ><span
9027 class="cmtt-12">[residue</span><span
9028 class="cmtt-12">_begin] </span>and <span
9029 class="cmtt-12">[residue</span><span
9030 class="cmtt-12">_end] </span>select the specific sub-portion of each vector that is
9031 actually coded; it implements akin to a bandpass where, for coding purposes, the vector
9032 effectively begins at element <span
9033 class="cmtt-12">[residue</span><span
9034 class="cmtt-12">_begin] </span>and ends at <span
9035 class="cmtt-12">[residue</span><span
9036 class="cmtt-12">_end]</span>. Preceding and
9037 following values in the unpacked vectors are zeroed. Note that for residue type 2, these
9038 values as well as <span
9039 class="cmtt-12">[residue</span><span
9040 class="cmtt-12">_partition</span><span
9041 class="cmtt-12">_size]</span>apply to the interleaved vector, not the
9042 individual vectors before interleave. <span
9043 class="cmtt-12">[residue</span><span
9044 class="cmtt-12">_partition</span><span
9045 class="cmtt-12">_size] </span>is as explained above,
9047 class="cmtt-12">[residue</span><span
9048 class="cmtt-12">_classifications] </span>is the number of possible classification to which a partition can
9050 class="cmtt-12">[residue</span><span
9051 class="cmtt-12">_classbook] </span>is the codebook number used to code classification
9052 codewords. The number of dimensions in book <span
9053 class="cmtt-12">[residue</span><span
9054 class="cmtt-12">_classbook] </span>determines how
9055 many classification values are grouped into a single classification codeword. Note that
9056 the number of entries and dimensions in book <span
9057 class="cmtt-12">[residue</span><span
9058 class="cmtt-12">_classbook]</span>, along with
9060 class="cmtt-12">[residue</span><span
9061 class="cmtt-12">_classifications]</span>, overdetermines to possible number of classification
9063 class="cmtt-12">[residue</span><span
9064 class="cmtt-12">_classifications]</span>ˆ<span
9065 class="cmtt-12">[residue</span><span
9066 class="cmtt-12">_classbook]</span>.dimensions exceeds
9068 class="cmtt-12">[residue</span><span
9069 class="cmtt-12">_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
9073 <!--l. 189--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
9075 <!--l. 192--><p class="noindent" >
9076 <div class="fancyvrb" id="fancyvrb36"><a
9077 id="x1-111012r1"></a><span
9078 class="cmr-6">1</span><span
9079 class="cmtt-8"> </span><span
9080 class="cmtt-8"> 1)</span><span
9081 class="cmtt-8"> iterate</span><span
9082 class="cmtt-8"> [i]</span><span
9083 class="cmtt-8"> over</span><span
9084 class="cmtt-8"> the</span><span
9085 class="cmtt-8"> range</span><span
9086 class="cmtt-8"> 0</span><span
9087 class="cmtt-8"> ...</span><span
9088 class="cmtt-8"> [residue\_classifications]-1</span><span
9089 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9090 id="x1-111014r2"></a><span
9091 class="cmr-6">2</span><br class="fancyvrb" /><a
9092 id="x1-111016r3"></a><span
9093 class="cmr-6">3</span><span
9094 class="cmtt-8"> </span><span
9095 class="cmtt-8"> </span><span
9096 class="cmtt-8"> </span><span
9097 class="cmtt-8"> </span><span
9098 class="cmtt-8"> </span><span
9099 class="cmtt-8"> </span><span
9100 class="cmtt-8"> 2)</span><span
9101 class="cmtt-8"> [high\_bits]</span><span
9102 class="cmtt-8"> =</span><span
9103 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
9104 id="x1-111018r4"></a><span
9105 class="cmr-6">4</span><span
9106 class="cmtt-8"> </span><span
9107 class="cmtt-8"> </span><span
9108 class="cmtt-8"> </span><span
9109 class="cmtt-8"> </span><span
9110 class="cmtt-8"> </span><span
9111 class="cmtt-8"> </span><span
9112 class="cmtt-8"> 3)</span><span
9113 class="cmtt-8"> [low\_bits]</span><span
9114 class="cmtt-8"> =</span><span
9115 class="cmtt-8"> read</span><span
9116 class="cmtt-8"> 3</span><span
9117 class="cmtt-8"> bits</span><span
9118 class="cmtt-8"> as</span><span
9119 class="cmtt-8"> unsigned</span><span
9120 class="cmtt-8"> integer</span>
9121 <br class="fancyvrb" /><a
9122 id="x1-111020r5"></a><span
9123 class="cmr-6">5</span><span
9124 class="cmtt-8"> </span><span
9125 class="cmtt-8"> </span><span
9126 class="cmtt-8"> </span><span
9127 class="cmtt-8"> </span><span
9128 class="cmtt-8"> </span><span
9129 class="cmtt-8"> </span><span
9130 class="cmtt-8"> 4)</span><span
9131 class="cmtt-8"> [bitflag]</span><span
9132 class="cmtt-8"> =</span><span
9133 class="cmtt-8"> read</span><span
9134 class="cmtt-8"> one</span><span
9135 class="cmtt-8"> bit</span><span
9136 class="cmtt-8"> as</span><span
9137 class="cmtt-8"> boolean</span><br class="fancyvrb" /><a
9138 id="x1-111022r6"></a><span
9139 class="cmr-6">6</span><span
9140 class="cmtt-8"> </span><span
9141 class="cmtt-8"> </span><span
9142 class="cmtt-8"> </span><span
9143 class="cmtt-8"> </span><span
9144 class="cmtt-8"> </span><span
9145 class="cmtt-8"> </span><span
9146 class="cmtt-8"> 5)</span><span
9147 class="cmtt-8"> if</span><span
9148 class="cmtt-8"> (</span><span
9149 class="cmtt-8"> [bitflag]</span><span
9150 class="cmtt-8"> is</span><span
9151 class="cmtt-8"> set</span><span
9152 class="cmtt-8"> )</span><span
9153 class="cmtt-8"> then</span><span
9154 class="cmtt-8"> [high\_bits]</span><span
9155 class="cmtt-8"> =</span><span
9156 class="cmtt-8"> read</span><span
9157 class="cmtt-8"> five</span><span
9158 class="cmtt-8"> bits</span><span
9159 class="cmtt-8"> as</span><span
9160 class="cmtt-8"> unsigned</span><span
9161 class="cmtt-8"> integer</span>
9162 <br class="fancyvrb" /><a
9163 id="x1-111024r7"></a><span
9164 class="cmr-6">7</span><span
9165 class="cmtt-8"> </span><span
9166 class="cmtt-8"> </span><span
9167 class="cmtt-8"> </span><span
9168 class="cmtt-8"> </span><span
9169 class="cmtt-8"> </span><span
9170 class="cmtt-8"> </span><span
9171 class="cmtt-8"> 6)</span><span
9172 class="cmtt-8"> vector</span><span
9173 class="cmtt-8"> [residue\_cascade]</span><span
9174 class="cmtt-8"> element</span><span
9175 class="cmtt-8"> [i]</span><span
9176 class="cmtt-8"> =</span><span
9177 class="cmtt-8"> [high\_bits]</span><span
9178 class="cmtt-8"> *</span><span
9179 class="cmtt-8"> 8</span><span
9180 class="cmtt-8"> +</span><span
9181 class="cmtt-8"> [low\_bits]</span><br class="fancyvrb" /><a
9182 id="x1-111026r8"></a><span
9183 class="cmr-6">8</span><span
9184 class="cmtt-8"> </span><span
9185 class="cmtt-8"> </span><span
9186 class="cmtt-8"> </span><span
9187 class="cmtt-8"> </span><span
9188 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9189 id="x1-111028r9"></a><span
9190 class="cmr-6">9</span><span
9191 class="cmtt-8"> </span><span
9192 class="cmtt-8"> 7)</span><span
9193 class="cmtt-8"> done</span></div>
9194 <!--l. 204--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
9195 bitmap. We loop over the possible codebook classifications and the maximum possible number of
9196 encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
9198 <!--l. 210--><p class="noindent" >
9199 <div class="fancyvrb" id="fancyvrb37"><a
9200 id="x1-111030r1"></a><span
9201 class="cmr-6">1</span><span
9202 class="cmtt-8"> </span><span
9203 class="cmtt-8"> 1)</span><span
9204 class="cmtt-8"> iterate</span><span
9205 class="cmtt-8"> [i]</span><span
9206 class="cmtt-8"> over</span><span
9207 class="cmtt-8"> the</span><span
9208 class="cmtt-8"> range</span><span
9209 class="cmtt-8"> 0</span><span
9210 class="cmtt-8"> ...</span><span
9211 class="cmtt-8"> [residue\_classifications]-1</span><span
9212 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9213 id="x1-111032r2"></a><span
9214 class="cmr-6">2</span><br class="fancyvrb" /><a
9215 id="x1-111034r3"></a><span
9216 class="cmr-6">3</span><span
9217 class="cmtt-8"> </span><span
9218 class="cmtt-8"> </span><span
9219 class="cmtt-8"> </span><span
9220 class="cmtt-8"> </span><span
9221 class="cmtt-8"> </span><span
9222 class="cmtt-8"> </span><span
9223 class="cmtt-8"> 2)</span><span
9224 class="cmtt-8"> iterate</span><span
9225 class="cmtt-8"> [j]</span><span
9226 class="cmtt-8"> over</span><span
9227 class="cmtt-8"> the</span><span
9228 class="cmtt-8"> range</span><span
9229 class="cmtt-8"> 0</span><span
9230 class="cmtt-8"> ...</span><span
9231 class="cmtt-8"> 7</span><span
9232 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9233 id="x1-111036r4"></a><span
9234 class="cmr-6">4</span>
9235 <br class="fancyvrb" /><a
9236 id="x1-111038r5"></a><span
9237 class="cmr-6">5</span><span
9238 class="cmtt-8"> </span><span
9239 class="cmtt-8"> </span><span
9240 class="cmtt-8"> </span><span
9241 class="cmtt-8"> </span><span
9242 class="cmtt-8"> </span><span
9243 class="cmtt-8"> </span><span
9244 class="cmtt-8"> </span><span
9245 class="cmtt-8"> </span><span
9246 class="cmtt-8"> </span><span
9247 class="cmtt-8"> </span><span
9248 class="cmtt-8"> </span><span
9249 class="cmtt-8"> 3)</span><span
9250 class="cmtt-8"> if</span><span
9251 class="cmtt-8"> (</span><span
9252 class="cmtt-8"> vector</span><span
9253 class="cmtt-8"> [residue\_cascade]</span><span
9254 class="cmtt-8"> element</span><span
9255 class="cmtt-8"> [i]</span><span
9256 class="cmtt-8"> bit</span><span
9257 class="cmtt-8"> [j]</span><span
9258 class="cmtt-8"> is</span><span
9259 class="cmtt-8"> set</span><span
9260 class="cmtt-8"> )</span><span
9261 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9262 id="x1-111040r6"></a><span
9263 class="cmr-6">6</span>
9264 <br class="fancyvrb" /><a
9265 id="x1-111042r7"></a><span
9266 class="cmr-6">7</span><span
9267 class="cmtt-8"> </span><span
9268 class="cmtt-8"> </span><span
9269 class="cmtt-8"> </span><span
9270 class="cmtt-8"> </span><span
9271 class="cmtt-8"> </span><span
9272 class="cmtt-8"> </span><span
9273 class="cmtt-8"> </span><span
9274 class="cmtt-8"> </span><span
9275 class="cmtt-8"> </span><span
9276 class="cmtt-8"> </span><span
9277 class="cmtt-8"> </span><span
9278 class="cmtt-8"> </span><span
9279 class="cmtt-8"> </span><span
9280 class="cmtt-8"> </span><span
9281 class="cmtt-8"> </span><span
9282 class="cmtt-8"> </span><span
9283 class="cmtt-8"> 4)</span><span
9284 class="cmtt-8"> array</span><span
9285 class="cmtt-8"> [residue\_books]</span><span
9286 class="cmtt-8"> element</span><span
9287 class="cmtt-8"> [i][j]</span><span
9288 class="cmtt-8"> =</span><span
9289 class="cmtt-8"> read</span><span
9290 class="cmtt-8"> 8</span><span
9291 class="cmtt-8"> bits</span><span
9292 class="cmtt-8"> as</span><span
9293 class="cmtt-8"> unsigned</span><span
9294 class="cmtt-8"> integer</span><br class="fancyvrb" /><a
9295 id="x1-111044r8"></a><span
9296 class="cmr-6">8</span><br class="fancyvrb" /><a
9297 id="x1-111046r9"></a><span
9298 class="cmr-6">9</span><span
9299 class="cmtt-8"> </span><span
9300 class="cmtt-8"> </span><span
9301 class="cmtt-8"> </span><span
9302 class="cmtt-8"> </span><span
9303 class="cmtt-8"> </span><span
9304 class="cmtt-8"> </span><span
9305 class="cmtt-8"> </span><span
9306 class="cmtt-8"> </span><span
9307 class="cmtt-8"> </span><span
9308 class="cmtt-8"> </span><span
9309 class="cmtt-8"> </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"> else</span><span
9315 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9316 id="x1-111048r10"></a><span
9317 class="cmr-6">10</span>
9318 <br class="fancyvrb" /><a
9319 id="x1-111050r11"></a><span
9320 class="cmr-6">11</span><span
9321 class="cmtt-8"> </span><span
9322 class="cmtt-8"> </span><span
9323 class="cmtt-8"> </span><span
9324 class="cmtt-8"> </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"> </span><span
9334 class="cmtt-8"> </span><span
9335 class="cmtt-8"> </span><span
9336 class="cmtt-8"> </span><span
9337 class="cmtt-8"> 5)</span><span
9338 class="cmtt-8"> array</span><span
9339 class="cmtt-8"> [residue\_books]</span><span
9340 class="cmtt-8"> element</span><span
9341 class="cmtt-8"> [i][j]</span><span
9342 class="cmtt-8"> =</span><span
9343 class="cmtt-8"> unused</span><br class="fancyvrb" /><a
9344 id="x1-111052r12"></a><span
9345 class="cmr-6">12</span><br class="fancyvrb" /><a
9346 id="x1-111054r13"></a><span
9347 class="cmr-6">13</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"> </span><span
9353 class="cmtt-8"> </span><span
9354 class="cmtt-8"> </span><span
9355 class="cmtt-8"> </span><span
9356 class="cmtt-8"> </span><span
9357 class="cmtt-8"> </span><span
9358 class="cmtt-8"> </span><span
9359 class="cmtt-8"> </span><span
9360 class="cmtt-8"> </span><span
9361 class="cmtt-8"> </span><span
9362 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9363 id="x1-111056r14"></a><span
9364 class="cmr-6">14</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"> </span><span
9372 class="cmtt-8"> </span><span
9373 class="cmtt-8"> </span><span
9374 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9375 id="x1-111058r15"></a><span
9376 class="cmr-6">15</span><span
9377 class="cmtt-8"> </span><span
9378 class="cmtt-8"> </span><span
9379 class="cmtt-8"> </span><span
9380 class="cmtt-8"> </span><span
9381 class="cmtt-8"> </span><span
9382 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9383 id="x1-111060r16"></a><span
9384 class="cmr-6">16</span><br class="fancyvrb" /><a
9385 id="x1-111062r17"></a><span
9386 class="cmr-6">17</span><span
9387 class="cmtt-8"> </span><span
9388 class="cmtt-8"> 6)</span><span
9389 class="cmtt-8"> done</span></div>
9390 <!--l. 230--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable.
9391 In addition, any codebook number greater than the maximum numbered codebook
9392 set up in this stream also renders the stream undecodable. All codebooks in array
9393 [residue_books] are required to have a value mapping. The presence of codebook in array
9394 [residue_books] without a value mapping (maptype equals zero) renders the stream
9396 <!--l. 240--><p class="noindent" >
9397 <h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a
9398 id="x1-1120008.6.2"></a>packet decode</h5>
9399 <!--l. 242--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
9400 decode can be built out of the format 1 decode process. Thus we describe first the decode
9401 infrastructure identical to all three formats.
9402 <!--l. 247--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
9403 vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
9404 decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
9405 decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
9406 allocated and zeroed.
9407 <!--l. 254--><p class="noindent" >Depending on the values of <span
9408 class="cmtt-12">[residue</span><span
9409 class="cmtt-12">_begin] </span>and <span
9410 class="cmtt-12">[residue</span><span
9411 class="cmtt-12">_end]</span>, it is obvious that the
9412 encoded portion of a residue vector may be the entire possible residue vector or some other strict
9413 subset of the actual residue vector size with zero padding at either uncoded end. However, it is
9414 also possible to set <span
9415 class="cmtt-12">[residue</span><span
9416 class="cmtt-12">_begin] </span>and <span
9417 class="cmtt-12">[residue</span><span
9418 class="cmtt-12">_end] </span>to specify a range partially or wholly
9422 beyond the maximum vector size. Before beginning residue decode, limit <span
9423 class="cmtt-12">[residue</span><span
9424 class="cmtt-12">_begin]</span>
9426 class="cmtt-12">[residue</span><span
9427 class="cmtt-12">_end] </span>to the maximum possible vector size as follows. We assume that
9428 the number of vectors being encoded, <span
9429 class="cmtt-12">[ch] </span>is provided by the higher level decoding
9431 <!--l. 268--><p class="noindent" >
9432 <div class="fancyvrb" id="fancyvrb38"><a
9433 id="x1-112002r1"></a><span
9434 class="cmr-6">1</span><span
9435 class="cmtt-8"> </span><span
9436 class="cmtt-8"> 1)</span><span
9437 class="cmtt-8"> [actual\_size]</span><span
9438 class="cmtt-8"> =</span><span
9439 class="cmtt-8"> current</span><span
9440 class="cmtt-8"> blocksize/2;</span><br class="fancyvrb" /><a
9441 id="x1-112004r2"></a><span
9442 class="cmr-6">2</span><span
9443 class="cmtt-8"> </span><span
9444 class="cmtt-8"> 2)</span><span
9445 class="cmtt-8"> if</span><span
9446 class="cmtt-8"> residue</span><span
9447 class="cmtt-8"> encoding</span><span
9448 class="cmtt-8"> is</span><span
9449 class="cmtt-8"> format</span><span
9450 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
9451 id="x1-112006r3"></a><span
9452 class="cmr-6">3</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"> 3)</span><span
9460 class="cmtt-8"> [actual\_size]</span><span
9461 class="cmtt-8"> =</span><span
9462 class="cmtt-8"> [actual\_size]</span><span
9463 class="cmtt-8"> *</span><span
9464 class="cmtt-8"> [ch];</span>
9465 <br class="fancyvrb" /><a
9466 id="x1-112008r4"></a><span
9467 class="cmr-6">4</span><span
9468 class="cmtt-8"> </span><span
9469 class="cmtt-8"> 4)</span><span
9470 class="cmtt-8"> [limit\_residue\_begin]</span><span
9471 class="cmtt-8"> =</span><span
9472 class="cmtt-8"> minimum</span><span
9473 class="cmtt-8"> of</span><span
9474 class="cmtt-8"> ([residue\_begin],[actual\_size]);</span><br class="fancyvrb" /><a
9475 id="x1-112010r5"></a><span
9476 class="cmr-6">5</span><span
9477 class="cmtt-8"> </span><span
9478 class="cmtt-8"> 5)</span><span
9479 class="cmtt-8"> [limit\_residue\_end]</span><span
9480 class="cmtt-8"> =</span><span
9481 class="cmtt-8"> minimum</span><span
9482 class="cmtt-8"> of</span><span
9483 class="cmtt-8"> ([residue\_end],[actual\_size]);</span></div>
9484 <!--l. 276--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
9485 <!--l. 279--><p class="noindent" >
9486 <div class="fancyvrb" id="fancyvrb39"><a
9487 id="x1-112012r1"></a><span
9488 class="cmr-6">1</span><span
9489 class="cmtt-8"> </span><span
9490 class="cmtt-8"> 1)</span><span
9491 class="cmtt-8"> [classwords\_per\_codeword]</span><span
9492 class="cmtt-8"> =</span><span
9493 class="cmtt-8"> [codebook\_dimensions]</span><span
9494 class="cmtt-8"> value</span><span
9495 class="cmtt-8"> of</span><span
9496 class="cmtt-8"> codebook</span><span
9497 class="cmtt-8"> [residue\_classbook]</span>
9498 <br class="fancyvrb" /><a
9499 id="x1-112014r2"></a><span
9500 class="cmr-6">2</span><span
9501 class="cmtt-8"> </span><span
9502 class="cmtt-8"> 2)</span><span
9503 class="cmtt-8"> [n\_to\_read]</span><span
9504 class="cmtt-8"> =</span><span
9505 class="cmtt-8"> [limit\_residue\_end]</span><span
9506 class="cmtt-8"> -</span><span
9507 class="cmtt-8"> [limit\_residue\_begin]</span><br class="fancyvrb" /><a
9508 id="x1-112016r3"></a><span
9509 class="cmr-6">3</span><span
9510 class="cmtt-8"> </span><span
9511 class="cmtt-8"> 3)</span><span
9512 class="cmtt-8"> [partitions\_to\_read]</span><span
9513 class="cmtt-8"> =</span><span
9514 class="cmtt-8"> [n\_to\_read]</span><span
9515 class="cmtt-8"> /</span><span
9516 class="cmtt-8"> [residue\_partition\_size]</span></div>
9517 <!--l. 285--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
9518 <div class="fancyvrb" id="fancyvrb40"><a
9519 id="x1-112018r1"></a><span
9520 class="cmr-6">1</span><span
9521 class="cmtt-8"> </span><span
9522 class="cmtt-8"> 1)</span><span
9523 class="cmtt-8"> allocate</span><span
9524 class="cmtt-8"> and</span><span
9525 class="cmtt-8"> zero</span><span
9526 class="cmtt-8"> all</span><span
9527 class="cmtt-8"> vectors</span><span
9528 class="cmtt-8"> that</span><span
9529 class="cmtt-8"> will</span><span
9530 class="cmtt-8"> be</span><span
9531 class="cmtt-8"> returned.</span><br class="fancyvrb" /><a
9532 id="x1-112020r2"></a><span
9533 class="cmr-6">2</span><span
9534 class="cmtt-8"> </span><span
9535 class="cmtt-8"> 2)</span><span
9536 class="cmtt-8"> if</span><span
9537 class="cmtt-8"> ([n\_to\_read]</span><span
9538 class="cmtt-8"> is</span><span
9539 class="cmtt-8"> zero),</span><span
9540 class="cmtt-8"> stop;</span><span
9541 class="cmtt-8"> there</span><span
9542 class="cmtt-8"> is</span><span
9543 class="cmtt-8"> no</span><span
9544 class="cmtt-8"> residue</span><span
9545 class="cmtt-8"> to</span><span
9546 class="cmtt-8"> decode.</span>
9547 <br class="fancyvrb" /><a
9548 id="x1-112022r3"></a><span
9549 class="cmr-6">3</span><span
9550 class="cmtt-8"> </span><span
9551 class="cmtt-8"> 3)</span><span
9552 class="cmtt-8"> iterate</span><span
9553 class="cmtt-8"> [pass]</span><span
9554 class="cmtt-8"> over</span><span
9555 class="cmtt-8"> the</span><span
9556 class="cmtt-8"> range</span><span
9557 class="cmtt-8"> 0</span><span
9558 class="cmtt-8"> ...</span><span
9559 class="cmtt-8"> 7</span><span
9560 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9561 id="x1-112024r4"></a><span
9562 class="cmr-6">4</span><br class="fancyvrb" /><a
9563 id="x1-112026r5"></a><span
9564 class="cmr-6">5</span><span
9565 class="cmtt-8"> </span><span
9566 class="cmtt-8"> </span><span
9567 class="cmtt-8"> </span><span
9568 class="cmtt-8"> </span><span
9569 class="cmtt-8"> </span><span
9570 class="cmtt-8"> </span><span
9571 class="cmtt-8"> 4)</span><span
9572 class="cmtt-8"> [partition\_count]</span><span
9573 class="cmtt-8"> =</span><span
9574 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
9575 id="x1-112028r6"></a><span
9576 class="cmr-6">6</span>
9577 <br class="fancyvrb" /><a
9578 id="x1-112030r7"></a><span
9579 class="cmr-6">7</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"> 5)</span><span
9587 class="cmtt-8"> while</span><span
9588 class="cmtt-8"> [partition\_count]</span><span
9589 class="cmtt-8"> is</span><span
9590 class="cmtt-8"> less</span><span
9591 class="cmtt-8"> than</span><span
9592 class="cmtt-8"> [partitions\_to\_read]</span><br class="fancyvrb" /><a
9593 id="x1-112032r8"></a><span
9594 class="cmr-6">8</span><br class="fancyvrb" /><a
9595 id="x1-112034r9"></a><span
9596 class="cmr-6">9</span><span
9597 class="cmtt-8"> </span><span
9598 class="cmtt-8"> </span><span
9599 class="cmtt-8"> </span><span
9600 class="cmtt-8"> </span><span
9601 class="cmtt-8"> </span><span
9602 class="cmtt-8"> </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"> 6)</span><span
9609 class="cmtt-8"> if</span><span
9610 class="cmtt-8"> ([pass]</span><span
9611 class="cmtt-8"> is</span><span
9612 class="cmtt-8"> zero)</span><span
9613 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9614 id="x1-112036r10"></a><span
9615 class="cmr-6">10</span>
9616 <br class="fancyvrb" /><a
9617 id="x1-112038r11"></a><span
9618 class="cmr-6">11</span><span
9619 class="cmtt-8"> </span><span
9620 class="cmtt-8"> </span><span
9621 class="cmtt-8"> </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><span
9634 class="cmtt-8"> </span><span
9635 class="cmtt-8"> 7)</span><span
9636 class="cmtt-8"> iterate</span><span
9637 class="cmtt-8"> [j]</span><span
9638 class="cmtt-8"> over</span><span
9639 class="cmtt-8"> the</span><span
9640 class="cmtt-8"> range</span><span
9641 class="cmtt-8"> 0</span><span
9642 class="cmtt-8"> ..</span><span
9643 class="cmtt-8"> [ch]-1</span><span
9644 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9645 id="x1-112040r12"></a><span
9646 class="cmr-6">12</span><br class="fancyvrb" /><a
9647 id="x1-112042r13"></a><span
9648 class="cmr-6">13</span><span
9649 class="cmtt-8"> </span><span
9650 class="cmtt-8"> </span><span
9651 class="cmtt-8"> </span><span
9652 class="cmtt-8"> </span><span
9653 class="cmtt-8"> </span><span
9654 class="cmtt-8"> </span><span
9655 class="cmtt-8"> </span><span
9656 class="cmtt-8"> </span><span
9657 class="cmtt-8"> </span><span
9658 class="cmtt-8"> </span><span
9659 class="cmtt-8"> </span><span
9660 class="cmtt-8"> </span><span
9661 class="cmtt-8"> </span><span
9662 class="cmtt-8"> </span><span
9663 class="cmtt-8"> </span><span
9664 class="cmtt-8"> </span><span
9665 class="cmtt-8"> </span><span
9666 class="cmtt-8"> </span><span
9667 class="cmtt-8"> </span><span
9668 class="cmtt-8"> </span><span
9669 class="cmtt-8"> </span><span
9670 class="cmtt-8"> 8)</span><span
9671 class="cmtt-8"> if</span><span
9672 class="cmtt-8"> vector</span><span
9673 class="cmtt-8"> [j]</span><span
9674 class="cmtt-8"> is</span><span
9675 class="cmtt-8"> not</span><span
9676 class="cmtt-8"> marked</span><span
9677 class="cmtt-8"> ’do</span><span
9678 class="cmtt-8"> not</span><span
9679 class="cmtt-8"> decode’</span><span
9680 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9681 id="x1-112044r14"></a><span
9682 class="cmr-6">14</span>
9683 <br class="fancyvrb" /><a
9684 id="x1-112046r15"></a><span
9685 class="cmr-6">15</span><span
9686 class="cmtt-8"> </span><span
9687 class="cmtt-8"> </span><span
9688 class="cmtt-8"> </span><span
9689 class="cmtt-8"> </span><span
9690 class="cmtt-8"> </span><span
9691 class="cmtt-8"> </span><span
9692 class="cmtt-8"> </span><span
9693 class="cmtt-8"> </span><span
9694 class="cmtt-8"> </span><span
9695 class="cmtt-8"> </span><span
9696 class="cmtt-8"> </span><span
9697 class="cmtt-8"> </span><span
9698 class="cmtt-8"> </span><span
9699 class="cmtt-8"> </span><span
9700 class="cmtt-8"> </span><span
9701 class="cmtt-8"> </span><span
9702 class="cmtt-8"> </span><span
9703 class="cmtt-8"> </span><span
9704 class="cmtt-8"> </span><span
9705 class="cmtt-8"> </span><span
9706 class="cmtt-8"> </span><span
9707 class="cmtt-8"> </span><span
9708 class="cmtt-8"> </span><span
9709 class="cmtt-8"> </span><span
9710 class="cmtt-8"> </span><span
9711 class="cmtt-8"> </span><span
9712 class="cmtt-8"> 9)</span><span
9713 class="cmtt-8"> [temp]</span><span
9714 class="cmtt-8"> =</span><span
9715 class="cmtt-8"> read</span><span
9716 class="cmtt-8"> from</span><span
9717 class="cmtt-8"> packet</span><span
9718 class="cmtt-8"> using</span><span
9719 class="cmtt-8"> codebook</span><span
9720 class="cmtt-8"> [residue\_classbook]</span><span
9721 class="cmtt-8"> in</span><span
9722 class="cmtt-8"> scalar</span><span
9723 class="cmtt-8"> context</span>
9724 <br class="fancyvrb" /><a
9725 id="x1-112048r16"></a><span
9726 class="cmr-6">16</span><span
9727 class="cmtt-8"> </span><span
9728 class="cmtt-8"> </span><span
9729 class="cmtt-8"> </span><span
9730 class="cmtt-8"> </span><span
9731 class="cmtt-8"> </span><span
9732 class="cmtt-8"> </span><span
9733 class="cmtt-8"> </span><span
9734 class="cmtt-8"> </span><span
9735 class="cmtt-8"> </span><span
9736 class="cmtt-8"> </span><span
9737 class="cmtt-8"> </span><span
9738 class="cmtt-8"> </span><span
9739 class="cmtt-8"> </span><span
9740 class="cmtt-8"> </span><span
9741 class="cmtt-8"> </span><span
9742 class="cmtt-8"> </span><span
9743 class="cmtt-8"> </span><span
9744 class="cmtt-8"> </span><span
9745 class="cmtt-8"> </span><span
9746 class="cmtt-8"> </span><span
9747 class="cmtt-8"> </span><span
9748 class="cmtt-8"> </span><span
9749 class="cmtt-8"> </span><span
9750 class="cmtt-8"> </span><span
9751 class="cmtt-8"> </span><span
9752 class="cmtt-8"> 10)</span><span
9753 class="cmtt-8"> iterate</span><span
9754 class="cmtt-8"> [i]</span><span
9755 class="cmtt-8"> descending</span><span
9756 class="cmtt-8"> over</span><span
9757 class="cmtt-8"> the</span><span
9758 class="cmtt-8"> range</span><span
9759 class="cmtt-8"> [classwords\_per\_codeword]-1</span><span
9760 class="cmtt-8"> ...</span><span
9761 class="cmtt-8"> 0</span><span
9762 class="cmtt-8"> {</span><br class="fancyvrb" /><a
9763 id="x1-112050r17"></a><span
9764 class="cmr-6">17</span>
9765 <br class="fancyvrb" /><a
9766 id="x1-112052r18"></a><span
9767 class="cmr-6">18</span><span
9768 class="cmtt-8"> </span><span
9769 class="cmtt-8"> </span><span
9770 class="cmtt-8"> </span><span
9771 class="cmtt-8"> </span><span
9772 class="cmtt-8"> </span><span
9773 class="cmtt-8"> </span><span
9774 class="cmtt-8"> </span><span
9775 class="cmtt-8"> </span><span
9776 class="cmtt-8"> </span><span
9777 class="cmtt-8"> </span><span
9778 class="cmtt-8"> </span><span
9779 class="cmtt-8"> </span><span
9780 class="cmtt-8"> </span><span
9781 class="cmtt-8"> </span><span
9782 class="cmtt-8"> </span><span
9783 class="cmtt-8"> </span><span
9784 class="cmtt-8"> </span><span
9785 class="cmtt-8"> </span><span
9786 class="cmtt-8"> </span><span
9787 class="cmtt-8"> </span><span
9788 class="cmtt-8"> </span><span
9789 class="cmtt-8"> </span><span
9790 class="cmtt-8"> </span><span
9791 class="cmtt-8"> </span><span
9792 class="cmtt-8"> </span><span
9793 class="cmtt-8"> </span><span
9794 class="cmtt-8"> </span><span
9795 class="cmtt-8"> </span><span
9796 class="cmtt-8"> </span><span
9797 class="cmtt-8"> </span><span
9798 class="cmtt-8"> 11)</span><span
9799 class="cmtt-8"> array</span><span
9800 class="cmtt-8"> [classifications]</span><span
9801 class="cmtt-8"> element</span><span
9802 class="cmtt-8"> [j],([i]+[partition\_count])</span><span
9803 class="cmtt-8"> =</span>
9804 <br class="fancyvrb" /><a
9805 id="x1-112054r19"></a><span
9806 class="cmr-6">19</span><span
9807 class="cmtt-8"> </span><span
9808 class="cmtt-8"> </span><span
9809 class="cmtt-8"> </span><span
9810 class="cmtt-8"> </span><span
9811 class="cmtt-8"> </span><span
9812 class="cmtt-8"> </span><span
9813 class="cmtt-8"> </span><span
9814 class="cmtt-8"> </span><span
9815 class="cmtt-8"> </span><span
9816 class="cmtt-8"> </span><span
9817 class="cmtt-8"> </span><span
9818 class="cmtt-8"> </span><span
9819 class="cmtt-8"> </span><span
9820 class="cmtt-8"> </span><span
9821 class="cmtt-8"> </span><span
9822 class="cmtt-8"> </span><span
9823 class="cmtt-8"> </span><span
9824 class="cmtt-8"> </span><span
9825 class="cmtt-8"> </span><span
9826 class="cmtt-8"> </span><span
9827 class="cmtt-8"> </span><span
9828 class="cmtt-8"> </span><span
9829 class="cmtt-8"> </span><span
9830 class="cmtt-8"> </span><span
9831 class="cmtt-8"> </span><span
9832 class="cmtt-8"> </span><span
9833 class="cmtt-8"> </span><span
9834 class="cmtt-8"> </span><span
9835 class="cmtt-8"> </span><span
9836 class="cmtt-8"> </span><span
9837 class="cmtt-8"> </span><span
9838 class="cmtt-8"> </span><span
9839 class="cmtt-8"> </span><span
9840 class="cmtt-8"> </span><span
9841 class="cmtt-8"> [temp]</span><span
9842 class="cmtt-8"> integer</span><span
9843 class="cmtt-8"> modulo</span><span
9844 class="cmtt-8"> [residue\_classifications]</span>
9845 <br class="fancyvrb" /><a
9846 id="x1-112056r20"></a><span
9847 class="cmr-6">20</span><span
9848 class="cmtt-8"> </span><span
9849 class="cmtt-8"> </span><span
9850 class="cmtt-8"> </span><span
9851 class="cmtt-8"> </span><span
9852 class="cmtt-8"> </span><span
9853 class="cmtt-8"> </span><span
9854 class="cmtt-8"> </span><span
9855 class="cmtt-8"> </span><span
9856 class="cmtt-8"> </span><span
9857 class="cmtt-8"> </span><span
9858 class="cmtt-8"> </span><span
9859 class="cmtt-8"> </span><span
9860 class="cmtt-8"> </span><span
9861 class="cmtt-8"> </span><span
9862 class="cmtt-8"> </span><span
9863 class="cmtt-8"> </span><span
9864 class="cmtt-8"> </span><span
9865 class="cmtt-8"> </span><span
9866 class="cmtt-8"> </span><span
9867 class="cmtt-8"> </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"> </span><span
9877 class="cmtt-8"> </span><span
9878 class="cmtt-8"> 12)</span><span
9879 class="cmtt-8"> [temp]</span><span
9880 class="cmtt-8"> =</span><span
9881 class="cmtt-8"> [temp]</span><span
9882 class="cmtt-8"> /</span><span
9883 class="cmtt-8"> [residue\_classifications]</span><span
9884 class="cmtt-8"> using</span><span
9885 class="cmtt-8"> integer</span><span
9886 class="cmtt-8"> division</span><br class="fancyvrb" /><a
9887 id="x1-112058r21"></a><span
9888 class="cmr-6">21</span>
9889 <br class="fancyvrb" /><a
9890 id="x1-112060r22"></a><span
9891 class="cmr-6">22</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"> </span><span
9903 class="cmtt-8"> </span><span
9904 class="cmtt-8"> </span><span
9905 class="cmtt-8"> </span><span
9906 class="cmtt-8"> </span><span
9907 class="cmtt-8"> </span><span
9908 class="cmtt-8"> </span><span
9909 class="cmtt-8"> </span><span
9910 class="cmtt-8"> </span><span
9911 class="cmtt-8"> </span><span
9912 class="cmtt-8"> </span><span
9913 class="cmtt-8"> </span><span
9914 class="cmtt-8"> </span><span
9915 class="cmtt-8"> </span><span
9916 class="cmtt-8"> </span><span
9917 class="cmtt-8"> </span><span
9918 class="cmtt-8"> </span><span
9919 class="cmtt-8"> </span><span
9920 class="cmtt-8"> </span><span
9921 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9922 id="x1-112062r23"></a><span
9923 class="cmr-6">23</span><br class="fancyvrb" /><a
9924 id="x1-112064r24"></a><span
9925 class="cmr-6">24</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"> </span><span
9934 class="cmtt-8"> </span><span
9935 class="cmtt-8"> </span><span
9936 class="cmtt-8"> </span><span
9937 class="cmtt-8"> </span><span
9938 class="cmtt-8"> </span><span
9939 class="cmtt-8"> </span><span
9940 class="cmtt-8"> </span><span
9941 class="cmtt-8"> </span><span
9942 class="cmtt-8"> </span><span
9943 class="cmtt-8"> </span><span
9944 class="cmtt-8"> </span><span
9945 class="cmtt-8"> </span><span
9946 class="cmtt-8"> </span><span
9947 class="cmtt-8"> </span><span
9948 class="cmtt-8"> </span><span
9949 class="cmtt-8"> </span><span
9950 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9951 id="x1-112066r25"></a><span
9952 class="cmr-6">25</span><br class="fancyvrb" /><a
9953 id="x1-112068r26"></a><span
9954 class="cmr-6">26</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"> </span><span
9973 class="cmtt-8"> </span><span
9974 class="cmtt-8"> }</span><br class="fancyvrb" /><a
9975 id="x1-112070r27"></a><span
9976 class="cmr-6">27</span><br class="fancyvrb" /><a
9977 id="x1-112072r28"></a><span
9978 class="cmr-6">28</span><span
9979 class="cmtt-8"> </span><span
9980 class="cmtt-8"> </span><span
9981 class="cmtt-8"> </span><span
9982 class="cmtt-8"> </span><span
9983 class="cmtt-8"> </span><span
9984 class="cmtt-8"> </span><span
9985 class="cmtt-8"> </span><span
9986 class="cmtt-8"> </span><span
9987 class="cmtt-8"> </span><span
9988 class="cmtt-8"> </span><span
9989 class="cmtt-8"> </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><br class="fancyvrb" /><a
9994 id="x1-112074r29"></a><span
9995 class="cmr-6">29</span>
9996 <br class="fancyvrb" /><a
9997 id="x1-112076r30"></a><span
9998 class="cmr-6">30</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"> 13)</span><span
10010 class="cmtt-8"> iterate</span><span
10011 class="cmtt-8"> [i]</span><span
10012 class="cmtt-8"> over</span><span
10013 class="cmtt-8"> the</span><span
10014 class="cmtt-8"> range</span><span
10015 class="cmtt-8"> 0</span><span
10016 class="cmtt-8"> ..</span><span
10017 class="cmtt-8"> ([classwords\_per\_codeword]</span><span
10018 class="cmtt-8"> -</span><span
10019 class="cmtt-8"> 1)</span><span
10020 class="cmtt-8"> while</span><span
10021 class="cmtt-8"> [partition\_count]</span>
10022 <br class="fancyvrb" /><a
10023 id="x1-112078r31"></a><span
10024 class="cmr-6">31</span><span
10025 class="cmtt-8"> </span><span
10026 class="cmtt-8"> </span><span
10027 class="cmtt-8"> </span><span
10028 class="cmtt-8"> </span><span
10029 class="cmtt-8"> </span><span
10030 class="cmtt-8"> </span><span
10031 class="cmtt-8"> </span><span
10032 class="cmtt-8"> </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"> is</span><span
10040 class="cmtt-8"> also</span><span
10041 class="cmtt-8"> less</span><span
10042 class="cmtt-8"> than</span><span
10043 class="cmtt-8"> [partitions\_to\_read]</span><span
10044 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10045 id="x1-112080r32"></a><span
10046 class="cmr-6">32</span><br class="fancyvrb" /><a
10047 id="x1-112082r33"></a><span
10048 class="cmr-6">33</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"> </span><span
10061 class="cmtt-8"> </span><span
10062 class="cmtt-8"> </span><span
10063 class="cmtt-8"> </span><span
10064 class="cmtt-8"> </span><span
10065 class="cmtt-8"> 14)</span><span
10066 class="cmtt-8"> iterate</span><span
10067 class="cmtt-8"> [j]</span><span
10068 class="cmtt-8"> over</span><span
10069 class="cmtt-8"> the</span><span
10070 class="cmtt-8"> range</span><span
10071 class="cmtt-8"> 0</span><span
10072 class="cmtt-8"> ..</span><span
10073 class="cmtt-8"> [ch]-1</span><span
10074 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10075 id="x1-112084r34"></a><span
10076 class="cmr-6">34</span>
10077 <br class="fancyvrb" /><a
10078 id="x1-112086r35"></a><span
10079 class="cmr-6">35</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"> 15)</span><span
10102 class="cmtt-8"> if</span><span
10103 class="cmtt-8"> vector</span><span
10104 class="cmtt-8"> [j]</span><span
10105 class="cmtt-8"> is</span><span
10106 class="cmtt-8"> not</span><span
10107 class="cmtt-8"> marked</span><span
10108 class="cmtt-8"> ’do</span><span
10109 class="cmtt-8"> not</span><span
10110 class="cmtt-8"> decode’</span><span
10111 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10112 id="x1-112088r36"></a><span
10113 class="cmr-6">36</span>
10114 <br class="fancyvrb" /><a
10115 id="x1-112090r37"></a><span
10116 class="cmr-6">37</span><span
10117 class="cmtt-8"> </span><span
10118 class="cmtt-8"> </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"> 16)</span><span
10144 class="cmtt-8"> [vqclass]</span><span
10145 class="cmtt-8"> =</span><span
10146 class="cmtt-8"> array</span><span
10147 class="cmtt-8"> [classifications]</span><span
10148 class="cmtt-8"> element</span><span
10149 class="cmtt-8"> [j],[partition\_count]</span>
10150 <br class="fancyvrb" /><a
10151 id="x1-112092r38"></a><span
10152 class="cmr-6">38</span><span
10153 class="cmtt-8"> </span><span
10154 class="cmtt-8"> </span><span
10155 class="cmtt-8"> </span><span
10156 class="cmtt-8"> </span><span
10157 class="cmtt-8"> </span><span
10158 class="cmtt-8"> </span><span
10159 class="cmtt-8"> </span><span
10160 class="cmtt-8"> </span><span
10161 class="cmtt-8"> </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"> 17)</span><span
10180 class="cmtt-8"> [vqbook]</span><span
10181 class="cmtt-8"> =</span><span
10182 class="cmtt-8"> array</span><span
10183 class="cmtt-8"> [residue\_books]</span><span
10184 class="cmtt-8"> element</span><span
10185 class="cmtt-8"> [vqclass],[pass]</span><br class="fancyvrb" /><a
10186 id="x1-112094r39"></a><span
10187 class="cmr-6">39</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"> </span><span
10195 class="cmtt-8"> </span><span
10196 class="cmtt-8"> </span><span
10197 class="cmtt-8"> </span><span
10198 class="cmtt-8"> </span><span
10199 class="cmtt-8"> </span><span
10200 class="cmtt-8"> </span><span
10201 class="cmtt-8"> </span><span
10202 class="cmtt-8"> </span><span
10203 class="cmtt-8"> </span><span
10204 class="cmtt-8"> </span><span
10205 class="cmtt-8"> </span><span
10206 class="cmtt-8"> </span><span
10207 class="cmtt-8"> </span><span
10208 class="cmtt-8"> </span><span
10209 class="cmtt-8"> </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"> 18)</span><span
10215 class="cmtt-8"> if</span><span
10216 class="cmtt-8"> ([vqbook]</span><span
10217 class="cmtt-8"> is</span><span
10218 class="cmtt-8"> not</span><span
10219 class="cmtt-8"> ’unused’)</span><span
10220 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10221 id="x1-112096r40"></a><span
10222 class="cmr-6">40</span>
10223 <br class="fancyvrb" /><a
10224 id="x1-112098r41"></a><span
10225 class="cmr-6">41</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><span
10242 class="cmtt-8"> </span><span
10243 class="cmtt-8"> </span><span
10244 class="cmtt-8"> </span><span
10245 class="cmtt-8"> </span><span
10246 class="cmtt-8"> </span><span
10247 class="cmtt-8"> </span><span
10248 class="cmtt-8"> </span><span
10249 class="cmtt-8"> </span><span
10250 class="cmtt-8"> </span><span
10251 class="cmtt-8"> </span><span
10252 class="cmtt-8"> </span><span
10253 class="cmtt-8"> </span><span
10254 class="cmtt-8"> </span><span
10255 class="cmtt-8"> </span><span
10256 class="cmtt-8"> </span><span
10257 class="cmtt-8"> 19)</span><span
10258 class="cmtt-8"> decode</span><span
10259 class="cmtt-8"> partition</span><span
10260 class="cmtt-8"> into</span><span
10261 class="cmtt-8"> output</span><span
10262 class="cmtt-8"> vector</span><span
10263 class="cmtt-8"> number</span><span
10264 class="cmtt-8"> [j],</span><span
10265 class="cmtt-8"> starting</span><span
10266 class="cmtt-8"> at</span><span
10267 class="cmtt-8"> scalar</span>
10268 <br class="fancyvrb" /><a
10269 id="x1-112100r42"></a><span
10270 class="cmr-6">42</span><span
10271 class="cmtt-8"> </span><span
10272 class="cmtt-8"> </span><span
10273 class="cmtt-8"> </span><span
10274 class="cmtt-8"> </span><span
10275 class="cmtt-8"> </span><span
10276 class="cmtt-8"> </span><span
10277 class="cmtt-8"> </span><span
10278 class="cmtt-8"> </span><span
10279 class="cmtt-8"> </span><span
10280 class="cmtt-8"> </span><span
10281 class="cmtt-8"> </span><span
10282 class="cmtt-8"> </span><span
10283 class="cmtt-8"> </span><span
10284 class="cmtt-8"> </span><span
10285 class="cmtt-8"> </span><span
10286 class="cmtt-8"> </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><span
10303 class="cmtt-8"> </span><span
10304 class="cmtt-8"> </span><span
10305 class="cmtt-8"> </span><span
10306 class="cmtt-8"> offset</span><span
10307 class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span
10308 class="cmtt-8"> using</span>
10309 <br class="fancyvrb" /><a
10310 id="x1-112102r43"></a><span
10311 class="cmr-6">43</span><span
10312 class="cmtt-8"> </span><span
10313 class="cmtt-8"> </span><span
10314 class="cmtt-8"> </span><span
10315 class="cmtt-8"> </span><span
10316 class="cmtt-8"> </span><span
10317 class="cmtt-8"> </span><span
10318 class="cmtt-8"> </span><span
10319 class="cmtt-8"> </span><span
10320 class="cmtt-8"> </span><span
10321 class="cmtt-8"> </span><span
10322 class="cmtt-8"> </span><span
10323 class="cmtt-8"> </span><span
10324 class="cmtt-8"> </span><span
10325 class="cmtt-8"> </span><span
10326 class="cmtt-8"> </span><span
10327 class="cmtt-8"> </span><span
10328 class="cmtt-8"> </span><span
10329 class="cmtt-8"> </span><span
10330 class="cmtt-8"> </span><span
10331 class="cmtt-8"> </span><span
10332 class="cmtt-8"> </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"> </span><span
10346 class="cmtt-8"> </span><span
10347 class="cmtt-8"> codebook</span><span
10348 class="cmtt-8"> number</span><span
10349 class="cmtt-8"> [vqbook]</span><span
10350 class="cmtt-8"> in</span><span
10351 class="cmtt-8"> VQ</span><span
10352 class="cmtt-8"> context</span><br class="fancyvrb" /><a
10353 id="x1-112104r44"></a><span
10354 class="cmr-6">44</span><span
10355 class="cmtt-8"> </span><span
10356 class="cmtt-8"> </span><span
10357 class="cmtt-8"> </span><span
10358 class="cmtt-8"> </span><span
10359 class="cmtt-8"> </span><span
10360 class="cmtt-8"> </span><span
10361 class="cmtt-8"> </span><span
10362 class="cmtt-8"> </span><span
10363 class="cmtt-8"> </span><span
10364 class="cmtt-8"> </span><span
10365 class="cmtt-8"> </span><span
10366 class="cmtt-8"> </span><span
10367 class="cmtt-8"> </span><span
10368 class="cmtt-8"> </span><span
10369 class="cmtt-8"> </span><span
10370 class="cmtt-8"> </span><span
10371 class="cmtt-8"> </span><span
10372 class="cmtt-8"> </span><span
10373 class="cmtt-8"> </span><span
10374 class="cmtt-8"> </span><span
10375 class="cmtt-8"> </span><span
10376 class="cmtt-8"> </span><span
10377 class="cmtt-8"> </span><span
10378 class="cmtt-8"> </span><span
10379 class="cmtt-8"> </span><span
10380 class="cmtt-8"> }</span>
10381 <br class="fancyvrb" /><a
10382 id="x1-112106r45"></a><span
10383 class="cmr-6">45</span><span
10384 class="cmtt-8"> </span><span
10385 class="cmtt-8"> </span><span
10386 class="cmtt-8"> </span><span
10387 class="cmtt-8"> </span><span
10388 class="cmtt-8"> </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><br class="fancyvrb" /><a
10405 id="x1-112108r46"></a><span
10406 class="cmr-6">46</span><br class="fancyvrb" /><a
10407 id="x1-112110r47"></a><span
10408 class="cmr-6">47</span><span
10409 class="cmtt-8"> </span><span
10410 class="cmtt-8"> </span><span
10411 class="cmtt-8"> </span><span
10412 class="cmtt-8"> </span><span
10413 class="cmtt-8"> </span><span
10414 class="cmtt-8"> </span><span
10415 class="cmtt-8"> </span><span
10416 class="cmtt-8"> </span><span
10417 class="cmtt-8"> </span><span
10418 class="cmtt-8"> </span><span
10419 class="cmtt-8"> </span><span
10420 class="cmtt-8"> </span><span
10421 class="cmtt-8"> </span><span
10422 class="cmtt-8"> </span><span
10423 class="cmtt-8"> </span><span
10424 class="cmtt-8"> </span><span
10425 class="cmtt-8"> 20)</span><span
10426 class="cmtt-8"> increment</span><span
10427 class="cmtt-8"> [partition\_count]</span><span
10428 class="cmtt-8"> by</span><span
10429 class="cmtt-8"> one</span><br class="fancyvrb" /><a
10430 id="x1-112112r48"></a><span
10431 class="cmr-6">48</span><br class="fancyvrb" /><a
10432 id="x1-112114r49"></a><span
10433 class="cmr-6">49</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"> </span><span
10448 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10449 id="x1-112116r50"></a><span
10450 class="cmr-6">50</span><span
10451 class="cmtt-8"> </span><span
10452 class="cmtt-8"> </span><span
10453 class="cmtt-8"> </span><span
10454 class="cmtt-8"> </span><span
10455 class="cmtt-8"> </span><span
10456 class="cmtt-8"> </span><span
10457 class="cmtt-8"> </span><span
10458 class="cmtt-8"> </span><span
10459 class="cmtt-8"> </span><span
10460 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10461 id="x1-112118r51"></a><span
10462 class="cmr-6">51</span><span
10463 class="cmtt-8"> </span><span
10464 class="cmtt-8"> </span><span
10465 class="cmtt-8"> </span><span
10466 class="cmtt-8"> </span><span
10467 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10468 id="x1-112120r52"></a><span
10469 class="cmr-6">52</span><br class="fancyvrb" /><a
10470 id="x1-112122r53"></a><span
10471 class="cmr-6">53</span><span
10472 class="cmtt-8"> 21)</span><span
10473 class="cmtt-8"> done</span><br class="fancyvrb" /><a
10474 id="x1-112124r54"></a><span
10475 class="cmr-6">54</span></div>
10476 <!--l. 343--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
10477 Decode returns the result of vector decode up to that point.
10478 <!--l. 349--><p class="noindent" >
10479 <h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a
10480 id="x1-1130008.6.3"></a>format 0 specifics</h5>
10481 <!--l. 351--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
10482 section. The following pseudocode presents the same algorithm. Assume:
10486 <ul class="itemize1">
10487 <li class="itemize"><span
10488 class="cmtt-12">[n] </span>is the value in <span
10489 class="cmtt-12">[residue</span><span
10490 class="cmtt-12">_partition</span><span
10491 class="cmtt-12">_size]</span>
10493 <li class="itemize"><span
10494 class="cmtt-12">[v] </span>is the residue vector
10496 <li class="itemize"><span
10497 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
10498 <!--l. 362--><p class="noindent" >
10499 <div class="fancyvrb" id="fancyvrb41"><a
10500 id="x1-113002r1"></a><span
10501 class="cmr-6">1</span><span
10502 class="cmtt-8"> 1)</span><span
10503 class="cmtt-8"> [step]</span><span
10504 class="cmtt-8"> =</span><span
10505 class="cmtt-8"> [n]</span><span
10506 class="cmtt-8"> /</span><span
10507 class="cmtt-8"> [codebook\_dimensions]</span><br class="fancyvrb" /><a
10508 id="x1-113004r2"></a><span
10509 class="cmr-6">2</span><span
10510 class="cmtt-8"> 2)</span><span
10511 class="cmtt-8"> iterate</span><span
10512 class="cmtt-8"> [i]</span><span
10513 class="cmtt-8"> over</span><span
10514 class="cmtt-8"> the</span><span
10515 class="cmtt-8"> range</span><span
10516 class="cmtt-8"> 0</span><span
10517 class="cmtt-8"> ...</span><span
10518 class="cmtt-8"> [step]-1</span><span
10519 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10520 id="x1-113006r3"></a><span
10521 class="cmr-6">3</span>
10522 <br class="fancyvrb" /><a
10523 id="x1-113008r4"></a><span
10524 class="cmr-6">4</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"> 3)</span><span
10531 class="cmtt-8"> vector</span><span
10532 class="cmtt-8"> [entry\_temp]</span><span
10533 class="cmtt-8"> =</span><span
10534 class="cmtt-8"> read</span><span
10535 class="cmtt-8"> vector</span><span
10536 class="cmtt-8"> from</span><span
10537 class="cmtt-8"> packet</span><span
10538 class="cmtt-8"> using</span><span
10539 class="cmtt-8"> current</span><span
10540 class="cmtt-8"> codebook</span><span
10541 class="cmtt-8"> in</span><span
10542 class="cmtt-8"> VQ</span><span
10543 class="cmtt-8"> context</span>
10544 <br class="fancyvrb" /><a
10545 id="x1-113010r5"></a><span
10546 class="cmr-6">5</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"> 4)</span><span
10553 class="cmtt-8"> iterate</span><span
10554 class="cmtt-8"> [j]</span><span
10555 class="cmtt-8"> over</span><span
10556 class="cmtt-8"> the</span><span
10557 class="cmtt-8"> range</span><span
10558 class="cmtt-8"> 0</span><span
10559 class="cmtt-8"> ...</span><span
10560 class="cmtt-8"> [codebook\_dimensions]-1</span><span
10561 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10562 id="x1-113012r6"></a><span
10563 class="cmr-6">6</span><br class="fancyvrb" /><a
10564 id="x1-113014r7"></a><span
10565 class="cmr-6">7</span><span
10566 class="cmtt-8"> </span><span
10567 class="cmtt-8"> </span><span
10568 class="cmtt-8"> </span><span
10569 class="cmtt-8"> </span><span
10570 class="cmtt-8"> </span><span
10571 class="cmtt-8"> </span><span
10572 class="cmtt-8"> </span><span
10573 class="cmtt-8"> </span><span
10574 class="cmtt-8"> </span><span
10575 class="cmtt-8"> </span><span
10576 class="cmtt-8"> 5)</span><span
10577 class="cmtt-8"> vector</span><span
10578 class="cmtt-8"> [v]</span><span
10579 class="cmtt-8"> element</span><span
10580 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
10581 class="cmtt-8"> =</span>
10582 <br class="fancyvrb" /><a
10583 id="x1-113016r8"></a><span
10584 class="cmr-6">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"> vector</span><span
10593 class="cmtt-8"> [v]</span><span
10594 class="cmtt-8"> element</span><span
10595 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
10596 class="cmtt-8"> +</span><br class="fancyvrb" /><a
10597 id="x1-113018r9"></a><span
10598 class="cmr-6">9</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"> vector</span><span
10615 class="cmtt-8"> [entry\_temp]</span><span
10616 class="cmtt-8"> element</span><span
10617 class="cmtt-8"> [j]</span><br class="fancyvrb" /><a
10618 id="x1-113020r10"></a><span
10619 class="cmr-6">10</span><br class="fancyvrb" /><a
10620 id="x1-113022r11"></a><span
10621 class="cmr-6">11</span><span
10622 class="cmtt-8"> </span><span
10623 class="cmtt-8"> </span><span
10624 class="cmtt-8"> </span><span
10625 class="cmtt-8"> </span><span
10626 class="cmtt-8"> </span><span
10627 class="cmtt-8"> </span><span
10628 class="cmtt-8"> </span><span
10629 class="cmtt-8"> </span><span
10630 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10631 id="x1-113024r12"></a><span
10632 class="cmr-6">12</span><br class="fancyvrb" /><a
10633 id="x1-113026r13"></a><span
10634 class="cmr-6">13</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><br class="fancyvrb" /><a
10639 id="x1-113028r14"></a><span
10640 class="cmr-6">14</span><br class="fancyvrb" /><a
10641 id="x1-113030r15"></a><span
10642 class="cmr-6">15</span><span
10643 class="cmtt-8"> </span><span
10644 class="cmtt-8"> 6)</span><span
10645 class="cmtt-8"> done</span><br class="fancyvrb" /><a
10646 id="x1-113032r16"></a><span
10647 class="cmr-6">16</span></div>
10648 <!--l. 383--><p class="noindent" >
10649 <h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a
10650 id="x1-1140008.6.4"></a>format 1 specifics</h5>
10651 <!--l. 385--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
10652 section. The following pseudocode presents the same algorithm. Assume:
10653 <ul class="itemize1">
10654 <li class="itemize"><span
10655 class="cmtt-12">[n] </span>is the value in <span
10656 class="cmtt-12">[residue</span><span
10657 class="cmtt-12">_partition</span><span
10658 class="cmtt-12">_size]</span>
10660 <li class="itemize"><span
10661 class="cmtt-12">[v] </span>is the residue vector
10663 <li class="itemize"><span
10664 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
10665 <!--l. 397--><p class="noindent" >
10666 <div class="fancyvrb" id="fancyvrb42"><a
10667 id="x1-114002r1"></a><span
10668 class="cmr-6">1</span><span
10669 class="cmtt-8"> 1)</span><span
10670 class="cmtt-8"> [i]</span><span
10671 class="cmtt-8"> =</span><span
10672 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
10673 id="x1-114004r2"></a><span
10674 class="cmr-6">2</span><span
10675 class="cmtt-8"> 2)</span><span
10676 class="cmtt-8"> vector</span><span
10677 class="cmtt-8"> [entry\_temp]</span><span
10678 class="cmtt-8"> =</span><span
10679 class="cmtt-8"> read</span><span
10680 class="cmtt-8"> vector</span><span
10681 class="cmtt-8"> from</span><span
10682 class="cmtt-8"> packet</span><span
10683 class="cmtt-8"> using</span><span
10684 class="cmtt-8"> current</span><span
10685 class="cmtt-8"> codebook</span><span
10686 class="cmtt-8"> in</span><span
10687 class="cmtt-8"> VQ</span><span
10688 class="cmtt-8"> context</span>
10689 <br class="fancyvrb" /><a
10690 id="x1-114006r3"></a><span
10691 class="cmr-6">3</span><span
10692 class="cmtt-8"> 3)</span><span
10693 class="cmtt-8"> iterate</span><span
10694 class="cmtt-8"> [j]</span><span
10695 class="cmtt-8"> over</span><span
10696 class="cmtt-8"> the</span><span
10697 class="cmtt-8"> range</span><span
10698 class="cmtt-8"> 0</span><span
10699 class="cmtt-8"> ...</span><span
10700 class="cmtt-8"> [codebook\_dimensions]-1</span><span
10701 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10702 id="x1-114008r4"></a><span
10703 class="cmr-6">4</span><br class="fancyvrb" /><a
10704 id="x1-114010r5"></a><span
10705 class="cmr-6">5</span><span
10706 class="cmtt-8"> </span><span
10707 class="cmtt-8"> </span><span
10708 class="cmtt-8"> </span><span
10709 class="cmtt-8"> </span><span
10710 class="cmtt-8"> </span><span
10711 class="cmtt-8"> 4)</span><span
10712 class="cmtt-8"> vector</span><span
10713 class="cmtt-8"> [v]</span><span
10714 class="cmtt-8"> element</span><span
10715 class="cmtt-8"> ([offset]+[i])</span><span
10716 class="cmtt-8"> =</span><br class="fancyvrb" /><a
10717 id="x1-114012r6"></a><span
10718 class="cmr-6">6</span> <span
10719 class="cmtt-8"> </span><span
10720 class="cmtt-8"> vector</span><span
10721 class="cmtt-8"> [v]</span><span
10722 class="cmtt-8"> element</span><span
10723 class="cmtt-8"> ([offset]+[i])</span><span
10724 class="cmtt-8"> +</span>
10725 <br class="fancyvrb" /><a
10726 id="x1-114014r7"></a><span
10727 class="cmr-6">7</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"> vector</span><span
10738 class="cmtt-8"> [entry\_temp]</span><span
10739 class="cmtt-8"> element</span><span
10740 class="cmtt-8"> [j]</span><br class="fancyvrb" /><a
10741 id="x1-114016r8"></a><span
10742 class="cmr-6">8</span><span
10743 class="cmtt-8"> </span><span
10744 class="cmtt-8"> </span><span
10745 class="cmtt-8"> </span><span
10746 class="cmtt-8"> </span><span
10747 class="cmtt-8"> </span><span
10748 class="cmtt-8"> 5)</span><span
10749 class="cmtt-8"> increment</span><span
10750 class="cmtt-8"> [i]</span><br class="fancyvrb" /><a
10751 id="x1-114018r9"></a><span
10752 class="cmr-6">9</span><br class="fancyvrb" /><a
10753 id="x1-114020r10"></a><span
10754 class="cmr-6">10</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><br class="fancyvrb" /><a
10759 id="x1-114022r11"></a><span
10760 class="cmr-6">11</span><br class="fancyvrb" /><a
10761 id="x1-114024r12"></a><span
10762 class="cmr-6">12</span><span
10763 class="cmtt-8"> </span><span
10764 class="cmtt-8"> 6)</span><span
10765 class="cmtt-8"> if</span><span
10766 class="cmtt-8"> (</span><span
10767 class="cmtt-8"> [i]</span><span
10768 class="cmtt-8"> is</span><span
10769 class="cmtt-8"> less</span><span
10770 class="cmtt-8"> than</span><span
10771 class="cmtt-8"> [n]</span><span
10772 class="cmtt-8"> )</span><span
10773 class="cmtt-8"> continue</span><span
10774 class="cmtt-8"> at</span><span
10775 class="cmtt-8"> step</span><span
10776 class="cmtt-8"> 2</span><br class="fancyvrb" /><a
10777 id="x1-114026r13"></a><span
10778 class="cmr-6">13</span><span
10779 class="cmtt-8"> </span><span
10780 class="cmtt-8"> 7)</span><span
10781 class="cmtt-8"> done</span></div>
10782 <!--l. 415--><p class="noindent" >
10783 <h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a
10784 id="x1-1150008.6.5"></a>format 2 specifics</h5>
10788 <!--l. 417--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
10789 additional post-decode step after a normal format 1 decode.
10790 <!--l. 420--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
10791 ’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
10792 the vectors are decoded. We then request normal format 1 to decode a single vector
10793 representing all output channels, rather than a vector for each channel. After decode,
10794 deinterleave the vector into independent vectors, one for each output channel. That
10796 <!--l. 428--><p class="noindent" >
10797 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
10799 class="enumerate-enumitem">If all vectors 0 through <span
10800 class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
10802 class="cmtt-12">[v]</span>of length <span
10803 class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
10805 </dd><dt class="enumerate-enumitem">
10807 class="enumerate-enumitem">Rather than performing format 1 decode to produce <span
10808 class="cmti-12">ch </span>vectors of length <span
10809 class="cmti-12">n </span>each, call
10810 format 1 decode to produce a single vector <span
10811 class="cmtt-12">[v] </span>of length <span
10812 class="cmti-12">ch*n</span>.
10813 </dd><dt class="enumerate-enumitem">
10815 class="enumerate-enumitem">Post decode: Deinterleave the single vector <span
10816 class="cmtt-12">[v] </span>returned by format 1 decode as
10817 described above into <span
10818 class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
10820 <div class="fancyvrb" id="fancyvrb43"><a
10821 id="x1-115005r1"></a><span
10822 class="cmr-6">1</span><span
10823 class="cmtt-8"> </span><span
10824 class="cmtt-8"> 1)</span><span
10825 class="cmtt-8"> iterate</span><span
10826 class="cmtt-8"> [i]</span><span
10827 class="cmtt-8"> over</span><span
10828 class="cmtt-8"> the</span><span
10829 class="cmtt-8"> range</span><span
10830 class="cmtt-8"> 0</span><span
10831 class="cmtt-8"> ...</span><span
10832 class="cmtt-8"> [n]-1</span><span
10833 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10834 id="x1-115007r2"></a><span
10835 class="cmr-6">2</span><br class="fancyvrb" /><a
10836 id="x1-115009r3"></a><span
10837 class="cmr-6">3</span><span
10838 class="cmtt-8"> </span><span
10839 class="cmtt-8"> </span><span
10840 class="cmtt-8"> </span><span
10841 class="cmtt-8"> </span><span
10842 class="cmtt-8"> </span><span
10843 class="cmtt-8"> </span><span
10844 class="cmtt-8"> 2)</span><span
10845 class="cmtt-8"> iterate</span><span
10846 class="cmtt-8"> [j]</span><span
10847 class="cmtt-8"> over</span><span
10848 class="cmtt-8"> the</span><span
10849 class="cmtt-8"> range</span><span
10850 class="cmtt-8"> 0</span><span
10851 class="cmtt-8"> ...</span><span
10852 class="cmtt-8"> [ch]-1</span><span
10853 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10854 id="x1-115011r4"></a><span
10855 class="cmr-6">4</span>
10856 <br class="fancyvrb" /><a
10857 id="x1-115013r5"></a><span
10858 class="cmr-6">5</span><span
10859 class="cmtt-8"> </span><span
10860 class="cmtt-8"> </span><span
10861 class="cmtt-8"> </span><span
10862 class="cmtt-8"> </span><span
10863 class="cmtt-8"> </span><span
10864 class="cmtt-8"> </span><span
10865 class="cmtt-8"> </span><span
10866 class="cmtt-8"> </span><span
10867 class="cmtt-8"> </span><span
10868 class="cmtt-8"> </span><span
10869 class="cmtt-8"> </span><span
10870 class="cmtt-8"> 3)</span><span
10871 class="cmtt-8"> output</span><span
10872 class="cmtt-8"> vector</span><span
10873 class="cmtt-8"> number</span><span
10874 class="cmtt-8"> [j]</span><span
10875 class="cmtt-8"> element</span><span
10876 class="cmtt-8"> [i]</span><span
10877 class="cmtt-8"> =</span><span
10878 class="cmtt-8"> vector</span><span
10879 class="cmtt-8"> [v]</span><span
10880 class="cmtt-8"> element</span><span
10881 class="cmtt-8"> ([i]</span><span
10882 class="cmtt-8"> *</span><span
10883 class="cmtt-8"> [ch]</span><span
10884 class="cmtt-8"> +</span><span
10885 class="cmtt-8"> [j])</span><br class="fancyvrb" /><a
10886 id="x1-115015r6"></a><span
10887 class="cmr-6">6</span><br class="fancyvrb" /><a
10888 id="x1-115017r7"></a><span
10889 class="cmr-6">7</span><span
10890 class="cmtt-8"> </span><span
10891 class="cmtt-8"> </span><span
10892 class="cmtt-8"> </span><span
10893 class="cmtt-8"> </span><span
10894 class="cmtt-8"> </span><span
10895 class="cmtt-8"> </span><span
10896 class="cmtt-8"> </span><span
10897 class="cmtt-8"> </span><span
10898 class="cmtt-8"> </span><span
10899 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10900 id="x1-115019r8"></a><span
10901 class="cmr-6">8</span><span
10902 class="cmtt-8"> </span><span
10903 class="cmtt-8"> </span><span
10904 class="cmtt-8"> </span><span
10905 class="cmtt-8"> </span><span
10906 class="cmtt-8"> }</span><br class="fancyvrb" /><a
10907 id="x1-115021r9"></a><span
10908 class="cmr-6">9</span><br class="fancyvrb" /><a
10909 id="x1-115023r10"></a><span
10910 class="cmr-6">10</span><span
10911 class="cmtt-8"> </span><span
10912 class="cmtt-8"> 4)</span><span
10913 class="cmtt-8"> done</span></div>
10921 <h3 class="sectionHead"><span class="titlemark">9. </span> <a
10922 id="x1-1160009"></a>Helper equations</h3>
10923 <!--l. 5--><p class="noindent" >
10924 <h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a
10925 id="x1-1170009.1"></a>Overview</h4>
10926 <!--l. 7--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
10927 cluttering up the main specification documents, they are defined here and referenced where
10929 <!--l. 12--><p class="noindent" >
10930 <h4 class="subsectionHead"><span class="titlemark">9.2. </span> <a
10931 id="x1-1180009.2"></a>Functions</h4>
10932 <!--l. 14--><p class="noindent" >
10933 <h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a
10934 id="x1-1190009.2.1"></a>ilog</h5>
10935 <!--l. 16--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
10936 two’s complement integer value <span
10937 class="cmtt-12">[x]</span>. Values of <span
10938 class="cmtt-12">[x] </span>less than zero are defined to return
10940 <!--l. 19--><p class="noindent" >
10941 <div class="fancyvrb" id="fancyvrb44"><a
10942 id="x1-119002r1"></a><span
10943 class="cmr-6">1</span><span
10944 class="cmtt-8"> </span><span
10945 class="cmtt-8"> 1)</span><span
10946 class="cmtt-8"> [return\_value]</span><span
10947 class="cmtt-8"> =</span><span
10948 class="cmtt-8"> 0;</span><br class="fancyvrb" /><a
10949 id="x1-119004r2"></a><span
10950 class="cmr-6">2</span><span
10951 class="cmtt-8"> </span><span
10952 class="cmtt-8"> 2)</span><span
10953 class="cmtt-8"> if</span><span
10954 class="cmtt-8"> (</span><span
10955 class="cmtt-8"> [x]</span><span
10956 class="cmtt-8"> is</span><span
10957 class="cmtt-8"> greater</span><span
10958 class="cmtt-8"> than</span><span
10959 class="cmtt-8"> zero</span><span
10960 class="cmtt-8"> )</span><span
10961 class="cmtt-8"> {</span><br class="fancyvrb" /><a
10962 id="x1-119006r3"></a><span
10963 class="cmr-6">3</span><br class="fancyvrb" /><a
10964 id="x1-119008r4"></a><span
10965 class="cmr-6">4</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"> 3)</span><span
10973 class="cmtt-8"> increment</span><span
10974 class="cmtt-8"> [return\_value];</span>
10975 <br class="fancyvrb" /><a
10976 id="x1-119010r5"></a><span
10977 class="cmr-6">5</span><span
10978 class="cmtt-8"> </span><span
10979 class="cmtt-8"> </span><span
10980 class="cmtt-8"> </span><span
10981 class="cmtt-8"> </span><span
10982 class="cmtt-8"> </span><span
10983 class="cmtt-8"> </span><span
10984 class="cmtt-8"> 4)</span><span
10985 class="cmtt-8"> logical</span><span
10986 class="cmtt-8"> shift</span><span
10987 class="cmtt-8"> [x]</span><span
10988 class="cmtt-8"> one</span><span
10989 class="cmtt-8"> bit</span><span
10990 class="cmtt-8"> to</span><span
10991 class="cmtt-8"> the</span><span
10992 class="cmtt-8"> right,</span><span
10993 class="cmtt-8"> padding</span><span
10994 class="cmtt-8"> the</span><span
10995 class="cmtt-8"> MSb</span><span
10996 class="cmtt-8"> with</span><span
10997 class="cmtt-8"> zero</span><br class="fancyvrb" /><a
10998 id="x1-119012r6"></a><span
10999 class="cmr-6">6</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"> 5)</span><span
11007 class="cmtt-8"> repeat</span><span
11008 class="cmtt-8"> at</span><span
11009 class="cmtt-8"> step</span><span
11010 class="cmtt-8"> 2)</span><br class="fancyvrb" /><a
11011 id="x1-119014r7"></a><span
11012 class="cmr-6">7</span><br class="fancyvrb" /><a
11013 id="x1-119016r8"></a><span
11014 class="cmr-6">8</span><span
11015 class="cmtt-8"> </span><span
11016 class="cmtt-8"> </span><span
11017 class="cmtt-8"> </span><span
11018 class="cmtt-8"> </span><span
11019 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11020 id="x1-119018r9"></a><span
11021 class="cmr-6">9</span><br class="fancyvrb" /><a
11022 id="x1-119020r10"></a><span
11023 class="cmr-6">10</span><span
11024 class="cmtt-8"> </span><span
11025 class="cmtt-8"> </span><span
11026 class="cmtt-8"> 6)</span><span
11027 class="cmtt-8"> done</span></div>
11028 <!--l. 32--><p class="noindent" >Examples:
11029 <ul class="itemize1">
11030 <li class="itemize">ilog(0) = 0;
11032 <li class="itemize">ilog(1) = 1;
11037 <li class="itemize">ilog(2) = 2;
11039 <li class="itemize">ilog(3) = 2;
11041 <li class="itemize">ilog(4) = 3;
11043 <li class="itemize">ilog(7) = 3;
11045 <li class="itemize">ilog(negative number) = 0;</li></ul>
11046 <!--l. 47--><p class="noindent" >
11047 <h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a
11048 id="x1-1200009.2.2"></a>float32_unpack</h5>
11049 <!--l. 49--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis
11050 codebook float value into the representation used by the decoder for floating point numbers. For
11051 purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
11053 <!--l. 55--><p class="noindent" >
11054 <div class="fancyvrb" id="fancyvrb45"><a
11055 id="x1-120002r1"></a><span
11056 class="cmr-6">1</span><span
11057 class="cmtt-8"> </span><span
11058 class="cmtt-8"> 1)</span><span
11059 class="cmtt-8"> [mantissa]</span><span
11060 class="cmtt-8"> =</span><span
11061 class="cmtt-8"> [x]</span><span
11062 class="cmtt-8"> bitwise</span><span
11063 class="cmtt-8"> AND</span><span
11064 class="cmtt-8"> 0x1fffff</span><span
11065 class="cmtt-8"> (unsigned</span><span
11066 class="cmtt-8"> result)</span><br class="fancyvrb" /><a
11067 id="x1-120004r2"></a><span
11068 class="cmr-6">2</span><span
11069 class="cmtt-8"> </span><span
11070 class="cmtt-8"> 2)</span><span
11071 class="cmtt-8"> [sign]</span><span
11072 class="cmtt-8"> =</span><span
11073 class="cmtt-8"> [x]</span><span
11074 class="cmtt-8"> bitwise</span><span
11075 class="cmtt-8"> AND</span><span
11076 class="cmtt-8"> 0x80000000</span><span
11077 class="cmtt-8"> (unsigned</span><span
11078 class="cmtt-8"> result)</span>
11079 <br class="fancyvrb" /><a
11080 id="x1-120006r3"></a><span
11081 class="cmr-6">3</span><span
11082 class="cmtt-8"> </span><span
11083 class="cmtt-8"> 3)</span><span
11084 class="cmtt-8"> [exponent]</span><span
11085 class="cmtt-8"> =</span><span
11086 class="cmtt-8"> (</span><span
11087 class="cmtt-8"> [x]</span><span
11088 class="cmtt-8"> bitwise</span><span
11089 class="cmtt-8"> AND</span><span
11090 class="cmtt-8"> 0x7fe00000)</span><span
11091 class="cmtt-8"> shifted</span><span
11092 class="cmtt-8"> right</span><span
11093 class="cmtt-8"> 21</span><span
11094 class="cmtt-8"> bits</span><span
11095 class="cmtt-8"> (unsigned</span><span
11096 class="cmtt-8"> result)</span>
11097 <br class="fancyvrb" /><a
11098 id="x1-120008r4"></a><span
11099 class="cmr-6">4</span><span
11100 class="cmtt-8"> </span><span
11101 class="cmtt-8"> 4)</span><span
11102 class="cmtt-8"> if</span><span
11103 class="cmtt-8"> (</span><span
11104 class="cmtt-8"> [sign]</span><span
11105 class="cmtt-8"> is</span><span
11106 class="cmtt-8"> nonzero</span><span
11107 class="cmtt-8"> )</span><span
11108 class="cmtt-8"> then</span><span
11109 class="cmtt-8"> negate</span><span
11110 class="cmtt-8"> [mantissa]</span><br class="fancyvrb" /><a
11111 id="x1-120010r5"></a><span
11112 class="cmr-6">5</span><span
11113 class="cmtt-8"> </span><span
11114 class="cmtt-8"> 5)</span><span
11115 class="cmtt-8"> return</span><span
11116 class="cmtt-8"> [mantissa]</span><span
11117 class="cmtt-8"> *</span><span
11118 class="cmtt-8"> (</span><span
11119 class="cmtt-8"> 2</span><span
11120 class="cmtt-8"> ^</span><span
11121 class="cmtt-8"> (</span><span
11122 class="cmtt-8"> [exponent]</span><span
11123 class="cmtt-8"> -</span><span
11124 class="cmtt-8"> 788</span><span
11125 class="cmtt-8"> )</span><span
11126 class="cmtt-8"> )</span></div>
11127 <!--l. 65--><p class="noindent" >
11128 <h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a
11129 id="x1-1210009.2.3"></a>lookup1_values</h5>
11130 <!--l. 67--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the
11131 correct length of the value index for a codebook VQ lookup table of lookup type 1.
11132 The values on this list are permuted to construct the VQ vector lookup table of size
11134 class="cmtt-12">[codebook</span><span
11135 class="cmtt-12">_entries]</span>.
11136 <!--l. 73--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
11138 class="cmtt-12">[return</span><span
11139 class="cmtt-12">_value] </span>to the power of <span
11140 class="cmtt-12">[codebook</span><span
11141 class="cmtt-12">_dimensions] </span>is less than or equal to
11143 class="cmtt-12">[codebook</span><span
11144 class="cmtt-12">_entries]</span>’.
11148 <!--l. 80--><p class="noindent" >
11149 <h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a
11150 id="x1-1220009.2.4"></a>low_neighbor</h5>
11151 <!--l. 82--><p class="noindent" >”low_neighbor(v,x)” finds the position <span
11152 class="cmtt-12">n </span>in vector <span
11153 class="cmtt-12">[v] </span>of the greatest value scalar element for
11155 class="cmtt-12">n </span>is less than <span
11156 class="cmtt-12">[x] </span>and vector <span
11157 class="cmtt-12">[v] </span>element <span
11158 class="cmtt-12">n </span>is less than vector <span
11159 class="cmtt-12">[v] </span>element
11161 class="cmtt-12">[x]</span>.
11162 <!--l. 87--><p class="noindent" >
11163 <h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a
11164 id="x1-1230009.2.5"></a>high_neighbor</h5>
11165 <!--l. 89--><p class="noindent" >”high_neighbor(v,x)” finds the position <span
11166 class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
11168 class="cmtt-12">n </span>is less than <span
11169 class="cmtt-12">[x] </span>and vector <span
11170 class="cmtt-12">[v] </span>element <span
11171 class="cmtt-12">n </span>is greater than vector <span
11172 class="cmtt-12">[v] </span>element
11174 class="cmtt-12">[x]</span>.
11175 <!--l. 96--><p class="noindent" >
11176 <h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a
11177 id="x1-1240009.2.6"></a>render_point</h5>
11178 <!--l. 98--><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
11179 x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
11180 calculating intervening values along the line.
11181 <!--l. 103--><p class="noindent" >
11182 <div class="fancyvrb" id="fancyvrb46"><a
11183 id="x1-124002r1"></a><span
11184 class="cmr-6">1</span><span
11185 class="cmtt-8"> </span><span
11186 class="cmtt-8"> 1)</span><span
11187 class="cmtt-8"> </span><span
11188 class="cmtt-8"> [dy]</span><span
11189 class="cmtt-8"> =</span><span
11190 class="cmtt-8"> [y1]</span><span
11191 class="cmtt-8"> -</span><span
11192 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11193 id="x1-124004r2"></a><span
11194 class="cmr-6">2</span><span
11195 class="cmtt-8"> </span><span
11196 class="cmtt-8"> 2)</span><span
11197 class="cmtt-8"> [adx]</span><span
11198 class="cmtt-8"> =</span><span
11199 class="cmtt-8"> [x1]</span><span
11200 class="cmtt-8"> -</span><span
11201 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11202 id="x1-124006r3"></a><span
11203 class="cmr-6">3</span><span
11204 class="cmtt-8"> </span><span
11205 class="cmtt-8"> 3)</span><span
11206 class="cmtt-8"> [ady]</span><span
11207 class="cmtt-8"> =</span><span
11208 class="cmtt-8"> absolute</span><span
11209 class="cmtt-8"> value</span><span
11210 class="cmtt-8"> of</span><span
11211 class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a
11212 id="x1-124008r4"></a><span
11213 class="cmr-6">4</span><span
11214 class="cmtt-8"> </span><span
11215 class="cmtt-8"> 4)</span><span
11216 class="cmtt-8"> [err]</span><span
11217 class="cmtt-8"> =</span><span
11218 class="cmtt-8"> [ady]</span><span
11219 class="cmtt-8"> *</span><span
11220 class="cmtt-8"> ([X]</span><span
11221 class="cmtt-8"> -</span><span
11222 class="cmtt-8"> [x0])</span>
11223 <br class="fancyvrb" /><a
11224 id="x1-124010r5"></a><span
11225 class="cmr-6">5</span><span
11226 class="cmtt-8"> </span><span
11227 class="cmtt-8"> 5)</span><span
11228 class="cmtt-8"> [off]</span><span
11229 class="cmtt-8"> =</span><span
11230 class="cmtt-8"> [err]</span><span
11231 class="cmtt-8"> /</span><span
11232 class="cmtt-8"> [adx]</span><span
11233 class="cmtt-8"> using</span><span
11234 class="cmtt-8"> integer</span><span
11235 class="cmtt-8"> division</span><br class="fancyvrb" /><a
11236 id="x1-124012r6"></a><span
11237 class="cmr-6">6</span><span
11238 class="cmtt-8"> </span><span
11239 class="cmtt-8"> 6)</span><span
11240 class="cmtt-8"> if</span><span
11241 class="cmtt-8"> (</span><span
11242 class="cmtt-8"> [dy]</span><span
11243 class="cmtt-8"> is</span><span
11244 class="cmtt-8"> less</span><span
11245 class="cmtt-8"> than</span><span
11246 class="cmtt-8"> zero</span><span
11247 class="cmtt-8"> )</span><span
11248 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11249 id="x1-124014r7"></a><span
11250 class="cmr-6">7</span><br class="fancyvrb" /><a
11251 id="x1-124016r8"></a><span
11252 class="cmr-6">8</span><span
11253 class="cmtt-8"> </span><span
11254 class="cmtt-8"> </span><span
11255 class="cmtt-8"> </span><span
11256 class="cmtt-8"> </span><span
11257 class="cmtt-8"> </span><span
11258 class="cmtt-8"> </span><span
11259 class="cmtt-8"> 7)</span><span
11260 class="cmtt-8"> [Y]</span><span
11261 class="cmtt-8"> =</span><span
11262 class="cmtt-8"> [y0]</span><span
11263 class="cmtt-8"> -</span><span
11264 class="cmtt-8"> [off]</span><br class="fancyvrb" /><a
11265 id="x1-124018r9"></a><span
11266 class="cmr-6">9</span>
11267 <br class="fancyvrb" /><a
11268 id="x1-124020r10"></a><span
11269 class="cmr-6">10</span><span
11270 class="cmtt-8"> </span><span
11271 class="cmtt-8"> </span><span
11272 class="cmtt-8"> </span><span
11273 class="cmtt-8"> </span><span
11274 class="cmtt-8"> }</span><span
11275 class="cmtt-8"> else</span><span
11276 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11277 id="x1-124022r11"></a><span
11278 class="cmr-6">11</span><br class="fancyvrb" /><a
11279 id="x1-124024r12"></a><span
11280 class="cmr-6">12</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"> 8)</span><span
11288 class="cmtt-8"> [Y]</span><span
11289 class="cmtt-8"> =</span><span
11290 class="cmtt-8"> [y0]</span><span
11291 class="cmtt-8"> +</span><span
11292 class="cmtt-8"> [off]</span><br class="fancyvrb" /><a
11293 id="x1-124026r13"></a><span
11294 class="cmr-6">13</span><br class="fancyvrb" /><a
11295 id="x1-124028r14"></a><span
11296 class="cmr-6">14</span><span
11297 class="cmtt-8"> </span><span
11298 class="cmtt-8"> </span><span
11299 class="cmtt-8"> </span><span
11300 class="cmtt-8"> </span><span
11301 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11302 id="x1-124030r15"></a><span
11303 class="cmr-6">15</span><br class="fancyvrb" /><a
11304 id="x1-124032r16"></a><span
11305 class="cmr-6">16</span><span
11306 class="cmtt-8"> </span><span
11307 class="cmtt-8"> 9)</span><span
11308 class="cmtt-8"> done</span></div>
11309 <!--l. 124--><p class="noindent" >
11310 <h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a
11311 id="x1-1250009.2.7"></a>render_line</h5>
11315 <!--l. 126--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)”
11316 to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
11317 been relevant elsewhere, but here we must define integer division as rounding division of both
11318 positive and negative numbers toward zero.
11319 <!--l. 133--><p class="noindent" >
11320 <div class="fancyvrb" id="fancyvrb47"><a
11321 id="x1-125002r1"></a><span
11322 class="cmr-6">1</span><span
11323 class="cmtt-8"> </span><span
11324 class="cmtt-8"> 1)</span><span
11325 class="cmtt-8"> </span><span
11326 class="cmtt-8"> </span><span
11327 class="cmtt-8"> [dy]</span><span
11328 class="cmtt-8"> =</span><span
11329 class="cmtt-8"> [y1]</span><span
11330 class="cmtt-8"> -</span><span
11331 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11332 id="x1-125004r2"></a><span
11333 class="cmr-6">2</span><span
11334 class="cmtt-8"> </span><span
11335 class="cmtt-8"> 2)</span><span
11336 class="cmtt-8"> </span><span
11337 class="cmtt-8"> [adx]</span><span
11338 class="cmtt-8"> =</span><span
11339 class="cmtt-8"> [x1]</span><span
11340 class="cmtt-8"> -</span><span
11341 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11342 id="x1-125006r3"></a><span
11343 class="cmr-6">3</span><span
11344 class="cmtt-8"> </span><span
11345 class="cmtt-8"> 3)</span><span
11346 class="cmtt-8"> </span><span
11347 class="cmtt-8"> [ady]</span><span
11348 class="cmtt-8"> =</span><span
11349 class="cmtt-8"> absolute</span><span
11350 class="cmtt-8"> value</span><span
11351 class="cmtt-8"> of</span><span
11352 class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a
11353 id="x1-125008r4"></a><span
11354 class="cmr-6">4</span><span
11355 class="cmtt-8"> </span><span
11356 class="cmtt-8"> 4)</span><span
11357 class="cmtt-8"> [base]</span><span
11358 class="cmtt-8"> =</span><span
11359 class="cmtt-8"> [dy]</span><span
11360 class="cmtt-8"> /</span><span
11361 class="cmtt-8"> [adx]</span><span
11362 class="cmtt-8"> using</span><span
11363 class="cmtt-8"> integer</span><span
11364 class="cmtt-8"> division</span>
11365 <br class="fancyvrb" /><a
11366 id="x1-125010r5"></a><span
11367 class="cmr-6">5</span><span
11368 class="cmtt-8"> </span><span
11369 class="cmtt-8"> 5)</span><span
11370 class="cmtt-8"> </span><span
11371 class="cmtt-8"> </span><span
11372 class="cmtt-8"> </span><span
11373 class="cmtt-8"> [x]</span><span
11374 class="cmtt-8"> =</span><span
11375 class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a
11376 id="x1-125012r6"></a><span
11377 class="cmr-6">6</span><span
11378 class="cmtt-8"> </span><span
11379 class="cmtt-8"> 6)</span><span
11380 class="cmtt-8"> </span><span
11381 class="cmtt-8"> </span><span
11382 class="cmtt-8"> </span><span
11383 class="cmtt-8"> [y]</span><span
11384 class="cmtt-8"> =</span><span
11385 class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a
11386 id="x1-125014r7"></a><span
11387 class="cmr-6">7</span><span
11388 class="cmtt-8"> </span><span
11389 class="cmtt-8"> 7)</span><span
11390 class="cmtt-8"> </span><span
11391 class="cmtt-8"> [err]</span><span
11392 class="cmtt-8"> =</span><span
11393 class="cmtt-8"> 0</span><br class="fancyvrb" /><a
11394 id="x1-125016r8"></a><span
11395 class="cmr-6">8</span><br class="fancyvrb" /><a
11396 id="x1-125018r9"></a><span
11397 class="cmr-6">9</span><span
11398 class="cmtt-8"> </span><span
11399 class="cmtt-8"> 8)</span><span
11400 class="cmtt-8"> if</span><span
11401 class="cmtt-8"> (</span><span
11402 class="cmtt-8"> [dy]</span><span
11403 class="cmtt-8"> is</span><span
11404 class="cmtt-8"> less</span><span
11405 class="cmtt-8"> than</span><span
11406 class="cmtt-8"> 0</span><span
11407 class="cmtt-8"> )</span><span
11408 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11409 id="x1-125020r10"></a><span
11410 class="cmr-6">10</span><br class="fancyvrb" /><a
11411 id="x1-125022r11"></a><span
11412 class="cmr-6">11</span><span
11413 class="cmtt-8"> </span><span
11414 class="cmtt-8"> </span><span
11415 class="cmtt-8"> </span><span
11416 class="cmtt-8"> </span><span
11417 class="cmtt-8"> </span><span
11418 class="cmtt-8"> </span><span
11419 class="cmtt-8"> </span><span
11420 class="cmtt-8"> 9)</span><span
11421 class="cmtt-8"> [sy]</span><span
11422 class="cmtt-8"> =</span><span
11423 class="cmtt-8"> [base]</span><span
11424 class="cmtt-8"> -</span><span
11425 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
11426 id="x1-125024r12"></a><span
11427 class="cmr-6">12</span>
11428 <br class="fancyvrb" /><a
11429 id="x1-125026r13"></a><span
11430 class="cmr-6">13</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"> else</span><span
11437 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11438 id="x1-125028r14"></a><span
11439 class="cmr-6">14</span><br class="fancyvrb" /><a
11440 id="x1-125030r15"></a><span
11441 class="cmr-6">15</span><span
11442 class="cmtt-8"> </span><span
11443 class="cmtt-8"> </span><span
11444 class="cmtt-8"> </span><span
11445 class="cmtt-8"> </span><span
11446 class="cmtt-8"> </span><span
11447 class="cmtt-8"> </span><span
11448 class="cmtt-8"> 10)</span><span
11449 class="cmtt-8"> [sy]</span><span
11450 class="cmtt-8"> =</span><span
11451 class="cmtt-8"> [base]</span><span
11452 class="cmtt-8"> +</span><span
11453 class="cmtt-8"> 1</span><br class="fancyvrb" /><a
11454 id="x1-125032r16"></a><span
11455 class="cmr-6">16</span><br class="fancyvrb" /><a
11456 id="x1-125034r17"></a><span
11457 class="cmr-6">17</span><span
11458 class="cmtt-8"> </span><span
11459 class="cmtt-8"> </span><span
11460 class="cmtt-8"> </span><span
11461 class="cmtt-8"> </span><span
11462 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11463 id="x1-125036r18"></a><span
11464 class="cmr-6">18</span><br class="fancyvrb" /><a
11465 id="x1-125038r19"></a><span
11466 class="cmr-6">19</span><span
11467 class="cmtt-8"> 11)</span><span
11468 class="cmtt-8"> [ady]</span><span
11469 class="cmtt-8"> =</span><span
11470 class="cmtt-8"> [ady]</span><span
11471 class="cmtt-8"> -</span><span
11472 class="cmtt-8"> (absolute</span><span
11473 class="cmtt-8"> value</span><span
11474 class="cmtt-8"> of</span><span
11475 class="cmtt-8"> [base])</span><span
11476 class="cmtt-8"> *</span><span
11477 class="cmtt-8"> [adx]</span>
11478 <br class="fancyvrb" /><a
11479 id="x1-125040r20"></a><span
11480 class="cmr-6">20</span><span
11481 class="cmtt-8"> 12)</span><span
11482 class="cmtt-8"> vector</span><span
11483 class="cmtt-8"> [v]</span><span
11484 class="cmtt-8"> element</span><span
11485 class="cmtt-8"> [x]</span><span
11486 class="cmtt-8"> =</span><span
11487 class="cmtt-8"> [y]</span><br class="fancyvrb" /><a
11488 id="x1-125042r21"></a><span
11489 class="cmr-6">21</span><br class="fancyvrb" /><a
11490 id="x1-125044r22"></a><span
11491 class="cmr-6">22</span><span
11492 class="cmtt-8"> 13)</span><span
11493 class="cmtt-8"> iterate</span><span
11494 class="cmtt-8"> [x]</span><span
11495 class="cmtt-8"> over</span><span
11496 class="cmtt-8"> the</span><span
11497 class="cmtt-8"> range</span><span
11498 class="cmtt-8"> [x0]+1</span><span
11499 class="cmtt-8"> ...</span><span
11500 class="cmtt-8"> [x1]-1</span><span
11501 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11502 id="x1-125046r23"></a><span
11503 class="cmr-6">23</span><br class="fancyvrb" /><a
11504 id="x1-125048r24"></a><span
11505 class="cmr-6">24</span><span
11506 class="cmtt-8"> </span><span
11507 class="cmtt-8"> </span><span
11508 class="cmtt-8"> </span><span
11509 class="cmtt-8"> </span><span
11510 class="cmtt-8"> </span><span
11511 class="cmtt-8"> </span><span
11512 class="cmtt-8"> 14)</span><span
11513 class="cmtt-8"> [err]</span><span
11514 class="cmtt-8"> =</span><span
11515 class="cmtt-8"> [err]</span><span
11516 class="cmtt-8"> +</span><span
11517 class="cmtt-8"> [ady];</span>
11518 <br class="fancyvrb" /><a
11519 id="x1-125050r25"></a><span
11520 class="cmr-6">25</span><span
11521 class="cmtt-8"> </span><span
11522 class="cmtt-8"> </span><span
11523 class="cmtt-8"> </span><span
11524 class="cmtt-8"> </span><span
11525 class="cmtt-8"> </span><span
11526 class="cmtt-8"> </span><span
11527 class="cmtt-8"> 15)</span><span
11528 class="cmtt-8"> if</span><span
11529 class="cmtt-8"> (</span><span
11530 class="cmtt-8"> [err]</span><span
11531 class="cmtt-8"> >=</span><span
11532 class="cmtt-8"> [adx]</span><span
11533 class="cmtt-8"> )</span><span
11534 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11535 id="x1-125052r26"></a><span
11536 class="cmr-6">26</span><br class="fancyvrb" /><a
11537 id="x1-125054r27"></a><span
11538 class="cmr-6">27</span><span
11539 class="cmtt-8"> </span><span
11540 class="cmtt-8"> </span><span
11541 class="cmtt-8"> </span><span
11542 class="cmtt-8"> </span><span
11543 class="cmtt-8"> </span><span
11544 class="cmtt-8"> </span><span
11545 class="cmtt-8"> </span><span
11546 class="cmtt-8"> </span><span
11547 class="cmtt-8"> </span><span
11548 class="cmtt-8"> </span><span
11549 class="cmtt-8"> </span><span
11550 class="cmtt-8"> </span><span
11551 class="cmtt-8"> 16)</span><span
11552 class="cmtt-8"> [err]</span><span
11553 class="cmtt-8"> =</span><span
11554 class="cmtt-8"> [err]</span><span
11555 class="cmtt-8"> -</span><span
11556 class="cmtt-8"> [adx]</span><br class="fancyvrb" /><a
11557 id="x1-125056r28"></a><span
11558 class="cmr-6">28</span><span
11559 class="cmtt-8"> </span><span
11560 class="cmtt-8"> </span><span
11561 class="cmtt-8"> </span><span
11562 class="cmtt-8"> </span><span
11563 class="cmtt-8"> </span><span
11564 class="cmtt-8"> </span><span
11565 class="cmtt-8"> </span><span
11566 class="cmtt-8"> </span><span
11567 class="cmtt-8"> </span><span
11568 class="cmtt-8"> </span><span
11569 class="cmtt-8"> </span><span
11570 class="cmtt-8"> </span><span
11571 class="cmtt-8"> 17)</span><span
11572 class="cmtt-8"> </span><span
11573 class="cmtt-8"> </span><span
11574 class="cmtt-8"> [y]</span><span
11575 class="cmtt-8"> =</span><span
11576 class="cmtt-8"> [y]</span><span
11577 class="cmtt-8"> +</span><span
11578 class="cmtt-8"> [sy]</span><br class="fancyvrb" /><a
11579 id="x1-125058r29"></a><span
11580 class="cmr-6">29</span>
11581 <br class="fancyvrb" /><a
11582 id="x1-125060r30"></a><span
11583 class="cmr-6">30</span><span
11584 class="cmtt-8"> </span><span
11585 class="cmtt-8"> </span><span
11586 class="cmtt-8"> </span><span
11587 class="cmtt-8"> </span><span
11588 class="cmtt-8"> </span><span
11589 class="cmtt-8"> </span><span
11590 class="cmtt-8"> </span><span
11591 class="cmtt-8"> </span><span
11592 class="cmtt-8"> </span><span
11593 class="cmtt-8"> </span><span
11594 class="cmtt-8"> }</span><span
11595 class="cmtt-8"> else</span><span
11596 class="cmtt-8"> {</span><br class="fancyvrb" /><a
11597 id="x1-125062r31"></a><span
11598 class="cmr-6">31</span><br class="fancyvrb" /><a
11599 id="x1-125064r32"></a><span
11600 class="cmr-6">32</span><span
11601 class="cmtt-8"> </span><span
11602 class="cmtt-8"> </span><span
11603 class="cmtt-8"> </span><span
11604 class="cmtt-8"> </span><span
11605 class="cmtt-8"> </span><span
11606 class="cmtt-8"> </span><span
11607 class="cmtt-8"> </span><span
11608 class="cmtt-8"> </span><span
11609 class="cmtt-8"> </span><span
11610 class="cmtt-8"> </span><span
11611 class="cmtt-8"> </span><span
11612 class="cmtt-8"> </span><span
11613 class="cmtt-8"> 18)</span><span
11614 class="cmtt-8"> [y]</span><span
11615 class="cmtt-8"> =</span><span
11616 class="cmtt-8"> [y]</span><span
11617 class="cmtt-8"> +</span><span
11618 class="cmtt-8"> [base]</span><br class="fancyvrb" /><a
11619 id="x1-125066r33"></a><span
11620 class="cmr-6">33</span><br class="fancyvrb" /><a
11621 id="x1-125068r34"></a><span
11622 class="cmr-6">34</span><span
11623 class="cmtt-8"> </span><span
11624 class="cmtt-8"> </span><span
11625 class="cmtt-8"> </span><span
11626 class="cmtt-8"> </span><span
11627 class="cmtt-8"> </span><span
11628 class="cmtt-8"> </span><span
11629 class="cmtt-8"> </span><span
11630 class="cmtt-8"> </span><span
11631 class="cmtt-8"> </span><span
11632 class="cmtt-8"> </span><span
11633 class="cmtt-8"> }</span><br class="fancyvrb" /><a
11634 id="x1-125070r35"></a><span
11635 class="cmr-6">35</span><br class="fancyvrb" /><a
11636 id="x1-125072r36"></a><span
11637 class="cmr-6">36</span><span
11638 class="cmtt-8"> </span><span
11639 class="cmtt-8"> </span><span
11640 class="cmtt-8"> </span><span
11641 class="cmtt-8"> </span><span
11642 class="cmtt-8"> </span><span
11643 class="cmtt-8"> </span><span
11644 class="cmtt-8"> 19)</span><span
11645 class="cmtt-8"> vector</span><span
11646 class="cmtt-8"> [v]</span><span
11647 class="cmtt-8"> element</span><span
11648 class="cmtt-8"> [x]</span><span
11649 class="cmtt-8"> =</span><span
11650 class="cmtt-8"> [y]</span><br class="fancyvrb" /><a
11651 id="x1-125074r37"></a><span
11652 class="cmr-6">37</span><br class="fancyvrb" /><a
11653 id="x1-125076r38"></a><span
11654 class="cmr-6">38</span><span
11655 class="cmtt-8"> </span><span
11656 class="cmtt-8"> </span><span
11657 class="cmtt-8"> </span><span
11658 class="cmtt-8"> </span><span
11659 class="cmtt-8"> }</span></div>
11666 <h3 class="sectionHead"><span class="titlemark">10. </span> <a
11667 id="x1-12600010"></a>Tables</h3>
11668 <!--l. 5--><p class="noindent" >
11669 <h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a
11670 id="x1-12700010.1"></a>floor1_inverse_dB_table</h4>
11671 <!--l. 7--><p class="noindent" >The vector <span
11672 class="cmtt-12">[floor1</span><span
11673 class="cmtt-12">_inverse</span><span
11674 class="cmtt-12">_dB</span><span
11675 class="cmtt-12">_table] </span>is a 256 element static lookup table consisting of the
11676 following values (read left to right then top to bottom):
11677 <!--l. 11--><p class="noindent" >
11678 <div class="fancyvrb" id="fancyvrb48"><a
11679 id="x1-127002r1"></a><span
11680 class="cmr-6">1</span><span
11681 class="cmtt-8"> </span><span
11682 class="cmtt-8"> 1.0649863e-07,</span><span
11683 class="cmtt-8"> 1.1341951e-07,</span><span
11684 class="cmtt-8"> 1.2079015e-07,</span><span
11685 class="cmtt-8"> 1.2863978e-07,</span><br class="fancyvrb" /><a
11686 id="x1-127004r2"></a><span
11687 class="cmr-6">2</span><span
11688 class="cmtt-8"> </span><span
11689 class="cmtt-8"> 1.3699951e-07,</span><span
11690 class="cmtt-8"> 1.4590251e-07,</span><span
11691 class="cmtt-8"> 1.5538408e-07,</span><span
11692 class="cmtt-8"> 1.6548181e-07,</span>
11693 <br class="fancyvrb" /><a
11694 id="x1-127006r3"></a><span
11695 class="cmr-6">3</span><span
11696 class="cmtt-8"> </span><span
11697 class="cmtt-8"> 1.7623575e-07,</span><span
11698 class="cmtt-8"> 1.8768855e-07,</span><span
11699 class="cmtt-8"> 1.9988561e-07,</span><span
11700 class="cmtt-8"> 2.1287530e-07,</span><br class="fancyvrb" /><a
11701 id="x1-127008r4"></a><span
11702 class="cmr-6">4</span><span
11703 class="cmtt-8"> </span><span
11704 class="cmtt-8"> 2.2670913e-07,</span><span
11705 class="cmtt-8"> 2.4144197e-07,</span><span
11706 class="cmtt-8"> 2.5713223e-07,</span><span
11707 class="cmtt-8"> 2.7384213e-07,</span>
11708 <br class="fancyvrb" /><a
11709 id="x1-127010r5"></a><span
11710 class="cmr-6">5</span><span
11711 class="cmtt-8"> </span><span
11712 class="cmtt-8"> 2.9163793e-07,</span><span
11713 class="cmtt-8"> 3.1059021e-07,</span><span
11714 class="cmtt-8"> 3.3077411e-07,</span><span
11715 class="cmtt-8"> 3.5226968e-07,</span><br class="fancyvrb" /><a
11716 id="x1-127012r6"></a><span
11717 class="cmr-6">6</span><span
11718 class="cmtt-8"> </span><span
11719 class="cmtt-8"> 3.7516214e-07,</span><span
11720 class="cmtt-8"> 3.9954229e-07,</span><span
11721 class="cmtt-8"> 4.2550680e-07,</span><span
11722 class="cmtt-8"> 4.5315863e-07,</span>
11723 <br class="fancyvrb" /><a
11724 id="x1-127014r7"></a><span
11725 class="cmr-6">7</span><span
11726 class="cmtt-8"> </span><span
11727 class="cmtt-8"> 4.8260743e-07,</span><span
11728 class="cmtt-8"> 5.1396998e-07,</span><span
11729 class="cmtt-8"> 5.4737065e-07,</span><span
11730 class="cmtt-8"> 5.8294187e-07,</span><br class="fancyvrb" /><a
11731 id="x1-127016r8"></a><span
11732 class="cmr-6">8</span><span
11733 class="cmtt-8"> </span><span
11734 class="cmtt-8"> 6.2082472e-07,</span><span
11735 class="cmtt-8"> 6.6116941e-07,</span><span
11736 class="cmtt-8"> 7.0413592e-07,</span><span
11737 class="cmtt-8"> 7.4989464e-07,</span>
11738 <br class="fancyvrb" /><a
11739 id="x1-127018r9"></a><span
11740 class="cmr-6">9</span><span
11741 class="cmtt-8"> </span><span
11742 class="cmtt-8"> 7.9862701e-07,</span><span
11743 class="cmtt-8"> 8.5052630e-07,</span><span
11744 class="cmtt-8"> 9.0579828e-07,</span><span
11745 class="cmtt-8"> 9.6466216e-07,</span><br class="fancyvrb" /><a
11746 id="x1-127020r10"></a><span
11747 class="cmr-6">10</span><span
11748 class="cmtt-8"> </span><span
11749 class="cmtt-8"> 1.0273513e-06,</span><span
11750 class="cmtt-8"> 1.0941144e-06,</span><span
11751 class="cmtt-8"> 1.1652161e-06,</span><span
11752 class="cmtt-8"> 1.2409384e-06,</span>
11753 <br class="fancyvrb" /><a
11754 id="x1-127022r11"></a><span
11755 class="cmr-6">11</span><span
11756 class="cmtt-8"> </span><span
11757 class="cmtt-8"> 1.3215816e-06,</span><span
11758 class="cmtt-8"> 1.4074654e-06,</span><span
11759 class="cmtt-8"> 1.4989305e-06,</span><span
11760 class="cmtt-8"> 1.5963394e-06,</span><br class="fancyvrb" /><a
11761 id="x1-127024r12"></a><span
11762 class="cmr-6">12</span><span
11763 class="cmtt-8"> </span><span
11764 class="cmtt-8"> 1.7000785e-06,</span><span
11765 class="cmtt-8"> 1.8105592e-06,</span><span
11766 class="cmtt-8"> 1.9282195e-06,</span><span
11767 class="cmtt-8"> 2.0535261e-06,</span>
11768 <br class="fancyvrb" /><a
11769 id="x1-127026r13"></a><span
11770 class="cmr-6">13</span><span
11771 class="cmtt-8"> </span><span
11772 class="cmtt-8"> 2.1869758e-06,</span><span
11773 class="cmtt-8"> 2.3290978e-06,</span><span
11774 class="cmtt-8"> 2.4804557e-06,</span><span
11775 class="cmtt-8"> 2.6416497e-06,</span><br class="fancyvrb" /><a
11776 id="x1-127028r14"></a><span
11777 class="cmr-6">14</span><span
11778 class="cmtt-8"> </span><span
11779 class="cmtt-8"> 2.8133190e-06,</span><span
11780 class="cmtt-8"> 2.9961443e-06,</span><span
11781 class="cmtt-8"> 3.1908506e-06,</span><span
11782 class="cmtt-8"> 3.3982101e-06,</span>
11783 <br class="fancyvrb" /><a
11784 id="x1-127030r15"></a><span
11785 class="cmr-6">15</span><span
11786 class="cmtt-8"> </span><span
11787 class="cmtt-8"> 3.6190449e-06,</span><span
11788 class="cmtt-8"> 3.8542308e-06,</span><span
11789 class="cmtt-8"> 4.1047004e-06,</span><span
11790 class="cmtt-8"> 4.3714470e-06,</span><br class="fancyvrb" /><a
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11795 class="cmtt-8"> 4.9580707e-06,</span><span
11796 class="cmtt-8"> 5.2802740e-06,</span><span
11797 class="cmtt-8"> 5.6234160e-06,</span>
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11804 class="cmtt-8"> 6.7925283e-06,</span><span
11805 class="cmtt-8"> 7.2339451e-06,</span><br class="fancyvrb" /><a
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11810 class="cmtt-8"> 8.2047000e-06,</span><span
11811 class="cmtt-8"> 8.7378876e-06,</span><span
11812 class="cmtt-8"> 9.3057248e-06,</span>
11813 <br class="fancyvrb" /><a
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11815 class="cmr-6">19</span><span
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11818 class="cmtt-8"> 1.0554501e-05,</span><span
11819 class="cmtt-8"> 1.1240392e-05,</span><span
11820 class="cmtt-8"> 1.1970856e-05,</span><br class="fancyvrb" /><a
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11822 class="cmr-6">20</span><span
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11825 class="cmtt-8"> 1.3577278e-05,</span><span
11826 class="cmtt-8"> 1.4459606e-05,</span><span
11827 class="cmtt-8"> 1.5399272e-05,</span>
11828 <br class="fancyvrb" /><a
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11830 class="cmr-6">21</span><span
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11832 class="cmtt-8"> 1.6400004e-05,</span><span
11833 class="cmtt-8"> 1.7465768e-05,</span><span
11834 class="cmtt-8"> 1.8600792e-05,</span><span
11835 class="cmtt-8"> 1.9809576e-05,</span><br class="fancyvrb" /><a
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11840 class="cmtt-8"> 2.2467911e-05,</span><span
11841 class="cmtt-8"> 2.3928002e-05,</span><span
11842 class="cmtt-8"> 2.5482978e-05,</span>
11843 <br class="fancyvrb" /><a
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11845 class="cmr-6">23</span><span
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11848 class="cmtt-8"> 2.8902651e-05,</span><span
11849 class="cmtt-8"> 3.0780908e-05,</span><span
11850 class="cmtt-8"> 3.2781225e-05,</span><br class="fancyvrb" /><a
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11855 class="cmtt-8"> 3.7180282e-05,</span><span
11856 class="cmtt-8"> 3.9596466e-05,</span><span
11857 class="cmtt-8"> 4.2169667e-05,</span>
11858 <br class="fancyvrb" /><a
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11863 class="cmtt-8"> 4.7828601e-05,</span><span
11864 class="cmtt-8"> 5.0936773e-05,</span><span
11865 class="cmtt-8"> 5.4246931e-05,</span><br class="fancyvrb" /><a
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11870 class="cmtt-8"> 6.1526565e-05,</span><span
11871 class="cmtt-8"> 6.5524908e-05,</span><span
11872 class="cmtt-8"> 6.9783085e-05,</span>
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11878 class="cmtt-8"> 7.9147585e-05,</span><span
11879 class="cmtt-8"> 8.4291040e-05,</span><span
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11886 class="cmtt-8"> 0.00010843174,</span><span
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11902 class="cmtt-8"> 0.00019109536,</span>
11903 <br class="fancyvrb" /><a
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11918 <br class="fancyvrb" /><a
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11930 class="cmtt-8"> 0.00046138411,</span><span
11931 class="cmtt-8"> 0.00049136745,</span><span
11932 class="cmtt-8"> 0.00052329927,</span>
11933 <br class="fancyvrb" /><a
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11946 class="cmtt-8"> 0.00081312324,</span><span
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11948 <br class="fancyvrb" /><a
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11954 class="cmtt-8"> 0.0010459992,</span><span
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11962 class="cmtt-8"> 0.0012634633,</span><span
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11964 class="cmtt-8"> 0.0013455702,</span><span
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11966 class="cmtt-8"> 0.0014330129,</span>
11967 <br class="fancyvrb" /><a
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11983 class="cmtt-8"> 0.0020908006,</span><span
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11988 <br class="fancyvrb" /><a
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12030 <br class="fancyvrb" /><a
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12053 <br class="fancyvrb" /><a
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12080 <br class="fancyvrb" /><a
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12191 <br class="fancyvrb" /><a
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12202 class="cmtt-8"> </span><span
12203 class="cmtt-8"> 0.16107617,</span><span
12204 class="cmtt-8"> </span><span
12205 class="cmtt-8"> </span><span
12206 class="cmtt-8"> </span><span
12207 class="cmtt-8"> 0.17154380,</span><br class="fancyvrb" /><a
12208 id="x1-127116r58"></a><span
12209 class="cmr-6">58</span><span
12210 class="cmtt-8"> </span><span
12211 class="cmtt-8"> 0.18269168,</span><span
12212 class="cmtt-8"> </span><span
12213 class="cmtt-8"> </span><span
12214 class="cmtt-8"> </span><span
12215 class="cmtt-8"> 0.19456402,</span><span
12216 class="cmtt-8"> </span><span
12217 class="cmtt-8"> </span><span
12218 class="cmtt-8"> </span><span
12219 class="cmtt-8"> 0.20720788,</span><span
12220 class="cmtt-8"> </span><span
12221 class="cmtt-8"> </span><span
12222 class="cmtt-8"> </span><span
12223 class="cmtt-8"> 0.22067342,</span>
12224 <br class="fancyvrb" /><a
12225 id="x1-127118r59"></a><span
12226 class="cmr-6">59</span><span
12227 class="cmtt-8"> </span><span
12228 class="cmtt-8"> 0.23501402,</span><span
12229 class="cmtt-8"> </span><span
12230 class="cmtt-8"> </span><span
12231 class="cmtt-8"> </span><span
12232 class="cmtt-8"> 0.25028656,</span><span
12233 class="cmtt-8"> </span><span
12234 class="cmtt-8"> </span><span
12235 class="cmtt-8"> </span><span
12236 class="cmtt-8"> 0.26655159,</span><span
12237 class="cmtt-8"> </span><span
12238 class="cmtt-8"> </span><span
12239 class="cmtt-8"> </span><span
12240 class="cmtt-8"> 0.28387361,</span><br class="fancyvrb" /><a
12241 id="x1-127120r60"></a><span
12242 class="cmr-6">60</span><span
12243 class="cmtt-8"> </span><span
12244 class="cmtt-8"> 0.30232132,</span><span
12245 class="cmtt-8"> </span><span
12246 class="cmtt-8"> </span><span
12247 class="cmtt-8"> </span><span
12248 class="cmtt-8"> 0.32196786,</span><span
12249 class="cmtt-8"> </span><span
12250 class="cmtt-8"> </span><span
12251 class="cmtt-8"> </span><span
12252 class="cmtt-8"> 0.34289114,</span><span
12253 class="cmtt-8"> </span><span
12254 class="cmtt-8"> </span><span
12255 class="cmtt-8"> </span><span
12256 class="cmtt-8"> 0.36517414,</span>
12257 <br class="fancyvrb" /><a
12258 id="x1-127122r61"></a><span
12259 class="cmr-6">61</span><span
12260 class="cmtt-8"> </span><span
12261 class="cmtt-8"> 0.38890521,</span><span
12262 class="cmtt-8"> </span><span
12263 class="cmtt-8"> </span><span
12264 class="cmtt-8"> </span><span
12265 class="cmtt-8"> 0.41417847,</span><span
12266 class="cmtt-8"> </span><span
12267 class="cmtt-8"> </span><span
12268 class="cmtt-8"> </span><span
12269 class="cmtt-8"> 0.44109412,</span><span
12270 class="cmtt-8"> </span><span
12271 class="cmtt-8"> </span><span
12272 class="cmtt-8"> </span><span
12273 class="cmtt-8"> 0.46975890,</span><br class="fancyvrb" /><a
12274 id="x1-127124r62"></a><span
12275 class="cmr-6">62</span><span
12276 class="cmtt-8"> </span><span
12277 class="cmtt-8"> 0.50028648,</span><span
12278 class="cmtt-8"> </span><span
12279 class="cmtt-8"> </span><span
12280 class="cmtt-8"> </span><span
12281 class="cmtt-8"> 0.53279791,</span><span
12282 class="cmtt-8"> </span><span
12283 class="cmtt-8"> </span><span
12284 class="cmtt-8"> </span><span
12285 class="cmtt-8"> 0.56742212,</span><span
12286 class="cmtt-8"> </span><span
12287 class="cmtt-8"> </span><span
12288 class="cmtt-8"> </span><span
12289 class="cmtt-8"> 0.60429640,</span>
12290 <br class="fancyvrb" /><a
12291 id="x1-127126r63"></a><span
12292 class="cmr-6">63</span><span
12293 class="cmtt-8"> </span><span
12294 class="cmtt-8"> 0.64356699,</span><span
12295 class="cmtt-8"> </span><span
12296 class="cmtt-8"> </span><span
12297 class="cmtt-8"> </span><span
12298 class="cmtt-8"> 0.68538959,</span><span
12299 class="cmtt-8"> </span><span
12300 class="cmtt-8"> </span><span
12301 class="cmtt-8"> </span><span
12302 class="cmtt-8"> 0.72993007,</span><span
12303 class="cmtt-8"> </span><span
12304 class="cmtt-8"> </span><span
12305 class="cmtt-8"> </span><span
12306 class="cmtt-8"> 0.77736504,</span><br class="fancyvrb" /><a
12307 id="x1-127128r64"></a><span
12308 class="cmr-6">64</span><span
12309 class="cmtt-8"> </span><span
12310 class="cmtt-8"> 0.82788260,</span><span
12311 class="cmtt-8"> </span><span
12312 class="cmtt-8"> </span><span
12313 class="cmtt-8"> </span><span
12314 class="cmtt-8"> 0.88168307,</span><span
12315 class="cmtt-8"> </span><span
12316 class="cmtt-8"> </span><span
12317 class="cmtt-8"> </span><span
12318 class="cmtt-8"> 0.9389798,</span><span
12319 class="cmtt-8"> </span><span
12320 class="cmtt-8"> </span><span
12321 class="cmtt-8"> </span><span
12322 class="cmtt-8"> </span><span
12323 class="cmtt-8"> 1.</span></div>
12330 <h3 class="sectionHead"><span class="titlemark">A. </span> <a
12331 id="x1-128000A"></a>Embedding Vorbis into an Ogg stream</h3>
12332 <!--l. 5--><p class="noindent" >
12333 <h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a
12334 id="x1-129000A.1"></a>Overview</h4>
12335 <!--l. 7--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
12336 compressed audio packet data into file form.
12337 <!--l. 11--><p class="noindent" >The <a
12338 href="#x1-20001">section 1</a>, “<a
12339 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of Vorbis
12341 <!--l. 14--><p class="noindent" >The <a
12342 href="oggstream.html" >Ogg bitstream overview</a> and <a
12343 href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
12344 descriptions of Ogg transport streams. This specification document assumes a working
12345 knowledge of the concepts covered in these named backround documents. Please read them
12347 <!--l. 21--><p class="noindent" >
12348 <h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a
12349 id="x1-130000A.1.1"></a>Restrictions</h5>
12350 <!--l. 23--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
12351 streams in degenerate, unmultiplexed form only. That is:
12352 <ul class="itemize1">
12353 <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
12355 <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
12358 <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
12364 <!--l. 40--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
12365 types into a multi-stream Ogg file. At the time this document was written, Ogg was
12366 becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
12367 audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
12368 within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
12369 implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
12370 stream (naturally, application authors are encouraged to support full multiplexed Ogg
12372 <!--l. 54--><p class="noindent" >
12373 <h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a
12374 id="x1-131000A.1.2"></a>MIME type</h5>
12375 <!--l. 56--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
12376 applications should use <span
12377 class="cmtt-12">application/ogg</span>, while visual media should use <span
12378 class="cmtt-12">video/ogg</span>, and audio
12380 class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP
12381 encapsulated Vorbis should use <span
12382 class="cmtt-12">audio/vorbis </span>+ <span
12383 class="cmtt-12">audio/vorbis-config</span>.
12384 <!--l. 64--><p class="noindent" >
12385 <h4 class="subsectionHead"><span class="titlemark">A.2. </span> <a
12386 id="x1-132000A.2"></a>Encapsulation</h4>
12387 <!--l. 66--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
12388 <ul class="itemize1">
12389 <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
12390 as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
12391 results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
12394 <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
12396 <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
12397 more pages beginning on the second page of the logical stream. However many pages
12398 they span, the third header packet finishes the page on which it ends. The next (first
12399 audio) packet must begin on a fresh page.
12404 <li class="itemize">The granule position of these first pages containing only headers is zero.
12406 <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
12408 <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
12410 <li class="itemize">The last page is marked ’end of stream’ in the page flags.
12412 <li class="itemize">Vorbis packets may span page boundaries.
12414 <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
12415 samples (per channel; a stereo stream’s granule position does not increment at twice
12416 the speed of a mono stream).
12418 <li class="itemize">The granule position of a page represents the end PCM sample position of the last
12420 class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
12421 returned by decode, not an internal sample awaiting lapping with a subsequent block.
12422 A page that is entirely spanned by a single packet (that completes on a subsequent
12423 page) has no granule position, and the granule position is set to ’-1’.
12424 <!--l. 125--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
12425 necessarily the middle sample from that block. If, eg, the current Vorbis packet
12426 encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
12427 decodable sample from the current packet be at position (3*long_block_length/4) -
12428 (short_block_length/4).
12430 <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
12431 started at position zero. Although the granule position belongs to the last completed
12432 packet on the page and a valid granule position must be positive, by inference it may
12433 indicate that the PCM position of the beginning of audio is positive or negative.
12434 <ul class="itemize2">
12435 <li class="itemize">A positive starting value simply indicates that this stream begins at some
12436 positive time offset, potentially within a larger program. This is a common case
12437 when connecting to the middle of broadcast stream.
12439 <li class="itemize">A negative value indicates that output samples preceeding time zero should be
12443 discarded during decoding; this technique is used to allow sample-granularity
12444 editing of the stream start time of already-encoded Vorbis streams. The number
12445 of samples to be discarded must not exceed the overlap-add span of the first two
12448 <!--l. 160--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
12449 second finished audio packet must flush the page on which it appears and the
12450 third packet begin a fresh page. This allows the decoder to always be able to
12451 perform PCM position adjustments before needing to return any PCM data from
12452 synthesis, resulting in correct positioning information without any aditional seeking
12454 <!--l. 169--><p class="noindent" ><span class="likesubparagraphHead"><a
12455 id="x1-133000A.2"></a><span
12456 class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return
12457 incorrect positioning information for seeking operations at the very beginning of the
12460 <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the
12461 final packet would normally return is used to end the stream on other than even frame
12462 boundaries. The difference between the actual available data returned and the
12463 declared amount indicates how many trailing samples to discard from the decoding
12469 <h3 class="sectionHead"><span class="titlemark">B. </span> <a
12470 id="x1-134000B"></a>Vorbis encapsulation in RTP</h3>
12471 <!--l. 7--><p class="noindent" >Please consult RFC 5215 <span
12472 class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
12473 how to embed Vorbis audio in an RTP stream.
12480 <h3 class="likesectionHead"><a
12481 id="x1-135000B"></a>Colophon</h3>
12482 <!--l. 5--><p class="noindent" ><img
12483 src="fish_xiph_org.png" alt="PIC"
12485 <!--l. 8--><p class="noindent" >Ogg is a <a
12486 href="https://xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from
12487 corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
12489 href="https://xiph.org/about/" >About the Xiph.Org Foundation</a> for details.
12490 <!--l. 15--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
12491 Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.Org
12492 Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification
12493 and certify specification compliance.
12494 <!--l. 21--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
12495 does not restrict third parties from distributing independent implementations of Vorbis software
12496 under other licenses.
12497 <!--l. 26--><p class="noindent" >Ogg, Vorbis, Xiph.Org Foundation and their logos are trademarks (tm) of the <a
12498 href="https://xiph.org/" >Xiph.Org
12499 Foundation</a>. These pages are copyright (C) 1994-2015 Xiph.Org Foundation. All rights
12501 <!--l. 31--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
12502 class="E">E</span>X</span></span>.
12506 <h3 class="likesectionHead"><a
12507 id="x1-136000B"></a>References</h3>
12508 <!--l. 132--><p class="noindent" >
12509 <div class="thebibliography">
12510 <p class="bibitem" ><span class="biblabel">
12511 [1]<span class="bibsp">   </span></span><a
12512 id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
12513 B. Edler, The use of multirate filter banks for coding of high quality digital audio,
12515 href="https://media.taricorp.net/eusipco_corrected.pdf" class="url" ><span
12516 class="cmtt-12">https://media.taricorp.net/eusipco_corrected.pdf</span></a>.
projects / platform / upstream / libvorbis.git / blob