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14 <div class="maketitle">
22 <h2 class="titleHead">Vorbis I specification</h2>
23 <div class="author" ><span
24 class="cmr-12x-x-120">Xiph.org Foundation</span></div>
26 <div class="date" ><span
27 class="cmr-12x-x-120">March 6, 2009</span></div>
29 <h3 class="likesectionHead"><a
30 id="x1-1000"></a>Contents</h3>
31 <div class="tableofcontents">
32 <span class="sectionToc" >1 <a
33 href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
34 <br /> <span class="subsectionToc" >1.1 <a
35 href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
36 <br />  <span class="subsubsectionToc" >1.1.1 <a
37 href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
38 <br />  <span class="subsubsectionToc" >1.1.2 <a
39 href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
40 <br />  <span class="subsubsectionToc" >1.1.3 <a
41 href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
42 <br />  <span class="subsubsectionToc" >1.1.4 <a
43 href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
44 <br />  <span class="subsubsectionToc" >1.1.5 <a
45 href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
46 <br />  <span class="subsubsectionToc" >1.1.6 <a
47 href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
48 <br /> <span class="subsectionToc" >1.2 <a
49 href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
50 <br />  <span class="subsubsectionToc" >1.2.1 <a
51 href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
52 <br />  <span class="subsubsectionToc" >1.2.2 <a
53 href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
54 <br />  <span class="subsubsectionToc" >1.2.3 <a
55 href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
56 <br />  <span class="subsubsectionToc" >1.2.4 <a
57 href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
58 <br />  <span class="subsubsectionToc" >1.2.5 <a
59 href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
60 <br />  <span class="subsubsectionToc" >1.2.6 <a
61 href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
65 <br /> <span class="subsectionToc" >1.3 <a
66 href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
67 <br />  <span class="subsubsectionToc" >1.3.1 <a
68 href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
69 <br />  <span class="subsubsectionToc" >1.3.2 <a
70 href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
71 <br /><span class="sectionToc" >2 <a
72 href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
73 <br /> <span class="subsectionToc" >2.1 <a
74 href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
75 <br />  <span class="subsubsectionToc" >2.1.1 <a
76 href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
77 <br />  <span class="subsubsectionToc" >2.1.2 <a
78 href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
79 <br />  <span class="subsubsectionToc" >2.1.3 <a
80 href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
81 <br />  <span class="subsubsectionToc" >2.1.4 <a
82 href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
83 <br />  <span class="subsubsectionToc" >2.1.5 <a
84 href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
85 <br />  <span class="subsubsectionToc" >2.1.6 <a
86 href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
87 <br />  <span class="subsubsectionToc" >2.1.7 <a
88 href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
89 <br />  <span class="subsubsectionToc" >2.1.8 <a
90 href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
91 <br />  <span class="subsubsectionToc" >2.1.9 <a
92 href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
93 <br /><span class="sectionToc" >3 <a
94 href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
95 <br /> <span class="subsectionToc" >3.1 <a
96 href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
97 <br />  <span class="subsubsectionToc" >3.1.1 <a
98 href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
99 <br /> <span class="subsectionToc" >3.2 <a
100 href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
101 <br />  <span class="subsubsectionToc" >3.2.1 <a
102 href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
103 <br /> <span class="subsectionToc" >3.3 <a
104 href="#x1-570003.3" id="QQ2-1-62">Use of the codebook abstraction</a></span>
105 <br /><span class="sectionToc" >4 <a
106 href="#x1-580004" id="QQ2-1-63">Codec Setup and Packet Decode</a></span>
107 <br /> <span class="subsectionToc" >4.1 <a
108 href="#x1-590004.1" id="QQ2-1-64">Overview</a></span>
109 <br /> <span class="subsectionToc" >4.2 <a
110 href="#x1-600004.2" id="QQ2-1-65">Header decode and decode setup</a></span>
111 <br />  <span class="subsubsectionToc" >4.2.1 <a
112 href="#x1-610004.2.1" id="QQ2-1-66">Common header decode</a></span>
113 <br />  <span class="subsubsectionToc" >4.2.2 <a
114 href="#x1-620004.2.2" id="QQ2-1-67">Identification header</a></span>
115 <br />  <span class="subsubsectionToc" >4.2.3 <a
116 href="#x1-630004.2.3" id="QQ2-1-68">Comment header</a></span>
117 <br />  <span class="subsubsectionToc" >4.2.4 <a
118 href="#x1-640004.2.4" id="QQ2-1-69">Setup header</a></span>
119 <br /> <span class="subsectionToc" >4.3 <a
120 href="#x1-710004.3" id="QQ2-1-77">Audio packet decode and synthesis</a></span>
121 <br />  <span class="subsubsectionToc" >4.3.1 <a
122 href="#x1-720004.3.1" id="QQ2-1-78">packet type, mode and window decode</a></span>
123 <br />  <span class="subsubsectionToc" >4.3.2 <a
124 href="#x1-730004.3.2" id="QQ2-1-79">floor curve decode</a></span>
125 <br />  <span class="subsubsectionToc" >4.3.3 <a
126 href="#x1-740004.3.3" id="QQ2-1-80">nonzero vector propagate</a></span>
130 <br />  <span class="subsubsectionToc" >4.3.4 <a
131 href="#x1-750004.3.4" id="QQ2-1-81">residue decode</a></span>
132 <br />  <span class="subsubsectionToc" >4.3.5 <a
133 href="#x1-760004.3.5" id="QQ2-1-82">inverse coupling</a></span>
134 <br />  <span class="subsubsectionToc" >4.3.6 <a
135 href="#x1-770004.3.6" id="QQ2-1-83">dot product</a></span>
136 <br />  <span class="subsubsectionToc" >4.3.7 <a
137 href="#x1-780004.3.7" id="QQ2-1-84">inverse MDCT</a></span>
138 <br />  <span class="subsubsectionToc" >4.3.8 <a
139 href="#x1-790004.3.8" id="QQ2-1-85">overlap˙add</a></span>
140 <br />  <span class="subsubsectionToc" >4.3.9 <a
141 href="#x1-800004.3.9" id="QQ2-1-86">output channel order</a></span>
142 <br /><span class="sectionToc" >5 <a
143 href="#x1-810005" id="QQ2-1-87">comment field and header specification</a></span>
144 <br /> <span class="subsectionToc" >5.1 <a
145 href="#x1-820005.1" id="QQ2-1-88">Overview</a></span>
146 <br /> <span class="subsectionToc" >5.2 <a
147 href="#x1-830005.2" id="QQ2-1-89">Comment encoding</a></span>
148 <br />  <span class="subsubsectionToc" >5.2.1 <a
149 href="#x1-840005.2.1" id="QQ2-1-90">Structure</a></span>
150 <br />  <span class="subsubsectionToc" >5.2.2 <a
151 href="#x1-850005.2.2" id="QQ2-1-91">Content vector format</a></span>
152 <br />  <span class="subsubsectionToc" >5.2.3 <a
153 href="#x1-880005.2.3" id="QQ2-1-94">Encoding</a></span>
154 <br /><span class="sectionToc" >6 <a
155 href="#x1-890006" id="QQ2-1-95">Floor type 0 setup and decode</a></span>
156 <br /> <span class="subsectionToc" >6.1 <a
157 href="#x1-900006.1" id="QQ2-1-96">Overview</a></span>
158 <br /> <span class="subsectionToc" >6.2 <a
159 href="#x1-910006.2" id="QQ2-1-97">Floor 0 format</a></span>
160 <br />  <span class="subsubsectionToc" >6.2.1 <a
161 href="#x1-920006.2.1" id="QQ2-1-98">header decode</a></span>
162 <br />  <span class="subsubsectionToc" >6.2.2 <a
163 href="#x1-930006.2.2" id="QQ2-1-99">packet decode</a></span>
164 <br />  <span class="subsubsectionToc" >6.2.3 <a
165 href="#x1-940006.2.3" id="QQ2-1-100">curve computation</a></span>
166 <br /><span class="sectionToc" >7 <a
167 href="#x1-950007" id="QQ2-1-101">Floor type 1 setup and decode</a></span>
168 <br /> <span class="subsectionToc" >7.1 <a
169 href="#x1-960007.1" id="QQ2-1-102">Overview</a></span>
170 <br /> <span class="subsectionToc" >7.2 <a
171 href="#x1-970007.2" id="QQ2-1-103">Floor 1 format</a></span>
172 <br />  <span class="subsubsectionToc" >7.2.1 <a
173 href="#x1-980007.2.1" id="QQ2-1-104">model</a></span>
174 <br />  <span class="subsubsectionToc" >7.2.2 <a
175 href="#x1-990007.2.2" id="QQ2-1-109">header decode</a></span>
176 <br /><span class="sectionToc" >8 <a
177 href="#x1-1020008" id="QQ2-1-112">Residue setup and decode</a></span>
178 <br /> <span class="subsectionToc" >8.1 <a
179 href="#x1-1030008.1" id="QQ2-1-113">Overview</a></span>
180 <br /> <span class="subsectionToc" >8.2 <a
181 href="#x1-1040008.2" id="QQ2-1-114">Residue format</a></span>
182 <br /> <span class="subsectionToc" >8.3 <a
183 href="#x1-1050008.3" id="QQ2-1-116">residue 0</a></span>
184 <br /> <span class="subsectionToc" >8.4 <a
185 href="#x1-1060008.4" id="QQ2-1-117">residue 1</a></span>
186 <br /> <span class="subsectionToc" >8.5 <a
187 href="#x1-1070008.5" id="QQ2-1-118">residue 2</a></span>
188 <br /> <span class="subsectionToc" >8.6 <a
189 href="#x1-1080008.6" id="QQ2-1-120">Residue decode</a></span>
190 <br />  <span class="subsubsectionToc" >8.6.1 <a
191 href="#x1-1090008.6.1" id="QQ2-1-121">header decode</a></span>
195 <br />  <span class="subsubsectionToc" >8.6.2 <a
196 href="#x1-1100008.6.2" id="QQ2-1-122">packet decode</a></span>
197 <br />  <span class="subsubsectionToc" >8.6.3 <a
198 href="#x1-1110008.6.3" id="QQ2-1-123">format 0 specifics</a></span>
199 <br />  <span class="subsubsectionToc" >8.6.4 <a
200 href="#x1-1120008.6.4" id="QQ2-1-124">format 1 specifics</a></span>
201 <br />  <span class="subsubsectionToc" >8.6.5 <a
202 href="#x1-1130008.6.5" id="QQ2-1-125">format 2 specifics</a></span>
203 <br /><span class="sectionToc" >9 <a
204 href="#x1-1140009" id="QQ2-1-126">Helper equations</a></span>
205 <br /> <span class="subsectionToc" >9.1 <a
206 href="#x1-1150009.1" id="QQ2-1-127">Overview</a></span>
207 <br /> <span class="subsectionToc" >9.2 <a
208 href="#x1-1160009.2" id="QQ2-1-128">Functions</a></span>
209 <br />  <span class="subsubsectionToc" >9.2.1 <a
210 href="#x1-1170009.2.1" id="QQ2-1-129">ilog</a></span>
211 <br />  <span class="subsubsectionToc" >9.2.2 <a
212 href="#x1-1180009.2.2" id="QQ2-1-130">float32˙unpack</a></span>
213 <br />  <span class="subsubsectionToc" >9.2.3 <a
214 href="#x1-1190009.2.3" id="QQ2-1-131">lookup1˙values</a></span>
215 <br />  <span class="subsubsectionToc" >9.2.4 <a
216 href="#x1-1200009.2.4" id="QQ2-1-132">low˙neighbor</a></span>
217 <br />  <span class="subsubsectionToc" >9.2.5 <a
218 href="#x1-1210009.2.5" id="QQ2-1-133">high˙neighbor</a></span>
219 <br />  <span class="subsubsectionToc" >9.2.6 <a
220 href="#x1-1220009.2.6" id="QQ2-1-134">render˙point</a></span>
221 <br />  <span class="subsubsectionToc" >9.2.7 <a
222 href="#x1-1230009.2.7" id="QQ2-1-135">render˙line</a></span>
223 <br /><span class="sectionToc" >10 <a
224 href="#x1-12400010" id="QQ2-1-136">Tables</a></span>
225 <br /> <span class="subsectionToc" >10.1 <a
226 href="#x1-12500010.1" id="QQ2-1-137">floor1_inverse_dB_table</a></span>
227 <br /><span class="sectionToc" >A <a
228 href="#x1-126000A" id="QQ2-1-138">Embedding Vorbis into an Ogg stream</a></span>
229 <br /> <span class="subsectionToc" >A.1 <a
230 href="#x1-127000A.1" id="QQ2-1-139">Overview</a></span>
231 <br />  <span class="subsubsectionToc" >A.1.1 <a
232 href="#x1-128000A.1.1" id="QQ2-1-140">Restrictions</a></span>
233 <br />  <span class="subsubsectionToc" >A.1.2 <a
234 href="#x1-129000A.1.2" id="QQ2-1-141">MIME type</a></span>
235 <br /> <span class="subsectionToc" >A.2 <a
236 href="#x1-130000A.2" id="QQ2-1-142">Encapsulation</a></span>
237 <br /><span class="sectionToc" >B <a
238 href="#x1-132000B" id="QQ2-1-144">Vorbis encapsulation in RTP</a></span>
243 <h3 class="sectionHead"><span class="titlemark">1 </span> <a
244 id="x1-20001"></a>Introduction and Description</h3>
245 <!--l. 6--><p class="noindent" >
246 <h4 class="subsectionHead"><span class="titlemark">1.1 </span> <a
247 id="x1-30001.1"></a>Overview</h4>
248 <!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
249 specification appears beginning in <a
250 href="#x1-580004">Section 4<!--tex4ht:ref: vorbis:spec:codec --></a>, “<a
251 href="#x1-580004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later
252 sections assume a high-level understanding of the Vorbis decode process, which is provided
254 <!--l. 15--><p class="noindent" >
255 <h5 class="subsubsectionHead"><span class="titlemark">1.1.1 </span> <a
256 id="x1-40001.1.1"></a>Application</h5>
257 <!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
258 flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At the
259 high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same league as
260 MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT rate stereo at
261 below 48kbps without resampling to a lower rate. Vorbis is also intended for lower and higher
262 sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
263 representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255 discrete
265 <!--l. 29--><p class="noindent" >
266 <h5 class="subsubsectionHead"><span class="titlemark">1.1.2 </span> <a
267 id="x1-50001.1.2"></a>Classification</h5>
268 <!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete Cosine
269 Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in Vorbis II to
270 offer better transient response and reproduction using a transform better suited to localized time
272 <!--l. 37--><p class="noindent" >
273 <h5 class="subsubsectionHead"><span class="titlemark">1.1.3 </span> <a
274 id="x1-60001.1.3"></a>Assumptions</h5>
278 <!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
279 low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
280 require more working memory as Vorbis has no static probability model; the vector codebooks used
281 in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
282 bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent
283 to which they are pre-decoded into a cache is the dominant factor in decoder memory
285 <!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it is solely a
286 method of accepting input audio, dividing it into individual frames and compressing these frames
287 into raw, unformatted ’packets’. The decoder then accepts these raw packets in sequence, decodes
288 them, synthesizes audio frames from them, and reassembles the frames into a facsimile of the
289 original audio stream. Vorbis is a free-form variable bit rate (VBR) codec and packets have no
290 minimum size, maximum size, or fixed/expected size. Packets are designed that they may be
291 truncated (or padded) and remain decodable; this is not to be considered an error condition and is
292 used extensively in bitrate management in peeling. Both the transport mechanism and
293 decoder must allow that a packet may be any size, or end before or after packet decode
295 <!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
296 framing, sync, positioning and error correction in accordance with these design assumptions, such as
297 Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
298 document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
299 although this is by no means a requirement or fundamental assumption in the Vorbis
301 <!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
302 href="#x1-126000A">Section A<!--tex4ht:ref: vorbis:over:ogg --></a>, “<a
303 href="#x1-126000A">Embedding
304 Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
305 <!--l. 77--><p class="noindent" >
306 <h5 class="subsubsectionHead"><span class="titlemark">1.1.4 </span> <a
307 id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
308 <!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
309 decades of continuous encoder improvement before running out of room within the codec
310 specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
311 extreme of forward adaptive.
312 <!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis developer
313 to keep in mind) is that the entire probability model of the codec, the Huffman and
314 VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
315 parameters (often several hundred fields). This makes it impossible, as it would be with
316 MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
317 decode at any frame in the stream without having previously fetched the codec setup
322 <!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a
323 id="x1-80001.1.4"></a><span
324 class="cmbx-10x-x-109">Note:</span></span> Vorbis <span
325 class="cmti-10x-x-109">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
326 has been initialized/setup with the setup headers.
327 <!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream headers
328 go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less is
329 recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
330 <!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is an
331 unusual design and thus causes some amount of complaint among engineers as this runs against
332 current design trends (and also points out limitations in some existing software/interface designs,
333 such as Windows’ ACM codec framework). However, we find that it does not fundamentally limit
334 Vorbis’ suitable application space.
335 <!--l. 115--><p class="noindent" >
336 <h5 class="subsubsectionHead"><span class="titlemark">1.1.5 </span> <a
337 id="x1-90001.1.5"></a>Format Specification</h5>
338 <!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces
339 packets that are correctly decoded by the reference Vorbis decoder described below may be
340 considered a proper Vorbis encoder. A decoder must faithfully and completely implement
341 the specification defined below (except where noted) to be considered a proper Vorbis
343 <!--l. 123--><p class="noindent" >
344 <h5 class="subsubsectionHead"><span class="titlemark">1.1.6 </span> <a
345 id="x1-100001.1.6"></a>Hardware Profile</h5>
346 <!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
347 embedded design. For this reason, embedded designs are allowed to deviate in limited ways from the
348 ‘full’ decode specification yet still be certified compliant. These optional omissions are labelled in
349 the spec where relevant.
350 <!--l. 131--><p class="noindent" >
351 <h4 class="subsectionHead"><span class="titlemark">1.2 </span> <a
352 id="x1-110001.2"></a>Decoder Configuration</h4>
353 <!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
354 perform specific functions in the decode pipeline. Each different component instance of a specific
355 type is semantically interchangeable; decoder configuration consists both of internal component
356 configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
360 arrangement is roughly as follows:
363 <!--l. 141--><p class="noindent" >
365 <!--l. 142--><p class="noindent" ><img
366 src="components.png" alt="PIC"
368 <br /> <table class="caption"
369 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 1: </td><td
370 class="content">decoder pipeline configuration</td></tr></table><!--tex4ht:label?: x1-110011 -->
372 <!--l. 146--><p class="noindent" >
373 <h5 class="subsubsectionHead"><span class="titlemark">1.2.1 </span> <a
374 id="x1-120001.2.1"></a>Global Config</h5>
375 <!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
376 version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
377 configuration is in the context of specific components.
378 <!--l. 152--><p class="noindent" >
379 <h5 class="subsubsectionHead"><span class="titlemark">1.2.2 </span> <a
380 id="x1-130001.2.2"></a>Mode</h5>
381 <!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
383 <!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
384 methods with the intention of choosing a method best suited to that frame. Different
385 modes are, e.g. how frame size is changed from frame to frame. The mode number of a
386 frame serves as a top level configuration switch for all other specific aspects of frame
388 <!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis window,
389 in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping number. The
390 mapping number specifies which mapping configuration instance to use for low-level packet decode
392 <!--l. 171--><p class="noindent" >
393 <h5 class="subsubsectionHead"><span class="titlemark">1.2.3 </span> <a
394 id="x1-140001.2.3"></a>Mapping</h5>
398 <!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle
399 sets of channel vectors together for grouped encoding and decoding. These submaps
400 are not references to external components; the submap list is internal and specific to a
402 <!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors within a
403 mapping. The submap functions as a last layer of indirection such that specific special floor or
404 residue settings can be applied not only to all the vectors in a given mode, but also
405 specific vectors in a specific mode. Each submap specifies the proper floor and residue
406 instance number to use for decoding that submap’s spectral floor and spectral residue
408 <!--l. 186--><p class="noindent" >As an example:
409 <!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth channel, as
410 is normal in 5.1, is bass only. Therefore it would be wasteful to encode a full-spectrum version of it
411 as with the other channels. The submapping mechanism can be used to apply a full range floor and
412 residue encoding to channels 0 through 4, and a bass-only representation to the bass channel,
413 thus saving space. In this example, channels 0-4 belong to submap 0 (which indicates
414 use of a full-range floor) and channel 5 belongs to submap 1, which uses a bass-only
416 <!--l. 199--><p class="noindent" >
417 <h5 class="subsubsectionHead"><span class="titlemark">1.2.4 </span> <a
418 id="x1-150001.2.4"></a>Floor</h5>
419 <!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
420 representation of the audio spectrum for the given channel in the current frame, generally used akin
421 to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has historically
422 used it as a unit-baseline for spectral resolution.
423 <!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
424 amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
425 interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
426 are semantically interchangeable in encoding/decoding. However, floor type 1 provides
427 more stable inter-frame behavior, and so is the preferred choice in all coupled-stereo
428 and high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
430 <!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
431 encoder past Xiph.org’s own beta 4 makes use of floor 0.
432 <!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of
433 entropy coding to save space. For this reason, a floor configuration generally refers to
434 multiple codebooks in the codebook component list. Entropy coding is thus provided as an
435 abstraction, and each floor instance may choose from any and all available codebooks when
440 <!--l. 230--><p class="noindent" >
441 <h5 class="subsubsectionHead"><span class="titlemark">1.2.5 </span> <a
442 id="x1-160001.2.5"></a>Residue</h5>
443 <!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve
444 has been subtracted out. In simplest terms, it is coded in the bitstream using cascaded
445 (multi-pass) vector quantization according to one of three specific packing/coding algorithms
446 numbered 0 through 2. The packing algorithm details are configured by residue instance.
447 As with the floor components, the final VQ/entropy encoding is provided by external
448 codebook instances and each residue instance may choose from any and all available
450 <!--l. 241--><p class="noindent" >
451 <h5 class="subsubsectionHead"><span class="titlemark">1.2.6 </span> <a
452 id="x1-170001.2.6"></a>Codebooks</h5>
453 <!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use the
454 entropy-decoded integer value as an offset into an index of output value vectors, returning the
455 indicated vector of values.
456 <!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
457 representation. This tree is tightly packed using one of several methods, depending on whether
458 codeword lengths are ordered or unordered, or the tree is sparse.
459 <!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
460 the vector index is encoded as a single list of values of possible values that are then permuted into a
461 list of n-dimensional rows (lattice VQ).
462 <!--l. 260--><p class="noindent" >
463 <h4 class="subsectionHead"><span class="titlemark">1.3 </span> <a
464 id="x1-180001.3"></a>High-level Decode Process</h4>
465 <!--l. 262--><p class="noindent" >
466 <h5 class="subsubsectionHead"><span class="titlemark">1.3.1 </span> <a
467 id="x1-190001.3.1"></a>Decode Setup</h5>
468 <!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
469 stream to be decoded. Vorbis uses three header packets; all are required, in-order, by this
473 specification. Once set up, decode may begin at any audio packet belonging to the Vorbis stream. In
474 Vorbis I, all packets after the three initial headers are audio packets.
475 <!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
477 <!--l. 274--><p class="noindent" ><span class="paragraphHead"><a
478 id="x1-200001.3.1"></a><span
479 class="cmbx-10x-x-109">Identification Header</span></span>
480 The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
481 characteristics of the stream such as sample rate and number of channels.
482 <!--l. 279--><p class="noindent" ><span class="paragraphHead"><a
483 id="x1-210001.3.1"></a><span
484 class="cmbx-10x-x-109">Comment Header</span></span>
485 The comment header includes user text comments (“tags”) and a vendor string for the
486 application/library that produced the bitstream. The encoding and proper use of the comment
487 header is described in <a
488 href="#x1-810005">Section 5<!--tex4ht:ref: vorbis:spec:comment --></a>, “<a
489 href="#x1-810005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
490 <!--l. 284--><p class="noindent" ><span class="paragraphHead"><a
491 id="x1-220001.3.1"></a><span
492 class="cmbx-10x-x-109">Setup Header</span></span>
493 The setup header includes extensive CODEC setup information as well as the complete VQ and
494 Huffman codebooks needed for decode.
495 <!--l. 289--><p class="noindent" >
496 <h5 class="subsubsectionHead"><span class="titlemark">1.3.2 </span> <a
497 id="x1-230001.3.2"></a>Decode Procedure</h5>
498 <!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
499 <ol class="enumerate1" >
501 class="enumerate" id="x1-23002x1">decode packet type flag
504 class="enumerate" id="x1-23004x2">decode mode number
507 class="enumerate" id="x1-23006x3">decode window shape (long windows only)
510 class="enumerate" id="x1-23008x4">decode floor
513 class="enumerate" id="x1-23010x5">decode residue into residue vectors
519 class="enumerate" id="x1-23012x6">inverse channel coupling of residue vectors
522 class="enumerate" id="x1-23014x7">generate floor curve from decoded floor data
525 class="enumerate" id="x1-23016x8">compute dot product of floor and residue, producing audio spectrum vector
528 class="enumerate" id="x1-23018x9">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis I
531 class="enumerate" id="x1-23020x10">overlap/add left-hand output of transform with right-hand output of previous frame
534 class="enumerate" id="x1-23022x11">store right hand-data from transform of current frame for future lapping
537 class="enumerate" id="x1-23024x12">if not first frame, return results of overlap/add as audio result of current frame</li></ol>
538 <!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can take
539 advantage of symmetries in the MDCT to store the right-hand transform data of a partial MDCT
540 for a 50% inter-frame buffer space savings, and then complete the transform later before
541 overlap/add with the next frame. This optimization produces entirely equivalent output and is
542 naturally perfectly legal. The decoder must be <span
543 class="cmti-10x-x-109">entirely mathematically equivalent </span>to the
544 specification, it need not be a literal semantic implementation.
545 <!--l. 317--><p class="noindent" ><span class="paragraphHead"><a
546 id="x1-240001.3.2"></a><span
547 class="cmbx-10x-x-109">Packet type decode</span></span>
548 Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis headers
549 described above. The fourth packet type marks an audio packet. All other packet types are reserved;
550 packets marked with a reserved type should be ignored.
551 <!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
552 audio packet decode is to read and verify the packet type; <span
553 class="cmti-10x-x-109">a non-audio packet when audio is</span>
555 class="cmti-10x-x-109">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the packet</span>
557 class="cmti-10x-x-109">and not attempt decoding it to audio</span>.
558 <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
559 id="x1-250001.3.2"></a><span
560 class="cmbx-10x-x-109">Mode decode</span></span>
561 Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
562 which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
563 offset into the mode instance index.
567 <!--l. 341--><p class="noindent" ><span class="paragraphHead"><a
568 id="x1-260001.3.2"></a><span
569 class="cmbx-10x-x-109">Window shape decode (long windows only)</span></span>
570 Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis
571 I, legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling,
572 Vorbis handles channels as independent vectors and these frame sizes are in samples per
574 <!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
575 avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
576 according to MDCT requirements, overlapped 50% with the output of the previous frame and
577 added. The window shape assures seamless reconstruction.
578 <!--l. 354--><p class="noindent" >This is easy to visualize in the case of equal sized-windows:
581 <!--l. 356--><p class="noindent" >
583 <!--l. 357--><p class="noindent" ><img
584 src="window1.png" alt="PIC"
586 <br /> <table class="caption"
587 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 2: </td><td
588 class="content">overlap of two equal-sized windows</td></tr></table><!--tex4ht:label?: x1-260012 -->
590 <!--l. 361--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows:
593 <!--l. 364--><p class="noindent" >
595 <!--l. 365--><p class="noindent" ><img
596 src="window2.png" alt="PIC"
598 <br /> <table class="caption"
599 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 3: </td><td
600 class="content">overlap of a long and a short window</td></tr></table><!--tex4ht:label?: x1-260023 -->
602 <!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
603 seamless lapping as above. It is possible to correctly infer window shape to be applied to the current
604 window from knowing the sizes of the current, previous and next window. It is legal for a decoder to
605 use this method. However, in the case of a long window (short windows require no modification),
606 Vorbis also codes two flag bits to specify pre- and post- window shape. Although not strictly
607 necessary for function, this minor redundancy allows a packet to be fully decoded to the
608 point of lapping entirely independently of any other packet, allowing easier abstraction
609 of decode layers as well as allowing a greater level of easy parallelism in encode and
611 <!--l. 382--><p class="noindent" >A description of valid window functions for use with an inverse MDCT can be found in <span class="cite">[<a
612 href="#XSporer/Brandenburg/Edler">1</a>]</span>. Vorbis
613 windows all use the slope function
614 <center class="math-display" >
616 src="Vorbis_I_spec0x.png" alt="y = sin (.5* π sin2((x + .5)∕n *π )).
617 " class="math-display" ></center>
618 <!--l. 385--><p class="nopar" >
619 <!--l. 389--><p class="noindent" ><span class="paragraphHead"><a
620 id="x1-270001.3.2"></a><span
621 class="cmbx-10x-x-109">floor decode</span></span>
622 Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
623 specifies which floor configuration to use. All floors are decoded before residue decode
625 <!--l. 395--><p class="noindent" ><span class="paragraphHead"><a
626 id="x1-280001.3.2"></a><span
627 class="cmbx-10x-x-109">residue decode</span></span>
628 Although the number of residue vectors equals the number of channels, channel coupling may mean
629 that the raw residue vectors extracted during decode do not map directly to specific channels. When
630 channel coupling is in use, some vectors will correspond to coupled magnitude or angle. The
631 coupling relationships are described in the codec setup and may differ from frame to frame, due to
632 different mode numbers.
633 <!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from submap
634 0 through n-1. This differs from floors which are coded using a configuration provided by submap
635 number, but are coded individually in channel order.
636 <!--l. 411--><p class="noindent" ><span class="paragraphHead"><a
637 id="x1-290001.3.2"></a><span
638 class="cmbx-10x-x-109">inverse channel coupling</span></span>
639 A detailed discussion of stereo in the Vorbis codec can be found in the document <a
640 href="stereo.html" >Stereo Channel
641 Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo coupling, but the stereo
642 document also gives a good overview of the generic coupling mechanism.
643 <!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place
644 a pair at a time in the order and using the vectors specified in the current mapping
645 configuration. The decoupling operation is the same for all pairs, converting square polar
646 representation (where one vector is magnitude and the second angle) back to Cartesian
648 <!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
649 represent the fine spectral detail of each output channel.
650 <!--l. 432--><p class="noindent" ><span class="paragraphHead"><a
651 id="x1-300001.3.2"></a><span
652 class="cmbx-10x-x-109">generate floor curve</span></span>
656 The decoder may choose to generate the floor curve at any appropriate time. It is reasonable
657 to generate the output curve when the floor data is decoded from the raw packet, or
658 it can be generated after inverse coupling and applied to the spectral residue directly,
659 combining generation and the dot product into one step and eliminating some working
661 <!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied (dot
662 product) by the linear-range, linear-domain spectral residue.
663 <!--l. 447--><p class="noindent" ><span class="paragraphHead"><a
664 id="x1-310001.3.2"></a><span
665 class="cmbx-10x-x-109">compute floor/residue dot product</span></span>
666 This step is straightforward; for each output channel, the decoder multiplies the floor curve
667 and residue vectors element by element, producing the finished audio spectrum of each
669 <!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
670 implementation might be to assume that a 32 bit fixed-point representation for floor
671 and residue and direct multiplication of the vectors is sufficient for acceptable spectral
672 depth in all cases because it happens to mostly work with the current Xiph.Org reference
674 <!--l. 462--><p class="noindent" >However, floor vector values can span <span
675 class="cmsy-10x-x-109">~</span>140dB (<span
676 class="cmsy-10x-x-109">~</span>24 bits unsigned), and the audio spectrum vector
677 should represent a minimum of 120dB (<span
678 class="cmsy-10x-x-109">~</span>21 bits with sign), even when output is to a 16 bit PCM
679 device. For the residue vector to represent full scale if the floor is nailed to <span
680 class="cmsy-10x-x-109">-</span>140dB, it must be able
681 to span 0 to +140dB. For the residue vector to reach full scale if the floor is nailed at 0dB, it must
682 be able to represent <span
683 class="cmsy-10x-x-109">-</span>140dB to +0dB. Thus, in order to handle full range dynamics, a residue
684 vector may span <span
685 class="cmsy-10x-x-109">-</span>140dB to +140dB entirely within spec. A 280dB range is approximately 48 bits
686 with sign; thus the residue vector must be able to represent a 48 bit range and the dot product
687 must be able to handle an effective 48 bit times 24 bit multiplication. This range may be
688 achieved using large (64 bit or larger) integers, or implementing a movable binary point
690 <!--l. 479--><p class="noindent" ><span class="paragraphHead"><a
691 id="x1-320001.3.2"></a><span
692 class="cmbx-10x-x-109">inverse monolithic transform (MDCT)</span></span>
693 The audio spectrum is converted back into time domain PCM audio via an inverse Modified
694 Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
695 <span class="cite">[<a
696 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
697 <!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be lapped
698 with surrounding frames using an appropriate window (such as the Vorbis window) before the
699 MDCT can be considered orthogonal.
703 <!--l. 492--><p class="noindent" ><span class="paragraphHead"><a
704 id="x1-330001.3.2"></a><span
705 class="cmbx-10x-x-109">overlap/add data</span></span>
706 Windowed MDCT output is overlapped and added with the right hand data of the previous window
707 such that the 3/4 point of the previous window is aligned with the 1/4 point of the current window
708 (as illustrated in the window overlap diagram). At this point, the audio data between the center of
709 the previous frame and the center of the current frame is now finished and ready to be
711 <!--l. 501--><p class="noindent" ><span class="paragraphHead"><a
712 id="x1-340001.3.2"></a><span
713 class="cmbx-10x-x-109">cache right hand data</span></span>
714 The decoder must cache the right hand portion of the current frame to be lapped with the left hand
715 portion of the next frame.
716 <!--l. 507--><p class="noindent" ><span class="paragraphHead"><a
717 id="x1-350001.3.2"></a><span
718 class="cmbx-10x-x-109">return finished audio data</span></span>
719 The overlapped portion produced from overlapping the previous and current frame data is finished
720 data to be returned by the decoder. This data spans from the center of the previous window to the
721 center of the current window. In the case of same-sized windows, the amount of data to return is
722 one-half block consisting of and only of the overlapped portions. When overlapping a short and long
723 window, much of the returned range is not actually overlap. This does not damage transform
724 orthogonality. Pay attention however to returning the correct data range; the amount of data to be
726 <!--l. 519--><p class="noindent" >
727 <div class="fancyvrb" id="fancyvrb1">
729 id="x1-35002r1"></a><span
730 class="cmtt-10"> </span><span
731 class="cmtt-10"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
733 <!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
734 <!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The encoder
735 accounts for this priming when calculating PCM offsets; after the first frame, the proper PCM
736 output offset is ’0’ (as no data has been returned yet).
743 <h3 class="sectionHead"><span class="titlemark">2 </span> <a
744 id="x1-360002"></a>Bitpacking Convention</h3>
745 <!--l. 6--><p class="noindent" >
746 <h4 class="subsectionHead"><span class="titlemark">2.1 </span> <a
747 id="x1-370002.1"></a>Overview</h4>
748 <!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary integer
749 fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the encoder
750 and then read one-by-one in the same monotonically increasing order by the decoder. Most current
751 binary storage arrangements group bits into a native word size of eight bits (octets), sixteen bits,
752 thirty-two bits or, less commonly other fixed word sizes. The Vorbis bitpacking convention specifies
753 the correct mapping of the logical packet bitstream into an actual representation in fixed-width
755 <!--l. 19--><p class="noindent" >
756 <h5 class="subsubsectionHead"><span class="titlemark">2.1.1 </span> <a
757 id="x1-380002.1.1"></a>octets, bytes and words</h5>
758 <!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits. This
759 has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
760 For purposes of the bitpacking convention, a byte implies the native, smallest integer
761 storage representation offered by a platform. On modern platforms, this is generally
762 assumed to be eight bits (not necessarily because of the processor but because of the
763 filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
764 atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
766 <!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word to
767 be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis bitpacking
768 convention is still well defined for any native byte size; Vorbis uses the native bit-width of a
769 given storage system. This document assumes that a byte is one octet for purposes of
771 <!--l. 39--><p class="noindent" >
772 <h5 class="subsubsectionHead"><span class="titlemark">2.1.2 </span> <a
773 id="x1-390002.1.2"></a>bit order</h5>
774 <!--l. 41--><p class="noindent" >A byte has a well-defined ’least significant’ bit (LSb), which is the only bit set when the byte is
775 storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
779 opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
780 class="cmmi-10x-x-109">n </span>(<span
781 class="cmmi-10x-x-109">n </span>= 7 in an octet)
783 <!--l. 50--><p class="noindent" >
784 <h5 class="subsubsectionHead"><span class="titlemark">2.1.3 </span> <a
785 id="x1-400002.1.3"></a>byte order</h5>
786 <!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word;
787 the common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
788 highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
789 which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
791 <!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
792 word, level, thus host word ordering is of a concern only during optimization when writing high
793 performance code that operates on a word of storage at a time rather than by byte.
794 Logically, bytes are always coded and decoded in order from byte zero through byte
796 class="cmmi-10x-x-109">n</span>.
797 <!--l. 68--><p class="noindent" >
798 <h5 class="subsubsectionHead"><span class="titlemark">2.1.4 </span> <a
799 id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
800 <!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
801 wide, into packets. These integer fields are not aligned to the boundaries of the byte
802 representation; the next field is written at the bit position at which the previous field
804 <!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical bitstream
805 first, followed by next least significant bit, etc, until the requested number of bits have been coded.
806 When packing the bits into bytes, the encoder begins by placing the LSb of the integer to be written
807 into the least significant unused bit position of the destination byte, followed by the next-least
808 significant bit of the source integer and so on up to the requested number of bits. When all bits of
809 the destination byte have been filled, encoding continues by zeroing all bits of the next byte
810 and writing the next bit into the bit position 0 of that byte. Decoding follows the same
811 process as encoding, but by reading bits from the byte stream and reassembling them into
813 <!--l. 90--><p class="noindent" >
814 <h5 class="subsubsectionHead"><span class="titlemark">2.1.5 </span> <a
815 id="x1-420002.1.5"></a>signedness</h5>
819 <!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder given
820 decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
821 either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
822 encoder and decoder are responsible for knowing if fields are to be treated as signed or
824 <!--l. 101--><p class="noindent" >
825 <h5 class="subsubsectionHead"><span class="titlemark">2.1.6 </span> <a
826 id="x1-430002.1.6"></a>coding example</h5>
827 <!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
828 <!--l. 106--><p class="noindent" >
829 <div class="fancyvrb" id="fancyvrb2">
831 id="x1-43002r1"></a><span
832 class="cmtt-10"> </span><span
833 class="cmtt-10"> </span><span
834 class="cmtt-10"> </span><span
835 class="cmtt-10"> </span><span
836 class="cmtt-10"> </span><span
837 class="cmtt-10"> </span><span
838 class="cmtt-10"> </span><span
839 class="cmtt-10"> </span><span
840 class="cmtt-10"> </span><span
841 class="cmtt-10"> </span><span
842 class="cmtt-10"> </span><span
843 class="cmtt-10"> </span><span
844 class="cmtt-10"> </span><span
845 class="cmtt-10"> </span><span
846 class="cmtt-10"> </span><span
847 class="cmtt-10"> |</span>
848 <br class="fancyvrb" /><a
849 id="x1-43004r2"></a><span
850 class="cmtt-10"> </span><span
851 class="cmtt-10"> </span><span
852 class="cmtt-10"> </span><span
853 class="cmtt-10"> </span><span
854 class="cmtt-10"> </span><span
855 class="cmtt-10"> </span><span
856 class="cmtt-10"> </span><span
857 class="cmtt-10"> </span><span
858 class="cmtt-10"> </span><span
859 class="cmtt-10"> </span><span
860 class="cmtt-10"> </span><span
861 class="cmtt-10"> </span><span
862 class="cmtt-10"> </span><span
863 class="cmtt-10"> </span><span
864 class="cmtt-10"> </span><span
865 class="cmtt-10"> V</span>
866 <br class="fancyvrb" /><a
867 id="x1-43006r3"></a><span
868 class="cmtt-10"> </span><span
869 class="cmtt-10"> </span>
870 <br class="fancyvrb" /><a
871 id="x1-43008r4"></a><span
872 class="cmtt-10"> </span><span
873 class="cmtt-10"> </span><span
874 class="cmtt-10"> </span><span
875 class="cmtt-10"> </span><span
876 class="cmtt-10"> </span><span
877 class="cmtt-10"> </span><span
878 class="cmtt-10"> </span><span
879 class="cmtt-10"> </span><span
880 class="cmtt-10"> </span><span
881 class="cmtt-10"> 7</span><span
882 class="cmtt-10"> 6</span><span
883 class="cmtt-10"> 5</span><span
884 class="cmtt-10"> 4</span><span
885 class="cmtt-10"> 3</span><span
886 class="cmtt-10"> 2</span><span
887 class="cmtt-10"> 1</span><span
888 class="cmtt-10"> 0</span>
889 <br class="fancyvrb" /><a
890 id="x1-43010r5"></a><span
891 class="cmtt-10"> </span><span
892 class="cmtt-10"> byte</span><span
893 class="cmtt-10"> 0</span><span
894 class="cmtt-10"> [0</span><span
895 class="cmtt-10"> 0</span><span
896 class="cmtt-10"> 0</span><span
897 class="cmtt-10"> 0</span><span
898 class="cmtt-10"> 1</span><span
899 class="cmtt-10"> 1</span><span
900 class="cmtt-10"> 0</span><span
901 class="cmtt-10"> 0]</span><span
902 class="cmtt-10"> </span><span
903 class="cmtt-10"> <-</span>
904 <br class="fancyvrb" /><a
905 id="x1-43012r6"></a><span
906 class="cmtt-10"> </span><span
907 class="cmtt-10"> byte</span><span
908 class="cmtt-10"> 1</span><span
909 class="cmtt-10"> [</span><span
910 class="cmtt-10"> </span><span
911 class="cmtt-10"> </span><span
912 class="cmtt-10"> </span><span
913 class="cmtt-10"> </span><span
914 class="cmtt-10"> </span><span
915 class="cmtt-10"> </span><span
916 class="cmtt-10"> </span><span
917 class="cmtt-10"> </span><span
918 class="cmtt-10"> </span><span
919 class="cmtt-10"> </span><span
920 class="cmtt-10"> </span><span
921 class="cmtt-10"> </span><span
922 class="cmtt-10"> </span><span
923 class="cmtt-10"> </span><span
924 class="cmtt-10"> ]</span>
925 <br class="fancyvrb" /><a
926 id="x1-43014r7"></a><span
927 class="cmtt-10"> </span><span
928 class="cmtt-10"> byte</span><span
929 class="cmtt-10"> 2</span><span
930 class="cmtt-10"> [</span><span
931 class="cmtt-10"> </span><span
932 class="cmtt-10"> </span><span
933 class="cmtt-10"> </span><span
934 class="cmtt-10"> </span><span
935 class="cmtt-10"> </span><span
936 class="cmtt-10"> </span><span
937 class="cmtt-10"> </span><span
938 class="cmtt-10"> </span><span
939 class="cmtt-10"> </span><span
940 class="cmtt-10"> </span><span
941 class="cmtt-10"> </span><span
942 class="cmtt-10"> </span><span
943 class="cmtt-10"> </span><span
944 class="cmtt-10"> </span><span
945 class="cmtt-10"> ]</span>
946 <br class="fancyvrb" /><a
947 id="x1-43016r8"></a><span
948 class="cmtt-10"> </span><span
949 class="cmtt-10"> byte</span><span
950 class="cmtt-10"> 3</span><span
951 class="cmtt-10"> [</span><span
952 class="cmtt-10"> </span><span
953 class="cmtt-10"> </span><span
954 class="cmtt-10"> </span><span
955 class="cmtt-10"> </span><span
956 class="cmtt-10"> </span><span
957 class="cmtt-10"> </span><span
958 class="cmtt-10"> </span><span
959 class="cmtt-10"> </span><span
960 class="cmtt-10"> </span><span
961 class="cmtt-10"> </span><span
962 class="cmtt-10"> </span><span
963 class="cmtt-10"> </span><span
964 class="cmtt-10"> </span><span
965 class="cmtt-10"> </span><span
966 class="cmtt-10"> ]</span>
967 <br class="fancyvrb" /><a
968 id="x1-43018r9"></a><span
969 class="cmtt-10"> </span><span
970 class="cmtt-10"> </span><span
971 class="cmtt-10"> </span><span
972 class="cmtt-10"> </span><span
973 class="cmtt-10"> </span><span
974 class="cmtt-10"> </span><span
975 class="cmtt-10"> </span><span
976 class="cmtt-10"> </span><span
977 class="cmtt-10"> </span><span
978 class="cmtt-10"> </span><span
979 class="cmtt-10"> </span><span
980 class="cmtt-10"> </span><span
981 class="cmtt-10"> </span><span
982 class="cmtt-10"> </span><span
983 class="cmtt-10"> ...</span>
984 <br class="fancyvrb" /><a
985 id="x1-43020r10"></a><span
986 class="cmtt-10"> </span><span
987 class="cmtt-10"> byte</span><span
988 class="cmtt-10"> n</span><span
989 class="cmtt-10"> [</span><span
990 class="cmtt-10"> </span><span
991 class="cmtt-10"> </span><span
992 class="cmtt-10"> </span><span
993 class="cmtt-10"> </span><span
994 class="cmtt-10"> </span><span
995 class="cmtt-10"> </span><span
996 class="cmtt-10"> </span><span
997 class="cmtt-10"> </span><span
998 class="cmtt-10"> </span><span
999 class="cmtt-10"> </span><span
1000 class="cmtt-10"> </span><span
1001 class="cmtt-10"> </span><span
1002 class="cmtt-10"> </span><span
1003 class="cmtt-10"> </span><span
1004 class="cmtt-10"> ]</span><span
1005 class="cmtt-10"> </span><span
1006 class="cmtt-10"> bytestream</span><span
1007 class="cmtt-10"> length</span><span
1008 class="cmtt-10"> ==</span><span
1009 class="cmtt-10"> 1</span><span
1010 class="cmtt-10"> byte</span>
1011 <br class="fancyvrb" /><a
1012 id="x1-43022r11"></a><span
1013 class="cmtt-10"> </span><span
1014 class="cmtt-10"> </span>
1016 <!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
1017 <!--l. 123--><p class="noindent" >
1018 <div class="fancyvrb" id="fancyvrb3">
1020 id="x1-43024r1"></a><span
1021 class="cmtt-10"> </span><span
1022 class="cmtt-10"> </span><span
1023 class="cmtt-10"> </span><span
1024 class="cmtt-10"> </span><span
1025 class="cmtt-10"> </span><span
1026 class="cmtt-10"> </span><span
1027 class="cmtt-10"> </span><span
1028 class="cmtt-10"> </span><span
1029 class="cmtt-10"> </span><span
1030 class="cmtt-10"> |</span>
1031 <br class="fancyvrb" /><a
1032 id="x1-43026r2"></a><span
1033 class="cmtt-10"> </span><span
1034 class="cmtt-10"> </span><span
1035 class="cmtt-10"> </span><span
1036 class="cmtt-10"> </span><span
1037 class="cmtt-10"> </span><span
1038 class="cmtt-10"> </span><span
1039 class="cmtt-10"> </span><span
1040 class="cmtt-10"> </span><span
1041 class="cmtt-10"> </span><span
1042 class="cmtt-10"> V</span>
1043 <br class="fancyvrb" /><a
1044 id="x1-43028r3"></a><span
1045 class="cmtt-10"> </span><span
1046 class="cmtt-10"> </span>
1047 <br class="fancyvrb" /><a
1048 id="x1-43030r4"></a><span
1049 class="cmtt-10"> </span><span
1050 class="cmtt-10"> </span><span
1051 class="cmtt-10"> </span><span
1052 class="cmtt-10"> </span><span
1053 class="cmtt-10"> </span><span
1054 class="cmtt-10"> </span><span
1055 class="cmtt-10"> </span><span
1056 class="cmtt-10"> </span><span
1057 class="cmtt-10"> </span><span
1058 class="cmtt-10"> 7</span><span
1059 class="cmtt-10"> 6</span><span
1060 class="cmtt-10"> 5</span><span
1061 class="cmtt-10"> 4</span><span
1062 class="cmtt-10"> 3</span><span
1063 class="cmtt-10"> 2</span><span
1064 class="cmtt-10"> 1</span><span
1065 class="cmtt-10"> 0</span>
1066 <br class="fancyvrb" /><a
1067 id="x1-43032r5"></a><span
1068 class="cmtt-10"> </span><span
1069 class="cmtt-10"> byte</span><span
1070 class="cmtt-10"> 0</span><span
1071 class="cmtt-10"> [0</span><span
1072 class="cmtt-10"> 1</span><span
1073 class="cmtt-10"> 1</span><span
1074 class="cmtt-10"> 1</span><span
1075 class="cmtt-10"> 1</span><span
1076 class="cmtt-10"> 1</span><span
1077 class="cmtt-10"> 0</span><span
1078 class="cmtt-10"> 0]</span><span
1079 class="cmtt-10"> </span><span
1080 class="cmtt-10"> <-</span>
1081 <br class="fancyvrb" /><a
1082 id="x1-43034r6"></a><span
1083 class="cmtt-10"> </span><span
1084 class="cmtt-10"> byte</span><span
1085 class="cmtt-10"> 1</span><span
1086 class="cmtt-10"> [</span><span
1087 class="cmtt-10"> </span><span
1088 class="cmtt-10"> </span><span
1089 class="cmtt-10"> </span><span
1090 class="cmtt-10"> </span><span
1091 class="cmtt-10"> </span><span
1092 class="cmtt-10"> </span><span
1093 class="cmtt-10"> </span><span
1094 class="cmtt-10"> </span><span
1095 class="cmtt-10"> </span><span
1096 class="cmtt-10"> </span><span
1097 class="cmtt-10"> </span><span
1098 class="cmtt-10"> </span><span
1099 class="cmtt-10"> </span><span
1100 class="cmtt-10"> </span><span
1101 class="cmtt-10"> ]</span>
1102 <br class="fancyvrb" /><a
1103 id="x1-43036r7"></a><span
1104 class="cmtt-10"> </span><span
1105 class="cmtt-10"> byte</span><span
1106 class="cmtt-10"> 2</span><span
1107 class="cmtt-10"> [</span><span
1108 class="cmtt-10"> </span><span
1109 class="cmtt-10"> </span><span
1110 class="cmtt-10"> </span><span
1111 class="cmtt-10"> </span><span
1112 class="cmtt-10"> </span><span
1113 class="cmtt-10"> </span><span
1114 class="cmtt-10"> </span><span
1115 class="cmtt-10"> </span><span
1116 class="cmtt-10"> </span><span
1117 class="cmtt-10"> </span><span
1118 class="cmtt-10"> </span><span
1119 class="cmtt-10"> </span><span
1120 class="cmtt-10"> </span><span
1121 class="cmtt-10"> </span><span
1122 class="cmtt-10"> ]</span>
1123 <br class="fancyvrb" /><a
1124 id="x1-43038r8"></a><span
1125 class="cmtt-10"> </span><span
1126 class="cmtt-10"> byte</span><span
1127 class="cmtt-10"> 3</span><span
1128 class="cmtt-10"> [</span><span
1129 class="cmtt-10"> </span><span
1130 class="cmtt-10"> </span><span
1131 class="cmtt-10"> </span><span
1132 class="cmtt-10"> </span><span
1133 class="cmtt-10"> </span><span
1134 class="cmtt-10"> </span><span
1135 class="cmtt-10"> </span><span
1136 class="cmtt-10"> </span><span
1137 class="cmtt-10"> </span><span
1138 class="cmtt-10"> </span><span
1139 class="cmtt-10"> </span><span
1140 class="cmtt-10"> </span><span
1141 class="cmtt-10"> </span><span
1142 class="cmtt-10"> </span><span
1143 class="cmtt-10"> ]</span>
1144 <br class="fancyvrb" /><a
1145 id="x1-43040r9"></a><span
1146 class="cmtt-10"> </span><span
1147 class="cmtt-10"> </span><span
1148 class="cmtt-10"> </span><span
1149 class="cmtt-10"> </span><span
1150 class="cmtt-10"> </span><span
1151 class="cmtt-10"> </span><span
1152 class="cmtt-10"> </span><span
1153 class="cmtt-10"> </span><span
1154 class="cmtt-10"> </span><span
1155 class="cmtt-10"> </span><span
1156 class="cmtt-10"> </span><span
1157 class="cmtt-10"> </span><span
1158 class="cmtt-10"> </span><span
1159 class="cmtt-10"> </span><span
1160 class="cmtt-10"> ...</span>
1161 <br class="fancyvrb" /><a
1162 id="x1-43042r10"></a><span
1163 class="cmtt-10"> </span><span
1164 class="cmtt-10"> byte</span><span
1165 class="cmtt-10"> n</span><span
1166 class="cmtt-10"> [</span><span
1167 class="cmtt-10"> </span><span
1168 class="cmtt-10"> </span><span
1169 class="cmtt-10"> </span><span
1170 class="cmtt-10"> </span><span
1171 class="cmtt-10"> </span><span
1172 class="cmtt-10"> </span><span
1173 class="cmtt-10"> </span><span
1174 class="cmtt-10"> </span><span
1175 class="cmtt-10"> </span><span
1176 class="cmtt-10"> </span><span
1177 class="cmtt-10"> </span><span
1178 class="cmtt-10"> </span><span
1179 class="cmtt-10"> </span><span
1180 class="cmtt-10"> </span><span
1181 class="cmtt-10"> ]</span><span
1182 class="cmtt-10"> </span><span
1183 class="cmtt-10"> bytestream</span><span
1184 class="cmtt-10"> length</span><span
1185 class="cmtt-10"> ==</span><span
1186 class="cmtt-10"> 1</span><span
1187 class="cmtt-10"> byte</span>
1189 <!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
1190 <!--l. 139--><p class="noindent" >
1194 <div class="fancyvrb" id="fancyvrb4">
1196 id="x1-43044r1"></a><span
1197 class="cmtt-10"> </span><span
1198 class="cmtt-10"> </span><span
1199 class="cmtt-10"> </span><span
1200 class="cmtt-10"> </span><span
1201 class="cmtt-10"> </span><span
1202 class="cmtt-10"> </span><span
1203 class="cmtt-10"> </span><span
1204 class="cmtt-10"> </span><span
1205 class="cmtt-10"> </span><span
1206 class="cmtt-10"> </span><span
1207 class="cmtt-10"> </span><span
1208 class="cmtt-10"> |</span>
1209 <br class="fancyvrb" /><a
1210 id="x1-43046r2"></a><span
1211 class="cmtt-10"> </span><span
1212 class="cmtt-10"> </span><span
1213 class="cmtt-10"> </span><span
1214 class="cmtt-10"> </span><span
1215 class="cmtt-10"> </span><span
1216 class="cmtt-10"> </span><span
1217 class="cmtt-10"> </span><span
1218 class="cmtt-10"> </span><span
1219 class="cmtt-10"> </span><span
1220 class="cmtt-10"> </span><span
1221 class="cmtt-10"> </span><span
1222 class="cmtt-10"> V</span>
1223 <br class="fancyvrb" /><a
1224 id="x1-43048r3"></a><span
1225 class="cmtt-10"> </span><span
1226 class="cmtt-10"> </span>
1227 <br class="fancyvrb" /><a
1228 id="x1-43050r4"></a><span
1229 class="cmtt-10"> </span><span
1230 class="cmtt-10"> </span><span
1231 class="cmtt-10"> </span><span
1232 class="cmtt-10"> </span><span
1233 class="cmtt-10"> </span><span
1234 class="cmtt-10"> </span><span
1235 class="cmtt-10"> </span><span
1236 class="cmtt-10"> </span><span
1237 class="cmtt-10"> </span><span
1238 class="cmtt-10"> 7</span><span
1239 class="cmtt-10"> 6</span><span
1240 class="cmtt-10"> 5</span><span
1241 class="cmtt-10"> 4</span><span
1242 class="cmtt-10"> 3</span><span
1243 class="cmtt-10"> 2</span><span
1244 class="cmtt-10"> 1</span><span
1245 class="cmtt-10"> 0</span>
1246 <br class="fancyvrb" /><a
1247 id="x1-43052r5"></a><span
1248 class="cmtt-10"> </span><span
1249 class="cmtt-10"> byte</span><span
1250 class="cmtt-10"> 0</span><span
1251 class="cmtt-10"> [1</span><span
1252 class="cmtt-10"> 1</span><span
1253 class="cmtt-10"> 1</span><span
1254 class="cmtt-10"> 1</span><span
1255 class="cmtt-10"> 1</span><span
1256 class="cmtt-10"> 1</span><span
1257 class="cmtt-10"> 0</span><span
1258 class="cmtt-10"> 0]</span>
1259 <br class="fancyvrb" /><a
1260 id="x1-43054r6"></a><span
1261 class="cmtt-10"> </span><span
1262 class="cmtt-10"> byte</span><span
1263 class="cmtt-10"> 1</span><span
1264 class="cmtt-10"> [0</span><span
1265 class="cmtt-10"> 0</span><span
1266 class="cmtt-10"> 0</span><span
1267 class="cmtt-10"> 0</span><span
1268 class="cmtt-10"> 1</span><span
1269 class="cmtt-10"> 0</span><span
1270 class="cmtt-10"> 0</span><span
1271 class="cmtt-10"> 0]</span><span
1272 class="cmtt-10"> </span><span
1273 class="cmtt-10"> <-</span>
1274 <br class="fancyvrb" /><a
1275 id="x1-43056r7"></a><span
1276 class="cmtt-10"> </span><span
1277 class="cmtt-10"> byte</span><span
1278 class="cmtt-10"> 2</span><span
1279 class="cmtt-10"> [</span><span
1280 class="cmtt-10"> </span><span
1281 class="cmtt-10"> </span><span
1282 class="cmtt-10"> </span><span
1283 class="cmtt-10"> </span><span
1284 class="cmtt-10"> </span><span
1285 class="cmtt-10"> </span><span
1286 class="cmtt-10"> </span><span
1287 class="cmtt-10"> </span><span
1288 class="cmtt-10"> </span><span
1289 class="cmtt-10"> </span><span
1290 class="cmtt-10"> </span><span
1291 class="cmtt-10"> </span><span
1292 class="cmtt-10"> </span><span
1293 class="cmtt-10"> </span><span
1294 class="cmtt-10"> ]</span>
1295 <br class="fancyvrb" /><a
1296 id="x1-43058r8"></a><span
1297 class="cmtt-10"> </span><span
1298 class="cmtt-10"> byte</span><span
1299 class="cmtt-10"> 3</span><span
1300 class="cmtt-10"> [</span><span
1301 class="cmtt-10"> </span><span
1302 class="cmtt-10"> </span><span
1303 class="cmtt-10"> </span><span
1304 class="cmtt-10"> </span><span
1305 class="cmtt-10"> </span><span
1306 class="cmtt-10"> </span><span
1307 class="cmtt-10"> </span><span
1308 class="cmtt-10"> </span><span
1309 class="cmtt-10"> </span><span
1310 class="cmtt-10"> </span><span
1311 class="cmtt-10"> </span><span
1312 class="cmtt-10"> </span><span
1313 class="cmtt-10"> </span><span
1314 class="cmtt-10"> </span><span
1315 class="cmtt-10"> ]</span>
1316 <br class="fancyvrb" /><a
1317 id="x1-43060r9"></a><span
1318 class="cmtt-10"> </span><span
1319 class="cmtt-10"> </span><span
1320 class="cmtt-10"> </span><span
1321 class="cmtt-10"> </span><span
1322 class="cmtt-10"> </span><span
1323 class="cmtt-10"> </span><span
1324 class="cmtt-10"> </span><span
1325 class="cmtt-10"> </span><span
1326 class="cmtt-10"> </span><span
1327 class="cmtt-10"> </span><span
1328 class="cmtt-10"> </span><span
1329 class="cmtt-10"> </span><span
1330 class="cmtt-10"> </span><span
1331 class="cmtt-10"> </span><span
1332 class="cmtt-10"> ...</span>
1333 <br class="fancyvrb" /><a
1334 id="x1-43062r10"></a><span
1335 class="cmtt-10"> </span><span
1336 class="cmtt-10"> byte</span><span
1337 class="cmtt-10"> n</span><span
1338 class="cmtt-10"> [</span><span
1339 class="cmtt-10"> </span><span
1340 class="cmtt-10"> </span><span
1341 class="cmtt-10"> </span><span
1342 class="cmtt-10"> </span><span
1343 class="cmtt-10"> </span><span
1344 class="cmtt-10"> </span><span
1345 class="cmtt-10"> </span><span
1346 class="cmtt-10"> </span><span
1347 class="cmtt-10"> </span><span
1348 class="cmtt-10"> </span><span
1349 class="cmtt-10"> </span><span
1350 class="cmtt-10"> </span><span
1351 class="cmtt-10"> </span><span
1352 class="cmtt-10"> </span><span
1353 class="cmtt-10"> ]</span><span
1354 class="cmtt-10"> </span><span
1355 class="cmtt-10"> bytestream</span><span
1356 class="cmtt-10"> length</span><span
1357 class="cmtt-10"> ==</span><span
1358 class="cmtt-10"> 2</span><span
1359 class="cmtt-10"> bytes</span>
1360 <br class="fancyvrb" /><a
1361 id="x1-43064r11"></a><span
1362 class="cmtt-10"> </span><span
1363 class="cmtt-10"> </span><span
1364 class="cmtt-10"> </span><span
1365 class="cmtt-10"> </span><span
1366 class="cmtt-10"> </span><span
1367 class="cmtt-10"> </span><span
1368 class="cmtt-10"> </span><span
1369 class="cmtt-10"> </span><span
1370 class="cmtt-10"> </span><span
1371 class="cmtt-10"> </span><span
1372 class="cmtt-10"> </span><span
1373 class="cmtt-10"> </span><span
1374 class="cmtt-10"> </span><span
1375 class="cmtt-10"> </span><span
1376 class="cmtt-10"> </span><span
1377 class="cmtt-10"> </span><span
1378 class="cmtt-10"> </span><span
1379 class="cmtt-10"> </span><span
1380 class="cmtt-10"> </span><span
1381 class="cmtt-10"> </span><span
1382 class="cmtt-10"> </span><span
1383 class="cmtt-10"> </span><span
1384 class="cmtt-10"> </span><span
1385 class="cmtt-10"> </span><span
1386 class="cmtt-10"> </span><span
1387 class="cmtt-10"> </span><span
1388 class="cmtt-10"> </span><span
1389 class="cmtt-10"> bit</span><span
1390 class="cmtt-10"> cursor</span><span
1391 class="cmtt-10"> ==</span><span
1392 class="cmtt-10"> 6</span>
1394 <!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
1395 <!--l. 156--><p class="noindent" >
1396 <div class="fancyvrb" id="fancyvrb5">
1398 id="x1-43066r1"></a><span
1399 class="cmtt-10"> </span><span
1400 class="cmtt-10"> </span><span
1401 class="cmtt-10"> </span><span
1402 class="cmtt-10"> </span><span
1403 class="cmtt-10"> </span><span
1404 class="cmtt-10"> </span><span
1405 class="cmtt-10"> </span><span
1406 class="cmtt-10"> </span><span
1407 class="cmtt-10"> </span><span
1408 class="cmtt-10"> </span><span
1409 class="cmtt-10"> </span><span
1410 class="cmtt-10"> </span><span
1411 class="cmtt-10"> </span><span
1412 class="cmtt-10"> </span><span
1413 class="cmtt-10"> </span><span
1414 class="cmtt-10"> </span><span
1415 class="cmtt-10"> </span><span
1416 class="cmtt-10"> |</span>
1417 <br class="fancyvrb" /><a
1418 id="x1-43068r2"></a><span
1419 class="cmtt-10"> </span><span
1420 class="cmtt-10"> </span><span
1421 class="cmtt-10"> </span><span
1422 class="cmtt-10"> </span><span
1423 class="cmtt-10"> </span><span
1424 class="cmtt-10"> </span><span
1425 class="cmtt-10"> </span><span
1426 class="cmtt-10"> </span><span
1427 class="cmtt-10"> </span><span
1428 class="cmtt-10"> </span><span
1429 class="cmtt-10"> </span><span
1430 class="cmtt-10"> </span><span
1431 class="cmtt-10"> </span><span
1432 class="cmtt-10"> </span><span
1433 class="cmtt-10"> </span><span
1434 class="cmtt-10"> </span><span
1435 class="cmtt-10"> </span><span
1436 class="cmtt-10"> V</span>
1437 <br class="fancyvrb" /><a
1438 id="x1-43070r3"></a><span
1439 class="cmtt-10"> </span><span
1440 class="cmtt-10"> </span>
1441 <br class="fancyvrb" /><a
1442 id="x1-43072r4"></a><span
1443 class="cmtt-10"> </span><span
1444 class="cmtt-10"> </span><span
1445 class="cmtt-10"> </span><span
1446 class="cmtt-10"> </span><span
1447 class="cmtt-10"> </span><span
1448 class="cmtt-10"> </span><span
1449 class="cmtt-10"> </span><span
1450 class="cmtt-10"> </span><span
1451 class="cmtt-10"> </span><span
1452 class="cmtt-10"> 7</span><span
1453 class="cmtt-10"> 6</span><span
1454 class="cmtt-10"> 5</span><span
1455 class="cmtt-10"> 4</span><span
1456 class="cmtt-10"> 3</span><span
1457 class="cmtt-10"> 2</span><span
1458 class="cmtt-10"> 1</span><span
1459 class="cmtt-10"> 0</span>
1460 <br class="fancyvrb" /><a
1461 id="x1-43074r5"></a><span
1462 class="cmtt-10"> </span><span
1463 class="cmtt-10"> byte</span><span
1464 class="cmtt-10"> 0</span><span
1465 class="cmtt-10"> [1</span><span
1466 class="cmtt-10"> 1</span><span
1467 class="cmtt-10"> 1</span><span
1468 class="cmtt-10"> 1</span><span
1469 class="cmtt-10"> 1</span><span
1470 class="cmtt-10"> 1</span><span
1471 class="cmtt-10"> 0</span><span
1472 class="cmtt-10"> 0]</span>
1473 <br class="fancyvrb" /><a
1474 id="x1-43076r6"></a><span
1475 class="cmtt-10"> </span><span
1476 class="cmtt-10"> byte</span><span
1477 class="cmtt-10"> 1</span><span
1478 class="cmtt-10"> [0</span><span
1479 class="cmtt-10"> 1</span><span
1480 class="cmtt-10"> 0</span><span
1481 class="cmtt-10"> 0</span><span
1482 class="cmtt-10"> 1</span><span
1483 class="cmtt-10"> 0</span><span
1484 class="cmtt-10"> 0</span><span
1485 class="cmtt-10"> 0]</span>
1486 <br class="fancyvrb" /><a
1487 id="x1-43078r7"></a><span
1488 class="cmtt-10"> </span><span
1489 class="cmtt-10"> byte</span><span
1490 class="cmtt-10"> 2</span><span
1491 class="cmtt-10"> [1</span><span
1492 class="cmtt-10"> 1</span><span
1493 class="cmtt-10"> 0</span><span
1494 class="cmtt-10"> 0</span><span
1495 class="cmtt-10"> 1</span><span
1496 class="cmtt-10"> 1</span><span
1497 class="cmtt-10"> 1</span><span
1498 class="cmtt-10"> 0]</span>
1499 <br class="fancyvrb" /><a
1500 id="x1-43080r8"></a><span
1501 class="cmtt-10"> </span><span
1502 class="cmtt-10"> byte</span><span
1503 class="cmtt-10"> 3</span><span
1504 class="cmtt-10"> [0</span><span
1505 class="cmtt-10"> 0</span><span
1506 class="cmtt-10"> 0</span><span
1507 class="cmtt-10"> 0</span><span
1508 class="cmtt-10"> 0</span><span
1509 class="cmtt-10"> 1</span><span
1510 class="cmtt-10"> 1</span><span
1511 class="cmtt-10"> 0]</span><span
1512 class="cmtt-10"> </span><span
1513 class="cmtt-10"> <-</span>
1514 <br class="fancyvrb" /><a
1515 id="x1-43082r9"></a><span
1516 class="cmtt-10"> </span><span
1517 class="cmtt-10"> </span><span
1518 class="cmtt-10"> </span><span
1519 class="cmtt-10"> </span><span
1520 class="cmtt-10"> </span><span
1521 class="cmtt-10"> </span><span
1522 class="cmtt-10"> </span><span
1523 class="cmtt-10"> </span><span
1524 class="cmtt-10"> </span><span
1525 class="cmtt-10"> </span><span
1526 class="cmtt-10"> </span><span
1527 class="cmtt-10"> </span><span
1528 class="cmtt-10"> </span><span
1529 class="cmtt-10"> </span><span
1530 class="cmtt-10"> ...</span>
1531 <br class="fancyvrb" /><a
1532 id="x1-43084r10"></a><span
1533 class="cmtt-10"> </span><span
1534 class="cmtt-10"> byte</span><span
1535 class="cmtt-10"> n</span><span
1536 class="cmtt-10"> [</span><span
1537 class="cmtt-10"> </span><span
1538 class="cmtt-10"> </span><span
1539 class="cmtt-10"> </span><span
1540 class="cmtt-10"> </span><span
1541 class="cmtt-10"> </span><span
1542 class="cmtt-10"> </span><span
1543 class="cmtt-10"> </span><span
1544 class="cmtt-10"> </span><span
1545 class="cmtt-10"> </span><span
1546 class="cmtt-10"> </span><span
1547 class="cmtt-10"> </span><span
1548 class="cmtt-10"> </span><span
1549 class="cmtt-10"> </span><span
1550 class="cmtt-10"> </span><span
1551 class="cmtt-10"> ]</span><span
1552 class="cmtt-10"> </span><span
1553 class="cmtt-10"> bytestream</span><span
1554 class="cmtt-10"> length</span><span
1555 class="cmtt-10"> ==</span><span
1556 class="cmtt-10"> 4</span><span
1557 class="cmtt-10"> bytes</span>
1558 <br class="fancyvrb" /><a
1559 id="x1-43086r11"></a><span
1560 class="cmtt-10"> </span><span
1561 class="cmtt-10"> </span>
1563 <!--l. 173--><p class="noindent" >
1564 <h5 class="subsubsectionHead"><span class="titlemark">2.1.7 </span> <a
1565 id="x1-440002.1.7"></a>decoding example</h5>
1566 <!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
1567 <!--l. 177--><p class="noindent" >
1568 <div class="fancyvrb" id="fancyvrb6">
1570 id="x1-44002r1"></a><span
1571 class="cmtt-10"> </span><span
1572 class="cmtt-10"> </span><span
1573 class="cmtt-10"> </span><span
1574 class="cmtt-10"> </span><span
1575 class="cmtt-10"> </span><span
1576 class="cmtt-10"> </span><span
1577 class="cmtt-10"> </span><span
1578 class="cmtt-10"> </span><span
1579 class="cmtt-10"> </span><span
1580 class="cmtt-10"> </span><span
1581 class="cmtt-10"> </span><span
1582 class="cmtt-10"> </span><span
1583 class="cmtt-10"> </span><span
1584 class="cmtt-10"> </span><span
1585 class="cmtt-10"> </span><span
1586 class="cmtt-10"> </span><span
1587 class="cmtt-10"> </span><span
1588 class="cmtt-10"> </span><span
1589 class="cmtt-10"> </span><span
1590 class="cmtt-10"> </span><span
1591 class="cmtt-10"> </span><span
1592 class="cmtt-10"> </span><span
1593 class="cmtt-10"> </span><span
1594 class="cmtt-10"> |</span>
1595 <br class="fancyvrb" /><a
1596 id="x1-44004r2"></a><span
1597 class="cmtt-10"> </span><span
1598 class="cmtt-10"> </span><span
1599 class="cmtt-10"> </span><span
1600 class="cmtt-10"> </span><span
1601 class="cmtt-10"> </span><span
1602 class="cmtt-10"> </span><span
1603 class="cmtt-10"> </span><span
1604 class="cmtt-10"> </span><span
1605 class="cmtt-10"> </span><span
1606 class="cmtt-10"> </span><span
1607 class="cmtt-10"> </span><span
1608 class="cmtt-10"> </span><span
1609 class="cmtt-10"> </span><span
1610 class="cmtt-10"> </span><span
1611 class="cmtt-10"> </span><span
1612 class="cmtt-10"> </span><span
1613 class="cmtt-10"> </span><span
1614 class="cmtt-10"> </span><span
1615 class="cmtt-10"> </span><span
1616 class="cmtt-10"> </span><span
1617 class="cmtt-10"> </span><span
1618 class="cmtt-10"> </span><span
1619 class="cmtt-10"> </span><span
1620 class="cmtt-10"> V</span>
1621 <br class="fancyvrb" /><a
1622 id="x1-44006r3"></a><span
1623 class="cmtt-10"> </span><span
1624 class="cmtt-10"> </span>
1625 <br class="fancyvrb" /><a
1626 id="x1-44008r4"></a><span
1627 class="cmtt-10"> </span><span
1628 class="cmtt-10"> </span><span
1629 class="cmtt-10"> </span><span
1630 class="cmtt-10"> </span><span
1631 class="cmtt-10"> </span><span
1632 class="cmtt-10"> </span><span
1633 class="cmtt-10"> </span><span
1634 class="cmtt-10"> </span><span
1635 class="cmtt-10"> </span><span
1636 class="cmtt-10"> 7</span><span
1637 class="cmtt-10"> 6</span><span
1638 class="cmtt-10"> 5</span><span
1639 class="cmtt-10"> 4</span><span
1640 class="cmtt-10"> 3</span><span
1641 class="cmtt-10"> 2</span><span
1642 class="cmtt-10"> 1</span><span
1643 class="cmtt-10"> 0</span>
1644 <br class="fancyvrb" /><a
1645 id="x1-44010r5"></a><span
1646 class="cmtt-10"> </span><span
1647 class="cmtt-10"> byte</span><span
1648 class="cmtt-10"> 0</span><span
1649 class="cmtt-10"> [1</span><span
1650 class="cmtt-10"> 1</span><span
1651 class="cmtt-10"> 1</span><span
1652 class="cmtt-10"> 1</span><span
1653 class="cmtt-10"> 1</span><span
1654 class="cmtt-10"> 1</span><span
1655 class="cmtt-10"> 0</span><span
1656 class="cmtt-10"> 0]</span><span
1657 class="cmtt-10"> </span><span
1658 class="cmtt-10"> <-</span>
1659 <br class="fancyvrb" /><a
1660 id="x1-44012r6"></a><span
1661 class="cmtt-10"> </span><span
1662 class="cmtt-10"> byte</span><span
1663 class="cmtt-10"> 1</span><span
1664 class="cmtt-10"> [0</span><span
1665 class="cmtt-10"> 1</span><span
1666 class="cmtt-10"> 0</span><span
1667 class="cmtt-10"> 0</span><span
1668 class="cmtt-10"> 1</span><span
1669 class="cmtt-10"> 0</span><span
1670 class="cmtt-10"> 0</span><span
1671 class="cmtt-10"> 0]</span>
1672 <br class="fancyvrb" /><a
1673 id="x1-44014r7"></a><span
1674 class="cmtt-10"> </span><span
1675 class="cmtt-10"> byte</span><span
1676 class="cmtt-10"> 2</span><span
1677 class="cmtt-10"> [1</span><span
1678 class="cmtt-10"> 1</span><span
1679 class="cmtt-10"> 0</span><span
1680 class="cmtt-10"> 0</span><span
1681 class="cmtt-10"> 1</span><span
1682 class="cmtt-10"> 1</span><span
1683 class="cmtt-10"> 1</span><span
1684 class="cmtt-10"> 0]</span>
1685 <br class="fancyvrb" /><a
1686 id="x1-44016r8"></a><span
1687 class="cmtt-10"> </span><span
1688 class="cmtt-10"> byte</span><span
1689 class="cmtt-10"> 3</span><span
1690 class="cmtt-10"> [0</span><span
1691 class="cmtt-10"> 0</span><span
1692 class="cmtt-10"> 0</span><span
1693 class="cmtt-10"> 0</span><span
1694 class="cmtt-10"> 0</span><span
1695 class="cmtt-10"> 1</span><span
1696 class="cmtt-10"> 1</span><span
1697 class="cmtt-10"> 0]</span><span
1698 class="cmtt-10"> </span><span
1699 class="cmtt-10"> bytestream</span><span
1700 class="cmtt-10"> length</span><span
1701 class="cmtt-10"> ==</span><span
1702 class="cmtt-10"> 4</span><span
1703 class="cmtt-10"> bytes</span>
1707 <br class="fancyvrb" /><a
1708 id="x1-44018r9"></a><span
1709 class="cmtt-10"> </span><span
1710 class="cmtt-10"> </span>
1712 <!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
1713 are worth noting here:
1714 <ul class="itemize1">
1715 <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
1716 some other combination of bit-widths from the bitstream is well defined. There are no
1717 artificial alignment boundaries maintained in the bitstream.
1719 <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted either
1720 as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on decode
1722 <!--l. 208--><p class="noindent" >
1723 <h5 class="subsubsectionHead"><span class="titlemark">2.1.8 </span> <a
1724 id="x1-450002.1.8"></a>end-of-packet alignment</h5>
1725 <!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
1726 embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
1727 Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
1728 the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space in
1729 the last byte of a packet.
1730 <!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
1731 should this unused space be read, it will return binary zeroes.
1732 <!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
1733 End-of-packet is not to be considered an error; it is merely a state indicating that there is
1734 insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a normal
1735 mode of operation, and as such, decoders must handle reading past the end of a packet as a typical
1736 mode of operation. Any further read operations after an ’end-of-packet’ condition shall also return
1737 ’end-of-packet’.
1738 <!--l. 233--><p class="noindent" >
1739 <h5 class="subsubsectionHead"><span class="titlemark">2.1.9 </span> <a
1740 id="x1-460002.1.9"></a>reading zero bits</h5>
1741 <!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
1742 Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
1743 triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
1747 end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
1748 shall also fail with ’end-of-packet’.
1755 <h3 class="sectionHead"><span class="titlemark">3 </span> <a
1756 id="x1-470003"></a>Probability Model and Codebooks</h3>
1757 <!--l. 6--><p class="noindent" >
1758 <h4 class="subsectionHead"><span class="titlemark">3.1 </span> <a
1759 id="x1-480003.1"></a>Overview</h4>
1760 <!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
1761 probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
1762 bitstream itself in the third header, the codec setup header. This packed configuration consists of
1763 multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
1764 compressed codewords as well as an optional lookup table of output vector values to which a
1765 decoded Huffman value is applied as an offset, generating the final decoded output corresponding to
1766 a given compressed codeword.
1767 <!--l. 18--><p class="noindent" >
1768 <h5 class="subsubsectionHead"><span class="titlemark">3.1.1 </span> <a
1769 id="x1-490003.1.1"></a>Bitwise operation</h5>
1770 <!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
1771 and the codewords they decode are unrolled from a packet as a series of arbitrary-width values read
1772 from the stream according to <a
1773 href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
1774 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
1775 <!--l. 27--><p class="noindent" >
1776 <h4 class="subsectionHead"><span class="titlemark">3.2 </span> <a
1777 id="x1-500003.2"></a>Packed codebook format</h4>
1778 <!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is eight
1779 bits. This is not universally true; see <a
1780 href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
1781 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion relating to
1782 non-eight-bit bytes.
1783 <!--l. 34--><p class="noindent" >
1784 <h5 class="subsubsectionHead"><span class="titlemark">3.2.1 </span> <a
1785 id="x1-510003.2.1"></a>codebook decode</h5>
1786 <!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
1787 <!--l. 38--><p class="noindent" >
1791 <div class="fancyvrb" id="fancyvrb7">
1793 id="x1-51002r1"></a><span
1794 class="cmtt-10"> </span><span
1795 class="cmtt-10"> byte</span><span
1796 class="cmtt-10"> 0:</span><span
1797 class="cmtt-10"> [</span><span
1798 class="cmtt-10"> 0</span><span
1799 class="cmtt-10"> 1</span><span
1800 class="cmtt-10"> 0</span><span
1801 class="cmtt-10"> 0</span><span
1802 class="cmtt-10"> 0</span><span
1803 class="cmtt-10"> 0</span><span
1804 class="cmtt-10"> 1</span><span
1805 class="cmtt-10"> 0</span><span
1806 class="cmtt-10"> ]</span><span
1807 class="cmtt-10"> (0x42)</span>
1808 <br class="fancyvrb" /><a
1809 id="x1-51004r2"></a><span
1810 class="cmtt-10"> </span><span
1811 class="cmtt-10"> byte</span><span
1812 class="cmtt-10"> 1:</span><span
1813 class="cmtt-10"> [</span><span
1814 class="cmtt-10"> 0</span><span
1815 class="cmtt-10"> 1</span><span
1816 class="cmtt-10"> 0</span><span
1817 class="cmtt-10"> 0</span><span
1818 class="cmtt-10"> 0</span><span
1819 class="cmtt-10"> 0</span><span
1820 class="cmtt-10"> 1</span><span
1821 class="cmtt-10"> 1</span><span
1822 class="cmtt-10"> ]</span><span
1823 class="cmtt-10"> (0x43)</span>
1824 <br class="fancyvrb" /><a
1825 id="x1-51006r3"></a><span
1826 class="cmtt-10"> </span><span
1827 class="cmtt-10"> byte</span><span
1828 class="cmtt-10"> 2:</span><span
1829 class="cmtt-10"> [</span><span
1830 class="cmtt-10"> 0</span><span
1831 class="cmtt-10"> 1</span><span
1832 class="cmtt-10"> 0</span><span
1833 class="cmtt-10"> 1</span><span
1834 class="cmtt-10"> 0</span><span
1835 class="cmtt-10"> 1</span><span
1836 class="cmtt-10"> 1</span><span
1837 class="cmtt-10"> 0</span><span
1838 class="cmtt-10"> ]</span><span
1839 class="cmtt-10"> (0x56)</span>
1841 <!--l. 44--><p class="noindent" >16 bit <span
1842 class="cmtt-10x-x-109">[codebook_dimensions] </span>and 24 bit <span
1843 class="cmtt-10x-x-109">[codebook_entries] </span>fields:
1844 <!--l. 46--><p class="noindent" >
1845 <div class="fancyvrb" id="fancyvrb8">
1847 id="x1-51008r1"></a><span
1848 class="cmtt-10"> </span><span
1849 class="cmtt-10"> </span>
1850 <br class="fancyvrb" /><a
1851 id="x1-51010r2"></a><span
1852 class="cmtt-10"> </span><span
1853 class="cmtt-10"> byte</span><span
1854 class="cmtt-10"> 3:</span><span
1855 class="cmtt-10"> [</span><span
1856 class="cmtt-10"> X</span><span
1857 class="cmtt-10"> X</span><span
1858 class="cmtt-10"> X</span><span
1859 class="cmtt-10"> X</span><span
1860 class="cmtt-10"> X</span><span
1861 class="cmtt-10"> X</span><span
1862 class="cmtt-10"> X</span><span
1863 class="cmtt-10"> X</span><span
1864 class="cmtt-10"> ]</span>
1865 <br class="fancyvrb" /><a
1866 id="x1-51012r3"></a><span
1867 class="cmtt-10"> </span><span
1868 class="cmtt-10"> byte</span><span
1869 class="cmtt-10"> 4:</span><span
1870 class="cmtt-10"> [</span><span
1871 class="cmtt-10"> X</span><span
1872 class="cmtt-10"> X</span><span
1873 class="cmtt-10"> X</span><span
1874 class="cmtt-10"> X</span><span
1875 class="cmtt-10"> X</span><span
1876 class="cmtt-10"> X</span><span
1877 class="cmtt-10"> X</span><span
1878 class="cmtt-10"> X</span><span
1879 class="cmtt-10"> ]</span><span
1880 class="cmtt-10"> [codebook_dimensions]</span><span
1881 class="cmtt-10"> (16</span><span
1882 class="cmtt-10"> bit</span><span
1883 class="cmtt-10"> unsigned)</span>
1884 <br class="fancyvrb" /><a
1885 id="x1-51014r4"></a><span
1886 class="cmtt-10"> </span><span
1887 class="cmtt-10"> </span>
1888 <br class="fancyvrb" /><a
1889 id="x1-51016r5"></a><span
1890 class="cmtt-10"> </span><span
1891 class="cmtt-10"> byte</span><span
1892 class="cmtt-10"> 5:</span><span
1893 class="cmtt-10"> [</span><span
1894 class="cmtt-10"> X</span><span
1895 class="cmtt-10"> X</span><span
1896 class="cmtt-10"> X</span><span
1897 class="cmtt-10"> X</span><span
1898 class="cmtt-10"> X</span><span
1899 class="cmtt-10"> X</span><span
1900 class="cmtt-10"> X</span><span
1901 class="cmtt-10"> X</span><span
1902 class="cmtt-10"> ]</span>
1903 <br class="fancyvrb" /><a
1904 id="x1-51018r6"></a><span
1905 class="cmtt-10"> </span><span
1906 class="cmtt-10"> byte</span><span
1907 class="cmtt-10"> 6:</span><span
1908 class="cmtt-10"> [</span><span
1909 class="cmtt-10"> X</span><span
1910 class="cmtt-10"> X</span><span
1911 class="cmtt-10"> X</span><span
1912 class="cmtt-10"> X</span><span
1913 class="cmtt-10"> X</span><span
1914 class="cmtt-10"> X</span><span
1915 class="cmtt-10"> X</span><span
1916 class="cmtt-10"> X</span><span
1917 class="cmtt-10"> ]</span>
1918 <br class="fancyvrb" /><a
1919 id="x1-51020r7"></a><span
1920 class="cmtt-10"> </span><span
1921 class="cmtt-10"> byte</span><span
1922 class="cmtt-10"> 7:</span><span
1923 class="cmtt-10"> [</span><span
1924 class="cmtt-10"> X</span><span
1925 class="cmtt-10"> X</span><span
1926 class="cmtt-10"> X</span><span
1927 class="cmtt-10"> X</span><span
1928 class="cmtt-10"> X</span><span
1929 class="cmtt-10"> X</span><span
1930 class="cmtt-10"> X</span><span
1931 class="cmtt-10"> X</span><span
1932 class="cmtt-10"> ]</span><span
1933 class="cmtt-10"> [codebook_entries]</span><span
1934 class="cmtt-10"> (24</span><span
1935 class="cmtt-10"> bit</span><span
1936 class="cmtt-10"> unsigned)</span>
1937 <br class="fancyvrb" /><a
1938 id="x1-51022r8"></a><span
1939 class="cmtt-10"> </span><span
1940 class="cmtt-10"> </span>
1942 <!--l. 57--><p class="noindent" >Next is the <span
1943 class="cmtt-10x-x-109">[ordered] </span>bit flag:
1944 <!--l. 59--><p class="noindent" >
1945 <div class="fancyvrb" id="fancyvrb9">
1947 id="x1-51024r1"></a><span
1948 class="cmtt-10"> </span><span
1949 class="cmtt-10"> </span>
1950 <br class="fancyvrb" /><a
1951 id="x1-51026r2"></a><span
1952 class="cmtt-10"> </span><span
1953 class="cmtt-10"> byte</span><span
1954 class="cmtt-10"> 8:</span><span
1955 class="cmtt-10"> [</span><span
1956 class="cmtt-10"> </span><span
1957 class="cmtt-10"> </span><span
1958 class="cmtt-10"> </span><span
1959 class="cmtt-10"> </span><span
1960 class="cmtt-10"> </span><span
1961 class="cmtt-10"> </span><span
1962 class="cmtt-10"> </span><span
1963 class="cmtt-10"> </span><span
1964 class="cmtt-10"> </span><span
1965 class="cmtt-10"> </span><span
1966 class="cmtt-10"> </span><span
1967 class="cmtt-10"> </span><span
1968 class="cmtt-10"> </span><span
1969 class="cmtt-10"> </span><span
1970 class="cmtt-10"> X</span><span
1971 class="cmtt-10"> ]</span><span
1972 class="cmtt-10"> [ordered]</span><span
1973 class="cmtt-10"> (1</span><span
1974 class="cmtt-10"> bit)</span>
1975 <br class="fancyvrb" /><a
1976 id="x1-51028r3"></a><span
1977 class="cmtt-10"> </span><span
1978 class="cmtt-10"> </span>
1980 <!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
1981 class="cmtt-10x-x-109">[codebook_entries]</span>, is assigned a codeword length. We now read
1982 the list of codeword lengths and store these lengths in the array <span
1983 class="cmtt-10x-x-109">[codebook_codeword_lengths]</span>.
1984 Decode of lengths is according to whether the <span
1985 class="cmtt-10x-x-109">[ordered] </span>flag is set or unset.
1986 <ul class="itemize1">
1987 <li class="itemize">If the <span
1988 class="cmtt-10x-x-109">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
1989 needs to read each codeword length one-by-one.
1990 <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
1991 class="cmtt-10x-x-109">[sparse] </span>flag. This flag determines
1992 whether or not the codebook contains unused entries that are not to be included in the
1993 codeword decode tree:
1994 <!--l. 82--><p class="noindent" >
1995 <div class="fancyvrb" id="fancyvrb10">
1997 id="x1-51030r1"></a><span
1998 class="cmtt-10"> </span><span
1999 class="cmtt-10"> byte</span><span
2000 class="cmtt-10"> 8:</span><span
2001 class="cmtt-10"> [</span><span
2002 class="cmtt-10"> </span><span
2003 class="cmtt-10"> </span><span
2004 class="cmtt-10"> </span><span
2005 class="cmtt-10"> </span><span
2006 class="cmtt-10"> </span><span
2007 class="cmtt-10"> </span><span
2008 class="cmtt-10"> </span><span
2009 class="cmtt-10"> </span><span
2010 class="cmtt-10"> </span><span
2011 class="cmtt-10"> </span><span
2012 class="cmtt-10"> </span><span
2013 class="cmtt-10"> </span><span
2014 class="cmtt-10"> X</span><span
2015 class="cmtt-10"> 1</span><span
2016 class="cmtt-10"> ]</span><span
2017 class="cmtt-10"> [sparse]</span><span
2018 class="cmtt-10"> flag</span><span
2019 class="cmtt-10"> (1</span><span
2020 class="cmtt-10"> bit)</span>
2025 <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
2026 class="cmtt-10x-x-109">[codebook_entries] </span>codebook entries:
2027 <!--l. 89--><p class="noindent" >
2028 <div class="fancyvrb" id="fancyvrb11">
2030 id="x1-51032r1"></a><span
2031 class="cmtt-10"> </span><span
2032 class="cmtt-10"> </span>
2033 <br class="fancyvrb" /><a
2034 id="x1-51034r2"></a><span
2035 class="cmtt-10"> </span><span
2036 class="cmtt-10"> </span><span
2037 class="cmtt-10"> </span><span
2038 class="cmtt-10"> 1)</span><span
2039 class="cmtt-10"> if([sparse]</span><span
2040 class="cmtt-10"> is</span><span
2041 class="cmtt-10"> set)</span><span
2042 class="cmtt-10"> </span><span
2043 class="cmsy-10">{</span>
2044 <br class="fancyvrb" /><a
2045 id="x1-51036r3"></a><span
2046 class="cmtt-10"> </span><span
2047 class="cmtt-10"> </span>
2048 <br class="fancyvrb" /><a
2049 id="x1-51038r4"></a><span
2050 class="cmtt-10"> </span><span
2051 class="cmtt-10"> </span><span
2052 class="cmtt-10"> </span><span
2053 class="cmtt-10"> </span><span
2054 class="cmtt-10"> </span><span
2055 class="cmtt-10"> </span><span
2056 class="cmtt-10"> </span><span
2057 class="cmtt-10"> </span><span
2058 class="cmtt-10"> </span><span
2059 class="cmtt-10"> </span><span
2060 class="cmtt-10"> 2)</span><span
2061 class="cmtt-10"> [flag]</span><span
2062 class="cmtt-10"> =</span><span
2063 class="cmtt-10"> read</span><span
2064 class="cmtt-10"> one</span><span
2065 class="cmtt-10"> bit;</span>
2066 <br class="fancyvrb" /><a
2067 id="x1-51040r5"></a><span
2068 class="cmtt-10"> </span><span
2069 class="cmtt-10"> </span><span
2070 class="cmtt-10"> </span><span
2071 class="cmtt-10"> </span><span
2072 class="cmtt-10"> </span><span
2073 class="cmtt-10"> </span><span
2074 class="cmtt-10"> </span><span
2075 class="cmtt-10"> </span><span
2076 class="cmtt-10"> </span><span
2077 class="cmtt-10"> </span><span
2078 class="cmtt-10"> 3)</span><span
2079 class="cmtt-10"> if([flag]</span><span
2080 class="cmtt-10"> is</span><span
2081 class="cmtt-10"> set)</span><span
2082 class="cmtt-10"> </span><span
2083 class="cmsy-10">{</span>
2084 <br class="fancyvrb" /><a
2085 id="x1-51042r6"></a><span
2086 class="cmtt-10"> </span><span
2087 class="cmtt-10"> </span>
2088 <br class="fancyvrb" /><a
2089 id="x1-51044r7"></a><span
2090 class="cmtt-10"> </span><span
2091 class="cmtt-10"> </span><span
2092 class="cmtt-10"> </span><span
2093 class="cmtt-10"> </span><span
2094 class="cmtt-10"> </span><span
2095 class="cmtt-10"> </span><span
2096 class="cmtt-10"> </span><span
2097 class="cmtt-10"> </span><span
2098 class="cmtt-10"> </span><span
2099 class="cmtt-10"> </span><span
2100 class="cmtt-10"> </span><span
2101 class="cmtt-10"> </span><span
2102 class="cmtt-10"> </span><span
2103 class="cmtt-10"> </span><span
2104 class="cmtt-10"> </span><span
2105 class="cmtt-10"> 4)</span><span
2106 class="cmtt-10"> [length]</span><span
2107 class="cmtt-10"> =</span><span
2108 class="cmtt-10"> read</span><span
2109 class="cmtt-10"> a</span><span
2110 class="cmtt-10"> five</span><span
2111 class="cmtt-10"> bit</span><span
2112 class="cmtt-10"> unsigned</span><span
2113 class="cmtt-10"> integer;</span>
2114 <br class="fancyvrb" /><a
2115 id="x1-51046r8"></a><span
2116 class="cmtt-10"> </span><span
2117 class="cmtt-10"> </span><span
2118 class="cmtt-10"> </span><span
2119 class="cmtt-10"> </span><span
2120 class="cmtt-10"> </span><span
2121 class="cmtt-10"> </span><span
2122 class="cmtt-10"> </span><span
2123 class="cmtt-10"> </span><span
2124 class="cmtt-10"> </span><span
2125 class="cmtt-10"> </span><span
2126 class="cmtt-10"> </span><span
2127 class="cmtt-10"> </span><span
2128 class="cmtt-10"> </span><span
2129 class="cmtt-10"> </span><span
2130 class="cmtt-10"> </span><span
2131 class="cmtt-10"> 5)</span><span
2132 class="cmtt-10"> codeword</span><span
2133 class="cmtt-10"> length</span><span
2134 class="cmtt-10"> for</span><span
2135 class="cmtt-10"> this</span><span
2136 class="cmtt-10"> entry</span><span
2137 class="cmtt-10"> is</span><span
2138 class="cmtt-10"> [length]+1;</span>
2139 <br class="fancyvrb" /><a
2140 id="x1-51048r9"></a><span
2141 class="cmtt-10"> </span><span
2142 class="cmtt-10"> </span>
2143 <br class="fancyvrb" /><a
2144 id="x1-51050r10"></a><span
2145 class="cmtt-10"> </span><span
2146 class="cmtt-10"> </span><span
2147 class="cmtt-10"> </span><span
2148 class="cmtt-10"> </span><span
2149 class="cmtt-10"> </span><span
2150 class="cmtt-10"> </span><span
2151 class="cmtt-10"> </span><span
2152 class="cmtt-10"> </span><span
2153 class="cmtt-10"> </span><span
2154 class="cmtt-10"> </span><span
2155 class="cmtt-10"> </span><span
2156 class="cmtt-10"> </span><span
2157 class="cmtt-10"> </span><span
2158 class="cmtt-10"> </span><span
2159 class="cmsy-10">}</span><span
2160 class="cmtt-10"> else</span><span
2161 class="cmtt-10"> </span><span
2162 class="cmsy-10">{</span>
2163 <br class="fancyvrb" /><a
2164 id="x1-51052r11"></a><span
2165 class="cmtt-10"> </span><span
2166 class="cmtt-10"> </span>
2167 <br class="fancyvrb" /><a
2168 id="x1-51054r12"></a><span
2169 class="cmtt-10"> </span><span
2170 class="cmtt-10"> </span><span
2171 class="cmtt-10"> </span><span
2172 class="cmtt-10"> </span><span
2173 class="cmtt-10"> </span><span
2174 class="cmtt-10"> </span><span
2175 class="cmtt-10"> </span><span
2176 class="cmtt-10"> </span><span
2177 class="cmtt-10"> </span><span
2178 class="cmtt-10"> </span><span
2179 class="cmtt-10"> </span><span
2180 class="cmtt-10"> </span><span
2181 class="cmtt-10"> </span><span
2182 class="cmtt-10"> </span><span
2183 class="cmtt-10"> </span><span
2184 class="cmtt-10"> 6)</span><span
2185 class="cmtt-10"> this</span><span
2186 class="cmtt-10"> entry</span><span
2187 class="cmtt-10"> is</span><span
2188 class="cmtt-10"> unused.</span><span
2189 class="cmtt-10"> </span><span
2190 class="cmtt-10"> mark</span><span
2191 class="cmtt-10"> it</span><span
2192 class="cmtt-10"> as</span><span
2193 class="cmtt-10"> such.</span>
2194 <br class="fancyvrb" /><a
2195 id="x1-51056r13"></a><span
2196 class="cmtt-10"> </span><span
2197 class="cmtt-10"> </span>
2198 <br class="fancyvrb" /><a
2199 id="x1-51058r14"></a><span
2200 class="cmtt-10"> </span><span
2201 class="cmtt-10"> </span><span
2202 class="cmtt-10"> </span><span
2203 class="cmtt-10"> </span><span
2204 class="cmtt-10"> </span><span
2205 class="cmtt-10"> </span><span
2206 class="cmtt-10"> </span><span
2207 class="cmtt-10"> </span><span
2208 class="cmtt-10"> </span><span
2209 class="cmtt-10"> </span><span
2210 class="cmtt-10"> </span><span
2211 class="cmtt-10"> </span><span
2212 class="cmtt-10"> </span><span
2213 class="cmtt-10"> </span><span
2214 class="cmsy-10">}</span>
2215 <br class="fancyvrb" /><a
2216 id="x1-51060r15"></a><span
2217 class="cmtt-10"> </span><span
2218 class="cmtt-10"> </span>
2219 <br class="fancyvrb" /><a
2220 id="x1-51062r16"></a><span
2221 class="cmtt-10"> </span><span
2222 class="cmtt-10"> </span><span
2223 class="cmtt-10"> </span><span
2224 class="cmtt-10"> </span><span
2225 class="cmtt-10"> </span><span
2226 class="cmtt-10"> </span><span
2227 class="cmtt-10"> </span><span
2228 class="cmsy-10">}</span><span
2229 class="cmtt-10"> else</span><span
2230 class="cmtt-10"> the</span><span
2231 class="cmtt-10"> sparse</span><span
2232 class="cmtt-10"> flag</span><span
2233 class="cmtt-10"> is</span><span
2234 class="cmtt-10"> not</span><span
2235 class="cmtt-10"> set</span><span
2236 class="cmtt-10"> </span><span
2237 class="cmsy-10">{</span>
2238 <br class="fancyvrb" /><a
2239 id="x1-51064r17"></a><span
2240 class="cmtt-10"> </span><span
2241 class="cmtt-10"> </span>
2242 <br class="fancyvrb" /><a
2243 id="x1-51066r18"></a><span
2244 class="cmtt-10"> </span><span
2245 class="cmtt-10"> </span><span
2246 class="cmtt-10"> </span><span
2247 class="cmtt-10"> </span><span
2248 class="cmtt-10"> </span><span
2249 class="cmtt-10"> </span><span
2250 class="cmtt-10"> </span><span
2251 class="cmtt-10"> </span><span
2252 class="cmtt-10"> </span><span
2253 class="cmtt-10"> 7)</span><span
2254 class="cmtt-10"> [length]</span><span
2255 class="cmtt-10"> =</span><span
2256 class="cmtt-10"> read</span><span
2257 class="cmtt-10"> a</span><span
2258 class="cmtt-10"> five</span><span
2259 class="cmtt-10"> bit</span><span
2260 class="cmtt-10"> unsigned</span><span
2261 class="cmtt-10"> integer;</span>
2262 <br class="fancyvrb" /><a
2263 id="x1-51068r19"></a><span
2264 class="cmtt-10"> </span><span
2265 class="cmtt-10"> </span><span
2266 class="cmtt-10"> </span><span
2267 class="cmtt-10"> </span><span
2268 class="cmtt-10"> </span><span
2269 class="cmtt-10"> </span><span
2270 class="cmtt-10"> </span><span
2271 class="cmtt-10"> </span><span
2272 class="cmtt-10"> </span><span
2273 class="cmtt-10"> 8)</span><span
2274 class="cmtt-10"> the</span><span
2275 class="cmtt-10"> codeword</span><span
2276 class="cmtt-10"> length</span><span
2277 class="cmtt-10"> for</span><span
2278 class="cmtt-10"> this</span><span
2279 class="cmtt-10"> entry</span><span
2280 class="cmtt-10"> is</span><span
2281 class="cmtt-10"> [length]+1;</span>
2282 <br class="fancyvrb" /><a
2283 id="x1-51070r20"></a><span
2284 class="cmtt-10"> </span><span
2285 class="cmtt-10"> </span>
2286 <br class="fancyvrb" /><a
2287 id="x1-51072r21"></a><span
2288 class="cmtt-10"> </span><span
2289 class="cmtt-10"> </span><span
2290 class="cmtt-10"> </span><span
2291 class="cmtt-10"> </span><span
2292 class="cmtt-10"> </span><span
2293 class="cmtt-10"> </span><span
2294 class="cmtt-10"> </span><span
2295 class="cmsy-10">}</span>
2296 <br class="fancyvrb" /><a
2297 id="x1-51074r22"></a><span
2298 class="cmtt-10"> </span><span
2299 class="cmtt-10"> </span>
2302 <li class="itemize">If the <span
2303 class="cmtt-10x-x-109">[ordered] </span>flag is set, the codeword list for this codebook is encoded in ascending length
2304 order. Rather than reading a length for every codeword, the encoder reads the number of
2305 codewords per length. That is, beginning at entry zero:
2306 <!--l. 120--><p class="noindent" >
2307 <div class="fancyvrb" id="fancyvrb12">
2309 id="x1-51076r1"></a><span
2310 class="cmtt-10"> </span><span
2311 class="cmtt-10"> </span><span
2312 class="cmtt-10"> </span><span
2313 class="cmtt-10"> 1)</span><span
2314 class="cmtt-10"> [current_entry]</span><span
2315 class="cmtt-10"> =</span><span
2316 class="cmtt-10"> 0;</span>
2317 <br class="fancyvrb" /><a
2318 id="x1-51078r2"></a><span
2319 class="cmtt-10"> </span><span
2320 class="cmtt-10"> </span><span
2321 class="cmtt-10"> </span><span
2322 class="cmtt-10"> 2)</span><span
2323 class="cmtt-10"> [current_length]</span><span
2324 class="cmtt-10"> =</span><span
2325 class="cmtt-10"> read</span><span
2326 class="cmtt-10"> a</span><span
2327 class="cmtt-10"> five</span><span
2328 class="cmtt-10"> bit</span><span
2329 class="cmtt-10"> unsigned</span><span
2330 class="cmtt-10"> integer</span><span
2331 class="cmtt-10"> and</span><span
2332 class="cmtt-10"> add</span><span
2333 class="cmtt-10"> 1;</span>
2334 <br class="fancyvrb" /><a
2335 id="x1-51080r3"></a><span
2336 class="cmtt-10"> </span><span
2337 class="cmtt-10"> </span><span
2338 class="cmtt-10"> </span><span
2339 class="cmtt-10"> 3)</span><span
2340 class="cmtt-10"> [number]</span><span
2341 class="cmtt-10"> =</span><span
2342 class="cmtt-10"> read</span><span
2343 class="cmtt-10"> </span><a
2344 href="#x1-1170009.2.1"><span
2345 class="cmtt-10">ilog</span></a><span
2346 class="cmtt-10">([codebook_entries]</span><span
2347 class="cmtt-10"> -</span><span
2348 class="cmtt-10"> [current_entry])</span><span
2349 class="cmtt-10"> bits</span><span
2350 class="cmtt-10"> as</span><span
2351 class="cmtt-10"> an</span><span
2352 class="cmtt-10"> unsigned</span><span
2353 class="cmtt-10"> integer</span>
2354 <br class="fancyvrb" /><a
2355 id="x1-51082r4"></a><span
2356 class="cmtt-10"> </span><span
2357 class="cmtt-10"> </span><span
2358 class="cmtt-10"> </span><span
2359 class="cmtt-10"> 4)</span><span
2360 class="cmtt-10"> set</span><span
2361 class="cmtt-10"> the</span><span
2362 class="cmtt-10"> entries</span><span
2363 class="cmtt-10"> [current_entry]</span><span
2364 class="cmtt-10"> through</span><span
2365 class="cmtt-10"> [current_entry]+[number]-1,</span><span
2366 class="cmtt-10"> inclusive,</span>
2367 <br class="fancyvrb" /><a
2368 id="x1-51084r5"></a><span
2369 class="cmtt-10"> </span><span
2370 class="cmtt-10"> </span><span
2371 class="cmtt-10"> </span><span
2372 class="cmtt-10"> </span><span
2373 class="cmtt-10"> </span><span
2374 class="cmtt-10"> of</span><span
2375 class="cmtt-10"> the</span><span
2376 class="cmtt-10"> [codebook_codeword_lengths]</span><span
2377 class="cmtt-10"> array</span><span
2378 class="cmtt-10"> to</span><span
2379 class="cmtt-10"> [current_length]</span>
2380 <br class="fancyvrb" /><a
2381 id="x1-51086r6"></a><span
2382 class="cmtt-10"> </span><span
2383 class="cmtt-10"> </span><span
2384 class="cmtt-10"> </span><span
2385 class="cmtt-10"> 5)</span><span
2386 class="cmtt-10"> set</span><span
2387 class="cmtt-10"> [current_entry]</span><span
2388 class="cmtt-10"> to</span><span
2389 class="cmtt-10"> [number]</span><span
2390 class="cmtt-10"> +</span><span
2391 class="cmtt-10"> [current_entry]</span>
2392 <br class="fancyvrb" /><a
2393 id="x1-51088r7"></a><span
2394 class="cmtt-10"> </span><span
2395 class="cmtt-10"> </span><span
2396 class="cmtt-10"> </span><span
2397 class="cmtt-10"> 6)</span><span
2398 class="cmtt-10"> increment</span><span
2399 class="cmtt-10"> [current_length]</span><span
2400 class="cmtt-10"> by</span><span
2401 class="cmtt-10"> 1</span>
2402 <br class="fancyvrb" /><a
2403 id="x1-51090r8"></a><span
2404 class="cmtt-10"> </span><span
2405 class="cmtt-10"> </span><span
2406 class="cmtt-10"> </span><span
2407 class="cmtt-10"> 7)</span><span
2408 class="cmtt-10"> if</span><span
2409 class="cmtt-10"> [current_entry]</span><span
2410 class="cmtt-10"> is</span><span
2411 class="cmtt-10"> greater</span><span
2412 class="cmtt-10"> than</span><span
2413 class="cmtt-10"> [codebook_entries]</span><span
2414 class="cmtt-10"> ERROR</span><span
2415 class="cmtt-10"> CONDITION;</span>
2416 <br class="fancyvrb" /><a
2417 id="x1-51092r9"></a><span
2418 class="cmtt-10"> </span><span
2419 class="cmtt-10"> </span><span
2420 class="cmtt-10"> </span><span
2421 class="cmtt-10"> </span><span
2422 class="cmtt-10"> </span><span
2423 class="cmtt-10"> the</span><span
2424 class="cmtt-10"> decoder</span><span
2425 class="cmtt-10"> will</span><span
2426 class="cmtt-10"> not</span><span
2427 class="cmtt-10"> be</span><span
2428 class="cmtt-10"> able</span><span
2429 class="cmtt-10"> to</span><span
2430 class="cmtt-10"> read</span><span
2431 class="cmtt-10"> this</span><span
2432 class="cmtt-10"> stream.</span>
2433 <br class="fancyvrb" /><a
2434 id="x1-51094r10"></a><span
2435 class="cmtt-10"> </span><span
2436 class="cmtt-10"> </span><span
2437 class="cmtt-10"> </span><span
2438 class="cmtt-10"> 8)</span><span
2439 class="cmtt-10"> if</span><span
2440 class="cmtt-10"> [current_entry]</span><span
2441 class="cmtt-10"> is</span><span
2442 class="cmtt-10"> less</span><span
2443 class="cmtt-10"> than</span><span
2444 class="cmtt-10"> [codebook_entries],</span><span
2445 class="cmtt-10"> repeat</span><span
2446 class="cmtt-10"> process</span><span
2447 class="cmtt-10"> starting</span><span
2448 class="cmtt-10"> at</span><span
2449 class="cmtt-10"> 3)</span>
2450 <br class="fancyvrb" /><a
2451 id="x1-51096r11"></a><span
2452 class="cmtt-10"> </span><span
2453 class="cmtt-10"> </span><span
2454 class="cmtt-10"> </span><span
2455 class="cmtt-10"> 9)</span><span
2456 class="cmtt-10"> done.</span>
2462 <!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis I
2463 supports three lookup types:
2464 <ol class="enumerate1" >
2466 class="enumerate" id="x1-51098x1">No lookup
2469 class="enumerate" id="x1-51100x2">Implicitly populated value mapping (lattice VQ)
2472 class="enumerate" id="x1-51102x3">Explicitly populated value mapping (tessellated or ’foam’ VQ)</li></ol>
2473 <!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
2474 <div class="fancyvrb" id="fancyvrb13">
2476 id="x1-51104r1"></a><span
2477 class="cmtt-10"> </span><span
2478 class="cmtt-10"> </span><span
2479 class="cmtt-10"> </span><span
2480 class="cmtt-10"> 1)</span><span
2481 class="cmtt-10"> [codebook_lookup_type]</span><span
2482 class="cmtt-10"> =</span><span
2483 class="cmtt-10"> read</span><span
2484 class="cmtt-10"> four</span><span
2485 class="cmtt-10"> bits</span><span
2486 class="cmtt-10"> as</span><span
2487 class="cmtt-10"> an</span><span
2488 class="cmtt-10"> unsigned</span><span
2489 class="cmtt-10"> integer</span>
2491 <!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
2492 class="cmtt-10x-x-109">[codebook_lookup_type]</span>:
2493 <ul class="itemize1">
2494 <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
2496 <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values
2497 to be read. Lookup type one reads a list of values that are permuted in a set pattern
2498 to build a list of vectors, each vector of order <span
2499 class="cmtt-10x-x-109">[codebook_dimensions] </span>scalars. Lookup
2500 type two builds the same vector list, but reads each scalar for each vector explicitly,
2501 rather than building vectors from a smaller list of possible scalar values. Lookup decode
2502 proceeds as follows:
2503 <!--l. 168--><p class="noindent" >
2504 <div class="fancyvrb" id="fancyvrb14">
2506 id="x1-51106r1"></a><span
2507 class="cmtt-10"> </span><span
2508 class="cmtt-10"> </span><span
2509 class="cmtt-10"> </span><span
2510 class="cmtt-10"> 1)</span><span
2511 class="cmtt-10"> [codebook_minimum_value]</span><span
2512 class="cmtt-10"> =</span><span
2513 class="cmtt-10"> </span><a
2514 href="#x1-1180009.2.2"><span
2515 class="cmtt-10">float32_unpack</span></a><span
2516 class="cmtt-10">(</span><span
2517 class="cmtt-10"> read</span><span
2518 class="cmtt-10"> 32</span><span
2519 class="cmtt-10"> bits</span><span
2520 class="cmtt-10"> as</span><span
2521 class="cmtt-10"> an</span><span
2522 class="cmtt-10"> unsigned</span><span
2523 class="cmtt-10"> integer)</span>
2524 <br class="fancyvrb" /><a
2525 id="x1-51108r2"></a><span
2526 class="cmtt-10"> </span><span
2527 class="cmtt-10"> </span><span
2528 class="cmtt-10"> </span><span
2529 class="cmtt-10"> 2)</span><span
2530 class="cmtt-10"> [codebook_delta_value]</span><span
2531 class="cmtt-10"> =</span><span
2532 class="cmtt-10"> </span><a
2533 href="#x1-1180009.2.2"><span
2534 class="cmtt-10">float32_unpack</span></a><span
2535 class="cmtt-10">(</span><span
2536 class="cmtt-10"> read</span><span
2537 class="cmtt-10"> 32</span><span
2538 class="cmtt-10"> bits</span><span
2539 class="cmtt-10"> as</span><span
2540 class="cmtt-10"> an</span><span
2541 class="cmtt-10"> unsigned</span><span
2542 class="cmtt-10"> integer)</span>
2543 <br class="fancyvrb" /><a
2544 id="x1-51110r3"></a><span
2545 class="cmtt-10"> </span><span
2546 class="cmtt-10"> </span><span
2547 class="cmtt-10"> </span><span
2548 class="cmtt-10"> 3)</span><span
2549 class="cmtt-10"> [codebook_value_bits]</span><span
2550 class="cmtt-10"> =</span><span
2551 class="cmtt-10"> read</span><span
2552 class="cmtt-10"> 4</span><span
2553 class="cmtt-10"> bits</span><span
2554 class="cmtt-10"> as</span><span
2555 class="cmtt-10"> an</span><span
2556 class="cmtt-10"> unsigned</span><span
2557 class="cmtt-10"> integer</span><span
2558 class="cmtt-10"> and</span><span
2559 class="cmtt-10"> add</span><span
2560 class="cmtt-10"> 1</span>
2561 <br class="fancyvrb" /><a
2562 id="x1-51112r4"></a><span
2563 class="cmtt-10"> </span><span
2564 class="cmtt-10"> </span><span
2565 class="cmtt-10"> </span><span
2566 class="cmtt-10"> 4)</span><span
2567 class="cmtt-10"> [codebook_sequence_p]</span><span
2568 class="cmtt-10"> =</span><span
2569 class="cmtt-10"> read</span><span
2570 class="cmtt-10"> 1</span><span
2571 class="cmtt-10"> bit</span><span
2572 class="cmtt-10"> as</span><span
2573 class="cmtt-10"> a</span><span
2574 class="cmtt-10"> boolean</span><span
2575 class="cmtt-10"> flag</span>
2576 <br class="fancyvrb" /><a
2577 id="x1-51114r5"></a><span
2578 class="cmtt-10"> </span><span
2579 class="cmtt-10"> </span>
2580 <br class="fancyvrb" /><a
2581 id="x1-51116r6"></a><span
2582 class="cmtt-10"> </span><span
2583 class="cmtt-10"> </span><span
2584 class="cmtt-10"> </span><span
2585 class="cmtt-10"> if</span><span
2586 class="cmtt-10"> (</span><span
2587 class="cmtt-10"> [codebook_lookup_type]</span><span
2588 class="cmtt-10"> is</span><span
2589 class="cmtt-10"> 1</span><span
2590 class="cmtt-10"> )</span><span
2591 class="cmtt-10"> </span><span
2592 class="cmsy-10">{</span>
2593 <br class="fancyvrb" /><a
2594 id="x1-51118r7"></a><span
2595 class="cmtt-10"> </span><span
2596 class="cmtt-10"> </span>
2597 <br class="fancyvrb" /><a
2598 id="x1-51120r8"></a><span
2599 class="cmtt-10"> </span><span
2600 class="cmtt-10"> </span><span
2601 class="cmtt-10"> </span><span
2602 class="cmtt-10"> </span><span
2603 class="cmtt-10"> </span><span
2604 class="cmtt-10"> </span><span
2605 class="cmtt-10"> 5)</span><span
2606 class="cmtt-10"> [codebook_lookup_values]</span><span
2607 class="cmtt-10"> =</span><span
2608 class="cmtt-10"> </span><a
2609 href="#x1-1190009.2.3"><span
2610 class="cmtt-10">lookup1_values</span></a><span
2611 class="cmtt-10">([codebook_entries],</span><span
2612 class="cmtt-10"> [codebook_dimensions]</span><span
2613 class="cmtt-10"> )</span>
2614 <br class="fancyvrb" /><a
2615 id="x1-51122r9"></a><span
2616 class="cmtt-10"> </span><span
2617 class="cmtt-10"> </span>
2618 <br class="fancyvrb" /><a
2619 id="x1-51124r10"></a><span
2620 class="cmtt-10"> </span><span
2621 class="cmtt-10"> </span><span
2622 class="cmtt-10"> </span><span
2623 class="cmtt-10"> </span><span
2624 class="cmsy-10">}</span><span
2625 class="cmtt-10"> else</span><span
2626 class="cmtt-10"> </span><span
2627 class="cmsy-10">{</span>
2628 <br class="fancyvrb" /><a
2629 id="x1-51126r11"></a><span
2630 class="cmtt-10"> </span><span
2631 class="cmtt-10"> </span>
2632 <br class="fancyvrb" /><a
2633 id="x1-51128r12"></a><span
2634 class="cmtt-10"> </span><span
2635 class="cmtt-10"> </span><span
2636 class="cmtt-10"> </span><span
2637 class="cmtt-10"> </span><span
2638 class="cmtt-10"> </span><span
2639 class="cmtt-10"> </span><span
2640 class="cmtt-10"> 6)</span><span
2641 class="cmtt-10"> [codebook_lookup_values]</span><span
2642 class="cmtt-10"> =</span><span
2643 class="cmtt-10"> [codebook_entries]</span><span
2644 class="cmtt-10"> *</span><span
2645 class="cmtt-10"> [codebook_dimensions]</span>
2646 <br class="fancyvrb" /><a
2647 id="x1-51130r13"></a><span
2648 class="cmtt-10"> </span><span
2649 class="cmtt-10"> </span>
2650 <br class="fancyvrb" /><a
2651 id="x1-51132r14"></a><span
2652 class="cmtt-10"> </span><span
2653 class="cmtt-10"> </span><span
2654 class="cmtt-10"> </span><span
2655 class="cmtt-10"> </span><span
2656 class="cmsy-10">}</span>
2657 <br class="fancyvrb" /><a
2658 id="x1-51134r15"></a><span
2659 class="cmtt-10"> </span><span
2660 class="cmtt-10"> </span>
2661 <br class="fancyvrb" /><a
2662 id="x1-51136r16"></a><span
2663 class="cmtt-10"> </span><span
2664 class="cmtt-10"> </span><span
2665 class="cmtt-10"> </span><span
2666 class="cmtt-10"> 7)</span><span
2667 class="cmtt-10"> read</span><span
2668 class="cmtt-10"> a</span><span
2669 class="cmtt-10"> total</span><span
2670 class="cmtt-10"> of</span><span
2671 class="cmtt-10"> [codebook_lookup_values]</span><span
2672 class="cmtt-10"> unsigned</span><span
2673 class="cmtt-10"> integers</span><span
2674 class="cmtt-10"> of</span><span
2675 class="cmtt-10"> [codebook_value_bits]</span><span
2676 class="cmtt-10"> each;</span>
2677 <br class="fancyvrb" /><a
2678 id="x1-51138r17"></a><span
2679 class="cmtt-10"> </span><span
2680 class="cmtt-10"> </span><span
2681 class="cmtt-10"> </span><span
2682 class="cmtt-10"> </span><span
2683 class="cmtt-10"> </span><span
2684 class="cmtt-10"> </span><span
2685 class="cmtt-10"> store</span><span
2686 class="cmtt-10"> these</span><span
2687 class="cmtt-10"> in</span><span
2688 class="cmtt-10"> order</span><span
2689 class="cmtt-10"> in</span><span
2690 class="cmtt-10"> the</span><span
2691 class="cmtt-10"> array</span><span
2692 class="cmtt-10"> [codebook_multiplicands]</span>
2698 <li class="itemize">A <span
2699 class="cmtt-10x-x-109">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is not
2700 decodable by the specification in this document.
2702 <!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
2703 rendering the stream undecodable.
2704 <!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
2705 id="x1-520003.2.1"></a><span
2706 class="cmbx-10x-x-109">Huffman decision tree representation</span></span>
2708 class="cmtt-10x-x-109">[codebook_codeword_lengths] </span>array and <span
2709 class="cmtt-10x-x-109">[codebook_entries] </span>value uniquely define the
2710 Huffman decision tree used for entropy decoding.
2711 <!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused codeword
2712 entries) is assigned, in order, the lowest valued unused binary Huffman codeword possible. Assume
2713 the following codeword length list:
2714 <!--l. 209--><p class="noindent" >
2715 <div class="fancyvrb" id="fancyvrb15">
2717 id="x1-52002r1"></a><span
2718 class="cmtt-10"> </span><span
2719 class="cmtt-10"> entry</span><span
2720 class="cmtt-10"> 0:</span><span
2721 class="cmtt-10"> length</span><span
2722 class="cmtt-10"> 2</span>
2723 <br class="fancyvrb" /><a
2724 id="x1-52004r2"></a><span
2725 class="cmtt-10"> </span><span
2726 class="cmtt-10"> entry</span><span
2727 class="cmtt-10"> 1:</span><span
2728 class="cmtt-10"> length</span><span
2729 class="cmtt-10"> 4</span>
2730 <br class="fancyvrb" /><a
2731 id="x1-52006r3"></a><span
2732 class="cmtt-10"> </span><span
2733 class="cmtt-10"> entry</span><span
2734 class="cmtt-10"> 2:</span><span
2735 class="cmtt-10"> length</span><span
2736 class="cmtt-10"> 4</span>
2737 <br class="fancyvrb" /><a
2738 id="x1-52008r4"></a><span
2739 class="cmtt-10"> </span><span
2740 class="cmtt-10"> entry</span><span
2741 class="cmtt-10"> 3:</span><span
2742 class="cmtt-10"> length</span><span
2743 class="cmtt-10"> 4</span>
2744 <br class="fancyvrb" /><a
2745 id="x1-52010r5"></a><span
2746 class="cmtt-10"> </span><span
2747 class="cmtt-10"> entry</span><span
2748 class="cmtt-10"> 4:</span><span
2749 class="cmtt-10"> length</span><span
2750 class="cmtt-10"> 4</span>
2751 <br class="fancyvrb" /><a
2752 id="x1-52012r6"></a><span
2753 class="cmtt-10"> </span><span
2754 class="cmtt-10"> entry</span><span
2755 class="cmtt-10"> 5:</span><span
2756 class="cmtt-10"> length</span><span
2757 class="cmtt-10"> 2</span>
2758 <br class="fancyvrb" /><a
2759 id="x1-52014r7"></a><span
2760 class="cmtt-10"> </span><span
2761 class="cmtt-10"> entry</span><span
2762 class="cmtt-10"> 6:</span><span
2763 class="cmtt-10"> length</span><span
2764 class="cmtt-10"> 3</span>
2765 <br class="fancyvrb" /><a
2766 id="x1-52016r8"></a><span
2767 class="cmtt-10"> </span><span
2768 class="cmtt-10"> entry</span><span
2769 class="cmtt-10"> 7:</span><span
2770 class="cmtt-10"> length</span><span
2771 class="cmtt-10"> 3</span>
2773 <!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results in
2774 the following codeword list:
2775 <!--l. 223--><p class="noindent" >
2776 <div class="fancyvrb" id="fancyvrb16">
2778 id="x1-52018r1"></a><span
2779 class="cmtt-10"> </span><span
2780 class="cmtt-10"> entry</span><span
2781 class="cmtt-10"> 0:</span><span
2782 class="cmtt-10"> length</span><span
2783 class="cmtt-10"> 2</span><span
2784 class="cmtt-10"> codeword</span><span
2785 class="cmtt-10"> 00</span>
2786 <br class="fancyvrb" /><a
2787 id="x1-52020r2"></a><span
2788 class="cmtt-10"> </span><span
2789 class="cmtt-10"> entry</span><span
2790 class="cmtt-10"> 1:</span><span
2791 class="cmtt-10"> length</span><span
2792 class="cmtt-10"> 4</span><span
2793 class="cmtt-10"> codeword</span><span
2794 class="cmtt-10"> 0100</span>
2795 <br class="fancyvrb" /><a
2796 id="x1-52022r3"></a><span
2797 class="cmtt-10"> </span><span
2798 class="cmtt-10"> entry</span><span
2799 class="cmtt-10"> 2:</span><span
2800 class="cmtt-10"> length</span><span
2801 class="cmtt-10"> 4</span><span
2802 class="cmtt-10"> codeword</span><span
2803 class="cmtt-10"> 0101</span>
2804 <br class="fancyvrb" /><a
2805 id="x1-52024r4"></a><span
2806 class="cmtt-10"> </span><span
2807 class="cmtt-10"> entry</span><span
2808 class="cmtt-10"> 3:</span><span
2809 class="cmtt-10"> length</span><span
2810 class="cmtt-10"> 4</span><span
2811 class="cmtt-10"> codeword</span><span
2812 class="cmtt-10"> 0110</span>
2813 <br class="fancyvrb" /><a
2814 id="x1-52026r5"></a><span
2815 class="cmtt-10"> </span><span
2816 class="cmtt-10"> entry</span><span
2817 class="cmtt-10"> 4:</span><span
2818 class="cmtt-10"> length</span><span
2819 class="cmtt-10"> 4</span><span
2820 class="cmtt-10"> codeword</span><span
2821 class="cmtt-10"> 0111</span>
2822 <br class="fancyvrb" /><a
2823 id="x1-52028r6"></a><span
2824 class="cmtt-10"> </span><span
2825 class="cmtt-10"> entry</span><span
2826 class="cmtt-10"> 5:</span><span
2827 class="cmtt-10"> length</span><span
2828 class="cmtt-10"> 2</span><span
2829 class="cmtt-10"> codeword</span><span
2830 class="cmtt-10"> 10</span>
2831 <br class="fancyvrb" /><a
2832 id="x1-52030r7"></a><span
2833 class="cmtt-10"> </span><span
2834 class="cmtt-10"> entry</span><span
2835 class="cmtt-10"> 6:</span><span
2836 class="cmtt-10"> length</span><span
2837 class="cmtt-10"> 3</span><span
2838 class="cmtt-10"> codeword</span><span
2839 class="cmtt-10"> 110</span>
2840 <br class="fancyvrb" /><a
2841 id="x1-52032r8"></a><span
2842 class="cmtt-10"> </span><span
2843 class="cmtt-10"> entry</span><span
2844 class="cmtt-10"> 7:</span><span
2845 class="cmtt-10"> length</span><span
2846 class="cmtt-10"> 3</span><span
2847 class="cmtt-10"> codeword</span><span
2848 class="cmtt-10"> 111</span>
2853 <!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
2854 id="x1-530003.2.1"></a><span
2855 class="cmbx-10x-x-109">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to be
2856 read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero, one’.
2857 When determining ’lowest possible value’ in the assignment definition above, the leftmost bit is the
2859 <!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry numbers
2860 equivalent to the leaves numbered left-to-right:
2863 <!--l. 247--><p class="noindent" >
2865 <!--l. 248--><p class="noindent" ><img
2866 src="hufftree.png" alt="PIC"
2868 <br /> <table class="caption"
2869 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 4: </td><td
2870 class="content">huffman tree illustration</td></tr></table><!--tex4ht:label?: x1-530014 -->
2872 <!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
2874 <!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list. In the above
2875 example, if codeword seven were eliminated, it’s clear that the tree is unfinished:
2878 <!--l. 260--><p class="noindent" >
2880 <!--l. 261--><p class="noindent" ><img
2881 src="hufftree-under.png" alt="PIC"
2883 <br /> <table class="caption"
2884 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 5: </td><td
2885 class="content">underspecified huffman tree illustration</td></tr></table><!--tex4ht:label?: x1-530025 -->
2887 <!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth codeword is
2888 impossible. Both underspecified and overspecified trees are an error condition rendering the stream
2890 <!--l. 271--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
2891 codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read from
2892 the stream to decode to that entry number.
2893 <!--l. 278--><p class="noindent" ><span class="paragraphHead"><a
2894 id="x1-540003.2.1"></a><span
2895 class="cmbx-10x-x-109">VQ lookup table vector representation</span></span>
2896 Unpacking the VQ lookup table vectors relies on the following values:
2897 <div class="fancyvrb" id="fancyvrb17">
2902 id="x1-54002r1"></a><span
2903 class="cmtt-10"> </span><span
2904 class="cmtt-10"> the</span><span
2905 class="cmtt-10"> [codebook_multiplicands]</span><span
2906 class="cmtt-10"> array</span>
2907 <br class="fancyvrb" /><a
2908 id="x1-54004r2"></a><span
2909 class="cmtt-10"> </span><span
2910 class="cmtt-10"> [codebook_minimum_value]</span>
2911 <br class="fancyvrb" /><a
2912 id="x1-54006r3"></a><span
2913 class="cmtt-10"> </span><span
2914 class="cmtt-10"> [codebook_delta_value]</span>
2915 <br class="fancyvrb" /><a
2916 id="x1-54008r4"></a><span
2917 class="cmtt-10"> </span><span
2918 class="cmtt-10"> [codebook_sequence_p]</span>
2919 <br class="fancyvrb" /><a
2920 id="x1-54010r5"></a><span
2921 class="cmtt-10"> </span><span
2922 class="cmtt-10"> [codebook_lookup_type]</span>
2923 <br class="fancyvrb" /><a
2924 id="x1-54012r6"></a><span
2925 class="cmtt-10"> </span><span
2926 class="cmtt-10"> [codebook_entries]</span>
2927 <br class="fancyvrb" /><a
2928 id="x1-54014r7"></a><span
2929 class="cmtt-10"> </span><span
2930 class="cmtt-10"> [codebook_dimensions]</span>
2931 <br class="fancyvrb" /><a
2932 id="x1-54016r8"></a><span
2933 class="cmtt-10"> </span><span
2934 class="cmtt-10"> [codebook_lookup_values]</span>
2936 <!--l. 294--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
2938 class="cmtt-10x-x-109">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return during
2939 audio packet decode in a VQ context.
2940 <!--l. 299--><p class="noindent" ><span class="paragraphHead"><a
2941 id="x1-550003.2.1"></a><span
2942 class="cmbx-10x-x-109">Vector value decode: Lookup type 1</span></span>
2943 Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of scalar
2944 values. Calculate (unpack) the final values of a codebook entry vector from the entries in
2946 class="cmtt-10x-x-109">[codebook_multiplicands] </span>as follows (<span
2947 class="cmtt-10x-x-109">[value_vector] </span>is the output vector representing the
2948 vector of values for entry number <span
2949 class="cmtt-10x-x-109">[lookup_offset] </span>in this codebook):
2950 <!--l. 308--><p class="noindent" >
2951 <div class="fancyvrb" id="fancyvrb18">
2953 id="x1-55002r1"></a><span
2954 class="cmtt-10"> </span><span
2955 class="cmtt-10"> </span><span
2956 class="cmtt-10"> </span><span
2957 class="cmtt-10"> 1)</span><span
2958 class="cmtt-10"> [last]</span><span
2959 class="cmtt-10"> =</span><span
2960 class="cmtt-10"> 0;</span>
2961 <br class="fancyvrb" /><a
2962 id="x1-55004r2"></a><span
2963 class="cmtt-10"> </span><span
2964 class="cmtt-10"> </span><span
2965 class="cmtt-10"> </span><span
2966 class="cmtt-10"> 2)</span><span
2967 class="cmtt-10"> [index_divisor]</span><span
2968 class="cmtt-10"> =</span><span
2969 class="cmtt-10"> 1;</span>
2970 <br class="fancyvrb" /><a
2971 id="x1-55006r3"></a><span
2972 class="cmtt-10"> </span><span
2973 class="cmtt-10"> </span><span
2974 class="cmtt-10"> </span><span
2975 class="cmtt-10"> 3)</span><span
2976 class="cmtt-10"> iterate</span><span
2977 class="cmtt-10"> [i]</span><span
2978 class="cmtt-10"> over</span><span
2979 class="cmtt-10"> the</span><span
2980 class="cmtt-10"> range</span><span
2981 class="cmtt-10"> 0</span><span
2982 class="cmtt-10"> ...</span><span
2983 class="cmtt-10"> [codebook_dimensions]-1</span><span
2984 class="cmtt-10"> (once</span><span
2985 class="cmtt-10"> for</span><span
2986 class="cmtt-10"> each</span><span
2987 class="cmtt-10"> scalar</span><span
2988 class="cmtt-10"> value</span><span
2989 class="cmtt-10"> in</span><span
2990 class="cmtt-10"> the</span><span
2991 class="cmtt-10"> value</span><span
2992 class="cmtt-10"> vector)</span><span
2993 class="cmtt-10"> </span><span
2994 class="cmsy-10">{</span>
2995 <br class="fancyvrb" /><a
2996 id="x1-55008r4"></a><span
2997 class="cmtt-10"> </span><span
2998 class="cmtt-10"> </span>
2999 <br class="fancyvrb" /><a
3000 id="x1-55010r5"></a><span
3001 class="cmtt-10"> </span><span
3002 class="cmtt-10"> </span><span
3003 class="cmtt-10"> </span><span
3004 class="cmtt-10"> </span><span
3005 class="cmtt-10"> </span><span
3006 class="cmtt-10"> </span><span
3007 class="cmtt-10"> </span><span
3008 class="cmtt-10"> </span><span
3009 class="cmtt-10"> 4)</span><span
3010 class="cmtt-10"> [multiplicand_offset]</span><span
3011 class="cmtt-10"> =</span><span
3012 class="cmtt-10"> (</span><span
3013 class="cmtt-10"> [lookup_offset]</span><span
3014 class="cmtt-10"> divided</span><span
3015 class="cmtt-10"> by</span><span
3016 class="cmtt-10"> [index_divisor]</span><span
3017 class="cmtt-10"> using</span><span
3018 class="cmtt-10"> integer</span>
3019 <br class="fancyvrb" /><a
3020 id="x1-55012r6"></a><span
3021 class="cmtt-10"> </span><span
3022 class="cmtt-10"> </span><span
3023 class="cmtt-10"> </span><span
3024 class="cmtt-10"> </span><span
3025 class="cmtt-10"> </span><span
3026 class="cmtt-10"> </span><span
3027 class="cmtt-10"> </span><span
3028 class="cmtt-10"> </span><span
3029 class="cmtt-10"> </span><span
3030 class="cmtt-10"> </span><span
3031 class="cmtt-10"> </span><span
3032 class="cmtt-10"> division</span><span
3033 class="cmtt-10"> )</span><span
3034 class="cmtt-10"> integer</span><span
3035 class="cmtt-10"> modulo</span><span
3036 class="cmtt-10"> [codebook_lookup_values]</span>
3037 <br class="fancyvrb" /><a
3038 id="x1-55014r7"></a><span
3039 class="cmtt-10"> </span><span
3040 class="cmtt-10"> </span>
3041 <br class="fancyvrb" /><a
3042 id="x1-55016r8"></a><span
3043 class="cmtt-10"> </span><span
3044 class="cmtt-10"> </span><span
3045 class="cmtt-10"> </span><span
3046 class="cmtt-10"> </span><span
3047 class="cmtt-10"> </span><span
3048 class="cmtt-10"> </span><span
3049 class="cmtt-10"> </span><span
3050 class="cmtt-10"> </span><span
3051 class="cmtt-10"> 5)</span><span
3052 class="cmtt-10"> vector</span><span
3053 class="cmtt-10"> [value_vector]</span><span
3054 class="cmtt-10"> element</span><span
3055 class="cmtt-10"> [i]</span><span
3056 class="cmtt-10"> =</span>
3057 <br class="fancyvrb" /><a
3058 id="x1-55018r9"></a><span
3059 class="cmtt-10"> </span><span
3060 class="cmtt-10"> </span><span
3061 class="cmtt-10"> </span><span
3062 class="cmtt-10"> </span><span
3063 class="cmtt-10"> </span><span
3064 class="cmtt-10"> </span><span
3065 class="cmtt-10"> </span><span
3066 class="cmtt-10"> </span><span
3067 class="cmtt-10"> </span><span
3068 class="cmtt-10"> </span><span
3069 class="cmtt-10"> </span><span
3070 class="cmtt-10"> </span><span
3071 class="cmtt-10"> </span><span
3072 class="cmtt-10"> (</span><span
3073 class="cmtt-10"> [codebook_multiplicands]</span><span
3074 class="cmtt-10"> array</span><span
3075 class="cmtt-10"> element</span><span
3076 class="cmtt-10"> number</span><span
3077 class="cmtt-10"> [multiplicand_offset]</span><span
3078 class="cmtt-10"> )</span><span
3079 class="cmtt-10"> *</span>
3080 <br class="fancyvrb" /><a
3081 id="x1-55020r10"></a><span
3082 class="cmtt-10"> </span><span
3083 class="cmtt-10"> </span><span
3084 class="cmtt-10"> </span><span
3085 class="cmtt-10"> </span><span
3086 class="cmtt-10"> </span><span
3087 class="cmtt-10"> </span><span
3088 class="cmtt-10"> </span><span
3089 class="cmtt-10"> </span><span
3090 class="cmtt-10"> </span><span
3091 class="cmtt-10"> </span><span
3092 class="cmtt-10"> </span><span
3093 class="cmtt-10"> </span><span
3094 class="cmtt-10"> </span><span
3095 class="cmtt-10"> [codebook_delta_value]</span><span
3096 class="cmtt-10"> +</span><span
3097 class="cmtt-10"> [codebook_minimum_value]</span><span
3098 class="cmtt-10"> +</span><span
3099 class="cmtt-10"> [last];</span>
3100 <br class="fancyvrb" /><a
3101 id="x1-55022r11"></a><span
3102 class="cmtt-10"> </span><span
3103 class="cmtt-10"> </span>
3104 <br class="fancyvrb" /><a
3105 id="x1-55024r12"></a><span
3106 class="cmtt-10"> </span><span
3107 class="cmtt-10"> </span><span
3108 class="cmtt-10"> </span><span
3109 class="cmtt-10"> </span><span
3110 class="cmtt-10"> </span><span
3111 class="cmtt-10"> </span><span
3112 class="cmtt-10"> </span><span
3113 class="cmtt-10"> </span><span
3114 class="cmtt-10"> 6)</span><span
3115 class="cmtt-10"> if</span><span
3116 class="cmtt-10"> (</span><span
3117 class="cmtt-10"> [codebook_sequence_p]</span><span
3118 class="cmtt-10"> is</span><span
3119 class="cmtt-10"> set</span><span
3120 class="cmtt-10"> )</span><span
3121 class="cmtt-10"> then</span><span
3122 class="cmtt-10"> set</span><span
3123 class="cmtt-10"> [last]</span><span
3124 class="cmtt-10"> =</span><span
3125 class="cmtt-10"> vector</span><span
3126 class="cmtt-10"> [value_vector]</span><span
3127 class="cmtt-10"> element</span><span
3128 class="cmtt-10"> [i]</span>
3129 <br class="fancyvrb" /><a
3130 id="x1-55026r13"></a><span
3131 class="cmtt-10"> </span><span
3132 class="cmtt-10"> </span>
3133 <br class="fancyvrb" /><a
3134 id="x1-55028r14"></a><span
3135 class="cmtt-10"> </span><span
3136 class="cmtt-10"> </span><span
3137 class="cmtt-10"> </span><span
3138 class="cmtt-10"> </span><span
3139 class="cmtt-10"> </span><span
3140 class="cmtt-10"> </span><span
3141 class="cmtt-10"> </span><span
3142 class="cmtt-10"> </span><span
3143 class="cmtt-10"> 7)</span><span
3144 class="cmtt-10"> [index_divisor]</span><span
3145 class="cmtt-10"> =</span><span
3146 class="cmtt-10"> [index_divisor]</span><span
3147 class="cmtt-10"> *</span><span
3148 class="cmtt-10"> [codebook_lookup_values]</span>
3149 <br class="fancyvrb" /><a
3150 id="x1-55030r15"></a><span
3151 class="cmtt-10"> </span><span
3152 class="cmtt-10"> </span>
3153 <br class="fancyvrb" /><a
3154 id="x1-55032r16"></a><span
3155 class="cmtt-10"> </span><span
3156 class="cmtt-10"> </span><span
3157 class="cmtt-10"> </span><span
3158 class="cmtt-10"> </span><span
3159 class="cmtt-10"> </span><span
3160 class="cmtt-10"> </span><span
3161 class="cmtt-10"> </span><span
3162 class="cmsy-10">}</span>
3163 <br class="fancyvrb" /><a
3164 id="x1-55034r17"></a><span
3165 class="cmtt-10"> </span><span
3166 class="cmtt-10"> </span>
3167 <br class="fancyvrb" /><a
3168 id="x1-55036r18"></a><span
3169 class="cmtt-10"> </span><span
3170 class="cmtt-10"> </span><span
3171 class="cmtt-10"> </span><span
3172 class="cmtt-10"> 8)</span><span
3173 class="cmtt-10"> vector</span><span
3174 class="cmtt-10"> calculation</span><span
3175 class="cmtt-10"> completed.</span>
3177 <!--l. 331--><p class="noindent" ><span class="paragraphHead"><a
3178 id="x1-560003.2.1"></a><span
3179 class="cmbx-10x-x-109">Vector value decode: Lookup type 2</span></span>
3183 Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set by
3185 class="cmtt-10x-x-109">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final values
3186 of a codebook entry vector from the entries in <span
3187 class="cmtt-10x-x-109">[codebook_multiplicands] </span>as follows
3189 class="cmtt-10x-x-109">[value_vector] </span>is the output vector representing the vector of values for entry number
3191 class="cmtt-10x-x-109">[lookup_offset] </span>in this codebook):
3192 <!--l. 341--><p class="noindent" >
3193 <div class="fancyvrb" id="fancyvrb19">
3195 id="x1-56002r1"></a><span
3196 class="cmtt-10"> </span><span
3197 class="cmtt-10"> </span><span
3198 class="cmtt-10"> </span><span
3199 class="cmtt-10"> 1)</span><span
3200 class="cmtt-10"> [last]</span><span
3201 class="cmtt-10"> =</span><span
3202 class="cmtt-10"> 0;</span>
3203 <br class="fancyvrb" /><a
3204 id="x1-56004r2"></a><span
3205 class="cmtt-10"> </span><span
3206 class="cmtt-10"> </span><span
3207 class="cmtt-10"> </span><span
3208 class="cmtt-10"> 2)</span><span
3209 class="cmtt-10"> [multiplicand_offset]</span><span
3210 class="cmtt-10"> =</span><span
3211 class="cmtt-10"> [lookup_offset]</span><span
3212 class="cmtt-10"> *</span><span
3213 class="cmtt-10"> [codebook_dimensions]</span>
3214 <br class="fancyvrb" /><a
3215 id="x1-56006r3"></a><span
3216 class="cmtt-10"> </span><span
3217 class="cmtt-10"> </span><span
3218 class="cmtt-10"> </span><span
3219 class="cmtt-10"> 3)</span><span
3220 class="cmtt-10"> iterate</span><span
3221 class="cmtt-10"> [i]</span><span
3222 class="cmtt-10"> over</span><span
3223 class="cmtt-10"> the</span><span
3224 class="cmtt-10"> range</span><span
3225 class="cmtt-10"> 0</span><span
3226 class="cmtt-10"> ...</span><span
3227 class="cmtt-10"> [codebook_dimensions]-1</span><span
3228 class="cmtt-10"> (once</span><span
3229 class="cmtt-10"> for</span><span
3230 class="cmtt-10"> each</span><span
3231 class="cmtt-10"> scalar</span><span
3232 class="cmtt-10"> value</span><span
3233 class="cmtt-10"> in</span><span
3234 class="cmtt-10"> the</span><span
3235 class="cmtt-10"> value</span><span
3236 class="cmtt-10"> vector)</span><span
3237 class="cmtt-10"> </span><span
3238 class="cmsy-10">{</span>
3239 <br class="fancyvrb" /><a
3240 id="x1-56008r4"></a><span
3241 class="cmtt-10"> </span><span
3242 class="cmtt-10"> </span>
3243 <br class="fancyvrb" /><a
3244 id="x1-56010r5"></a><span
3245 class="cmtt-10"> </span><span
3246 class="cmtt-10"> </span><span
3247 class="cmtt-10"> </span><span
3248 class="cmtt-10"> </span><span
3249 class="cmtt-10"> </span><span
3250 class="cmtt-10"> </span><span
3251 class="cmtt-10"> </span><span
3252 class="cmtt-10"> </span><span
3253 class="cmtt-10"> 4)</span><span
3254 class="cmtt-10"> vector</span><span
3255 class="cmtt-10"> [value_vector]</span><span
3256 class="cmtt-10"> element</span><span
3257 class="cmtt-10"> [i]</span><span
3258 class="cmtt-10"> =</span>
3259 <br class="fancyvrb" /><a
3260 id="x1-56012r6"></a><span
3261 class="cmtt-10"> </span><span
3262 class="cmtt-10"> </span><span
3263 class="cmtt-10"> </span><span
3264 class="cmtt-10"> </span><span
3265 class="cmtt-10"> </span><span
3266 class="cmtt-10"> </span><span
3267 class="cmtt-10"> </span><span
3268 class="cmtt-10"> </span><span
3269 class="cmtt-10"> </span><span
3270 class="cmtt-10"> </span><span
3271 class="cmtt-10"> </span><span
3272 class="cmtt-10"> </span><span
3273 class="cmtt-10"> </span><span
3274 class="cmtt-10"> (</span><span
3275 class="cmtt-10"> [codebook_multiplicands]</span><span
3276 class="cmtt-10"> array</span><span
3277 class="cmtt-10"> element</span><span
3278 class="cmtt-10"> number</span><span
3279 class="cmtt-10"> [multiplicand_offset]</span><span
3280 class="cmtt-10"> )</span><span
3281 class="cmtt-10"> *</span>
3282 <br class="fancyvrb" /><a
3283 id="x1-56014r7"></a><span
3284 class="cmtt-10"> </span><span
3285 class="cmtt-10"> </span><span
3286 class="cmtt-10"> </span><span
3287 class="cmtt-10"> </span><span
3288 class="cmtt-10"> </span><span
3289 class="cmtt-10"> </span><span
3290 class="cmtt-10"> </span><span
3291 class="cmtt-10"> </span><span
3292 class="cmtt-10"> </span><span
3293 class="cmtt-10"> </span><span
3294 class="cmtt-10"> </span><span
3295 class="cmtt-10"> </span><span
3296 class="cmtt-10"> </span><span
3297 class="cmtt-10"> [codebook_delta_value]</span><span
3298 class="cmtt-10"> +</span><span
3299 class="cmtt-10"> [codebook_minimum_value]</span><span
3300 class="cmtt-10"> +</span><span
3301 class="cmtt-10"> [last];</span>
3302 <br class="fancyvrb" /><a
3303 id="x1-56016r8"></a><span
3304 class="cmtt-10"> </span><span
3305 class="cmtt-10"> </span>
3306 <br class="fancyvrb" /><a
3307 id="x1-56018r9"></a><span
3308 class="cmtt-10"> </span><span
3309 class="cmtt-10"> </span><span
3310 class="cmtt-10"> </span><span
3311 class="cmtt-10"> </span><span
3312 class="cmtt-10"> </span><span
3313 class="cmtt-10"> </span><span
3314 class="cmtt-10"> </span><span
3315 class="cmtt-10"> </span><span
3316 class="cmtt-10"> 5)</span><span
3317 class="cmtt-10"> if</span><span
3318 class="cmtt-10"> (</span><span
3319 class="cmtt-10"> [codebook_sequence_p]</span><span
3320 class="cmtt-10"> is</span><span
3321 class="cmtt-10"> set</span><span
3322 class="cmtt-10"> )</span><span
3323 class="cmtt-10"> then</span><span
3324 class="cmtt-10"> set</span><span
3325 class="cmtt-10"> [last]</span><span
3326 class="cmtt-10"> =</span><span
3327 class="cmtt-10"> vector</span><span
3328 class="cmtt-10"> [value_vector]</span><span
3329 class="cmtt-10"> element</span><span
3330 class="cmtt-10"> [i]</span>
3331 <br class="fancyvrb" /><a
3332 id="x1-56020r10"></a><span
3333 class="cmtt-10"> </span><span
3334 class="cmtt-10"> </span>
3335 <br class="fancyvrb" /><a
3336 id="x1-56022r11"></a><span
3337 class="cmtt-10"> </span><span
3338 class="cmtt-10"> </span><span
3339 class="cmtt-10"> </span><span
3340 class="cmtt-10"> </span><span
3341 class="cmtt-10"> </span><span
3342 class="cmtt-10"> </span><span
3343 class="cmtt-10"> </span><span
3344 class="cmtt-10"> </span><span
3345 class="cmtt-10"> 6)</span><span
3346 class="cmtt-10"> increment</span><span
3347 class="cmtt-10"> [multiplicand_offset]</span>
3348 <br class="fancyvrb" /><a
3349 id="x1-56024r12"></a><span
3350 class="cmtt-10"> </span><span
3351 class="cmtt-10"> </span>
3352 <br class="fancyvrb" /><a
3353 id="x1-56026r13"></a><span
3354 class="cmtt-10"> </span><span
3355 class="cmtt-10"> </span><span
3356 class="cmtt-10"> </span><span
3357 class="cmtt-10"> </span><span
3358 class="cmtt-10"> </span><span
3359 class="cmtt-10"> </span><span
3360 class="cmtt-10"> </span><span
3361 class="cmsy-10">}</span>
3362 <br class="fancyvrb" /><a
3363 id="x1-56028r14"></a><span
3364 class="cmtt-10"> </span><span
3365 class="cmtt-10"> </span>
3366 <br class="fancyvrb" /><a
3367 id="x1-56030r15"></a><span
3368 class="cmtt-10"> </span><span
3369 class="cmtt-10"> </span><span
3370 class="cmtt-10"> </span><span
3371 class="cmtt-10"> 7)</span><span
3372 class="cmtt-10"> vector</span><span
3373 class="cmtt-10"> calculation</span><span
3374 class="cmtt-10"> completed.</span>
3376 <!--l. 367--><p class="noindent" >
3377 <h4 class="subsectionHead"><span class="titlemark">3.3 </span> <a
3378 id="x1-570003.3"></a>Use of the codebook abstraction</h4>
3379 <!--l. 369--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a specific
3380 codebook reads a codeword from the bitstream, decoding it into an entry number, and then returns
3381 that entry number to the decoder (when used in a scalar entropy coding context), or uses
3382 that entry number as an offset into the VQ lookup table, returning a vector of values
3383 (when used in a context desiring a VQ value). Scalar or VQ context is always explicit;
3384 any call to the codebook mechanism requests either a scalar entry number or a lookup
3386 <!--l. 379--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting decode using a
3387 codebook of lookup type 0 in any context expecting a vector return value (even in a case where a
3388 vector of dimension one) is forbidden. If decoder setup or decode requests such an action, that is an
3389 error condition rendering the packet undecodable.
3390 <!--l. 386--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding
3391 the next codeword in the bitstream. The decoder reads bits until the accumulated bits
3392 match a codeword in the codebook. This process can be though of as logically walking
3393 the Huffman decode tree by reading one bit at a time from the bitstream, and using
3397 the bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
3398 branch (right in the above examples). Walking the tree finishes when the decode process
3399 hits a leaf in the decision tree; the result is the entry number corresponding to that
3400 leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
3402 <!--l. 398--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return value.
3403 <!--l. 401--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
3404 table. The value returned to the decoder is the vector of scalars corresponding to this
3412 <h3 class="sectionHead"><span class="titlemark">4 </span> <a
3413 id="x1-580004"></a>Codec Setup and Packet Decode</h3>
3414 <!--l. 6--><p class="noindent" >
3415 <h4 class="subsectionHead"><span class="titlemark">4.1 </span> <a
3416 id="x1-590004.1"></a>Overview</h4>
3417 <!--l. 8--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification of
3418 Vorbis I. This document assumes a high-level understanding of the Vorbis decode process, which is
3420 href="#x1-20001">Section 1<!--tex4ht:ref: vorbis:spec:intro --></a>, “<a
3421 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
3422 href="#x1-360002">Section 2<!--tex4ht:ref: vorbis:spec:bitpacking --></a>, “<a
3423 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers
3424 reading and writing bit fields from and to bitstream packets.
3425 <!--l. 16--><p class="noindent" >
3426 <h4 class="subsectionHead"><span class="titlemark">4.2 </span> <a
3427 id="x1-600004.2"></a>Header decode and decode setup</h4>
3428 <!--l. 18--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
3429 identification header, the comments header, and the setup header. All are required for decode
3430 compliance. An end-of-packet condition during decoding the first or third header packet renders the
3431 stream undecodable. End-of-packet decoding the comment header is a non-fatal error
3433 <!--l. 25--><p class="noindent" >
3434 <h5 class="subsubsectionHead"><span class="titlemark">4.2.1 </span> <a
3435 id="x1-610004.2.1"></a>Common header decode</h5>
3436 <!--l. 27--><p class="noindent" >Each header packet begins with the same header fields.
3437 <!--l. 30--><p class="noindent" >
3438 <div class="fancyvrb" id="fancyvrb20">
3440 id="x1-61002r1"></a><span
3441 class="cmtt-10"> </span><span
3442 class="cmtt-10"> </span><span
3443 class="cmtt-10"> </span><span
3444 class="cmtt-10"> 1)</span><span
3445 class="cmtt-10"> [packet_type]</span><span
3446 class="cmtt-10"> :</span><span
3447 class="cmtt-10"> 8</span><span
3448 class="cmtt-10"> bit</span><span
3449 class="cmtt-10"> value</span>
3450 <br class="fancyvrb" /><a
3451 id="x1-61004r2"></a><span
3452 class="cmtt-10"> </span><span
3453 class="cmtt-10"> </span><span
3454 class="cmtt-10"> </span><span
3455 class="cmtt-10"> 2)</span><span
3456 class="cmtt-10"> 0x76,</span><span
3457 class="cmtt-10"> 0x6f,</span><span
3458 class="cmtt-10"> 0x72,</span><span
3459 class="cmtt-10"> 0x62,</span><span
3460 class="cmtt-10"> 0x69,</span><span
3461 class="cmtt-10"> 0x73:</span><span
3462 class="cmtt-10"> the</span><span
3463 class="cmtt-10"> characters</span><span
3464 class="cmtt-10"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
3465 class="cmtt-10"> as</span><span
3466 class="cmtt-10"> six</span><span
3467 class="cmtt-10"> octets</span>
3469 <!--l. 35--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment header
3470 type 3 and the setup header type 5 (these types are all odd as a packet with a leading single bit of
3471 ’0’ is an audio packet). The packets must occur in the order of identification, comment,
3476 <!--l. 43--><p class="noindent" >
3477 <h5 class="subsubsectionHead"><span class="titlemark">4.2.2 </span> <a
3478 id="x1-620004.2.2"></a>Identification header</h5>
3479 <!--l. 45--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream definitively
3480 as Vorbis, and provide a few externally relevant pieces of information about the audio stream. The
3481 identification header is coded as follows:
3482 <!--l. 50--><p class="noindent" >
3483 <div class="fancyvrb" id="fancyvrb21">
3485 id="x1-62002r1"></a><span
3486 class="cmtt-10"> </span><span
3487 class="cmtt-10"> </span><span
3488 class="cmtt-10"> 1)</span><span
3489 class="cmtt-10"> [vorbis_version]</span><span
3490 class="cmtt-10"> =</span><span
3491 class="cmtt-10"> read</span><span
3492 class="cmtt-10"> 32</span><span
3493 class="cmtt-10"> bits</span><span
3494 class="cmtt-10"> as</span><span
3495 class="cmtt-10"> unsigned</span><span
3496 class="cmtt-10"> integer</span>
3497 <br class="fancyvrb" /><a
3498 id="x1-62004r2"></a><span
3499 class="cmtt-10"> </span><span
3500 class="cmtt-10"> </span><span
3501 class="cmtt-10"> 2)</span><span
3502 class="cmtt-10"> [audio_channels]</span><span
3503 class="cmtt-10"> =</span><span
3504 class="cmtt-10"> read</span><span
3505 class="cmtt-10"> 8</span><span
3506 class="cmtt-10"> bit</span><span
3507 class="cmtt-10"> integer</span><span
3508 class="cmtt-10"> as</span><span
3509 class="cmtt-10"> unsigned</span>
3510 <br class="fancyvrb" /><a
3511 id="x1-62006r3"></a><span
3512 class="cmtt-10"> </span><span
3513 class="cmtt-10"> </span><span
3514 class="cmtt-10"> 3)</span><span
3515 class="cmtt-10"> [audio_sample_rate]</span><span
3516 class="cmtt-10"> =</span><span
3517 class="cmtt-10"> read</span><span
3518 class="cmtt-10"> 32</span><span
3519 class="cmtt-10"> bits</span><span
3520 class="cmtt-10"> as</span><span
3521 class="cmtt-10"> unsigned</span><span
3522 class="cmtt-10"> integer</span>
3523 <br class="fancyvrb" /><a
3524 id="x1-62008r4"></a><span
3525 class="cmtt-10"> </span><span
3526 class="cmtt-10"> </span><span
3527 class="cmtt-10"> 4)</span><span
3528 class="cmtt-10"> [bitrate_maximum]</span><span
3529 class="cmtt-10"> =</span><span
3530 class="cmtt-10"> read</span><span
3531 class="cmtt-10"> 32</span><span
3532 class="cmtt-10"> bits</span><span
3533 class="cmtt-10"> as</span><span
3534 class="cmtt-10"> signed</span><span
3535 class="cmtt-10"> integer</span>
3536 <br class="fancyvrb" /><a
3537 id="x1-62010r5"></a><span
3538 class="cmtt-10"> </span><span
3539 class="cmtt-10"> </span><span
3540 class="cmtt-10"> 5)</span><span
3541 class="cmtt-10"> [bitrate_nominal]</span><span
3542 class="cmtt-10"> =</span><span
3543 class="cmtt-10"> read</span><span
3544 class="cmtt-10"> 32</span><span
3545 class="cmtt-10"> bits</span><span
3546 class="cmtt-10"> as</span><span
3547 class="cmtt-10"> signed</span><span
3548 class="cmtt-10"> integer</span>
3549 <br class="fancyvrb" /><a
3550 id="x1-62012r6"></a><span
3551 class="cmtt-10"> </span><span
3552 class="cmtt-10"> </span><span
3553 class="cmtt-10"> 6)</span><span
3554 class="cmtt-10"> [bitrate_minimum]</span><span
3555 class="cmtt-10"> =</span><span
3556 class="cmtt-10"> read</span><span
3557 class="cmtt-10"> 32</span><span
3558 class="cmtt-10"> bits</span><span
3559 class="cmtt-10"> as</span><span
3560 class="cmtt-10"> signed</span><span
3561 class="cmtt-10"> integer</span>
3562 <br class="fancyvrb" /><a
3563 id="x1-62014r7"></a><span
3564 class="cmtt-10"> </span><span
3565 class="cmtt-10"> </span><span
3566 class="cmtt-10"> 7)</span><span
3567 class="cmtt-10"> [blocksize_0]</span><span
3568 class="cmtt-10"> =</span><span
3569 class="cmtt-10"> 2</span><span
3570 class="cmtt-10"> exponent</span><span
3571 class="cmtt-10"> (read</span><span
3572 class="cmtt-10"> 4</span><span
3573 class="cmtt-10"> bits</span><span
3574 class="cmtt-10"> as</span><span
3575 class="cmtt-10"> unsigned</span><span
3576 class="cmtt-10"> integer)</span>
3577 <br class="fancyvrb" /><a
3578 id="x1-62016r8"></a><span
3579 class="cmtt-10"> </span><span
3580 class="cmtt-10"> </span><span
3581 class="cmtt-10"> 8)</span><span
3582 class="cmtt-10"> [blocksize_1]</span><span
3583 class="cmtt-10"> =</span><span
3584 class="cmtt-10"> 2</span><span
3585 class="cmtt-10"> exponent</span><span
3586 class="cmtt-10"> (read</span><span
3587 class="cmtt-10"> 4</span><span
3588 class="cmtt-10"> bits</span><span
3589 class="cmtt-10"> as</span><span
3590 class="cmtt-10"> unsigned</span><span
3591 class="cmtt-10"> integer)</span>
3592 <br class="fancyvrb" /><a
3593 id="x1-62018r9"></a><span
3594 class="cmtt-10"> </span><span
3595 class="cmtt-10"> </span><span
3596 class="cmtt-10"> 9)</span><span
3597 class="cmtt-10"> [framing_flag]</span><span
3598 class="cmtt-10"> =</span><span
3599 class="cmtt-10"> read</span><span
3600 class="cmtt-10"> one</span><span
3601 class="cmtt-10"> bit</span>
3603 <!--l. 62--><p class="noindent" ><span
3604 class="cmtt-10x-x-109">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
3606 class="cmtt-10x-x-109">[audio_channels] </span>and <span
3607 class="cmtt-10x-x-109">[audio_sample_rate] </span>must read greater than zero. Allowed final blocksize
3608 values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
3609 class="cmtt-10x-x-109">[blocksize_0] </span>must be less
3610 than or equal to <span
3611 class="cmtt-10x-x-109">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet any of these
3612 conditions renders a stream undecodable.
3613 <!--l. 70--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
3614 considerably off in purely VBR streams. The fields are meaningful only when greater than
3616 <ul class="itemize1">
3617 <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
3618 fixed-rate bitstream
3620 <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
3622 <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
3624 <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
3625 <!--l. 84--><p class="noindent" >
3629 <h5 class="subsubsectionHead"><span class="titlemark">4.2.3 </span> <a
3630 id="x1-630004.2.3"></a>Comment header</h5>
3631 <!--l. 85--><p class="noindent" >Comment header decode and data specification is covered in <a
3632 href="#x1-810005">Section 5<!--tex4ht:ref: vorbis:spec:comment --></a>, “<a
3633 href="#x1-810005">comment field and header
3634 specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
3635 <!--l. 89--><p class="noindent" >
3636 <h5 class="subsubsectionHead"><span class="titlemark">4.2.4 </span> <a
3637 id="x1-640004.2.4"></a>Setup header</h5>
3638 <!--l. 91--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
3641 <!--l. 93--><p class="noindent" >
3643 <!--l. 94--><p class="noindent" ><img
3644 src="components.png" alt="PIC"
3646 <br /> <table class="caption"
3647 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 6: </td><td
3648 class="content">decoder pipeline configuration</td></tr></table><!--tex4ht:label?: x1-640016 -->
3650 <!--l. 99--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
3651 header contains, in order, the lists of codebook configurations, time-domain transform
3652 configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
3653 mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header decode
3654 proceeds in the following order:
3655 <!--l. 107--><p class="noindent" ><span class="paragraphHead"><a
3656 id="x1-650004.2.4"></a><span
3657 class="cmbx-10x-x-109">Codebooks</span></span>
3658 <ol class="enumerate1" >
3660 class="enumerate" id="x1-65002x1"><span
3661 class="cmtt-10x-x-109">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
3664 class="enumerate" id="x1-65004x2">Decode <span
3665 class="cmtt-10x-x-109">[vorbis_codebook_count] </span>codebooks in order as defined in <a
3666 href="#x1-470003">Section 3<!--tex4ht:ref: vorbis:spec:codebook --></a>,
3668 href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array of
3669 codebook configurations <span
3670 class="cmtt-10x-x-109">[vorbis_codebook_configurations]</span>.</li></ol>
3671 <!--l. 119--><p class="noindent" ><span class="paragraphHead"><a
3672 id="x1-660004.2.4"></a><span
3673 class="cmbx-10x-x-109">Time domain transforms</span></span>
3674 These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must be
3675 read to maintain bitstream sync.
3679 <!--l. 126--><p class="noindent" >
3680 <ol class="enumerate1" >
3682 class="enumerate" id="x1-66002x1"><span
3683 class="cmtt-10x-x-109">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
3686 class="enumerate" id="x1-66004x2">read <span
3687 class="cmtt-10x-x-109">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
3688 nonzero, this is an error condition and the stream is undecodable.</li></ol>
3689 <!--l. 132--><p class="noindent" ><span class="paragraphHead"><a
3690 id="x1-670004.2.4"></a><span
3691 class="cmbx-10x-x-109">Floors</span></span>
3692 Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
3694 <!--l. 138--><p class="noindent" >
3695 <ol class="enumerate1" >
3697 class="enumerate" id="x1-67002x1"><span
3698 class="cmtt-10x-x-109">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
3701 class="enumerate" id="x1-67004x2">For each <span
3702 class="cmtt-10x-x-109">[i] </span>of <span
3703 class="cmtt-10x-x-109">[vorbis_floor_count] </span>floor numbers:
3704 <ol class="enumerate2" >
3706 class="enumerate" id="x1-67006x1">read the floor type: vector <span
3707 class="cmtt-10x-x-109">[vorbis_floor_types] </span>element <span
3708 class="cmtt-10x-x-109">[i] </span>= read 16 bits as
3712 class="enumerate" id="x1-67008x2">If the floor type is zero, decode the floor configuration as defined in <a
3713 href="#x1-890006">Section 6<!--tex4ht:ref: vorbis:spec:floor0 --></a>,
3715 href="#x1-890006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
3716 class="cmtt-10x-x-109">[i] </span>of the floor
3717 configuration array <span
3718 class="cmtt-10x-x-109">[vorbis_floor_configurations]</span>.
3721 class="enumerate" id="x1-67010x3">If the floor type is one, decode the floor configuration as defined in <a
3722 href="#x1-950007">Section 7<!--tex4ht:ref: vorbis:spec:floor1 --></a>,
3724 href="#x1-950007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
3725 class="cmtt-10x-x-109">[i] </span>of the floor
3726 configuration array <span
3727 class="cmtt-10x-x-109">[vorbis_floor_configurations]</span>.
3730 class="enumerate" id="x1-67012x4">If the the floor type is greater than one, this stream is undecodable; ERROR
3733 <!--l. 156--><p class="noindent" ><span class="paragraphHead"><a
3734 id="x1-680004.2.4"></a><span
3735 class="cmbx-10x-x-109">Residues</span></span>
3736 Vorbis uses three residue types; header decode of each type is identical.
3737 <!--l. 162--><p class="noindent" >
3741 <ol class="enumerate1" >
3743 class="enumerate" id="x1-68002x1"><span
3744 class="cmtt-10x-x-109">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
3747 class="enumerate" id="x1-68004x2">For each of <span
3748 class="cmtt-10x-x-109">[vorbis_residue_count] </span>residue numbers:
3749 <ol class="enumerate2" >
3751 class="enumerate" id="x1-68006x1">read the residue type; vector <span
3752 class="cmtt-10x-x-109">[vorbis_residue_types] </span>element <span
3753 class="cmtt-10x-x-109">[i] </span>= read 16
3754 bits as unsigned integer
3757 class="enumerate" id="x1-68008x2">If the residue type is zero, one or two, decode the residue configuration as defined
3759 href="#x1-1020008">Section 8<!--tex4ht:ref: vorbis:spec:residue --></a>, “<a
3760 href="#x1-1020008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
3761 class="cmtt-10x-x-109">[i] </span>of
3762 the residue configuration array <span
3763 class="cmtt-10x-x-109">[vorbis_residue_configurations]</span>.
3766 class="enumerate" id="x1-68010x3">If the the residue type is greater than two, this stream is undecodable; ERROR
3769 <!--l. 176--><p class="noindent" ><span class="paragraphHead"><a
3770 id="x1-690004.2.4"></a><span
3771 class="cmbx-10x-x-109">Mappings</span></span>
3772 Mappings are used to set up specific pipelines for encoding multichannel audio with varying channel
3773 mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM channel
3775 <!--l. 187--><p class="noindent" >
3776 <ol class="enumerate1" >
3778 class="enumerate" id="x1-69002x1"><span
3779 class="cmtt-10x-x-109">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
3782 class="enumerate" id="x1-69004x2">For each <span
3783 class="cmtt-10x-x-109">[i] </span>of <span
3784 class="cmtt-10x-x-109">[vorbis_mapping_count] </span>mapping numbers:
3785 <ol class="enumerate2" >
3787 class="enumerate" id="x1-69006x1">read the mapping type: 16 bits as unsigned integer. There’s no reason to save the
3788 mapping type in Vorbis I.
3791 class="enumerate" id="x1-69008x2">If the mapping type is nonzero, the stream is undecodable
3794 class="enumerate" id="x1-69010x3">If the mapping type is zero:
3795 <ol class="enumerate3" >
3797 class="enumerate" id="x1-69012x1">read 1 bit as a boolean flag
3798 <ol class="enumerate4" >
3800 class="enumerate" id="x1-69014x1">if set, <span
3801 class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer and
3808 class="enumerate" id="x1-69016x2">if unset, <span
3809 class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>= 1</li></ol>
3812 class="enumerate" id="x1-69018x2">read 1 bit as a boolean flag
3813 <ol class="enumerate4" >
3815 class="enumerate" id="x1-69020x1">if set, square polar channel mapping is in use:
3816 <ul class="itemize1">
3817 <li class="itemize"><span
3818 class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned integer
3821 <li class="itemize">for <span
3822 class="cmtt-10x-x-109">[j] </span>each of <span
3823 class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>steps:
3824 <ul class="itemize2">
3825 <li class="itemize">vector <span
3826 class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
3827 class="cmtt-10x-x-109">[j]</span>= read
3829 href="#x1-1170009.2.1">ilog</a>(<span
3830 class="cmtt-10x-x-109">[audio_channels] </span>- 1) bits as unsigned integer
3832 <li class="itemize">vector <span
3833 class="cmtt-10x-x-109">[vorbis_mapping_angle] </span>element <span
3834 class="cmtt-10x-x-109">[j]</span>= read
3836 href="#x1-1170009.2.1">ilog</a>(<span
3837 class="cmtt-10x-x-109">[audio_channels] </span>- 1) bits as unsigned integer
3839 <li class="itemize">the numbers read in the above two steps are channel numbers
3840 representing the channel to treat as magnitude and the channel to
3841 treat as angle, respectively. If for any coupling step the angle channel
3842 number equals the magnitude channel number, the magnitude channel
3843 number is greater than <span
3844 class="cmtt-10x-x-109">[audio_channels]</span>-1, or the angle channel is
3846 class="cmtt-10x-x-109">[audio_channels]</span>-1, the stream is undecodable.</li></ul>
3850 class="enumerate" id="x1-69022x2">if unset, <span
3851 class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps] </span>= 0</li></ol>
3854 class="enumerate" id="x1-69024x3">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
3857 class="enumerate" id="x1-69026x4">if <span
3858 class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
3859 settings. For each <span
3860 class="cmtt-10x-x-109">[j] </span>of <span
3861 class="cmtt-10x-x-109">[audio_channels] </span>channels:
3862 <ol class="enumerate4" >
3864 class="enumerate" id="x1-69028x1">vector <span
3865 class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
3866 class="cmtt-10x-x-109">[j] </span>= read 4 bits as unsigned
3870 class="enumerate" id="x1-69030x2">if the value is
3871 greater than the highest numbered submap (<span
3872 class="cmtt-10x-x-109">[vorbis_mapping_submaps]</span>
3873 - 1), this in an error condition rendering the stream undecodable</li></ol>
3879 class="enumerate" id="x1-69032x5">for each submap <span
3880 class="cmtt-10x-x-109">[j] </span>of <span
3881 class="cmtt-10x-x-109">[vorbis_mapping_submaps] </span>submaps, read the floor and
3882 residue numbers for use in decoding that submap:
3883 <ol class="enumerate4" >
3885 class="enumerate" id="x1-69034x1">read and discard 8 bits (the unused time configuration placeholder)
3888 class="enumerate" id="x1-69036x2">read 8 bits as unsigned integer for the floor number; save in vector
3890 class="cmtt-10x-x-109">[vorbis_mapping_submap_floor] </span>element <span
3891 class="cmtt-10x-x-109">[j]</span>
3894 class="enumerate" id="x1-69038x3">verify the floor number is not greater than the highest number floor
3895 configured for the bitstream. If it is, the bitstream is undecodable
3898 class="enumerate" id="x1-69040x4">read 8 bits as unsigned integer for the residue number; save in vector
3900 class="cmtt-10x-x-109">[vorbis_mapping_submap_residue] </span>element <span
3901 class="cmtt-10x-x-109">[j]</span>
3904 class="enumerate" id="x1-69042x5">verify the residue number is not greater than the highest number residue
3905 configured for the bitstream. If it is, the bitstream is undecodable</li></ol>
3908 class="enumerate" id="x1-69044x6">save this mapping configuration in slot <span
3909 class="cmtt-10x-x-109">[i] </span>of the mapping configuration array
3911 class="cmtt-10x-x-109">[vorbis_mapping_configurations]</span>.</li></ol>
3914 <!--l. 246--><p class="noindent" ><span class="paragraphHead"><a
3915 id="x1-700004.2.4"></a><span
3916 class="cmbx-10x-x-109">Modes</span></span>
3917 <ol class="enumerate1" >
3919 class="enumerate" id="x1-70002x1"><span
3920 class="cmtt-10x-x-109">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
3923 class="enumerate" id="x1-70004x2">For each of <span
3924 class="cmtt-10x-x-109">[vorbis_mode_count] </span>mode numbers:
3925 <ol class="enumerate2" >
3927 class="enumerate" id="x1-70006x1"><span
3928 class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>= read 1 bit
3931 class="enumerate" id="x1-70008x2"><span
3932 class="cmtt-10x-x-109">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
3935 class="enumerate" id="x1-70010x3"><span
3936 class="cmtt-10x-x-109">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
3939 class="enumerate" id="x1-70012x4"><span
3940 class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
3946 class="enumerate" id="x1-70014x5">verify ranges; zero is the only legal value
3947 in Vorbis I for <span
3948 class="cmtt-10x-x-109">[vorbis_mode_windowtype] </span>and <span
3949 class="cmtt-10x-x-109">[vorbis_mode_transformtype]</span>.
3951 class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
3952 in use. Any illegal values render the stream undecodable.
3955 class="enumerate" id="x1-70016x6">save this mode configuration in slot <span
3956 class="cmtt-10x-x-109">[i] </span>of the mode configuration array
3958 class="cmtt-10x-x-109">[vorbis_mode_configurations]</span>.</li></ol>
3961 class="enumerate" id="x1-70018x3">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
3962 decodable.</li></ol>
3963 <!--l. 267--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
3964 <!--l. 276--><p class="noindent" >
3965 <h4 class="subsectionHead"><span class="titlemark">4.3 </span> <a
3966 id="x1-710004.3"></a>Audio packet decode and synthesis</h4>
3967 <!--l. 278--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
3968 audio packet decode is to read and verify the packet type. <span
3969 class="cmti-10x-x-109">A non-audio packet when audio is</span>
3971 class="cmti-10x-x-109">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the packet</span>
3973 class="cmti-10x-x-109">and not attempt decoding it to audio</span>.
3974 <!--l. 285--><p class="noindent" >
3975 <h5 class="subsubsectionHead"><span class="titlemark">4.3.1 </span> <a
3976 id="x1-720004.3.1"></a>packet type, mode and window decode</h5>
3977 <!--l. 288--><p class="noindent" >
3978 <ol class="enumerate1" >
3980 class="enumerate" id="x1-72002x1">read 1 bit <span
3981 class="cmtt-10x-x-109">[packet_type]</span>; check that packet type is 0 (audio)
3984 class="enumerate" id="x1-72004x2">read <a
3985 href="#x1-1170009.2.1">ilog</a>([vorbis˙mode˙count]-1) bits <span
3986 class="cmtt-10x-x-109">[mode_number]</span>
3989 class="enumerate" id="x1-72006x3">decode blocksize <span
3990 class="cmtt-10x-x-109">[n] </span>is equal to <span
3991 class="cmtt-10x-x-109">[blocksize_0] </span>if <span
3992 class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is 0, else
3994 class="cmtt-10x-x-109">[n] </span>is equal to <span
3995 class="cmtt-10x-x-109">[blocksize_1]</span>.
3998 class="enumerate" id="x1-72008x4">perform window selection and setup; this window is used later by the inverse MDCT:
3999 <ol class="enumerate2" >
4001 class="enumerate" id="x1-72010x1">if this is a long window (the <span
4002 class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>flag of this mode is
4007 <ol class="enumerate3" >
4009 class="enumerate" id="x1-72012x1">read 1 bit for <span
4010 class="cmtt-10x-x-109">[previous_window_flag]</span>
4013 class="enumerate" id="x1-72014x2">read 1 bit for <span
4014 class="cmtt-10x-x-109">[next_window_flag]</span>
4017 class="enumerate" id="x1-72016x3">if <span
4018 class="cmtt-10x-x-109">[previous_window_flag] </span>is not set, the left half of the window will be a
4019 hybrid window for lapping with a short block. See <a
4020 href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
4021 href="#x1-260001.3.2">Window
4022 shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of overlapping dissimilar
4023 windows. Else, the left half window will have normal long shape.
4026 class="enumerate" id="x1-72018x4">if <span
4027 class="cmtt-10x-x-109">[next_window_flag] </span>is not set, the right half of the window will be a
4028 hybrid window for lapping with a short block. See <a
4029 href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
4030 href="#x1-260001.3.2">Window
4031 shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of overlapping dissimilar
4032 windows. Else, the left right window will have normal long shape.</li></ol>
4035 class="enumerate" id="x1-72020x2">if this is a short window, the window is always the same short-window shape.</li></ol>
4037 <!--l. 320--><p class="noindent" >Vorbis windows all use the slope function <span
4038 class="cmmi-10x-x-109">y </span>= sin(<img
4039 src="Vorbis_I_spec1x.png" alt="π
4040 2" class="frac" align="middle"> <span
4041 class="cmsy-10x-x-109">*</span> sin<sup><span
4042 class="cmr-8">2</span></sup>((<span
4043 class="cmmi-10x-x-109">x </span>+ 0<span
4044 class="cmmi-10x-x-109">.</span>5)<span
4045 class="cmmi-10x-x-109">∕n</span><span
4046 class="cmsy-10x-x-109">*</span><span
4047 class="cmmi-10x-x-109">π</span>)), where <span
4048 class="cmmi-10x-x-109">n </span>is window size
4050 class="cmmi-10x-x-109">x </span>ranges 0<span
4051 class="cmmi-10x-x-109">…</span><span
4052 class="cmmi-10x-x-109">n </span><span
4053 class="cmsy-10x-x-109">- </span>1, but dissimilar lapping requirements can affect overall shape. Window
4054 generation proceeds as follows:
4055 <!--l. 326--><p class="noindent" >
4056 <ol class="enumerate1" >
4058 class="enumerate" id="x1-72022x1"><span
4059 class="cmtt-10x-x-109">[window_center] </span>= <span
4060 class="cmtt-10x-x-109">[n] </span>/ 2
4063 class="enumerate" id="x1-72024x2">if (<span
4064 class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is set and <span
4065 class="cmtt-10x-x-109">[previous_window_flag] </span>is not set)
4067 <ol class="enumerate2" >
4069 class="enumerate" id="x1-72026x1"><span
4070 class="cmtt-10x-x-109">[left_window_start] </span>= <span
4071 class="cmtt-10x-x-109">[n]</span>/4 - <span
4072 class="cmtt-10x-x-109">[blocksize_0]</span>/4
4075 class="enumerate" id="x1-72028x2"><span
4076 class="cmtt-10x-x-109">[left_window_end] </span>= <span
4077 class="cmtt-10x-x-109">[n]</span>/4 + <span
4078 class="cmtt-10x-x-109">[blocksize_0]</span>/4
4081 class="enumerate" id="x1-72030x3"><span
4082 class="cmtt-10x-x-109">[left_n] </span>= <span
4083 class="cmtt-10x-x-109">[blocksize_0]</span>/2</li></ol>
4084 <!--l. 335--><p class="noindent" >else
4085 <ol class="enumerate2" >
4087 class="enumerate" id="x1-72032x1"><span
4088 class="cmtt-10x-x-109">[left_window_start] </span>= 0
4091 class="enumerate" id="x1-72034x2"><span
4092 class="cmtt-10x-x-109">[left_window_end] </span>= <span
4093 class="cmtt-10x-x-109">[window_center]</span>
4099 class="enumerate" id="x1-72036x3"><span
4100 class="cmtt-10x-x-109">[left_n] </span>= <span
4101 class="cmtt-10x-x-109">[n]</span>/2</li></ol>
4104 class="enumerate" id="x1-72038x3">if (<span
4105 class="cmtt-10x-x-109">[vorbis_mode_blockflag] </span>is set and <span
4106 class="cmtt-10x-x-109">[next_window_flag] </span>is not set) then
4107 <ol class="enumerate2" >
4109 class="enumerate" id="x1-72040x1"><span
4110 class="cmtt-10x-x-109">[right_window_start] </span>= <span
4111 class="cmtt-10x-x-109">[n]*3</span>/4 - <span
4112 class="cmtt-10x-x-109">[blocksize_0]</span>/4
4115 class="enumerate" id="x1-72042x2"><span
4116 class="cmtt-10x-x-109">[right_window_end] </span>= <span
4117 class="cmtt-10x-x-109">[n]*3</span>/4 + <span
4118 class="cmtt-10x-x-109">[blocksize_0]</span>/4
4121 class="enumerate" id="x1-72044x3"><span
4122 class="cmtt-10x-x-109">[right_n] </span>= <span
4123 class="cmtt-10x-x-109">[blocksize_0]</span>/2</li></ol>
4124 <!--l. 351--><p class="noindent" >else
4125 <ol class="enumerate2" >
4127 class="enumerate" id="x1-72046x1"><span
4128 class="cmtt-10x-x-109">[right_window_start] </span>= <span
4129 class="cmtt-10x-x-109">[window_center]</span>
4132 class="enumerate" id="x1-72048x2"><span
4133 class="cmtt-10x-x-109">[right_window_end] </span>= <span
4134 class="cmtt-10x-x-109">[n]</span>
4137 class="enumerate" id="x1-72050x3"><span
4138 class="cmtt-10x-x-109">[right_n] </span>= <span
4139 class="cmtt-10x-x-109">[n]</span>/2</li></ol>
4142 class="enumerate" id="x1-72052x4">window from range 0 ... <span
4143 class="cmtt-10x-x-109">[left_window_start]</span>-1 inclusive is zero
4146 class="enumerate" id="x1-72054x5">for <span
4147 class="cmtt-10x-x-109">[i] </span>in range <span
4148 class="cmtt-10x-x-109">[left_window_start] </span>... <span
4149 class="cmtt-10x-x-109">[left_window_end]</span>-1, window(<span
4150 class="cmtt-10x-x-109">[i]</span>) =
4152 src="Vorbis_I_spec2x.png" alt="π
4153 2" class="frac" align="middle"> <span
4154 class="cmsy-10x-x-109">*</span> sin<sup><span
4155 class="cmr-8">2</span></sup>( (<span
4156 class="cmtt-10x-x-109">[i]</span>-<span
4157 class="cmtt-10x-x-109">[left_window_start]</span>+0.5) / <span
4158 class="cmtt-10x-x-109">[left_n] </span><span
4159 class="cmsy-10x-x-109">*</span><img
4160 src="Vorbis_I_spec3x.png" alt="π
4161 2" class="frac" align="middle">) )
4164 class="enumerate" id="x1-72056x6">window from range <span
4165 class="cmtt-10x-x-109">[left_window_end] </span>... <span
4166 class="cmtt-10x-x-109">[right_window_start]</span>-1 inclusive is
4170 class="enumerate" id="x1-72058x7">for <span
4171 class="cmtt-10x-x-109">[i] </span>in range <span
4172 class="cmtt-10x-x-109">[right_window_start] </span>... <span
4173 class="cmtt-10x-x-109">[right_window_end]</span>-1, window(<span
4174 class="cmtt-10x-x-109">[i]</span>) =
4176 src="Vorbis_I_spec4x.png" alt="π
4177 2" class="frac" align="middle"> <span
4178 class="cmsy-10x-x-109">*</span> sin<sup><span
4179 class="cmr-8">2</span></sup>( (<span
4180 class="cmtt-10x-x-109">[i]</span>-<span
4181 class="cmtt-10x-x-109">[right_window_start]</span>+0.5) / <span
4182 class="cmtt-10x-x-109">[right_n] </span><span
4183 class="cmsy-10x-x-109">*</span><img
4184 src="Vorbis_I_spec5x.png" alt="π
4185 2" class="frac" align="middle"> + <img
4186 src="Vorbis_I_spec6x.png" alt="π
4187 2" class="frac" align="middle">) )
4190 class="enumerate" id="x1-72060x8">window from range <span
4191 class="cmtt-10x-x-109">[right_window_start] </span>... <span
4192 class="cmtt-10x-x-109">[n]</span>-1 is zero</li></ol>
4193 <!--l. 367--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this packet
4194 from the stream. An end of packet condition past this point is to be considered a possible nominal
4196 <!--l. 374--><p class="noindent" >
4197 <h5 class="subsubsectionHead"><span class="titlemark">4.3.2 </span> <a
4198 id="x1-730004.3.2"></a>floor curve decode</h5>
4202 <!--l. 376--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
4203 class="cmtt-10x-x-109">[mode_number]</span>
4204 from configuration array <span
4205 class="cmtt-10x-x-109">[vorbis_mode_configurations] </span>and the map number
4207 class="cmtt-10x-x-109">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
4209 class="cmtt-10x-x-109">[vorbis_mapping_configurations]</span>.
4210 <!--l. 383--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
4211 <!--l. 385--><p class="noindent" >For each floor <span
4212 class="cmtt-10x-x-109">[i] </span>of <span
4213 class="cmtt-10x-x-109">[audio_channels]</span>
4214 <ol class="enumerate1" >
4216 class="enumerate" id="x1-73002x1"><span
4217 class="cmtt-10x-x-109">[submap_number] </span>= element <span
4218 class="cmtt-10x-x-109">[i] </span>of vector [vorbis˙mapping˙mux]
4221 class="enumerate" id="x1-73004x2"><span
4222 class="cmtt-10x-x-109">[floor_number] </span>= element <span
4223 class="cmtt-10x-x-109">[submap_number] </span>of vector [vorbis˙submap˙floor]
4226 class="enumerate" id="x1-73006x3">if the floor type of this floor (vector <span
4227 class="cmtt-10x-x-109">[vorbis_floor_types] </span>element <span
4228 class="cmtt-10x-x-109">[floor_number]</span>)
4229 is zero then decode the floor for channel <span
4230 class="cmtt-10x-x-109">[i] </span>according to the <a
4231 href="#x1-930006.2.2">subsubsection 6.2.2<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>,
4233 href="#x1-930006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
4236 class="enumerate" id="x1-73008x4">if the type of this floor is one then decode the floor for channel <span
4237 class="cmtt-10x-x-109">[i] </span>according to the
4239 href="#x1-1000007.2.2">paragraph 7.2.2<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>, “<a
4240 href="#x1-1000007.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
4243 class="enumerate" id="x1-73010x5">save the needed decoded floor information for channel for later synthesis
4246 class="enumerate" id="x1-73012x6">if the decoded floor returned ’unused’, set vector <span
4247 class="cmtt-10x-x-109">[no_residue] </span>element <span
4248 class="cmtt-10x-x-109">[i] </span>to true,
4249 else set vector <span
4250 class="cmtt-10x-x-109">[no_residue] </span>element <span
4251 class="cmtt-10x-x-109">[i] </span>to false</li></ol>
4252 <!--l. 405--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
4253 output vectors and skipping to the add/overlap output stage.
4254 <!--l. 411--><p class="noindent" >
4255 <h5 class="subsubsectionHead"><span class="titlemark">4.3.3 </span> <a
4256 id="x1-740004.3.3"></a>nonzero vector propagate</h5>
4257 <!--l. 413--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
4258 that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
4259 coded in the stream, save for one complication. If some vectors are used and some are not, channel
4260 coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
4262 <!--l. 420--><p class="noindent" >for each <span
4263 class="cmtt-10x-x-109">[i] </span>from 0 ... <span
4264 class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps]</span>-1
4265 <!--l. 423--><p class="noindent" >
4266 <ol class="enumerate1" >
4268 class="enumerate" id="x1-74002x1">if either <span
4269 class="cmtt-10x-x-109">[no_residue] </span>entry for channel (<span
4270 class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
4271 class="cmtt-10x-x-109">[i]</span>)
4276 class="cmtt-10x-x-109">[vorbis_mapping_angle] </span>element <span
4277 class="cmtt-10x-x-109">[i]</span>) are set to false, then both must be
4278 set to false. Note that an ’unused’ floor has no decoded floor information; it is important
4279 that this is remembered at floor curve synthesis time.</li></ol>
4280 <!--l. 435--><p class="noindent" >
4281 <h5 class="subsubsectionHead"><span class="titlemark">4.3.4 </span> <a
4282 id="x1-750004.3.4"></a>residue decode</h5>
4283 <!--l. 437--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
4285 <!--l. 440--><p class="noindent" >for each submap <span
4286 class="cmtt-10x-x-109">[i] </span>in order from 0 ... <span
4287 class="cmtt-10x-x-109">[vorbis_mapping_submaps]</span>-1
4288 <!--l. 443--><p class="noindent" >
4289 <ol class="enumerate1" >
4291 class="enumerate" id="x1-75002x1"><span
4292 class="cmtt-10x-x-109">[ch] </span>= 0
4295 class="enumerate" id="x1-75004x2">for each channel <span
4296 class="cmtt-10x-x-109">[j] </span>in order from 0 ... <span
4297 class="cmtt-10x-x-109">[audio_channels] </span>- 1
4298 <ol class="enumerate2" >
4300 class="enumerate" id="x1-75006x1">if channel <span
4301 class="cmtt-10x-x-109">[j] </span>in submap <span
4302 class="cmtt-10x-x-109">[i] </span>(vector <span
4303 class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
4304 class="cmtt-10x-x-109">[j] </span>is equal to
4306 class="cmtt-10x-x-109">[i]</span>)
4307 <ol class="enumerate3" >
4309 class="enumerate" id="x1-75008x1">if vector <span
4310 class="cmtt-10x-x-109">[no_residue] </span>element <span
4311 class="cmtt-10x-x-109">[j] </span>is true
4312 <ol class="enumerate4" >
4314 class="enumerate" id="x1-75010x1">vector <span
4315 class="cmtt-10x-x-109">[do_not_decode_flag] </span>element <span
4316 class="cmtt-10x-x-109">[ch] </span>is set</li></ol>
4317 <!--l. 452--><p class="noindent" >else
4318 <ol class="enumerate4" >
4320 class="enumerate" id="x1-75012x1">vector <span
4321 class="cmtt-10x-x-109">[do_not_decode_flag] </span>element <span
4322 class="cmtt-10x-x-109">[ch] </span>is unset</li></ol>
4325 class="enumerate" id="x1-75014x2">increment <span
4326 class="cmtt-10x-x-109">[ch]</span></li></ol>
4330 class="enumerate" id="x1-75016x3"><span
4331 class="cmtt-10x-x-109">[residue_number] </span>= vector <span
4332 class="cmtt-10x-x-109">[vorbis_mapping_submap_residue] </span>element <span
4333 class="cmtt-10x-x-109">[i]</span>
4336 class="enumerate" id="x1-75018x4"><span
4337 class="cmtt-10x-x-109">[residue_type] </span>= vector <span
4338 class="cmtt-10x-x-109">[vorbis_residue_types] </span>element <span
4339 class="cmtt-10x-x-109">[residue_number]</span>
4342 class="enumerate" id="x1-75020x5">decode <span
4343 class="cmtt-10x-x-109">[ch] </span>vectors using residue <span
4344 class="cmtt-10x-x-109">[residue_number]</span>, according to type <span
4345 class="cmtt-10x-x-109">[residue_type]</span>,
4346 also passing vector <span
4347 class="cmtt-10x-x-109">[do_not_decode_flag] </span>to indicate which vectors in the bundle should not
4348 be decoded. Correct per-vector decode length is <span
4349 class="cmtt-10x-x-109">[n]</span>/2.
4355 class="enumerate" id="x1-75022x6"><span
4356 class="cmtt-10x-x-109">[ch] </span>= 0
4359 class="enumerate" id="x1-75024x7">for each channel <span
4360 class="cmtt-10x-x-109">[j] </span>in order from 0 ... <span
4361 class="cmtt-10x-x-109">[audio_channels]</span>
4362 <ol class="enumerate2" >
4364 class="enumerate" id="x1-75026x1">if channel <span
4365 class="cmtt-10x-x-109">[j] </span>is in submap <span
4366 class="cmtt-10x-x-109">[i] </span>(vector <span
4367 class="cmtt-10x-x-109">[vorbis_mapping_mux] </span>element <span
4368 class="cmtt-10x-x-109">[j] </span>is equal to
4370 class="cmtt-10x-x-109">[i]</span>)
4371 <ol class="enumerate3" >
4373 class="enumerate" id="x1-75028x1">residue vector for channel <span
4374 class="cmtt-10x-x-109">[j] </span>is set to decoded residue vector <span
4375 class="cmtt-10x-x-109">[ch]</span>
4378 class="enumerate" id="x1-75030x2">increment <span
4379 class="cmtt-10x-x-109">[ch]</span></li></ol>
4382 <!--l. 479--><p class="noindent" >
4383 <h5 class="subsubsectionHead"><span class="titlemark">4.3.5 </span> <a
4384 id="x1-760004.3.5"></a>inverse coupling</h5>
4385 <!--l. 481--><p class="noindent" >for each <span
4386 class="cmtt-10x-x-109">[i] </span>from <span
4387 class="cmtt-10x-x-109">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
4388 <!--l. 484--><p class="noindent" >
4389 <ol class="enumerate1" >
4391 class="enumerate" id="x1-76002x1"><span
4392 class="cmtt-10x-x-109">[magnitude_vector] </span>= the residue vector for channel (vector
4394 class="cmtt-10x-x-109">[vorbis_mapping_magnitude] </span>element <span
4395 class="cmtt-10x-x-109">[i]</span>)
4398 class="enumerate" id="x1-76004x2"><span
4399 class="cmtt-10x-x-109">[angle_vector] </span>= the residue vector for channel (vector <span
4400 class="cmtt-10x-x-109">[vorbis_mapping_angle]</span>
4402 class="cmtt-10x-x-109">[i]</span>)
4405 class="enumerate" id="x1-76006x3">for each scalar value <span
4406 class="cmtt-10x-x-109">[M] </span>in vector <span
4407 class="cmtt-10x-x-109">[magnitude_vector] </span>and the corresponding scalar value
4409 class="cmtt-10x-x-109">[A] </span>in vector <span
4410 class="cmtt-10x-x-109">[angle_vector]</span>:
4411 <ol class="enumerate2" >
4413 class="enumerate" id="x1-76008x1">if (<span
4414 class="cmtt-10x-x-109">[M] </span>is greater than zero)
4415 <ol class="enumerate3" >
4417 class="enumerate" id="x1-76010x1">if (<span
4418 class="cmtt-10x-x-109">[A] </span>is greater than zero)
4419 <ol class="enumerate4" >
4421 class="enumerate" id="x1-76012x1"><span
4422 class="cmtt-10x-x-109">[new_M] </span>= <span
4423 class="cmtt-10x-x-109">[M]</span>
4426 class="enumerate" id="x1-76014x2"><span
4427 class="cmtt-10x-x-109">[new_A] </span>= <span
4428 class="cmtt-10x-x-109">[M]</span>-<span
4429 class="cmtt-10x-x-109">[A]</span></li></ol>
4433 <!--l. 497--><p class="noindent" >else
4434 <ol class="enumerate4" >
4436 class="enumerate" id="x1-76016x1"><span
4437 class="cmtt-10x-x-109">[new_A] </span>= <span
4438 class="cmtt-10x-x-109">[M]</span>
4441 class="enumerate" id="x1-76018x2"><span
4442 class="cmtt-10x-x-109">[new_M] </span>= <span
4443 class="cmtt-10x-x-109">[M]</span>+<span
4444 class="cmtt-10x-x-109">[A]</span></li></ol>
4446 <!--l. 504--><p class="noindent" >else
4447 <ol class="enumerate3" >
4449 class="enumerate" id="x1-76020x1">if (<span
4450 class="cmtt-10x-x-109">[A] </span>is greater than zero)
4451 <ol class="enumerate4" >
4453 class="enumerate" id="x1-76022x1"><span
4454 class="cmtt-10x-x-109">[new_M] </span>= <span
4455 class="cmtt-10x-x-109">[M]</span>
4458 class="enumerate" id="x1-76024x2"><span
4459 class="cmtt-10x-x-109">[new_A] </span>= <span
4460 class="cmtt-10x-x-109">[M]</span>+<span
4461 class="cmtt-10x-x-109">[A]</span></li></ol>
4462 <!--l. 511--><p class="noindent" >else
4463 <ol class="enumerate4" >
4465 class="enumerate" id="x1-76026x1"><span
4466 class="cmtt-10x-x-109">[new_A] </span>= <span
4467 class="cmtt-10x-x-109">[M]</span>
4470 class="enumerate" id="x1-76028x2"><span
4471 class="cmtt-10x-x-109">[new_M] </span>= <span
4472 class="cmtt-10x-x-109">[M]</span>-<span
4473 class="cmtt-10x-x-109">[A]</span></li></ol>
4477 class="enumerate" id="x1-76030x2">set scalar value <span
4478 class="cmtt-10x-x-109">[M] </span>in vector <span
4479 class="cmtt-10x-x-109">[magnitude_vector] </span>to <span
4480 class="cmtt-10x-x-109">[new_M]</span>
4483 class="enumerate" id="x1-76032x3">set scalar value <span
4484 class="cmtt-10x-x-109">[A] </span>in vector <span
4485 class="cmtt-10x-x-109">[angle_vector] </span>to <span
4486 class="cmtt-10x-x-109">[new_A]</span></li></ol>
4488 <!--l. 528--><p class="noindent" >
4489 <h5 class="subsubsectionHead"><span class="titlemark">4.3.6 </span> <a
4490 id="x1-770004.3.6"></a>dot product</h5>
4491 <!--l. 530--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to packet
4492 type. Note that the vector synthesis length for floor computation is <span
4493 class="cmtt-10x-x-109">[n]</span>/2.
4494 <!--l. 534--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that channel’s residue
4495 vector. The result is the dot product of the floor and residue vectors for each channel; the produced
4496 vectors are the length <span
4497 class="cmtt-10x-x-109">[n]</span>/2 audio spectrum for each channel.
4498 <!--l. 542--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
4499 implementation might be to assume that a 32 bit fixed-point representation for floor
4503 and residue and direct multiplication of the vectors is sufficient for acceptable spectral
4504 depth in all cases because it happens to mostly work with the current Xiph.Org reference
4506 <!--l. 549--><p class="noindent" >However, floor vector values can span <span
4507 class="cmsy-10x-x-109">~</span>140dB (<span
4508 class="cmsy-10x-x-109">~</span>24 bits unsigned), and the audio spectrum vector
4509 should represent a minimum of 120dB (<span
4510 class="cmsy-10x-x-109">~</span>21 bits with sign), even when output is to a 16 bit PCM
4511 device. For the residue vector to represent full scale if the floor is nailed to <span
4512 class="cmsy-10x-x-109">-</span>140dB, it must be able
4513 to span 0 to +140dB. For the residue vector to reach full scale if the floor is nailed at 0dB, it must
4514 be able to represent <span
4515 class="cmsy-10x-x-109">-</span>140dB to +0dB. Thus, in order to handle full range dynamics, a residue
4516 vector may span <span
4517 class="cmsy-10x-x-109">-</span>140dB to +140dB entirely within spec. A 280dB range is approximately 48 bits
4518 with sign; thus the residue vector must be able to represent a 48 bit range and the dot product
4519 must be able to handle an effective 48 bit times 24 bit multiplication. This range may be
4520 achieved using large (64 bit or larger) integers, or implementing a movable binary point
4522 <!--l. 566--><p class="noindent" >
4523 <h5 class="subsubsectionHead"><span class="titlemark">4.3.7 </span> <a
4524 id="x1-780004.3.7"></a>inverse MDCT</h5>
4525 <!--l. 568--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
4526 inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT
4527 is available in <span class="cite">[<a
4528 href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
4530 <!--l. 575--><p class="noindent" >
4531 <h5 class="subsubsectionHead"><span class="titlemark">4.3.8 </span> <a
4532 id="x1-790004.3.8"></a>overlap˙add</h5>
4533 <!--l. 577--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
4534 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
4535 current window (as illustrated in <a
4536 href="#x1-260001.3.2">paragraph 1.3.2<!--tex4ht:ref: vorbis:spec:window --></a>, “<a
4537 href="#x1-260001.3.2">Window shape decode (long windows
4538 only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame
4539 data is finished data to be returned by the decoder. This data spans from the center
4540 of the previous window to the center of the current window. In the case of same-sized
4541 windows, the amount of data to return is one-half block consisting of and only of the
4542 overlapped portions. When overlapping a short and long window, much of the returned
4543 range does not actually overlap. This does not damage transform orthogonality. Pay
4544 attention however to returning the correct data range; the amount of data to be returned
4546 <!--l. 591--><p class="noindent" >
4547 <div class="fancyvrb" id="fancyvrb22">
4549 id="x1-79002r1"></a><span
4550 class="cmtt-10"> </span><span
4551 class="cmtt-10"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
4556 <!--l. 595--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
4557 windowsize/2-1, inclusive) of the current window.
4558 <!--l. 598--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The encoder
4559 accounts for this priming when calculating PCM offsets; after the first frame, the proper PCM
4560 output offset is ’0’ (as no data has been returned yet).
4561 <!--l. 605--><p class="noindent" >
4562 <h5 class="subsubsectionHead"><span class="titlemark">4.3.9 </span> <a
4563 id="x1-800004.3.9"></a>output channel order</h5>
4564 <!--l. 607--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is implicitly
4565 defined as follows for standard audio applications:
4566 <!--l. 612--><p class="noindent" >
4567 <dl class="description"><dt class="description">
4569 class="cmssbx-10x-x-109">three channels</span> </dt><dd
4570 class="description">the stream is monophonic
4571 </dd><dt class="description">
4573 class="cmssbx-10x-x-109">two channels</span> </dt><dd
4574 class="description">the stream is stereo. channel order: left, right
4575 </dd><dt class="description">
4577 class="cmssbx-10x-x-109">three channels</span> </dt><dd
4578 class="description">the stream is a 1d-surround encoding. channel order: left, center, right
4579 </dd><dt class="description">
4581 class="cmssbx-10x-x-109">four channels</span> </dt><dd
4582 class="description">the stream is quadraphonic surround. channel order: front left, front right, rear
4584 </dd><dt class="description">
4586 class="cmssbx-10x-x-109">five channels</span> </dt><dd
4587 class="description">the stream is five-channel surround. channel order: front left, front center, front
4588 right, rear left, rear right
4589 </dd><dt class="description">
4591 class="cmssbx-10x-x-109">six channels</span> </dt><dd
4592 class="description">the stream is 5.1 surround. channel order: front left, front center, front right,
4593 rear left, rear right, LFE
4594 </dd><dt class="description">
4596 class="cmssbx-10x-x-109">greater than six channels</span> </dt><dd
4597 class="description">channel use and order is defined by the application
4599 <!--l. 639--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
4600 channel mappings (such as three and four channel <a
4601 href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel mappings
4602 other than mapping 0.
4609 <h3 class="sectionHead"><span class="titlemark">5 </span> <a
4610 id="x1-810005"></a>comment field and header specification</h3>
4611 <!--l. 6--><p class="noindent" >
4612 <h4 class="subsectionHead"><span class="titlemark">5.1 </span> <a
4613 id="x1-820005.1"></a>Overview</h4>
4614 <!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
4615 bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata belongs
4616 in a separate logical bitstream (usually an XML stream type) that provides greater structure and
4617 machine parseability.
4618 <!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of a
4619 CDR. It should be a little information to remember the disc by and explain it to others; a short,
4620 to-the-point text note that need not only be a couple words, but isn’t going to be more
4621 than a short paragraph. The essentials, in other words, whatever they turn out to be,
4623 <!--l. 21--><p class="noindent" >
4625 <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
4626 class="cmti-10x-x-109">“I’m Still Around”</span>, opening for
4627 Moxy Früvous, 1997.</div>
4628 <!--l. 29--><p class="noindent" >
4629 <h4 class="subsectionHead"><span class="titlemark">5.2 </span> <a
4630 id="x1-830005.2"></a>Comment encoding</h4>
4631 <!--l. 31--><p class="noindent" >
4632 <h5 class="subsubsectionHead"><span class="titlemark">5.2.1 </span> <a
4633 id="x1-840005.2.1"></a>Structure</h5>
4634 <!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is bounded
4636 class="cmr-8">32</span></sup> <span
4637 class="cmsy-10x-x-109">- </span>1 and the length of each vector is limited to 2<sup><span
4638 class="cmr-8">32</span></sup> <span
4639 class="cmsy-10x-x-109">- </span>1 bytes. The vector length is encoded;
4640 the vector contents themselves are not null terminated. In addition to the vector list,
4641 there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits).
4642 For example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
4647 <!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit packing
4648 conventions of the vorbis codec. However, since data in the comment header is octet-aligned, they
4649 can simply be read as unaligned 32 bit little endian unsigned integers.
4650 <!--l. 46--><p class="noindent" >The comment header is decoded as follows:
4651 <!--l. 48--><p class="noindent" >
4652 <div class="fancyvrb" id="fancyvrb23">
4654 id="x1-84002r1"></a><span
4655 class="cmtt-10"> </span><span
4656 class="cmtt-10"> </span><span
4657 class="cmtt-10"> </span><span
4658 class="cmtt-10"> 1)</span><span
4659 class="cmtt-10"> [vendor_length]</span><span
4660 class="cmtt-10"> =</span><span
4661 class="cmtt-10"> read</span><span
4662 class="cmtt-10"> an</span><span
4663 class="cmtt-10"> unsigned</span><span
4664 class="cmtt-10"> integer</span><span
4665 class="cmtt-10"> of</span><span
4666 class="cmtt-10"> 32</span><span
4667 class="cmtt-10"> bits</span>
4668 <br class="fancyvrb" /><a
4669 id="x1-84004r2"></a><span
4670 class="cmtt-10"> </span><span
4671 class="cmtt-10"> </span><span
4672 class="cmtt-10"> </span><span
4673 class="cmtt-10"> 2)</span><span
4674 class="cmtt-10"> [vendor_string]</span><span
4675 class="cmtt-10"> =</span><span
4676 class="cmtt-10"> read</span><span
4677 class="cmtt-10"> a</span><span
4678 class="cmtt-10"> UTF-8</span><span
4679 class="cmtt-10"> vector</span><span
4680 class="cmtt-10"> as</span><span
4681 class="cmtt-10"> [vendor_length]</span><span
4682 class="cmtt-10"> octets</span>
4683 <br class="fancyvrb" /><a
4684 id="x1-84006r3"></a><span
4685 class="cmtt-10"> </span><span
4686 class="cmtt-10"> </span><span
4687 class="cmtt-10"> </span><span
4688 class="cmtt-10"> 3)</span><span
4689 class="cmtt-10"> [user_comment_list_length]</span><span
4690 class="cmtt-10"> =</span><span
4691 class="cmtt-10"> read</span><span
4692 class="cmtt-10"> an</span><span
4693 class="cmtt-10"> unsigned</span><span
4694 class="cmtt-10"> integer</span><span
4695 class="cmtt-10"> of</span><span
4696 class="cmtt-10"> 32</span><span
4697 class="cmtt-10"> bits</span>
4698 <br class="fancyvrb" /><a
4699 id="x1-84008r4"></a><span
4700 class="cmtt-10"> </span><span
4701 class="cmtt-10"> </span><span
4702 class="cmtt-10"> </span><span
4703 class="cmtt-10"> 4)</span><span
4704 class="cmtt-10"> iterate</span><span
4705 class="cmtt-10"> [user_comment_list_length]</span><span
4706 class="cmtt-10"> times</span><span
4707 class="cmtt-10"> {</span>
4708 <br class="fancyvrb" /><a
4709 id="x1-84010r5"></a><span
4710 class="cmtt-10"> </span><span
4711 class="cmtt-10"> </span><span
4712 class="cmtt-10"> </span><span
4713 class="cmtt-10"> </span><span
4714 class="cmtt-10"> </span><span
4715 class="cmtt-10"> </span><span
4716 class="cmtt-10"> </span><span
4717 class="cmtt-10"> </span><span
4718 class="cmtt-10"> 5)</span><span
4719 class="cmtt-10"> [length]</span><span
4720 class="cmtt-10"> =</span><span
4721 class="cmtt-10"> read</span><span
4722 class="cmtt-10"> an</span><span
4723 class="cmtt-10"> unsigned</span><span
4724 class="cmtt-10"> integer</span><span
4725 class="cmtt-10"> of</span><span
4726 class="cmtt-10"> 32</span><span
4727 class="cmtt-10"> bits</span>
4728 <br class="fancyvrb" /><a
4729 id="x1-84012r6"></a><span
4730 class="cmtt-10"> </span><span
4731 class="cmtt-10"> </span><span
4732 class="cmtt-10"> </span><span
4733 class="cmtt-10"> </span><span
4734 class="cmtt-10"> </span><span
4735 class="cmtt-10"> </span><span
4736 class="cmtt-10"> </span><span
4737 class="cmtt-10"> </span><span
4738 class="cmtt-10"> 6)</span><span
4739 class="cmtt-10"> this</span><span
4740 class="cmtt-10"> iteration’s</span><span
4741 class="cmtt-10"> user</span><span
4742 class="cmtt-10"> comment</span><span
4743 class="cmtt-10"> =</span><span
4744 class="cmtt-10"> read</span><span
4745 class="cmtt-10"> a</span><span
4746 class="cmtt-10"> UTF-8</span><span
4747 class="cmtt-10"> vector</span><span
4748 class="cmtt-10"> as</span><span
4749 class="cmtt-10"> [length]</span><span
4750 class="cmtt-10"> octets</span>
4751 <br class="fancyvrb" /><a
4752 id="x1-84014r7"></a><span
4753 class="cmtt-10"> </span><span
4754 class="cmtt-10"> </span><span
4755 class="cmtt-10"> </span><span
4756 class="cmtt-10"> </span><span
4757 class="cmtt-10"> </span><span
4758 class="cmtt-10"> </span><span
4759 class="cmtt-10"> }</span>
4760 <br class="fancyvrb" /><a
4761 id="x1-84016r8"></a><span
4762 class="cmtt-10"> </span><span
4763 class="cmtt-10"> </span><span
4764 class="cmtt-10"> </span><span
4765 class="cmtt-10"> 7)</span><span
4766 class="cmtt-10"> [framing_bit]</span><span
4767 class="cmtt-10"> =</span><span
4768 class="cmtt-10"> read</span><span
4769 class="cmtt-10"> a</span><span
4770 class="cmtt-10"> single</span><span
4771 class="cmtt-10"> bit</span><span
4772 class="cmtt-10"> as</span><span
4773 class="cmtt-10"> boolean</span>
4774 <br class="fancyvrb" /><a
4775 id="x1-84018r9"></a><span
4776 class="cmtt-10"> </span><span
4777 class="cmtt-10"> </span><span
4778 class="cmtt-10"> </span><span
4779 class="cmtt-10"> 8)</span><span
4780 class="cmtt-10"> if</span><span
4781 class="cmtt-10"> (</span><span
4782 class="cmtt-10"> [framing_bit]</span><span
4783 class="cmtt-10"> unset</span><span
4784 class="cmtt-10"> or</span><span
4785 class="cmtt-10"> end-of-packet</span><span
4786 class="cmtt-10"> )</span><span
4787 class="cmtt-10"> then</span><span
4788 class="cmtt-10"> ERROR</span>
4789 <br class="fancyvrb" /><a
4790 id="x1-84020r10"></a><span
4791 class="cmtt-10"> </span><span
4792 class="cmtt-10"> </span><span
4793 class="cmtt-10"> </span><span
4794 class="cmtt-10"> 9)</span><span
4795 class="cmtt-10"> done.</span>
4797 <!--l. 64--><p class="noindent" >
4798 <h5 class="subsubsectionHead"><span class="titlemark">5.2.2 </span> <a
4799 id="x1-850005.2.2"></a>Content vector format</h5>
4800 <!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is, comment
4801 fields consist of a field name and a corresponding value and look like:
4802 <!--l. 70--><p class="noindent" >
4804 <!--l. 71--><p class="noindent" >
4805 <div class="fancyvrb" id="fancyvrb24">
4807 id="x1-85002r1"></a><span
4808 class="cmtt-10"> </span><span
4809 class="cmtt-10"> comment[0]="ARTIST=me";</span>
4810 <br class="fancyvrb" /><a
4811 id="x1-85004r2"></a><span
4812 class="cmtt-10"> </span><span
4813 class="cmtt-10"> comment[1]="TITLE=the</span><span
4814 class="cmtt-10"> sound</span><span
4815 class="cmtt-10"> of</span><span
4816 class="cmtt-10"> Vorbis";</span>
4819 <!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
4820 excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
4821 ASCII 0x61 through 0x7A inclusive (characters a-z).
4822 <!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to terminate
4827 <!--l. 87--><p class="noindent" >0x3D is followed by 8 bit clean UTF-8 encoded value of the field contents to the end of the
4829 <!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
4830 id="x1-860005.2.2"></a><span
4831 class="cmbx-10x-x-109">Field names</span></span>
4832 Below is a proposed, minimal list of standard field names with a description of intended use. No
4833 single or group of field names is mandatory; a comment header may contain one, all or none of the
4835 <!--l. 99--><p class="noindent" >
4836 <dl class="description"><dt class="description">
4838 class="cmssbx-10x-x-109">TITLE</span> </dt><dd
4839 class="description">Track/Work name
4840 </dd><dt class="description">
4842 class="cmssbx-10x-x-109">VERSION</span> </dt><dd
4843 class="description">The version field may be used to differentiate multiple versions of the same track
4844 title in a single collection. (e.g. remix info)
4845 </dd><dt class="description">
4847 class="cmssbx-10x-x-109">ALBUM</span> </dt><dd
4848 class="description">The collection name to which this track belongs
4849 </dd><dt class="description">
4851 class="cmssbx-10x-x-109">TRACKNUMBER</span> </dt><dd
4852 class="description">The track number of this piece if part of a specific larger collection or
4854 </dd><dt class="description">
4856 class="cmssbx-10x-x-109">ARTIST</span> </dt><dd
4857 class="description">The artist generally considered responsible for the work. In popular music this is
4858 usually the performing band or singer. For classical music it would be the composer.
4859 For an audio book it would be the author of the original text.
4860 </dd><dt class="description">
4862 class="cmssbx-10x-x-109">PERFORMER</span> </dt><dd
4863 class="description">The artist(s) who performed the work. In classical music this would be the
4864 conductor, orchestra, soloists. In an audio book it would be the actor who did the
4865 reading. In popular music this is typically the same as the ARTIST and is omitted.
4866 </dd><dt class="description">
4868 class="cmssbx-10x-x-109">COPYRIGHT</span> </dt><dd
4869 class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
4870 </dd><dt class="description">
4872 class="cmssbx-10x-x-109">LICENSE</span> </dt><dd
4873 class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to a
4875 Creative Commons license (”www.creativecommons.org/blahblah/license.html”) or the
4876 EFF Open Audio License (’distributed under the terms of the Open Audio License. see
4877 http://www.eff.org/IP/Open˙licenses/eff˙oal.html for details’), etc.
4878 </dd><dt class="description">
4880 class="cmssbx-10x-x-109">ORGANIZATION</span> </dt><dd
4881 class="description">Name of the organization producing the track (i.e. the ’record label’)
4882 </dd><dt class="description">
4884 class="cmssbx-10x-x-109">DESCRIPTION</span> </dt><dd
4885 class="description">A short text description of the contents
4889 </dd><dt class="description">
4891 class="cmssbx-10x-x-109">GENRE</span> </dt><dd
4892 class="description">A short text indication of music genre
4893 </dd><dt class="description">
4895 class="cmssbx-10x-x-109">DATE</span> </dt><dd
4896 class="description">Date the track was recorded
4897 </dd><dt class="description">
4899 class="cmssbx-10x-x-109">LOCATION</span> </dt><dd
4900 class="description">Location where track was recorded
4901 </dd><dt class="description">
4903 class="cmssbx-10x-x-109">CONTACT</span> </dt><dd
4904 class="description">Contact information for the creators or distributors of the track. This could be
4905 a URL, an email address, the physical address of the producing label.
4906 </dd><dt class="description">
4908 class="cmssbx-10x-x-109">ISRC</span> </dt><dd
4909 class="description">International Standard Recording Code for the track; see <a
4910 href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for more
4911 information on ISRC numbers.
4913 <!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
4914 id="x1-870005.2.2"></a><span
4915 class="cmbx-10x-x-109">Implications</span></span>
4916 Field names should not be ’internationalized’; this is a concession to simplicity not an attempt to
4917 exclude the majority of the world that doesn’t speak English. Field <span
4918 class="cmti-10x-x-109">contents</span>, however, use the
4919 UTF-8 character encoding to allow easy representation of any language.
4920 <!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
4921 the field name is bounded in a known way. Thus we also have the length of the field
4923 <!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper use of comment
4924 fields should be clear through context at this point. Abuse will be discouraged.
4925 <!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort to
4926 avoid arbitrarily polluting the common namespace. We will generally collect the more useful tags
4927 here to help with standardization.
4928 <!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an example,
4929 assume a track was recorded by three well know artists; the following is permissible, and
4931 <!--l. 183--><p class="noindent" >
4933 <!--l. 184--><p class="noindent" >
4934 <div class="fancyvrb" id="fancyvrb25">
4936 id="x1-87002r1"></a><span
4937 class="cmtt-10"> </span><span
4938 class="cmtt-10"> ARTIST=Dizzy</span><span
4939 class="cmtt-10"> Gillespie</span>
4940 <br class="fancyvrb" /><a
4941 id="x1-87004r2"></a><span
4942 class="cmtt-10"> </span><span
4943 class="cmtt-10"> ARTIST=Sonny</span><span
4944 class="cmtt-10"> Rollins</span>
4945 <br class="fancyvrb" /><a
4946 id="x1-87006r3"></a><span
4947 class="cmtt-10"> </span><span
4948 class="cmtt-10"> ARTIST=Sonny</span><span
4949 class="cmtt-10"> Stitt</span>
4955 <!--l. 197--><p class="noindent" >
4956 <h5 class="subsubsectionHead"><span class="titlemark">5.2.3 </span> <a
4957 id="x1-880005.2.3"></a>Encoding</h5>
4958 <!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the first
4959 bitstream header packet, it is not generally the only packet on the second page and may not be
4960 restricted to within the second bitstream page. The length of the comment header packet is
4961 (practically) unbounded. The comment header packet is not optional; it must be present in the
4962 bitstream even if it is effectively empty.
4963 <!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which renders
4964 least-significant-bit of the word to be coded into the least significant available bit of the current
4965 bitstream octet first):
4966 <!--l. 213--><p class="noindent" >
4967 <ol class="enumerate1" >
4969 class="enumerate" id="x1-88002x1">Vendor string length (32 bit unsigned quantity specifying number of octets)
4972 class="enumerate" id="x1-88004x2">Vendor string ([vendor string length] octets coded from beginning of string to end of
4973 string, not null terminated)
4976 class="enumerate" id="x1-88006x3">Number of comment fields (32 bit unsigned quantity specifying number of fields)
4979 class="enumerate" id="x1-88008x4">Comment field 0 length (if [Number of comment fields] <span
4980 class="cmmi-10x-x-109">> </span>0; 32 bit unsigned quantity
4981 specifying number of octets)
4984 class="enumerate" id="x1-88010x5">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to end
4985 of string, not null terminated)
4988 class="enumerate" id="x1-88012x6">Comment field 1 length (if [Number of comment fields] <span
4989 class="cmmi-10x-x-109">> </span>1...)...
4991 <!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found in
4993 class="cmtt-10x-x-109">vorbis/lib/info.c</span>, <span
4994 class="cmtt-10x-x-109">_vorbis_pack_comment() </span>and <span
4995 class="cmtt-10x-x-109">_vorbis_unpack_comment()</span>.
5002 <h3 class="sectionHead"><span class="titlemark">6 </span> <a
5003 id="x1-890006"></a>Floor type 0 setup and decode</h3>
5004 <!--l. 6--><p class="noindent" >
5005 <h4 class="subsectionHead"><span class="titlemark">6.1 </span> <a
5006 id="x1-900006.1"></a>Overview</h4>
5007 <!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
5008 Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
5009 response of the LSP filter. This representation is equivalent to a traditional all-pole infinite impulse
5010 response filter as would be used in linear predictive coding; LSP representation may be converted to
5011 LPC representation and vice-versa.
5012 <!--l. 18--><p class="noindent" >
5013 <h4 class="subsectionHead"><span class="titlemark">6.2 </span> <a
5014 id="x1-910006.2"></a>Floor 0 format</h4>
5015 <!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
5016 coding/decoding the LSP filter coefficient values used by each frame.
5017 <!--l. 24--><p class="noindent" >
5018 <h5 class="subsubsectionHead"><span class="titlemark">6.2.1 </span> <a
5019 id="x1-920006.2.1"></a>header decode</h5>
5020 <!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
5021 packet). configuration decode proceeds as follows:
5022 <!--l. 30--><p class="noindent" >
5023 <div class="fancyvrb" id="fancyvrb26">
5025 id="x1-92002r1"></a><span
5026 class="cmtt-10"> </span><span
5027 class="cmtt-10"> </span><span
5028 class="cmtt-10"> </span><span
5029 class="cmtt-10"> 1)</span><span
5030 class="cmtt-10"> [floor0_order]</span><span
5031 class="cmtt-10"> =</span><span
5032 class="cmtt-10"> read</span><span
5033 class="cmtt-10"> an</span><span
5034 class="cmtt-10"> unsigned</span><span
5035 class="cmtt-10"> integer</span><span
5036 class="cmtt-10"> of</span><span
5037 class="cmtt-10"> 8</span><span
5038 class="cmtt-10"> bits</span>
5039 <br class="fancyvrb" /><a
5040 id="x1-92004r2"></a><span
5041 class="cmtt-10"> </span><span
5042 class="cmtt-10"> </span><span
5043 class="cmtt-10"> </span><span
5044 class="cmtt-10"> 2)</span><span
5045 class="cmtt-10"> [floor0_rate]</span><span
5046 class="cmtt-10"> =</span><span
5047 class="cmtt-10"> read</span><span
5048 class="cmtt-10"> an</span><span
5049 class="cmtt-10"> unsigned</span><span
5050 class="cmtt-10"> integer</span><span
5051 class="cmtt-10"> of</span><span
5052 class="cmtt-10"> 16</span><span
5053 class="cmtt-10"> bits</span>
5054 <br class="fancyvrb" /><a
5055 id="x1-92006r3"></a><span
5056 class="cmtt-10"> </span><span
5057 class="cmtt-10"> </span><span
5058 class="cmtt-10"> </span><span
5059 class="cmtt-10"> 3)</span><span
5060 class="cmtt-10"> [floor0_bark_map_size]</span><span
5061 class="cmtt-10"> =</span><span
5062 class="cmtt-10"> read</span><span
5063 class="cmtt-10"> an</span><span
5064 class="cmtt-10"> unsigned</span><span
5065 class="cmtt-10"> integer</span><span
5066 class="cmtt-10"> of</span><span
5067 class="cmtt-10"> 16</span><span
5068 class="cmtt-10"> bits</span>
5069 <br class="fancyvrb" /><a
5070 id="x1-92008r4"></a><span
5071 class="cmtt-10"> </span><span
5072 class="cmtt-10"> </span><span
5073 class="cmtt-10"> </span><span
5074 class="cmtt-10"> 4)</span><span
5075 class="cmtt-10"> [floor0_amplitude_bits]</span><span
5076 class="cmtt-10"> =</span><span
5077 class="cmtt-10"> read</span><span
5078 class="cmtt-10"> an</span><span
5079 class="cmtt-10"> unsigned</span><span
5080 class="cmtt-10"> integer</span><span
5081 class="cmtt-10"> of</span><span
5082 class="cmtt-10"> six</span><span
5083 class="cmtt-10"> bits</span>
5084 <br class="fancyvrb" /><a
5085 id="x1-92010r5"></a><span
5086 class="cmtt-10"> </span><span
5087 class="cmtt-10"> </span><span
5088 class="cmtt-10"> </span><span
5089 class="cmtt-10"> 5)</span><span
5090 class="cmtt-10"> [floor0_amplitude_offset]</span><span
5091 class="cmtt-10"> =</span><span
5092 class="cmtt-10"> read</span><span
5093 class="cmtt-10"> an</span><span
5094 class="cmtt-10"> unsigned</span><span
5095 class="cmtt-10"> integer</span><span
5096 class="cmtt-10"> of</span><span
5097 class="cmtt-10"> eight</span><span
5098 class="cmtt-10"> bits</span>
5099 <br class="fancyvrb" /><a
5100 id="x1-92012r6"></a><span
5101 class="cmtt-10"> </span><span
5102 class="cmtt-10"> </span><span
5103 class="cmtt-10"> </span><span
5104 class="cmtt-10"> 6)</span><span
5105 class="cmtt-10"> [floor0_number_of_books]</span><span
5106 class="cmtt-10"> =</span><span
5107 class="cmtt-10"> read</span><span
5108 class="cmtt-10"> an</span><span
5109 class="cmtt-10"> unsigned</span><span
5110 class="cmtt-10"> integer</span><span
5111 class="cmtt-10"> of</span><span
5112 class="cmtt-10"> four</span><span
5113 class="cmtt-10"> bits</span><span
5114 class="cmtt-10"> and</span><span
5115 class="cmtt-10"> add</span><span
5116 class="cmtt-10"> 1</span>
5117 <br class="fancyvrb" /><a
5118 id="x1-92014r7"></a><span
5119 class="cmtt-10"> </span><span
5120 class="cmtt-10"> </span><span
5121 class="cmtt-10"> </span><span
5122 class="cmtt-10"> 7)</span><span
5123 class="cmtt-10"> array</span><span
5124 class="cmtt-10"> [floor0_book_list]</span><span
5125 class="cmtt-10"> =</span><span
5126 class="cmtt-10"> read</span><span
5127 class="cmtt-10"> a</span><span
5128 class="cmtt-10"> list</span><span
5129 class="cmtt-10"> of</span><span
5130 class="cmtt-10"> [floor0_number_of_books]</span><span
5131 class="cmtt-10"> unsigned</span><span
5132 class="cmtt-10"> integers</span><span
5133 class="cmtt-10"> of</span><span
5134 class="cmtt-10"> eight</span><span
5135 class="cmtt-10"> bits</span><span
5136 class="cmtt-10"> each;</span>
5141 <!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable. In
5142 addition, any element of the array <span
5143 class="cmtt-10x-x-109">[floor0_book_list] </span>that is greater than the maximum
5144 codebook number for this bitstream is an error condition that also renders the stream
5146 <!--l. 48--><p class="noindent" >
5147 <h5 class="subsubsectionHead"><span class="titlemark">6.2.2 </span> <a
5148 id="x1-930006.2.2"></a>packet decode</h5>
5149 <!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve amplitude and
5151 class="cmtt-10x-x-109">[floor0_order] </span>LSP coefficient values from the bitstream, and then computing the floor curve,
5152 which is defined as the frequency response of the decoded LSP filter.
5153 <!--l. 56--><p class="noindent" >Packet decode proceeds as follows:
5154 <div class="fancyvrb" id="fancyvrb27">
5156 id="x1-93002r1"></a><span
5157 class="cmtt-10"> </span><span
5158 class="cmtt-10"> </span><span
5159 class="cmtt-10"> </span><span
5160 class="cmtt-10"> 1)</span><span
5161 class="cmtt-10"> [amplitude]</span><span
5162 class="cmtt-10"> =</span><span
5163 class="cmtt-10"> read</span><span
5164 class="cmtt-10"> an</span><span
5165 class="cmtt-10"> unsigned</span><span
5166 class="cmtt-10"> integer</span><span
5167 class="cmtt-10"> of</span><span
5168 class="cmtt-10"> [floor0_amplitude_bits]</span><span
5169 class="cmtt-10"> bits</span>
5170 <br class="fancyvrb" /><a
5171 id="x1-93004r2"></a><span
5172 class="cmtt-10"> </span><span
5173 class="cmtt-10"> </span><span
5174 class="cmtt-10"> </span><span
5175 class="cmtt-10"> 2)</span><span
5176 class="cmtt-10"> if</span><span
5177 class="cmtt-10"> (</span><span
5178 class="cmtt-10"> [amplitude]</span><span
5179 class="cmtt-10"> is</span><span
5180 class="cmtt-10"> greater</span><span
5181 class="cmtt-10"> than</span><span
5182 class="cmtt-10"> zero</span><span
5183 class="cmtt-10"> )</span><span
5184 class="cmtt-10"> </span><span
5185 class="cmsy-10">{</span>
5186 <br class="fancyvrb" /><a
5187 id="x1-93006r3"></a><span
5188 class="cmtt-10"> </span><span
5189 class="cmtt-10"> </span><span
5190 class="cmtt-10"> </span><span
5191 class="cmtt-10"> </span><span
5192 class="cmtt-10"> </span><span
5193 class="cmtt-10"> </span><span
5194 class="cmtt-10"> </span><span
5195 class="cmtt-10"> </span><span
5196 class="cmtt-10"> 3)</span><span
5197 class="cmtt-10"> [coefficients]</span><span
5198 class="cmtt-10"> is</span><span
5199 class="cmtt-10"> an</span><span
5200 class="cmtt-10"> empty,</span><span
5201 class="cmtt-10"> zero</span><span
5202 class="cmtt-10"> length</span><span
5203 class="cmtt-10"> vector</span>
5204 <br class="fancyvrb" /><a
5205 id="x1-93008r4"></a><span
5206 class="cmtt-10"> </span><span
5207 class="cmtt-10"> </span><span
5208 class="cmtt-10"> </span><span
5209 class="cmtt-10"> </span><span
5210 class="cmtt-10"> </span><span
5211 class="cmtt-10"> </span><span
5212 class="cmtt-10"> </span><span
5213 class="cmtt-10"> </span><span
5214 class="cmtt-10"> 4)</span><span
5215 class="cmtt-10"> [booknumber]</span><span
5216 class="cmtt-10"> =</span><span
5217 class="cmtt-10"> read</span><span
5218 class="cmtt-10"> an</span><span
5219 class="cmtt-10"> unsigned</span><span
5220 class="cmtt-10"> integer</span><span
5221 class="cmtt-10"> of</span><span
5222 class="cmtt-10"> </span><a
5223 href="#x1-1170009.2.1"><span
5224 class="cmtt-10">ilog</span></a><span
5225 class="cmtt-10">(</span><span
5226 class="cmtt-10"> [floor0_number_of_books]</span><span
5227 class="cmtt-10"> )</span><span
5228 class="cmtt-10"> bits</span>
5229 <br class="fancyvrb" /><a
5230 id="x1-93010r5"></a><span
5231 class="cmtt-10"> </span><span
5232 class="cmtt-10"> </span><span
5233 class="cmtt-10"> </span><span
5234 class="cmtt-10"> </span><span
5235 class="cmtt-10"> </span><span
5236 class="cmtt-10"> </span><span
5237 class="cmtt-10"> </span><span
5238 class="cmtt-10"> </span><span
5239 class="cmtt-10"> 5)</span><span
5240 class="cmtt-10"> if</span><span
5241 class="cmtt-10"> (</span><span
5242 class="cmtt-10"> [booknumber]</span><span
5243 class="cmtt-10"> is</span><span
5244 class="cmtt-10"> greater</span><span
5245 class="cmtt-10"> than</span><span
5246 class="cmtt-10"> the</span><span
5247 class="cmtt-10"> highest</span><span
5248 class="cmtt-10"> number</span><span
5249 class="cmtt-10"> decode</span><span
5250 class="cmtt-10"> codebook</span><span
5251 class="cmtt-10"> )</span><span
5252 class="cmtt-10"> then</span><span
5253 class="cmtt-10"> packet</span><span
5254 class="cmtt-10"> is</span><span
5255 class="cmtt-10"> undecodable</span>
5256 <br class="fancyvrb" /><a
5257 id="x1-93012r6"></a><span
5258 class="cmtt-10"> </span><span
5259 class="cmtt-10"> </span><span
5260 class="cmtt-10"> </span><span
5261 class="cmtt-10"> </span><span
5262 class="cmtt-10"> </span><span
5263 class="cmtt-10"> </span><span
5264 class="cmtt-10"> </span><span
5265 class="cmtt-10"> </span><span
5266 class="cmtt-10"> 6)</span><span
5267 class="cmtt-10"> [last]</span><span
5268 class="cmtt-10"> =</span><span
5269 class="cmtt-10"> zero;</span>
5270 <br class="fancyvrb" /><a
5271 id="x1-93014r7"></a><span
5272 class="cmtt-10"> </span><span
5273 class="cmtt-10"> </span><span
5274 class="cmtt-10"> </span><span
5275 class="cmtt-10"> </span><span
5276 class="cmtt-10"> </span><span
5277 class="cmtt-10"> </span><span
5278 class="cmtt-10"> </span><span
5279 class="cmtt-10"> </span><span
5280 class="cmtt-10"> 7)</span><span
5281 class="cmtt-10"> vector</span><span
5282 class="cmtt-10"> [temp_vector]</span><span
5283 class="cmtt-10"> =</span><span
5284 class="cmtt-10"> read</span><span
5285 class="cmtt-10"> vector</span><span
5286 class="cmtt-10"> from</span><span
5287 class="cmtt-10"> bitstream</span><span
5288 class="cmtt-10"> using</span><span
5289 class="cmtt-10"> codebook</span><span
5290 class="cmtt-10"> number</span><span
5291 class="cmtt-10"> [floor0_book_list]</span><span
5292 class="cmtt-10"> element</span><span
5293 class="cmtt-10"> [booknumber]</span><span
5294 class="cmtt-10"> in</span><span
5295 class="cmtt-10"> VQ</span><span
5296 class="cmtt-10"> context.</span>
5297 <br class="fancyvrb" /><a
5298 id="x1-93016r8"></a><span
5299 class="cmtt-10"> </span><span
5300 class="cmtt-10"> </span><span
5301 class="cmtt-10"> </span><span
5302 class="cmtt-10"> </span><span
5303 class="cmtt-10"> </span><span
5304 class="cmtt-10"> </span><span
5305 class="cmtt-10"> </span><span
5306 class="cmtt-10"> </span><span
5307 class="cmtt-10"> 8)</span><span
5308 class="cmtt-10"> add</span><span
5309 class="cmtt-10"> the</span><span
5310 class="cmtt-10"> scalar</span><span
5311 class="cmtt-10"> value</span><span
5312 class="cmtt-10"> [last]</span><span
5313 class="cmtt-10"> to</span><span
5314 class="cmtt-10"> each</span><span
5315 class="cmtt-10"> scalar</span><span
5316 class="cmtt-10"> in</span><span
5317 class="cmtt-10"> vector</span><span
5318 class="cmtt-10"> [temp_vector]</span>
5319 <br class="fancyvrb" /><a
5320 id="x1-93018r9"></a><span
5321 class="cmtt-10"> </span><span
5322 class="cmtt-10"> </span><span
5323 class="cmtt-10"> </span><span
5324 class="cmtt-10"> </span><span
5325 class="cmtt-10"> </span><span
5326 class="cmtt-10"> </span><span
5327 class="cmtt-10"> </span><span
5328 class="cmtt-10"> </span><span
5329 class="cmtt-10"> 9)</span><span
5330 class="cmtt-10"> [last]</span><span
5331 class="cmtt-10"> =</span><span
5332 class="cmtt-10"> the</span><span
5333 class="cmtt-10"> value</span><span
5334 class="cmtt-10"> of</span><span
5335 class="cmtt-10"> the</span><span
5336 class="cmtt-10"> last</span><span
5337 class="cmtt-10"> scalar</span><span
5338 class="cmtt-10"> in</span><span
5339 class="cmtt-10"> vector</span><span
5340 class="cmtt-10"> [temp_vector]</span>
5341 <br class="fancyvrb" /><a
5342 id="x1-93020r10"></a><span
5343 class="cmtt-10"> </span><span
5344 class="cmtt-10"> </span><span
5345 class="cmtt-10"> </span><span
5346 class="cmtt-10"> </span><span
5347 class="cmtt-10"> </span><span
5348 class="cmtt-10"> </span><span
5349 class="cmtt-10"> </span><span
5350 class="cmtt-10"> 10)</span><span
5351 class="cmtt-10"> concatenate</span><span
5352 class="cmtt-10"> [temp_vector]</span><span
5353 class="cmtt-10"> onto</span><span
5354 class="cmtt-10"> the</span><span
5355 class="cmtt-10"> end</span><span
5356 class="cmtt-10"> of</span><span
5357 class="cmtt-10"> the</span><span
5358 class="cmtt-10"> [coefficients]</span><span
5359 class="cmtt-10"> vector</span>
5360 <br class="fancyvrb" /><a
5361 id="x1-93022r11"></a><span
5362 class="cmtt-10"> </span><span
5363 class="cmtt-10"> </span><span
5364 class="cmtt-10"> </span><span
5365 class="cmtt-10"> </span><span
5366 class="cmtt-10"> </span><span
5367 class="cmtt-10"> </span><span
5368 class="cmtt-10"> </span><span
5369 class="cmtt-10"> 11)</span><span
5370 class="cmtt-10"> if</span><span
5371 class="cmtt-10"> (length</span><span
5372 class="cmtt-10"> of</span><span
5373 class="cmtt-10"> vector</span><span
5374 class="cmtt-10"> [coefficients]</span><span
5375 class="cmtt-10"> is</span><span
5376 class="cmtt-10"> less</span><span
5377 class="cmtt-10"> than</span><span
5378 class="cmtt-10"> [floor0_order],</span><span
5379 class="cmtt-10"> continue</span><span
5380 class="cmtt-10"> at</span><span
5381 class="cmtt-10"> step</span><span
5382 class="cmtt-10"> 6</span>
5383 <br class="fancyvrb" /><a
5384 id="x1-93024r12"></a><span
5385 class="cmtt-10"> </span><span
5386 class="cmtt-10"> </span>
5387 <br class="fancyvrb" /><a
5388 id="x1-93026r13"></a><span
5389 class="cmtt-10"> </span><span
5390 class="cmtt-10"> </span><span
5391 class="cmtt-10"> </span><span
5392 class="cmtt-10"> </span><span
5393 class="cmtt-10"> </span><span
5394 class="cmtt-10"> </span><span
5395 class="cmtt-10"> </span><span
5396 class="cmsy-10">}</span>
5397 <br class="fancyvrb" /><a
5398 id="x1-93028r14"></a><span
5399 class="cmtt-10"> </span><span
5400 class="cmtt-10"> </span>
5401 <br class="fancyvrb" /><a
5402 id="x1-93030r15"></a><span
5403 class="cmtt-10"> </span><span
5404 class="cmtt-10"> </span><span
5405 class="cmtt-10"> 12)</span><span
5406 class="cmtt-10"> done.</span>
5407 <br class="fancyvrb" /><a
5408 id="x1-93032r16"></a><span
5409 class="cmtt-10"> </span><span
5410 class="cmtt-10"> </span>
5412 <!--l. 76--><p class="noindent" >Take note of the following properties of decode:
5413 <ul class="itemize1">
5414 <li class="itemize">An <span
5415 class="cmtt-10x-x-109">[amplitude] </span>value of zero must result in a return code that indicates this channel is
5416 unused in this frame (the output of the channel will be all-zeroes in synthesis). Several
5417 later stages of decode don’t occur for an unused channel.
5419 <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
5420 if end-of-packet is reached during any read operation above, floor decode is to return
5421 ’unused’ status as if the <span
5422 class="cmtt-10x-x-109">[amplitude] </span>value had read zero at the beginning of decode.
5424 <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
5425 href="#x1-1170009.2.1">ilog</a>(
5427 class="cmtt-10x-x-109">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
5431 and values greater than the maximum possible book value are reserved.
5433 <li class="itemize">The number of scalars read into the vector <span
5434 class="cmtt-10x-x-109">[coefficients] </span>may be greater
5436 class="cmtt-10x-x-109">[floor0_order]</span>, the number actually required for curve computation. For
5437 example, if the VQ codebook used for the floor currently being decoded has a
5439 class="cmtt-10x-x-109">[codebook_dimensions] </span>value of three and <span
5440 class="cmtt-10x-x-109">[floor0_order] </span>is ten, the only way to fill
5441 all the needed scalars in <span
5442 class="cmtt-10x-x-109">[coefficients] </span>is to to read a total of twelve scalars as four
5443 vectors of three scalars each. This is not an error condition, and care must be taken not
5444 to allow a buffer overflow in decode. The extra values are not used and may be ignored
5445 or discarded.</li></ul>
5446 <!--l. 104--><p class="noindent" >
5447 <h5 class="subsubsectionHead"><span class="titlemark">6.2.3 </span> <a
5448 id="x1-940006.2.3"></a>curve computation</h5>
5449 <!--l. 106--><p class="noindent" >Given an <span
5450 class="cmtt-10x-x-109">[amplitude] </span>integer and <span
5451 class="cmtt-10x-x-109">[coefficients] </span>vector from packet decode as well as the
5452 [floor0˙order], [floor0˙rate], [floor0˙bark˙map˙size], [floor0˙amplitude˙bits] and [floor0˙amplitude˙offset]
5453 values from floor setup, and an output vector size <span
5454 class="cmtt-10x-x-109">[n] </span>specified by the decode process, we compute
5455 a floor output vector.
5456 <!--l. 113--><p class="noindent" >If the value <span
5457 class="cmtt-10x-x-109">[amplitude] </span>is zero, the return value is a length <span
5458 class="cmtt-10x-x-109">[n] </span>vector with all-zero
5459 scalars. Otherwise, begin by assuming the following definitions for the given vector to be
5461 <center class="par-math-display" >
5463 src="Vorbis_I_spec7x.png" alt=" {
5464 min (floor0xbarkxmapxsize - 1,foobar) for i ∈ [0,n - 1]
5465 mapi = - 1 for i = n
5466 " class="par-math-display" ></center>
5467 <!--l. 128--><p class="nopar" >
5468 <!--l. 130--><p class="noindent" >where
5469 <center class="par-math-display" >
5471 src="Vorbis_I_spec8x.png" alt=" ⌊ ( ) ⌋
5472 f oobar = bark floor0xrate-⋅i- ⋅ floor0xbarkxmapxsize-
5473 2n bark(.5 ⋅floor0xrate )
5474 " class="par-math-display" ></center>
5475 <!--l. 137--><p class="nopar" >
5476 <!--l. 139--><p class="noindent" >and
5480 <center class="par-math-display" >
5482 src="Vorbis_I_spec9x.png" alt="bark(x) = 13.1 arctan (.00074x) + 2.24 arctan (.0000000185x2 + .0001x)
5483 " class="par-math-display" ></center>
5484 <!--l. 143--><p class="nopar" >
5485 <!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the result
5486 to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output LSP
5488 class="cmtt-10x-x-109">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
5490 <!--l. 151--><p class="noindent" >
5491 <ol class="enumerate1" >
5493 class="enumerate" id="x1-94002x1"><span
5494 class="cmtt-10x-x-109">[i] </span>= 0
5497 class="enumerate" id="x1-94004x2"><span
5498 class="cmtt-10x-x-109">[</span><span
5499 class="cmmi-10x-x-109">ω</span><span
5500 class="cmtt-10x-x-109">] </span>= <span
5501 class="cmmi-10x-x-109">π </span>* map element <span
5502 class="cmtt-10x-x-109">[i] </span>/ <span
5503 class="cmtt-10x-x-109">[floor0_bark_map_size]</span>
5506 class="enumerate" id="x1-94006x3">if ( <span
5507 class="cmtt-10x-x-109">[floor0_order] </span>is odd )
5508 <ol class="enumerate2" >
5510 class="enumerate" id="x1-94008x1">calculate <span
5511 class="cmtt-10x-x-109">[p] </span>and <span
5512 class="cmtt-10x-x-109">[q] </span>according to: <span id="textcolor1">*** the following is generated from the TeX code
5513 embedded into the DocBook files: ***</span> <div class="eqnarray">
5514 <center class="math-display" >
5516 src="Vorbis_I_spec10x.png" alt=" (orde∏r- 3)∕2
5517 p = (1 - cos2ω) 4(cosc2j+1 - cosω )2
5521 q = 4 4(cosc2j+1 - cosω )
5523 " class="math-display" ></center>
5525 <!--l. 162--><p class="noindent" ><span id="textcolor2">*** the following is what oddlsp.png contains: ***</span> <div class="eqnarray">
5529 <center class="math-display" >
5531 src="Vorbis_I_spec11x.png" alt=" floor0xorder-3
5533 p = (1- cos ω ) 4(cos([coefficients ]2j+1 )- cosω )
5535 1 floor0∏x2order-1
5536 q = -- 4(cos([coefficients ]2j) - cosω)2
5538 " class="math-display" ></center>
5541 <!--l. 169--><p class="noindent" >else <span
5542 class="cmtt-10x-x-109">[floor0_order] </span>is even
5543 <ol class="enumerate2" >
5545 class="enumerate" id="x1-94012x1">calculate <span
5546 class="cmtt-10x-x-109">[p] </span>and <span
5547 class="cmtt-10x-x-109">[q] </span>according to: <span id="textcolor3">*** the following is generated from the TeX code
5548 embedded into the DocBook files: ***</span> <div class="eqnarray">
5549 <center class="math-display" >
5551 src="Vorbis_I_spec12x.png" alt=" (1--cos2ω-)(orde∏r-2)∕2 2
5552 p = 2 4(cosc2j - cosω )
5554 (1+ cos2ω )(orde∏r-2)∕2
5555 q = ----------- 4(cosc2j - cosω )2
5557 " class="math-display" ></center>
5559 <!--l. 178--><p class="noindent" ><span id="textcolor4">*** the following is what oddlsp.png contains: ***</span> <div class="eqnarray">
5563 <center class="math-display" >
5565 src="Vorbis_I_spec13x.png" alt=" floor0xorder-2
5566 (1--cos2ω-) ∏2 2
5567 p = 2 4(cos([coefficients ]2j+1)- cosω )
5569 (1+ cos2ω )floor0x∏o2rder-2
5570 q = ----------- 4(cos([coefficients ]2j)- cosω )2
5572 " class="math-display" ></center>
5577 class="enumerate" id="x1-94016x4">calculate <span
5578 class="cmtt-10x-x-109">[linear_floor_value] </span>according to:
5579 <center class="math-display" >
5581 src="Vorbis_I_spec14x.png" alt=" ( ( ))
5582 exp .11512925 amplitude--⋅floor0xamplitutex√offset-- - floor0xamplitudexoffset
5583 (2floor0xamplitudexbits - 1) p + q
5584 " class="math-display" ></center>
5585 <!--l. 191--><p class="nopar" >
5588 class="enumerate" id="x1-94018x5"><span
5589 class="cmtt-10x-x-109">[iteration_condition] </span>= map element <span
5590 class="cmtt-10x-x-109">[i]</span>
5593 class="enumerate" id="x1-94020x6"><span
5594 class="cmtt-10x-x-109">[output] </span>element <span
5595 class="cmtt-10x-x-109">[i] </span>= <span
5596 class="cmtt-10x-x-109">[linear_floor_value]</span>
5599 class="enumerate" id="x1-94022x7">increment <span
5600 class="cmtt-10x-x-109">[i]</span>
5603 class="enumerate" id="x1-94024x8">if ( map element <span
5604 class="cmtt-10x-x-109">[i] </span>is equal to <span
5605 class="cmtt-10x-x-109">[iteration_condition] </span>) continue at step 5
5608 class="enumerate" id="x1-94026x9">if ( <span
5609 class="cmtt-10x-x-109">[i] </span>is less than <span
5610 class="cmtt-10x-x-109">[n] </span>) continue at step 2
5613 class="enumerate" id="x1-94028x10">done</li></ol>
5620 <h3 class="sectionHead"><span class="titlemark">7 </span> <a
5621 id="x1-950007"></a>Floor type 1 setup and decode</h3>
5622 <!--l. 6--><p class="noindent" >
5623 <h4 class="subsectionHead"><span class="titlemark">7.1 </span> <a
5624 id="x1-960007.1"></a>Overview</h4>
5625 <!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
5626 curve. The representation plots this curve mechanically on a linear frequency axis and a
5627 logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
5629 <!--l. 16--><p class="noindent" >
5630 <h4 class="subsectionHead"><span class="titlemark">7.2 </span> <a
5631 id="x1-970007.2"></a>Floor 1 format</h4>
5632 <!--l. 18--><p class="noindent" >
5633 <h5 class="subsubsectionHead"><span class="titlemark">7.2.1 </span> <a
5634 id="x1-980007.2.1"></a>model</h5>
5635 <!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a floor
5636 curve using iterative prediction in a process roughly equivalent to the following simplified
5638 <ul class="itemize1">
5639 <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1 where
5640 in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be computed.
5642 <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
5643 produces a y˙new value at that point computed from the existing line’s y value at x˙new
5644 (as plotted by the line) and a difference value decoded from the bitstream packet.
5646 <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
5647 x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
5648 y˙new represents no change to the amplitude value at x˙new so that later refinement is
5649 additionally bounded at x˙new.
5654 <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
5655 at floor 1 initialization time. Computation is completed at the end of the x value list.
5657 <!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
5658 representing typical configuration:
5659 <!--l. 51--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values in
5660 increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0, 128, 64,
5661 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an example
5662 packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following way,
5663 beginning with the first line:
5666 <!--l. 59--><p class="noindent" >
5668 <!--l. 60--><p class="noindent" ><img
5669 src="floor1-1.png" alt="PIC"
5671 <br /> <table class="caption"
5672 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 7: </td><td
5673 class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980017 -->
5675 <!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32 and
5679 <!--l. 67--><p class="noindent" >
5681 <!--l. 68--><p class="noindent" ><img
5682 src="floor1-2.png" alt="PIC"
5684 <br /> <table class="caption"
5685 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 8: </td><td
5686 class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980028 -->
5688 <!--l. 72--><p class="noindent" >Although the new Y value at X position 96 is unchanged, it is still used later as an endpoint for
5689 further refinement. From here on, the pattern should be clear; we complete the floor computation as
5693 <!--l. 76--><p class="noindent" >
5695 <!--l. 77--><p class="noindent" ><img
5696 src="floor1-3.png" alt="PIC"
5698 <br /> <table class="caption"
5699 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 9: </td><td
5700 class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-980039 -->
5707 <!--l. 81--><p class="noindent" >
5709 <!--l. 82--><p class="noindent" ><img
5710 src="floor1-4.png" alt="PIC"
5712 <br /> <table class="caption"
5713 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 10: </td><td
5714 class="content">graph of example floor</td></tr></table><!--tex4ht:label?: x1-9800410 -->
5716 <!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
5717 decode, as described later. The actual algorithm splits Y value computation and line plotting into
5718 two steps with modifications to the above algorithm to eliminate noise accumulation through integer
5719 roundoff/truncation.
5720 <!--l. 94--><p class="noindent" >
5721 <h5 class="subsubsectionHead"><span class="titlemark">7.2.2 </span> <a
5722 id="x1-990007.2.2"></a>header decode</h5>
5723 <!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order during
5724 packet decode and synthesis). This list is split into partitions, and each partition is assigned to a
5725 partition class. X positions 0 and [n] are implicit and do not belong to an explicit partition or
5727 <!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which the
5728 partition class encodes at once), a ’subclass’ value representing the number of alternate entropy
5729 books the partition class may use in representing Y values, the list of [subclass] books and a master
5730 book used to encode which alternate books were chosen for representation in a given packet. The
5731 master/subclass mechanism is meant to be used as a flexible representation cascade while still using
5732 codebooks only in a scalar context.
5733 <!--l. 112--><p class="noindent" >
5734 <div class="fancyvrb" id="fancyvrb28">
5736 id="x1-99002r1"></a><span
5737 class="cmtt-10"> </span><span
5738 class="cmtt-10"> </span>
5739 <br class="fancyvrb" /><a
5740 id="x1-99004r2"></a><span
5741 class="cmtt-10"> </span><span
5742 class="cmtt-10"> </span><span
5743 class="cmtt-10"> </span><span
5744 class="cmtt-10"> 1)</span><span
5745 class="cmtt-10"> [floor1_partitions]</span><span
5746 class="cmtt-10"> =</span><span
5747 class="cmtt-10"> read</span><span
5748 class="cmtt-10"> 5</span><span
5749 class="cmtt-10"> bits</span><span
5750 class="cmtt-10"> as</span><span
5751 class="cmtt-10"> unsigned</span><span
5752 class="cmtt-10"> integer</span>
5753 <br class="fancyvrb" /><a
5754 id="x1-99006r3"></a><span
5755 class="cmtt-10"> </span><span
5756 class="cmtt-10"> </span><span
5757 class="cmtt-10"> </span><span
5758 class="cmtt-10"> 2)</span><span
5759 class="cmtt-10"> [maximum_class]</span><span
5760 class="cmtt-10"> =</span><span
5761 class="cmtt-10"> -1</span>
5762 <br class="fancyvrb" /><a
5763 id="x1-99008r4"></a><span
5764 class="cmtt-10"> </span><span
5765 class="cmtt-10"> </span><span
5766 class="cmtt-10"> </span><span
5767 class="cmtt-10"> 3)</span><span
5768 class="cmtt-10"> iterate</span><span
5769 class="cmtt-10"> [i]</span><span
5770 class="cmtt-10"> over</span><span
5771 class="cmtt-10"> the</span><span
5772 class="cmtt-10"> range</span><span
5773 class="cmtt-10"> 0</span><span
5774 class="cmtt-10"> ...</span><span
5775 class="cmtt-10"> [floor1_partitions]-1</span><span
5776 class="cmtt-10"> </span><span
5777 class="cmsy-10">{</span>
5778 <br class="fancyvrb" /><a
5779 id="x1-99010r5"></a><span
5780 class="cmtt-10"> </span><span
5781 class="cmtt-10"> </span>
5782 <br class="fancyvrb" /><a
5783 id="x1-99012r6"></a><span
5784 class="cmtt-10"> </span><span
5785 class="cmtt-10"> </span><span
5786 class="cmtt-10"> </span><span
5787 class="cmtt-10"> </span><span
5788 class="cmtt-10"> </span><span
5789 class="cmtt-10"> </span><span
5790 class="cmtt-10"> </span><span
5791 class="cmtt-10"> </span><span
5792 class="cmtt-10"> </span><span
5793 class="cmtt-10"> 4)</span><span
5794 class="cmtt-10"> vector</span><span
5795 class="cmtt-10"> [floor1_partition_class_list]</span><span
5796 class="cmtt-10"> element</span><span
5797 class="cmtt-10"> [i]</span><span
5798 class="cmtt-10"> =</span><span
5799 class="cmtt-10"> read</span><span
5800 class="cmtt-10"> 4</span><span
5801 class="cmtt-10"> bits</span><span
5802 class="cmtt-10"> as</span><span
5803 class="cmtt-10"> unsigned</span><span
5804 class="cmtt-10"> integer</span>
5805 <br class="fancyvrb" /><a
5806 id="x1-99014r7"></a><span
5807 class="cmtt-10"> </span><span
5808 class="cmtt-10"> </span>
5809 <br class="fancyvrb" /><a
5810 id="x1-99016r8"></a><span
5811 class="cmtt-10"> </span><span
5812 class="cmtt-10"> </span><span
5813 class="cmtt-10"> </span><span
5814 class="cmtt-10"> </span><span
5815 class="cmtt-10"> </span><span
5816 class="cmtt-10"> </span><span
5817 class="cmtt-10"> </span><span
5818 class="cmsy-10">}</span>
5819 <br class="fancyvrb" /><a
5820 id="x1-99018r9"></a><span
5821 class="cmtt-10"> </span><span
5822 class="cmtt-10"> </span>
5823 <br class="fancyvrb" /><a
5824 id="x1-99020r10"></a><span
5825 class="cmtt-10"> </span><span
5826 class="cmtt-10"> </span><span
5827 class="cmtt-10"> </span><span
5828 class="cmtt-10"> 5)</span><span
5829 class="cmtt-10"> [maximum_class]</span><span
5830 class="cmtt-10"> =</span><span
5831 class="cmtt-10"> largest</span><span
5832 class="cmtt-10"> integer</span><span
5833 class="cmtt-10"> scalar</span><span
5834 class="cmtt-10"> value</span><span
5835 class="cmtt-10"> in</span><span
5836 class="cmtt-10"> vector</span><span
5837 class="cmtt-10"> [floor1_partition_class_list]</span>
5838 <br class="fancyvrb" /><a
5839 id="x1-99022r11"></a><span
5840 class="cmtt-10"> </span><span
5841 class="cmtt-10"> </span><span
5842 class="cmtt-10"> </span><span
5843 class="cmtt-10"> 6)</span><span
5844 class="cmtt-10"> iterate</span><span
5845 class="cmtt-10"> [i]</span><span
5846 class="cmtt-10"> over</span><span
5847 class="cmtt-10"> the</span><span
5848 class="cmtt-10"> range</span><span
5849 class="cmtt-10"> 0</span><span
5850 class="cmtt-10"> ...</span><span
5851 class="cmtt-10"> [maximum_class]</span><span
5852 class="cmtt-10"> </span><span
5853 class="cmsy-10">{</span>
5854 <br class="fancyvrb" /><a
5855 id="x1-99024r12"></a><span
5856 class="cmtt-10"> </span><span
5857 class="cmtt-10"> </span>
5858 <br class="fancyvrb" /><a
5859 id="x1-99026r13"></a><span
5860 class="cmtt-10"> </span><span
5861 class="cmtt-10"> </span><span
5862 class="cmtt-10"> </span><span
5863 class="cmtt-10"> </span><span
5864 class="cmtt-10"> </span><span
5865 class="cmtt-10"> </span><span
5866 class="cmtt-10"> </span><span
5867 class="cmtt-10"> </span><span
5868 class="cmtt-10"> </span><span
5869 class="cmtt-10"> 7)</span><span
5870 class="cmtt-10"> vector</span><span
5871 class="cmtt-10"> [floor1_class_dimensions]</span><span
5872 class="cmtt-10"> element</span><span
5873 class="cmtt-10"> [i]</span><span
5874 class="cmtt-10"> =</span><span
5875 class="cmtt-10"> read</span><span
5876 class="cmtt-10"> 3</span><span
5877 class="cmtt-10"> bits</span><span
5878 class="cmtt-10"> as</span><span
5879 class="cmtt-10"> unsigned</span><span
5880 class="cmtt-10"> integer</span><span
5881 class="cmtt-10"> and</span><span
5882 class="cmtt-10"> add</span><span
5883 class="cmtt-10"> 1</span>
5884 <br class="fancyvrb" /><a
5885 id="x1-99028r14"></a><span
5886 class="cmtt-10"> </span><span
5887 class="cmtt-10">  8)</span><span
5888 class="cmtt-10"> vector</span><span
5889 class="cmtt-10"> [floor1_class_subclasses]</span><span
5890 class="cmtt-10"> element</span><span
5891 class="cmtt-10"> [i]</span><span
5892 class="cmtt-10"> =</span><span
5893 class="cmtt-10"> read</span><span
5894 class="cmtt-10"> 2</span><span
5895 class="cmtt-10"> bits</span><span
5896 class="cmtt-10"> as</span><span
5897 class="cmtt-10"> unsigned</span><span
5898 class="cmtt-10"> integer</span>
5902 <br class="fancyvrb" /><a
5903 id="x1-99030r15"></a><span
5904 class="cmtt-10"> </span><span
5905 class="cmtt-10"> </span><span
5906 class="cmtt-10"> </span><span
5907 class="cmtt-10"> </span><span
5908 class="cmtt-10"> </span><span
5909 class="cmtt-10"> </span><span
5910 class="cmtt-10"> </span><span
5911 class="cmtt-10"> </span><span
5912 class="cmtt-10"> </span><span
5913 class="cmtt-10"> 9)</span><span
5914 class="cmtt-10"> if</span><span
5915 class="cmtt-10"> (</span><span
5916 class="cmtt-10"> vector</span><span
5917 class="cmtt-10"> [floor1_class_subclasses]</span><span
5918 class="cmtt-10"> element</span><span
5919 class="cmtt-10"> [i]</span><span
5920 class="cmtt-10"> is</span><span
5921 class="cmtt-10"> nonzero</span><span
5922 class="cmtt-10"> )</span><span
5923 class="cmtt-10"> </span><span
5924 class="cmsy-10">{</span>
5925 <br class="fancyvrb" /><a
5926 id="x1-99032r16"></a><span
5927 class="cmtt-10"> </span><span
5928 class="cmtt-10"> </span>
5929 <br class="fancyvrb" /><a
5930 id="x1-99034r17"></a><span
5931 class="cmtt-10"> </span><span
5932 class="cmtt-10"> </span><span
5933 class="cmtt-10"> </span><span
5934 class="cmtt-10"> </span><span
5935 class="cmtt-10"> </span><span
5936 class="cmtt-10"> </span><span
5937 class="cmtt-10"> </span><span
5938 class="cmtt-10"> </span><span
5939 class="cmtt-10"> </span><span
5940 class="cmtt-10"> </span><span
5941 class="cmtt-10"> </span><span
5942 class="cmtt-10"> </span><span
5943 class="cmtt-10"> </span><span
5944 class="cmtt-10"> </span><span
5945 class="cmtt-10"> 10)</span><span
5946 class="cmtt-10"> vector</span><span
5947 class="cmtt-10"> [floor1_class_masterbooks]</span><span
5948 class="cmtt-10"> element</span><span
5949 class="cmtt-10"> [i]</span><span
5950 class="cmtt-10"> =</span><span
5951 class="cmtt-10"> read</span><span
5952 class="cmtt-10"> 8</span><span
5953 class="cmtt-10"> bits</span><span
5954 class="cmtt-10"> as</span><span
5955 class="cmtt-10"> unsigned</span><span
5956 class="cmtt-10"> integer</span>
5957 <br class="fancyvrb" /><a
5958 id="x1-99036r18"></a><span
5959 class="cmtt-10"> </span><span
5960 class="cmtt-10"> </span>
5961 <br class="fancyvrb" /><a
5962 id="x1-99038r19"></a><span
5963 class="cmtt-10"> </span><span
5964 class="cmtt-10"> </span><span
5965 class="cmtt-10"> </span><span
5966 class="cmtt-10"> </span><span
5967 class="cmtt-10"> </span><span
5968 class="cmtt-10"> </span><span
5969 class="cmtt-10"> </span><span
5970 class="cmtt-10"> </span><span
5971 class="cmtt-10"> </span><span
5972 class="cmtt-10"> </span><span
5973 class="cmtt-10"> </span><span
5974 class="cmtt-10"> </span><span
5975 class="cmtt-10"> </span><span
5976 class="cmsy-10">}</span>
5977 <br class="fancyvrb" /><a
5978 id="x1-99040r20"></a><span
5979 class="cmtt-10"> </span><span
5980 class="cmtt-10"> </span>
5981 <br class="fancyvrb" /><a
5982 id="x1-99042r21"></a><span
5983 class="cmtt-10"> </span><span
5984 class="cmtt-10"> </span><span
5985 class="cmtt-10"> </span><span
5986 class="cmtt-10"> </span><span
5987 class="cmtt-10"> </span><span
5988 class="cmtt-10"> </span><span
5989 class="cmtt-10"> </span><span
5990 class="cmtt-10"> </span><span
5991 class="cmtt-10"> 11)</span><span
5992 class="cmtt-10"> iterate</span><span
5993 class="cmtt-10"> [j]</span><span
5994 class="cmtt-10"> over</span><span
5995 class="cmtt-10"> the</span><span
5996 class="cmtt-10"> range</span><span
5997 class="cmtt-10"> 0</span><span
5998 class="cmtt-10"> ...</span><span
5999 class="cmtt-10"> (2</span><span
6000 class="cmtt-10"> exponent</span><span
6001 class="cmtt-10"> [floor1_class_subclasses]</span><span
6002 class="cmtt-10"> element</span><span
6003 class="cmtt-10"> [i])</span><span
6004 class="cmtt-10"> -</span><span
6005 class="cmtt-10"> 1</span><span
6006 class="cmtt-10"> </span><span
6007 class="cmsy-10">{</span>
6008 <br class="fancyvrb" /><a
6009 id="x1-99044r22"></a><span
6010 class="cmtt-10"> </span><span
6011 class="cmtt-10"> </span>
6012 <br class="fancyvrb" /><a
6013 id="x1-99046r23"></a><span
6014 class="cmtt-10"> </span><span
6015 class="cmtt-10"> </span><span
6016 class="cmtt-10"> </span><span
6017 class="cmtt-10"> </span><span
6018 class="cmtt-10"> </span><span
6019 class="cmtt-10"> </span><span
6020 class="cmtt-10"> </span><span
6021 class="cmtt-10"> </span><span
6022 class="cmtt-10"> </span><span
6023 class="cmtt-10"> </span><span
6024 class="cmtt-10"> </span><span
6025 class="cmtt-10"> </span><span
6026 class="cmtt-10"> </span><span
6027 class="cmtt-10"> </span><span
6028 class="cmtt-10"> 12)</span><span
6029 class="cmtt-10"> array</span><span
6030 class="cmtt-10"> [floor1_subclass_books]</span><span
6031 class="cmtt-10"> element</span><span
6032 class="cmtt-10"> [i],[j]</span><span
6033 class="cmtt-10"> =</span>
6034 <br class="fancyvrb" /><a
6035 id="x1-99048r24"></a><span
6036 class="cmtt-10"> </span><span
6037 class="cmtt-10"> </span><span
6038 class="cmtt-10"> </span><span
6039 class="cmtt-10"> </span><span
6040 class="cmtt-10"> </span><span
6041 class="cmtt-10"> </span><span
6042 class="cmtt-10"> </span><span
6043 class="cmtt-10"> </span><span
6044 class="cmtt-10"> </span><span
6045 class="cmtt-10"> </span><span
6046 class="cmtt-10"> </span><span
6047 class="cmtt-10"> </span><span
6048 class="cmtt-10"> </span><span
6049 class="cmtt-10"> </span><span
6050 class="cmtt-10"> </span><span
6051 class="cmtt-10"> </span><span
6052 class="cmtt-10"> </span><span
6053 class="cmtt-10"> </span><span
6054 class="cmtt-10"> read</span><span
6055 class="cmtt-10"> 8</span><span
6056 class="cmtt-10"> bits</span><span
6057 class="cmtt-10"> as</span><span
6058 class="cmtt-10"> unsigned</span><span
6059 class="cmtt-10"> integer</span><span
6060 class="cmtt-10"> and</span><span
6061 class="cmtt-10"> subtract</span><span
6062 class="cmtt-10"> one</span>
6063 <br class="fancyvrb" /><a
6064 id="x1-99050r25"></a><span
6065 class="cmtt-10"> </span><span
6066 class="cmtt-10"> </span><span
6067 class="cmtt-10"> </span><span
6068 class="cmtt-10"> </span><span
6069 class="cmtt-10"> </span><span
6070 class="cmtt-10"> </span><span
6071 class="cmtt-10"> </span><span
6072 class="cmtt-10"> </span><span
6073 class="cmtt-10"> </span><span
6074 class="cmtt-10"> </span><span
6075 class="cmtt-10"> </span><span
6076 class="cmtt-10"> </span><span
6077 class="cmtt-10"> </span><span
6078 class="cmsy-10">}</span>
6079 <br class="fancyvrb" /><a
6080 id="x1-99052r26"></a><span
6081 class="cmtt-10"> </span><span
6082 class="cmtt-10"> </span><span
6083 class="cmtt-10"> </span><span
6084 class="cmtt-10"> </span><span
6085 class="cmtt-10"> </span><span
6086 class="cmtt-10"> </span><span
6087 class="cmtt-10"> </span><span
6088 class="cmtt-10"> </span><span
6089 class="cmsy-10">}</span>
6090 <br class="fancyvrb" /><a
6091 id="x1-99054r27"></a><span
6092 class="cmtt-10"> </span><span
6093 class="cmtt-10"> </span>
6094 <br class="fancyvrb" /><a
6095 id="x1-99056r28"></a><span
6096 class="cmtt-10"> </span><span
6097 class="cmtt-10"> </span><span
6098 class="cmtt-10"> 13)</span><span
6099 class="cmtt-10"> [floor1_multiplier]</span><span
6100 class="cmtt-10"> =</span><span
6101 class="cmtt-10"> read</span><span
6102 class="cmtt-10"> 2</span><span
6103 class="cmtt-10"> bits</span><span
6104 class="cmtt-10"> as</span><span
6105 class="cmtt-10"> unsigned</span><span
6106 class="cmtt-10"> integer</span><span
6107 class="cmtt-10"> and</span><span
6108 class="cmtt-10"> add</span><span
6109 class="cmtt-10"> one</span>
6110 <br class="fancyvrb" /><a
6111 id="x1-99058r29"></a><span
6112 class="cmtt-10"> </span><span
6113 class="cmtt-10"> </span><span
6114 class="cmtt-10"> 14)</span><span
6115 class="cmtt-10"> [rangebits]</span><span
6116 class="cmtt-10"> =</span><span
6117 class="cmtt-10"> read</span><span
6118 class="cmtt-10"> 4</span><span
6119 class="cmtt-10"> bits</span><span
6120 class="cmtt-10"> as</span><span
6121 class="cmtt-10"> unsigned</span><span
6122 class="cmtt-10"> integer</span>
6123 <br class="fancyvrb" /><a
6124 id="x1-99060r30"></a><span
6125 class="cmtt-10"> </span><span
6126 class="cmtt-10"> </span><span
6127 class="cmtt-10"> 15)</span><span
6128 class="cmtt-10"> vector</span><span
6129 class="cmtt-10"> [floor1_X_list]</span><span
6130 class="cmtt-10"> element</span><span
6131 class="cmtt-10"> [0]</span><span
6132 class="cmtt-10"> =</span><span
6133 class="cmtt-10"> 0</span>
6134 <br class="fancyvrb" /><a
6135 id="x1-99062r31"></a><span
6136 class="cmtt-10"> </span><span
6137 class="cmtt-10"> </span><span
6138 class="cmtt-10"> 16)</span><span
6139 class="cmtt-10"> vector</span><span
6140 class="cmtt-10"> [floor1_X_list]</span><span
6141 class="cmtt-10"> element</span><span
6142 class="cmtt-10"> [1]</span><span
6143 class="cmtt-10"> =</span><span
6144 class="cmtt-10"> 2</span><span
6145 class="cmtt-10"> exponent</span><span
6146 class="cmtt-10"> [rangebits];</span>
6147 <br class="fancyvrb" /><a
6148 id="x1-99064r32"></a><span
6149 class="cmtt-10"> </span><span
6150 class="cmtt-10"> </span><span
6151 class="cmtt-10"> 17)</span><span
6152 class="cmtt-10"> [floor1_values]</span><span
6153 class="cmtt-10"> =</span><span
6154 class="cmtt-10"> 2</span>
6155 <br class="fancyvrb" /><a
6156 id="x1-99066r33"></a><span
6157 class="cmtt-10"> </span><span
6158 class="cmtt-10"> </span><span
6159 class="cmtt-10"> 18)</span><span
6160 class="cmtt-10"> iterate</span><span
6161 class="cmtt-10"> [i]</span><span
6162 class="cmtt-10"> over</span><span
6163 class="cmtt-10"> the</span><span
6164 class="cmtt-10"> range</span><span
6165 class="cmtt-10"> 0</span><span
6166 class="cmtt-10"> ...</span><span
6167 class="cmtt-10"> [floor1_partitions]-1</span><span
6168 class="cmtt-10"> </span><span
6169 class="cmsy-10">{</span>
6170 <br class="fancyvrb" /><a
6171 id="x1-99068r34"></a><span
6172 class="cmtt-10"> </span><span
6173 class="cmtt-10"> </span>
6174 <br class="fancyvrb" /><a
6175 id="x1-99070r35"></a><span
6176 class="cmtt-10"> </span><span
6177 class="cmtt-10"> </span><span
6178 class="cmtt-10"> </span><span
6179 class="cmtt-10"> </span><span
6180 class="cmtt-10"> </span><span
6181 class="cmtt-10"> </span><span
6182 class="cmtt-10"> </span><span
6183 class="cmtt-10"> </span><span
6184 class="cmtt-10"> 19)</span><span
6185 class="cmtt-10"> [current_class_number]</span><span
6186 class="cmtt-10"> =</span><span
6187 class="cmtt-10"> vector</span><span
6188 class="cmtt-10"> [floor1_partition_class_list]</span><span
6189 class="cmtt-10"> element</span><span
6190 class="cmtt-10"> [i]</span>
6191 <br class="fancyvrb" /><a
6192 id="x1-99072r36"></a><span
6193 class="cmtt-10"> </span><span
6194 class="cmtt-10"> </span><span
6195 class="cmtt-10"> </span><span
6196 class="cmtt-10"> </span><span
6197 class="cmtt-10"> </span><span
6198 class="cmtt-10"> </span><span
6199 class="cmtt-10"> </span><span
6200 class="cmtt-10"> </span><span
6201 class="cmtt-10"> 20)</span><span
6202 class="cmtt-10"> iterate</span><span
6203 class="cmtt-10"> [j]</span><span
6204 class="cmtt-10"> over</span><span
6205 class="cmtt-10"> the</span><span
6206 class="cmtt-10"> range</span><span
6207 class="cmtt-10"> 0</span><span
6208 class="cmtt-10"> ...</span><span
6209 class="cmtt-10"> ([floor1_class_dimensions]</span><span
6210 class="cmtt-10"> element</span><span
6211 class="cmtt-10"> [current_class_number])-1</span><span
6212 class="cmtt-10"> </span><span
6213 class="cmsy-10">{</span>
6214 <br class="fancyvrb" /><a
6215 id="x1-99074r37"></a><span
6216 class="cmtt-10"> </span><span
6217 class="cmtt-10"> </span><span
6218 class="cmtt-10"> </span><span
6219 class="cmtt-10"> </span><span
6220 class="cmtt-10"> </span><span
6221 class="cmtt-10"> </span><span
6222 class="cmtt-10"> </span><span
6223 class="cmtt-10"> </span><span
6224 class="cmtt-10"> </span><span
6225 class="cmtt-10"> </span><span
6226 class="cmtt-10"> </span><span
6227 class="cmtt-10"> </span><span
6228 class="cmtt-10"> </span><span
6229 class="cmtt-10"> </span><span
6230 class="cmtt-10"> 21)</span><span
6231 class="cmtt-10"> vector</span><span
6232 class="cmtt-10"> [floor1_X_list]</span><span
6233 class="cmtt-10"> element</span><span
6234 class="cmtt-10"> ([floor1_values])</span><span
6235 class="cmtt-10"> =</span>
6236 <br class="fancyvrb" /><a
6237 id="x1-99076r38"></a><span
6238 class="cmtt-10"> </span><span
6239 class="cmtt-10"> </span><span
6240 class="cmtt-10"> </span><span
6241 class="cmtt-10"> </span><span
6242 class="cmtt-10"> </span><span
6243 class="cmtt-10"> </span><span
6244 class="cmtt-10"> </span><span
6245 class="cmtt-10"> </span><span
6246 class="cmtt-10"> </span><span
6247 class="cmtt-10"> </span><span
6248 class="cmtt-10"> </span><span
6249 class="cmtt-10"> </span><span
6250 class="cmtt-10"> </span><span
6251 class="cmtt-10"> </span><span
6252 class="cmtt-10"> </span><span
6253 class="cmtt-10"> </span><span
6254 class="cmtt-10"> </span><span
6255 class="cmtt-10"> </span><span
6256 class="cmtt-10"> read</span><span
6257 class="cmtt-10"> [rangebits]</span><span
6258 class="cmtt-10"> bits</span><span
6259 class="cmtt-10"> as</span><span
6260 class="cmtt-10"> unsigned</span><span
6261 class="cmtt-10"> integer</span>
6262 <br class="fancyvrb" /><a
6263 id="x1-99078r39"></a><span
6264 class="cmtt-10"> </span><span
6265 class="cmtt-10"> </span><span
6266 class="cmtt-10"> </span><span
6267 class="cmtt-10"> </span><span
6268 class="cmtt-10"> </span><span
6269 class="cmtt-10"> </span><span
6270 class="cmtt-10"> </span><span
6271 class="cmtt-10"> </span><span
6272 class="cmtt-10"> </span><span
6273 class="cmtt-10"> </span><span
6274 class="cmtt-10"> </span><span
6275 class="cmtt-10"> </span><span
6276 class="cmtt-10"> </span><span
6277 class="cmtt-10"> </span><span
6278 class="cmtt-10"> 22)</span><span
6279 class="cmtt-10"> increment</span><span
6280 class="cmtt-10"> [floor1_values]</span><span
6281 class="cmtt-10"> by</span><span
6282 class="cmtt-10"> one</span>
6283 <br class="fancyvrb" /><a
6284 id="x1-99080r40"></a><span
6285 class="cmtt-10"> </span><span
6286 class="cmtt-10"> </span><span
6287 class="cmtt-10"> </span><span
6288 class="cmtt-10"> </span><span
6289 class="cmtt-10"> </span><span
6290 class="cmtt-10"> </span><span
6291 class="cmtt-10"> </span><span
6292 class="cmtt-10"> </span><span
6293 class="cmtt-10"> </span><span
6294 class="cmtt-10"> </span><span
6295 class="cmtt-10"> </span><span
6296 class="cmtt-10"> </span><span
6297 class="cmtt-10"> </span><span
6298 class="cmsy-10">}</span>
6299 <br class="fancyvrb" /><a
6300 id="x1-99082r41"></a><span
6301 class="cmtt-10"> </span><span
6302 class="cmtt-10"> </span><span
6303 class="cmtt-10"> </span><span
6304 class="cmtt-10"> </span><span
6305 class="cmtt-10"> </span><span
6306 class="cmtt-10"> </span><span
6307 class="cmtt-10"> </span><span
6308 class="cmsy-10">}</span>
6309 <br class="fancyvrb" /><a
6310 id="x1-99084r42"></a><span
6311 class="cmtt-10"> </span><span
6312 class="cmtt-10"> </span>
6313 <br class="fancyvrb" /><a
6314 id="x1-99086r43"></a><span
6315 class="cmtt-10"> </span><span
6316 class="cmtt-10"> </span><span
6317 class="cmtt-10"> 23)</span><span
6318 class="cmtt-10"> done</span>
6320 <!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during setup renders
6321 a stream undecodable. In addition, a <span
6322 class="cmtt-10x-x-109">[floor1_class_masterbooks] </span>or <span
6323 class="cmtt-10x-x-109">[floor1_subclass_books]</span>
6324 scalar element greater than the highest numbered codebook configured in this stream is an error
6325 condition that renders the stream undecodable.
6326 <!--l. 165--><p class="noindent" ><span class="paragraphHead"><a
6327 id="x1-1000007.2.2"></a><span
6328 class="cmbx-10x-x-109">packet decode</span></span>
6329 Packet decode begins by checking the <span
6330 class="cmtt-10x-x-109">[nonzero] </span>flag:
6331 <!--l. 169--><p class="noindent" >
6332 <div class="fancyvrb" id="fancyvrb29">
6334 id="x1-100002r1"></a><span
6335 class="cmtt-10"> </span><span
6336 class="cmtt-10"> </span><span
6337 class="cmtt-10"> </span><span
6338 class="cmtt-10"> 1)</span><span
6339 class="cmtt-10"> [nonzero]</span><span
6340 class="cmtt-10"> =</span><span
6341 class="cmtt-10"> read</span><span
6342 class="cmtt-10"> 1</span><span
6343 class="cmtt-10"> bit</span><span
6344 class="cmtt-10"> as</span><span
6345 class="cmtt-10"> boolean</span>
6347 <!--l. 173--><p class="noindent" >If <span
6348 class="cmtt-10x-x-109">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame. Decode
6349 immediately returns a status indicating this floor curve (and thus this channel) is unused
6350 this frame. (A return status of ’unused’ is different from decoding a floor that has all
6354 points set to minimum representation amplitude, which happens to be approximately
6356 <!--l. 181--><p class="noindent" >Assuming <span
6357 class="cmtt-10x-x-109">[nonzero] </span>is set, decode proceeds as follows:
6358 <!--l. 183--><p class="noindent" >
6359 <div class="fancyvrb" id="fancyvrb30">
6361 id="x1-100004r1"></a><span
6362 class="cmtt-10"> </span><span
6363 class="cmtt-10"> </span><span
6364 class="cmtt-10"> </span><span
6365 class="cmtt-10"> 1)</span><span
6366 class="cmtt-10"> [range]</span><span
6367 class="cmtt-10"> =</span><span
6368 class="cmtt-10"> vector</span><span
6369 class="cmtt-10"> </span><span
6370 class="cmsy-10">{</span><span
6371 class="cmtt-10"> 256,</span><span
6372 class="cmtt-10"> 128,</span><span
6373 class="cmtt-10"> 86,</span><span
6374 class="cmtt-10"> 64</span><span
6375 class="cmtt-10"> </span><span
6376 class="cmsy-10">}</span><span
6377 class="cmtt-10"> element</span><span
6378 class="cmtt-10"> ([floor1_multiplier]-1)</span>
6379 <br class="fancyvrb" /><a
6380 id="x1-100006r2"></a><span
6381 class="cmtt-10"> </span><span
6382 class="cmtt-10"> </span><span
6383 class="cmtt-10"> </span><span
6384 class="cmtt-10"> 2)</span><span
6385 class="cmtt-10"> vector</span><span
6386 class="cmtt-10"> [floor1_Y]</span><span
6387 class="cmtt-10"> element</span><span
6388 class="cmtt-10"> [0]</span><span
6389 class="cmtt-10"> =</span><span
6390 class="cmtt-10"> read</span><span
6391 class="cmtt-10"> </span><a
6392 href="#x1-1170009.2.1"><span
6393 class="cmtt-10">ilog</span></a><span
6394 class="cmtt-10">([range]-1)</span><span
6395 class="cmtt-10"> bits</span><span
6396 class="cmtt-10"> as</span><span
6397 class="cmtt-10"> unsigned</span><span
6398 class="cmtt-10"> integer</span>
6399 <br class="fancyvrb" /><a
6400 id="x1-100008r3"></a><span
6401 class="cmtt-10"> </span><span
6402 class="cmtt-10"> </span><span
6403 class="cmtt-10"> </span><span
6404 class="cmtt-10"> 3)</span><span
6405 class="cmtt-10"> vector</span><span
6406 class="cmtt-10"> [floor1_Y]</span><span
6407 class="cmtt-10"> element</span><span
6408 class="cmtt-10"> [1]</span><span
6409 class="cmtt-10"> =</span><span
6410 class="cmtt-10"> read</span><span
6411 class="cmtt-10"> </span><a
6412 href="#x1-1170009.2.1"><span
6413 class="cmtt-10">ilog</span></a><span
6414 class="cmtt-10">([range]-1)</span><span
6415 class="cmtt-10"> bits</span><span
6416 class="cmtt-10"> as</span><span
6417 class="cmtt-10"> unsigned</span><span
6418 class="cmtt-10"> integer</span>
6419 <br class="fancyvrb" /><a
6420 id="x1-100010r4"></a><span
6421 class="cmtt-10"> </span><span
6422 class="cmtt-10"> </span><span
6423 class="cmtt-10"> </span><span
6424 class="cmtt-10"> 4)</span><span
6425 class="cmtt-10"> [offset]</span><span
6426 class="cmtt-10"> =</span><span
6427 class="cmtt-10"> 2;</span>
6428 <br class="fancyvrb" /><a
6429 id="x1-100012r5"></a><span
6430 class="cmtt-10"> </span><span
6431 class="cmtt-10"> </span><span
6432 class="cmtt-10"> </span><span
6433 class="cmtt-10"> 5)</span><span
6434 class="cmtt-10"> iterate</span><span
6435 class="cmtt-10"> [i]</span><span
6436 class="cmtt-10"> over</span><span
6437 class="cmtt-10"> the</span><span
6438 class="cmtt-10"> range</span><span
6439 class="cmtt-10"> 0</span><span
6440 class="cmtt-10"> ...</span><span
6441 class="cmtt-10"> [floor1_partitions]-1</span><span
6442 class="cmtt-10"> </span><span
6443 class="cmsy-10">{</span>
6444 <br class="fancyvrb" /><a
6445 id="x1-100014r6"></a><span
6446 class="cmtt-10"> </span><span
6447 class="cmtt-10"> </span>
6448 <br class="fancyvrb" /><a
6449 id="x1-100016r7"></a><span
6450 class="cmtt-10"> </span><span
6451 class="cmtt-10"> </span><span
6452 class="cmtt-10"> </span><span
6453 class="cmtt-10"> </span><span
6454 class="cmtt-10"> </span><span
6455 class="cmtt-10"> </span><span
6456 class="cmtt-10"> </span><span
6457 class="cmtt-10"> </span><span
6458 class="cmtt-10"> 6)</span><span
6459 class="cmtt-10"> [class]</span><span
6460 class="cmtt-10"> =</span><span
6461 class="cmtt-10"> vector</span><span
6462 class="cmtt-10"> [floor1_partition_class]</span><span
6463 class="cmtt-10"> </span><span
6464 class="cmtt-10"> element</span><span
6465 class="cmtt-10"> [i]</span>
6466 <br class="fancyvrb" /><a
6467 id="x1-100018r8"></a><span
6468 class="cmtt-10"> </span><span
6469 class="cmtt-10"> </span><span
6470 class="cmtt-10"> </span><span
6471 class="cmtt-10"> </span><span
6472 class="cmtt-10"> </span><span
6473 class="cmtt-10"> </span><span
6474 class="cmtt-10"> </span><span
6475 class="cmtt-10"> </span><span
6476 class="cmtt-10"> 7)</span><span
6477 class="cmtt-10"> [cdim]</span><span
6478 class="cmtt-10"> </span><span
6479 class="cmtt-10"> =</span><span
6480 class="cmtt-10"> vector</span><span
6481 class="cmtt-10"> [floor1_class_dimensions]</span><span
6482 class="cmtt-10"> element</span><span
6483 class="cmtt-10"> [class]</span>
6484 <br class="fancyvrb" /><a
6485 id="x1-100020r9"></a><span
6486 class="cmtt-10"> </span><span
6487 class="cmtt-10"> </span><span
6488 class="cmtt-10"> </span><span
6489 class="cmtt-10"> </span><span
6490 class="cmtt-10"> </span><span
6491 class="cmtt-10"> </span><span
6492 class="cmtt-10"> </span><span
6493 class="cmtt-10"> </span><span
6494 class="cmtt-10"> 8)</span><span
6495 class="cmtt-10"> [cbits]</span><span
6496 class="cmtt-10"> =</span><span
6497 class="cmtt-10"> vector</span><span
6498 class="cmtt-10"> [floor1_class_subclasses]</span><span
6499 class="cmtt-10"> element</span><span
6500 class="cmtt-10"> [class]</span>
6501 <br class="fancyvrb" /><a
6502 id="x1-100022r10"></a><span
6503 class="cmtt-10"> </span><span
6504 class="cmtt-10"> </span><span
6505 class="cmtt-10"> </span><span
6506 class="cmtt-10"> </span><span
6507 class="cmtt-10"> </span><span
6508 class="cmtt-10"> </span><span
6509 class="cmtt-10"> </span><span
6510 class="cmtt-10"> </span><span
6511 class="cmtt-10"> 9)</span><span
6512 class="cmtt-10"> [csub]</span><span
6513 class="cmtt-10"> </span><span
6514 class="cmtt-10"> =</span><span
6515 class="cmtt-10"> (2</span><span
6516 class="cmtt-10"> exponent</span><span
6517 class="cmtt-10"> [cbits])-1</span>
6518 <br class="fancyvrb" /><a
6519 id="x1-100024r11"></a><span
6520 class="cmtt-10"> </span><span
6521 class="cmtt-10"> </span><span
6522 class="cmtt-10"> </span><span
6523 class="cmtt-10"> </span><span
6524 class="cmtt-10"> </span><span
6525 class="cmtt-10"> </span><span
6526 class="cmtt-10"> </span><span
6527 class="cmtt-10"> 10)</span><span
6528 class="cmtt-10"> [cval]</span><span
6529 class="cmtt-10"> </span><span
6530 class="cmtt-10"> =</span><span
6531 class="cmtt-10"> 0</span>
6532 <br class="fancyvrb" /><a
6533 id="x1-100026r12"></a><span
6534 class="cmtt-10"> </span><span
6535 class="cmtt-10"> </span><span
6536 class="cmtt-10"> </span><span
6537 class="cmtt-10"> </span><span
6538 class="cmtt-10"> </span><span
6539 class="cmtt-10"> </span><span
6540 class="cmtt-10"> </span><span
6541 class="cmtt-10"> 11)</span><span
6542 class="cmtt-10"> if</span><span
6543 class="cmtt-10"> (</span><span
6544 class="cmtt-10"> [cbits]</span><span
6545 class="cmtt-10"> is</span><span
6546 class="cmtt-10"> greater</span><span
6547 class="cmtt-10"> than</span><span
6548 class="cmtt-10"> zero</span><span
6549 class="cmtt-10"> )</span><span
6550 class="cmtt-10"> </span><span
6551 class="cmsy-10">{</span>
6552 <br class="fancyvrb" /><a
6553 id="x1-100028r13"></a><span
6554 class="cmtt-10"> </span><span
6555 class="cmtt-10"> </span>
6556 <br class="fancyvrb" /><a
6557 id="x1-100030r14"></a><span
6558 class="cmtt-10"> </span><span
6559 class="cmtt-10"> </span><span
6560 class="cmtt-10"> </span><span
6561 class="cmtt-10"> </span><span
6562 class="cmtt-10"> </span><span
6563 class="cmtt-10"> </span><span
6564 class="cmtt-10"> </span><span
6565 class="cmtt-10"> </span><span
6566 class="cmtt-10"> </span><span
6567 class="cmtt-10"> </span><span
6568 class="cmtt-10"> </span><span
6569 class="cmtt-10"> </span><span
6570 class="cmtt-10"> </span><span
6571 class="cmtt-10"> </span><span
6572 class="cmtt-10"> 12)</span><span
6573 class="cmtt-10"> [cval]</span><span
6574 class="cmtt-10"> =</span><span
6575 class="cmtt-10"> read</span><span
6576 class="cmtt-10"> from</span><span
6577 class="cmtt-10"> packet</span><span
6578 class="cmtt-10"> using</span><span
6579 class="cmtt-10"> codebook</span><span
6580 class="cmtt-10"> number</span>
6581 <br class="fancyvrb" /><a
6582 id="x1-100032r15"></a><span
6583 class="cmtt-10"> </span><span
6584 class="cmtt-10"> </span><span
6585 class="cmtt-10"> </span><span
6586 class="cmtt-10"> </span><span
6587 class="cmtt-10"> </span><span
6588 class="cmtt-10"> </span><span
6589 class="cmtt-10"> </span><span
6590 class="cmtt-10"> </span><span
6591 class="cmtt-10"> </span><span
6592 class="cmtt-10"> </span><span
6593 class="cmtt-10"> </span><span
6594 class="cmtt-10"> </span><span
6595 class="cmtt-10"> </span><span
6596 class="cmtt-10"> </span><span
6597 class="cmtt-10"> </span><span
6598 class="cmtt-10"> </span><span
6599 class="cmtt-10"> </span><span
6600 class="cmtt-10"> </span><span
6601 class="cmtt-10"> (vector</span><span
6602 class="cmtt-10"> [floor1_class_masterbooks]</span><span
6603 class="cmtt-10"> element</span><span
6604 class="cmtt-10"> [class])</span><span
6605 class="cmtt-10"> in</span><span
6606 class="cmtt-10"> scalar</span><span
6607 class="cmtt-10"> context</span>
6608 <br class="fancyvrb" /><a
6609 id="x1-100034r16"></a><span
6610 class="cmtt-10"> </span><span
6611 class="cmtt-10"> </span><span
6612 class="cmtt-10"> </span><span
6613 class="cmtt-10"> </span><span
6614 class="cmtt-10"> </span><span
6615 class="cmtt-10"> </span><span
6616 class="cmtt-10"> </span><span
6617 class="cmtt-10"> </span><span
6618 class="cmtt-10"> </span><span
6619 class="cmtt-10"> </span><span
6620 class="cmtt-10"> </span><span
6621 class="cmtt-10"> </span><span
6622 class="cmsy-10">}</span>
6623 <br class="fancyvrb" /><a
6624 id="x1-100036r17"></a><span
6625 class="cmtt-10"> </span><span
6626 class="cmtt-10"> </span>
6627 <br class="fancyvrb" /><a
6628 id="x1-100038r18"></a><span
6629 class="cmtt-10"> </span><span
6630 class="cmtt-10"> </span><span
6631 class="cmtt-10"> </span><span
6632 class="cmtt-10"> </span><span
6633 class="cmtt-10"> </span><span
6634 class="cmtt-10"> </span><span
6635 class="cmtt-10"> </span><span
6636 class="cmtt-10"> 13)</span><span
6637 class="cmtt-10"> iterate</span><span
6638 class="cmtt-10"> [j]</span><span
6639 class="cmtt-10"> over</span><span
6640 class="cmtt-10"> the</span><span
6641 class="cmtt-10"> range</span><span
6642 class="cmtt-10"> 0</span><span
6643 class="cmtt-10"> ...</span><span
6644 class="cmtt-10"> [cdim]-1</span><span
6645 class="cmtt-10"> </span><span
6646 class="cmsy-10">{</span>
6647 <br class="fancyvrb" /><a
6648 id="x1-100040r19"></a><span
6649 class="cmtt-10"> </span><span
6650 class="cmtt-10"> </span>
6651 <br class="fancyvrb" /><a
6652 id="x1-100042r20"></a><span
6653 class="cmtt-10"> </span><span
6654 class="cmtt-10"> </span><span
6655 class="cmtt-10"> </span><span
6656 class="cmtt-10"> </span><span
6657 class="cmtt-10"> </span><span
6658 class="cmtt-10"> </span><span
6659 class="cmtt-10"> </span><span
6660 class="cmtt-10"> </span><span
6661 class="cmtt-10"> </span><span
6662 class="cmtt-10"> </span><span
6663 class="cmtt-10"> </span><span
6664 class="cmtt-10"> </span><span
6665 class="cmtt-10"> </span><span
6666 class="cmtt-10"> </span><span
6667 class="cmtt-10"> 14)</span><span
6668 class="cmtt-10"> [book]</span><span
6669 class="cmtt-10"> =</span><span
6670 class="cmtt-10"> array</span><span
6671 class="cmtt-10"> [floor1_subclass_books]</span><span
6672 class="cmtt-10"> element</span><span
6673 class="cmtt-10"> [class],([cval]</span><span
6674 class="cmtt-10"> bitwise</span><span
6675 class="cmtt-10"> AND</span><span
6676 class="cmtt-10"> [csub])</span>
6677 <br class="fancyvrb" /><a
6678 id="x1-100044r21"></a><span
6679 class="cmtt-10"> </span><span
6680 class="cmtt-10"> </span><span
6681 class="cmtt-10"> </span><span
6682 class="cmtt-10"> </span><span
6683 class="cmtt-10"> </span><span
6684 class="cmtt-10"> </span><span
6685 class="cmtt-10"> </span><span
6686 class="cmtt-10"> </span><span
6687 class="cmtt-10"> </span><span
6688 class="cmtt-10"> </span><span
6689 class="cmtt-10"> </span><span
6690 class="cmtt-10"> </span><span
6691 class="cmtt-10"> </span><span
6692 class="cmtt-10"> </span><span
6693 class="cmtt-10"> 15)</span><span
6694 class="cmtt-10"> [cval]</span><span
6695 class="cmtt-10"> =</span><span
6696 class="cmtt-10"> [cval]</span><span
6697 class="cmtt-10"> right</span><span
6698 class="cmtt-10"> shifted</span><span
6699 class="cmtt-10"> [cbits]</span><span
6700 class="cmtt-10"> bits</span>
6701 <br class="fancyvrb" /><a
6702 id="x1-100046r22"></a><span
6703 class="cmtt-10"> </span><span
6704 class="cmtt-10">  </span><span
6705 class="cmtt-10"> </span><span
6706 class="cmtt-10"> </span><span
6707 class="cmtt-10"> </span><span
6708 class="cmtt-10"> </span><span
6709 class="cmtt-10"> 16)</span><span
6710 class="cmtt-10"> if</span><span
6711 class="cmtt-10"> (</span><span
6712 class="cmtt-10"> [book]</span><span
6713 class="cmtt-10"> is</span><span
6714 class="cmtt-10"> not</span><span
6715 class="cmtt-10"> less</span><span
6716 class="cmtt-10"> than</span><span
6717 class="cmtt-10"> zero</span><span
6718 class="cmtt-10"> )</span><span
6719 class="cmtt-10"> </span><span
6720 class="cmsy-10">{</span>
6721 <br class="fancyvrb" /><a
6722 id="x1-100048r23"></a><span
6723 class="cmtt-10"> </span><span
6724 class="cmtt-10"> </span>
6725 <br class="fancyvrb" /><a
6726 id="x1-100050r24"></a><span
6727 class="cmtt-10"> </span><span
6728 class="cmtt-10">  </span><span
6729 class="cmtt-10"> </span><span
6730 class="cmtt-10"> </span><span
6731 class="cmtt-10"> </span><span
6732 class="cmtt-10"> </span><span
6733 class="cmtt-10"> </span><span
6734 class="cmtt-10"> </span><span
6735 class="cmtt-10"> </span><span
6736 class="cmtt-10"> </span><span
6737 class="cmtt-10"> </span><span
6738 class="cmtt-10"> </span><span
6739 class="cmtt-10"> 17)</span><span
6740 class="cmtt-10"> vector</span><span
6741 class="cmtt-10"> [floor1_Y]</span><span
6742 class="cmtt-10"> element</span><span
6743 class="cmtt-10"> ([j]+[offset])</span><span
6744 class="cmtt-10"> =</span><span
6745 class="cmtt-10"> read</span><span
6746 class="cmtt-10"> from</span><span
6747 class="cmtt-10"> packet</span><span
6748 class="cmtt-10"> using</span><span
6749 class="cmtt-10"> codebook</span>
6750 <br class="fancyvrb" /><a
6751 id="x1-100052r25"></a><span
6752 class="cmtt-10"> </span><span
6753 class="cmtt-10"> </span><span
6754 class="cmtt-10"> </span><span
6755 class="cmtt-10"> </span><span
6756 class="cmtt-10"> </span><span
6757 class="cmtt-10"> </span><span
6758 class="cmtt-10"> </span><span
6759 class="cmtt-10"> </span><span
6760 class="cmtt-10"> </span><span
6761 class="cmtt-10"> </span><span
6762 class="cmtt-10"> </span><span
6763 class="cmtt-10"> </span><span
6764 class="cmtt-10"> </span><span
6765 class="cmtt-10"> </span><span
6766 class="cmtt-10"> </span><span
6767 class="cmtt-10"> </span><span
6768 class="cmtt-10"> </span><span
6769 class="cmtt-10"> </span><span
6770 class="cmtt-10"> </span><span
6771 class="cmtt-10"> </span><span
6772 class="cmtt-10"> </span><span
6773 class="cmtt-10"> </span><span
6774 class="cmtt-10"> </span><span
6775 class="cmtt-10"> </span><span
6776 class="cmtt-10"> [book]</span><span
6777 class="cmtt-10"> in</span><span
6778 class="cmtt-10"> scalar</span><span
6779 class="cmtt-10"> context</span>
6780 <br class="fancyvrb" /><a
6781 id="x1-100054r26"></a><span
6782 class="cmtt-10"> </span><span
6783 class="cmtt-10"> </span>
6784 <br class="fancyvrb" /><a
6785 id="x1-100056r27"></a><span
6786 class="cmtt-10"> </span><span
6787 class="cmtt-10"> </span><span
6788 class="cmtt-10"> </span><span
6789 class="cmtt-10"> </span><span
6790 class="cmtt-10"> </span><span
6791 class="cmtt-10"> </span><span
6792 class="cmtt-10"> </span><span
6793 class="cmtt-10"> </span><span
6794 class="cmtt-10"> </span><span
6795 class="cmtt-10"> </span><span
6796 class="cmtt-10"> </span><span
6797 class="cmtt-10"> </span><span
6798 class="cmtt-10"> </span><span
6799 class="cmtt-10"> </span><span
6800 class="cmtt-10"> </span><span
6801 class="cmtt-10"> </span><span
6802 class="cmtt-10"> </span><span
6803 class="cmtt-10"> </span><span
6804 class="cmtt-10"> </span><span
6805 class="cmsy-10">}</span><span
6806 class="cmtt-10"> else</span><span
6807 class="cmtt-10"> [book]</span><span
6808 class="cmtt-10"> is</span><span
6809 class="cmtt-10"> less</span><span
6810 class="cmtt-10"> than</span><span
6811 class="cmtt-10"> zero</span><span
6812 class="cmtt-10"> </span><span
6813 class="cmsy-10">{</span>
6814 <br class="fancyvrb" /><a
6815 id="x1-100058r28"></a><span
6816 class="cmtt-10"> </span><span
6817 class="cmtt-10"> </span>
6818 <br class="fancyvrb" /><a
6819 id="x1-100060r29"></a><span
6820 class="cmtt-10"> </span><span
6821 class="cmtt-10">  </span><span
6822 class="cmtt-10"> </span><span
6823 class="cmtt-10"> </span><span
6824 class="cmtt-10"> </span><span
6825 class="cmtt-10"> </span><span
6826 class="cmtt-10"> </span><span
6827 class="cmtt-10"> </span><span
6828 class="cmtt-10"> </span><span
6829 class="cmtt-10"> </span><span
6830 class="cmtt-10"> </span><span
6831 class="cmtt-10"> </span><span
6832 class="cmtt-10"> 18)</span><span
6833 class="cmtt-10"> vector</span><span
6834 class="cmtt-10"> [floor1_Y]</span><span
6835 class="cmtt-10"> element</span><span
6836 class="cmtt-10"> ([j]+[offset])</span><span
6837 class="cmtt-10"> =</span><span
6838 class="cmtt-10"> 0</span>
6839 <br class="fancyvrb" /><a
6840 id="x1-100062r30"></a><span
6841 class="cmtt-10"> </span><span
6842 class="cmtt-10"> </span>
6843 <br class="fancyvrb" /><a
6844 id="x1-100064r31"></a><span
6845 class="cmtt-10"> </span><span
6846 class="cmtt-10"> </span><span
6847 class="cmtt-10"> </span><span
6848 class="cmtt-10"> </span><span
6849 class="cmtt-10"> </span><span
6850 class="cmtt-10"> </span><span
6851 class="cmtt-10"> </span><span
6852 class="cmtt-10"> </span><span
6853 class="cmtt-10"> </span><span
6854 class="cmtt-10"> </span><span
6855 class="cmtt-10"> </span><span
6856 class="cmtt-10"> </span><span
6857 class="cmtt-10"> </span><span
6858 class="cmtt-10"> </span><span
6859 class="cmtt-10"> </span><span
6860 class="cmtt-10"> </span><span
6861 class="cmtt-10"> </span><span
6862 class="cmtt-10"> </span><span
6863 class="cmtt-10"> </span><span
6864 class="cmsy-10">}</span>
6865 <br class="fancyvrb" /><a
6866 id="x1-100066r32"></a><span
6867 class="cmtt-10"> </span><span
6868 class="cmtt-10"> </span><span
6869 class="cmtt-10"> </span><span
6870 class="cmtt-10"> </span><span
6871 class="cmtt-10"> </span><span
6872 class="cmtt-10"> </span><span
6873 class="cmtt-10"> </span><span
6874 class="cmtt-10"> </span><span
6875 class="cmtt-10"> </span><span
6876 class="cmtt-10"> </span><span
6877 class="cmtt-10"> </span><span
6878 class="cmtt-10"> </span><span
6879 class="cmsy-10">}</span>
6880 <br class="fancyvrb" /><a
6881 id="x1-100068r33"></a><span
6882 class="cmtt-10"> </span><span
6883 class="cmtt-10"> </span>
6884 <br class="fancyvrb" /><a
6885 id="x1-100070r34"></a><span
6886 class="cmtt-10"> </span><span
6887 class="cmtt-10"> </span><span
6888 class="cmtt-10"> </span><span
6889 class="cmtt-10"> </span><span
6890 class="cmtt-10"> </span><span
6891 class="cmtt-10"> </span><span
6892 class="cmtt-10"> </span><span
6893 class="cmtt-10"> 19)</span><span
6894 class="cmtt-10"> [offset]</span><span
6895 class="cmtt-10"> =</span><span
6896 class="cmtt-10"> [offset]</span><span
6897 class="cmtt-10"> +</span><span
6898 class="cmtt-10"> [cdim]</span>
6899 <br class="fancyvrb" /><a
6900 id="x1-100072r35"></a><span
6901 class="cmtt-10"> </span><span
6902 class="cmtt-10"> </span>
6903 <br class="fancyvrb" /><a
6904 id="x1-100074r36"></a><span
6905 class="cmtt-10"> </span><span
6906 class="cmtt-10"> </span><span
6907 class="cmtt-10"> </span><span
6908 class="cmtt-10"> </span><span
6909 class="cmtt-10"> </span><span
6910 class="cmtt-10"> </span><span
6911 class="cmtt-10"> </span><span
6912 class="cmsy-10">}</span>
6913 <br class="fancyvrb" /><a
6914 id="x1-100076r37"></a><span
6915 class="cmtt-10"> </span><span
6916 class="cmtt-10"> </span>
6917 <br class="fancyvrb" /><a
6918 id="x1-100078r38"></a><span
6919 class="cmtt-10"> </span><span
6920 class="cmtt-10"> </span><span
6921 class="cmtt-10"> 20)</span><span
6922 class="cmtt-10"> done</span>
6924 <!--l. 224--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
6925 end-of-packet is reached during any read operation above, floor decode is to return ’unused’ status
6927 class="cmtt-10x-x-109">[nonzero] </span>flag had been unset at the beginning of decode.
6928 <!--l. 230--><p class="noindent" >Vector <span
6929 class="cmtt-10x-x-109">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
6933 <!--l. 235--><p class="noindent" ><span class="paragraphHead"><a
6934 id="x1-1010007.2.2"></a><span
6935 class="cmbx-10x-x-109">curve computation</span></span>
6936 Curve computation is split into two logical steps; the first step derives final Y amplitude values from
6937 the encoded, wrapped difference values taken from the bitstream. The second step plots the curve
6938 lines. Also, although zero-difference values are used in the iterative prediction to find final Y values,
6939 these points are conditionally skipped during final line computation in step two. Skipping
6940 zero-difference values allows a smoother line fit.
6941 <!--l. 245--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations, implementors
6942 are warned to follow the details closely. Deviation from implementing a strictly equivalent algorithm
6943 can result in serious decoding errors.
6944 <!--l. 251--><p class="noindent" >
6945 <dl class="description"><dt class="description">
6947 class="cmssbx-10x-x-109">step 1: amplitude value synthesis</span> </dt><dd
6948 class="description">
6949 <!--l. 253--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
6950 values, then apply to line prediction.
6951 <!--l. 256--><p class="noindent" >
6952 <div class="fancyvrb" id="fancyvrb31">
6954 id="x1-101002r1"></a><span
6955 class="cmtt-10"> </span><span
6956 class="cmtt-10"> </span><span
6957 class="cmtt-10"> </span><span
6958 class="cmtt-10"> 1)</span><span
6959 class="cmtt-10"> [range]</span><span
6960 class="cmtt-10"> =</span><span
6961 class="cmtt-10"> vector</span><span
6962 class="cmtt-10"> </span><span
6963 class="cmsy-10">{</span><span
6964 class="cmtt-10"> 256,</span><span
6965 class="cmtt-10"> 128,</span><span
6966 class="cmtt-10"> 86,</span><span
6967 class="cmtt-10"> 64</span><span
6968 class="cmtt-10"> </span><span
6969 class="cmsy-10">}</span><span
6970 class="cmtt-10"> element</span><span
6971 class="cmtt-10"> ([floor1_multiplier]-1)</span>
6972 <br class="fancyvrb" /><a
6973 id="x1-101004r2"></a><span
6974 class="cmtt-10"> </span><span
6975 class="cmtt-10"> </span><span
6976 class="cmtt-10"> </span><span
6977 class="cmtt-10"> 2)</span><span
6978 class="cmtt-10"> vector</span><span
6979 class="cmtt-10"> [floor1_step2_flag]</span><span
6980 class="cmtt-10"> element</span><span
6981 class="cmtt-10"> [0]</span><span
6982 class="cmtt-10"> =</span><span
6983 class="cmtt-10"> set</span>
6984 <br class="fancyvrb" /><a
6985 id="x1-101006r3"></a><span
6986 class="cmtt-10"> </span><span
6987 class="cmtt-10"> </span><span
6988 class="cmtt-10"> </span><span
6989 class="cmtt-10"> 3)</span><span
6990 class="cmtt-10"> vector</span><span
6991 class="cmtt-10"> [floor1_step2_flag]</span><span
6992 class="cmtt-10"> element</span><span
6993 class="cmtt-10"> [1]</span><span
6994 class="cmtt-10"> =</span><span
6995 class="cmtt-10"> set</span>
6996 <br class="fancyvrb" /><a
6997 id="x1-101008r4"></a><span
6998 class="cmtt-10"> </span><span
6999 class="cmtt-10"> </span><span
7000 class="cmtt-10"> </span><span
7001 class="cmtt-10"> 4)</span><span
7002 class="cmtt-10"> vector</span><span
7003 class="cmtt-10"> [floor1_final_Y]</span><span
7004 class="cmtt-10"> element</span><span
7005 class="cmtt-10"> [0]</span><span
7006 class="cmtt-10"> =</span><span
7007 class="cmtt-10"> vector</span><span
7008 class="cmtt-10"> [floor1_Y]</span><span
7009 class="cmtt-10"> element</span><span
7010 class="cmtt-10"> [0]</span>
7011 <br class="fancyvrb" /><a
7012 id="x1-101010r5"></a><span
7013 class="cmtt-10"> </span><span
7014 class="cmtt-10"> </span><span
7015 class="cmtt-10"> </span><span
7016 class="cmtt-10"> 5)</span><span
7017 class="cmtt-10"> vector</span><span
7018 class="cmtt-10"> [floor1_final_Y]</span><span
7019 class="cmtt-10"> element</span><span
7020 class="cmtt-10"> [1]</span><span
7021 class="cmtt-10"> =</span><span
7022 class="cmtt-10"> vector</span><span
7023 class="cmtt-10"> [floor1_Y]</span><span
7024 class="cmtt-10"> element</span><span
7025 class="cmtt-10"> [1]</span>
7026 <br class="fancyvrb" /><a
7027 id="x1-101012r6"></a><span
7028 class="cmtt-10"> </span><span
7029 class="cmtt-10"> </span><span
7030 class="cmtt-10"> </span><span
7031 class="cmtt-10"> 6)</span><span
7032 class="cmtt-10"> iterate</span><span
7033 class="cmtt-10"> [i]</span><span
7034 class="cmtt-10"> over</span><span
7035 class="cmtt-10"> the</span><span
7036 class="cmtt-10"> range</span><span
7037 class="cmtt-10"> 2</span><span
7038 class="cmtt-10"> ...</span><span
7039 class="cmtt-10"> [floor1_values]-1</span><span
7040 class="cmtt-10"> </span><span
7041 class="cmsy-10">{</span>
7042 <br class="fancyvrb" /><a
7043 id="x1-101014r7"></a><span
7044 class="cmtt-10"> </span><span
7045 class="cmtt-10"> </span>
7046 <br class="fancyvrb" /><a
7047 id="x1-101016r8"></a><span
7048 class="cmtt-10"> </span><span
7049 class="cmtt-10"> </span><span
7050 class="cmtt-10"> </span><span
7051 class="cmtt-10"> </span><span
7052 class="cmtt-10"> </span><span
7053 class="cmtt-10"> </span><span
7054 class="cmtt-10"> </span><span
7055 class="cmtt-10"> </span><span
7056 class="cmtt-10"> 7)</span><span
7057 class="cmtt-10"> [low_neighbor_offset]</span><span
7058 class="cmtt-10"> =</span><span
7059 class="cmtt-10"> </span><a
7060 href="#x1-1200009.2.4"><span
7061 class="cmtt-10">low_neighbor</span></a><span
7062 class="cmtt-10">([floor1_X_list],[i])</span>
7063 <br class="fancyvrb" /><a
7064 id="x1-101018r9"></a><span
7065 class="cmtt-10"> </span><span
7066 class="cmtt-10"> </span><span
7067 class="cmtt-10"> </span><span
7068 class="cmtt-10"> </span><span
7069 class="cmtt-10"> </span><span
7070 class="cmtt-10"> </span><span
7071 class="cmtt-10"> </span><span
7072 class="cmtt-10"> </span><span
7073 class="cmtt-10"> 8)</span><span
7074 class="cmtt-10"> [high_neighbor_offset]</span><span
7075 class="cmtt-10"> =</span><span
7076 class="cmtt-10"> </span><a
7077 href="#x1-1210009.2.5"><span
7078 class="cmtt-10">high_neighbor</span></a><span
7079 class="cmtt-10">([floor1_X_list],[i])</span>
7080 <br class="fancyvrb" /><a
7081 id="x1-101020r10"></a><span
7082 class="cmtt-10"> </span><span
7083 class="cmtt-10"> </span>
7084 <br class="fancyvrb" /><a
7085 id="x1-101022r11"></a><span
7086 class="cmtt-10"> </span><span
7087 class="cmtt-10"> </span><span
7088 class="cmtt-10"> </span><span
7089 class="cmtt-10"> </span><span
7090 class="cmtt-10"> </span><span
7091 class="cmtt-10"> </span><span
7092 class="cmtt-10"> </span><span
7093 class="cmtt-10"> </span><span
7094 class="cmtt-10"> 9)</span><span
7095 class="cmtt-10"> [predicted]</span><span
7096 class="cmtt-10"> =</span><span
7097 class="cmtt-10"> </span><a
7098 href="#x1-1220009.2.6"><span
7099 class="cmtt-10">render_point</span></a><span
7100 class="cmtt-10">(</span><span
7101 class="cmtt-10"> vector</span><span
7102 class="cmtt-10"> [floor1_X_list]</span><span
7103 class="cmtt-10"> element</span><span
7104 class="cmtt-10"> [low_neighbor_offset],</span>
7105 <br class="fancyvrb" /><a
7106 id="x1-101024r12"></a><span
7107 class="cmtt-10"> </span><span
7108 class="cmtt-10">  </span><span
7109 class="cmtt-10"> </span><span
7110 class="cmtt-10"> </span><span
7111 class="cmtt-10"> </span><span
7112 class="cmtt-10"> </span><span
7113 class="cmtt-10"> </span><span
7114 class="cmtt-10"> vector</span><span
7115 class="cmtt-10"> [floor1_final_Y]</span><span
7116 class="cmtt-10"> element</span><span
7117 class="cmtt-10"> [low_neighbor_offset],</span>
7118 <br class="fancyvrb" /><a
7119 id="x1-101026r13"></a><span
7120 class="cmtt-10"> </span><span
7121 class="cmtt-10"> </span><span
7122 class="cmtt-10"> </span><span
7123 class="cmtt-10"> </span><span
7124 class="cmtt-10"> </span><span
7125 class="cmtt-10"> </span><span
7126 class="cmtt-10"> </span><span
7127 class="cmtt-10"> </span><span
7128 class="cmtt-10"> </span><span
7129 class="cmtt-10"> </span><span
7130 class="cmtt-10"> </span><span
7131 class="cmtt-10"> </span><span
7132 class="cmtt-10"> </span><span
7133 class="cmtt-10"> </span><span
7134 class="cmtt-10"> </span><span
7135 class="cmtt-10"> </span><span
7136 class="cmtt-10"> </span><span
7137 class="cmtt-10"> </span><span
7138 class="cmtt-10"> </span><span
7139 class="cmtt-10"> </span><span
7140 class="cmtt-10"> </span><span
7141 class="cmtt-10"> </span><span
7142 class="cmtt-10"> </span><span
7143 class="cmtt-10"> </span><span
7144 class="cmtt-10"> </span><span
7145 class="cmtt-10"> </span><span
7146 class="cmtt-10"> </span><span
7147 class="cmtt-10"> </span><span
7148 class="cmtt-10"> </span><span
7149 class="cmtt-10"> </span><span
7150 class="cmtt-10"> </span><span
7151 class="cmtt-10"> </span><span
7152 class="cmtt-10"> </span><span
7153 class="cmtt-10"> </span><span
7154 class="cmtt-10"> </span><span
7155 class="cmtt-10"> </span><span
7156 class="cmtt-10"> </span><span
7157 class="cmtt-10"> </span><span
7158 class="cmtt-10"> </span><span
7159 class="cmtt-10"> vector</span><span
7160 class="cmtt-10"> [floor1_X_list]</span><span
7161 class="cmtt-10"> element</span><span
7162 class="cmtt-10"> [high_neighbor_offset],</span>
7163 <br class="fancyvrb" /><a
7164 id="x1-101028r14"></a><span
7165 class="cmtt-10"> </span><span
7166 class="cmtt-10">  </span><span
7167 class="cmtt-10"> </span><span
7168 class="cmtt-10"> </span><span
7169 class="cmtt-10"> </span><span
7170 class="cmtt-10"> </span><span
7171 class="cmtt-10"> </span><span
7172 class="cmtt-10"> vector</span><span
7173 class="cmtt-10"> [floor1_final_Y]</span><span
7174 class="cmtt-10"> element</span><span
7175 class="cmtt-10"> [high_neighbor_offset],</span>
7176 <br class="fancyvrb" /><a
7177 id="x1-101030r15"></a><span
7178 class="cmtt-10"> </span><span
7179 class="cmtt-10"> </span><span
7180 class="cmtt-10"> </span><span
7181 class="cmtt-10"> </span><span
7182 class="cmtt-10"> </span><span
7183 class="cmtt-10"> </span><span
7184 class="cmtt-10"> </span><span
7185 class="cmtt-10"> </span><span
7186 class="cmtt-10"> </span><span
7187 class="cmtt-10"> </span><span
7188 class="cmtt-10"> </span><span
7189 class="cmtt-10"> </span><span
7190 class="cmtt-10"> </span><span
7191 class="cmtt-10"> </span><span
7192 class="cmtt-10"> </span><span
7193 class="cmtt-10"> </span><span
7194 class="cmtt-10"> </span><span
7195 class="cmtt-10"> </span><span
7196 class="cmtt-10"> </span><span
7197 class="cmtt-10"> </span><span
7198 class="cmtt-10"> </span><span
7199 class="cmtt-10"> </span><span
7200 class="cmtt-10"> </span><span
7201 class="cmtt-10"> </span><span
7202 class="cmtt-10"> </span><span
7203 class="cmtt-10"> </span><span
7204 class="cmtt-10"> </span><span
7205 class="cmtt-10"> </span><span
7206 class="cmtt-10"> </span><span
7207 class="cmtt-10"> </span><span
7208 class="cmtt-10"> </span><span
7209 class="cmtt-10"> </span><span
7210 class="cmtt-10"> </span><span
7211 class="cmtt-10"> </span><span
7212 class="cmtt-10"> </span><span
7213 class="cmtt-10"> </span><span
7214 class="cmtt-10"> </span><span
7215 class="cmtt-10"> </span><span
7216 class="cmtt-10"> </span><span
7217 class="cmtt-10"> vector</span><span
7218 class="cmtt-10"> [floor1_X_list]</span><span
7219 class="cmtt-10"> element</span><span
7220 class="cmtt-10"> [i]</span><span
7221 class="cmtt-10"> )</span>
7222 <br class="fancyvrb" /><a
7223 id="x1-101032r16"></a><span
7224 class="cmtt-10"> </span><span
7225 class="cmtt-10"> </span>
7226 <br class="fancyvrb" /><a
7227 id="x1-101034r17"></a><span
7228 class="cmtt-10"> </span><span
7229 class="cmtt-10"> </span><span
7230 class="cmtt-10"> </span><span
7231 class="cmtt-10"> </span><span
7232 class="cmtt-10"> </span><span
7233 class="cmtt-10"> </span><span
7234 class="cmtt-10"> </span><span
7235 class="cmtt-10"> 10)</span><span
7236 class="cmtt-10"> [val]</span><span
7237 class="cmtt-10"> =</span><span
7238 class="cmtt-10"> vector</span><span
7239 class="cmtt-10"> [floor1_Y]</span><span
7240 class="cmtt-10"> element</span><span
7241 class="cmtt-10"> [i]</span>
7242 <br class="fancyvrb" /><a
7243 id="x1-101036r18"></a><span
7244 class="cmtt-10"> </span><span
7245 class="cmtt-10"> </span><span
7246 class="cmtt-10"> </span><span
7247 class="cmtt-10"> </span><span
7248 class="cmtt-10"> </span><span
7249 class="cmtt-10"> </span><span
7250 class="cmtt-10"> </span><span
7251 class="cmtt-10"> 11)</span><span
7252 class="cmtt-10"> [highroom]</span><span
7253 class="cmtt-10"> =</span><span
7254 class="cmtt-10"> [range]</span><span
7255 class="cmtt-10"> -</span><span
7256 class="cmtt-10"> [predicted]</span>
7257 <br class="fancyvrb" /><a
7258 id="x1-101038r19"></a><span
7259 class="cmtt-10"> </span><span
7260 class="cmtt-10"> </span><span
7261 class="cmtt-10"> </span><span
7262 class="cmtt-10"> </span><span
7263 class="cmtt-10"> </span><span
7264 class="cmtt-10"> </span><span
7265 class="cmtt-10"> </span><span
7266 class="cmtt-10"> 12)</span><span
7267 class="cmtt-10"> [lowroom]</span><span
7268 class="cmtt-10"> </span><span
7269 class="cmtt-10"> =</span><span
7270 class="cmtt-10"> [predicted]</span>
7271 <br class="fancyvrb" /><a
7272 id="x1-101040r20"></a><span
7273 class="cmtt-10"> </span><span
7274 class="cmtt-10"> </span><span
7275 class="cmtt-10"> </span><span
7276 class="cmtt-10"> </span><span
7277 class="cmtt-10"> </span><span
7278 class="cmtt-10"> </span><span
7279 class="cmtt-10"> </span><span
7280 class="cmtt-10"> 13)</span><span
7281 class="cmtt-10"> if</span><span
7282 class="cmtt-10"> (</span><span
7283 class="cmtt-10"> [highroom]</span><span
7284 class="cmtt-10"> is</span><span
7285 class="cmtt-10"> less</span><span
7286 class="cmtt-10"> than</span><span
7287 class="cmtt-10"> [lowroom]</span><span
7288 class="cmtt-10"> )</span><span
7289 class="cmtt-10"> </span><span
7290 class="cmsy-10">{</span>
7291 <br class="fancyvrb" /><a
7292 id="x1-101042r21"></a><span
7293 class="cmtt-10"> </span><span
7294 class="cmtt-10"> </span>
7295 <br class="fancyvrb" /><a
7296 id="x1-101044r22"></a><span
7297 class="cmtt-10"> </span><span
7298 class="cmtt-10"> </span><span
7299 class="cmtt-10"> </span><span
7300 class="cmtt-10"> </span><span
7301 class="cmtt-10"> </span><span
7302 class="cmtt-10"> </span><span
7303 class="cmtt-10"> </span><span
7304 class="cmtt-10"> </span><span
7305 class="cmtt-10"> </span><span
7306 class="cmtt-10"> </span><span
7307 class="cmtt-10"> </span><span
7308 class="cmtt-10"> </span><span
7309 class="cmtt-10"> </span><span
7310 class="cmtt-10"> 14)</span><span
7311 class="cmtt-10"> [room]</span><span
7312 class="cmtt-10"> =</span><span
7313 class="cmtt-10"> [highroom]</span><span
7314 class="cmtt-10"> *</span><span
7315 class="cmtt-10"> 2</span>
7316 <br class="fancyvrb" /><a
7317 id="x1-101046r23"></a><span
7318 class="cmtt-10"> </span><span
7319 class="cmtt-10"> </span>
7320 <br class="fancyvrb" /><a
7321 id="x1-101048r24"></a><span
7322 class="cmtt-10"> </span><span
7323 class="cmtt-10"> </span><span
7324 class="cmtt-10"> </span><span
7325 class="cmtt-10"> </span><span
7326 class="cmtt-10"> </span><span
7327 class="cmtt-10"> </span><span
7328 class="cmtt-10"> </span><span
7329 class="cmtt-10"> </span><span
7330 class="cmtt-10"> </span><span
7331 class="cmtt-10"> </span><span
7332 class="cmtt-10"> </span><span
7333 class="cmtt-10"> </span><span
7334 class="cmsy-10">}</span><span
7335 class="cmtt-10"> else</span><span
7336 class="cmtt-10"> [highroom]</span><span
7337 class="cmtt-10"> is</span><span
7338 class="cmtt-10"> not</span><span
7339 class="cmtt-10"> less</span><span
7340 class="cmtt-10"> than</span><span
7341 class="cmtt-10"> [lowroom]</span><span
7342 class="cmtt-10"> </span><span
7343 class="cmsy-10">{</span>
7344 <br class="fancyvrb" /><a
7345 id="x1-101050r25"></a><span
7346 class="cmtt-10"> </span><span
7347 class="cmtt-10"> </span>
7348 <br class="fancyvrb" /><a
7349 id="x1-101052r26"></a><span
7350 class="cmtt-10"> </span><span
7351 class="cmtt-10"> </span><span
7352 class="cmtt-10"> </span><span
7353 class="cmtt-10"> </span><span
7354 class="cmtt-10"> </span><span
7355 class="cmtt-10"> </span><span
7356 class="cmtt-10"> </span><span
7357 class="cmtt-10"> </span><span
7358 class="cmtt-10"> </span><span
7359 class="cmtt-10"> </span><span
7360 class="cmtt-10"> </span><span
7361 class="cmtt-10"> </span><span
7362 class="cmtt-10"> </span><span
7363 class="cmtt-10"> 15)</span><span
7364 class="cmtt-10"> [room]</span><span
7365 class="cmtt-10"> =</span><span
7366 class="cmtt-10"> [lowroom]</span><span
7367 class="cmtt-10"> *</span><span
7368 class="cmtt-10"> 2</span>
7369 <br class="fancyvrb" /><a
7370 id="x1-101054r27"></a><span
7371 class="cmtt-10"> </span><span
7372 class="cmtt-10"> </span>
7376 <br class="fancyvrb" /><a
7377 id="x1-101056r28"></a><span
7378 class="cmtt-10"> </span><span
7379 class="cmtt-10"> </span><span
7380 class="cmtt-10"> </span><span
7381 class="cmtt-10"> </span><span
7382 class="cmtt-10"> </span><span
7383 class="cmtt-10"> </span><span
7384 class="cmtt-10"> </span><span
7385 class="cmtt-10"> </span><span
7386 class="cmtt-10"> </span><span
7387 class="cmtt-10"> </span><span
7388 class="cmtt-10"> </span><span
7389 class="cmtt-10"> </span><span
7390 class="cmsy-10">}</span>
7391 <br class="fancyvrb" /><a
7392 id="x1-101058r29"></a><span
7393 class="cmtt-10"> </span><span
7394 class="cmtt-10"> </span>
7395 <br class="fancyvrb" /><a
7396 id="x1-101060r30"></a><span
7397 class="cmtt-10"> </span><span
7398 class="cmtt-10"> </span><span
7399 class="cmtt-10"> </span><span
7400 class="cmtt-10"> </span><span
7401 class="cmtt-10"> </span><span
7402 class="cmtt-10"> </span><span
7403 class="cmtt-10"> </span><span
7404 class="cmtt-10"> 16)</span><span
7405 class="cmtt-10"> if</span><span
7406 class="cmtt-10"> (</span><span
7407 class="cmtt-10"> [val]</span><span
7408 class="cmtt-10"> is</span><span
7409 class="cmtt-10"> nonzero</span><span
7410 class="cmtt-10"> )</span><span
7411 class="cmtt-10"> </span><span
7412 class="cmsy-10">{</span>
7413 <br class="fancyvrb" /><a
7414 id="x1-101062r31"></a><span
7415 class="cmtt-10"> </span><span
7416 class="cmtt-10"> </span>
7417 <br class="fancyvrb" /><a
7418 id="x1-101064r32"></a><span
7419 class="cmtt-10"> </span><span
7420 class="cmtt-10"> </span><span
7421 class="cmtt-10"> </span><span
7422 class="cmtt-10"> </span><span
7423 class="cmtt-10"> </span><span
7424 class="cmtt-10"> </span><span
7425 class="cmtt-10"> </span><span
7426 class="cmtt-10"> </span><span
7427 class="cmtt-10"> </span><span
7428 class="cmtt-10"> </span><span
7429 class="cmtt-10"> </span><span
7430 class="cmtt-10"> </span><span
7431 class="cmtt-10"> </span><span
7432 class="cmtt-10"> 17)</span><span
7433 class="cmtt-10"> vector</span><span
7434 class="cmtt-10"> [floor1_step2_flag]</span><span
7435 class="cmtt-10"> element</span><span
7436 class="cmtt-10"> [low_neighbor_offset]</span><span
7437 class="cmtt-10"> =</span><span
7438 class="cmtt-10"> set</span>
7439 <br class="fancyvrb" /><a
7440 id="x1-101066r33"></a><span
7441 class="cmtt-10"> </span><span
7442 class="cmtt-10"> </span><span
7443 class="cmtt-10"> </span><span
7444 class="cmtt-10"> </span><span
7445 class="cmtt-10"> </span><span
7446 class="cmtt-10"> </span><span
7447 class="cmtt-10"> </span><span
7448 class="cmtt-10"> </span><span
7449 class="cmtt-10"> </span><span
7450 class="cmtt-10"> </span><span
7451 class="cmtt-10"> </span><span
7452 class="cmtt-10"> </span><span
7453 class="cmtt-10"> </span><span
7454 class="cmtt-10"> 18)</span><span
7455 class="cmtt-10"> vector</span><span
7456 class="cmtt-10"> [floor1_step2_flag]</span><span
7457 class="cmtt-10"> element</span><span
7458 class="cmtt-10"> [high_neighbor_offset]</span><span
7459 class="cmtt-10"> =</span><span
7460 class="cmtt-10"> set</span>
7461 <br class="fancyvrb" /><a
7462 id="x1-101068r34"></a><span
7463 class="cmtt-10"> </span><span
7464 class="cmtt-10"> </span><span
7465 class="cmtt-10"> </span><span
7466 class="cmtt-10"> </span><span
7467 class="cmtt-10"> </span><span
7468 class="cmtt-10"> </span><span
7469 class="cmtt-10"> </span><span
7470 class="cmtt-10"> </span><span
7471 class="cmtt-10"> </span><span
7472 class="cmtt-10"> </span><span
7473 class="cmtt-10"> </span><span
7474 class="cmtt-10"> </span><span
7475 class="cmtt-10"> </span><span
7476 class="cmtt-10"> 19)</span><span
7477 class="cmtt-10"> vector</span><span
7478 class="cmtt-10"> [floor1_step2_flag]</span><span
7479 class="cmtt-10"> element</span><span
7480 class="cmtt-10"> [i]</span><span
7481 class="cmtt-10"> =</span><span
7482 class="cmtt-10"> set</span>
7483 <br class="fancyvrb" /><a
7484 id="x1-101070r35"></a><span
7485 class="cmtt-10"> </span><span
7486 class="cmtt-10"> </span><span
7487 class="cmtt-10"> </span><span
7488 class="cmtt-10"> </span><span
7489 class="cmtt-10"> </span><span
7490 class="cmtt-10"> </span><span
7491 class="cmtt-10"> </span><span
7492 class="cmtt-10"> </span><span
7493 class="cmtt-10"> </span><span
7494 class="cmtt-10"> </span><span
7495 class="cmtt-10"> </span><span
7496 class="cmtt-10"> </span><span
7497 class="cmtt-10"> </span><span
7498 class="cmtt-10"> 20)</span><span
7499 class="cmtt-10"> if</span><span
7500 class="cmtt-10"> (</span><span
7501 class="cmtt-10"> [val]</span><span
7502 class="cmtt-10"> is</span><span
7503 class="cmtt-10"> greater</span><span
7504 class="cmtt-10"> than</span><span
7505 class="cmtt-10"> or</span><span
7506 class="cmtt-10"> equal</span><span
7507 class="cmtt-10"> to</span><span
7508 class="cmtt-10"> [room]</span><span
7509 class="cmtt-10"> )</span><span
7510 class="cmtt-10"> </span><span
7511 class="cmsy-10">{</span>
7512 <br class="fancyvrb" /><a
7513 id="x1-101072r36"></a><span
7514 class="cmtt-10"> </span><span
7515 class="cmtt-10"> </span>
7516 <br class="fancyvrb" /><a
7517 id="x1-101074r37"></a><span
7518 class="cmtt-10"> </span><span
7519 class="cmtt-10"> </span><span
7520 class="cmtt-10"> </span><span
7521 class="cmtt-10"> </span><span
7522 class="cmtt-10"> </span><span
7523 class="cmtt-10"> </span><span
7524 class="cmtt-10"> </span><span
7525 class="cmtt-10"> </span><span
7526 class="cmtt-10"> </span><span
7527 class="cmtt-10"> </span><span
7528 class="cmtt-10"> </span><span
7529 class="cmtt-10"> </span><span
7530 class="cmtt-10"> </span><span
7531 class="cmtt-10"> </span><span
7532 class="cmtt-10"> </span><span
7533 class="cmtt-10"> </span><span
7534 class="cmtt-10"> </span><span
7535 class="cmtt-10"> </span><span
7536 class="cmtt-10"> </span><span
7537 class="cmtt-10"> 21)</span><span
7538 class="cmtt-10"> if</span><span
7539 class="cmtt-10"> (</span><span
7540 class="cmtt-10"> [highroom]</span><span
7541 class="cmtt-10"> is</span><span
7542 class="cmtt-10"> greater</span><span
7543 class="cmtt-10"> than</span><span
7544 class="cmtt-10"> [lowroom]</span><span
7545 class="cmtt-10"> )</span><span
7546 class="cmtt-10"> </span><span
7547 class="cmsy-10">{</span>
7548 <br class="fancyvrb" /><a
7549 id="x1-101076r38"></a><span
7550 class="cmtt-10"> </span><span
7551 class="cmtt-10"> </span>
7552 <br class="fancyvrb" /><a
7553 id="x1-101078r39"></a><span
7554 class="cmtt-10"> </span><span
7555 class="cmtt-10"> </span><span
7556 class="cmtt-10"> </span><span
7557 class="cmtt-10"> </span><span
7558 class="cmtt-10"> </span><span
7559 class="cmtt-10"> </span><span
7560 class="cmtt-10"> </span><span
7561 class="cmtt-10"> </span><span
7562 class="cmtt-10"> </span><span
7563 class="cmtt-10"> </span><span
7564 class="cmtt-10"> </span><span
7565 class="cmtt-10"> </span><span
7566 class="cmtt-10"> </span><span
7567 class="cmtt-10"> </span><span
7568 class="cmtt-10"> </span><span
7569 class="cmtt-10"> </span><span
7570 class="cmtt-10"> </span><span
7571 class="cmtt-10"> </span><span
7572 class="cmtt-10"> </span><span
7573 class="cmtt-10"> </span><span
7574 class="cmtt-10"> </span><span
7575 class="cmtt-10"> </span><span
7576 class="cmtt-10"> </span><span
7577 class="cmtt-10"> </span><span
7578 class="cmtt-10"> </span><span
7579 class="cmtt-10"> 22)</span><span
7580 class="cmtt-10"> vector</span><span
7581 class="cmtt-10"> [floor1_final_Y]</span><span
7582 class="cmtt-10"> element</span><span
7583 class="cmtt-10"> [i]</span><span
7584 class="cmtt-10"> =</span><span
7585 class="cmtt-10"> [val]</span><span
7586 class="cmtt-10"> -</span><span
7587 class="cmtt-10"> [lowroom]</span><span
7588 class="cmtt-10"> +</span><span
7589 class="cmtt-10"> [predicted]</span>
7590 <br class="fancyvrb" /><a
7591 id="x1-101080r40"></a><span
7592 class="cmtt-10"> </span><span
7593 class="cmtt-10"> </span>
7594 <br class="fancyvrb" /><a
7595 id="x1-101082r41"></a><span
7596 class="cmtt-10"> </span><span
7597 class="cmtt-10">  </span><span
7598 class="cmtt-10"> </span><span
7599 class="cmtt-10"> </span><span
7600 class="cmtt-10"> </span><span
7601 class="cmtt-10"> </span><span
7602 class="cmtt-10"> </span><span
7603 class="cmtt-10"> </span><span
7604 class="cmsy-10">}</span><span
7605 class="cmtt-10"> else</span><span
7606 class="cmtt-10"> [highroom]</span><span
7607 class="cmtt-10"> is</span><span
7608 class="cmtt-10"> not</span><span
7609 class="cmtt-10"> greater</span><span
7610 class="cmtt-10"> than</span><span
7611 class="cmtt-10"> [lowroom]</span><span
7612 class="cmtt-10"> </span><span
7613 class="cmsy-10">{</span>
7614 <br class="fancyvrb" /><a
7615 id="x1-101084r42"></a><span
7616 class="cmtt-10"> </span><span
7617 class="cmtt-10"> </span>
7618 <br class="fancyvrb" /><a
7619 id="x1-101086r43"></a><span
7620 class="cmtt-10"> </span><span
7621 class="cmtt-10"> </span><span
7622 class="cmtt-10"> </span><span
7623 class="cmtt-10"> </span><span
7624 class="cmtt-10"> </span><span
7625 class="cmtt-10"> </span><span
7626 class="cmtt-10"> </span><span
7627 class="cmtt-10"> </span><span
7628 class="cmtt-10"> </span><span
7629 class="cmtt-10"> </span><span
7630 class="cmtt-10"> </span><span
7631 class="cmtt-10"> </span><span
7632 class="cmtt-10"> </span><span
7633 class="cmtt-10"> </span><span
7634 class="cmtt-10"> </span><span
7635 class="cmtt-10"> </span><span
7636 class="cmtt-10"> </span><span
7637 class="cmtt-10"> </span><span
7638 class="cmtt-10"> </span><span
7639 class="cmtt-10"> </span><span
7640 class="cmtt-10"> </span><span
7641 class="cmtt-10"> </span><span
7642 class="cmtt-10"> </span><span
7643 class="cmtt-10"> </span><span
7644 class="cmtt-10"> </span><span
7645 class="cmtt-10"> 23)</span><span
7646 class="cmtt-10"> vector</span><span
7647 class="cmtt-10"> [floor1_final_Y]</span><span
7648 class="cmtt-10"> element</span><span
7649 class="cmtt-10"> [i]</span><span
7650 class="cmtt-10"> =</span><span
7651 class="cmtt-10"> [predicted]</span><span
7652 class="cmtt-10"> -</span><span
7653 class="cmtt-10"> [val]</span><span
7654 class="cmtt-10"> +</span><span
7655 class="cmtt-10"> [highroom]</span><span
7656 class="cmtt-10"> -</span><span
7657 class="cmtt-10"> 1</span>
7658 <br class="fancyvrb" /><a
7659 id="x1-101088r44"></a><span
7660 class="cmtt-10"> </span><span
7661 class="cmtt-10"> </span>
7662 <br class="fancyvrb" /><a
7663 id="x1-101090r45"></a><span
7664 class="cmtt-10"> </span><span
7665 class="cmtt-10"> </span><span
7666 class="cmtt-10"> </span><span
7667 class="cmtt-10"> </span><span
7668 class="cmtt-10"> </span><span
7669 class="cmtt-10"> </span><span
7670 class="cmtt-10"> </span><span
7671 class="cmtt-10"> </span><span
7672 class="cmtt-10"> </span><span
7673 class="cmtt-10"> </span><span
7674 class="cmtt-10"> </span><span
7675 class="cmtt-10"> </span><span
7676 class="cmtt-10"> </span><span
7677 class="cmtt-10"> </span><span
7678 class="cmtt-10"> </span><span
7679 class="cmtt-10"> </span><span
7680 class="cmtt-10"> </span><span
7681 class="cmtt-10"> </span><span
7682 class="cmtt-10"> </span><span
7683 class="cmtt-10"> </span><span
7684 class="cmtt-10"> </span><span
7685 class="cmtt-10"> </span><span
7686 class="cmtt-10"> </span><span
7687 class="cmtt-10"> </span><span
7688 class="cmsy-10">}</span>
7689 <br class="fancyvrb" /><a
7690 id="x1-101092r46"></a><span
7691 class="cmtt-10"> </span><span
7692 class="cmtt-10"> </span>
7693 <br class="fancyvrb" /><a
7694 id="x1-101094r47"></a><span
7695 class="cmtt-10"> </span><span
7696 class="cmtt-10"> </span><span
7697 class="cmtt-10"> </span><span
7698 class="cmtt-10"> </span><span
7699 class="cmtt-10"> </span><span
7700 class="cmtt-10"> </span><span
7701 class="cmtt-10"> </span><span
7702 class="cmtt-10"> </span><span
7703 class="cmtt-10"> </span><span
7704 class="cmtt-10"> </span><span
7705 class="cmtt-10"> </span><span
7706 class="cmtt-10"> </span><span
7707 class="cmtt-10"> </span><span
7708 class="cmtt-10"> </span><span
7709 class="cmtt-10"> </span><span
7710 class="cmtt-10"> </span><span
7711 class="cmtt-10"> </span><span
7712 class="cmtt-10"> </span><span
7713 class="cmsy-10">}</span><span
7714 class="cmtt-10"> else</span><span
7715 class="cmtt-10"> [val]</span><span
7716 class="cmtt-10"> is</span><span
7717 class="cmtt-10"> less</span><span
7718 class="cmtt-10"> than</span><span
7719 class="cmtt-10"> [room]</span><span
7720 class="cmtt-10"> </span><span
7721 class="cmsy-10">{</span>
7722 <br class="fancyvrb" /><a
7723 id="x1-101096r48"></a><span
7724 class="cmtt-10"> </span><span
7725 class="cmtt-10"> </span>
7726 <br class="fancyvrb" /><a
7727 id="x1-101098r49"></a><span
7728 class="cmtt-10"> </span><span
7729 class="cmtt-10">  </span><span
7730 class="cmtt-10"> </span><span
7731 class="cmtt-10"> 24)</span><span
7732 class="cmtt-10"> if</span><span
7733 class="cmtt-10"> ([val]</span><span
7734 class="cmtt-10"> is</span><span
7735 class="cmtt-10"> odd)</span><span
7736 class="cmtt-10"> </span><span
7737 class="cmsy-10">{</span>
7738 <br class="fancyvrb" /><a
7739 id="x1-101100r50"></a><span
7740 class="cmtt-10"> </span><span
7741 class="cmtt-10"> </span>
7742 <br class="fancyvrb" /><a
7743 id="x1-101102r51"></a><span
7744 class="cmtt-10"> </span><span
7745 class="cmtt-10"> </span><span
7746 class="cmtt-10"> </span><span
7747 class="cmtt-10"> </span><span
7748 class="cmtt-10"> </span><span
7749 class="cmtt-10"> </span><span
7750 class="cmtt-10"> </span><span
7751 class="cmtt-10"> </span><span
7752 class="cmtt-10"> </span><span
7753 class="cmtt-10"> </span><span
7754 class="cmtt-10"> </span><span
7755 class="cmtt-10"> </span><span
7756 class="cmtt-10"> </span><span
7757 class="cmtt-10"> </span><span
7758 class="cmtt-10"> </span><span
7759 class="cmtt-10"> </span><span
7760 class="cmtt-10"> </span><span
7761 class="cmtt-10"> </span><span
7762 class="cmtt-10"> </span><span
7763 class="cmtt-10"> </span><span
7764 class="cmtt-10"> </span><span
7765 class="cmtt-10"> </span><span
7766 class="cmtt-10"> </span><span
7767 class="cmtt-10"> </span><span
7768 class="cmtt-10"> </span><span
7769 class="cmtt-10"> 25)</span><span
7770 class="cmtt-10"> vector</span><span
7771 class="cmtt-10"> [floor1_final_Y]</span><span
7772 class="cmtt-10"> element</span><span
7773 class="cmtt-10"> [i]</span><span
7774 class="cmtt-10"> =</span>
7775 <br class="fancyvrb" /><a
7776 id="x1-101104r52"></a><span
7777 class="cmtt-10"> </span><span
7778 class="cmtt-10"> </span><span
7779 class="cmtt-10"> </span><span
7780 class="cmtt-10"> </span><span
7781 class="cmtt-10"> </span><span
7782 class="cmtt-10"> </span><span
7783 class="cmtt-10"> </span><span
7784 class="cmtt-10"> </span><span
7785 class="cmtt-10"> </span><span
7786 class="cmtt-10"> </span><span
7787 class="cmtt-10"> </span><span
7788 class="cmtt-10"> </span><span
7789 class="cmtt-10"> </span><span
7790 class="cmtt-10"> </span><span
7791 class="cmtt-10"> </span><span
7792 class="cmtt-10"> </span><span
7793 class="cmtt-10"> </span><span
7794 class="cmtt-10"> </span><span
7795 class="cmtt-10"> </span><span
7796 class="cmtt-10"> </span><span
7797 class="cmtt-10"> </span><span
7798 class="cmtt-10"> </span><span
7799 class="cmtt-10"> </span><span
7800 class="cmtt-10"> </span><span
7801 class="cmtt-10"> </span><span
7802 class="cmtt-10"> </span><span
7803 class="cmtt-10"> </span><span
7804 class="cmtt-10"> </span><span
7805 class="cmtt-10"> </span><span
7806 class="cmtt-10"> [predicted]</span><span
7807 class="cmtt-10"> -</span><span
7808 class="cmtt-10"> (([val]</span><span
7809 class="cmtt-10"> +</span><span
7810 class="cmtt-10"> 1)</span><span
7811 class="cmtt-10"> divided</span><span
7812 class="cmtt-10"> by</span><span
7813 class="cmtt-10"> </span><span
7814 class="cmtt-10"> 2</span><span
7815 class="cmtt-10"> using</span><span
7816 class="cmtt-10"> integer</span><span
7817 class="cmtt-10"> division)</span>
7818 <br class="fancyvrb" /><a
7819 id="x1-101106r53"></a><span
7820 class="cmtt-10"> </span><span
7821 class="cmtt-10"> </span>
7822 <br class="fancyvrb" /><a
7823 id="x1-101108r54"></a><span
7824 class="cmtt-10"> </span><span
7825 class="cmtt-10"> </span><span
7826 class="cmtt-10"> </span><span
7827 class="cmtt-10"> </span><span
7828 class="cmtt-10"> </span><span
7829 class="cmtt-10"> </span><span
7830 class="cmtt-10"> </span><span
7831 class="cmtt-10"> </span><span
7832 class="cmtt-10"> </span><span
7833 class="cmtt-10"> </span><span
7834 class="cmtt-10"> </span><span
7835 class="cmtt-10"> </span><span
7836 class="cmtt-10"> </span><span
7837 class="cmtt-10"> </span><span
7838 class="cmtt-10"> </span><span
7839 class="cmtt-10"> </span><span
7840 class="cmtt-10"> </span><span
7841 class="cmtt-10"> </span><span
7842 class="cmtt-10"> </span><span
7843 class="cmtt-10"> </span><span
7844 class="cmtt-10"> </span><span
7845 class="cmtt-10"> </span><span
7846 class="cmtt-10"> </span><span
7847 class="cmtt-10"> </span><span
7848 class="cmsy-10">}</span><span
7849 class="cmtt-10"> else</span><span
7850 class="cmtt-10"> [val]</span><span
7851 class="cmtt-10"> is</span><span
7852 class="cmtt-10"> even</span><span
7853 class="cmtt-10"> </span><span
7854 class="cmsy-10">{</span>
7855 <br class="fancyvrb" /><a
7856 id="x1-101110r55"></a><span
7857 class="cmtt-10"> </span><span
7858 class="cmtt-10"> </span>
7859 <br class="fancyvrb" /><a
7860 id="x1-101112r56"></a><span
7861 class="cmtt-10"> </span><span
7862 class="cmtt-10"> </span><span
7863 class="cmtt-10"> </span><span
7864 class="cmtt-10"> </span><span
7865 class="cmtt-10"> </span><span
7866 class="cmtt-10"> </span><span
7867 class="cmtt-10"> </span><span
7868 class="cmtt-10"> </span><span
7869 class="cmtt-10"> </span><span
7870 class="cmtt-10"> </span><span
7871 class="cmtt-10"> </span><span
7872 class="cmtt-10"> </span><span
7873 class="cmtt-10"> </span><span
7874 class="cmtt-10"> </span><span
7875 class="cmtt-10"> </span><span
7876 class="cmtt-10"> </span><span
7877 class="cmtt-10"> </span><span
7878 class="cmtt-10"> </span><span
7879 class="cmtt-10"> </span><span
7880 class="cmtt-10"> </span><span
7881 class="cmtt-10"> </span><span
7882 class="cmtt-10"> </span><span
7883 class="cmtt-10"> </span><span
7884 class="cmtt-10"> </span><span
7885 class="cmtt-10"> </span><span
7886 class="cmtt-10"> 26)</span><span
7887 class="cmtt-10"> vector</span><span
7888 class="cmtt-10"> [floor1_final_Y]</span><span
7889 class="cmtt-10"> element</span><span
7890 class="cmtt-10"> [i]</span><span
7891 class="cmtt-10"> =</span>
7892 <br class="fancyvrb" /><a
7893 id="x1-101114r57"></a><span
7894 class="cmtt-10"> </span><span
7895 class="cmtt-10"> </span><span
7896 class="cmtt-10"> </span><span
7897 class="cmtt-10"> </span><span
7898 class="cmtt-10"> </span><span
7899 class="cmtt-10"> </span><span
7900 class="cmtt-10"> </span><span
7901 class="cmtt-10"> </span><span
7902 class="cmtt-10"> </span><span
7903 class="cmtt-10"> </span><span
7904 class="cmtt-10"> </span><span
7905 class="cmtt-10"> </span><span
7906 class="cmtt-10"> </span><span
7907 class="cmtt-10"> </span><span
7908 class="cmtt-10"> </span><span
7909 class="cmtt-10"> </span><span
7910 class="cmtt-10"> </span><span
7911 class="cmtt-10"> </span><span
7912 class="cmtt-10"> </span><span
7913 class="cmtt-10"> </span><span
7914 class="cmtt-10"> </span><span
7915 class="cmtt-10"> </span><span
7916 class="cmtt-10"> </span><span
7917 class="cmtt-10"> </span><span
7918 class="cmtt-10"> </span><span
7919 class="cmtt-10"> </span><span
7920 class="cmtt-10"> </span><span
7921 class="cmtt-10"> </span><span
7922 class="cmtt-10"> </span><span
7923 class="cmtt-10"> [predicted]</span><span
7924 class="cmtt-10"> +</span><span
7925 class="cmtt-10"> ([val]</span><span
7926 class="cmtt-10"> /</span><span
7927 class="cmtt-10"> 2</span><span
7928 class="cmtt-10"> using</span><span
7929 class="cmtt-10"> integer</span><span
7930 class="cmtt-10"> division)</span>
7931 <br class="fancyvrb" /><a
7932 id="x1-101116r58"></a><span
7933 class="cmtt-10"> </span><span
7934 class="cmtt-10"> </span>
7935 <br class="fancyvrb" /><a
7936 id="x1-101118r59"></a><span
7937 class="cmtt-10"> </span><span
7938 class="cmtt-10"> </span><span
7939 class="cmtt-10"> </span><span
7940 class="cmtt-10"> </span><span
7941 class="cmtt-10"> </span><span
7942 class="cmtt-10"> </span><span
7943 class="cmtt-10"> </span><span
7944 class="cmtt-10"> </span><span
7945 class="cmtt-10"> </span><span
7946 class="cmtt-10"> </span><span
7947 class="cmtt-10"> </span><span
7948 class="cmtt-10"> </span><span
7949 class="cmtt-10"> </span><span
7950 class="cmtt-10"> </span><span
7951 class="cmtt-10"> </span><span
7952 class="cmtt-10"> </span><span
7953 class="cmtt-10"> </span><span
7954 class="cmtt-10"> </span><span
7955 class="cmtt-10"> </span><span
7956 class="cmtt-10"> </span><span
7957 class="cmtt-10"> </span><span
7958 class="cmtt-10"> </span><span
7959 class="cmtt-10"> </span><span
7960 class="cmtt-10"> </span><span
7961 class="cmsy-10">}</span>
7962 <br class="fancyvrb" /><a
7963 id="x1-101120r60"></a><span
7964 class="cmtt-10"> </span><span
7965 class="cmtt-10"> </span>
7966 <br class="fancyvrb" /><a
7967 id="x1-101122r61"></a><span
7968 class="cmtt-10"> </span><span
7969 class="cmtt-10"> </span><span
7970 class="cmtt-10"> </span><span
7971 class="cmtt-10"> </span><span
7972 class="cmtt-10"> </span><span
7973 class="cmtt-10"> </span><span
7974 class="cmtt-10"> </span><span
7975 class="cmtt-10"> </span><span
7976 class="cmtt-10"> </span><span
7977 class="cmtt-10"> </span><span
7978 class="cmtt-10"> </span><span
7979 class="cmtt-10"> </span><span
7980 class="cmtt-10"> </span><span
7981 class="cmtt-10"> </span><span
7982 class="cmtt-10"> </span><span
7983 class="cmtt-10"> </span><span
7984 class="cmtt-10"> </span><span
7985 class="cmtt-10"> </span><span
7986 class="cmsy-10">}</span>
7987 <br class="fancyvrb" /><a
7988 id="x1-101124r62"></a><span
7989 class="cmtt-10"> </span><span
7990 class="cmtt-10"> </span>
7991 <br class="fancyvrb" /><a
7992 id="x1-101126r63"></a><span
7993 class="cmtt-10"> </span><span
7994 class="cmtt-10"> </span><span
7995 class="cmtt-10"> </span><span
7996 class="cmtt-10"> </span><span
7997 class="cmtt-10"> </span><span
7998 class="cmtt-10"> </span><span
7999 class="cmtt-10"> </span><span
8000 class="cmtt-10"> </span><span
8001 class="cmtt-10"> </span><span
8002 class="cmtt-10"> </span><span
8003 class="cmtt-10"> </span><span
8004 class="cmtt-10"> </span><span
8005 class="cmsy-10">}</span><span
8006 class="cmtt-10"> else</span><span
8007 class="cmtt-10"> [val]</span><span
8008 class="cmtt-10"> is</span><span
8009 class="cmtt-10"> zero</span><span
8010 class="cmtt-10"> </span><span
8011 class="cmsy-10">{</span>
8012 <br class="fancyvrb" /><a
8013 id="x1-101128r64"></a><span
8014 class="cmtt-10"> </span><span
8015 class="cmtt-10"> </span>
8016 <br class="fancyvrb" /><a
8017 id="x1-101130r65"></a><span
8018 class="cmtt-10"> </span><span
8019 class="cmtt-10"> </span><span
8020 class="cmtt-10"> </span><span
8021 class="cmtt-10"> </span><span
8022 class="cmtt-10"> </span><span
8023 class="cmtt-10"> </span><span
8024 class="cmtt-10"> </span><span
8025 class="cmtt-10"> </span><span
8026 class="cmtt-10"> </span><span
8027 class="cmtt-10"> </span><span
8028 class="cmtt-10"> </span><span
8029 class="cmtt-10"> </span><span
8030 class="cmtt-10"> </span><span
8031 class="cmtt-10"> 27)</span><span
8032 class="cmtt-10"> vector</span><span
8033 class="cmtt-10"> [floor1_step2_flag]</span><span
8034 class="cmtt-10"> element</span><span
8035 class="cmtt-10"> [i]</span><span
8036 class="cmtt-10"> =</span><span
8037 class="cmtt-10"> unset</span>
8038 <br class="fancyvrb" /><a
8039 id="x1-101132r66"></a><span
8040 class="cmtt-10"> </span><span
8041 class="cmtt-10"> </span><span
8042 class="cmtt-10"> </span><span
8043 class="cmtt-10"> </span><span
8044 class="cmtt-10"> </span><span
8045 class="cmtt-10"> </span><span
8046 class="cmtt-10"> </span><span
8047 class="cmtt-10"> </span><span
8048 class="cmtt-10"> </span><span
8049 class="cmtt-10"> </span><span
8050 class="cmtt-10"> </span><span
8051 class="cmtt-10"> </span><span
8052 class="cmtt-10"> </span><span
8053 class="cmtt-10"> 28)</span><span
8054 class="cmtt-10"> vector</span><span
8055 class="cmtt-10"> [floor1_final_Y]</span><span
8056 class="cmtt-10"> element</span><span
8057 class="cmtt-10"> [i]</span><span
8058 class="cmtt-10"> =</span><span
8059 class="cmtt-10"> [predicted]</span>
8060 <br class="fancyvrb" /><a
8061 id="x1-101134r67"></a><span
8062 class="cmtt-10"> </span><span
8063 class="cmtt-10"> </span>
8064 <br class="fancyvrb" /><a
8065 id="x1-101136r68"></a><span
8066 class="cmtt-10"> </span><span
8067 class="cmtt-10"> </span><span
8068 class="cmtt-10"> </span><span
8069 class="cmtt-10"> </span><span
8070 class="cmtt-10"> </span><span
8071 class="cmtt-10"> </span><span
8072 class="cmtt-10"> </span><span
8073 class="cmtt-10"> </span><span
8074 class="cmtt-10"> </span><span
8075 class="cmtt-10"> </span><span
8076 class="cmtt-10"> </span><span
8077 class="cmtt-10"> </span><span
8078 class="cmsy-10">}</span>
8079 <br class="fancyvrb" /><a
8080 id="x1-101138r69"></a><span
8081 class="cmtt-10"> </span><span
8082 class="cmtt-10"> </span>
8083 <br class="fancyvrb" /><a
8084 id="x1-101140r70"></a><span
8085 class="cmtt-10"> </span><span
8086 class="cmtt-10"> </span><span
8087 class="cmtt-10"> </span><span
8088 class="cmtt-10"> </span><span
8089 class="cmtt-10"> </span><span
8090 class="cmtt-10"> </span><span
8091 class="cmtt-10"> </span><span
8092 class="cmsy-10">}</span>
8093 <br class="fancyvrb" /><a
8094 id="x1-101142r71"></a><span
8095 class="cmtt-10"> </span><span
8096 class="cmtt-10"> </span>
8097 <br class="fancyvrb" /><a
8098 id="x1-101144r72"></a><span
8099 class="cmtt-10"> </span><span
8100 class="cmtt-10"> </span><span
8101 class="cmtt-10"> 29)</span><span
8102 class="cmtt-10"> done</span>
8103 <br class="fancyvrb" /><a
8104 id="x1-101146r73"></a><span
8105 class="cmtt-10"> </span><span
8106 class="cmtt-10"> </span>
8108 </dd><dt class="description">
8110 class="cmssbx-10x-x-109">step 2: curve synthesis</span> </dt><dd
8111 class="description">
8112 <!--l. 336--><p class="noindent" >Curve synthesis generates a return vector <span
8113 class="cmtt-10x-x-109">[floor] </span>of length <span
8114 class="cmtt-10x-x-109">[n] </span>(where <span
8115 class="cmtt-10x-x-109">[n] </span>is provided by the
8119 decode process calling to floor decode). Floor 1 curve synthesis makes use of the
8121 class="cmtt-10x-x-109">[floor1_X_list]</span>, <span
8122 class="cmtt-10x-x-109">[floor1_final_Y] </span>and <span
8123 class="cmtt-10x-x-109">[floor1_step2_flag] </span>vectors, as well as
8124 [floor1˙multiplier] and [floor1˙values] values.
8125 <!--l. 343--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
8126 class="cmtt-10x-x-109">[floor1_X_list]</span>, <span
8127 class="cmtt-10x-x-109">[floor1_final_Y] </span>and
8129 class="cmtt-10x-x-109">[floor1_step2_flag] </span>together into new vectors <span
8130 class="cmtt-10x-x-109">[floor1_X_list]’</span>, <span
8131 class="cmtt-10x-x-109">[floor1_final_Y]’</span>
8133 class="cmtt-10x-x-109">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
8135 class="cmtt-10x-x-109">[floor1_X_list]</span>. That is, sort the values of <span
8136 class="cmtt-10x-x-109">[floor1_X_list] </span>and then apply the same
8137 permutation to elements of the other two vectors so that the X, Y and step2˙flag values still
8139 <!--l. 353--><p class="noindent" >Then compute the final curve in one pass:
8140 <!--l. 355--><p class="noindent" >
8141 <div class="fancyvrb" id="fancyvrb32">
8143 id="x1-101148r1"></a><span
8144 class="cmtt-10"> </span><span
8145 class="cmtt-10"> </span><span
8146 class="cmtt-10"> </span><span
8147 class="cmtt-10"> 1)</span><span
8148 class="cmtt-10"> [hx]</span><span
8149 class="cmtt-10"> =</span><span
8150 class="cmtt-10"> 0</span>
8151 <br class="fancyvrb" /><a
8152 id="x1-101150r2"></a><span
8153 class="cmtt-10"> </span><span
8154 class="cmtt-10"> </span><span
8155 class="cmtt-10"> </span><span
8156 class="cmtt-10"> 2)</span><span
8157 class="cmtt-10"> [lx]</span><span
8158 class="cmtt-10"> =</span><span
8159 class="cmtt-10"> 0</span>
8160 <br class="fancyvrb" /><a
8161 id="x1-101152r3"></a><span
8162 class="cmtt-10"> </span><span
8163 class="cmtt-10"> </span><span
8164 class="cmtt-10"> </span><span
8165 class="cmtt-10"> 3)</span><span
8166 class="cmtt-10"> [ly]</span><span
8167 class="cmtt-10"> =</span><span
8168 class="cmtt-10"> vector</span><span
8169 class="cmtt-10"> [floor1_final_Y]’</span><span
8170 class="cmtt-10"> element</span><span
8171 class="cmtt-10"> [0]</span><span
8172 class="cmtt-10"> *</span><span
8173 class="cmtt-10"> [floor1_multiplier]</span>
8174 <br class="fancyvrb" /><a
8175 id="x1-101154r4"></a><span
8176 class="cmtt-10"> </span><span
8177 class="cmtt-10"> </span><span
8178 class="cmtt-10"> </span><span
8179 class="cmtt-10"> 4)</span><span
8180 class="cmtt-10"> iterate</span><span
8181 class="cmtt-10"> [i]</span><span
8182 class="cmtt-10"> over</span><span
8183 class="cmtt-10"> the</span><span
8184 class="cmtt-10"> range</span><span
8185 class="cmtt-10"> 1</span><span
8186 class="cmtt-10"> ...</span><span
8187 class="cmtt-10"> [floor1_values]-1</span><span
8188 class="cmtt-10"> </span><span
8189 class="cmsy-10">{</span>
8190 <br class="fancyvrb" /><a
8191 id="x1-101156r5"></a><span
8192 class="cmtt-10"> </span><span
8193 class="cmtt-10"> </span>
8194 <br class="fancyvrb" /><a
8195 id="x1-101158r6"></a><span
8196 class="cmtt-10"> </span><span
8197 class="cmtt-10"> </span><span
8198 class="cmtt-10"> </span><span
8199 class="cmtt-10"> </span><span
8200 class="cmtt-10"> </span><span
8201 class="cmtt-10"> </span><span
8202 class="cmtt-10"> </span><span
8203 class="cmtt-10"> </span><span
8204 class="cmtt-10"> 5)</span><span
8205 class="cmtt-10"> if</span><span
8206 class="cmtt-10"> (</span><span
8207 class="cmtt-10"> [floor1_step2_flag]’</span><span
8208 class="cmtt-10"> element</span><span
8209 class="cmtt-10"> [i]</span><span
8210 class="cmtt-10"> is</span><span
8211 class="cmtt-10"> set</span><span
8212 class="cmtt-10"> )</span><span
8213 class="cmtt-10"> </span><span
8214 class="cmsy-10">{</span>
8215 <br class="fancyvrb" /><a
8216 id="x1-101160r7"></a><span
8217 class="cmtt-10"> </span><span
8218 class="cmtt-10"> </span>
8219 <br class="fancyvrb" /><a
8220 id="x1-101162r8"></a><span
8221 class="cmtt-10"> </span><span
8222 class="cmtt-10"> </span><span
8223 class="cmtt-10"> </span><span
8224 class="cmtt-10"> </span><span
8225 class="cmtt-10"> </span><span
8226 class="cmtt-10"> </span><span
8227 class="cmtt-10"> </span><span
8228 class="cmtt-10"> </span><span
8229 class="cmtt-10"> </span><span
8230 class="cmtt-10"> </span><span
8231 class="cmtt-10"> </span><span
8232 class="cmtt-10"> </span><span
8233 class="cmtt-10"> </span><span
8234 class="cmtt-10"> </span><span
8235 class="cmtt-10"> 6)</span><span
8236 class="cmtt-10"> [hy]</span><span
8237 class="cmtt-10"> =</span><span
8238 class="cmtt-10"> [floor1_final_Y]’</span><span
8239 class="cmtt-10"> element</span><span
8240 class="cmtt-10"> [i]</span><span
8241 class="cmtt-10"> *</span><span
8242 class="cmtt-10"> [floor1_multiplier]</span>
8243 <br class="fancyvrb" /><a
8244 id="x1-101164r9"></a><span
8245 class="cmtt-10"> </span><span
8246 class="cmtt-10"> </span><span
8247 class="cmtt-10">  </span><span
8248 class="cmtt-10"> </span><span
8249 class="cmtt-10"> </span><span
8250 class="cmtt-10"> </span><span
8251 class="cmtt-10"> </span><span
8252 class="cmtt-10"> 7)</span><span
8253 class="cmtt-10"> [hx]</span><span
8254 class="cmtt-10"> =</span><span
8255 class="cmtt-10"> [floor1_X_list]’</span><span
8256 class="cmtt-10"> element</span><span
8257 class="cmtt-10"> [i]</span>
8258 <br class="fancyvrb" /><a
8259 id="x1-101166r10"></a><span
8260 class="cmtt-10"> </span><span
8261 class="cmtt-10"> </span><span
8262 class="cmtt-10"> </span><span
8263 class="cmtt-10"> </span><span
8264 class="cmtt-10"> </span><span
8265 class="cmtt-10"> </span><span
8266 class="cmtt-10"> </span><span
8267 class="cmtt-10"> </span><span
8268 class="cmtt-10"> </span><span
8269 class="cmtt-10"> </span><span
8270 class="cmtt-10"> </span><span
8271 class="cmtt-10"> </span><span
8272 class="cmtt-10"> </span><span
8273 class="cmtt-10"> </span><span
8274 class="cmtt-10"> 8)</span><span
8275 class="cmtt-10"> </span><a
8276 href="#x1-1230009.2.7"><span
8277 class="cmtt-10">render_line</span></a><span
8278 class="cmtt-10">(</span><span
8279 class="cmtt-10"> [lx],</span><span
8280 class="cmtt-10"> [ly],</span><span
8281 class="cmtt-10"> [hx],</span><span
8282 class="cmtt-10"> [hy],</span><span
8283 class="cmtt-10"> [floor]</span><span
8284 class="cmtt-10"> )</span>
8285 <br class="fancyvrb" /><a
8286 id="x1-101168r11"></a><span
8287 class="cmtt-10"> </span><span
8288 class="cmtt-10"> </span><span
8289 class="cmtt-10"> </span><span
8290 class="cmtt-10"> </span><span
8291 class="cmtt-10"> </span><span
8292 class="cmtt-10"> </span><span
8293 class="cmtt-10"> </span><span
8294 class="cmtt-10"> </span><span
8295 class="cmtt-10"> </span><span
8296 class="cmtt-10"> </span><span
8297 class="cmtt-10"> </span><span
8298 class="cmtt-10"> </span><span
8299 class="cmtt-10"> </span><span
8300 class="cmtt-10"> </span><span
8301 class="cmtt-10"> 9)</span><span
8302 class="cmtt-10"> [lx]</span><span
8303 class="cmtt-10"> =</span><span
8304 class="cmtt-10"> [hx]</span>
8305 <br class="fancyvrb" /><a
8306 id="x1-101170r12"></a><span
8307 class="cmtt-10"> </span><span
8308 class="cmtt-10">  </span><span
8309 class="cmtt-10"> </span><span
8310 class="cmtt-10"> </span><span
8311 class="cmtt-10"> </span><span
8312 class="cmtt-10"> 10)</span><span
8313 class="cmtt-10"> [ly]</span><span
8314 class="cmtt-10"> =</span><span
8315 class="cmtt-10"> [hy]</span>
8316 <br class="fancyvrb" /><a
8317 id="x1-101172r13"></a><span
8318 class="cmtt-10"> </span><span
8319 class="cmtt-10"> </span><span
8320 class="cmtt-10"> </span><span
8321 class="cmtt-10"> </span><span
8322 class="cmtt-10"> </span><span
8323 class="cmtt-10"> </span><span
8324 class="cmtt-10"> </span><span
8325 class="cmtt-10"> </span><span
8326 class="cmtt-10"> </span><span
8327 class="cmtt-10"> </span><span
8328 class="cmtt-10"> </span><span
8329 class="cmtt-10"> </span><span
8330 class="cmsy-10">}</span>
8331 <br class="fancyvrb" /><a
8332 id="x1-101174r14"></a><span
8333 class="cmtt-10"> </span><span
8334 class="cmtt-10"> </span><span
8335 class="cmtt-10"> </span><span
8336 class="cmtt-10"> </span><span
8337 class="cmtt-10"> </span><span
8338 class="cmtt-10"> </span><span
8339 class="cmtt-10"> </span><span
8340 class="cmsy-10">}</span>
8341 <br class="fancyvrb" /><a
8342 id="x1-101176r15"></a><span
8343 class="cmtt-10"> </span><span
8344 class="cmtt-10"> </span>
8345 <br class="fancyvrb" /><a
8346 id="x1-101178r16"></a><span
8347 class="cmtt-10"> </span><span
8348 class="cmtt-10"> </span><span
8349 class="cmtt-10"> 11)</span><span
8350 class="cmtt-10"> if</span><span
8351 class="cmtt-10"> (</span><span
8352 class="cmtt-10"> [hx]</span><span
8353 class="cmtt-10"> is</span><span
8354 class="cmtt-10"> less</span><span
8355 class="cmtt-10"> than</span><span
8356 class="cmtt-10"> [n]</span><span
8357 class="cmtt-10"> )</span><span
8358 class="cmtt-10"> </span><span
8359 class="cmsy-10">{</span>
8360 <br class="fancyvrb" /><a
8361 id="x1-101180r17"></a><span
8362 class="cmtt-10"> </span><span
8363 class="cmtt-10"> </span>
8364 <br class="fancyvrb" /><a
8365 id="x1-101182r18"></a><span
8366 class="cmtt-10"> </span><span
8367 class="cmtt-10"> </span><span
8368 class="cmtt-10"> </span><span
8369 class="cmtt-10"> </span><span
8370 class="cmtt-10"> </span><span
8371 class="cmtt-10"> </span><span
8372 class="cmtt-10"> </span><span
8373 class="cmtt-10"> </span><span
8374 class="cmtt-10"> </span><span
8375 class="cmtt-10"> 12)</span><span
8376 class="cmtt-10"> </span><a
8377 href="#x1-1230009.2.7"><span
8378 class="cmtt-10">render_line</span></a><span
8379 class="cmtt-10">(</span><span
8380 class="cmtt-10"> [hx],</span><span
8381 class="cmtt-10"> [hy],</span><span
8382 class="cmtt-10"> [n],</span><span
8383 class="cmtt-10"> [hy],</span><span
8384 class="cmtt-10"> [floor]</span><span
8385 class="cmtt-10"> )</span>
8386 <br class="fancyvrb" /><a
8387 id="x1-101184r19"></a><span
8388 class="cmtt-10"> </span><span
8389 class="cmtt-10"> </span>
8390 <br class="fancyvrb" /><a
8391 id="x1-101186r20"></a><span
8392 class="cmtt-10"> </span><span
8393 class="cmtt-10"> </span><span
8394 class="cmtt-10"> </span><span
8395 class="cmtt-10"> </span><span
8396 class="cmtt-10"> </span><span
8397 class="cmtt-10"> </span><span
8398 class="cmtt-10"> </span><span
8399 class="cmsy-10">}</span>
8400 <br class="fancyvrb" /><a
8401 id="x1-101188r21"></a><span
8402 class="cmtt-10"> </span><span
8403 class="cmtt-10"> </span>
8404 <br class="fancyvrb" /><a
8405 id="x1-101190r22"></a><span
8406 class="cmtt-10"> </span><span
8407 class="cmtt-10"> </span><span
8408 class="cmtt-10"> 13)</span><span
8409 class="cmtt-10"> if</span><span
8410 class="cmtt-10"> (</span><span
8411 class="cmtt-10"> [hx]</span><span
8412 class="cmtt-10"> is</span><span
8413 class="cmtt-10"> greater</span><span
8414 class="cmtt-10"> than</span><span
8415 class="cmtt-10"> [n]</span><span
8416 class="cmtt-10"> )</span><span
8417 class="cmtt-10"> </span><span
8418 class="cmsy-10">{</span>
8419 <br class="fancyvrb" /><a
8420 id="x1-101192r23"></a><span
8421 class="cmtt-10"> </span><span
8422 class="cmtt-10"> </span>
8423 <br class="fancyvrb" /><a
8424 id="x1-101194r24"></a><span
8425 class="cmtt-10"> </span><span
8426 class="cmtt-10"> </span><span
8427 class="cmtt-10"> </span><span
8428 class="cmtt-10"> </span><span
8429 class="cmtt-10"> </span><span
8430 class="cmtt-10"> </span><span
8431 class="cmtt-10"> </span><span
8432 class="cmtt-10"> </span><span
8433 class="cmtt-10"> </span><span
8434 class="cmtt-10"> </span><span
8435 class="cmtt-10"> </span><span
8436 class="cmtt-10"> </span><span
8437 class="cmtt-10"> </span><span
8438 class="cmtt-10"> 14)</span><span
8439 class="cmtt-10"> truncate</span><span
8440 class="cmtt-10"> vector</span><span
8441 class="cmtt-10"> [floor]</span><span
8442 class="cmtt-10"> to</span><span
8443 class="cmtt-10"> [n]</span><span
8444 class="cmtt-10"> elements</span>
8445 <br class="fancyvrb" /><a
8446 id="x1-101196r25"></a><span
8447 class="cmtt-10"> </span><span
8448 class="cmtt-10"> </span>
8449 <br class="fancyvrb" /><a
8450 id="x1-101198r26"></a><span
8451 class="cmtt-10"> </span><span
8452 class="cmtt-10"> </span><span
8453 class="cmtt-10"> </span><span
8454 class="cmtt-10"> </span><span
8455 class="cmtt-10"> </span><span
8456 class="cmtt-10"> </span><span
8457 class="cmtt-10"> </span><span
8458 class="cmsy-10">}</span>
8459 <br class="fancyvrb" /><a
8460 id="x1-101200r27"></a><span
8461 class="cmtt-10"> </span><span
8462 class="cmtt-10"> </span>
8463 <br class="fancyvrb" /><a
8464 id="x1-101202r28"></a><span
8465 class="cmtt-10"> </span><span
8466 class="cmtt-10"> </span><span
8467 class="cmtt-10"> 15)</span><span
8468 class="cmtt-10"> for</span><span
8469 class="cmtt-10"> each</span><span
8470 class="cmtt-10"> scalar</span><span
8471 class="cmtt-10"> in</span><span
8472 class="cmtt-10"> vector</span><span
8473 class="cmtt-10"> [floor],</span><span
8474 class="cmtt-10"> perform</span><span
8475 class="cmtt-10"> a</span><span
8476 class="cmtt-10"> lookup</span><span
8477 class="cmtt-10"> substitution</span><span
8478 class="cmtt-10"> using</span>
8479 <br class="fancyvrb" /><a
8480 id="x1-101204r29"></a><span
8481 class="cmtt-10"> </span><span
8482 class="cmtt-10"> </span><span
8483 class="cmtt-10"> </span><span
8484 class="cmtt-10"> </span><span
8485 class="cmtt-10"> </span><span
8486 class="cmtt-10"> </span><span
8487 class="cmtt-10"> the</span><span
8488 class="cmtt-10"> scalar</span><span
8489 class="cmtt-10"> value</span><span
8490 class="cmtt-10"> from</span><span
8491 class="cmtt-10"> [floor]</span><span
8492 class="cmtt-10"> as</span><span
8493 class="cmtt-10"> an</span><span
8494 class="cmtt-10"> offset</span><span
8495 class="cmtt-10"> into</span><span
8496 class="cmtt-10"> the</span><span
8497 class="cmtt-10"> vector</span><span
8498 class="cmtt-10"> </span><span
8499 class="cmbx-10">??</span>
8500 <br class="fancyvrb" /><a
8501 id="x1-101206r30"></a><span
8502 class="cmtt-10"> </span><span
8503 class="cmtt-10"> </span>
8504 <br class="fancyvrb" /><a
8505 id="x1-101208r31"></a><span
8506 class="cmtt-10"> </span><span
8507 class="cmtt-10"> </span><span
8508 class="cmtt-10"> 16)</span><span
8509 class="cmtt-10"> done</span>
8510 <br class="fancyvrb" /><a
8511 id="x1-101210r32"></a><span
8512 class="cmtt-10"> </span><span
8513 class="cmtt-10"> </span>
8519 <h3 class="sectionHead"><span class="titlemark">8 </span> <a
8520 id="x1-1020008"></a>Residue setup and decode</h3>
8521 <!--l. 6--><p class="noindent" >
8522 <h4 class="subsectionHead"><span class="titlemark">8.1 </span> <a
8523 id="x1-1030008.1"></a>Overview</h4>
8524 <!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
8525 after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
8526 may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by
8527 channel coupling. The exact semantic content of the vector does not matter to the residue
8529 <!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
8530 bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
8531 different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
8533 <!--l. 23--><p class="noindent" >
8534 <h4 class="subsectionHead"><span class="titlemark">8.2 </span> <a
8535 id="x1-1040008.2"></a>Residue format</h4>
8536 <!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each chunk,
8537 encodes the chunk classifications and finally encodes the chunks themselves using the the specific
8538 VQ arrangement defined for each selected classification. The exact interleaving and partitioning
8539 vary by residue encoding number, however the high-level process used to classify and encode the
8540 residue vector is the same in all three variants.
8541 <!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring
8542 for the moment exactly how a partition is encoded and simply trusting that it is, is as
8544 <ul class="itemize1">
8545 <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
8546 specified. If we have a vector size of <span
8547 class="cmti-10x-x-109">n</span>, a partition size <span
8548 class="cmti-10x-x-109">residue˙partition˙size</span>, and
8550 class="cmti-10x-x-109">ch </span>residue vectors, the total number of partitioned chunks coded is
8552 class="cmti-10x-x-109">n</span>/<span
8553 class="cmti-10x-x-109">residue˙partition˙size</span>*<span
8554 class="cmti-10x-x-109">ch</span>. It is important to note that the integer division truncates.
8555 In the below example, we assume an example <span
8556 class="cmti-10x-x-109">residue˙partition˙size </span>of 8.
8558 <li class="itemize">Each partition in each vector has a classification number that specifies which of multiple
8559 configured VQ codebook setups are used to decode that partition. The classification
8563 numbers of each partition can be thought of as forming a vector in their own right, as
8564 in the illustration below. Just as the residue vectors are coded in grouped partitions
8565 to increase encoding efficiency, the classification vector is also partitioned into chunks.
8566 The integer elements of each scalar in a classification chunk are built into a single scalar
8567 that represents the classification numbers in that chunk. In the below example, the
8568 classification codeword encodes two classification numbers.
8570 <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
8571 the residue vector, but more often efficient codebook design dictates that each vector
8572 is encoded as the additive sum of several passes through the residue vector using more
8573 than one VQ codebook. Thus, each residue value potentially accumulates values from
8574 multiple decode passes. The classification value associated with a partition is the same
8575 in each pass, thus the classification codeword is coded only in the first pass.
8579 <!--l. 70--><p class="noindent" >
8581 <!--l. 71--><p class="noindent" ><img
8582 src="residue-pack.png" alt="PIC"
8584 <br /> <table class="caption"
8585 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 11: </td><td
8586 class="content">illustration of residue vector format</td></tr></table><!--tex4ht:label?: x1-10400111 -->
8588 <!--l. 77--><p class="noindent" >
8589 <h4 class="subsectionHead"><span class="titlemark">8.3 </span> <a
8590 id="x1-1050008.3"></a>residue 0</h4>
8591 <!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
8592 partition encoding (visually treated as a black box–or cyan box or brown box–in the above
8594 <!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
8595 encode a partition in a specific pass. The dimension of the codebook need not be the same in
8596 multiple passes, however the partition size must be an even multiple of the codebook
8598 <!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using codebook
8599 sizes of 8, 4, 2 and 1:
8600 <!--l. 92--><p class="noindent" >
8601 <div class="fancyvrb" id="fancyvrb33">
8606 id="x1-105002r1"></a><span
8607 class="cmtt-10"> </span><span
8608 class="cmtt-10"> </span>
8609 <br class="fancyvrb" /><a
8610 id="x1-105004r2"></a><span
8611 class="cmtt-10"> </span><span
8612 class="cmtt-10"> </span><span
8613 class="cmtt-10"> </span><span
8614 class="cmtt-10"> </span><span
8615 class="cmtt-10"> </span><span
8616 class="cmtt-10"> </span><span
8617 class="cmtt-10"> </span><span
8618 class="cmtt-10"> </span><span
8619 class="cmtt-10"> </span><span
8620 class="cmtt-10"> </span><span
8621 class="cmtt-10"> </span><span
8622 class="cmtt-10"> </span><span
8623 class="cmtt-10"> </span><span
8624 class="cmtt-10"> original</span><span
8625 class="cmtt-10"> residue</span><span
8626 class="cmtt-10"> vector:</span><span
8627 class="cmtt-10"> [</span><span
8628 class="cmtt-10"> 0</span><span
8629 class="cmtt-10"> 1</span><span
8630 class="cmtt-10"> 2</span><span
8631 class="cmtt-10"> 3</span><span
8632 class="cmtt-10"> 4</span><span
8633 class="cmtt-10"> 5</span><span
8634 class="cmtt-10"> 6</span><span
8635 class="cmtt-10"> 7</span><span
8636 class="cmtt-10"> ]</span>
8637 <br class="fancyvrb" /><a
8638 id="x1-105006r3"></a><span
8639 class="cmtt-10"> </span><span
8640 class="cmtt-10"> </span>
8641 <br class="fancyvrb" /><a
8642 id="x1-105008r4"></a><span
8643 class="cmtt-10"> </span><span
8644 class="cmtt-10"> codebook</span><span
8645 class="cmtt-10"> dimensions</span><span
8646 class="cmtt-10"> =</span><span
8647 class="cmtt-10"> 8</span><span
8648 class="cmtt-10"> </span><span
8649 class="cmtt-10"> encoded</span><span
8650 class="cmtt-10"> as:</span><span
8651 class="cmtt-10"> [</span><span
8652 class="cmtt-10"> 0</span><span
8653 class="cmtt-10"> 1</span><span
8654 class="cmtt-10"> 2</span><span
8655 class="cmtt-10"> 3</span><span
8656 class="cmtt-10"> 4</span><span
8657 class="cmtt-10"> 5</span><span
8658 class="cmtt-10"> 6</span><span
8659 class="cmtt-10"> 7</span><span
8660 class="cmtt-10"> ]</span>
8661 <br class="fancyvrb" /><a
8662 id="x1-105010r5"></a><span
8663 class="cmtt-10"> </span><span
8664 class="cmtt-10"> </span>
8665 <br class="fancyvrb" /><a
8666 id="x1-105012r6"></a><span
8667 class="cmtt-10"> </span><span
8668 class="cmtt-10"> codebook</span><span
8669 class="cmtt-10"> dimensions</span><span
8670 class="cmtt-10"> =</span><span
8671 class="cmtt-10"> 4</span><span
8672 class="cmtt-10"> </span><span
8673 class="cmtt-10"> encoded</span><span
8674 class="cmtt-10"> as:</span><span
8675 class="cmtt-10"> [</span><span
8676 class="cmtt-10"> 0</span><span
8677 class="cmtt-10"> 2</span><span
8678 class="cmtt-10"> 4</span><span
8679 class="cmtt-10"> 6</span><span
8680 class="cmtt-10"> ],</span><span
8681 class="cmtt-10"> [</span><span
8682 class="cmtt-10"> 1</span><span
8683 class="cmtt-10"> 3</span><span
8684 class="cmtt-10"> 5</span><span
8685 class="cmtt-10"> 7</span><span
8686 class="cmtt-10"> ]</span>
8687 <br class="fancyvrb" /><a
8688 id="x1-105014r7"></a><span
8689 class="cmtt-10"> </span><span
8690 class="cmtt-10"> </span>
8691 <br class="fancyvrb" /><a
8692 id="x1-105016r8"></a><span
8693 class="cmtt-10"> </span><span
8694 class="cmtt-10"> codebook</span><span
8695 class="cmtt-10"> dimensions</span><span
8696 class="cmtt-10"> =</span><span
8697 class="cmtt-10"> 2</span><span
8698 class="cmtt-10"> </span><span
8699 class="cmtt-10"> encoded</span><span
8700 class="cmtt-10"> as:</span><span
8701 class="cmtt-10"> [</span><span
8702 class="cmtt-10"> 0</span><span
8703 class="cmtt-10"> 4</span><span
8704 class="cmtt-10"> ],</span><span
8705 class="cmtt-10"> [</span><span
8706 class="cmtt-10"> 1</span><span
8707 class="cmtt-10"> 5</span><span
8708 class="cmtt-10"> ],</span><span
8709 class="cmtt-10"> [</span><span
8710 class="cmtt-10"> 2</span><span
8711 class="cmtt-10"> 6</span><span
8712 class="cmtt-10"> ],</span><span
8713 class="cmtt-10"> [</span><span
8714 class="cmtt-10"> 3</span><span
8715 class="cmtt-10"> 7</span><span
8716 class="cmtt-10"> ]</span>
8717 <br class="fancyvrb" /><a
8718 id="x1-105018r9"></a><span
8719 class="cmtt-10"> </span><span
8720 class="cmtt-10"> </span>
8721 <br class="fancyvrb" /><a
8722 id="x1-105020r10"></a><span
8723 class="cmtt-10"> </span><span
8724 class="cmtt-10"> codebook</span><span
8725 class="cmtt-10"> dimensions</span><span
8726 class="cmtt-10"> =</span><span
8727 class="cmtt-10"> 1</span><span
8728 class="cmtt-10"> </span><span
8729 class="cmtt-10"> encoded</span><span
8730 class="cmtt-10"> as:</span><span
8731 class="cmtt-10"> [</span><span
8732 class="cmtt-10"> 0</span><span
8733 class="cmtt-10"> ],</span><span
8734 class="cmtt-10"> [</span><span
8735 class="cmtt-10"> 1</span><span
8736 class="cmtt-10"> ],</span><span
8737 class="cmtt-10"> [</span><span
8738 class="cmtt-10"> 2</span><span
8739 class="cmtt-10"> ],</span><span
8740 class="cmtt-10"> [</span><span
8741 class="cmtt-10"> 3</span><span
8742 class="cmtt-10"> ],</span><span
8743 class="cmtt-10"> [</span><span
8744 class="cmtt-10"> 4</span><span
8745 class="cmtt-10"> ],</span><span
8746 class="cmtt-10"> [</span><span
8747 class="cmtt-10"> 5</span><span
8748 class="cmtt-10"> ],</span><span
8749 class="cmtt-10"> [</span><span
8750 class="cmtt-10"> 6</span><span
8751 class="cmtt-10"> ],</span><span
8752 class="cmtt-10"> [</span><span
8753 class="cmtt-10"> 7</span><span
8754 class="cmtt-10"> ]</span>
8755 <br class="fancyvrb" /><a
8756 id="x1-105022r11"></a><span
8757 class="cmtt-10"> </span><span
8758 class="cmtt-10"> </span>
8760 <!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
8761 restricted to a power of two.
8762 <!--l. 111--><p class="noindent" >
8763 <h4 class="subsectionHead"><span class="titlemark">8.4 </span> <a
8764 id="x1-1060008.4"></a>residue 1</h4>
8765 <!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As with
8766 residue 0, however, partition length must be an integer multiple of the codebook dimension,
8767 although dimension may vary from pass to pass.
8768 <!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using codebook
8769 sizes of 8, 4, 2 and 1:
8770 <!--l. 121--><p class="noindent" >
8771 <div class="fancyvrb" id="fancyvrb34">
8773 id="x1-106002r1"></a><span
8774 class="cmtt-10"> </span><span
8775 class="cmtt-10"> </span>
8776 <br class="fancyvrb" /><a
8777 id="x1-106004r2"></a><span
8778 class="cmtt-10"> </span><span
8779 class="cmtt-10"> </span><span
8780 class="cmtt-10"> </span><span
8781 class="cmtt-10"> </span><span
8782 class="cmtt-10"> </span><span
8783 class="cmtt-10"> </span><span
8784 class="cmtt-10"> </span><span
8785 class="cmtt-10"> </span><span
8786 class="cmtt-10"> </span><span
8787 class="cmtt-10"> </span><span
8788 class="cmtt-10"> </span><span
8789 class="cmtt-10"> </span><span
8790 class="cmtt-10"> </span><span
8791 class="cmtt-10"> original</span><span
8792 class="cmtt-10"> residue</span><span
8793 class="cmtt-10"> vector:</span><span
8794 class="cmtt-10"> [</span><span
8795 class="cmtt-10"> 0</span><span
8796 class="cmtt-10"> 1</span><span
8797 class="cmtt-10"> 2</span><span
8798 class="cmtt-10"> 3</span><span
8799 class="cmtt-10"> 4</span><span
8800 class="cmtt-10"> 5</span><span
8801 class="cmtt-10"> 6</span><span
8802 class="cmtt-10"> 7</span><span
8803 class="cmtt-10"> ]</span>
8804 <br class="fancyvrb" /><a
8805 id="x1-106006r3"></a><span
8806 class="cmtt-10"> </span><span
8807 class="cmtt-10"> </span>
8808 <br class="fancyvrb" /><a
8809 id="x1-106008r4"></a><span
8810 class="cmtt-10"> </span><span
8811 class="cmtt-10"> codebook</span><span
8812 class="cmtt-10"> dimensions</span><span
8813 class="cmtt-10"> =</span><span
8814 class="cmtt-10"> 8</span><span
8815 class="cmtt-10"> </span><span
8816 class="cmtt-10"> encoded</span><span
8817 class="cmtt-10"> as:</span><span
8818 class="cmtt-10"> [</span><span
8819 class="cmtt-10"> 0</span><span
8820 class="cmtt-10"> 1</span><span
8821 class="cmtt-10"> 2</span><span
8822 class="cmtt-10"> 3</span><span
8823 class="cmtt-10"> 4</span><span
8824 class="cmtt-10"> 5</span><span
8825 class="cmtt-10"> 6</span><span
8826 class="cmtt-10"> 7</span><span
8827 class="cmtt-10"> ]</span>
8828 <br class="fancyvrb" /><a
8829 id="x1-106010r5"></a><span
8830 class="cmtt-10"> </span><span
8831 class="cmtt-10"> </span>
8832 <br class="fancyvrb" /><a
8833 id="x1-106012r6"></a><span
8834 class="cmtt-10"> </span><span
8835 class="cmtt-10"> codebook</span><span
8836 class="cmtt-10"> dimensions</span><span
8837 class="cmtt-10"> =</span><span
8838 class="cmtt-10"> 4</span><span
8839 class="cmtt-10"> </span><span
8840 class="cmtt-10"> encoded</span><span
8841 class="cmtt-10"> as:</span><span
8842 class="cmtt-10"> [</span><span
8843 class="cmtt-10"> 0</span><span
8844 class="cmtt-10"> 1</span><span
8845 class="cmtt-10"> 2</span><span
8846 class="cmtt-10"> 3</span><span
8847 class="cmtt-10"> ],</span><span
8848 class="cmtt-10"> [</span><span
8849 class="cmtt-10"> 4</span><span
8850 class="cmtt-10"> 5</span><span
8851 class="cmtt-10"> 6</span><span
8852 class="cmtt-10"> 7</span><span
8853 class="cmtt-10"> ]</span>
8854 <br class="fancyvrb" /><a
8855 id="x1-106014r7"></a><span
8856 class="cmtt-10"> </span><span
8857 class="cmtt-10"> </span>
8858 <br class="fancyvrb" /><a
8859 id="x1-106016r8"></a><span
8860 class="cmtt-10"> </span><span
8861 class="cmtt-10"> codebook</span><span
8862 class="cmtt-10"> dimensions</span><span
8863 class="cmtt-10"> =</span><span
8864 class="cmtt-10"> 2</span><span
8865 class="cmtt-10"> </span><span
8866 class="cmtt-10"> encoded</span><span
8867 class="cmtt-10"> as:</span><span
8868 class="cmtt-10"> [</span><span
8869 class="cmtt-10"> 0</span><span
8870 class="cmtt-10"> 1</span><span
8871 class="cmtt-10"> ],</span><span
8872 class="cmtt-10"> [</span><span
8873 class="cmtt-10"> 2</span><span
8874 class="cmtt-10"> 3</span><span
8875 class="cmtt-10"> ],</span><span
8876 class="cmtt-10"> [</span><span
8877 class="cmtt-10"> 4</span><span
8878 class="cmtt-10"> 5</span><span
8879 class="cmtt-10"> ],</span><span
8880 class="cmtt-10"> [</span><span
8881 class="cmtt-10"> 6</span><span
8882 class="cmtt-10"> 7</span><span
8883 class="cmtt-10"> ]</span>
8884 <br class="fancyvrb" /><a
8885 id="x1-106018r9"></a><span
8886 class="cmtt-10"> </span><span
8887 class="cmtt-10"> </span>
8888 <br class="fancyvrb" /><a
8889 id="x1-106020r10"></a><span
8890 class="cmtt-10"> </span><span
8891 class="cmtt-10"> codebook</span><span
8892 class="cmtt-10"> dimensions</span><span
8893 class="cmtt-10"> =</span><span
8894 class="cmtt-10"> 1</span><span
8895 class="cmtt-10"> </span><span
8896 class="cmtt-10"> encoded</span><span
8897 class="cmtt-10"> as:</span><span
8898 class="cmtt-10"> [</span><span
8899 class="cmtt-10"> 0</span><span
8900 class="cmtt-10"> ],</span><span
8901 class="cmtt-10"> [</span><span
8902 class="cmtt-10"> 1</span><span
8903 class="cmtt-10"> ],</span><span
8904 class="cmtt-10"> [</span><span
8905 class="cmtt-10"> 2</span><span
8906 class="cmtt-10"> ],</span><span
8907 class="cmtt-10"> [</span><span
8908 class="cmtt-10"> 3</span><span
8909 class="cmtt-10"> ],</span><span
8910 class="cmtt-10"> [</span><span
8911 class="cmtt-10"> 4</span><span
8912 class="cmtt-10"> ],</span><span
8913 class="cmtt-10"> [</span><span
8914 class="cmtt-10"> 5</span><span
8915 class="cmtt-10"> ],</span><span
8916 class="cmtt-10"> [</span><span
8917 class="cmtt-10"> 6</span><span
8918 class="cmtt-10"> ],</span><span
8919 class="cmtt-10"> [</span><span
8920 class="cmtt-10"> 7</span><span
8921 class="cmtt-10"> ]</span>
8922 <br class="fancyvrb" /><a
8923 id="x1-106022r11"></a><span
8924 class="cmtt-10"> </span><span
8925 class="cmtt-10"> </span>
8927 <!--l. 137--><p class="noindent" >
8931 <h4 class="subsectionHead"><span class="titlemark">8.5 </span> <a
8932 id="x1-1070008.5"></a>residue 2</h4>
8933 <!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
8934 passed-in vectors as in residue type 1, the <span
8935 class="cmti-10x-x-109">ch </span>passed in vectors of length <span
8936 class="cmti-10x-x-109">n </span>are first interleaved and
8937 flattened into a single vector of length <span
8938 class="cmti-10x-x-109">ch</span>*<span
8939 class="cmti-10x-x-109">n</span>. Encoding then proceeds as in type 1. Decoding is as in
8940 type 1 with decode interleave reversed. If operating on a single vector to begin with, residue type 1
8941 and type 2 are equivalent.
8944 <!--l. 147--><p class="noindent" >
8946 <!--l. 148--><p class="noindent" ><img
8947 src="residue2.png" alt="PIC"
8949 <br /> <table class="caption"
8950 ><tr style="vertical-align:baseline;" class="caption"><td class="id">Figure 12: </td><td
8951 class="content">illustration of residue type 2</td></tr></table><!--tex4ht:label?: x1-10700112 -->
8953 <!--l. 153--><p class="noindent" >
8954 <h4 class="subsectionHead"><span class="titlemark">8.6 </span> <a
8955 id="x1-1080008.6"></a>Residue decode</h4>
8956 <!--l. 155--><p class="noindent" >
8957 <h5 class="subsubsectionHead"><span class="titlemark">8.6.1 </span> <a
8958 id="x1-1090008.6.1"></a>header decode</h5>
8959 <!--l. 157--><p class="noindent" >Header decode for all three residue types is identical.
8960 <div class="fancyvrb" id="fancyvrb35">
8962 id="x1-109002r1"></a><span
8963 class="cmtt-10"> </span><span
8964 class="cmtt-10"> </span><span
8965 class="cmtt-10"> </span><span
8966 class="cmtt-10"> 1)</span><span
8967 class="cmtt-10"> [residue_begin]</span><span
8968 class="cmtt-10"> =</span><span
8969 class="cmtt-10"> read</span><span
8970 class="cmtt-10"> 24</span><span
8971 class="cmtt-10"> bits</span><span
8972 class="cmtt-10"> as</span><span
8973 class="cmtt-10"> unsigned</span><span
8974 class="cmtt-10"> integer</span>
8975 <br class="fancyvrb" /><a
8976 id="x1-109004r2"></a><span
8977 class="cmtt-10"> </span><span
8978 class="cmtt-10"> </span><span
8979 class="cmtt-10"> </span><span
8980 class="cmtt-10"> 2)</span><span
8981 class="cmtt-10"> [residue_end]</span><span
8982 class="cmtt-10"> =</span><span
8983 class="cmtt-10"> read</span><span
8984 class="cmtt-10"> 24</span><span
8985 class="cmtt-10"> bits</span><span
8986 class="cmtt-10"> as</span><span
8987 class="cmtt-10"> unsigned</span><span
8988 class="cmtt-10"> integer</span>
8989 <br class="fancyvrb" /><a
8990 id="x1-109006r3"></a><span
8991 class="cmtt-10"> </span><span
8992 class="cmtt-10"> </span><span
8993 class="cmtt-10"> </span><span
8994 class="cmtt-10"> 3)</span><span
8995 class="cmtt-10"> [residue_partition_size]</span><span
8996 class="cmtt-10"> =</span><span
8997 class="cmtt-10"> read</span><span
8998 class="cmtt-10"> 24</span><span
8999 class="cmtt-10"> bits</span><span
9000 class="cmtt-10"> as</span><span
9001 class="cmtt-10"> unsigned</span><span
9002 class="cmtt-10"> integer</span><span
9003 class="cmtt-10"> and</span><span
9004 class="cmtt-10"> add</span><span
9005 class="cmtt-10"> one</span>
9006 <br class="fancyvrb" /><a
9007 id="x1-109008r4"></a><span
9008 class="cmtt-10"> </span><span
9009 class="cmtt-10"> </span><span
9010 class="cmtt-10"> </span><span
9011 class="cmtt-10"> 4)</span><span
9012 class="cmtt-10"> [residue_classifications]</span><span
9013 class="cmtt-10"> =</span><span
9014 class="cmtt-10"> read</span><span
9015 class="cmtt-10"> 6</span><span
9016 class="cmtt-10"> bits</span><span
9017 class="cmtt-10"> as</span><span
9018 class="cmtt-10"> unsigned</span><span
9019 class="cmtt-10"> integer</span><span
9020 class="cmtt-10"> and</span><span
9021 class="cmtt-10"> add</span><span
9022 class="cmtt-10"> one</span>
9023 <br class="fancyvrb" /><a
9024 id="x1-109010r5"></a><span
9025 class="cmtt-10"> </span><span
9026 class="cmtt-10"> </span><span
9027 class="cmtt-10"> </span><span
9028 class="cmtt-10"> 5)</span><span
9029 class="cmtt-10"> [residue_classbook]</span><span
9030 class="cmtt-10"> =</span><span
9031 class="cmtt-10"> read</span><span
9032 class="cmtt-10"> 8</span><span
9033 class="cmtt-10"> bits</span><span
9034 class="cmtt-10"> as</span><span
9035 class="cmtt-10"> unsigned</span><span
9036 class="cmtt-10"> integer</span>
9038 <!--l. 166--><p class="noindent" ><span
9039 class="cmtt-10x-x-109">[residue_begin] </span>and <span
9040 class="cmtt-10x-x-109">[residue_end] </span>select the specific sub-portion of each vector that is
9041 actually coded; it implements akin to a bandpass where, for coding purposes, the vector
9042 effectively begins at element <span
9043 class="cmtt-10x-x-109">[residue_begin] </span>and ends at <span
9044 class="cmtt-10x-x-109">[residue_end]</span>. Preceding
9045 and following values in the unpacked vectors are zeroed. Note that for residue type 2,
9046 these values as well as <span
9047 class="cmtt-10x-x-109">[residue_partition_size]</span>apply to the interleaved vector, not
9048 the individual vectors before interleave. <span
9049 class="cmtt-10x-x-109">[residue_partition_size] </span>is as explained
9051 class="cmtt-10x-x-109">[residue_classifications] </span>is the number of possible classification to which a
9052 partition can belong and <span
9053 class="cmtt-10x-x-109">[residue_classbook] </span>is the codebook number used to code
9057 classification codewords. The number of dimensions in book <span
9058 class="cmtt-10x-x-109">[residue_classbook] </span>determines
9059 how many classification values are grouped into a single classification codeword. Note
9060 that the number of entries and dimensions in book <span
9061 class="cmtt-10x-x-109">[residue_classbook]</span>, along with
9063 class="cmtt-10x-x-109">[residue_classifications]</span>, overdetermines to possible number of classification
9065 class="cmtt-10x-x-109">[residue_classifications]</span>ˆ<span
9066 class="cmtt-10x-x-109">[residue_classbook]</span>.dimensions exceeds
9068 class="cmtt-10x-x-109">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
9069 <!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
9071 <!--l. 193--><p class="noindent" >
9072 <div class="fancyvrb" id="fancyvrb36">
9074 id="x1-109012r1"></a><span
9075 class="cmtt-10"> </span><span
9076 class="cmtt-10"> </span><span
9077 class="cmtt-10"> </span><span
9078 class="cmtt-10"> 1)</span><span
9079 class="cmtt-10"> iterate</span><span
9080 class="cmtt-10"> [i]</span><span
9081 class="cmtt-10"> over</span><span
9082 class="cmtt-10"> the</span><span
9083 class="cmtt-10"> range</span><span
9084 class="cmtt-10"> 0</span><span
9085 class="cmtt-10"> ...</span><span
9086 class="cmtt-10"> [residue_classifications]-1</span><span
9087 class="cmtt-10"> {</span>
9088 <br class="fancyvrb" /><a
9089 id="x1-109014r2"></a><span
9090 class="cmtt-10"> </span><span
9091 class="cmtt-10"> </span>
9092 <br class="fancyvrb" /><a
9093 id="x1-109016r3"></a><span
9094 class="cmtt-10"> </span><span
9095 class="cmtt-10"> </span><span
9096 class="cmtt-10"> </span><span
9097 class="cmtt-10"> </span><span
9098 class="cmtt-10"> </span><span
9099 class="cmtt-10"> </span><span
9100 class="cmtt-10"> </span><span
9101 class="cmtt-10"> </span><span
9102 class="cmtt-10"> 2)</span><span
9103 class="cmtt-10"> [high_bits]</span><span
9104 class="cmtt-10"> =</span><span
9105 class="cmtt-10"> 0</span>
9106 <br class="fancyvrb" /><a
9107 id="x1-109018r4"></a><span
9108 class="cmtt-10"> </span><span
9109 class="cmtt-10"> </span><span
9110 class="cmtt-10"> </span><span
9111 class="cmtt-10"> </span><span
9112 class="cmtt-10"> </span><span
9113 class="cmtt-10"> </span><span
9114 class="cmtt-10"> </span><span
9115 class="cmtt-10"> </span><span
9116 class="cmtt-10"> 3)</span><span
9117 class="cmtt-10"> [low_bits]</span><span
9118 class="cmtt-10"> =</span><span
9119 class="cmtt-10"> read</span><span
9120 class="cmtt-10"> 3</span><span
9121 class="cmtt-10"> bits</span><span
9122 class="cmtt-10"> as</span><span
9123 class="cmtt-10"> unsigned</span><span
9124 class="cmtt-10"> integer</span>
9125 <br class="fancyvrb" /><a
9126 id="x1-109020r5"></a><span
9127 class="cmtt-10"> </span><span
9128 class="cmtt-10"> </span><span
9129 class="cmtt-10"> </span><span
9130 class="cmtt-10"> </span><span
9131 class="cmtt-10"> </span><span
9132 class="cmtt-10"> </span><span
9133 class="cmtt-10"> </span><span
9134 class="cmtt-10"> </span><span
9135 class="cmtt-10"> 4)</span><span
9136 class="cmtt-10"> [bitflag]</span><span
9137 class="cmtt-10"> =</span><span
9138 class="cmtt-10"> read</span><span
9139 class="cmtt-10"> one</span><span
9140 class="cmtt-10"> bit</span><span
9141 class="cmtt-10"> as</span><span
9142 class="cmtt-10"> boolean</span>
9143 <br class="fancyvrb" /><a
9144 id="x1-109022r6"></a><span
9145 class="cmtt-10"> </span><span
9146 class="cmtt-10"> </span><span
9147 class="cmtt-10"> </span><span
9148 class="cmtt-10"> </span><span
9149 class="cmtt-10"> </span><span
9150 class="cmtt-10"> </span><span
9151 class="cmtt-10"> </span><span
9152 class="cmtt-10"> </span><span
9153 class="cmtt-10"> 5)</span><span
9154 class="cmtt-10"> if</span><span
9155 class="cmtt-10"> (</span><span
9156 class="cmtt-10"> [bitflag]</span><span
9157 class="cmtt-10"> is</span><span
9158 class="cmtt-10"> set</span><span
9159 class="cmtt-10"> )</span><span
9160 class="cmtt-10"> then</span><span
9161 class="cmtt-10"> [high_bits]</span><span
9162 class="cmtt-10"> =</span><span
9163 class="cmtt-10"> read</span><span
9164 class="cmtt-10"> five</span><span
9165 class="cmtt-10"> bits</span><span
9166 class="cmtt-10"> as</span><span
9167 class="cmtt-10"> unsigned</span><span
9168 class="cmtt-10"> integer</span>
9169 <br class="fancyvrb" /><a
9170 id="x1-109024r7"></a><span
9171 class="cmtt-10"> </span><span
9172 class="cmtt-10"> </span><span
9173 class="cmtt-10"> </span><span
9174 class="cmtt-10"> </span><span
9175 class="cmtt-10"> </span><span
9176 class="cmtt-10"> </span><span
9177 class="cmtt-10"> </span><span
9178 class="cmtt-10"> </span><span
9179 class="cmtt-10"> 6)</span><span
9180 class="cmtt-10"> vector</span><span
9181 class="cmtt-10"> [residue_cascade]</span><span
9182 class="cmtt-10"> element</span><span
9183 class="cmtt-10"> [i]</span><span
9184 class="cmtt-10"> =</span><span
9185 class="cmtt-10"> [high_bits]</span><span
9186 class="cmtt-10"> *</span><span
9187 class="cmtt-10"> 8</span><span
9188 class="cmtt-10"> +</span><span
9189 class="cmtt-10"> [low_bits]</span>
9190 <br class="fancyvrb" /><a
9191 id="x1-109026r8"></a><span
9192 class="cmtt-10"> </span><span
9193 class="cmtt-10"> </span><span
9194 class="cmtt-10"> </span><span
9195 class="cmtt-10"> </span><span
9196 class="cmtt-10"> </span><span
9197 class="cmtt-10"> </span><span
9198 class="cmtt-10"> }</span>
9199 <br class="fancyvrb" /><a
9200 id="x1-109028r9"></a><span
9201 class="cmtt-10"> </span><span
9202 class="cmtt-10"> </span><span
9203 class="cmtt-10"> </span><span
9204 class="cmtt-10"> 7)</span><span
9205 class="cmtt-10"> done</span>
9207 <!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
9208 bitmap. We loop over the possible codebook classifications and the maximum possible number of
9209 encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
9211 <!--l. 211--><p class="noindent" >
9212 <div class="fancyvrb" id="fancyvrb37">
9214 id="x1-109030r1"></a><span
9215 class="cmtt-10"> </span><span
9216 class="cmtt-10"> </span><span
9217 class="cmtt-10"> </span><span
9218 class="cmtt-10"> 1)</span><span
9219 class="cmtt-10"> iterate</span><span
9220 class="cmtt-10"> [i]</span><span
9221 class="cmtt-10"> over</span><span
9222 class="cmtt-10"> the</span><span
9223 class="cmtt-10"> range</span><span
9224 class="cmtt-10"> 0</span><span
9225 class="cmtt-10"> ...</span><span
9226 class="cmtt-10"> [residue_classifications]-1</span><span
9227 class="cmtt-10"> {</span>
9228 <br class="fancyvrb" /><a
9229 id="x1-109032r2"></a><span
9230 class="cmtt-10"> </span><span
9231 class="cmtt-10"> </span>
9232 <br class="fancyvrb" /><a
9233 id="x1-109034r3"></a><span
9234 class="cmtt-10"> </span><span
9235 class="cmtt-10"> </span><span
9236 class="cmtt-10"> </span><span
9237 class="cmtt-10"> </span><span
9238 class="cmtt-10"> </span><span
9239 class="cmtt-10"> </span><span
9240 class="cmtt-10"> </span><span
9241 class="cmtt-10"> </span><span
9242 class="cmtt-10"> 2)</span><span
9243 class="cmtt-10"> iterate</span><span
9244 class="cmtt-10"> [j]</span><span
9245 class="cmtt-10"> over</span><span
9246 class="cmtt-10"> the</span><span
9247 class="cmtt-10"> range</span><span
9248 class="cmtt-10"> 0</span><span
9249 class="cmtt-10"> ...</span><span
9250 class="cmtt-10"> 7</span><span
9251 class="cmtt-10"> {</span>
9252 <br class="fancyvrb" /><a
9253 id="x1-109036r4"></a><span
9254 class="cmtt-10"> </span><span
9255 class="cmtt-10"> </span>
9256 <br class="fancyvrb" /><a
9257 id="x1-109038r5"></a><span
9258 class="cmtt-10"> </span><span
9259 class="cmtt-10"> </span><span
9260 class="cmtt-10"> </span><span
9261 class="cmtt-10"> </span><span
9262 class="cmtt-10"> </span><span
9263 class="cmtt-10"> </span><span
9264 class="cmtt-10"> </span><span
9265 class="cmtt-10"> </span><span
9266 class="cmtt-10"> </span><span
9267 class="cmtt-10"> </span><span
9268 class="cmtt-10"> </span><span
9269 class="cmtt-10"> </span><span
9270 class="cmtt-10"> </span><span
9271 class="cmtt-10"> 3)</span><span
9272 class="cmtt-10"> if</span><span
9273 class="cmtt-10"> (</span><span
9274 class="cmtt-10"> vector</span><span
9275 class="cmtt-10"> [residue_cascade]</span><span
9276 class="cmtt-10"> element</span><span
9277 class="cmtt-10"> [i]</span><span
9278 class="cmtt-10"> bit</span><span
9279 class="cmtt-10"> [j]</span><span
9280 class="cmtt-10"> is</span><span
9281 class="cmtt-10"> set</span><span
9282 class="cmtt-10"> )</span><span
9283 class="cmtt-10"> {</span>
9284 <br class="fancyvrb" /><a
9285 id="x1-109040r6"></a><span
9286 class="cmtt-10"> </span><span
9287 class="cmtt-10"> </span>
9288 <br class="fancyvrb" /><a
9289 id="x1-109042r7"></a><span
9290 class="cmtt-10"> </span><span
9291 class="cmtt-10"> </span><span
9292 class="cmtt-10"> </span><span
9293 class="cmtt-10"> </span><span
9294 class="cmtt-10"> </span><span
9295 class="cmtt-10"> </span><span
9296 class="cmtt-10"> </span><span
9297 class="cmtt-10"> </span><span
9298 class="cmtt-10"> </span><span
9299 class="cmtt-10"> </span><span
9300 class="cmtt-10"> </span><span
9301 class="cmtt-10"> </span><span
9302 class="cmtt-10"> </span><span
9303 class="cmtt-10"> </span><span
9304 class="cmtt-10"> </span><span
9305 class="cmtt-10"> </span><span
9306 class="cmtt-10"> </span><span
9307 class="cmtt-10"> </span><span
9308 class="cmtt-10"> 4)</span><span
9309 class="cmtt-10"> array</span><span
9310 class="cmtt-10"> [residue_books]</span><span
9311 class="cmtt-10"> element</span><span
9312 class="cmtt-10"> [i][j]</span><span
9313 class="cmtt-10"> =</span><span
9314 class="cmtt-10"> read</span><span
9315 class="cmtt-10"> 8</span><span
9316 class="cmtt-10"> bits</span><span
9317 class="cmtt-10"> as</span><span
9318 class="cmtt-10"> unsigned</span><span
9319 class="cmtt-10"> integer</span>
9320 <br class="fancyvrb" /><a
9321 id="x1-109044r8"></a><span
9322 class="cmtt-10"> </span><span
9323 class="cmtt-10"> </span>
9324 <br class="fancyvrb" /><a
9325 id="x1-109046r9"></a><span
9326 class="cmtt-10"> </span><span
9327 class="cmtt-10"> </span><span
9328 class="cmtt-10"> </span><span
9329 class="cmtt-10"> </span><span
9330 class="cmtt-10"> </span><span
9331 class="cmtt-10"> </span><span
9332 class="cmtt-10"> </span><span
9333 class="cmtt-10"> </span><span
9334 class="cmtt-10"> </span><span
9335 class="cmtt-10"> </span><span
9336 class="cmtt-10"> </span><span
9337 class="cmtt-10"> </span><span
9338 class="cmtt-10"> </span><span
9339 class="cmtt-10"> </span><span
9340 class="cmtt-10"> </span><span
9341 class="cmtt-10"> </span><span
9342 class="cmtt-10"> }</span><span
9343 class="cmtt-10"> else</span><span
9344 class="cmtt-10"> {</span>
9345 <br class="fancyvrb" /><a
9346 id="x1-109048r10"></a><span
9347 class="cmtt-10"> </span><span
9348 class="cmtt-10"> </span>
9349 <br class="fancyvrb" /><a
9350 id="x1-109050r11"></a><span
9351 class="cmtt-10"> </span><span
9352 class="cmtt-10"> </span><span
9353 class="cmtt-10"> </span><span
9354 class="cmtt-10"> </span><span
9355 class="cmtt-10"> </span><span
9356 class="cmtt-10"> </span><span
9357 class="cmtt-10"> </span><span
9358 class="cmtt-10"> </span><span
9359 class="cmtt-10"> </span><span
9360 class="cmtt-10"> </span><span
9361 class="cmtt-10"> </span><span
9362 class="cmtt-10"> </span><span
9363 class="cmtt-10"> </span><span
9364 class="cmtt-10"> </span><span
9365 class="cmtt-10"> </span><span
9366 class="cmtt-10"> </span><span
9367 class="cmtt-10"> </span><span
9368 class="cmtt-10"> </span><span
9369 class="cmtt-10"> 5)</span><span
9370 class="cmtt-10"> array</span><span
9371 class="cmtt-10"> [residue_books]</span><span
9372 class="cmtt-10"> element</span><span
9373 class="cmtt-10"> [i][j]</span><span
9374 class="cmtt-10"> =</span><span
9375 class="cmtt-10"> unused</span>
9376 <br class="fancyvrb" /><a
9377 id="x1-109052r12"></a><span
9378 class="cmtt-10"> </span><span
9379 class="cmtt-10"> </span>
9380 <br class="fancyvrb" /><a
9381 id="x1-109054r13"></a><span
9382 class="cmtt-10"> </span><span
9383 class="cmtt-10"> </span><span
9384 class="cmtt-10"> </span><span
9385 class="cmtt-10"> </span><span
9386 class="cmtt-10"> </span><span
9387 class="cmtt-10"> </span><span
9388 class="cmtt-10"> </span><span
9389 class="cmtt-10"> </span><span
9390 class="cmtt-10"> </span><span
9391 class="cmtt-10"> </span><span
9392 class="cmtt-10"> </span><span
9393 class="cmtt-10"> </span><span
9394 class="cmtt-10"> </span><span
9395 class="cmtt-10"> </span><span
9396 class="cmtt-10"> </span><span
9397 class="cmtt-10"> </span><span
9398 class="cmtt-10"> }</span>
9399 <br class="fancyvrb" /><a
9400 id="x1-109056r14"></a><span
9401 class="cmtt-10"> </span><span
9402 class="cmtt-10"> </span><span
9403 class="cmtt-10"> </span><span
9404 class="cmtt-10"> </span><span
9405 class="cmtt-10"> </span><span
9406 class="cmtt-10"> </span><span
9407 class="cmtt-10"> </span><span
9408 class="cmtt-10"> </span><span
9409 class="cmtt-10"> </span><span
9410 class="cmtt-10"> </span><span
9411 class="cmtt-10"> </span><span
9412 class="cmtt-10"> }</span>
9413 <br class="fancyvrb" /><a
9414 id="x1-109058r15"></a><span
9415 class="cmtt-10"> </span><span
9416 class="cmtt-10"> </span><span
9417 class="cmtt-10"> </span><span
9418 class="cmtt-10"> </span><span
9419 class="cmtt-10"> </span><span
9420 class="cmtt-10"> </span><span
9421 class="cmtt-10"> </span><span
9422 class="cmtt-10"> }</span>
9423 <br class="fancyvrb" /><a
9424 id="x1-109060r16"></a><span
9425 class="cmtt-10"> </span><span
9426 class="cmtt-10"> </span>
9427 <br class="fancyvrb" /><a
9428 id="x1-109062r17"></a><span
9429 class="cmtt-10"> </span><span
9430 class="cmtt-10"> </span><span
9431 class="cmtt-10"> </span><span
9432 class="cmtt-10"> 6)</span><span
9433 class="cmtt-10"> done</span>
9435 <!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable. In
9439 addition, any codebook number greater than the maximum numbered codebook set up in this
9440 stream also renders the stream undecodable.
9441 <!--l. 238--><p class="noindent" >
9442 <h5 class="subsubsectionHead"><span class="titlemark">8.6.2 </span> <a
9443 id="x1-1100008.6.2"></a>packet decode</h5>
9444 <!--l. 240--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
9445 decode can be built out of the format 1 decode process. Thus we describe first the decode
9446 infrastructure identical to all three formats.
9447 <!--l. 245--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of vectors
9448 in the submap bundle and a vector of flags indicating if any of the vectors are not to be decoded. If
9449 the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’, decode skips
9450 vector 1 during the decode loop. However, even ’do not decode’ vectors are allocated and
9452 <!--l. 252--><p class="noindent" >Depending on the values of <span
9453 class="cmtt-10x-x-109">[residue_begin] </span>and <span
9454 class="cmtt-10x-x-109">[residue_end]</span>, it is obvious that the encoded
9455 portion of a residue vector may be the entire possible residue vector or some other strict subset of
9456 the actual residue vector size with zero padding at either uncoded end. However, it is also
9457 possible to set <span
9458 class="cmtt-10x-x-109">[residue_begin] </span>and <span
9459 class="cmtt-10x-x-109">[residue_end] </span>to specify a range partially or wholly
9460 beyond the maximum vector size. Before beginning residue decode, limit <span
9461 class="cmtt-10x-x-109">[residue_begin]</span>
9463 class="cmtt-10x-x-109">[residue_end] </span>to the maximum possible vector size as follows. We assume that
9464 the number of vectors being encoded, <span
9465 class="cmtt-10x-x-109">[ch] </span>is provided by the higher level decoding
9467 <!--l. 266--><p class="noindent" >
9468 <div class="fancyvrb" id="fancyvrb38">
9470 id="x1-110002r1"></a><span
9471 class="cmtt-10"> </span><span
9472 class="cmtt-10"> </span><span
9473 class="cmtt-10"> </span><span
9474 class="cmtt-10"> 1)</span><span
9475 class="cmtt-10"> [actual_size]</span><span
9476 class="cmtt-10"> =</span><span
9477 class="cmtt-10"> current</span><span
9478 class="cmtt-10"> blocksize/2;</span>
9479 <br class="fancyvrb" /><a
9480 id="x1-110004r2"></a><span
9481 class="cmtt-10"> </span><span
9482 class="cmtt-10"> </span><span
9483 class="cmtt-10"> </span><span
9484 class="cmtt-10"> 2)</span><span
9485 class="cmtt-10"> if</span><span
9486 class="cmtt-10"> residue</span><span
9487 class="cmtt-10"> encoding</span><span
9488 class="cmtt-10"> is</span><span
9489 class="cmtt-10"> format</span><span
9490 class="cmtt-10"> 2</span>
9491 <br class="fancyvrb" /><a
9492 id="x1-110006r3"></a><span
9493 class="cmtt-10"> </span><span
9494 class="cmtt-10"> </span><span
9495 class="cmtt-10"> </span><span
9496 class="cmtt-10"> </span><span
9497 class="cmtt-10"> </span><span
9498 class="cmtt-10"> </span><span
9499 class="cmtt-10"> </span><span
9500 class="cmtt-10"> </span><span
9501 class="cmtt-10"> 3)</span><span
9502 class="cmtt-10"> [actual_size]</span><span
9503 class="cmtt-10"> =</span><span
9504 class="cmtt-10"> [actual_size]</span><span
9505 class="cmtt-10"> *</span><span
9506 class="cmtt-10"> [ch];</span>
9507 <br class="fancyvrb" /><a
9508 id="x1-110008r4"></a><span
9509 class="cmtt-10"> </span><span
9510 class="cmtt-10"> </span><span
9511 class="cmtt-10"> </span><span
9512 class="cmtt-10"> 4)</span><span
9513 class="cmtt-10"> [limit_residue_begin]</span><span
9514 class="cmtt-10"> =</span><span
9515 class="cmtt-10"> maximum</span><span
9516 class="cmtt-10"> of</span><span
9517 class="cmtt-10"> ([residue_begin],[actual_size]);</span>
9518 <br class="fancyvrb" /><a
9519 id="x1-110010r5"></a><span
9520 class="cmtt-10"> </span><span
9521 class="cmtt-10"> </span><span
9522 class="cmtt-10"> </span><span
9523 class="cmtt-10"> 5)</span><span
9524 class="cmtt-10"> [limit_residue_end]</span><span
9525 class="cmtt-10"> =</span><span
9526 class="cmtt-10"> maximum</span><span
9527 class="cmtt-10"> of</span><span
9528 class="cmtt-10"> ([residue_end],[actual_size]);</span>
9530 <!--l. 274--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
9531 <!--l. 277--><p class="noindent" >
9532 <div class="fancyvrb" id="fancyvrb39">
9534 id="x1-110012r1"></a><span
9535 class="cmtt-10"> </span><span
9536 class="cmtt-10"> </span><span
9537 class="cmtt-10"> </span><span
9538 class="cmtt-10"> 1)</span><span
9539 class="cmtt-10"> [classwords_per_codeword]</span><span
9540 class="cmtt-10"> =</span><span
9541 class="cmtt-10"> [codebook_dimensions]</span><span
9542 class="cmtt-10"> value</span><span
9543 class="cmtt-10"> of</span><span
9544 class="cmtt-10"> codebook</span><span
9545 class="cmtt-10"> [residue_classbook]</span>
9546 <br class="fancyvrb" /><a
9547 id="x1-110014r2"></a><span
9548 class="cmtt-10"> </span><span
9549 class="cmtt-10"> </span><span
9550 class="cmtt-10"> </span><span
9551 class="cmtt-10"> 2)</span><span
9552 class="cmtt-10"> [n_to_read]</span><span
9553 class="cmtt-10"> =</span><span
9554 class="cmtt-10"> [limit_residue_end]</span><span
9555 class="cmtt-10"> -</span><span
9556 class="cmtt-10"> [limit_residue_begin]</span>
9557 <br class="fancyvrb" /><a
9558 id="x1-110016r3"></a><span
9559 class="cmtt-10"> </span><span
9560 class="cmtt-10"> </span><span
9561 class="cmtt-10"> </span><span
9562 class="cmtt-10"> 3)</span><span
9563 class="cmtt-10"> [partitions_to_read]</span><span
9564 class="cmtt-10"> =</span><span
9565 class="cmtt-10"> [n_to_read]</span><span
9566 class="cmtt-10"> /</span><span
9567 class="cmtt-10"> [residue_partition_size]</span>
9569 <!--l. 283--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
9573 <div class="fancyvrb" id="fancyvrb40">
9575 id="x1-110018r1"></a><span
9576 class="cmtt-10"> </span><span
9577 class="cmtt-10"> </span><span
9578 class="cmtt-10"> </span><span
9579 class="cmtt-10"> 1)</span><span
9580 class="cmtt-10"> allocate</span><span
9581 class="cmtt-10"> and</span><span
9582 class="cmtt-10"> zero</span><span
9583 class="cmtt-10"> all</span><span
9584 class="cmtt-10"> vectors</span><span
9585 class="cmtt-10"> that</span><span
9586 class="cmtt-10"> will</span><span
9587 class="cmtt-10"> be</span><span
9588 class="cmtt-10"> returned.</span>
9589 <br class="fancyvrb" /><a
9590 id="x1-110020r2"></a><span
9591 class="cmtt-10"> </span><span
9592 class="cmtt-10"> </span><span
9593 class="cmtt-10"> </span><span
9594 class="cmtt-10"> 2)</span><span
9595 class="cmtt-10"> if</span><span
9596 class="cmtt-10"> ([n_to_read]</span><span
9597 class="cmtt-10"> is</span><span
9598 class="cmtt-10"> zero),</span><span
9599 class="cmtt-10"> stop;</span><span
9600 class="cmtt-10"> there</span><span
9601 class="cmtt-10"> is</span><span
9602 class="cmtt-10"> no</span><span
9603 class="cmtt-10"> residue</span><span
9604 class="cmtt-10"> to</span><span
9605 class="cmtt-10"> decode.</span>
9606 <br class="fancyvrb" /><a
9607 id="x1-110022r3"></a><span
9608 class="cmtt-10"> </span><span
9609 class="cmtt-10"> </span><span
9610 class="cmtt-10"> </span><span
9611 class="cmtt-10"> 3)</span><span
9612 class="cmtt-10"> iterate</span><span
9613 class="cmtt-10"> [pass]</span><span
9614 class="cmtt-10"> over</span><span
9615 class="cmtt-10"> the</span><span
9616 class="cmtt-10"> range</span><span
9617 class="cmtt-10"> 0</span><span
9618 class="cmtt-10"> ...</span><span
9619 class="cmtt-10"> 7</span><span
9620 class="cmtt-10"> {</span>
9621 <br class="fancyvrb" /><a
9622 id="x1-110024r4"></a><span
9623 class="cmtt-10"> </span><span
9624 class="cmtt-10"> </span>
9625 <br class="fancyvrb" /><a
9626 id="x1-110026r5"></a><span
9627 class="cmtt-10"> </span><span
9628 class="cmtt-10"> </span><span
9629 class="cmtt-10"> </span><span
9630 class="cmtt-10"> </span><span
9631 class="cmtt-10"> </span><span
9632 class="cmtt-10"> </span><span
9633 class="cmtt-10"> </span><span
9634 class="cmtt-10"> </span><span
9635 class="cmtt-10"> 4)</span><span
9636 class="cmtt-10"> [partition_count]</span><span
9637 class="cmtt-10"> =</span><span
9638 class="cmtt-10"> 0</span>
9639 <br class="fancyvrb" /><a
9640 id="x1-110028r6"></a><span
9641 class="cmtt-10"> </span><span
9642 class="cmtt-10"> </span>
9643 <br class="fancyvrb" /><a
9644 id="x1-110030r7"></a><span
9645 class="cmtt-10"> </span><span
9646 class="cmtt-10"> </span><span
9647 class="cmtt-10"> </span><span
9648 class="cmtt-10"> </span><span
9649 class="cmtt-10"> </span><span
9650 class="cmtt-10"> </span><span
9651 class="cmtt-10"> </span><span
9652 class="cmtt-10"> </span><span
9653 class="cmtt-10"> 5)</span><span
9654 class="cmtt-10"> while</span><span
9655 class="cmtt-10"> [partition_count]</span><span
9656 class="cmtt-10"> is</span><span
9657 class="cmtt-10"> less</span><span
9658 class="cmtt-10"> than</span><span
9659 class="cmtt-10"> [partitions_to_read]</span>
9660 <br class="fancyvrb" /><a
9661 id="x1-110032r8"></a><span
9662 class="cmtt-10"> </span><span
9663 class="cmtt-10"> </span>
9664 <br class="fancyvrb" /><a
9665 id="x1-110034r9"></a><span
9666 class="cmtt-10"> </span><span
9667 class="cmtt-10"> </span><span
9668 class="cmtt-10"> </span><span
9669 class="cmtt-10"> </span><span
9670 class="cmtt-10"> </span><span
9671 class="cmtt-10"> </span><span
9672 class="cmtt-10"> </span><span
9673 class="cmtt-10"> </span><span
9674 class="cmtt-10"> </span><span
9675 class="cmtt-10"> </span><span
9676 class="cmtt-10"> </span><span
9677 class="cmtt-10"> </span><span
9678 class="cmtt-10"> </span><span
9679 class="cmtt-10"> 6)</span><span
9680 class="cmtt-10"> if</span><span
9681 class="cmtt-10"> ([pass]</span><span
9682 class="cmtt-10"> is</span><span
9683 class="cmtt-10"> zero)</span><span
9684 class="cmtt-10"> {</span>
9685 <br class="fancyvrb" /><a
9686 id="x1-110036r10"></a><span
9687 class="cmtt-10"> </span><span
9688 class="cmtt-10"> </span>
9689 <br class="fancyvrb" /><a
9690 id="x1-110038r11"></a><span
9691 class="cmtt-10"> </span><span
9692 class="cmtt-10"> </span><span
9693 class="cmtt-10"> </span><span
9694 class="cmtt-10"> </span><span
9695 class="cmtt-10"> </span><span
9696 class="cmtt-10"> </span><span
9697 class="cmtt-10"> </span><span
9698 class="cmtt-10"> </span><span
9699 class="cmtt-10"> </span><span
9700 class="cmtt-10"> </span><span
9701 class="cmtt-10"> </span><span
9702 class="cmtt-10"> </span><span
9703 class="cmtt-10"> </span><span
9704 class="cmtt-10"> </span><span
9705 class="cmtt-10"> </span><span
9706 class="cmtt-10"> </span><span
9707 class="cmtt-10"> </span><span
9708 class="cmtt-10"> </span><span
9709 class="cmtt-10"> 7)</span><span
9710 class="cmtt-10"> iterate</span><span
9711 class="cmtt-10"> [j]</span><span
9712 class="cmtt-10"> over</span><span
9713 class="cmtt-10"> the</span><span
9714 class="cmtt-10"> range</span><span
9715 class="cmtt-10"> 0</span><span
9716 class="cmtt-10"> ..</span><span
9717 class="cmtt-10"> [ch]-1</span><span
9718 class="cmtt-10"> {</span>
9719 <br class="fancyvrb" /><a
9720 id="x1-110040r12"></a><span
9721 class="cmtt-10"> </span><span
9722 class="cmtt-10"> </span>
9723 <br class="fancyvrb" /><a
9724 id="x1-110042r13"></a><span
9725 class="cmtt-10"> </span><span
9726 class="cmtt-10"> </span><span
9727 class="cmtt-10"> </span><span
9728 class="cmtt-10"> </span><span
9729 class="cmtt-10"> </span><span
9730 class="cmtt-10"> </span><span
9731 class="cmtt-10"> </span><span
9732 class="cmtt-10"> </span><span
9733 class="cmtt-10"> </span><span
9734 class="cmtt-10"> </span><span
9735 class="cmtt-10"> </span><span
9736 class="cmtt-10"> </span><span
9737 class="cmtt-10"> </span><span
9738 class="cmtt-10"> </span><span
9739 class="cmtt-10"> </span><span
9740 class="cmtt-10"> </span><span
9741 class="cmtt-10"> </span><span
9742 class="cmtt-10"> </span><span
9743 class="cmtt-10"> </span><span
9744 class="cmtt-10"> </span><span
9745 class="cmtt-10"> </span><span
9746 class="cmtt-10"> </span><span
9747 class="cmtt-10"> </span><span
9748 class="cmtt-10"> 8)</span><span
9749 class="cmtt-10"> if</span><span
9750 class="cmtt-10"> vector</span><span
9751 class="cmtt-10"> [j]</span><span
9752 class="cmtt-10"> is</span><span
9753 class="cmtt-10"> not</span><span
9754 class="cmtt-10"> marked</span><span
9755 class="cmtt-10"> ’do</span><span
9756 class="cmtt-10"> not</span><span
9757 class="cmtt-10"> decode’</span><span
9758 class="cmtt-10"> {</span>
9759 <br class="fancyvrb" /><a
9760 id="x1-110044r14"></a><span
9761 class="cmtt-10"> </span><span
9762 class="cmtt-10"> </span>
9763 <br class="fancyvrb" /><a
9764 id="x1-110046r15"></a><span
9765 class="cmtt-10"> </span><span
9766 class="cmtt-10"> </span><span
9767 class="cmtt-10"> </span><span
9768 class="cmtt-10"> </span><span
9769 class="cmtt-10"> </span><span
9770 class="cmtt-10"> </span><span
9771 class="cmtt-10"> </span><span
9772 class="cmtt-10"> </span><span
9773 class="cmtt-10"> </span><span
9774 class="cmtt-10"> </span><span
9775 class="cmtt-10"> </span><span
9776 class="cmtt-10"> </span><span
9777 class="cmtt-10"> </span><span
9778 class="cmtt-10"> </span><span
9779 class="cmtt-10"> </span><span
9780 class="cmtt-10"> </span><span
9781 class="cmtt-10"> </span><span
9782 class="cmtt-10"> </span><span
9783 class="cmtt-10"> </span><span
9784 class="cmtt-10"> </span><span
9785 class="cmtt-10"> </span><span
9786 class="cmtt-10"> </span><span
9787 class="cmtt-10"> </span><span
9788 class="cmtt-10"> </span><span
9789 class="cmtt-10"> </span><span
9790 class="cmtt-10"> </span><span
9791 class="cmtt-10"> </span><span
9792 class="cmtt-10"> </span><span
9793 class="cmtt-10"> 9)</span><span
9794 class="cmtt-10"> [temp]</span><span
9795 class="cmtt-10"> =</span><span
9796 class="cmtt-10"> read</span><span
9797 class="cmtt-10"> from</span><span
9798 class="cmtt-10"> packet</span><span
9799 class="cmtt-10"> using</span><span
9800 class="cmtt-10"> codebook</span><span
9801 class="cmtt-10"> [residue_classbook]</span><span
9802 class="cmtt-10"> in</span><span
9803 class="cmtt-10"> scalar</span><span
9804 class="cmtt-10"> context</span>
9805 <br class="fancyvrb" /><a
9806 id="x1-110048r16"></a><span
9807 class="cmtt-10"> </span><span
9808 class="cmtt-10"> </span><span
9809 class="cmtt-10"> </span><span
9810 class="cmtt-10"> </span><span
9811 class="cmtt-10"> </span><span
9812 class="cmtt-10"> </span><span
9813 class="cmtt-10"> </span><span
9814 class="cmtt-10"> </span><span
9815 class="cmtt-10"> </span><span
9816 class="cmtt-10"> </span><span
9817 class="cmtt-10"> </span><span
9818 class="cmtt-10"> </span><span
9819 class="cmtt-10"> </span><span
9820 class="cmtt-10"> </span><span
9821 class="cmtt-10"> </span><span
9822 class="cmtt-10"> </span><span
9823 class="cmtt-10"> </span><span
9824 class="cmtt-10"> </span><span
9825 class="cmtt-10"> </span><span
9826 class="cmtt-10"> </span><span
9827 class="cmtt-10"> </span><span
9828 class="cmtt-10"> </span><span
9829 class="cmtt-10"> </span><span
9830 class="cmtt-10"> </span><span
9831 class="cmtt-10"> </span><span
9832 class="cmtt-10"> </span><span
9833 class="cmtt-10"> </span><span
9834 class="cmtt-10"> 10)</span><span
9835 class="cmtt-10"> iterate</span><span
9836 class="cmtt-10"> [i]</span><span
9837 class="cmtt-10"> descending</span><span
9838 class="cmtt-10"> over</span><span
9839 class="cmtt-10"> the</span><span
9840 class="cmtt-10"> range</span><span
9841 class="cmtt-10"> [classwords_per_codeword]-1</span><span
9842 class="cmtt-10"> ...</span><span
9843 class="cmtt-10"> 0</span><span
9844 class="cmtt-10"> {</span>
9845 <br class="fancyvrb" /><a
9846 id="x1-110050r17"></a><span
9847 class="cmtt-10"> </span><span
9848 class="cmtt-10"> </span>
9849 <br class="fancyvrb" /><a
9850 id="x1-110052r18"></a><span
9851 class="cmtt-10"> </span><span
9852 class="cmtt-10"> </span><span
9853 class="cmtt-10"> </span><span
9854 class="cmtt-10"> </span><span
9855 class="cmtt-10"> </span><span
9856 class="cmtt-10"> </span><span
9857 class="cmtt-10"> </span><span
9858 class="cmtt-10"> </span><span
9859 class="cmtt-10"> </span><span
9860 class="cmtt-10"> </span><span
9861 class="cmtt-10"> </span><span
9862 class="cmtt-10"> </span><span
9863 class="cmtt-10"> </span><span
9864 class="cmtt-10"> </span><span
9865 class="cmtt-10"> </span><span
9866 class="cmtt-10"> </span><span
9867 class="cmtt-10"> </span><span
9868 class="cmtt-10"> </span><span
9869 class="cmtt-10"> </span><span
9870 class="cmtt-10"> </span><span
9871 class="cmtt-10"> </span><span
9872 class="cmtt-10"> </span><span
9873 class="cmtt-10"> </span><span
9874 class="cmtt-10"> </span><span
9875 class="cmtt-10"> </span><span
9876 class="cmtt-10"> </span><span
9877 class="cmtt-10"> </span><span
9878 class="cmtt-10"> </span><span
9879 class="cmtt-10"> </span><span
9880 class="cmtt-10"> </span><span
9881 class="cmtt-10"> </span><span
9882 class="cmtt-10"> </span><span
9883 class="cmtt-10"> 11)</span><span
9884 class="cmtt-10"> array</span><span
9885 class="cmtt-10"> [classifications]</span><span
9886 class="cmtt-10"> element</span><span
9887 class="cmtt-10"> [j],([i]+[partition_count])</span><span
9888 class="cmtt-10"> =</span>
9889 <br class="fancyvrb" /><a
9890 id="x1-110054r19"></a><span
9891 class="cmtt-10"> </span><span
9892 class="cmtt-10"> </span><span
9893 class="cmtt-10"> </span><span
9894 class="cmtt-10"> </span><span
9895 class="cmtt-10"> </span><span
9896 class="cmtt-10"> </span><span
9897 class="cmtt-10"> </span><span
9898 class="cmtt-10"> </span><span
9899 class="cmtt-10"> </span><span
9900 class="cmtt-10"> </span><span
9901 class="cmtt-10"> </span><span
9902 class="cmtt-10"> </span><span
9903 class="cmtt-10"> </span><span
9904 class="cmtt-10"> </span><span
9905 class="cmtt-10"> </span><span
9906 class="cmtt-10"> </span><span
9907 class="cmtt-10"> </span><span
9908 class="cmtt-10"> </span><span
9909 class="cmtt-10"> </span><span
9910 class="cmtt-10"> </span><span
9911 class="cmtt-10"> </span><span
9912 class="cmtt-10"> </span><span
9913 class="cmtt-10"> </span><span
9914 class="cmtt-10"> </span><span
9915 class="cmtt-10"> </span><span
9916 class="cmtt-10"> </span><span
9917 class="cmtt-10"> </span><span
9918 class="cmtt-10"> </span><span
9919 class="cmtt-10"> </span><span
9920 class="cmtt-10"> </span><span
9921 class="cmtt-10"> </span><span
9922 class="cmtt-10"> </span><span
9923 class="cmtt-10"> </span><span
9924 class="cmtt-10"> </span><span
9925 class="cmtt-10"> </span><span
9926 class="cmtt-10"> </span><span
9927 class="cmtt-10"> [temp]</span><span
9928 class="cmtt-10"> integer</span><span
9929 class="cmtt-10"> modulo</span><span
9930 class="cmtt-10"> [residue_classifications]</span>
9931 <br class="fancyvrb" /><a
9932 id="x1-110056r20"></a><span
9933 class="cmtt-10"> </span><span
9934 class="cmtt-10"> </span><span
9935 class="cmtt-10"> </span><span
9936 class="cmtt-10"> </span><span
9937 class="cmtt-10"> </span><span
9938 class="cmtt-10"> </span><span
9939 class="cmtt-10"> </span><span
9940 class="cmtt-10"> </span><span
9941 class="cmtt-10"> </span><span
9942 class="cmtt-10"> </span><span
9943 class="cmtt-10"> </span><span
9944 class="cmtt-10"> </span><span
9945 class="cmtt-10"> </span><span
9946 class="cmtt-10"> </span><span
9947 class="cmtt-10"> </span><span
9948 class="cmtt-10"> </span><span
9949 class="cmtt-10"> </span><span
9950 class="cmtt-10"> </span><span
9951 class="cmtt-10"> </span><span
9952 class="cmtt-10"> </span><span
9953 class="cmtt-10"> </span><span
9954 class="cmtt-10"> </span><span
9955 class="cmtt-10"> </span><span
9956 class="cmtt-10"> </span><span
9957 class="cmtt-10"> </span><span
9958 class="cmtt-10"> </span><span
9959 class="cmtt-10"> </span><span
9960 class="cmtt-10"> </span><span
9961 class="cmtt-10"> </span><span
9962 class="cmtt-10"> </span><span
9963 class="cmtt-10"> </span><span
9964 class="cmtt-10"> </span><span
9965 class="cmtt-10"> 12)</span><span
9966 class="cmtt-10"> [temp]</span><span
9967 class="cmtt-10"> =</span><span
9968 class="cmtt-10"> [temp]</span><span
9969 class="cmtt-10"> /</span><span
9970 class="cmtt-10"> [residue_classifications]</span><span
9971 class="cmtt-10"> using</span><span
9972 class="cmtt-10"> integer</span><span
9973 class="cmtt-10"> division</span>
9974 <br class="fancyvrb" /><a
9975 id="x1-110058r21"></a><span
9976 class="cmtt-10"> </span><span
9977 class="cmtt-10"> </span>
9978 <br class="fancyvrb" /><a
9979 id="x1-110060r22"></a><span
9980 class="cmtt-10"> </span><span
9981 class="cmtt-10"> </span><span
9982 class="cmtt-10"> </span><span
9983 class="cmtt-10"> </span><span
9984 class="cmtt-10"> </span><span
9985 class="cmtt-10"> </span><span
9986 class="cmtt-10"> </span><span
9987 class="cmtt-10"> </span><span
9988 class="cmtt-10"> </span><span
9989 class="cmtt-10"> </span><span
9990 class="cmtt-10"> </span><span
9991 class="cmtt-10"> </span><span
9992 class="cmtt-10"> </span><span
9993 class="cmtt-10"> </span><span
9994 class="cmtt-10"> </span><span
9995 class="cmtt-10"> </span><span
9996 class="cmtt-10"> </span><span
9997 class="cmtt-10"> </span><span
9998 class="cmtt-10"> </span><span
9999 class="cmtt-10"> </span><span
10000 class="cmtt-10"> </span><span
10001 class="cmtt-10"> </span><span
10002 class="cmtt-10"> </span><span
10003 class="cmtt-10"> </span><span
10004 class="cmtt-10"> </span><span
10005 class="cmtt-10"> </span><span
10006 class="cmtt-10"> </span><span
10007 class="cmtt-10"> </span><span
10008 class="cmtt-10"> </span><span
10009 class="cmtt-10"> </span><span
10010 class="cmtt-10"> </span><span
10011 class="cmtt-10"> }</span>
10012 <br class="fancyvrb" /><a
10013 id="x1-110062r23"></a><span
10014 class="cmtt-10"> </span><span
10015 class="cmtt-10"> </span>
10016 <br class="fancyvrb" /><a
10017 id="x1-110064r24"></a><span
10018 class="cmtt-10"> </span><span
10019 class="cmtt-10"> </span><span
10020 class="cmtt-10"> </span><span
10021 class="cmtt-10"> </span><span
10022 class="cmtt-10"> </span><span
10023 class="cmtt-10"> </span><span
10024 class="cmtt-10"> </span><span
10025 class="cmtt-10"> </span><span
10026 class="cmtt-10"> </span><span
10027 class="cmtt-10"> </span><span
10028 class="cmtt-10"> </span><span
10029 class="cmtt-10"> </span><span
10030 class="cmtt-10"> </span><span
10031 class="cmtt-10"> </span><span
10032 class="cmtt-10"> </span><span
10033 class="cmtt-10"> </span><span
10034 class="cmtt-10"> </span><span
10035 class="cmtt-10"> </span><span
10036 class="cmtt-10"> </span><span
10037 class="cmtt-10"> </span><span
10038 class="cmtt-10"> </span><span
10039 class="cmtt-10"> </span><span
10040 class="cmtt-10"> </span><span
10041 class="cmtt-10"> </span><span
10042 class="cmtt-10"> </span><span
10043 class="cmtt-10"> </span><span
10044 class="cmtt-10"> }</span>
10045 <br class="fancyvrb" /><a
10046 id="x1-110066r25"></a><span
10047 class="cmtt-10"> </span><span
10048 class="cmtt-10"> </span>
10049 <br class="fancyvrb" /><a
10050 id="x1-110068r26"></a><span
10051 class="cmtt-10"> </span><span
10052 class="cmtt-10"> </span><span
10053 class="cmtt-10"> </span><span
10054 class="cmtt-10"> </span><span
10055 class="cmtt-10"> </span><span
10056 class="cmtt-10"> </span><span
10057 class="cmtt-10"> </span><span
10058 class="cmtt-10"> </span><span
10059 class="cmtt-10"> </span><span
10060 class="cmtt-10"> </span><span
10061 class="cmtt-10"> </span><span
10062 class="cmtt-10"> </span><span
10063 class="cmtt-10"> </span><span
10064 class="cmtt-10"> </span><span
10065 class="cmtt-10"> </span><span
10066 class="cmtt-10"> </span><span
10067 class="cmtt-10"> </span><span
10068 class="cmtt-10"> </span><span
10069 class="cmtt-10"> </span><span
10070 class="cmtt-10"> </span><span
10071 class="cmtt-10"> </span><span
10072 class="cmtt-10"> }</span>
10073 <br class="fancyvrb" /><a
10074 id="x1-110070r27"></a><span
10075 class="cmtt-10"> </span><span
10076 class="cmtt-10"> </span>
10077 <br class="fancyvrb" /><a
10078 id="x1-110072r28"></a><span
10079 class="cmtt-10"> </span><span
10080 class="cmtt-10"> </span><span
10081 class="cmtt-10"> </span><span
10082 class="cmtt-10"> </span><span
10083 class="cmtt-10"> </span><span
10084 class="cmtt-10"> </span><span
10085 class="cmtt-10"> </span><span
10086 class="cmtt-10"> </span><span
10087 class="cmtt-10"> </span><span
10088 class="cmtt-10"> </span><span
10089 class="cmtt-10"> </span><span
10090 class="cmtt-10"> </span><span
10091 class="cmtt-10"> </span><span
10092 class="cmtt-10"> </span><span
10093 class="cmtt-10"> </span><span
10094 class="cmtt-10"> </span><span
10095 class="cmtt-10"> }</span>
10096 <br class="fancyvrb" /><a
10097 id="x1-110074r29"></a><span
10098 class="cmtt-10"> </span><span
10099 class="cmtt-10"> </span>
10100 <br class="fancyvrb" /><a
10101 id="x1-110076r30"></a><span
10102 class="cmtt-10"> </span><span
10103 class="cmtt-10"> </span><span
10104 class="cmtt-10"> </span><span
10105 class="cmtt-10"> </span><span
10106 class="cmtt-10"> </span><span
10107 class="cmtt-10"> </span><span
10108 class="cmtt-10"> </span><span
10109 class="cmtt-10"> </span><span
10110 class="cmtt-10"> </span><span
10111 class="cmtt-10"> </span><span
10112 class="cmtt-10"> </span><span
10113 class="cmtt-10"> </span><span
10114 class="cmtt-10"> 13)</span><span
10115 class="cmtt-10"> iterate</span><span
10116 class="cmtt-10"> [i]</span><span
10117 class="cmtt-10"> over</span><span
10118 class="cmtt-10"> the</span><span
10119 class="cmtt-10"> range</span><span
10120 class="cmtt-10"> 0</span><span
10121 class="cmtt-10"> ..</span><span
10122 class="cmtt-10"> ([classwords_per_codeword]</span><span
10123 class="cmtt-10"> -</span><span
10124 class="cmtt-10"> 1)</span><span
10125 class="cmtt-10"> while</span><span
10126 class="cmtt-10"> [partition_count]</span>
10127 <br class="fancyvrb" /><a
10128 id="x1-110078r31"></a><span
10129 class="cmtt-10"> </span><span
10130 class="cmtt-10"> </span><span
10131 class="cmtt-10"> </span><span
10132 class="cmtt-10"> </span><span
10133 class="cmtt-10"> </span><span
10134 class="cmtt-10"> </span><span
10135 class="cmtt-10"> </span><span
10136 class="cmtt-10"> </span><span
10137 class="cmtt-10"> </span><span
10138 class="cmtt-10"> </span><span
10139 class="cmtt-10"> </span><span
10140 class="cmtt-10"> </span><span
10141 class="cmtt-10"> </span><span
10142 class="cmtt-10"> </span><span
10143 class="cmtt-10"> </span><span
10144 class="cmtt-10"> </span><span
10145 class="cmtt-10"> is</span><span
10146 class="cmtt-10"> also</span><span
10147 class="cmtt-10"> less</span><span
10148 class="cmtt-10"> than</span><span
10149 class="cmtt-10"> [partitions_to_read]</span><span
10150 class="cmtt-10"> {</span>
10151 <br class="fancyvrb" /><a
10152 id="x1-110080r32"></a><span
10153 class="cmtt-10"> </span><span
10154 class="cmtt-10"> </span>
10155 <br class="fancyvrb" /><a
10156 id="x1-110082r33"></a><span
10157 class="cmtt-10"> </span><span
10158 class="cmtt-10"> </span><span
10159 class="cmtt-10"> </span><span
10160 class="cmtt-10"> </span><span
10161 class="cmtt-10"> </span><span
10162 class="cmtt-10"> </span><span
10163 class="cmtt-10"> </span><span
10164 class="cmtt-10"> </span><span
10165 class="cmtt-10"> </span><span
10166 class="cmtt-10"> </span><span
10167 class="cmtt-10"> </span><span
10168 class="cmtt-10"> </span><span
10169 class="cmtt-10"> </span><span
10170 class="cmtt-10"> </span><span
10171 class="cmtt-10"> </span><span
10172 class="cmtt-10"> </span><span
10173 class="cmtt-10"> </span><span
10174 class="cmtt-10"> </span><span
10175 class="cmtt-10"> 14)</span><span
10176 class="cmtt-10"> iterate</span><span
10177 class="cmtt-10"> [j]</span><span
10178 class="cmtt-10"> over</span><span
10179 class="cmtt-10"> the</span><span
10180 class="cmtt-10"> range</span><span
10181 class="cmtt-10"> 0</span><span
10182 class="cmtt-10"> ..</span><span
10183 class="cmtt-10"> [ch]-1</span><span
10184 class="cmtt-10"> {</span>
10185 <br class="fancyvrb" /><a
10186 id="x1-110084r34"></a><span
10187 class="cmtt-10"> </span><span
10188 class="cmtt-10"> </span>
10189 <br class="fancyvrb" /><a
10190 id="x1-110086r35"></a><span
10191 class="cmtt-10"> </span><span
10192 class="cmtt-10"> </span><span
10193 class="cmtt-10"> </span><span
10194 class="cmtt-10"> </span><span
10195 class="cmtt-10"> </span><span
10196 class="cmtt-10"> </span><span
10197 class="cmtt-10"> </span><span
10198 class="cmtt-10"> </span><span
10199 class="cmtt-10"> </span><span
10200 class="cmtt-10"> </span><span
10201 class="cmtt-10"> </span><span
10202 class="cmtt-10"> </span><span
10203 class="cmtt-10"> </span><span
10204 class="cmtt-10"> </span><span
10205 class="cmtt-10"> </span><span
10206 class="cmtt-10"> </span><span
10207 class="cmtt-10"> </span><span
10208 class="cmtt-10"> </span><span
10209 class="cmtt-10"> </span><span
10210 class="cmtt-10"> </span><span
10211 class="cmtt-10"> </span><span
10212 class="cmtt-10"> </span><span
10213 class="cmtt-10"> </span><span
10214 class="cmtt-10"> 15)</span><span
10215 class="cmtt-10"> if</span><span
10216 class="cmtt-10"> vector</span><span
10217 class="cmtt-10"> [j]</span><span
10218 class="cmtt-10"> is</span><span
10219 class="cmtt-10"> not</span><span
10220 class="cmtt-10"> marked</span><span
10221 class="cmtt-10"> ’do</span><span
10222 class="cmtt-10"> not</span><span
10223 class="cmtt-10"> decode’</span><span
10224 class="cmtt-10"> {</span>
10225 <br class="fancyvrb" /><a
10226 id="x1-110088r36"></a><span
10227 class="cmtt-10"> </span><span
10228 class="cmtt-10"> </span>
10229 <br class="fancyvrb" /><a
10230 id="x1-110090r37"></a><span
10231 class="cmtt-10"> </span><span
10232 class="cmtt-10"> </span><span
10233 class="cmtt-10"> </span><span
10234 class="cmtt-10"> </span><span
10235 class="cmtt-10"> </span><span
10236 class="cmtt-10"> </span><span
10237 class="cmtt-10"> </span><span
10238 class="cmtt-10"> </span><span
10239 class="cmtt-10"> </span><span
10240 class="cmtt-10"> </span><span
10241 class="cmtt-10"> </span><span
10242 class="cmtt-10"> </span><span
10243 class="cmtt-10"> </span><span
10244 class="cmtt-10"> </span><span
10245 class="cmtt-10"> </span><span
10246 class="cmtt-10"> </span><span
10247 class="cmtt-10"> </span><span
10248 class="cmtt-10"> </span><span
10249 class="cmtt-10"> </span><span
10250 class="cmtt-10"> </span><span
10251 class="cmtt-10"> </span><span
10252 class="cmtt-10"> </span><span
10253 class="cmtt-10"> </span><span
10254 class="cmtt-10"> </span><span
10255 class="cmtt-10"> </span><span
10256 class="cmtt-10"> </span><span
10257 class="cmtt-10"> </span><span
10258 class="cmtt-10"> </span><span
10259 class="cmtt-10"> 16)</span><span
10260 class="cmtt-10"> [vqclass]</span><span
10261 class="cmtt-10"> =</span><span
10262 class="cmtt-10"> array</span><span
10263 class="cmtt-10"> [classifications]</span><span
10264 class="cmtt-10"> element</span><span
10265 class="cmtt-10"> [j],[partition_count]</span>
10266 <br class="fancyvrb" /><a
10267 id="x1-110092r38"></a><span
10268 class="cmtt-10"> </span><span
10269 class="cmtt-10"> </span><span
10270 class="cmtt-10"> </span><span
10271 class="cmtt-10"> </span><span
10272 class="cmtt-10"> </span><span
10273 class="cmtt-10"> </span><span
10274 class="cmtt-10"> </span><span
10275 class="cmtt-10"> </span><span
10276 class="cmtt-10"> </span><span
10277 class="cmtt-10"> </span><span
10278 class="cmtt-10"> </span><span
10279 class="cmtt-10"> </span><span
10280 class="cmtt-10"> </span><span
10281 class="cmtt-10"> </span><span
10282 class="cmtt-10"> </span><span
10283 class="cmtt-10"> </span><span
10284 class="cmtt-10"> </span><span
10285 class="cmtt-10"> </span><span
10286 class="cmtt-10"> </span><span
10287 class="cmtt-10"> </span><span
10288 class="cmtt-10"> </span><span
10289 class="cmtt-10"> </span><span
10290 class="cmtt-10"> </span><span
10291 class="cmtt-10"> </span><span
10292 class="cmtt-10"> </span><span
10293 class="cmtt-10"> </span><span
10294 class="cmtt-10"> </span><span
10295 class="cmtt-10"> </span><span
10296 class="cmtt-10"> 17)</span><span
10297 class="cmtt-10"> [vqbook]</span><span
10298 class="cmtt-10"> =</span><span
10299 class="cmtt-10"> array</span><span
10300 class="cmtt-10"> [residue_books]</span><span
10301 class="cmtt-10"> element</span><span
10302 class="cmtt-10"> [vqclass],[pass]</span>
10303 <br class="fancyvrb" /><a
10304 id="x1-110094r39"></a><span
10305 class="cmtt-10"> </span><span
10306 class="cmtt-10"> </span><span
10307 class="cmtt-10"> </span><span
10308 class="cmtt-10"> </span><span
10309 class="cmtt-10"> </span><span
10310 class="cmtt-10"> </span><span
10311 class="cmtt-10"> </span><span
10312 class="cmtt-10"> </span><span
10313 class="cmtt-10"> </span><span
10314 class="cmtt-10"> </span><span
10315 class="cmtt-10"> </span><span
10316 class="cmtt-10"> </span><span
10317 class="cmtt-10"> </span><span
10318 class="cmtt-10"> </span><span
10319 class="cmtt-10"> </span><span
10320 class="cmtt-10"> </span><span
10321 class="cmtt-10"> </span><span
10322 class="cmtt-10"> </span><span
10323 class="cmtt-10"> </span><span
10324 class="cmtt-10"> </span><span
10325 class="cmtt-10"> </span><span
10326 class="cmtt-10"> </span><span
10327 class="cmtt-10"> </span><span
10328 class="cmtt-10"> </span><span
10329 class="cmtt-10"> </span><span
10330 class="cmtt-10"> </span><span
10331 class="cmtt-10"> </span><span
10332 class="cmtt-10"> </span><span
10333 class="cmtt-10"> 18)</span><span
10334 class="cmtt-10"> if</span><span
10335 class="cmtt-10"> ([vqbook]</span><span
10336 class="cmtt-10"> is</span><span
10337 class="cmtt-10"> not</span><span
10338 class="cmtt-10"> ’unused’)</span><span
10339 class="cmtt-10"> {</span>
10340 <br class="fancyvrb" /><a
10341 id="x1-110096r40"></a><span
10342 class="cmtt-10"> </span><span
10343 class="cmtt-10"> </span>
10344 <br class="fancyvrb" /><a
10345 id="x1-110098r41"></a><span
10346 class="cmtt-10"> </span><span
10347 class="cmtt-10"> </span><span
10348 class="cmtt-10"> </span><span
10349 class="cmtt-10"> </span><span
10350 class="cmtt-10"> </span><span
10351 class="cmtt-10"> </span><span
10352 class="cmtt-10"> </span><span
10353 class="cmtt-10"> </span><span
10354 class="cmtt-10"> </span><span
10355 class="cmtt-10"> </span><span
10356 class="cmtt-10"> </span><span
10357 class="cmtt-10"> </span><span
10358 class="cmtt-10"> </span><span
10359 class="cmtt-10"> </span><span
10360 class="cmtt-10"> </span><span
10361 class="cmtt-10"> </span><span
10362 class="cmtt-10"> </span><span
10363 class="cmtt-10"> </span><span
10364 class="cmtt-10"> </span><span
10365 class="cmtt-10"> </span><span
10366 class="cmtt-10"> </span><span
10367 class="cmtt-10"> </span><span
10368 class="cmtt-10"> </span><span
10369 class="cmtt-10"> </span><span
10370 class="cmtt-10"> </span><span
10371 class="cmtt-10"> </span><span
10372 class="cmtt-10"> </span><span
10373 class="cmtt-10"> </span><span
10374 class="cmtt-10"> </span><span
10375 class="cmtt-10"> </span><span
10376 class="cmtt-10"> </span><span
10377 class="cmtt-10"> </span><span
10378 class="cmtt-10"> </span><span
10379 class="cmtt-10"> 19)</span><span
10380 class="cmtt-10"> decode</span><span
10381 class="cmtt-10"> partition</span><span
10382 class="cmtt-10"> into</span><span
10383 class="cmtt-10"> output</span><span
10384 class="cmtt-10"> vector</span><span
10385 class="cmtt-10"> number</span><span
10386 class="cmtt-10"> [j],</span><span
10387 class="cmtt-10"> starting</span><span
10388 class="cmtt-10"> at</span><span
10389 class="cmtt-10"> scalar</span>
10390 <br class="fancyvrb" /><a
10391 id="x1-110100r42"></a><span
10392 class="cmtt-10"> </span><span
10393 class="cmtt-10"> </span><span
10394 class="cmtt-10"> </span><span
10395 class="cmtt-10"> </span><span
10396 class="cmtt-10"> </span><span
10397 class="cmtt-10"> </span><span
10398 class="cmtt-10"> </span><span
10399 class="cmtt-10"> </span><span
10400 class="cmtt-10"> </span><span
10401 class="cmtt-10"> </span><span
10402 class="cmtt-10"> </span><span
10403 class="cmtt-10"> </span><span
10404 class="cmtt-10"> </span><span
10405 class="cmtt-10"> </span><span
10406 class="cmtt-10"> </span><span
10407 class="cmtt-10"> </span><span
10408 class="cmtt-10"> </span><span
10409 class="cmtt-10"> </span><span
10410 class="cmtt-10"> </span><span
10411 class="cmtt-10"> </span><span
10412 class="cmtt-10"> </span><span
10413 class="cmtt-10"> </span><span
10414 class="cmtt-10"> </span><span
10415 class="cmtt-10"> </span><span
10416 class="cmtt-10"> </span><span
10417 class="cmtt-10"> </span><span
10418 class="cmtt-10"> </span><span
10419 class="cmtt-10"> </span><span
10420 class="cmtt-10"> </span><span
10421 class="cmtt-10"> </span><span
10422 class="cmtt-10"> </span><span
10423 class="cmtt-10"> </span><span
10424 class="cmtt-10"> </span><span
10425 class="cmtt-10"> </span><span
10426 class="cmtt-10"> </span><span
10427 class="cmtt-10"> </span><span
10428 class="cmtt-10"> </span><span
10429 class="cmtt-10"> offset</span><span
10430 class="cmtt-10"> [limit_residue_begin]+[partition_count]*[residue_partition_size]</span><span
10431 class="cmtt-10"> using</span>
10432 <br class="fancyvrb" /><a
10433 id="x1-110102r43"></a><span
10434 class="cmtt-10"> </span><span
10435 class="cmtt-10"> </span><span
10436 class="cmtt-10"> </span><span
10437 class="cmtt-10"> </span><span
10438 class="cmtt-10"> </span><span
10439 class="cmtt-10"> </span><span
10440 class="cmtt-10"> </span><span
10441 class="cmtt-10"> </span><span
10442 class="cmtt-10"> </span><span
10443 class="cmtt-10"> </span><span
10444 class="cmtt-10"> </span><span
10445 class="cmtt-10"> </span><span
10446 class="cmtt-10"> </span><span
10447 class="cmtt-10"> </span><span
10448 class="cmtt-10"> </span><span
10449 class="cmtt-10"> </span><span
10450 class="cmtt-10"> </span><span
10451 class="cmtt-10"> </span><span
10452 class="cmtt-10"> </span><span
10453 class="cmtt-10"> </span><span
10454 class="cmtt-10"> </span><span
10455 class="cmtt-10"> </span><span
10456 class="cmtt-10"> </span><span
10457 class="cmtt-10"> </span><span
10458 class="cmtt-10"> </span><span
10459 class="cmtt-10"> </span><span
10460 class="cmtt-10"> </span><span
10461 class="cmtt-10"> </span><span
10462 class="cmtt-10"> </span><span
10463 class="cmtt-10"> </span><span
10464 class="cmtt-10"> </span><span
10465 class="cmtt-10"> </span><span
10466 class="cmtt-10"> </span><span
10467 class="cmtt-10"> </span><span
10468 class="cmtt-10"> </span><span
10469 class="cmtt-10"> </span><span
10470 class="cmtt-10"> </span><span
10471 class="cmtt-10"> codebook</span><span
10472 class="cmtt-10"> number</span><span
10473 class="cmtt-10"> [vqbook]</span><span
10474 class="cmtt-10"> in</span><span
10475 class="cmtt-10"> VQ</span><span
10476 class="cmtt-10"> context</span>
10477 <br class="fancyvrb" /><a
10478 id="x1-110104r44"></a><span
10479 class="cmtt-10"> </span><span
10480 class="cmtt-10"> </span><span
10481 class="cmtt-10"> </span><span
10482 class="cmtt-10"> </span><span
10483 class="cmtt-10"> </span><span
10484 class="cmtt-10"> </span><span
10485 class="cmtt-10"> </span><span
10486 class="cmtt-10"> </span><span
10487 class="cmtt-10"> </span><span
10488 class="cmtt-10"> </span><span
10489 class="cmtt-10"> </span><span
10490 class="cmtt-10"> </span><span
10491 class="cmtt-10"> </span><span
10492 class="cmtt-10"> </span><span
10493 class="cmtt-10"> </span><span
10494 class="cmtt-10"> </span><span
10495 class="cmtt-10"> </span><span
10496 class="cmtt-10"> </span><span
10497 class="cmtt-10"> </span><span
10498 class="cmtt-10"> </span><span
10499 class="cmtt-10"> </span><span
10500 class="cmtt-10"> </span><span
10501 class="cmtt-10"> </span><span
10502 class="cmtt-10"> </span><span
10503 class="cmtt-10"> </span><span
10504 class="cmtt-10"> </span><span
10505 class="cmtt-10"> </span><span
10506 class="cmtt-10"> }</span>
10507 <br class="fancyvrb" /><a
10508 id="x1-110106r45"></a><span
10509 class="cmtt-10"> </span><span
10510 class="cmtt-10"> </span><span
10511 class="cmtt-10"> </span><span
10512 class="cmtt-10"> </span><span
10513 class="cmtt-10"> </span><span
10514 class="cmtt-10"> </span><span
10515 class="cmtt-10"> </span><span
10516 class="cmtt-10"> </span><span
10517 class="cmtt-10"> </span><span
10518 class="cmtt-10"> </span><span
10519 class="cmtt-10"> </span><span
10520 class="cmtt-10"> </span><span
10521 class="cmtt-10"> </span><span
10522 class="cmtt-10"> </span><span
10523 class="cmtt-10"> </span><span
10524 class="cmtt-10"> </span><span
10525 class="cmtt-10"> </span><span
10526 class="cmtt-10"> </span><span
10527 class="cmtt-10"> </span><span
10528 class="cmtt-10"> </span><span
10529 class="cmtt-10"> </span><span
10530 class="cmtt-10"> </span><span
10531 class="cmtt-10"> }</span>
10532 <br class="fancyvrb" /><a
10533 id="x1-110108r46"></a><span
10534 class="cmtt-10"> </span><span
10535 class="cmtt-10"> </span>
10536 <br class="fancyvrb" /><a
10537 id="x1-110110r47"></a><span
10538 class="cmtt-10"> </span><span
10539 class="cmtt-10"> </span><span
10540 class="cmtt-10"> </span><span
10541 class="cmtt-10"> </span><span
10542 class="cmtt-10"> </span><span
10543 class="cmtt-10"> </span><span
10544 class="cmtt-10"> </span><span
10545 class="cmtt-10"> </span><span
10546 class="cmtt-10"> </span><span
10547 class="cmtt-10"> </span><span
10548 class="cmtt-10"> </span><span
10549 class="cmtt-10"> </span><span
10550 class="cmtt-10"> </span><span
10551 class="cmtt-10"> </span><span
10552 class="cmtt-10"> </span><span
10553 class="cmtt-10"> </span><span
10554 class="cmtt-10"> </span><span
10555 class="cmtt-10"> </span><span
10556 class="cmtt-10"> 20)</span><span
10557 class="cmtt-10"> increment</span><span
10558 class="cmtt-10"> [partition_count]</span><span
10559 class="cmtt-10"> by</span><span
10560 class="cmtt-10"> one</span>
10561 <br class="fancyvrb" /><a
10562 id="x1-110112r48"></a><span
10563 class="cmtt-10"> </span><span
10564 class="cmtt-10"> </span>
10565 <br class="fancyvrb" /><a
10566 id="x1-110114r49"></a><span
10567 class="cmtt-10"> </span><span
10568 class="cmtt-10"> </span><span
10569 class="cmtt-10"> </span><span
10570 class="cmtt-10"> </span><span
10571 class="cmtt-10"> </span><span
10572 class="cmtt-10"> </span><span
10573 class="cmtt-10"> </span><span
10574 class="cmtt-10"> </span><span
10575 class="cmtt-10"> </span><span
10576 class="cmtt-10"> </span><span
10577 class="cmtt-10"> </span><span
10578 class="cmtt-10"> </span><span
10579 class="cmtt-10"> </span><span
10580 class="cmtt-10"> </span><span
10581 class="cmtt-10"> </span><span
10582 class="cmtt-10"> </span><span
10583 class="cmtt-10"> }</span>
10584 <br class="fancyvrb" /><a
10585 id="x1-110116r50"></a><span
10586 class="cmtt-10"> </span><span
10587 class="cmtt-10"> </span><span
10588 class="cmtt-10"> </span><span
10589 class="cmtt-10"> </span><span
10590 class="cmtt-10"> </span><span
10591 class="cmtt-10"> </span><span
10592 class="cmtt-10"> </span><span
10593 class="cmtt-10"> </span><span
10594 class="cmtt-10"> </span><span
10595 class="cmtt-10"> </span><span
10596 class="cmtt-10"> </span><span
10597 class="cmtt-10"> }</span>
10598 <br class="fancyvrb" /><a
10599 id="x1-110118r51"></a><span
10600 class="cmtt-10"> </span><span
10601 class="cmtt-10"> </span><span
10602 class="cmtt-10"> </span><span
10603 class="cmtt-10"> </span><span
10604 class="cmtt-10"> </span><span
10605 class="cmtt-10"> </span><span
10606 class="cmtt-10"> }</span>
10607 <br class="fancyvrb" /><a
10608 id="x1-110120r52"></a><span
10609 class="cmtt-10"> </span><span
10610 class="cmtt-10"> </span>
10614 <br class="fancyvrb" /><a
10615 id="x1-110122r53"></a><span
10616 class="cmtt-10"> </span><span
10617 class="cmtt-10"> </span><span
10618 class="cmtt-10"> 21)</span><span
10619 class="cmtt-10"> done</span>
10620 <br class="fancyvrb" /><a
10621 id="x1-110124r54"></a><span
10622 class="cmtt-10"> </span><span
10623 class="cmtt-10"> </span>
10625 <!--l. 341--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence. Decode
10626 returns the result of vector decode up to that point.
10627 <!--l. 347--><p class="noindent" >
10628 <h5 class="subsubsectionHead"><span class="titlemark">8.6.3 </span> <a
10629 id="x1-1110008.6.3"></a>format 0 specifics</h5>
10630 <!--l. 349--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
10631 section. The following pseudocode presents the same algorithm. Assume:
10632 <ul class="itemize1">
10633 <li class="itemize"><span
10634 class="cmtt-10x-x-109">[n] </span>is the value in <span
10635 class="cmtt-10x-x-109">[residue_partition_size]</span>
10637 <li class="itemize"><span
10638 class="cmtt-10x-x-109">[v] </span>is the residue vector
10640 <li class="itemize"><span
10641 class="cmtt-10x-x-109">[offset] </span>is the beginning read offset in [v]</li></ul>
10642 <!--l. 360--><p class="noindent" >
10643 <div class="fancyvrb" id="fancyvrb41">
10645 id="x1-111002r1"></a><span
10646 class="cmtt-10"> </span><span
10647 class="cmtt-10"> </span><span
10648 class="cmtt-10"> 1)</span><span
10649 class="cmtt-10"> [step]</span><span
10650 class="cmtt-10"> =</span><span
10651 class="cmtt-10"> [n]</span><span
10652 class="cmtt-10"> /</span><span
10653 class="cmtt-10"> [codebook_dimensions]</span>
10654 <br class="fancyvrb" /><a
10655 id="x1-111004r2"></a><span
10656 class="cmtt-10"> </span><span
10657 class="cmtt-10"> </span><span
10658 class="cmtt-10"> 2)</span><span
10659 class="cmtt-10"> iterate</span><span
10660 class="cmtt-10"> [i]</span><span
10661 class="cmtt-10"> over</span><span
10662 class="cmtt-10"> the</span><span
10663 class="cmtt-10"> range</span><span
10664 class="cmtt-10"> 0</span><span
10665 class="cmtt-10"> ...</span><span
10666 class="cmtt-10"> [step]-1</span><span
10667 class="cmtt-10"> {</span>
10668 <br class="fancyvrb" /><a
10669 id="x1-111006r3"></a><span
10670 class="cmtt-10"> </span><span
10671 class="cmtt-10"> </span>
10672 <br class="fancyvrb" /><a
10673 id="x1-111008r4"></a><span
10674 class="cmtt-10"> </span><span
10675 class="cmtt-10"> </span><span
10676 class="cmtt-10"> </span><span
10677 class="cmtt-10"> </span><span
10678 class="cmtt-10"> </span><span
10679 class="cmtt-10"> </span><span
10680 class="cmtt-10"> </span><span
10681 class="cmtt-10"> 3)</span><span
10682 class="cmtt-10"> vector</span><span
10683 class="cmtt-10"> [entry_temp]</span><span
10684 class="cmtt-10"> =</span><span
10685 class="cmtt-10"> read</span><span
10686 class="cmtt-10"> vector</span><span
10687 class="cmtt-10"> from</span><span
10688 class="cmtt-10"> packet</span><span
10689 class="cmtt-10"> using</span><span
10690 class="cmtt-10"> current</span><span
10691 class="cmtt-10"> codebook</span><span
10692 class="cmtt-10"> in</span><span
10693 class="cmtt-10"> VQ</span><span
10694 class="cmtt-10"> context</span>
10695 <br class="fancyvrb" /><a
10696 id="x1-111010r5"></a><span
10697 class="cmtt-10"> </span><span
10698 class="cmtt-10"> </span><span
10699 class="cmtt-10"> </span><span
10700 class="cmtt-10"> </span><span
10701 class="cmtt-10"> </span><span
10702 class="cmtt-10"> </span><span
10703 class="cmtt-10"> </span><span
10704 class="cmtt-10"> 4)</span><span
10705 class="cmtt-10"> iterate</span><span
10706 class="cmtt-10"> [j]</span><span
10707 class="cmtt-10"> over</span><span
10708 class="cmtt-10"> the</span><span
10709 class="cmtt-10"> range</span><span
10710 class="cmtt-10"> 0</span><span
10711 class="cmtt-10"> ...</span><span
10712 class="cmtt-10"> [codebook_dimensions]-1</span><span
10713 class="cmtt-10"> {</span>
10714 <br class="fancyvrb" /><a
10715 id="x1-111012r6"></a><span
10716 class="cmtt-10"> </span><span
10717 class="cmtt-10"> </span>
10718 <br class="fancyvrb" /><a
10719 id="x1-111014r7"></a><span
10720 class="cmtt-10"> </span><span
10721 class="cmtt-10"> </span><span
10722 class="cmtt-10"> </span><span
10723 class="cmtt-10"> </span><span
10724 class="cmtt-10"> </span><span
10725 class="cmtt-10"> </span><span
10726 class="cmtt-10"> </span><span
10727 class="cmtt-10"> </span><span
10728 class="cmtt-10"> </span><span
10729 class="cmtt-10"> </span><span
10730 class="cmtt-10"> </span><span
10731 class="cmtt-10"> </span><span
10732 class="cmtt-10"> 5)</span><span
10733 class="cmtt-10"> vector</span><span
10734 class="cmtt-10"> [v]</span><span
10735 class="cmtt-10"> element</span><span
10736 class="cmtt-10"> ([offset]+[i]+[j]*[step])</span><span
10737 class="cmtt-10"> =</span>
10738 <br class="fancyvrb" /><a
10739 id="x1-111016r8"></a><span
10740 class="cmtt-10"> </span><span
10741 class="cmtt-10">  </span><span
10742 class="cmtt-10"> </span><span
10743 class="cmtt-10"> </span><span
10744 class="cmtt-10"> </span><span
10745 class="cmtt-10"> </span><span
10746 class="cmtt-10"> </span><span
10747 class="cmtt-10"> </span><span
10748 class="cmtt-10"> </span><span
10749 class="cmtt-10"> vector</span><span
10750 class="cmtt-10"> [v]</span><span
10751 class="cmtt-10"> element</span><span
10752 class="cmtt-10"> ([offset]+[i]+[j]*[step])</span><span
10753 class="cmtt-10"> +</span>
10754 <br class="fancyvrb" /><a
10755 id="x1-111018r9"></a><span
10756 class="cmtt-10"> </span><span
10757 class="cmtt-10"> </span><span
10758 class="cmtt-10"> </span><span
10759 class="cmtt-10"> </span><span
10760 class="cmtt-10"> </span><span
10761 class="cmtt-10"> </span><span
10762 class="cmtt-10"> </span><span
10763 class="cmtt-10"> </span><span
10764 class="cmtt-10"> </span><span
10765 class="cmtt-10"> </span><span
10766 class="cmtt-10"> </span><span
10767 class="cmtt-10"> </span><span
10768 class="cmtt-10"> </span><span
10769 class="cmtt-10"> </span><span
10770 class="cmtt-10"> </span><span
10771 class="cmtt-10"> </span><span
10772 class="cmtt-10"> </span><span
10773 class="cmtt-10"> vector</span><span
10774 class="cmtt-10"> [entry_temp]</span><span
10775 class="cmtt-10"> element</span><span
10776 class="cmtt-10"> [j]</span>
10777 <br class="fancyvrb" /><a
10778 id="x1-111020r10"></a><span
10779 class="cmtt-10"> </span><span
10780 class="cmtt-10"> </span>
10781 <br class="fancyvrb" /><a
10782 id="x1-111022r11"></a><span
10783 class="cmtt-10"> </span><span
10784 class="cmtt-10"> </span><span
10785 class="cmtt-10"> </span><span
10786 class="cmtt-10"> </span><span
10787 class="cmtt-10"> </span><span
10788 class="cmtt-10"> </span><span
10789 class="cmtt-10"> </span><span
10790 class="cmtt-10"> </span><span
10791 class="cmtt-10"> </span><span
10792 class="cmtt-10"> </span><span
10793 class="cmtt-10"> }</span>
10794 <br class="fancyvrb" /><a
10795 id="x1-111024r12"></a><span
10796 class="cmtt-10"> </span><span
10797 class="cmtt-10"> </span>
10798 <br class="fancyvrb" /><a
10799 id="x1-111026r13"></a><span
10800 class="cmtt-10"> </span><span
10801 class="cmtt-10"> </span><span
10802 class="cmtt-10"> </span><span
10803 class="cmtt-10"> </span><span
10804 class="cmtt-10"> </span><span
10805 class="cmtt-10"> }</span>
10806 <br class="fancyvrb" /><a
10807 id="x1-111028r14"></a><span
10808 class="cmtt-10"> </span><span
10809 class="cmtt-10"> </span>
10810 <br class="fancyvrb" /><a
10811 id="x1-111030r15"></a><span
10812 class="cmtt-10"> </span><span
10813 class="cmtt-10"> </span><span
10814 class="cmtt-10"> </span><span
10815 class="cmtt-10"> 6)</span><span
10816 class="cmtt-10"> done</span>
10817 <br class="fancyvrb" /><a
10818 id="x1-111032r16"></a><span
10819 class="cmtt-10"> </span><span
10820 class="cmtt-10"> </span>
10825 <!--l. 381--><p class="noindent" >
10826 <h5 class="subsubsectionHead"><span class="titlemark">8.6.4 </span> <a
10827 id="x1-1120008.6.4"></a>format 1 specifics</h5>
10828 <!--l. 383--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’ section.
10829 The following pseudocode presents the same algorithm. Assume:
10830 <ul class="itemize1">
10831 <li class="itemize"><span
10832 class="cmtt-10x-x-109">[n] </span>is the value in <span
10833 class="cmtt-10x-x-109">[residue_partition_size]</span>
10835 <li class="itemize"><span
10836 class="cmtt-10x-x-109">[v] </span>is the residue vector
10838 <li class="itemize"><span
10839 class="cmtt-10x-x-109">[offset] </span>is the beginning read offset in [v]</li></ul>
10840 <!--l. 395--><p class="noindent" >
10841 <div class="fancyvrb" id="fancyvrb42">
10843 id="x1-112002r1"></a><span
10844 class="cmtt-10"> </span><span
10845 class="cmtt-10"> </span><span
10846 class="cmtt-10"> 1)</span><span
10847 class="cmtt-10"> [i]</span><span
10848 class="cmtt-10"> =</span><span
10849 class="cmtt-10"> 0</span>
10850 <br class="fancyvrb" /><a
10851 id="x1-112004r2"></a><span
10852 class="cmtt-10"> </span><span
10853 class="cmtt-10"> </span><span
10854 class="cmtt-10"> 2)</span><span
10855 class="cmtt-10"> vector</span><span
10856 class="cmtt-10"> [entry_temp]</span><span
10857 class="cmtt-10"> =</span><span
10858 class="cmtt-10"> read</span><span
10859 class="cmtt-10"> vector</span><span
10860 class="cmtt-10"> from</span><span
10861 class="cmtt-10"> packet</span><span
10862 class="cmtt-10"> using</span><span
10863 class="cmtt-10"> current</span><span
10864 class="cmtt-10"> codebook</span><span
10865 class="cmtt-10"> in</span><span
10866 class="cmtt-10"> VQ</span><span
10867 class="cmtt-10"> context</span>
10868 <br class="fancyvrb" /><a
10869 id="x1-112006r3"></a><span
10870 class="cmtt-10"> </span><span
10871 class="cmtt-10"> </span><span
10872 class="cmtt-10"> 3)</span><span
10873 class="cmtt-10"> iterate</span><span
10874 class="cmtt-10"> [j]</span><span
10875 class="cmtt-10"> over</span><span
10876 class="cmtt-10"> the</span><span
10877 class="cmtt-10"> range</span><span
10878 class="cmtt-10"> 0</span><span
10879 class="cmtt-10"> ...</span><span
10880 class="cmtt-10"> [codebook_dimensions]-1</span><span
10881 class="cmtt-10"> {</span>
10882 <br class="fancyvrb" /><a
10883 id="x1-112008r4"></a><span
10884 class="cmtt-10"> </span><span
10885 class="cmtt-10"> </span>
10886 <br class="fancyvrb" /><a
10887 id="x1-112010r5"></a><span
10888 class="cmtt-10"> </span><span
10889 class="cmtt-10"> </span><span
10890 class="cmtt-10"> </span><span
10891 class="cmtt-10"> </span><span
10892 class="cmtt-10"> </span><span
10893 class="cmtt-10"> </span><span
10894 class="cmtt-10"> </span><span
10895 class="cmtt-10"> 4)</span><span
10896 class="cmtt-10"> vector</span><span
10897 class="cmtt-10"> [v]</span><span
10898 class="cmtt-10"> element</span><span
10899 class="cmtt-10"> ([offset]+[i])</span><span
10900 class="cmtt-10"> =</span>
10901 <br class="fancyvrb" /><a
10902 id="x1-112012r6"></a><span
10903 class="cmtt-10"> </span><span
10904 class="cmtt-10">  </span><span
10905 class="cmtt-10"> </span><span
10906 class="cmtt-10"> vector</span><span
10907 class="cmtt-10"> [v]</span><span
10908 class="cmtt-10"> element</span><span
10909 class="cmtt-10"> ([offset]+[i])</span><span
10910 class="cmtt-10"> +</span>
10911 <br class="fancyvrb" /><a
10912 id="x1-112014r7"></a><span
10913 class="cmtt-10"> </span><span
10914 class="cmtt-10"> </span><span
10915 class="cmtt-10"> </span><span
10916 class="cmtt-10"> </span><span
10917 class="cmtt-10"> </span><span
10918 class="cmtt-10"> </span><span
10919 class="cmtt-10"> </span><span
10920 class="cmtt-10"> </span><span
10921 class="cmtt-10"> </span><span
10922 class="cmtt-10"> </span><span
10923 class="cmtt-10"> </span><span
10924 class="cmtt-10"> vector</span><span
10925 class="cmtt-10"> [entry_temp]</span><span
10926 class="cmtt-10"> element</span><span
10927 class="cmtt-10"> [j]</span>
10928 <br class="fancyvrb" /><a
10929 id="x1-112016r8"></a><span
10930 class="cmtt-10"> </span><span
10931 class="cmtt-10"> </span><span
10932 class="cmtt-10"> </span><span
10933 class="cmtt-10"> </span><span
10934 class="cmtt-10"> </span><span
10935 class="cmtt-10"> </span><span
10936 class="cmtt-10"> </span><span
10937 class="cmtt-10"> 5)</span><span
10938 class="cmtt-10"> increment</span><span
10939 class="cmtt-10"> [i]</span>
10940 <br class="fancyvrb" /><a
10941 id="x1-112018r9"></a><span
10942 class="cmtt-10"> </span><span
10943 class="cmtt-10"> </span>
10944 <br class="fancyvrb" /><a
10945 id="x1-112020r10"></a><span
10946 class="cmtt-10"> </span><span
10947 class="cmtt-10"> </span><span
10948 class="cmtt-10"> </span><span
10949 class="cmtt-10"> </span><span
10950 class="cmtt-10"> </span><span
10951 class="cmtt-10"> }</span>
10952 <br class="fancyvrb" /><a
10953 id="x1-112022r11"></a><span
10954 class="cmtt-10"> </span><span
10955 class="cmtt-10"> </span>
10956 <br class="fancyvrb" /><a
10957 id="x1-112024r12"></a><span
10958 class="cmtt-10"> </span><span
10959 class="cmtt-10"> </span><span
10960 class="cmtt-10"> </span><span
10961 class="cmtt-10"> 6)</span><span
10962 class="cmtt-10"> if</span><span
10963 class="cmtt-10"> (</span><span
10964 class="cmtt-10"> [i]</span><span
10965 class="cmtt-10"> is</span><span
10966 class="cmtt-10"> less</span><span
10967 class="cmtt-10"> than</span><span
10968 class="cmtt-10"> [n]</span><span
10969 class="cmtt-10"> )</span><span
10970 class="cmtt-10"> continue</span><span
10971 class="cmtt-10"> at</span><span
10972 class="cmtt-10"> step</span><span
10973 class="cmtt-10"> 2</span>
10974 <br class="fancyvrb" /><a
10975 id="x1-112026r13"></a><span
10976 class="cmtt-10"> </span><span
10977 class="cmtt-10"> </span><span
10978 class="cmtt-10"> </span><span
10979 class="cmtt-10"> 7)</span><span
10980 class="cmtt-10"> done</span>
10982 <!--l. 413--><p class="noindent" >
10983 <h5 class="subsubsectionHead"><span class="titlemark">8.6.5 </span> <a
10984 id="x1-1130008.6.5"></a>format 2 specifics</h5>
10985 <!--l. 415--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
10986 additional post-decode step after a normal format 1 decode.
10987 <!--l. 418--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors
10988 are marked ’do not decode’, no decode occurrs. However, if at least one vector is to be
10989 decoded, all the vectors are decoded. We then request normal format 1 to decode a single
10990 vector representing all output channels, rather than a vector for each channel. After
10991 decode, deinterleave the vector into independent vectors, one for each output channel. That
10996 <!--l. 426--><p class="noindent" >
10997 <ol class="enumerate1" >
10999 class="enumerate" id="x1-113002x1">If all vectors 0 through <span
11000 class="cmti-10x-x-109">ch</span>-1 are marked ’do not decode’, allocate and clear a single
11002 class="cmtt-10x-x-109">[v]</span>of length <span
11003 class="cmti-10x-x-109">ch*n </span>and skip step 2 below; proceed directly to the post-decode
11007 class="enumerate" id="x1-113004x2">Rather than performing format 1 decode to produce <span
11008 class="cmti-10x-x-109">ch </span>vectors of length <span
11009 class="cmti-10x-x-109">n </span>each, call
11010 format 1 decode to produce a single vector <span
11011 class="cmtt-10x-x-109">[v] </span>of length <span
11012 class="cmti-10x-x-109">ch*n</span>.
11015 class="enumerate" id="x1-113006x3">Post decode: Deinterleave the single vector <span
11016 class="cmtt-10x-x-109">[v] </span>returned by format 1 decode as
11017 described above into <span
11018 class="cmti-10x-x-109">ch </span>independent vectors, one for each outputchannel, according
11020 <div class="fancyvrb" id="fancyvrb43">
11022 id="x1-113008r1"></a><span
11023 class="cmtt-10"> </span><span
11024 class="cmtt-10"> </span><span
11025 class="cmtt-10"> </span><span
11026 class="cmtt-10"> 1)</span><span
11027 class="cmtt-10"> iterate</span><span
11028 class="cmtt-10"> [i]</span><span
11029 class="cmtt-10"> over</span><span
11030 class="cmtt-10"> the</span><span
11031 class="cmtt-10"> range</span><span
11032 class="cmtt-10"> 0</span><span
11033 class="cmtt-10"> ...</span><span
11034 class="cmtt-10"> [n]-1</span><span
11035 class="cmtt-10"> {</span>
11036 <br class="fancyvrb" /><a
11037 id="x1-113010r2"></a><span
11038 class="cmtt-10"> </span><span
11039 class="cmtt-10"> </span>
11040 <br class="fancyvrb" /><a
11041 id="x1-113012r3"></a><span
11042 class="cmtt-10"> </span><span
11043 class="cmtt-10"> </span><span
11044 class="cmtt-10"> </span><span
11045 class="cmtt-10"> </span><span
11046 class="cmtt-10"> </span><span
11047 class="cmtt-10"> </span><span
11048 class="cmtt-10"> </span><span
11049 class="cmtt-10"> </span><span
11050 class="cmtt-10"> 2)</span><span
11051 class="cmtt-10"> iterate</span><span
11052 class="cmtt-10"> [j]</span><span
11053 class="cmtt-10"> over</span><span
11054 class="cmtt-10"> the</span><span
11055 class="cmtt-10"> range</span><span
11056 class="cmtt-10"> 0</span><span
11057 class="cmtt-10"> ...</span><span
11058 class="cmtt-10"> [ch]-1</span><span
11059 class="cmtt-10"> {</span>
11060 <br class="fancyvrb" /><a
11061 id="x1-113014r4"></a><span
11062 class="cmtt-10"> </span><span
11063 class="cmtt-10"> </span>
11064 <br class="fancyvrb" /><a
11065 id="x1-113016r5"></a><span
11066 class="cmtt-10"> </span><span
11067 class="cmtt-10"> </span><span
11068 class="cmtt-10"> </span><span
11069 class="cmtt-10"> </span><span
11070 class="cmtt-10"> </span><span
11071 class="cmtt-10"> </span><span
11072 class="cmtt-10"> </span><span
11073 class="cmtt-10"> </span><span
11074 class="cmtt-10"> </span><span
11075 class="cmtt-10"> </span><span
11076 class="cmtt-10"> </span><span
11077 class="cmtt-10"> </span><span
11078 class="cmtt-10"> </span><span
11079 class="cmtt-10"> 3)</span><span
11080 class="cmtt-10"> output</span><span
11081 class="cmtt-10"> vector</span><span
11082 class="cmtt-10"> number</span><span
11083 class="cmtt-10"> [j]</span><span
11084 class="cmtt-10"> element</span><span
11085 class="cmtt-10"> [i]</span><span
11086 class="cmtt-10"> =</span><span
11087 class="cmtt-10"> vector</span><span
11088 class="cmtt-10"> [v]</span><span
11089 class="cmtt-10"> element</span><span
11090 class="cmtt-10"> ([i]</span><span
11091 class="cmtt-10"> *</span><span
11092 class="cmtt-10"> [ch]</span><span
11093 class="cmtt-10"> +</span><span
11094 class="cmtt-10"> [j])</span>
11095 <br class="fancyvrb" /><a
11096 id="x1-113018r6"></a><span
11097 class="cmtt-10"> </span><span
11098 class="cmtt-10"> </span>
11099 <br class="fancyvrb" /><a
11100 id="x1-113020r7"></a><span
11101 class="cmtt-10"> </span><span
11102 class="cmtt-10"> </span><span
11103 class="cmtt-10"> </span><span
11104 class="cmtt-10"> </span><span
11105 class="cmtt-10"> </span><span
11106 class="cmtt-10"> </span><span
11107 class="cmtt-10"> </span><span
11108 class="cmtt-10"> </span><span
11109 class="cmtt-10"> </span><span
11110 class="cmtt-10"> </span><span
11111 class="cmtt-10"> </span><span
11112 class="cmtt-10"> }</span>
11113 <br class="fancyvrb" /><a
11114 id="x1-113022r8"></a><span
11115 class="cmtt-10"> </span><span
11116 class="cmtt-10"> </span><span
11117 class="cmtt-10"> </span><span
11118 class="cmtt-10"> </span><span
11119 class="cmtt-10"> </span><span
11120 class="cmtt-10"> </span><span
11121 class="cmtt-10"> }</span>
11122 <br class="fancyvrb" /><a
11123 id="x1-113024r9"></a><span
11124 class="cmtt-10"> </span><span
11125 class="cmtt-10"> </span>
11126 <br class="fancyvrb" /><a
11127 id="x1-113026r10"></a><span
11128 class="cmtt-10"> </span><span
11129 class="cmtt-10"> </span><span
11130 class="cmtt-10"> </span><span
11131 class="cmtt-10"> 4)</span><span
11132 class="cmtt-10"> done</span>
11141 <h3 class="sectionHead"><span class="titlemark">9 </span> <a
11142 id="x1-1140009"></a>Helper equations</h3>
11143 <!--l. 6--><p class="noindent" >
11144 <h4 class="subsectionHead"><span class="titlemark">9.1 </span> <a
11145 id="x1-1150009.1"></a>Overview</h4>
11146 <!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
11147 cluttering up the main specification documents, they are defined here and referenced where
11149 <!--l. 13--><p class="noindent" >
11150 <h4 class="subsectionHead"><span class="titlemark">9.2 </span> <a
11151 id="x1-1160009.2"></a>Functions</h4>
11152 <!--l. 15--><p class="noindent" >
11153 <h5 class="subsubsectionHead"><span class="titlemark">9.2.1 </span> <a
11154 id="x1-1170009.2.1"></a>ilog</h5>
11155 <!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
11156 two’s complement integer value <span
11157 class="cmtt-10x-x-109">[x]</span>. Values of <span
11158 class="cmtt-10x-x-109">[x] </span>less than zero are defined to return
11160 <!--l. 20--><p class="noindent" >
11161 <div class="fancyvrb" id="fancyvrb44">
11163 id="x1-117002r1"></a><span
11164 class="cmtt-10"> </span><span
11165 class="cmtt-10"> </span><span
11166 class="cmtt-10"> </span><span
11167 class="cmtt-10"> 1)</span><span
11168 class="cmtt-10"> [return_value]</span><span
11169 class="cmtt-10"> =</span><span
11170 class="cmtt-10"> 0;</span>
11171 <br class="fancyvrb" /><a
11172 id="x1-117004r2"></a><span
11173 class="cmtt-10"> </span><span
11174 class="cmtt-10"> </span><span
11175 class="cmtt-10"> </span><span
11176 class="cmtt-10"> 2)</span><span
11177 class="cmtt-10"> if</span><span
11178 class="cmtt-10"> (</span><span
11179 class="cmtt-10"> [x]</span><span
11180 class="cmtt-10"> is</span><span
11181 class="cmtt-10"> greater</span><span
11182 class="cmtt-10"> than</span><span
11183 class="cmtt-10"> zero</span><span
11184 class="cmtt-10"> )</span><span
11185 class="cmtt-10"> {</span>
11186 <br class="fancyvrb" /><a
11187 id="x1-117006r3"></a><span
11188 class="cmtt-10"> </span><span
11189 class="cmtt-10"> </span>
11190 <br class="fancyvrb" /><a
11191 id="x1-117008r4"></a><span
11192 class="cmtt-10"> </span><span
11193 class="cmtt-10"> </span><span
11194 class="cmtt-10"> </span><span
11195 class="cmtt-10"> </span><span
11196 class="cmtt-10"> </span><span
11197 class="cmtt-10"> </span><span
11198 class="cmtt-10"> </span><span
11199 class="cmtt-10"> </span><span
11200 class="cmtt-10"> 3)</span><span
11201 class="cmtt-10"> increment</span><span
11202 class="cmtt-10"> [return_value];</span>
11203 <br class="fancyvrb" /><a
11204 id="x1-117010r5"></a><span
11205 class="cmtt-10"> </span><span
11206 class="cmtt-10"> </span><span
11207 class="cmtt-10"> </span><span
11208 class="cmtt-10"> </span><span
11209 class="cmtt-10"> </span><span
11210 class="cmtt-10"> </span><span
11211 class="cmtt-10"> </span><span
11212 class="cmtt-10"> </span><span
11213 class="cmtt-10"> 4)</span><span
11214 class="cmtt-10"> logical</span><span
11215 class="cmtt-10"> shift</span><span
11216 class="cmtt-10"> [x]</span><span
11217 class="cmtt-10"> one</span><span
11218 class="cmtt-10"> bit</span><span
11219 class="cmtt-10"> to</span><span
11220 class="cmtt-10"> the</span><span
11221 class="cmtt-10"> right,</span><span
11222 class="cmtt-10"> padding</span><span
11223 class="cmtt-10"> the</span><span
11224 class="cmtt-10"> MSb</span><span
11225 class="cmtt-10"> with</span><span
11226 class="cmtt-10"> zero</span>
11227 <br class="fancyvrb" /><a
11228 id="x1-117012r6"></a><span
11229 class="cmtt-10"> </span><span
11230 class="cmtt-10"> </span><span
11231 class="cmtt-10"> </span><span
11232 class="cmtt-10"> </span><span
11233 class="cmtt-10"> </span><span
11234 class="cmtt-10"> </span><span
11235 class="cmtt-10"> </span><span
11236 class="cmtt-10"> </span><span
11237 class="cmtt-10"> 5)</span><span
11238 class="cmtt-10"> repeat</span><span
11239 class="cmtt-10"> at</span><span
11240 class="cmtt-10"> step</span><span
11241 class="cmtt-10"> 2)</span>
11242 <br class="fancyvrb" /><a
11243 id="x1-117014r7"></a><span
11244 class="cmtt-10"> </span><span
11245 class="cmtt-10"> </span>
11246 <br class="fancyvrb" /><a
11247 id="x1-117016r8"></a><span
11248 class="cmtt-10"> </span><span
11249 class="cmtt-10"> </span><span
11250 class="cmtt-10"> </span><span
11251 class="cmtt-10"> </span><span
11252 class="cmtt-10"> </span><span
11253 class="cmtt-10"> </span><span
11254 class="cmtt-10"> }</span>
11255 <br class="fancyvrb" /><a
11256 id="x1-117018r9"></a><span
11257 class="cmtt-10"> </span><span
11258 class="cmtt-10"> </span>
11259 <br class="fancyvrb" /><a
11260 id="x1-117020r10"></a><span
11261 class="cmtt-10"> </span><span
11262 class="cmtt-10"> </span><span
11263 class="cmtt-10"> </span><span
11264 class="cmtt-10"> </span><span
11265 class="cmtt-10"> 6)</span><span
11266 class="cmtt-10"> done</span>
11268 <!--l. 33--><p class="noindent" >Examples:
11272 <ul class="itemize1">
11273 <li class="itemize">ilog(0) = 0;
11275 <li class="itemize">ilog(1) = 1;
11277 <li class="itemize">ilog(2) = 2;
11279 <li class="itemize">ilog(3) = 2;
11281 <li class="itemize">ilog(4) = 3;
11283 <li class="itemize">ilog(7) = 3;
11285 <li class="itemize">ilog(negative number) = 0;</li></ul>
11286 <!--l. 48--><p class="noindent" >
11287 <h5 class="subsubsectionHead"><span class="titlemark">9.2.2 </span> <a
11288 id="x1-1180009.2.2"></a>float32˙unpack</h5>
11289 <!--l. 50--><p class="noindent" >”float32˙unpack(x)” is intended to translate the packed binary representation of a Vorbis codebook
11290 float value into the representation used by the decoder for floating point numbers. For
11291 purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
11293 <!--l. 56--><p class="noindent" >
11294 <div class="fancyvrb" id="fancyvrb45">
11296 id="x1-118002r1"></a><span
11297 class="cmtt-10"> </span><span
11298 class="cmtt-10"> </span><span
11299 class="cmtt-10"> </span><span
11300 class="cmtt-10"> 1)</span><span
11301 class="cmtt-10"> [mantissa]</span><span
11302 class="cmtt-10"> =</span><span
11303 class="cmtt-10"> [x]</span><span
11304 class="cmtt-10"> bitwise</span><span
11305 class="cmtt-10"> AND</span><span
11306 class="cmtt-10"> 0x1fffff</span><span
11307 class="cmtt-10"> (unsigned</span><span
11308 class="cmtt-10"> result)</span>
11309 <br class="fancyvrb" /><a
11310 id="x1-118004r2"></a><span
11311 class="cmtt-10"> </span><span
11312 class="cmtt-10"> </span><span
11313 class="cmtt-10"> </span><span
11314 class="cmtt-10"> 2)</span><span
11315 class="cmtt-10"> [sign]</span><span
11316 class="cmtt-10"> =</span><span
11317 class="cmtt-10"> [x]</span><span
11318 class="cmtt-10"> bitwise</span><span
11319 class="cmtt-10"> AND</span><span
11320 class="cmtt-10"> 0x80000000</span><span
11321 class="cmtt-10"> (unsigned</span><span
11322 class="cmtt-10"> result)</span>
11323 <br class="fancyvrb" /><a
11324 id="x1-118006r3"></a><span
11325 class="cmtt-10"> </span><span
11326 class="cmtt-10"> </span><span
11327 class="cmtt-10"> </span><span
11328 class="cmtt-10"> 3)</span><span
11329 class="cmtt-10"> [exponent]</span><span
11330 class="cmtt-10"> =</span><span
11331 class="cmtt-10"> (</span><span
11332 class="cmtt-10"> [x]</span><span
11333 class="cmtt-10"> bitwise</span><span
11334 class="cmtt-10"> AND</span><span
11335 class="cmtt-10"> 0x7fe00000)</span><span
11336 class="cmtt-10"> shifted</span><span
11337 class="cmtt-10"> right</span><span
11338 class="cmtt-10"> 21</span><span
11339 class="cmtt-10"> bits</span><span
11340 class="cmtt-10"> (unsigned</span><span
11341 class="cmtt-10"> result)</span>
11342 <br class="fancyvrb" /><a
11343 id="x1-118008r4"></a><span
11344 class="cmtt-10"> </span><span
11345 class="cmtt-10"> </span><span
11346 class="cmtt-10"> </span><span
11347 class="cmtt-10"> 4)</span><span
11348 class="cmtt-10"> if</span><span
11349 class="cmtt-10"> (</span><span
11350 class="cmtt-10"> [sign]</span><span
11351 class="cmtt-10"> is</span><span
11352 class="cmtt-10"> nonzero</span><span
11353 class="cmtt-10"> )</span><span
11354 class="cmtt-10"> then</span><span
11355 class="cmtt-10"> negate</span><span
11356 class="cmtt-10"> [mantissa]</span>
11357 <br class="fancyvrb" /><a
11358 id="x1-118010r5"></a><span
11359 class="cmtt-10"> </span><span
11360 class="cmtt-10"> </span><span
11361 class="cmtt-10"> </span><span
11362 class="cmtt-10"> 5)</span><span
11363 class="cmtt-10"> return</span><span
11364 class="cmtt-10"> [mantissa]</span><span
11365 class="cmtt-10"> *</span><span
11366 class="cmtt-10"> (</span><span
11367 class="cmtt-10"> 2</span><span
11368 class="cmtt-10"> ^</span><span
11369 class="cmtt-10"> (</span><span
11370 class="cmtt-10"> [exponent]</span><span
11371 class="cmtt-10"> -</span><span
11372 class="cmtt-10"> 788</span><span
11373 class="cmtt-10"> )</span><span
11374 class="cmtt-10"> )</span>
11376 <!--l. 66--><p class="noindent" >
11377 <h5 class="subsubsectionHead"><span class="titlemark">9.2.3 </span> <a
11378 id="x1-1190009.2.3"></a>lookup1˙values</h5>
11379 <!--l. 68--><p class="noindent" >”lookup1˙values(codebook˙entries,codebook˙dimensions)” is used to compute the correct length of
11380 the value index for a codebook VQ lookup table of lookup type 1. The values on this list are
11384 permuted to construct the VQ vector lookup table of size <span
11385 class="cmtt-10x-x-109">[codebook_entries]</span>.
11386 <!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
11388 class="cmtt-10x-x-109">[return_value] </span>to the power of <span
11389 class="cmtt-10x-x-109">[codebook_dimensions] </span>is less than or equal to
11391 class="cmtt-10x-x-109">[codebook_entries]</span>’.
11392 <!--l. 81--><p class="noindent" >
11393 <h5 class="subsubsectionHead"><span class="titlemark">9.2.4 </span> <a
11394 id="x1-1200009.2.4"></a>low˙neighbor</h5>
11395 <!--l. 83--><p class="noindent" >”low˙neighbor(v,x)” finds the position <span
11396 class="cmtt-10x-x-109">n </span>in vector <span
11397 class="cmtt-10x-x-109">[v] </span>of the greatest value scalar element
11399 class="cmtt-10x-x-109">n </span>is less than <span
11400 class="cmtt-10x-x-109">[x] </span>and vector <span
11401 class="cmtt-10x-x-109">[v] </span>element <span
11402 class="cmtt-10x-x-109">n </span>is less than vector <span
11403 class="cmtt-10x-x-109">[v] </span>element
11405 class="cmtt-10x-x-109">[x]</span>.
11406 <!--l. 88--><p class="noindent" >
11407 <h5 class="subsubsectionHead"><span class="titlemark">9.2.5 </span> <a
11408 id="x1-1210009.2.5"></a>high˙neighbor</h5>
11409 <!--l. 90--><p class="noindent" >”high˙neighbor(v,x)” finds the position <span
11410 class="cmtt-10x-x-109">n </span>in vector [v] of the lowest value scalar element for
11412 class="cmtt-10x-x-109">n </span>is less than <span
11413 class="cmtt-10x-x-109">[x] </span>and vector <span
11414 class="cmtt-10x-x-109">[v] </span>element <span
11415 class="cmtt-10x-x-109">n </span>is greater than vector <span
11416 class="cmtt-10x-x-109">[v] </span>element
11418 class="cmtt-10x-x-109">[x]</span>.
11419 <!--l. 97--><p class="noindent" >
11420 <h5 class="subsubsectionHead"><span class="titlemark">9.2.6 </span> <a
11421 id="x1-1220009.2.6"></a>render˙point</h5>
11422 <!--l. 99--><p class="noindent" >”render˙point(x0,y0,x1,y1,X)” is used to find the Y value at point X along the line specified by x0,
11423 x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
11424 calculating intervening values along the line.
11425 <!--l. 104--><p class="noindent" >
11426 <div class="fancyvrb" id="fancyvrb46">
11428 id="x1-122002r1"></a><span
11429 class="cmtt-10"> </span><span
11430 class="cmtt-10"> </span><span
11431 class="cmtt-10"> </span><span
11432 class="cmtt-10"> 1)</span><span
11433 class="cmtt-10"> </span><span
11434 class="cmtt-10"> [dy]</span><span
11435 class="cmtt-10"> =</span><span
11436 class="cmtt-10"> [y1]</span><span
11437 class="cmtt-10"> -</span><span
11438 class="cmtt-10"> [y0]</span>
11439 <br class="fancyvrb" /><a
11440 id="x1-122004r2"></a><span
11441 class="cmtt-10"> </span><span
11442 class="cmtt-10"> </span><span
11443 class="cmtt-10"> </span><span
11444 class="cmtt-10"> 2)</span><span
11445 class="cmtt-10"> [adx]</span><span
11446 class="cmtt-10"> =</span><span
11447 class="cmtt-10"> [x1]</span><span
11448 class="cmtt-10"> -</span><span
11449 class="cmtt-10"> [x0]</span>
11450 <br class="fancyvrb" /><a
11451 id="x1-122006r3"></a><span
11452 class="cmtt-10"> </span><span
11453 class="cmtt-10"> </span><span
11454 class="cmtt-10"> </span><span
11455 class="cmtt-10"> 3)</span><span
11456 class="cmtt-10"> [ady]</span><span
11457 class="cmtt-10"> =</span><span
11458 class="cmtt-10"> absolute</span><span
11459 class="cmtt-10"> value</span><span
11460 class="cmtt-10"> of</span><span
11461 class="cmtt-10"> [dy]</span>
11462 <br class="fancyvrb" /><a
11463 id="x1-122008r4"></a><span
11464 class="cmtt-10"> </span><span
11465 class="cmtt-10"> </span><span
11466 class="cmtt-10"> </span><span
11467 class="cmtt-10"> 4)</span><span
11468 class="cmtt-10"> [err]</span><span
11469 class="cmtt-10"> =</span><span
11470 class="cmtt-10"> [ady]</span><span
11471 class="cmtt-10"> *</span><span
11472 class="cmtt-10"> ([X]</span><span
11473 class="cmtt-10"> -</span><span
11474 class="cmtt-10"> [x0])</span>
11475 <br class="fancyvrb" /><a
11476 id="x1-122010r5"></a><span
11477 class="cmtt-10"> </span><span
11478 class="cmtt-10"> </span><span
11479 class="cmtt-10"> </span><span
11480 class="cmtt-10"> 5)</span><span
11481 class="cmtt-10"> [off]</span><span
11482 class="cmtt-10"> =</span><span
11483 class="cmtt-10"> [err]</span><span
11484 class="cmtt-10"> /</span><span
11485 class="cmtt-10"> [adx]</span><span
11486 class="cmtt-10"> using</span><span
11487 class="cmtt-10"> integer</span><span
11488 class="cmtt-10"> division</span>
11489 <br class="fancyvrb" /><a
11490 id="x1-122012r6"></a><span
11491 class="cmtt-10"> </span><span
11492 class="cmtt-10"> </span><span
11493 class="cmtt-10"> </span><span
11494 class="cmtt-10"> 6)</span><span
11495 class="cmtt-10"> if</span><span
11496 class="cmtt-10"> (</span><span
11497 class="cmtt-10"> [dy]</span><span
11498 class="cmtt-10"> is</span><span
11499 class="cmtt-10"> less</span><span
11500 class="cmtt-10"> than</span><span
11501 class="cmtt-10"> zero</span><span
11502 class="cmtt-10"> )</span><span
11503 class="cmtt-10"> {</span>
11504 <br class="fancyvrb" /><a
11505 id="x1-122014r7"></a><span
11506 class="cmtt-10"> </span><span
11507 class="cmtt-10"> </span>
11508 <br class="fancyvrb" /><a
11509 id="x1-122016r8"></a><span
11510 class="cmtt-10"> </span><span
11511 class="cmtt-10"> </span><span
11512 class="cmtt-10"> </span><span
11513 class="cmtt-10"> </span><span
11514 class="cmtt-10"> </span><span
11515 class="cmtt-10"> </span><span
11516 class="cmtt-10"> </span><span
11517 class="cmtt-10"> </span><span
11518 class="cmtt-10"> 7)</span><span
11519 class="cmtt-10"> [Y]</span><span
11520 class="cmtt-10"> =</span><span
11521 class="cmtt-10"> [y0]</span><span
11522 class="cmtt-10"> -</span><span
11523 class="cmtt-10"> [off]</span>
11524 <br class="fancyvrb" /><a
11525 id="x1-122018r9"></a><span
11526 class="cmtt-10"> </span><span
11527 class="cmtt-10"> </span>
11531 <br class="fancyvrb" /><a
11532 id="x1-122020r10"></a><span
11533 class="cmtt-10"> </span><span
11534 class="cmtt-10"> </span><span
11535 class="cmtt-10"> </span><span
11536 class="cmtt-10"> </span><span
11537 class="cmtt-10"> </span><span
11538 class="cmtt-10"> </span><span
11539 class="cmtt-10"> }</span><span
11540 class="cmtt-10"> else</span><span
11541 class="cmtt-10"> {</span>
11542 <br class="fancyvrb" /><a
11543 id="x1-122022r11"></a><span
11544 class="cmtt-10"> </span><span
11545 class="cmtt-10"> </span>
11546 <br class="fancyvrb" /><a
11547 id="x1-122024r12"></a><span
11548 class="cmtt-10"> </span><span
11549 class="cmtt-10"> </span><span
11550 class="cmtt-10"> </span><span
11551 class="cmtt-10"> </span><span
11552 class="cmtt-10"> </span><span
11553 class="cmtt-10"> </span><span
11554 class="cmtt-10"> </span><span
11555 class="cmtt-10"> </span><span
11556 class="cmtt-10"> 8)</span><span
11557 class="cmtt-10"> [Y]</span><span
11558 class="cmtt-10"> =</span><span
11559 class="cmtt-10"> [y0]</span><span
11560 class="cmtt-10"> +</span><span
11561 class="cmtt-10"> [off]</span>
11562 <br class="fancyvrb" /><a
11563 id="x1-122026r13"></a><span
11564 class="cmtt-10"> </span><span
11565 class="cmtt-10"> </span>
11566 <br class="fancyvrb" /><a
11567 id="x1-122028r14"></a><span
11568 class="cmtt-10"> </span><span
11569 class="cmtt-10"> </span><span
11570 class="cmtt-10"> </span><span
11571 class="cmtt-10"> </span><span
11572 class="cmtt-10"> </span><span
11573 class="cmtt-10"> </span><span
11574 class="cmtt-10"> }</span>
11575 <br class="fancyvrb" /><a
11576 id="x1-122030r15"></a><span
11577 class="cmtt-10"> </span><span
11578 class="cmtt-10"> </span>
11579 <br class="fancyvrb" /><a
11580 id="x1-122032r16"></a><span
11581 class="cmtt-10"> </span><span
11582 class="cmtt-10"> </span><span
11583 class="cmtt-10"> </span><span
11584 class="cmtt-10"> 9)</span><span
11585 class="cmtt-10"> done</span>
11587 <!--l. 125--><p class="noindent" >
11588 <h5 class="subsubsectionHead"><span class="titlemark">9.2.7 </span> <a
11589 id="x1-1230009.2.7"></a>render˙line</h5>
11590 <!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render˙line(x0, y0, x1, y1, v)” to
11591 construct an integer floor curve for contiguous piecewise line segments. Note that it has not been
11592 relevant elsewhere, but here we must define integer division as rounding division of both positive
11593 and negative numbers toward zero.
11594 <!--l. 134--><p class="noindent" >
11595 <div class="fancyvrb" id="fancyvrb47">
11597 id="x1-123002r1"></a><span
11598 class="cmtt-10"> </span><span
11599 class="cmtt-10"> </span><span
11600 class="cmtt-10"> </span><span
11601 class="cmtt-10"> 1)</span><span
11602 class="cmtt-10"> </span><span
11603 class="cmtt-10"> </span><span
11604 class="cmtt-10"> [dy]</span><span
11605 class="cmtt-10"> =</span><span
11606 class="cmtt-10"> [y1]</span><span
11607 class="cmtt-10"> -</span><span
11608 class="cmtt-10"> [y0]</span>
11609 <br class="fancyvrb" /><a
11610 id="x1-123004r2"></a><span
11611 class="cmtt-10"> </span><span
11612 class="cmtt-10"> </span><span
11613 class="cmtt-10"> </span><span
11614 class="cmtt-10"> 2)</span><span
11615 class="cmtt-10"> </span><span
11616 class="cmtt-10"> [adx]</span><span
11617 class="cmtt-10"> =</span><span
11618 class="cmtt-10"> [x1]</span><span
11619 class="cmtt-10"> -</span><span
11620 class="cmtt-10"> [x0]</span>
11621 <br class="fancyvrb" /><a
11622 id="x1-123006r3"></a><span
11623 class="cmtt-10"> </span><span
11624 class="cmtt-10"> </span><span
11625 class="cmtt-10"> </span><span
11626 class="cmtt-10"> 3)</span><span
11627 class="cmtt-10"> </span><span
11628 class="cmtt-10"> [ady]</span><span
11629 class="cmtt-10"> =</span><span
11630 class="cmtt-10"> absolute</span><span
11631 class="cmtt-10"> value</span><span
11632 class="cmtt-10"> of</span><span
11633 class="cmtt-10"> [dy]</span>
11634 <br class="fancyvrb" /><a
11635 id="x1-123008r4"></a><span
11636 class="cmtt-10"> </span><span
11637 class="cmtt-10"> </span><span
11638 class="cmtt-10"> </span><span
11639 class="cmtt-10"> 4)</span><span
11640 class="cmtt-10"> [base]</span><span
11641 class="cmtt-10"> =</span><span
11642 class="cmtt-10"> [dy]</span><span
11643 class="cmtt-10"> /</span><span
11644 class="cmtt-10"> [adx]</span><span
11645 class="cmtt-10"> using</span><span
11646 class="cmtt-10"> integer</span><span
11647 class="cmtt-10"> division</span>
11648 <br class="fancyvrb" /><a
11649 id="x1-123010r5"></a><span
11650 class="cmtt-10"> </span><span
11651 class="cmtt-10"> </span><span
11652 class="cmtt-10"> </span><span
11653 class="cmtt-10"> 5)</span><span
11654 class="cmtt-10"> </span><span
11655 class="cmtt-10"> </span><span
11656 class="cmtt-10"> </span><span
11657 class="cmtt-10"> [x]</span><span
11658 class="cmtt-10"> =</span><span
11659 class="cmtt-10"> [x0]</span>
11660 <br class="fancyvrb" /><a
11661 id="x1-123012r6"></a><span
11662 class="cmtt-10"> </span><span
11663 class="cmtt-10"> </span><span
11664 class="cmtt-10"> </span><span
11665 class="cmtt-10"> 6)</span><span
11666 class="cmtt-10"> </span><span
11667 class="cmtt-10"> </span><span
11668 class="cmtt-10"> </span><span
11669 class="cmtt-10"> [y]</span><span
11670 class="cmtt-10"> =</span><span
11671 class="cmtt-10"> [y0]</span>
11672 <br class="fancyvrb" /><a
11673 id="x1-123014r7"></a><span
11674 class="cmtt-10"> </span><span
11675 class="cmtt-10"> </span><span
11676 class="cmtt-10"> </span><span
11677 class="cmtt-10"> 7)</span><span
11678 class="cmtt-10"> </span><span
11679 class="cmtt-10"> [err]</span><span
11680 class="cmtt-10"> =</span><span
11681 class="cmtt-10"> 0</span>
11682 <br class="fancyvrb" /><a
11683 id="x1-123016r8"></a><span
11684 class="cmtt-10"> </span><span
11685 class="cmtt-10"> </span>
11686 <br class="fancyvrb" /><a
11687 id="x1-123018r9"></a><span
11688 class="cmtt-10"> </span><span
11689 class="cmtt-10"> </span><span
11690 class="cmtt-10"> </span><span
11691 class="cmtt-10"> 8)</span><span
11692 class="cmtt-10"> if</span><span
11693 class="cmtt-10"> (</span><span
11694 class="cmtt-10"> [dy]</span><span
11695 class="cmtt-10"> is</span><span
11696 class="cmtt-10"> less</span><span
11697 class="cmtt-10"> than</span><span
11698 class="cmtt-10"> 0</span><span
11699 class="cmtt-10"> )</span><span
11700 class="cmtt-10"> {</span>
11701 <br class="fancyvrb" /><a
11702 id="x1-123020r10"></a><span
11703 class="cmtt-10"> </span><span
11704 class="cmtt-10"> </span>
11705 <br class="fancyvrb" /><a
11706 id="x1-123022r11"></a><span
11707 class="cmtt-10"> </span><span
11708 class="cmtt-10"> </span><span
11709 class="cmtt-10"> </span><span
11710 class="cmtt-10"> </span><span
11711 class="cmtt-10"> </span><span
11712 class="cmtt-10"> </span><span
11713 class="cmtt-10"> </span><span
11714 class="cmtt-10"> </span><span
11715 class="cmtt-10"> </span><span
11716 class="cmtt-10"> 9)</span><span
11717 class="cmtt-10"> [sy]</span><span
11718 class="cmtt-10"> =</span><span
11719 class="cmtt-10"> [base]</span><span
11720 class="cmtt-10"> -</span><span
11721 class="cmtt-10"> 1</span>
11722 <br class="fancyvrb" /><a
11723 id="x1-123024r12"></a><span
11724 class="cmtt-10"> </span><span
11725 class="cmtt-10"> </span>
11726 <br class="fancyvrb" /><a
11727 id="x1-123026r13"></a><span
11728 class="cmtt-10"> </span><span
11729 class="cmtt-10"> </span><span
11730 class="cmtt-10"> </span><span
11731 class="cmtt-10"> </span><span
11732 class="cmtt-10"> </span><span
11733 class="cmtt-10"> </span><span
11734 class="cmtt-10"> }</span><span
11735 class="cmtt-10"> else</span><span
11736 class="cmtt-10"> {</span>
11737 <br class="fancyvrb" /><a
11738 id="x1-123028r14"></a><span
11739 class="cmtt-10"> </span><span
11740 class="cmtt-10"> </span>
11741 <br class="fancyvrb" /><a
11742 id="x1-123030r15"></a><span
11743 class="cmtt-10"> </span><span
11744 class="cmtt-10"> </span><span
11745 class="cmtt-10"> </span><span
11746 class="cmtt-10"> </span><span
11747 class="cmtt-10"> </span><span
11748 class="cmtt-10"> </span><span
11749 class="cmtt-10"> </span><span
11750 class="cmtt-10"> </span><span
11751 class="cmtt-10"> 10)</span><span
11752 class="cmtt-10"> [sy]</span><span
11753 class="cmtt-10"> =</span><span
11754 class="cmtt-10"> [base]</span><span
11755 class="cmtt-10"> +</span><span
11756 class="cmtt-10"> 1</span>
11757 <br class="fancyvrb" /><a
11758 id="x1-123032r16"></a><span
11759 class="cmtt-10"> </span><span
11760 class="cmtt-10"> </span>
11761 <br class="fancyvrb" /><a
11762 id="x1-123034r17"></a><span
11763 class="cmtt-10"> </span><span
11764 class="cmtt-10"> </span><span
11765 class="cmtt-10"> </span><span
11766 class="cmtt-10"> </span><span
11767 class="cmtt-10"> </span><span
11768 class="cmtt-10"> </span><span
11769 class="cmtt-10"> }</span>
11770 <br class="fancyvrb" /><a
11771 id="x1-123036r18"></a><span
11772 class="cmtt-10"> </span><span
11773 class="cmtt-10"> </span>
11774 <br class="fancyvrb" /><a
11775 id="x1-123038r19"></a><span
11776 class="cmtt-10"> </span><span
11777 class="cmtt-10"> </span><span
11778 class="cmtt-10"> 11)</span><span
11779 class="cmtt-10"> [ady]</span><span
11780 class="cmtt-10"> =</span><span
11781 class="cmtt-10"> [ady]</span><span
11782 class="cmtt-10"> -</span><span
11783 class="cmtt-10"> (absolute</span><span
11784 class="cmtt-10"> value</span><span
11785 class="cmtt-10"> of</span><span
11786 class="cmtt-10"> [base])</span><span
11787 class="cmtt-10"> *</span><span
11788 class="cmtt-10"> [adx]</span>
11789 <br class="fancyvrb" /><a
11790 id="x1-123040r20"></a><span
11791 class="cmtt-10"> </span><span
11792 class="cmtt-10"> </span><span
11793 class="cmtt-10"> 12)</span><span
11794 class="cmtt-10"> vector</span><span
11795 class="cmtt-10"> [v]</span><span
11796 class="cmtt-10"> element</span><span
11797 class="cmtt-10"> [x]</span><span
11798 class="cmtt-10"> =</span><span
11799 class="cmtt-10"> [y]</span>
11800 <br class="fancyvrb" /><a
11801 id="x1-123042r21"></a><span
11802 class="cmtt-10"> </span><span
11803 class="cmtt-10"> </span>
11804 <br class="fancyvrb" /><a
11805 id="x1-123044r22"></a><span
11806 class="cmtt-10"> </span><span
11807 class="cmtt-10"> </span><span
11808 class="cmtt-10"> 13)</span><span
11809 class="cmtt-10"> iterate</span><span
11810 class="cmtt-10"> [x]</span><span
11811 class="cmtt-10"> over</span><span
11812 class="cmtt-10"> the</span><span
11813 class="cmtt-10"> range</span><span
11814 class="cmtt-10"> [x0]+1</span><span
11815 class="cmtt-10"> ...</span><span
11816 class="cmtt-10"> [x1]-1</span><span
11817 class="cmtt-10"> {</span>
11818 <br class="fancyvrb" /><a
11819 id="x1-123046r23"></a><span
11820 class="cmtt-10"> </span><span
11821 class="cmtt-10"> </span>
11822 <br class="fancyvrb" /><a
11823 id="x1-123048r24"></a><span
11824 class="cmtt-10"> </span><span
11825 class="cmtt-10"> </span><span
11826 class="cmtt-10"> </span><span
11827 class="cmtt-10"> </span><span
11828 class="cmtt-10"> </span><span
11829 class="cmtt-10"> </span><span
11830 class="cmtt-10"> </span><span
11831 class="cmtt-10"> </span><span
11832 class="cmtt-10"> 14)</span><span
11833 class="cmtt-10"> [err]</span><span
11834 class="cmtt-10"> =</span><span
11835 class="cmtt-10"> [err]</span><span
11836 class="cmtt-10"> +</span><span
11837 class="cmtt-10"> [ady];</span>
11838 <br class="fancyvrb" /><a
11839 id="x1-123050r25"></a><span
11840 class="cmtt-10"> </span><span
11841 class="cmtt-10"> </span><span
11842 class="cmtt-10"> </span><span
11843 class="cmtt-10"> </span><span
11844 class="cmtt-10"> </span><span
11845 class="cmtt-10"> </span><span
11846 class="cmtt-10"> </span><span
11847 class="cmtt-10"> </span><span
11848 class="cmtt-10"> 15)</span><span
11849 class="cmtt-10"> if</span><span
11850 class="cmtt-10"> (</span><span
11851 class="cmtt-10"> [err]</span><span
11852 class="cmtt-10"> >=</span><span
11853 class="cmtt-10"> [adx]</span><span
11854 class="cmtt-10"> )</span><span
11855 class="cmtt-10"> {</span>
11856 <br class="fancyvrb" /><a
11857 id="x1-123052r26"></a><span
11858 class="cmtt-10"> </span><span
11859 class="cmtt-10"> </span>
11860 <br class="fancyvrb" /><a
11861 id="x1-123054r27"></a><span
11862 class="cmtt-10"> </span><span
11863 class="cmtt-10"> </span><span
11864 class="cmtt-10"> </span><span
11865 class="cmtt-10"> </span><span
11866 class="cmtt-10"> </span><span
11867 class="cmtt-10"> </span><span
11868 class="cmtt-10"> </span><span
11869 class="cmtt-10"> </span><span
11870 class="cmtt-10"> </span><span
11871 class="cmtt-10"> </span><span
11872 class="cmtt-10"> </span><span
11873 class="cmtt-10"> </span><span
11874 class="cmtt-10"> </span><span
11875 class="cmtt-10"> </span><span
11876 class="cmtt-10"> 16)</span><span
11877 class="cmtt-10"> [err]</span><span
11878 class="cmtt-10"> =</span><span
11879 class="cmtt-10"> [err]</span><span
11880 class="cmtt-10"> -</span><span
11881 class="cmtt-10"> [adx]</span>
11882 <br class="fancyvrb" /><a
11883 id="x1-123056r28"></a><span
11884 class="cmtt-10"> </span><span
11885 class="cmtt-10"> </span><span
11886 class="cmtt-10"> </span><span
11887 class="cmtt-10"> </span><span
11888 class="cmtt-10"> </span><span
11889 class="cmtt-10"> </span><span
11890 class="cmtt-10"> </span><span
11891 class="cmtt-10"> </span><span
11892 class="cmtt-10"> </span><span
11893 class="cmtt-10"> </span><span
11894 class="cmtt-10"> </span><span
11895 class="cmtt-10"> </span><span
11896 class="cmtt-10"> </span><span
11897 class="cmtt-10"> </span><span
11898 class="cmtt-10"> 17)</span><span
11899 class="cmtt-10"> </span><span
11900 class="cmtt-10"> </span><span
11901 class="cmtt-10"> [y]</span><span
11902 class="cmtt-10"> =</span><span
11903 class="cmtt-10"> [y]</span><span
11904 class="cmtt-10"> +</span><span
11905 class="cmtt-10"> [sy]</span>
11909 <br class="fancyvrb" /><a
11910 id="x1-123058r29"></a><span
11911 class="cmtt-10"> </span><span
11912 class="cmtt-10"> </span>
11913 <br class="fancyvrb" /><a
11914 id="x1-123060r30"></a><span
11915 class="cmtt-10"> </span><span
11916 class="cmtt-10"> </span><span
11917 class="cmtt-10"> </span><span
11918 class="cmtt-10"> </span><span
11919 class="cmtt-10"> </span><span
11920 class="cmtt-10"> </span><span
11921 class="cmtt-10"> </span><span
11922 class="cmtt-10"> </span><span
11923 class="cmtt-10"> </span><span
11924 class="cmtt-10"> </span><span
11925 class="cmtt-10"> </span><span
11926 class="cmtt-10"> </span><span
11927 class="cmtt-10"> }</span><span
11928 class="cmtt-10"> else</span><span
11929 class="cmtt-10"> {</span>
11930 <br class="fancyvrb" /><a
11931 id="x1-123062r31"></a><span
11932 class="cmtt-10"> </span><span
11933 class="cmtt-10"> </span>
11934 <br class="fancyvrb" /><a
11935 id="x1-123064r32"></a><span
11936 class="cmtt-10"> </span><span
11937 class="cmtt-10"> </span><span
11938 class="cmtt-10"> </span><span
11939 class="cmtt-10"> </span><span
11940 class="cmtt-10"> </span><span
11941 class="cmtt-10"> </span><span
11942 class="cmtt-10"> </span><span
11943 class="cmtt-10"> </span><span
11944 class="cmtt-10"> </span><span
11945 class="cmtt-10"> </span><span
11946 class="cmtt-10"> </span><span
11947 class="cmtt-10"> </span><span
11948 class="cmtt-10"> </span><span
11949 class="cmtt-10"> </span><span
11950 class="cmtt-10"> 18)</span><span
11951 class="cmtt-10"> [y]</span><span
11952 class="cmtt-10"> =</span><span
11953 class="cmtt-10"> [y]</span><span
11954 class="cmtt-10"> +</span><span
11955 class="cmtt-10"> [base]</span>
11956 <br class="fancyvrb" /><a
11957 id="x1-123066r33"></a><span
11958 class="cmtt-10"> </span><span
11959 class="cmtt-10"> </span>
11960 <br class="fancyvrb" /><a
11961 id="x1-123068r34"></a><span
11962 class="cmtt-10"> </span><span
11963 class="cmtt-10"> </span><span
11964 class="cmtt-10"> </span><span
11965 class="cmtt-10"> </span><span
11966 class="cmtt-10"> </span><span
11967 class="cmtt-10"> </span><span
11968 class="cmtt-10"> </span><span
11969 class="cmtt-10"> </span><span
11970 class="cmtt-10"> </span><span
11971 class="cmtt-10"> </span><span
11972 class="cmtt-10"> </span><span
11973 class="cmtt-10"> </span><span
11974 class="cmtt-10"> }</span>
11975 <br class="fancyvrb" /><a
11976 id="x1-123070r35"></a><span
11977 class="cmtt-10"> </span><span
11978 class="cmtt-10"> </span>
11979 <br class="fancyvrb" /><a
11980 id="x1-123072r36"></a><span
11981 class="cmtt-10"> </span><span
11982 class="cmtt-10"> </span><span
11983 class="cmtt-10"> </span><span
11984 class="cmtt-10"> </span><span
11985 class="cmtt-10"> </span><span
11986 class="cmtt-10"> </span><span
11987 class="cmtt-10"> </span><span
11988 class="cmtt-10"> </span><span
11989 class="cmtt-10"> 19)</span><span
11990 class="cmtt-10"> vector</span><span
11991 class="cmtt-10"> [v]</span><span
11992 class="cmtt-10"> element</span><span
11993 class="cmtt-10"> [x]</span><span
11994 class="cmtt-10"> =</span><span
11995 class="cmtt-10"> [y]</span>
11996 <br class="fancyvrb" /><a
11997 id="x1-123074r37"></a><span
11998 class="cmtt-10"> </span><span
11999 class="cmtt-10"> </span>
12000 <br class="fancyvrb" /><a
12001 id="x1-123076r38"></a><span
12002 class="cmtt-10"> </span><span
12003 class="cmtt-10"> </span><span
12004 class="cmtt-10"> </span><span
12005 class="cmtt-10"> </span><span
12006 class="cmtt-10"> </span><span
12007 class="cmtt-10"> </span><span
12008 class="cmtt-10"> }</span>
12016 <h3 class="sectionHead"><span class="titlemark">10 </span> <a
12017 id="x1-12400010"></a>Tables</h3>
12018 <!--l. 6--><p class="noindent" >
12019 <h4 class="subsectionHead"><span class="titlemark">10.1 </span> <a
12020 id="x1-12500010.1"></a>floor1_inverse_dB_table</h4>
12021 <!--l. 8--><p class="noindent" >The vector <span
12022 class="cmtt-10x-x-109">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consiting of the
12023 following values (read left to right then top to bottom):
12024 <!--l. 12--><p class="noindent" >
12025 <div class="fancyvrb" id="fancyvrb48">
12027 id="x1-125002r1"></a><span
12028 class="cmtt-10"> </span><span
12029 class="cmtt-10"> </span><span
12030 class="cmtt-10"> </span><span
12031 class="cmtt-10"> 1.0649863e-07,</span><span
12032 class="cmtt-10"> 1.1341951e-07,</span><span
12033 class="cmtt-10"> 1.2079015e-07,</span><span
12034 class="cmtt-10"> 1.2863978e-07,</span>
12035 <br class="fancyvrb" /><a
12036 id="x1-125004r2"></a><span
12037 class="cmtt-10"> </span><span
12038 class="cmtt-10"> </span><span
12039 class="cmtt-10"> </span><span
12040 class="cmtt-10"> 1.3699951e-07,</span><span
12041 class="cmtt-10"> 1.4590251e-07,</span><span
12042 class="cmtt-10"> 1.5538408e-07,</span><span
12043 class="cmtt-10"> 1.6548181e-07,</span>
12044 <br class="fancyvrb" /><a
12045 id="x1-125006r3"></a><span
12046 class="cmtt-10"> </span><span
12047 class="cmtt-10"> </span><span
12048 class="cmtt-10"> </span><span
12049 class="cmtt-10"> 1.7623575e-07,</span><span
12050 class="cmtt-10"> 1.8768855e-07,</span><span
12051 class="cmtt-10"> 1.9988561e-07,</span><span
12052 class="cmtt-10"> 2.1287530e-07,</span>
12053 <br class="fancyvrb" /><a
12054 id="x1-125008r4"></a><span
12055 class="cmtt-10"> </span><span
12056 class="cmtt-10"> </span><span
12057 class="cmtt-10"> </span><span
12058 class="cmtt-10"> 2.2670913e-07,</span><span
12059 class="cmtt-10"> 2.4144197e-07,</span><span
12060 class="cmtt-10"> 2.5713223e-07,</span><span
12061 class="cmtt-10"> 2.7384213e-07,</span>
12062 <br class="fancyvrb" /><a
12063 id="x1-125010r5"></a><span
12064 class="cmtt-10"> </span><span
12065 class="cmtt-10"> </span><span
12066 class="cmtt-10"> </span><span
12067 class="cmtt-10"> 2.9163793e-07,</span><span
12068 class="cmtt-10"> 3.1059021e-07,</span><span
12069 class="cmtt-10"> 3.3077411e-07,</span><span
12070 class="cmtt-10"> 3.5226968e-07,</span>
12071 <br class="fancyvrb" /><a
12072 id="x1-125012r6"></a><span
12073 class="cmtt-10"> </span><span
12074 class="cmtt-10"> </span><span
12075 class="cmtt-10"> </span><span
12076 class="cmtt-10"> 3.7516214e-07,</span><span
12077 class="cmtt-10"> 3.9954229e-07,</span><span
12078 class="cmtt-10"> 4.2550680e-07,</span><span
12079 class="cmtt-10"> 4.5315863e-07,</span>
12080 <br class="fancyvrb" /><a
12081 id="x1-125014r7"></a><span
12082 class="cmtt-10"> </span><span
12083 class="cmtt-10"> </span><span
12084 class="cmtt-10"> </span><span
12085 class="cmtt-10"> 4.8260743e-07,</span><span
12086 class="cmtt-10"> 5.1396998e-07,</span><span
12087 class="cmtt-10"> 5.4737065e-07,</span><span
12088 class="cmtt-10"> 5.8294187e-07,</span>
12089 <br class="fancyvrb" /><a
12090 id="x1-125016r8"></a><span
12091 class="cmtt-10"> </span><span
12092 class="cmtt-10"> </span><span
12093 class="cmtt-10"> </span><span
12094 class="cmtt-10"> 6.2082472e-07,</span><span
12095 class="cmtt-10"> 6.6116941e-07,</span><span
12096 class="cmtt-10"> 7.0413592e-07,</span><span
12097 class="cmtt-10"> 7.4989464e-07,</span>
12098 <br class="fancyvrb" /><a
12099 id="x1-125018r9"></a><span
12100 class="cmtt-10"> </span><span
12101 class="cmtt-10"> </span><span
12102 class="cmtt-10"> </span><span
12103 class="cmtt-10"> 7.9862701e-07,</span><span
12104 class="cmtt-10"> 8.5052630e-07,</span><span
12105 class="cmtt-10"> 9.0579828e-07,</span><span
12106 class="cmtt-10"> 9.6466216e-07,</span>
12107 <br class="fancyvrb" /><a
12108 id="x1-125020r10"></a><span
12109 class="cmtt-10"> </span><span
12110 class="cmtt-10"> </span><span
12111 class="cmtt-10"> </span><span
12112 class="cmtt-10"> 1.0273513e-06,</span><span
12113 class="cmtt-10"> 1.0941144e-06,</span><span
12114 class="cmtt-10"> 1.1652161e-06,</span><span
12115 class="cmtt-10"> 1.2409384e-06,</span>
12116 <br class="fancyvrb" /><a
12117 id="x1-125022r11"></a><span
12118 class="cmtt-10"> </span><span
12119 class="cmtt-10"> </span><span
12120 class="cmtt-10"> </span><span
12121 class="cmtt-10"> 1.3215816e-06,</span><span
12122 class="cmtt-10"> 1.4074654e-06,</span><span
12123 class="cmtt-10"> 1.4989305e-06,</span><span
12124 class="cmtt-10"> 1.5963394e-06,</span>
12125 <br class="fancyvrb" /><a
12126 id="x1-125024r12"></a><span
12127 class="cmtt-10"> </span><span
12128 class="cmtt-10"> </span><span
12129 class="cmtt-10"> </span><span
12130 class="cmtt-10"> 1.7000785e-06,</span><span
12131 class="cmtt-10"> 1.8105592e-06,</span><span
12132 class="cmtt-10"> 1.9282195e-06,</span><span
12133 class="cmtt-10"> 2.0535261e-06,</span>
12134 <br class="fancyvrb" /><a
12135 id="x1-125026r13"></a><span
12136 class="cmtt-10"> </span><span
12137 class="cmtt-10"> </span><span
12138 class="cmtt-10"> </span><span
12139 class="cmtt-10"> 2.1869758e-06,</span><span
12140 class="cmtt-10"> 2.3290978e-06,</span><span
12141 class="cmtt-10"> 2.4804557e-06,</span><span
12142 class="cmtt-10"> 2.6416497e-06,</span>
12143 <br class="fancyvrb" /><a
12144 id="x1-125028r14"></a><span
12145 class="cmtt-10"> </span><span
12146 class="cmtt-10"> </span><span
12147 class="cmtt-10"> </span><span
12148 class="cmtt-10"> 2.8133190e-06,</span><span
12149 class="cmtt-10"> 2.9961443e-06,</span><span
12150 class="cmtt-10"> 3.1908506e-06,</span><span
12151 class="cmtt-10"> 3.3982101e-06,</span>
12152 <br class="fancyvrb" /><a
12153 id="x1-125030r15"></a><span
12154 class="cmtt-10"> </span><span
12155 class="cmtt-10"> </span><span
12156 class="cmtt-10"> </span><span
12157 class="cmtt-10"> 3.6190449e-06,</span><span
12158 class="cmtt-10"> 3.8542308e-06,</span><span
12159 class="cmtt-10"> 4.1047004e-06,</span><span
12160 class="cmtt-10"> 4.3714470e-06,</span>
12161 <br class="fancyvrb" /><a
12162 id="x1-125032r16"></a><span
12163 class="cmtt-10"> </span><span
12164 class="cmtt-10"> </span><span
12165 class="cmtt-10"> </span><span
12166 class="cmtt-10"> 4.6555282e-06,</span><span
12167 class="cmtt-10"> 4.9580707e-06,</span><span
12168 class="cmtt-10"> 5.2802740e-06,</span><span
12169 class="cmtt-10"> 5.6234160e-06,</span>
12170 <br class="fancyvrb" /><a
12171 id="x1-125034r17"></a><span
12172 class="cmtt-10"> </span><span
12173 class="cmtt-10"> </span><span
12174 class="cmtt-10"> </span><span
12175 class="cmtt-10"> 5.9888572e-06,</span><span
12176 class="cmtt-10"> 6.3780469e-06,</span><span
12177 class="cmtt-10"> 6.7925283e-06,</span><span
12178 class="cmtt-10"> 7.2339451e-06,</span>
12179 <br class="fancyvrb" /><a
12180 id="x1-125036r18"></a><span
12181 class="cmtt-10"> </span><span
12182 class="cmtt-10"> </span><span
12183 class="cmtt-10"> </span><span
12184 class="cmtt-10"> 7.7040476e-06,</span><span
12185 class="cmtt-10"> 8.2047000e-06,</span><span
12186 class="cmtt-10"> 8.7378876e-06,</span><span
12187 class="cmtt-10"> 9.3057248e-06,</span>
12188 <br class="fancyvrb" /><a
12189 id="x1-125038r19"></a><span
12190 class="cmtt-10"> </span><span
12191 class="cmtt-10"> </span><span
12192 class="cmtt-10"> </span><span
12193 class="cmtt-10"> 9.9104632e-06,</span><span
12194 class="cmtt-10"> 1.0554501e-05,</span><span
12195 class="cmtt-10"> 1.1240392e-05,</span><span
12196 class="cmtt-10"> 1.1970856e-05,</span>
12197 <br class="fancyvrb" /><a
12198 id="x1-125040r20"></a><span
12199 class="cmtt-10"> </span><span
12200 class="cmtt-10"> </span><span
12201 class="cmtt-10"> </span><span
12202 class="cmtt-10"> 1.2748789e-05,</span><span
12203 class="cmtt-10"> 1.3577278e-05,</span><span
12204 class="cmtt-10"> 1.4459606e-05,</span><span
12205 class="cmtt-10"> 1.5399272e-05,</span>
12206 <br class="fancyvrb" /><a
12207 id="x1-125042r21"></a><span
12208 class="cmtt-10"> </span><span
12209 class="cmtt-10"> </span><span
12210 class="cmtt-10"> </span><span
12211 class="cmtt-10"> 1.6400004e-05,</span><span
12212 class="cmtt-10"> 1.7465768e-05,</span><span
12213 class="cmtt-10"> 1.8600792e-05,</span><span
12214 class="cmtt-10"> 1.9809576e-05,</span>
12215 <br class="fancyvrb" /><a
12216 id="x1-125044r22"></a><span
12217 class="cmtt-10"> </span><span
12218 class="cmtt-10"> </span><span
12219 class="cmtt-10"> </span><span
12220 class="cmtt-10"> 2.1096914e-05,</span><span
12221 class="cmtt-10"> 2.2467911e-05,</span><span
12222 class="cmtt-10"> 2.3928002e-05,</span><span
12223 class="cmtt-10"> 2.5482978e-05,</span>
12224 <br class="fancyvrb" /><a
12225 id="x1-125046r23"></a><span
12226 class="cmtt-10"> </span><span
12227 class="cmtt-10"> </span><span
12228 class="cmtt-10"> </span><span
12229 class="cmtt-10"> 2.7139006e-05,</span><span
12230 class="cmtt-10"> 2.8902651e-05,</span><span
12231 class="cmtt-10"> 3.0780908e-05,</span><span
12232 class="cmtt-10"> 3.2781225e-05,</span>
12233 <br class="fancyvrb" /><a
12234 id="x1-125048r24"></a><span
12235 class="cmtt-10"> </span><span
12236 class="cmtt-10"> </span><span
12237 class="cmtt-10"> </span><span
12238 class="cmtt-10"> 3.4911534e-05,</span><span
12239 class="cmtt-10"> 3.7180282e-05,</span><span
12240 class="cmtt-10"> 3.9596466e-05,</span><span
12241 class="cmtt-10"> 4.2169667e-05,</span>
12242 <br class="fancyvrb" /><a
12243 id="x1-125050r25"></a><span
12244 class="cmtt-10"> </span><span
12245 class="cmtt-10"> </span><span
12246 class="cmtt-10"> </span><span
12247 class="cmtt-10"> 4.4910090e-05,</span><span
12248 class="cmtt-10"> 4.7828601e-05,</span><span
12249 class="cmtt-10"> 5.0936773e-05,</span><span
12250 class="cmtt-10"> 5.4246931e-05,</span>
12251 <br class="fancyvrb" /><a
12252 id="x1-125052r26"></a><span
12253 class="cmtt-10"> </span><span
12254 class="cmtt-10"> </span><span
12255 class="cmtt-10"> </span><span
12256 class="cmtt-10"> 5.7772202e-05,</span><span
12257 class="cmtt-10"> 6.1526565e-05,</span><span
12258 class="cmtt-10"> 6.5524908e-05,</span><span
12259 class="cmtt-10"> 6.9783085e-05,</span>
12260 <br class="fancyvrb" /><a
12261 id="x1-125054r27"></a><span
12262 class="cmtt-10"> </span><span
12263 class="cmtt-10"> </span><span
12264 class="cmtt-10"> </span><span
12265 class="cmtt-10"> 7.4317983e-05,</span><span
12266 class="cmtt-10"> 7.9147585e-05,</span><span
12267 class="cmtt-10"> 8.4291040e-05,</span><span
12268 class="cmtt-10"> 8.9768747e-05,</span>
12269 <br class="fancyvrb" /><a
12270 id="x1-125056r28"></a><span
12271 class="cmtt-10"> </span><span
12272 class="cmtt-10"> </span><span
12273 class="cmtt-10"> </span><span
12274 class="cmtt-10"> 9.5602426e-05,</span><span
12275 class="cmtt-10"> 0.00010181521,</span><span
12276 class="cmtt-10"> 0.00010843174,</span><span
12277 class="cmtt-10"> 0.00011547824,</span>
12278 <br class="fancyvrb" /><a
12279 id="x1-125058r29"></a><span
12280 class="cmtt-10"> </span><span
12281 class="cmtt-10"> </span><span
12282 class="cmtt-10"> </span><span
12283 class="cmtt-10"> 0.00012298267,</span><span
12284 class="cmtt-10"> 0.00013097477,</span><span
12285 class="cmtt-10"> 0.00013948625,</span><span
12286 class="cmtt-10"> 0.00014855085,</span>
12287 <br class="fancyvrb" /><a
12288 id="x1-125060r30"></a><span
12289 class="cmtt-10"> </span><span
12290 class="cmtt-10"> </span><span
12291 class="cmtt-10"> </span><span
12292 class="cmtt-10"> 0.00015820453,</span><span
12293 class="cmtt-10"> 0.00016848555,</span><span
12294 class="cmtt-10"> 0.00017943469,</span><span
12295 class="cmtt-10"> 0.00019109536,</span>
12296 <br class="fancyvrb" /><a
12297 id="x1-125062r31"></a><span
12298 class="cmtt-10"> </span><span
12299 class="cmtt-10"> </span><span
12300 class="cmtt-10"> </span><span
12301 class="cmtt-10"> 0.00020351382,</span><span
12302 class="cmtt-10"> 0.00021673929,</span><span
12303 class="cmtt-10"> 0.00023082423,</span><span
12304 class="cmtt-10"> 0.00024582449,</span>
12305 <br class="fancyvrb" /><a
12306 id="x1-125064r32"></a><span
12307 class="cmtt-10"> </span><span
12308 class="cmtt-10"> </span><span
12309 class="cmtt-10"> </span><span
12310 class="cmtt-10"> 0.00026179955,</span><span
12311 class="cmtt-10"> 0.00027881276,</span><span
12312 class="cmtt-10"> 0.00029693158,</span><span
12313 class="cmtt-10"> 0.00031622787,</span>
12314 <br class="fancyvrb" /><a
12315 id="x1-125066r33"></a><span
12316 class="cmtt-10"> </span><span
12317 class="cmtt-10"> </span><span
12318 class="cmtt-10"> </span><span
12319 class="cmtt-10"> 0.00033677814,</span><span
12320 class="cmtt-10"> 0.00035866388,</span><span
12321 class="cmtt-10"> 0.00038197188,</span><span
12322 class="cmtt-10"> 0.00040679456,</span>
12323 <br class="fancyvrb" /><a
12324 id="x1-125068r34"></a><span
12325 class="cmtt-10"> </span><span
12326 class="cmtt-10"> </span><span
12327 class="cmtt-10"> </span><span
12328 class="cmtt-10"> 0.00043323036,</span><span
12329 class="cmtt-10"> 0.00046138411,</span><span
12330 class="cmtt-10"> 0.00049136745,</span><span
12331 class="cmtt-10"> 0.00052329927,</span>
12332 <br class="fancyvrb" /><a
12333 id="x1-125070r35"></a><span
12334 class="cmtt-10"> </span><span
12335 class="cmtt-10"> </span><span
12336 class="cmtt-10"> </span><span
12337 class="cmtt-10"> 0.00055730621,</span><span
12338 class="cmtt-10"> 0.00059352311,</span><span
12339 class="cmtt-10"> 0.00063209358,</span><span
12340 class="cmtt-10"> 0.00067317058,</span>
12341 <br class="fancyvrb" /><a
12342 id="x1-125072r36"></a><span
12343 class="cmtt-10"> </span><span
12344 class="cmtt-10"> </span><span
12345 class="cmtt-10"> </span><span
12346 class="cmtt-10"> 0.00071691700,</span><span
12347 class="cmtt-10"> 0.00076350630,</span><span
12348 class="cmtt-10"> 0.00081312324,</span><span
12349 class="cmtt-10"> 0.00086596457,</span>
12353 <br class="fancyvrb" /><a
12354 id="x1-125074r37"></a><span
12355 class="cmtt-10"> </span><span
12356 class="cmtt-10"> </span><span
12357 class="cmtt-10"> </span><span
12358 class="cmtt-10"> 0.00092223983,</span><span
12359 class="cmtt-10"> 0.00098217216,</span><span
12360 class="cmtt-10"> 0.0010459992,</span><span
12361 class="cmtt-10"> </span><span
12362 class="cmtt-10"> 0.0011139742,</span>
12363 <br class="fancyvrb" /><a
12364 id="x1-125076r38"></a><span
12365 class="cmtt-10"> </span><span
12366 class="cmtt-10"> </span><span
12367 class="cmtt-10"> </span><span
12368 class="cmtt-10"> 0.0011863665,</span><span
12369 class="cmtt-10"> </span><span
12370 class="cmtt-10"> 0.0012634633,</span><span
12371 class="cmtt-10"> </span><span
12372 class="cmtt-10"> 0.0013455702,</span><span
12373 class="cmtt-10"> </span><span
12374 class="cmtt-10"> 0.0014330129,</span>
12375 <br class="fancyvrb" /><a
12376 id="x1-125078r39"></a><span
12377 class="cmtt-10"> </span><span
12378 class="cmtt-10"> </span><span
12379 class="cmtt-10"> </span><span
12380 class="cmtt-10"> 0.0015261382,</span><span
12381 class="cmtt-10"> </span><span
12382 class="cmtt-10"> 0.0016253153,</span><span
12383 class="cmtt-10"> </span><span
12384 class="cmtt-10"> 0.0017309374,</span><span
12385 class="cmtt-10"> </span><span
12386 class="cmtt-10"> 0.0018434235,</span>
12387 <br class="fancyvrb" /><a
12388 id="x1-125080r40"></a><span
12389 class="cmtt-10"> </span><span
12390 class="cmtt-10"> </span><span
12391 class="cmtt-10"> </span><span
12392 class="cmtt-10"> 0.0019632195,</span><span
12393 class="cmtt-10"> </span><span
12394 class="cmtt-10"> 0.0020908006,</span><span
12395 class="cmtt-10"> </span><span
12396 class="cmtt-10"> 0.0022266726,</span><span
12397 class="cmtt-10"> </span><span
12398 class="cmtt-10"> 0.0023713743,</span>
12399 <br class="fancyvrb" /><a
12400 id="x1-125082r41"></a><span
12401 class="cmtt-10"> </span><span
12402 class="cmtt-10"> </span><span
12403 class="cmtt-10"> </span><span
12404 class="cmtt-10"> 0.0025254795,</span><span
12405 class="cmtt-10"> </span><span
12406 class="cmtt-10"> 0.0026895994,</span><span
12407 class="cmtt-10"> </span><span
12408 class="cmtt-10"> 0.0028643847,</span><span
12409 class="cmtt-10"> </span><span
12410 class="cmtt-10"> 0.0030505286,</span>
12411 <br class="fancyvrb" /><a
12412 id="x1-125084r42"></a><span
12413 class="cmtt-10"> </span><span
12414 class="cmtt-10"> </span><span
12415 class="cmtt-10"> </span><span
12416 class="cmtt-10"> 0.0032487691,</span><span
12417 class="cmtt-10"> </span><span
12418 class="cmtt-10"> 0.0034598925,</span><span
12419 class="cmtt-10"> </span><span
12420 class="cmtt-10"> 0.0036847358,</span><span
12421 class="cmtt-10"> </span><span
12422 class="cmtt-10"> 0.0039241906,</span>
12423 <br class="fancyvrb" /><a
12424 id="x1-125086r43"></a><span
12425 class="cmtt-10"> </span><span
12426 class="cmtt-10"> </span><span
12427 class="cmtt-10"> </span><span
12428 class="cmtt-10"> 0.0041792066,</span><span
12429 class="cmtt-10"> </span><span
12430 class="cmtt-10"> 0.0044507950,</span><span
12431 class="cmtt-10"> </span><span
12432 class="cmtt-10"> 0.0047400328,</span><span
12433 class="cmtt-10"> </span><span
12434 class="cmtt-10"> 0.0050480668,</span>
12435 <br class="fancyvrb" /><a
12436 id="x1-125088r44"></a><span
12437 class="cmtt-10"> </span><span
12438 class="cmtt-10"> </span><span
12439 class="cmtt-10"> </span><span
12440 class="cmtt-10"> 0.0053761186,</span><span
12441 class="cmtt-10"> </span><span
12442 class="cmtt-10"> 0.0057254891,</span><span
12443 class="cmtt-10"> </span><span
12444 class="cmtt-10"> 0.0060975636,</span><span
12445 class="cmtt-10"> </span><span
12446 class="cmtt-10"> 0.0064938176,</span>
12447 <br class="fancyvrb" /><a
12448 id="x1-125090r45"></a><span
12449 class="cmtt-10"> </span><span
12450 class="cmtt-10"> </span><span
12451 class="cmtt-10"> </span><span
12452 class="cmtt-10"> 0.0069158225,</span><span
12453 class="cmtt-10"> </span><span
12454 class="cmtt-10"> 0.0073652516,</span><span
12455 class="cmtt-10"> </span><span
12456 class="cmtt-10"> 0.0078438871,</span><span
12457 class="cmtt-10"> </span><span
12458 class="cmtt-10"> 0.0083536271,</span>
12459 <br class="fancyvrb" /><a
12460 id="x1-125092r46"></a><span
12461 class="cmtt-10"> </span><span
12462 class="cmtt-10"> </span><span
12463 class="cmtt-10"> </span><span
12464 class="cmtt-10"> 0.0088964928,</span><span
12465 class="cmtt-10"> </span><span
12466 class="cmtt-10"> 0.009474637,</span><span
12467 class="cmtt-10"> </span><span
12468 class="cmtt-10"> </span><span
12469 class="cmtt-10"> 0.010090352,</span><span
12470 class="cmtt-10"> </span><span
12471 class="cmtt-10"> </span><span
12472 class="cmtt-10"> 0.010746080,</span>
12473 <br class="fancyvrb" /><a
12474 id="x1-125094r47"></a><span
12475 class="cmtt-10"> </span><span
12476 class="cmtt-10"> </span><span
12477 class="cmtt-10"> </span><span
12478 class="cmtt-10"> 0.011444421,</span><span
12479 class="cmtt-10"> </span><span
12480 class="cmtt-10"> </span><span
12481 class="cmtt-10"> 0.012188144,</span><span
12482 class="cmtt-10"> </span><span
12483 class="cmtt-10"> </span><span
12484 class="cmtt-10"> 0.012980198,</span><span
12485 class="cmtt-10"> </span><span
12486 class="cmtt-10"> </span><span
12487 class="cmtt-10"> 0.013823725,</span>
12488 <br class="fancyvrb" /><a
12489 id="x1-125096r48"></a><span
12490 class="cmtt-10"> </span><span
12491 class="cmtt-10"> </span><span
12492 class="cmtt-10"> </span><span
12493 class="cmtt-10"> 0.014722068,</span><span
12494 class="cmtt-10"> </span><span
12495 class="cmtt-10"> </span><span
12496 class="cmtt-10"> 0.015678791,</span><span
12497 class="cmtt-10"> </span><span
12498 class="cmtt-10"> </span><span
12499 class="cmtt-10"> 0.016697687,</span><span
12500 class="cmtt-10"> </span><span
12501 class="cmtt-10"> </span><span
12502 class="cmtt-10"> 0.017782797,</span>
12503 <br class="fancyvrb" /><a
12504 id="x1-125098r49"></a><span
12505 class="cmtt-10"> </span><span
12506 class="cmtt-10"> </span><span
12507 class="cmtt-10"> </span><span
12508 class="cmtt-10"> 0.018938423,</span><span
12509 class="cmtt-10"> </span><span
12510 class="cmtt-10"> </span><span
12511 class="cmtt-10"> 0.020169149,</span><span
12512 class="cmtt-10"> </span><span
12513 class="cmtt-10"> </span><span
12514 class="cmtt-10"> 0.021479854,</span><span
12515 class="cmtt-10"> </span><span
12516 class="cmtt-10"> </span><span
12517 class="cmtt-10"> 0.022875735,</span>
12518 <br class="fancyvrb" /><a
12519 id="x1-125100r50"></a><span
12520 class="cmtt-10"> </span><span
12521 class="cmtt-10"> </span><span
12522 class="cmtt-10"> </span><span
12523 class="cmtt-10"> 0.024362330,</span><span
12524 class="cmtt-10"> </span><span
12525 class="cmtt-10"> </span><span
12526 class="cmtt-10"> 0.025945531,</span><span
12527 class="cmtt-10"> </span><span
12528 class="cmtt-10"> </span><span
12529 class="cmtt-10"> 0.027631618,</span><span
12530 class="cmtt-10"> </span><span
12531 class="cmtt-10"> </span><span
12532 class="cmtt-10"> 0.029427276,</span>
12533 <br class="fancyvrb" /><a
12534 id="x1-125102r51"></a><span
12535 class="cmtt-10"> </span><span
12536 class="cmtt-10"> </span><span
12537 class="cmtt-10"> </span><span
12538 class="cmtt-10"> 0.031339626,</span><span
12539 class="cmtt-10"> </span><span
12540 class="cmtt-10"> </span><span
12541 class="cmtt-10"> 0.033376252,</span><span
12542 class="cmtt-10"> </span><span
12543 class="cmtt-10"> </span><span
12544 class="cmtt-10"> 0.035545228,</span><span
12545 class="cmtt-10"> </span><span
12546 class="cmtt-10"> </span><span
12547 class="cmtt-10"> 0.037855157,</span>
12548 <br class="fancyvrb" /><a
12549 id="x1-125104r52"></a><span
12550 class="cmtt-10"> </span><span
12551 class="cmtt-10"> </span><span
12552 class="cmtt-10"> </span><span
12553 class="cmtt-10"> 0.040315199,</span><span
12554 class="cmtt-10"> </span><span
12555 class="cmtt-10"> </span><span
12556 class="cmtt-10"> 0.042935108,</span><span
12557 class="cmtt-10"> </span><span
12558 class="cmtt-10"> </span><span
12559 class="cmtt-10"> 0.045725273,</span><span
12560 class="cmtt-10"> </span><span
12561 class="cmtt-10"> </span><span
12562 class="cmtt-10"> 0.048696758,</span>
12563 <br class="fancyvrb" /><a
12564 id="x1-125106r53"></a><span
12565 class="cmtt-10"> </span><span
12566 class="cmtt-10"> </span><span
12567 class="cmtt-10"> </span><span
12568 class="cmtt-10"> 0.051861348,</span><span
12569 class="cmtt-10"> </span><span
12570 class="cmtt-10"> </span><span
12571 class="cmtt-10"> 0.055231591,</span><span
12572 class="cmtt-10"> </span><span
12573 class="cmtt-10"> </span><span
12574 class="cmtt-10"> 0.058820850,</span><span
12575 class="cmtt-10"> </span><span
12576 class="cmtt-10"> </span><span
12577 class="cmtt-10"> 0.062643361,</span>
12578 <br class="fancyvrb" /><a
12579 id="x1-125108r54"></a><span
12580 class="cmtt-10"> </span><span
12581 class="cmtt-10"> </span><span
12582 class="cmtt-10"> </span><span
12583 class="cmtt-10"> 0.066714279,</span><span
12584 class="cmtt-10"> </span><span
12585 class="cmtt-10"> </span><span
12586 class="cmtt-10"> 0.071049749,</span><span
12587 class="cmtt-10"> </span><span
12588 class="cmtt-10"> </span><span
12589 class="cmtt-10"> 0.075666962,</span><span
12590 class="cmtt-10"> </span><span
12591 class="cmtt-10"> </span><span
12592 class="cmtt-10"> 0.080584227,</span>
12593 <br class="fancyvrb" /><a
12594 id="x1-125110r55"></a><span
12595 class="cmtt-10"> </span><span
12596 class="cmtt-10"> </span><span
12597 class="cmtt-10"> </span><span
12598 class="cmtt-10"> 0.085821044,</span><span
12599 class="cmtt-10"> </span><span
12600 class="cmtt-10"> </span><span
12601 class="cmtt-10"> 0.091398179,</span><span
12602 class="cmtt-10"> </span><span
12603 class="cmtt-10"> </span><span
12604 class="cmtt-10"> 0.097337747,</span><span
12605 class="cmtt-10"> </span><span
12606 class="cmtt-10"> </span><span
12607 class="cmtt-10"> 0.10366330,</span>
12608 <br class="fancyvrb" /><a
12609 id="x1-125112r56"></a><span
12610 class="cmtt-10"> </span><span
12611 class="cmtt-10"> </span><span
12612 class="cmtt-10"> </span><span
12613 class="cmtt-10"> 0.11039993,</span><span
12614 class="cmtt-10"> </span><span
12615 class="cmtt-10"> </span><span
12616 class="cmtt-10"> </span><span
12617 class="cmtt-10"> 0.11757434,</span><span
12618 class="cmtt-10"> </span><span
12619 class="cmtt-10"> </span><span
12620 class="cmtt-10"> </span><span
12621 class="cmtt-10"> 0.12521498,</span><span
12622 class="cmtt-10"> </span><span
12623 class="cmtt-10"> </span><span
12624 class="cmtt-10"> </span><span
12625 class="cmtt-10"> 0.13335215,</span>
12626 <br class="fancyvrb" /><a
12627 id="x1-125114r57"></a><span
12628 class="cmtt-10"> </span><span
12629 class="cmtt-10"> </span><span
12630 class="cmtt-10"> </span><span
12631 class="cmtt-10"> 0.14201813,</span><span
12632 class="cmtt-10"> </span><span
12633 class="cmtt-10"> </span><span
12634 class="cmtt-10"> </span><span
12635 class="cmtt-10"> 0.15124727,</span><span
12636 class="cmtt-10"> </span><span
12637 class="cmtt-10"> </span><span
12638 class="cmtt-10"> </span><span
12639 class="cmtt-10"> 0.16107617,</span><span
12640 class="cmtt-10"> </span><span
12641 class="cmtt-10"> </span><span
12642 class="cmtt-10"> </span><span
12643 class="cmtt-10"> 0.17154380,</span>
12644 <br class="fancyvrb" /><a
12645 id="x1-125116r58"></a><span
12646 class="cmtt-10"> </span><span
12647 class="cmtt-10"> </span><span
12648 class="cmtt-10"> </span><span
12649 class="cmtt-10"> 0.18269168,</span><span
12650 class="cmtt-10"> </span><span
12651 class="cmtt-10"> </span><span
12652 class="cmtt-10"> </span><span
12653 class="cmtt-10"> 0.19456402,</span><span
12654 class="cmtt-10"> </span><span
12655 class="cmtt-10"> </span><span
12656 class="cmtt-10"> </span><span
12657 class="cmtt-10"> 0.20720788,</span><span
12658 class="cmtt-10"> </span><span
12659 class="cmtt-10"> </span><span
12660 class="cmtt-10"> </span><span
12661 class="cmtt-10"> 0.22067342,</span>
12662 <br class="fancyvrb" /><a
12663 id="x1-125118r59"></a><span
12664 class="cmtt-10"> </span><span
12665 class="cmtt-10"> </span><span
12666 class="cmtt-10"> </span><span
12667 class="cmtt-10"> 0.23501402,</span><span
12668 class="cmtt-10"> </span><span
12669 class="cmtt-10"> </span><span
12670 class="cmtt-10"> </span><span
12671 class="cmtt-10"> 0.25028656,</span><span
12672 class="cmtt-10"> </span><span
12673 class="cmtt-10"> </span><span
12674 class="cmtt-10"> </span><span
12675 class="cmtt-10"> 0.26655159,</span><span
12676 class="cmtt-10"> </span><span
12677 class="cmtt-10"> </span><span
12678 class="cmtt-10"> </span><span
12679 class="cmtt-10"> 0.28387361,</span>
12680 <br class="fancyvrb" /><a
12681 id="x1-125120r60"></a><span
12682 class="cmtt-10"> </span><span
12683 class="cmtt-10"> </span><span
12684 class="cmtt-10"> </span><span
12685 class="cmtt-10"> 0.30232132,</span><span
12686 class="cmtt-10"> </span><span
12687 class="cmtt-10"> </span><span
12688 class="cmtt-10"> </span><span
12689 class="cmtt-10"> 0.32196786,</span><span
12690 class="cmtt-10"> </span><span
12691 class="cmtt-10"> </span><span
12692 class="cmtt-10"> </span><span
12693 class="cmtt-10"> 0.34289114,</span><span
12694 class="cmtt-10"> </span><span
12695 class="cmtt-10"> </span><span
12696 class="cmtt-10"> </span><span
12697 class="cmtt-10"> 0.36517414,</span>
12698 <br class="fancyvrb" /><a
12699 id="x1-125122r61"></a><span
12700 class="cmtt-10"> </span><span
12701 class="cmtt-10"> </span><span
12702 class="cmtt-10"> </span><span
12703 class="cmtt-10"> 0.38890521,</span><span
12704 class="cmtt-10"> </span><span
12705 class="cmtt-10"> </span><span
12706 class="cmtt-10"> </span><span
12707 class="cmtt-10"> 0.41417847,</span><span
12708 class="cmtt-10"> </span><span
12709 class="cmtt-10"> </span><span
12710 class="cmtt-10"> </span><span
12711 class="cmtt-10"> 0.44109412,</span><span
12712 class="cmtt-10"> </span><span
12713 class="cmtt-10"> </span><span
12714 class="cmtt-10"> </span><span
12715 class="cmtt-10"> 0.46975890,</span>
12716 <br class="fancyvrb" /><a
12717 id="x1-125124r62"></a><span
12718 class="cmtt-10"> </span><span
12719 class="cmtt-10"> </span><span
12720 class="cmtt-10"> </span><span
12721 class="cmtt-10"> 0.50028648,</span><span
12722 class="cmtt-10"> </span><span
12723 class="cmtt-10"> </span><span
12724 class="cmtt-10"> </span><span
12725 class="cmtt-10"> 0.53279791,</span><span
12726 class="cmtt-10"> </span><span
12727 class="cmtt-10"> </span><span
12728 class="cmtt-10"> </span><span
12729 class="cmtt-10"> 0.56742212,</span><span
12730 class="cmtt-10"> </span><span
12731 class="cmtt-10"> </span><span
12732 class="cmtt-10"> </span><span
12733 class="cmtt-10"> 0.60429640,</span>
12734 <br class="fancyvrb" /><a
12735 id="x1-125126r63"></a><span
12736 class="cmtt-10"> </span><span
12737 class="cmtt-10"> </span><span
12738 class="cmtt-10"> </span><span
12739 class="cmtt-10"> 0.64356699,</span><span
12740 class="cmtt-10"> </span><span
12741 class="cmtt-10"> </span><span
12742 class="cmtt-10"> </span><span
12743 class="cmtt-10"> 0.68538959,</span><span
12744 class="cmtt-10"> </span><span
12745 class="cmtt-10"> </span><span
12746 class="cmtt-10"> </span><span
12747 class="cmtt-10"> 0.72993007,</span><span
12748 class="cmtt-10"> </span><span
12749 class="cmtt-10"> </span><span
12750 class="cmtt-10"> </span><span
12751 class="cmtt-10"> 0.77736504,</span>
12752 <br class="fancyvrb" /><a
12753 id="x1-125128r64"></a><span
12754 class="cmtt-10"> </span><span
12755 class="cmtt-10"> </span><span
12756 class="cmtt-10"> </span><span
12757 class="cmtt-10"> 0.82788260,</span><span
12758 class="cmtt-10"> </span><span
12759 class="cmtt-10"> </span><span
12760 class="cmtt-10"> </span><span
12761 class="cmtt-10"> 0.88168307,</span><span
12762 class="cmtt-10"> </span><span
12763 class="cmtt-10"> </span><span
12764 class="cmtt-10"> </span><span
12765 class="cmtt-10"> 0.9389798,</span><span
12766 class="cmtt-10"> </span><span
12767 class="cmtt-10"> </span><span
12768 class="cmtt-10"> </span><span
12769 class="cmtt-10"> </span><span
12770 class="cmtt-10"> 1.</span>
12778 <h3 class="sectionHead"><span class="titlemark">A </span> <a
12779 id="x1-126000A"></a>Embedding Vorbis into an Ogg stream</h3>
12780 <!--l. 6--><p class="noindent" >
12781 <h4 class="subsectionHead"><span class="titlemark">A.1 </span> <a
12782 id="x1-127000A.1"></a>Overview</h4>
12783 <!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
12784 compressed audio packet data into file form.
12785 <!--l. 12--><p class="noindent" >The <a
12786 href="#x1-20001">Section 1<!--tex4ht:ref: vorbis:spec:intro --></a>, “<a
12787 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of Vorbis
12789 <!--l. 15--><p class="noindent" >The <a
12790 href="oggstream.html" >Ogg bitstream overview</a> and <a
12791 href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
12792 descriptions of Ogg transport streams. This specification document assumes a working
12793 knowledge of the concepts covered in these named backround documents. Please read them
12795 <!--l. 22--><p class="noindent" >
12796 <h5 class="subsubsectionHead"><span class="titlemark">A.1.1 </span> <a
12797 id="x1-128000A.1.1"></a>Restrictions</h5>
12798 <!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
12799 streams in degenerate, unmultiplexed form only. That is:
12800 <ul class="itemize1">
12801 <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
12803 <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams (links).
12805 <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream, per
12808 <!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media types into a
12809 multi-stream Ogg file. At the time this document was written, Ogg was becoming a popular
12810 container for low-bitrate movies consisting of DivX video and Vorbis audio. However, a ’Vorbis I
12811 audio file’ is taken to imply Vorbis audio existing alone within a degenerate Ogg stream. A
12812 compliant ’Vorbis audio player’ is not required to implement Ogg support beyond the specific
12813 support of Vorbis within a degenrate Ogg stream (naturally, application authors are encouraged to
12814 support full multiplexed Ogg handling).
12818 <!--l. 55--><p class="noindent" >
12819 <h5 class="subsubsectionHead"><span class="titlemark">A.1.2 </span> <a
12820 id="x1-129000A.1.2"></a>MIME type</h5>
12821 <!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
12822 applications should use <span
12823 class="cmtt-10x-x-109">application/ogg</span>, while visual media should use <span
12824 class="cmtt-10x-x-109">video/ogg</span>, and audio
12826 class="cmtt-10x-x-109">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP encapsulated
12827 Vorbis should use <span
12828 class="cmtt-10x-x-109">audio/vorbis </span>+ <span
12829 class="cmtt-10x-x-109">audio/vorbis-config</span>.
12830 <!--l. 65--><p class="noindent" >
12831 <h4 class="subsectionHead"><span class="titlemark">A.2 </span> <a
12832 id="x1-130000A.2"></a>Encapsulation</h4>
12833 <!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
12834 <ul class="itemize1">
12835 <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
12836 as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This results
12837 in a first Ogg page of exactly 58 bytes at the very beginning of the logical stream.
12839 <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
12841 <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
12842 more pages beginning on the second page of the logical stream. However many pages
12843 they span, the third header packet finishes the page on which it ends. The next (first
12844 audio) packet must begin on a fresh page.
12846 <li class="itemize">The granule position of these first pages containing only headers is zero.
12848 <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
12850 <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
12852 <li class="itemize">The last page is marked ’end of stream’ in the page flags.
12854 <li class="itemize">Vorbis packets may span page boundaries.
12859 <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio samples
12860 (per channel; a stereo stream’s granule position does not increment at twice the speed
12863 <li class="itemize">The granule position of a page represents the end PCM sample position of the last
12865 class="cmti-10x-x-109">completed </span>on that page. The ’last PCM sample’ is the last complete sample
12866 returned by decode, not an internal sample awaiting lapping with a subsequent block. A
12867 page that is entirely spanned by a single packet (that completes on a subsequent page)
12868 has no granule position, and the granule position is set to ’-1’.
12869 <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
12870 necessarily the middle sample from that block. If, eg, the current Vorbis packet
12871 encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
12872 decodable sample from the current packet be at position (3*long_block_length/4) -
12873 (short_block_length/4).
12875 <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream started
12876 at position zero. Although the granule position belongs to the last completed packet
12877 on the page and a valid granule position must be positive, by inference it may indicate
12878 that the PCM position of the beginning of audio is positive or negative.
12879 <ul class="itemize2">
12880 <li class="itemize">A positive starting value simply indicates that this stream begins at some positive
12881 time offset, potentially within a larger program. This is a common case when
12882 connecting to the middle of broadcast stream.
12884 <li class="itemize">A negative value indicates that output samples preceeding time zero should be
12885 discarded during decoding; this technique is used to allow sample-granularity
12886 editing of the stream start time of already-encoded Vorbis streams. The number
12887 of samples to be discarded must not exceed the overlap-add span of the first two
12890 <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the second
12891 finished audio packet must flush the page on which it appears and the third packet begin a
12892 fresh page. This allows the decoder to always be able to perform PCM position adjustments
12893 before needing to return any PCM data from synthesis, resulting in correct positioning
12894 information without any aditional seeking logic.
12895 <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
12896 id="x1-131000A.2"></a><span
12897 class="cmbx-10x-x-109">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return incorrect
12898 positioning information for seeking operations at the very beginning of the stream.
12903 <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the final
12904 packet would normally return is used to end the stream on other than even frame
12905 boundaries. The difference between the actual available data returned and the
12906 declared amount indicates how many trailing samples to discard from the decoding
12912 <h3 class="sectionHead"><span class="titlemark">B </span> <a
12913 id="x1-132000B"></a>Vorbis encapsulation in RTP</h3>
12914 <!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
12915 class="cmti-10x-x-109">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of how
12916 to embed Vorbis audio in an RTP stream.
12923 <h3 class="likesectionHead"><a
12924 id="x1-133000B"></a>Colophon</h3>
12925 <!--l. 6--><p class="noindent" ><img
12926 src="Vorbis_I_spec15x.png" alt="PIC" class="graphics"><!--tex4ht:graphics
12927 name="Vorbis_I_spec15x.png" src="xifish.pdf"
12929 <!--l. 10--><p class="noindent" >Ogg is a <a
12930 href="http://www.xiph.org/" >Xiph.org Foundation</a> effort to protect essential tenets of Internet multimedia from
12931 corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See <a
12932 href="http://www.xiph.org/about.html" >About
12933 the Xiph.org Foundation</a> for details.
12934 <!--l. 17--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
12935 Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.org
12936 Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification and
12937 certify specification compliance.
12938 <!--l. 23--><p class="noindent" >Xiph.org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
12939 does not restrict third parties from distributing independent implementations of Vorbis software
12940 under other licenses.
12941 <!--l. 28--><p class="noindent" >Ogg, Vorbis, Xiph.org Foundation and their logos are trademarks (tm) of the <a
12942 href="http://www.xiph.org/" >Xiph.org
12943 Foundation</a>. These pages are copyright (C) 1994-2007 Xiph.org Foundation. All rights
12945 <!--l. 33--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
12946 class="E">E</span>X</span></span>.
12950 <h3 class="likesectionHead"><a
12951 id="x1-134000B"></a>References</h3>
12952 <!--l. 129--><p class="noindent" >
12953 <div class="thebibliography">
12954 <p class="bibitem" ><span class="biblabel">
12955 [1]<span class="bibsp">   </span></span><a
12956 id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg
12957 and B. Edler, The use of multirate filter banks for coding of high quality digital audio,
12959 href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span
12960 class="cmtt-10x-x-109">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.
projects / platform / upstream / libvorbis.git / blob