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22 <h2 class="titleHead">Vorbis I specification</h2>
23 <div class="author" ><span
24 class="cmr-17">Xiph.Org Foundation</span></div><br />
25 <div class="date" ><span
26 class="cmr-17">August 11, 2011</span></div>
28 <h3 class="likesectionHead"><a
29 id="x1-1000"></a>Contents</h3>
30 <div class="tableofcontents">
31  <span class="sectionToc" >1 <a
32 href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
33 <br />  <span class="subsectionToc" >1.1 <a
34 href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
35 <br />   <span class="subsubsectionToc" >1.1.1 <a
36 href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
37 <br />   <span class="subsubsectionToc" >1.1.2 <a
38 href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
39 <br />   <span class="subsubsectionToc" >1.1.3 <a
40 href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
41 <br />   <span class="subsubsectionToc" >1.1.4 <a
42 href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
43 <br />   <span class="subsubsectionToc" >1.1.5 <a
44 href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
45 <br />   <span class="subsubsectionToc" >1.1.6 <a
46 href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
47 <br />  <span class="subsectionToc" >1.2 <a
48 href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
49 <br />   <span class="subsubsectionToc" >1.2.1 <a
50 href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
51 <br />   <span class="subsubsectionToc" >1.2.2 <a
52 href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
53 <br />   <span class="subsubsectionToc" >1.2.3 <a
54 href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
58 <br />   <span class="subsubsectionToc" >1.2.4 <a
59 href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
60 <br />   <span class="subsubsectionToc" >1.2.5 <a
61 href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
62 <br />   <span class="subsubsectionToc" >1.2.6 <a
63 href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
64 <br />  <span class="subsectionToc" >1.3 <a
65 href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
66 <br />   <span class="subsubsectionToc" >1.3.1 <a
67 href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
68 <br />   <span class="subsubsectionToc" >1.3.2 <a
69 href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
70 <br /> <span class="sectionToc" >2 <a
71 href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
72 <br />  <span class="subsectionToc" >2.1 <a
73 href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
74 <br />   <span class="subsubsectionToc" >2.1.1 <a
75 href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
76 <br />   <span class="subsubsectionToc" >2.1.2 <a
77 href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
78 <br />   <span class="subsubsectionToc" >2.1.3 <a
79 href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
80 <br />   <span class="subsubsectionToc" >2.1.4 <a
81 href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
82 <br />   <span class="subsubsectionToc" >2.1.5 <a
83 href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
84 <br />   <span class="subsubsectionToc" >2.1.6 <a
85 href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
86 <br />   <span class="subsubsectionToc" >2.1.7 <a
87 href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
88 <br />   <span class="subsubsectionToc" >2.1.8 <a
89 href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
90 <br />   <span class="subsubsectionToc" >2.1.9 <a
91 href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
92 <br /> <span class="sectionToc" >3 <a
93 href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
94 <br />  <span class="subsectionToc" >3.1 <a
95 href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
96 <br />   <span class="subsubsectionToc" >3.1.1 <a
97 href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
98 <br />  <span class="subsectionToc" >3.2 <a
99 href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
100 <br />   <span class="subsubsectionToc" >3.2.1 <a
101 href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
102 <br />  <span class="subsectionToc" >3.3 <a
103 href="#x1-570003.3" id="QQ2-1-62">Use of the codebook abstraction</a></span>
104 <br /> <span class="sectionToc" >4 <a
105 href="#x1-580004" id="QQ2-1-63">Codec Setup and Packet Decode</a></span>
106 <br />  <span class="subsectionToc" >4.1 <a
107 href="#x1-590004.1" id="QQ2-1-64">Overview</a></span>
108 <br />  <span class="subsectionToc" >4.2 <a
109 href="#x1-600004.2" id="QQ2-1-65">Header decode and decode setup</a></span>
110 <br />   <span class="subsubsectionToc" >4.2.1 <a
111 href="#x1-610004.2.1" id="QQ2-1-66">Common header decode</a></span>
112 <br />   <span class="subsubsectionToc" >4.2.2 <a
113 href="#x1-620004.2.2" id="QQ2-1-67">Identification header</a></span>
114 <br />   <span class="subsubsectionToc" >4.2.3 <a
115 href="#x1-630004.2.3" id="QQ2-1-68">Comment header</a></span>
119 <br />   <span class="subsubsectionToc" >4.2.4 <a
120 href="#x1-640004.2.4" id="QQ2-1-69">Setup header</a></span>
121 <br />  <span class="subsectionToc" >4.3 <a
122 href="#x1-710004.3" id="QQ2-1-77">Audio packet decode and synthesis</a></span>
123 <br />   <span class="subsubsectionToc" >4.3.1 <a
124 href="#x1-720004.3.1" id="QQ2-1-78">packet type, mode and window decode</a></span>
125 <br />   <span class="subsubsectionToc" >4.3.2 <a
126 href="#x1-730004.3.2" id="QQ2-1-79">floor curve decode</a></span>
127 <br />   <span class="subsubsectionToc" >4.3.3 <a
128 href="#x1-740004.3.3" id="QQ2-1-80">nonzero vector propagate</a></span>
129 <br />   <span class="subsubsectionToc" >4.3.4 <a
130 href="#x1-750004.3.4" id="QQ2-1-81">residue decode</a></span>
131 <br />   <span class="subsubsectionToc" >4.3.5 <a
132 href="#x1-760004.3.5" id="QQ2-1-82">inverse coupling</a></span>
133 <br />   <span class="subsubsectionToc" >4.3.6 <a
134 href="#x1-770004.3.6" id="QQ2-1-83">dot product</a></span>
135 <br />   <span class="subsubsectionToc" >4.3.7 <a
136 href="#x1-780004.3.7" id="QQ2-1-84">inverse MDCT</a></span>
137 <br />   <span class="subsubsectionToc" >4.3.8 <a
138 href="#x1-790004.3.8" id="QQ2-1-85">overlap_add</a></span>
139 <br />   <span class="subsubsectionToc" >4.3.9 <a
140 href="#x1-800004.3.9" id="QQ2-1-86">output channel order</a></span>
141 <br /> <span class="sectionToc" >5 <a
142 href="#x1-810005" id="QQ2-1-87">comment field and header specification</a></span>
143 <br />  <span class="subsectionToc" >5.1 <a
144 href="#x1-820005.1" id="QQ2-1-88">Overview</a></span>
145 <br />  <span class="subsectionToc" >5.2 <a
146 href="#x1-830005.2" id="QQ2-1-89">Comment encoding</a></span>
147 <br />   <span class="subsubsectionToc" >5.2.1 <a
148 href="#x1-840005.2.1" id="QQ2-1-90">Structure</a></span>
149 <br />   <span class="subsubsectionToc" >5.2.2 <a
150 href="#x1-850005.2.2" id="QQ2-1-91">Content vector format</a></span>
151 <br />   <span class="subsubsectionToc" >5.2.3 <a
152 href="#x1-880005.2.3" id="QQ2-1-94">Encoding</a></span>
153 <br /> <span class="sectionToc" >6 <a
154 href="#x1-890006" id="QQ2-1-95">Floor type 0 setup and decode</a></span>
155 <br />  <span class="subsectionToc" >6.1 <a
156 href="#x1-900006.1" id="QQ2-1-96">Overview</a></span>
157 <br />  <span class="subsectionToc" >6.2 <a
158 href="#x1-910006.2" id="QQ2-1-97">Floor 0 format</a></span>
159 <br />   <span class="subsubsectionToc" >6.2.1 <a
160 href="#x1-920006.2.1" id="QQ2-1-98">header decode</a></span>
161 <br />   <span class="subsubsectionToc" >6.2.2 <a
162 href="#x1-930006.2.2" id="QQ2-1-99">packet decode</a></span>
163 <br />   <span class="subsubsectionToc" >6.2.3 <a
164 href="#x1-940006.2.3" id="QQ2-1-100">curve computation</a></span>
165 <br /> <span class="sectionToc" >7 <a
166 href="#x1-950007" id="QQ2-1-101">Floor type 1 setup and decode</a></span>
167 <br />  <span class="subsectionToc" >7.1 <a
168 href="#x1-960007.1" id="QQ2-1-102">Overview</a></span>
169 <br />  <span class="subsectionToc" >7.2 <a
170 href="#x1-970007.2" id="QQ2-1-103">Floor 1 format</a></span>
171 <br />   <span class="subsubsectionToc" >7.2.1 <a
172 href="#x1-980007.2.1" id="QQ2-1-104">model</a></span>
173 <br />   <span class="subsubsectionToc" >7.2.2 <a
174 href="#x1-990007.2.2" id="QQ2-1-109">header decode</a></span>
175 <br /> <span class="sectionToc" >8 <a
176 href="#x1-1020008" id="QQ2-1-112">Residue setup and decode</a></span>
180 <br />  <span class="subsectionToc" >8.1 <a
181 href="#x1-1030008.1" id="QQ2-1-113">Overview</a></span>
182 <br />  <span class="subsectionToc" >8.2 <a
183 href="#x1-1040008.2" id="QQ2-1-114">Residue format</a></span>
184 <br />  <span class="subsectionToc" >8.3 <a
185 href="#x1-1050008.3" id="QQ2-1-116">residue 0</a></span>
186 <br />  <span class="subsectionToc" >8.4 <a
187 href="#x1-1060008.4" id="QQ2-1-117">residue 1</a></span>
188 <br />  <span class="subsectionToc" >8.5 <a
189 href="#x1-1070008.5" id="QQ2-1-118">residue 2</a></span>
190 <br />  <span class="subsectionToc" >8.6 <a
191 href="#x1-1080008.6" id="QQ2-1-120">Residue decode</a></span>
192 <br />   <span class="subsubsectionToc" >8.6.1 <a
193 href="#x1-1090008.6.1" id="QQ2-1-121">header decode</a></span>
194 <br />   <span class="subsubsectionToc" >8.6.2 <a
195 href="#x1-1100008.6.2" id="QQ2-1-122">packet decode</a></span>
196 <br />   <span class="subsubsectionToc" >8.6.3 <a
197 href="#x1-1110008.6.3" id="QQ2-1-123">format 0 specifics</a></span>
198 <br />   <span class="subsubsectionToc" >8.6.4 <a
199 href="#x1-1120008.6.4" id="QQ2-1-124">format 1 specifics</a></span>
200 <br />   <span class="subsubsectionToc" >8.6.5 <a
201 href="#x1-1130008.6.5" id="QQ2-1-125">format 2 specifics</a></span>
202 <br /> <span class="sectionToc" >9 <a
203 href="#x1-1140009" id="QQ2-1-126">Helper equations</a></span>
204 <br />  <span class="subsectionToc" >9.1 <a
205 href="#x1-1150009.1" id="QQ2-1-127">Overview</a></span>
206 <br />  <span class="subsectionToc" >9.2 <a
207 href="#x1-1160009.2" id="QQ2-1-128">Functions</a></span>
208 <br />   <span class="subsubsectionToc" >9.2.1 <a
209 href="#x1-1170009.2.1" id="QQ2-1-129">ilog</a></span>
210 <br />   <span class="subsubsectionToc" >9.2.2 <a
211 href="#x1-1180009.2.2" id="QQ2-1-130">float32_unpack</a></span>
212 <br />   <span class="subsubsectionToc" >9.2.3 <a
213 href="#x1-1190009.2.3" id="QQ2-1-131">lookup1_values</a></span>
214 <br />   <span class="subsubsectionToc" >9.2.4 <a
215 href="#x1-1200009.2.4" id="QQ2-1-132">low_neighbor</a></span>
216 <br />   <span class="subsubsectionToc" >9.2.5 <a
217 href="#x1-1210009.2.5" id="QQ2-1-133">high_neighbor</a></span>
218 <br />   <span class="subsubsectionToc" >9.2.6 <a
219 href="#x1-1220009.2.6" id="QQ2-1-134">render_point</a></span>
220 <br />   <span class="subsubsectionToc" >9.2.7 <a
221 href="#x1-1230009.2.7" id="QQ2-1-135">render_line</a></span>
222 <br /> <span class="sectionToc" >10 <a
223 href="#x1-12400010" id="QQ2-1-136">Tables</a></span>
224 <br />  <span class="subsectionToc" >10.1 <a
225 href="#x1-12500010.1" id="QQ2-1-137">floor1_inverse_dB_table</a></span>
226 <br /> <span class="sectionToc" >A <a
227 href="#x1-126000A" id="QQ2-1-138">Embedding Vorbis into an Ogg stream</a></span>
228 <br />  <span class="subsectionToc" >A.1 <a
229 href="#x1-127000A.1" id="QQ2-1-139">Overview</a></span>
230 <br />   <span class="subsubsectionToc" >A.1.1 <a
231 href="#x1-128000A.1.1" id="QQ2-1-140">Restrictions</a></span>
232 <br />   <span class="subsubsectionToc" >A.1.2 <a
233 href="#x1-129000A.1.2" id="QQ2-1-141">MIME type</a></span>
234 <br />  <span class="subsectionToc" >A.2 <a
235 href="#x1-130000A.2" id="QQ2-1-142">Encapsulation</a></span>
236 <br /> <span class="sectionToc" >B <a
237 href="#x1-132000B" id="QQ2-1-144">Vorbis encapsulation in RTP</a></span>
245 <h3 class="sectionHead"><span class="titlemark">1. </span> <a
246 id="x1-20001"></a>Introduction and Description</h3>
247 <!--l. 6--><p class="noindent" >
248 <h4 class="subsectionHead"><span class="titlemark">1.1. </span> <a
249 id="x1-30001.1"></a>Overview</h4>
250 <!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
251 specification appears beginning in <a
252 href="#x1-580004">Section 4</a>, “<a
253 href="#x1-580004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later
254 sections assume a high-level understanding of the Vorbis decode process, which is provided
256 <!--l. 15--><p class="noindent" >
257 <h5 class="subsubsectionHead"><span class="titlemark">1.1.1. </span> <a
258 id="x1-40001.1.1"></a>Application</h5>
259 <!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
260 flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At
261 the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same
262 league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT
263 rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower
264 and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
265 representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
267 <!--l. 29--><p class="noindent" >
268 <h5 class="subsubsectionHead"><span class="titlemark">1.1.2. </span> <a
269 id="x1-50001.1.2"></a>Classification</h5>
270 <!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete
271 Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in
272 Vorbis II to offer better transient response and reproduction using a transform better suited to
273 localized time events.
277 <!--l. 37--><p class="noindent" >
278 <h5 class="subsubsectionHead"><span class="titlemark">1.1.3. </span> <a
279 id="x1-60001.1.3"></a>Assumptions</h5>
280 <!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
281 low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
282 require more working memory as Vorbis has no static probability model; the vector codebooks
283 used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
284 bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to
285 which they are pre-decoded into a cache is the dominant factor in decoder memory
287 <!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it
288 is solely a method of accepting input audio, dividing it into individual frames and
289 compressing these frames into raw, unformatted ’packets’. The decoder then accepts
290 these raw packets in sequence, decodes them, synthesizes audio frames from them, and
291 reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form
292 variable bit rate (VBR) codec and packets have no minimum size, maximum size, or
293 fixed/expected size. Packets are designed that they may be truncated (or padded)
294 and remain decodable; this is not to be considered an error condition and is used
295 extensively in bitrate management in peeling. Both the transport mechanism and
296 decoder must allow that a packet may be any size, or end before or after packet decode
298 <!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
299 framing, sync, positioning and error correction in accordance with these design assumptions, such
300 as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
301 document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
302 although this is by no means a requirement or fundamental assumption in the Vorbis
304 <!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
305 href="#x1-126000A">Section A</a>,
307 href="#x1-126000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
308 <!--l. 77--><p class="noindent" >
309 <h5 class="subsubsectionHead"><span class="titlemark">1.1.4. </span> <a
310 id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
311 <!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
312 decades of continuous encoder improvement before running out of room within the codec
313 specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
314 extreme of forward adaptive.
318 <!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis
319 developer to keep in mind) is that the entire probability model of the codec, the Huffman and
320 VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
321 parameters (often several hundred fields). This makes it impossible, as it would be with
322 MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
323 decode at any frame in the stream without having previously fetched the codec setup
325 <!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a
326 id="x1-80001.1.4"></a><span
327 class="cmbx-12">Note:</span></span> Vorbis <span
328 class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
329 has been initialized/setup with the setup headers.
330 <!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream
331 headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less
332 is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
333 <!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is
334 an unusual design and thus causes some amount of complaint among engineers as this runs
335 against current design trends (and also points out limitations in some existing software/interface
336 designs, such as Windows’ ACM codec framework). However, we find that it does not
337 fundamentally limit Vorbis’ suitable application space.
338 <!--l. 115--><p class="noindent" >
339 <h5 class="subsubsectionHead"><span class="titlemark">1.1.5. </span> <a
340 id="x1-90001.1.5"></a>Format Specification</h5>
341 <!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets
342 that are correctly decoded by the reference Vorbis decoder described below may be considered
343 a proper Vorbis encoder. A decoder must faithfully and completely implement the
344 specification defined below (except where noted) to be considered a proper Vorbis
346 <!--l. 123--><p class="noindent" >
347 <h5 class="subsubsectionHead"><span class="titlemark">1.1.6. </span> <a
348 id="x1-100001.1.6"></a>Hardware Profile</h5>
352 <!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
353 embedded design. For this reason, embedded designs are allowed to deviate in limited ways from
354 the ‘full’ decode specification yet still be certified compliant. These optional omissions are
355 labelled in the spec where relevant.
356 <!--l. 131--><p class="noindent" >
357 <h4 class="subsectionHead"><span class="titlemark">1.2. </span> <a
358 id="x1-110001.2"></a>Decoder Configuration</h4>
359 <!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
360 perform specific functions in the decode pipeline. Each different component instance of a specific
361 type is semantically interchangeable; decoder configuration consists both of internal component
362 configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
363 arrangement is roughly as follows:
366 <!--l. 141--><p class="noindent" >
368 <!--l. 142--><p class="noindent" ><img
369 src="components.png" alt="PIC"
371 <br /> <div class="caption"
372 ><span class="id">Figure 1: </span><span
373 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-110011 -->
375 <!--l. 146--><p class="noindent" >
376 <h5 class="subsubsectionHead"><span class="titlemark">1.2.1. </span> <a
377 id="x1-120001.2.1"></a>Global Config</h5>
378 <!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
379 version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
380 configuration is in the context of specific components.
381 <!--l. 152--><p class="noindent" >
382 <h5 class="subsubsectionHead"><span class="titlemark">1.2.2. </span> <a
383 id="x1-130001.2.2"></a>Mode</h5>
387 <!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
389 <!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
390 methods with the intention of choosing a method best suited to that frame. Different
391 modes are, e.g. how frame size is changed from frame to frame. The mode number of a
392 frame serves as a top level configuration switch for all other specific aspects of frame
394 <!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis
395 window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping
396 number. The mapping number specifies which mapping configuration instance to use for low-level
397 packet decode and synthesis.
398 <!--l. 171--><p class="noindent" >
399 <h5 class="subsubsectionHead"><span class="titlemark">1.2.3. </span> <a
400 id="x1-140001.2.3"></a>Mapping</h5>
401 <!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets
402 of channel vectors together for grouped encoding and decoding. These submaps are
403 not references to external components; the submap list is internal and specific to a
405 <!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors
406 within a mapping. The submap functions as a last layer of indirection such that specific special
407 floor or residue settings can be applied not only to all the vectors in a given mode, but also
408 specific vectors in a specific mode. Each submap specifies the proper floor and residue
409 instance number to use for decoding that submap’s spectral floor and spectral residue
411 <!--l. 186--><p class="noindent" >As an example:
412 <!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth
413 channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a
414 full-spectrum version of it as with the other channels. The submapping mechanism can be used
415 to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only
416 representation to the bass channel, thus saving space. In this example, channels 0-4 belong to
417 submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which
418 uses a bass-only representation.
422 <!--l. 199--><p class="noindent" >
423 <h5 class="subsubsectionHead"><span class="titlemark">1.2.4. </span> <a
424 id="x1-150001.2.4"></a>Floor</h5>
425 <!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
426 representation of the audio spectrum for the given channel in the current frame, generally used
427 akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has
428 historically used it as a unit-baseline for spectral resolution.
429 <!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
430 amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
431 interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
432 are semantically interchangeable in encoding/decoding. However, floor type 1 provides more
433 stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and
434 high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
436 <!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
437 encoder past Xiph.Org’s own beta 4 makes use of floor 0.
438 <!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy
439 coding to save space. For this reason, a floor configuration generally refers to multiple
440 codebooks in the codebook component list. Entropy coding is thus provided as an
441 abstraction, and each floor instance may choose from any and all available codebooks when
443 <!--l. 230--><p class="noindent" >
444 <h5 class="subsubsectionHead"><span class="titlemark">1.2.5. </span> <a
445 id="x1-160001.2.5"></a>Residue</h5>
446 <!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been
447 subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector
448 quantization according to one of three specific packing/coding algorithms numbered
449 0 through 2. The packing algorithm details are configured by residue instance. As
450 with the floor components, the final VQ/entropy encoding is provided by external
451 codebook instances and each residue instance may choose from any and all available
453 <!--l. 241--><p class="noindent" >
457 <h5 class="subsubsectionHead"><span class="titlemark">1.2.6. </span> <a
458 id="x1-170001.2.6"></a>Codebooks</h5>
459 <!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use
460 the entropy-decoded integer value as an offset into an index of output value vectors, returning
461 the indicated vector of values.
462 <!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
463 representation. This tree is tightly packed using one of several methods, depending on whether
464 codeword lengths are ordered or unordered, or the tree is sparse.
465 <!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
466 the vector index is encoded as a single list of values of possible values that are then permuted
467 into a list of n-dimensional rows (lattice VQ).
468 <!--l. 260--><p class="noindent" >
469 <h4 class="subsectionHead"><span class="titlemark">1.3. </span> <a
470 id="x1-180001.3"></a>High-level Decode Process</h4>
471 <!--l. 262--><p class="noindent" >
472 <h5 class="subsubsectionHead"><span class="titlemark">1.3.1. </span> <a
473 id="x1-190001.3.1"></a>Decode Setup</h5>
474 <!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
475 stream to be decoded. Vorbis uses three header packets; all are required, in-order, by
476 this specification. Once set up, decode may begin at any audio packet belonging to
477 the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio
479 <!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
481 <!--l. 274--><p class="noindent" ><span class="paragraphHead"><a
482 id="x1-200001.3.1"></a><span
483 class="cmbx-12">Identification Header</span></span>
484 The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
485 characteristics of the stream such as sample rate and number of channels.
489 <!--l. 279--><p class="noindent" ><span class="paragraphHead"><a
490 id="x1-210001.3.1"></a><span
491 class="cmbx-12">Comment Header</span></span>
492 The comment header includes user text comments (“tags”) and a vendor string for the
493 application/library that produced the bitstream. The encoding and proper use of the comment
494 header is described in <a
495 href="#x1-810005">Section 5</a>, “<a
496 href="#x1-810005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
497 <!--l. 284--><p class="noindent" ><span class="paragraphHead"><a
498 id="x1-220001.3.1"></a><span
499 class="cmbx-12">Setup Header</span></span>
500 The setup header includes extensive CODEC setup information as well as the complete VQ and
501 Huffman codebooks needed for decode.
502 <!--l. 289--><p class="noindent" >
503 <h5 class="subsubsectionHead"><span class="titlemark">1.3.2. </span> <a
504 id="x1-230001.3.2"></a>Decode Procedure</h5>
505 <!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
506 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
508 class="enumerate-enumitem">decode packet type flag
509 </dd><dt class="enumerate-enumitem">
511 class="enumerate-enumitem">decode mode number
512 </dd><dt class="enumerate-enumitem">
514 class="enumerate-enumitem">decode window shape (long windows only)
515 </dd><dt class="enumerate-enumitem">
517 class="enumerate-enumitem">decode floor
518 </dd><dt class="enumerate-enumitem">
520 class="enumerate-enumitem">decode residue into residue vectors
521 </dd><dt class="enumerate-enumitem">
523 class="enumerate-enumitem">inverse channel coupling of residue vectors
524 </dd><dt class="enumerate-enumitem">
526 class="enumerate-enumitem">generate floor curve from decoded floor data
527 </dd><dt class="enumerate-enumitem">
529 class="enumerate-enumitem">compute dot product of floor and residue, producing audio spectrum vector
530 </dd><dt class="enumerate-enumitem">
532 class="enumerate-enumitem">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis
537 </dd><dt class="enumerate-enumitem">
539 class="enumerate-enumitem">overlap/add left-hand output of transform with right-hand output of previous frame
540 </dd><dt class="enumerate-enumitem">
542 class="enumerate-enumitem">store right hand-data from transform of current frame for future lapping
543 </dd><dt class="enumerate-enumitem">
545 class="enumerate-enumitem">if not first frame, return results of overlap/add as audio result of current frame</dd></dl>
546 <!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can
547 take advantage of symmetries in the MDCT to store the right-hand transform data of a partial
548 MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before
549 overlap/add with the next frame. This optimization produces entirely equivalent output and is
550 naturally perfectly legal. The decoder must be <span
551 class="cmti-12">entirely mathematically equivalent </span>to the
552 specification, it need not be a literal semantic implementation.
553 <!--l. 317--><p class="noindent" ><span class="paragraphHead"><a
554 id="x1-240001.3.2"></a><span
555 class="cmbx-12">Packet type decode</span></span>
556 Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis
557 headers described above. The fourth packet type marks an audio packet. All other packet types
558 are reserved; packets marked with a reserved type should be ignored.
559 <!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
560 audio packet decode is to read and verify the packet type; <span
561 class="cmti-12">a non-audio packet when audio is</span>
563 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
565 class="cmti-12">packet and not attempt decoding it to audio</span>.
566 <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
567 id="x1-250001.3.2"></a><span
568 class="cmbx-12">Mode decode</span></span>
569 Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
570 which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
571 offset into the mode instance index.
572 <!--l. 341--><p class="noindent" ><span class="paragraphHead"><a
573 id="x1-260001.3.2"></a><span
574 class="cmbx-12">Window shape decode (long windows only)</span></span>
575 Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I,
576 legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis
577 handles channels as independent vectors and these frame sizes are in samples per
582 <!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
583 avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
584 according to MDCT requirements, overlapped 50% with the output of the previous frame and
585 added. The window shape assures seamless reconstruction.
586 <!--l. 354--><p class="noindent" >This is easy to visualize in the case of equal sized-windows:
589 <!--l. 356--><p class="noindent" >
591 <!--l. 357--><p class="noindent" ><img
592 src="window1.png" alt="PIC"
594 <br /> <div class="caption"
595 ><span class="id">Figure 2: </span><span
596 class="content">overlap of two equal-sized windows</span></div><!--tex4ht:label?: x1-260012 -->
598 <!--l. 361--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows:
601 <!--l. 364--><p class="noindent" >
603 <!--l. 365--><p class="noindent" ><img
604 src="window2.png" alt="PIC"
606 <br /> <div class="caption"
607 ><span class="id">Figure 3: </span><span
608 class="content">overlap of a long and a short window</span></div><!--tex4ht:label?: x1-260023 -->
610 <!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
611 seamless lapping as above. It is possible to correctly infer window shape to be applied to the
612 current window from knowing the sizes of the current, previous and next window. It is legal for a
613 decoder to use this method. However, in the case of a long window (short windows require no
614 modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although
615 not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to
616 the point of lapping entirely independently of any other packet, allowing easier abstraction of
617 decode layers as well as allowing a greater level of easy parallelism in encode and
619 <!--l. 382--><p class="noindent" >A description of valid window functions for use with an inverse MDCT can be found in <span class="cite">[<a
620 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
621 Vorbis windows all use the slope function
622 <center class="math-display" >
624 src="Vorbis_I_spec0x.png" alt="y = sin (.5 ∗ π sin2((x + .5)∕n ∗ π)).
628 " class="math-display" ></center>
629 <!--l. 385--><p class="nopar" >
630 <!--l. 389--><p class="noindent" ><span class="paragraphHead"><a
631 id="x1-270001.3.2"></a><span
632 class="cmbx-12">floor decode</span></span>
633 Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
634 specifies which floor configuration to use. All floors are decoded before residue decode
636 <!--l. 395--><p class="noindent" ><span class="paragraphHead"><a
637 id="x1-280001.3.2"></a><span
638 class="cmbx-12">residue decode</span></span>
639 Although the number of residue vectors equals the number of channels, channel coupling may
640 mean that the raw residue vectors extracted during decode do not map directly to specific
641 channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or
642 angle. The coupling relationships are described in the codec setup and may differ from frame to
643 frame, due to different mode numbers.
644 <!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from
645 submap 0 through n-1. This differs from floors which are coded using a configuration provided by
646 submap number, but are coded individually in channel order.
647 <!--l. 411--><p class="noindent" ><span class="paragraphHead"><a
648 id="x1-290001.3.2"></a><span
649 class="cmbx-12">inverse channel coupling</span></span>
650 A detailed discussion of stereo in the Vorbis codec can be found in the document
652 href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo
653 coupling, but the stereo document also gives a good overview of the generic coupling
655 <!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a
656 pair at a time in the order and using the vectors specified in the current mapping
657 configuration. The decoupling operation is the same for all pairs, converting square polar
658 representation (where one vector is magnitude and the second angle) back to Cartesian
660 <!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
661 represent the fine spectral detail of each output channel.
665 <!--l. 432--><p class="noindent" ><span class="paragraphHead"><a
666 id="x1-300001.3.2"></a><span
667 class="cmbx-12">generate floor curve</span></span>
668 The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to
669 generate the output curve when the floor data is decoded from the raw packet, or it
670 can be generated after inverse coupling and applied to the spectral residue directly,
671 combining generation and the dot product into one step and eliminating some working
673 <!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied
674 (dot product) by the linear-range, linear-domain spectral residue.
675 <!--l. 447--><p class="noindent" ><span class="paragraphHead"><a
676 id="x1-310001.3.2"></a><span
677 class="cmbx-12">compute floor/residue dot product</span></span>
678 This step is straightforward; for each output channel, the decoder multiplies the floor curve and
679 residue vectors element by element, producing the finished audio spectrum of each
681 <!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
682 implementation might be to assume that a 32 bit fixed-point representation for floor and
683 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
684 in all cases because it happens to mostly work with the current Xiph.Org reference
686 <!--l. 462--><p class="noindent" >However, floor vector values can span <span
687 class="cmsy-10x-x-120">∼</span>140dB (<span
688 class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
689 vector should represent a minimum of 120dB (<span
690 class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
691 bit PCM device. For the residue vector to represent full scale if the floor is nailed
693 class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
694 full scale if the floor is nailed at 0dB, it must be able to represent <span
695 class="cmsy-10x-x-120">−</span>140dB to +0dB.
696 Thus, in order to handle full range dynamics, a residue vector may span <span
697 class="cmsy-10x-x-120">−</span>140dB to
698 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
699 residue vector must be able to represent a 48 bit range and the dot product must
700 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
701 achieved using large (64 bit or larger) integers, or implementing a movable binary point
703 <!--l. 479--><p class="noindent" ><span class="paragraphHead"><a
704 id="x1-320001.3.2"></a><span
705 class="cmbx-12">inverse monolithic transform (MDCT)</span></span>
706 The audio spectrum is converted back into time domain PCM audio via an inverse Modified
707 Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
708 <span class="cite">[<a
709 href="#XSporer/Brandenburg/Edler">1</a>]</span>.
710 <!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be
714 lapped with surrounding frames using an appropriate window (such as the Vorbis window) before
715 the MDCT can be considered orthogonal.
716 <!--l. 492--><p class="noindent" ><span class="paragraphHead"><a
717 id="x1-330001.3.2"></a><span
718 class="cmbx-12">overlap/add data</span></span>
719 Windowed MDCT output is overlapped and added with the right hand data of the previous
720 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
721 current window (as illustrated in the window overlap diagram). At this point, the audio data
722 between the center of the previous frame and the center of the current frame is now finished and
723 ready to be returned.
724 <!--l. 501--><p class="noindent" ><span class="paragraphHead"><a
725 id="x1-340001.3.2"></a><span
726 class="cmbx-12">cache right hand data</span></span>
727 The decoder must cache the right hand portion of the current frame to be lapped with the left
728 hand portion of the next frame.
729 <!--l. 507--><p class="noindent" ><span class="paragraphHead"><a
730 id="x1-350001.3.2"></a><span
731 class="cmbx-12">return finished audio data</span></span>
732 The overlapped portion produced from overlapping the previous and current frame data
733 is finished data to be returned by the decoder. This data spans from the center of
734 the previous window to the center of the current window. In the case of same-sized
735 windows, the amount of data to return is one-half block consisting of and only of the
736 overlapped portions. When overlapping a short and long window, much of the returned
737 range is not actually overlap. This does not damage transform orthogonality. Pay
738 attention however to returning the correct data range; the amount of data to be returned
740 <!--l. 519--><p class="noindent" >
741 <div class="fancyvrb" id="fancyvrb1">
743 id="x1-35002r1"></a><span
744 class="cmr-6">1</span><span
745 class="cmtt-8"> </span><span
746 class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
748 <!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
749 <!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
750 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
751 PCM output offset is ’0’ (as no data has been returned yet).
758 <h3 class="sectionHead"><span class="titlemark">2. </span> <a
759 id="x1-360002"></a>Bitpacking Convention</h3>
760 <!--l. 6--><p class="noindent" >
761 <h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a
762 id="x1-370002.1"></a>Overview</h4>
763 <!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
764 integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
765 encoder and then read one-by-one in the same monotonically increasing order by the decoder.
766 Most current binary storage arrangements group bits into a native word size of eight bits
767 (octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
768 bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
769 representation in fixed-width words.
770 <!--l. 19--><p class="noindent" >
771 <h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a
772 id="x1-380002.1.1"></a>octets, bytes and words</h5>
773 <!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
774 This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
775 For purposes of the bitpacking convention, a byte implies the native, smallest integer
776 storage representation offered by a platform. On modern platforms, this is generally
777 assumed to be eight bits (not necessarily because of the processor but because of the
778 filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
779 atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
781 <!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
782 to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
783 bitpacking convention is still well defined for any native byte size; Vorbis uses the native
784 bit-width of a given storage system. This document assumes that a byte is one octet for purposes
786 <!--l. 39--><p class="noindent" >
790 <h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a
791 id="x1-390002.1.2"></a>bit order</h5>
792 <!--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
793 storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
794 opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
795 class="cmmi-12">n </span>(<span
796 class="cmmi-12">n </span>= 7 in an
798 <!--l. 50--><p class="noindent" >
799 <h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a
800 id="x1-400002.1.3"></a>byte order</h5>
801 <!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
802 common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
803 highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
804 which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
806 <!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
807 word, level, thus host word ordering is of a concern only during optimization when writing high
808 performance code that operates on a word of storage at a time rather than by byte.
809 Logically, bytes are always coded and decoded in order from byte zero through byte
811 class="cmmi-12">n</span>.
812 <!--l. 68--><p class="noindent" >
813 <h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a
814 id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
815 <!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
816 wide, into packets. These integer fields are not aligned to the boundaries of the byte
817 representation; the next field is written at the bit position at which the previous field
819 <!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
820 bitstream first, followed by next least significant bit, etc, until the requested number of bits
821 have been coded. When packing the bits into bytes, the encoder begins by placing
822 the LSb of the integer to be written into the least significant unused bit position of
823 the destination byte, followed by the next-least significant bit of the source integer
824 and so on up to the requested number of bits. When all bits of the destination byte
825 have been filled, encoding continues by zeroing all bits of the next byte and writing
826 the next bit into the bit position 0 of that byte. Decoding follows the same process
830 as encoding, but by reading bits from the byte stream and reassembling them into
832 <!--l. 90--><p class="noindent" >
833 <h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a
834 id="x1-420002.1.5"></a>signedness</h5>
835 <!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
836 given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
837 either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
838 encoder and decoder are responsible for knowing if fields are to be treated as signed or
840 <!--l. 101--><p class="noindent" >
841 <h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a
842 id="x1-430002.1.6"></a>coding example</h5>
843 <!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
844 <!--l. 106--><p class="noindent" >
845 <div class="fancyvrb" id="fancyvrb2">
847 id="x1-43002r1"></a><span
848 class="cmr-6">1</span><span
849 class="cmtt-8"> </span><span
850 class="cmtt-8"> </span><span
851 class="cmtt-8"> </span><span
852 class="cmtt-8"> </span><span
853 class="cmtt-8"> </span><span
854 class="cmtt-8"> </span><span
855 class="cmtt-8"> </span><span
856 class="cmtt-8"> </span><span
857 class="cmtt-8"> </span><span
858 class="cmtt-8"> </span><span
859 class="cmtt-8"> </span><span
860 class="cmtt-8"> </span><span
861 class="cmtt-8"> </span><span
862 class="cmtt-8"> </span><span
863 class="cmtt-8"> </span><span
864 class="cmtt-8"> |</span>
865 <br class="fancyvrb" /><a
866 id="x1-43004r2"></a><span
867 class="cmr-6">2</span><span
868 class="cmtt-8"> </span><span
869 class="cmtt-8"> </span><span
870 class="cmtt-8"> </span><span
871 class="cmtt-8"> </span><span
872 class="cmtt-8"> </span><span
873 class="cmtt-8"> </span><span
874 class="cmtt-8"> </span><span
875 class="cmtt-8"> </span><span
876 class="cmtt-8"> </span><span
877 class="cmtt-8"> </span><span
878 class="cmtt-8"> </span><span
879 class="cmtt-8"> </span><span
880 class="cmtt-8"> </span><span
881 class="cmtt-8"> </span><span
882 class="cmtt-8"> </span><span
883 class="cmtt-8"> V</span>
884 <br class="fancyvrb" /><a
885 id="x1-43006r3"></a><span
886 class="cmr-6">3</span><span
887 class="cmtt-8"> </span><span
888 class="cmtt-8"> </span>
889 <br class="fancyvrb" /><a
890 id="x1-43008r4"></a><span
891 class="cmr-6">4</span><span
892 class="cmtt-8"> </span><span
893 class="cmtt-8"> </span><span
894 class="cmtt-8"> </span><span
895 class="cmtt-8"> </span><span
896 class="cmtt-8"> </span><span
897 class="cmtt-8"> </span><span
898 class="cmtt-8"> </span><span
899 class="cmtt-8"> </span><span
900 class="cmtt-8"> </span><span
901 class="cmtt-8"> 7</span><span
902 class="cmtt-8"> 6</span><span
903 class="cmtt-8"> 5</span><span
904 class="cmtt-8"> 4</span><span
905 class="cmtt-8"> 3</span><span
906 class="cmtt-8"> 2</span><span
907 class="cmtt-8"> 1</span><span
908 class="cmtt-8"> 0</span>
909 <br class="fancyvrb" /><a
910 id="x1-43010r5"></a><span
911 class="cmr-6">5</span><span
912 class="cmtt-8"> </span><span
913 class="cmtt-8"> byte</span><span
914 class="cmtt-8"> 0</span><span
915 class="cmtt-8"> [0</span><span
916 class="cmtt-8"> 0</span><span
917 class="cmtt-8"> 0</span><span
918 class="cmtt-8"> 0</span><span
919 class="cmtt-8"> 1</span><span
920 class="cmtt-8"> 1</span><span
921 class="cmtt-8"> 0</span><span
922 class="cmtt-8"> 0]</span><span
923 class="cmtt-8"> </span><span
924 class="cmtt-8"> <-</span>
925 <br class="fancyvrb" /><a
926 id="x1-43012r6"></a><span
927 class="cmr-6">6</span><span
928 class="cmtt-8"> </span><span
929 class="cmtt-8"> byte</span><span
930 class="cmtt-8"> 1</span><span
931 class="cmtt-8"> [</span><span
932 class="cmtt-8"> </span><span
933 class="cmtt-8"> </span><span
934 class="cmtt-8"> </span><span
935 class="cmtt-8"> </span><span
936 class="cmtt-8"> </span><span
937 class="cmtt-8"> </span><span
938 class="cmtt-8"> </span><span
939 class="cmtt-8"> </span><span
940 class="cmtt-8"> </span><span
941 class="cmtt-8"> </span><span
942 class="cmtt-8"> </span><span
943 class="cmtt-8"> </span><span
944 class="cmtt-8"> </span><span
945 class="cmtt-8"> </span><span
946 class="cmtt-8"> ]</span>
947 <br class="fancyvrb" /><a
948 id="x1-43014r7"></a><span
949 class="cmr-6">7</span><span
950 class="cmtt-8"> </span><span
951 class="cmtt-8"> byte</span><span
952 class="cmtt-8"> 2</span><span
953 class="cmtt-8"> [</span><span
954 class="cmtt-8"> </span><span
955 class="cmtt-8"> </span><span
956 class="cmtt-8"> </span><span
957 class="cmtt-8"> </span><span
958 class="cmtt-8"> </span><span
959 class="cmtt-8"> </span><span
960 class="cmtt-8"> </span><span
961 class="cmtt-8"> </span><span
962 class="cmtt-8"> </span><span
963 class="cmtt-8"> </span><span
964 class="cmtt-8"> </span><span
965 class="cmtt-8"> </span><span
966 class="cmtt-8"> </span><span
967 class="cmtt-8"> </span><span
968 class="cmtt-8"> ]</span>
969 <br class="fancyvrb" /><a
970 id="x1-43016r8"></a><span
971 class="cmr-6">8</span><span
972 class="cmtt-8"> </span><span
973 class="cmtt-8"> byte</span><span
974 class="cmtt-8"> 3</span><span
975 class="cmtt-8"> [</span><span
976 class="cmtt-8"> </span><span
977 class="cmtt-8"> </span><span
978 class="cmtt-8"> </span><span
979 class="cmtt-8"> </span><span
980 class="cmtt-8"> </span><span
981 class="cmtt-8"> </span><span
982 class="cmtt-8"> </span><span
983 class="cmtt-8"> </span><span
984 class="cmtt-8"> </span><span
985 class="cmtt-8"> </span><span
986 class="cmtt-8"> </span><span
987 class="cmtt-8"> </span><span
988 class="cmtt-8"> </span><span
989 class="cmtt-8"> </span><span
990 class="cmtt-8"> ]</span>
991 <br class="fancyvrb" /><a
992 id="x1-43018r9"></a><span
993 class="cmr-6">9</span><span
994 class="cmtt-8"> </span><span
995 class="cmtt-8"> </span><span
996 class="cmtt-8"> </span><span
997 class="cmtt-8"> </span><span
998 class="cmtt-8"> </span><span
999 class="cmtt-8"> </span><span
1000 class="cmtt-8"> </span><span
1001 class="cmtt-8"> </span><span
1002 class="cmtt-8"> </span><span
1003 class="cmtt-8"> </span><span
1004 class="cmtt-8"> </span><span
1005 class="cmtt-8"> </span><span
1006 class="cmtt-8"> </span><span
1007 class="cmtt-8"> </span><span
1008 class="cmtt-8"> ...</span>
1009 <br class="fancyvrb" /><a
1010 id="x1-43020r10"></a><span
1011 class="cmr-6">10</span><span
1012 class="cmtt-8"> </span><span
1013 class="cmtt-8"> byte</span><span
1014 class="cmtt-8"> n</span><span
1015 class="cmtt-8"> [</span><span
1016 class="cmtt-8"> </span><span
1017 class="cmtt-8"> </span><span
1018 class="cmtt-8"> </span><span
1019 class="cmtt-8"> </span><span
1020 class="cmtt-8"> </span><span
1021 class="cmtt-8"> </span><span
1022 class="cmtt-8"> </span><span
1023 class="cmtt-8"> </span><span
1024 class="cmtt-8"> </span><span
1025 class="cmtt-8"> </span><span
1026 class="cmtt-8"> </span><span
1027 class="cmtt-8"> </span><span
1028 class="cmtt-8"> </span><span
1029 class="cmtt-8"> </span><span
1030 class="cmtt-8"> ]</span><span
1031 class="cmtt-8"> </span><span
1032 class="cmtt-8"> bytestream</span><span
1033 class="cmtt-8"> length</span><span
1034 class="cmtt-8"> ==</span><span
1035 class="cmtt-8"> 1</span><span
1036 class="cmtt-8"> byte</span>
1037 <br class="fancyvrb" /><a
1038 id="x1-43022r11"></a><span
1039 class="cmr-6">11</span><span
1040 class="cmtt-8"> </span><span
1041 class="cmtt-8"> </span>
1043 <!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
1044 <!--l. 123--><p class="noindent" >
1045 <div class="fancyvrb" id="fancyvrb3">
1047 id="x1-43024r1"></a><span
1048 class="cmr-6">1</span><span
1049 class="cmtt-8"> </span><span
1050 class="cmtt-8"> </span><span
1051 class="cmtt-8"> </span><span
1052 class="cmtt-8"> </span><span
1053 class="cmtt-8"> </span><span
1054 class="cmtt-8"> </span><span
1055 class="cmtt-8"> </span><span
1056 class="cmtt-8"> </span><span
1057 class="cmtt-8"> </span><span
1058 class="cmtt-8"> |</span>
1059 <br class="fancyvrb" /><a
1060 id="x1-43026r2"></a><span
1061 class="cmr-6">2</span><span
1062 class="cmtt-8"> </span><span
1063 class="cmtt-8"> </span><span
1064 class="cmtt-8"> </span><span
1065 class="cmtt-8"> </span><span
1066 class="cmtt-8"> </span><span
1067 class="cmtt-8"> </span><span
1068 class="cmtt-8"> </span><span
1069 class="cmtt-8"> </span><span
1070 class="cmtt-8"> </span><span
1071 class="cmtt-8"> V</span>
1072 <br class="fancyvrb" /><a
1073 id="x1-43028r3"></a><span
1074 class="cmr-6">3</span><span
1075 class="cmtt-8"> </span><span
1076 class="cmtt-8"> </span>
1077 <br class="fancyvrb" /><a
1078 id="x1-43030r4"></a><span
1079 class="cmr-6">4</span><span
1080 class="cmtt-8"> </span><span
1081 class="cmtt-8"> </span><span
1082 class="cmtt-8"> </span><span
1083 class="cmtt-8"> </span><span
1084 class="cmtt-8"> </span><span
1085 class="cmtt-8"> </span><span
1086 class="cmtt-8"> </span><span
1087 class="cmtt-8"> </span><span
1088 class="cmtt-8"> </span><span
1089 class="cmtt-8"> 7</span><span
1090 class="cmtt-8"> 6</span><span
1091 class="cmtt-8"> 5</span><span
1092 class="cmtt-8"> 4</span><span
1093 class="cmtt-8"> 3</span><span
1094 class="cmtt-8"> 2</span><span
1095 class="cmtt-8"> 1</span><span
1096 class="cmtt-8"> 0</span>
1097 <br class="fancyvrb" /><a
1098 id="x1-43032r5"></a><span
1099 class="cmr-6">5</span><span
1100 class="cmtt-8"> </span><span
1101 class="cmtt-8"> byte</span><span
1102 class="cmtt-8"> 0</span><span
1103 class="cmtt-8"> [0</span><span
1104 class="cmtt-8"> 1</span><span
1105 class="cmtt-8"> 1</span><span
1106 class="cmtt-8"> 1</span><span
1107 class="cmtt-8"> 1</span><span
1108 class="cmtt-8"> 1</span><span
1109 class="cmtt-8"> 0</span><span
1110 class="cmtt-8"> 0]</span><span
1111 class="cmtt-8"> </span><span
1112 class="cmtt-8"> <-</span>
1113 <br class="fancyvrb" /><a
1114 id="x1-43034r6"></a><span
1115 class="cmr-6">6</span><span
1116 class="cmtt-8"> </span><span
1117 class="cmtt-8"> byte</span><span
1118 class="cmtt-8"> 1</span><span
1119 class="cmtt-8"> [</span><span
1120 class="cmtt-8"> </span><span
1121 class="cmtt-8"> </span><span
1122 class="cmtt-8"> </span><span
1123 class="cmtt-8"> </span><span
1124 class="cmtt-8"> </span><span
1125 class="cmtt-8"> </span><span
1126 class="cmtt-8"> </span><span
1127 class="cmtt-8"> </span><span
1128 class="cmtt-8"> </span><span
1129 class="cmtt-8"> </span><span
1130 class="cmtt-8"> </span><span
1131 class="cmtt-8"> </span><span
1132 class="cmtt-8"> </span><span
1133 class="cmtt-8"> </span><span
1134 class="cmtt-8"> ]</span>
1138 <br class="fancyvrb" /><a
1139 id="x1-43036r7"></a><span
1140 class="cmr-6">7</span><span
1141 class="cmtt-8"> </span><span
1142 class="cmtt-8"> byte</span><span
1143 class="cmtt-8"> 2</span><span
1144 class="cmtt-8"> [</span><span
1145 class="cmtt-8"> </span><span
1146 class="cmtt-8"> </span><span
1147 class="cmtt-8"> </span><span
1148 class="cmtt-8"> </span><span
1149 class="cmtt-8"> </span><span
1150 class="cmtt-8"> </span><span
1151 class="cmtt-8"> </span><span
1152 class="cmtt-8"> </span><span
1153 class="cmtt-8"> </span><span
1154 class="cmtt-8"> </span><span
1155 class="cmtt-8"> </span><span
1156 class="cmtt-8"> </span><span
1157 class="cmtt-8"> </span><span
1158 class="cmtt-8"> </span><span
1159 class="cmtt-8"> ]</span>
1160 <br class="fancyvrb" /><a
1161 id="x1-43038r8"></a><span
1162 class="cmr-6">8</span><span
1163 class="cmtt-8"> </span><span
1164 class="cmtt-8"> byte</span><span
1165 class="cmtt-8"> 3</span><span
1166 class="cmtt-8"> [</span><span
1167 class="cmtt-8"> </span><span
1168 class="cmtt-8"> </span><span
1169 class="cmtt-8"> </span><span
1170 class="cmtt-8"> </span><span
1171 class="cmtt-8"> </span><span
1172 class="cmtt-8"> </span><span
1173 class="cmtt-8"> </span><span
1174 class="cmtt-8"> </span><span
1175 class="cmtt-8"> </span><span
1176 class="cmtt-8"> </span><span
1177 class="cmtt-8"> </span><span
1178 class="cmtt-8"> </span><span
1179 class="cmtt-8"> </span><span
1180 class="cmtt-8"> </span><span
1181 class="cmtt-8"> ]</span>
1182 <br class="fancyvrb" /><a
1183 id="x1-43040r9"></a><span
1184 class="cmr-6">9</span><span
1185 class="cmtt-8"> </span><span
1186 class="cmtt-8"> </span><span
1187 class="cmtt-8"> </span><span
1188 class="cmtt-8"> </span><span
1189 class="cmtt-8"> </span><span
1190 class="cmtt-8"> </span><span
1191 class="cmtt-8"> </span><span
1192 class="cmtt-8"> </span><span
1193 class="cmtt-8"> </span><span
1194 class="cmtt-8"> </span><span
1195 class="cmtt-8"> </span><span
1196 class="cmtt-8"> </span><span
1197 class="cmtt-8"> </span><span
1198 class="cmtt-8"> </span><span
1199 class="cmtt-8"> ...</span>
1200 <br class="fancyvrb" /><a
1201 id="x1-43042r10"></a><span
1202 class="cmr-6">10</span><span
1203 class="cmtt-8"> </span><span
1204 class="cmtt-8"> byte</span><span
1205 class="cmtt-8"> n</span><span
1206 class="cmtt-8"> [</span><span
1207 class="cmtt-8"> </span><span
1208 class="cmtt-8"> </span><span
1209 class="cmtt-8"> </span><span
1210 class="cmtt-8"> </span><span
1211 class="cmtt-8"> </span><span
1212 class="cmtt-8"> </span><span
1213 class="cmtt-8"> </span><span
1214 class="cmtt-8"> </span><span
1215 class="cmtt-8"> </span><span
1216 class="cmtt-8"> </span><span
1217 class="cmtt-8"> </span><span
1218 class="cmtt-8"> </span><span
1219 class="cmtt-8"> </span><span
1220 class="cmtt-8"> </span><span
1221 class="cmtt-8"> ]</span><span
1222 class="cmtt-8"> </span><span
1223 class="cmtt-8"> bytestream</span><span
1224 class="cmtt-8"> length</span><span
1225 class="cmtt-8"> ==</span><span
1226 class="cmtt-8"> 1</span><span
1227 class="cmtt-8"> byte</span>
1229 <!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
1230 <!--l. 139--><p class="noindent" >
1231 <div class="fancyvrb" id="fancyvrb4">
1233 id="x1-43044r1"></a><span
1234 class="cmr-6">1</span><span
1235 class="cmtt-8"> </span><span
1236 class="cmtt-8"> </span><span
1237 class="cmtt-8"> </span><span
1238 class="cmtt-8"> </span><span
1239 class="cmtt-8"> </span><span
1240 class="cmtt-8"> </span><span
1241 class="cmtt-8"> </span><span
1242 class="cmtt-8"> </span><span
1243 class="cmtt-8"> </span><span
1244 class="cmtt-8"> </span><span
1245 class="cmtt-8"> </span><span
1246 class="cmtt-8"> |</span>
1247 <br class="fancyvrb" /><a
1248 id="x1-43046r2"></a><span
1249 class="cmr-6">2</span><span
1250 class="cmtt-8"> </span><span
1251 class="cmtt-8"> </span><span
1252 class="cmtt-8"> </span><span
1253 class="cmtt-8"> </span><span
1254 class="cmtt-8"> </span><span
1255 class="cmtt-8"> </span><span
1256 class="cmtt-8"> </span><span
1257 class="cmtt-8"> </span><span
1258 class="cmtt-8"> </span><span
1259 class="cmtt-8"> </span><span
1260 class="cmtt-8"> </span><span
1261 class="cmtt-8"> V</span>
1262 <br class="fancyvrb" /><a
1263 id="x1-43048r3"></a><span
1264 class="cmr-6">3</span><span
1265 class="cmtt-8"> </span><span
1266 class="cmtt-8"> </span>
1267 <br class="fancyvrb" /><a
1268 id="x1-43050r4"></a><span
1269 class="cmr-6">4</span><span
1270 class="cmtt-8"> </span><span
1271 class="cmtt-8"> </span><span
1272 class="cmtt-8"> </span><span
1273 class="cmtt-8"> </span><span
1274 class="cmtt-8"> </span><span
1275 class="cmtt-8"> </span><span
1276 class="cmtt-8"> </span><span
1277 class="cmtt-8"> </span><span
1278 class="cmtt-8"> </span><span
1279 class="cmtt-8"> 7</span><span
1280 class="cmtt-8"> 6</span><span
1281 class="cmtt-8"> 5</span><span
1282 class="cmtt-8"> 4</span><span
1283 class="cmtt-8"> 3</span><span
1284 class="cmtt-8"> 2</span><span
1285 class="cmtt-8"> 1</span><span
1286 class="cmtt-8"> 0</span>
1287 <br class="fancyvrb" /><a
1288 id="x1-43052r5"></a><span
1289 class="cmr-6">5</span><span
1290 class="cmtt-8"> </span><span
1291 class="cmtt-8"> byte</span><span
1292 class="cmtt-8"> 0</span><span
1293 class="cmtt-8"> [1</span><span
1294 class="cmtt-8"> 1</span><span
1295 class="cmtt-8"> 1</span><span
1296 class="cmtt-8"> 1</span><span
1297 class="cmtt-8"> 1</span><span
1298 class="cmtt-8"> 1</span><span
1299 class="cmtt-8"> 0</span><span
1300 class="cmtt-8"> 0]</span>
1301 <br class="fancyvrb" /><a
1302 id="x1-43054r6"></a><span
1303 class="cmr-6">6</span><span
1304 class="cmtt-8"> </span><span
1305 class="cmtt-8"> byte</span><span
1306 class="cmtt-8"> 1</span><span
1307 class="cmtt-8"> [0</span><span
1308 class="cmtt-8"> 0</span><span
1309 class="cmtt-8"> 0</span><span
1310 class="cmtt-8"> 0</span><span
1311 class="cmtt-8"> 1</span><span
1312 class="cmtt-8"> 0</span><span
1313 class="cmtt-8"> 0</span><span
1314 class="cmtt-8"> 0]</span><span
1315 class="cmtt-8"> </span><span
1316 class="cmtt-8"> <-</span>
1317 <br class="fancyvrb" /><a
1318 id="x1-43056r7"></a><span
1319 class="cmr-6">7</span><span
1320 class="cmtt-8"> </span><span
1321 class="cmtt-8"> byte</span><span
1322 class="cmtt-8"> 2</span><span
1323 class="cmtt-8"> [</span><span
1324 class="cmtt-8"> </span><span
1325 class="cmtt-8"> </span><span
1326 class="cmtt-8"> </span><span
1327 class="cmtt-8"> </span><span
1328 class="cmtt-8"> </span><span
1329 class="cmtt-8"> </span><span
1330 class="cmtt-8"> </span><span
1331 class="cmtt-8"> </span><span
1332 class="cmtt-8"> </span><span
1333 class="cmtt-8"> </span><span
1334 class="cmtt-8"> </span><span
1335 class="cmtt-8"> </span><span
1336 class="cmtt-8"> </span><span
1337 class="cmtt-8"> </span><span
1338 class="cmtt-8"> ]</span>
1339 <br class="fancyvrb" /><a
1340 id="x1-43058r8"></a><span
1341 class="cmr-6">8</span><span
1342 class="cmtt-8"> </span><span
1343 class="cmtt-8"> byte</span><span
1344 class="cmtt-8"> 3</span><span
1345 class="cmtt-8"> [</span><span
1346 class="cmtt-8"> </span><span
1347 class="cmtt-8"> </span><span
1348 class="cmtt-8"> </span><span
1349 class="cmtt-8"> </span><span
1350 class="cmtt-8"> </span><span
1351 class="cmtt-8"> </span><span
1352 class="cmtt-8"> </span><span
1353 class="cmtt-8"> </span><span
1354 class="cmtt-8"> </span><span
1355 class="cmtt-8"> </span><span
1356 class="cmtt-8"> </span><span
1357 class="cmtt-8"> </span><span
1358 class="cmtt-8"> </span><span
1359 class="cmtt-8"> </span><span
1360 class="cmtt-8"> ]</span>
1361 <br class="fancyvrb" /><a
1362 id="x1-43060r9"></a><span
1363 class="cmr-6">9</span><span
1364 class="cmtt-8"> </span><span
1365 class="cmtt-8"> </span><span
1366 class="cmtt-8"> </span><span
1367 class="cmtt-8"> </span><span
1368 class="cmtt-8"> </span><span
1369 class="cmtt-8"> </span><span
1370 class="cmtt-8"> </span><span
1371 class="cmtt-8"> </span><span
1372 class="cmtt-8"> </span><span
1373 class="cmtt-8"> </span><span
1374 class="cmtt-8"> </span><span
1375 class="cmtt-8"> </span><span
1376 class="cmtt-8"> </span><span
1377 class="cmtt-8"> </span><span
1378 class="cmtt-8"> ...</span>
1379 <br class="fancyvrb" /><a
1380 id="x1-43062r10"></a><span
1381 class="cmr-6">10</span><span
1382 class="cmtt-8"> </span><span
1383 class="cmtt-8"> byte</span><span
1384 class="cmtt-8"> n</span><span
1385 class="cmtt-8"> [</span><span
1386 class="cmtt-8"> </span><span
1387 class="cmtt-8"> </span><span
1388 class="cmtt-8"> </span><span
1389 class="cmtt-8"> </span><span
1390 class="cmtt-8"> </span><span
1391 class="cmtt-8"> </span><span
1392 class="cmtt-8"> </span><span
1393 class="cmtt-8"> </span><span
1394 class="cmtt-8"> </span><span
1395 class="cmtt-8"> </span><span
1396 class="cmtt-8"> </span><span
1397 class="cmtt-8"> </span><span
1398 class="cmtt-8"> </span><span
1399 class="cmtt-8"> </span><span
1400 class="cmtt-8"> ]</span><span
1401 class="cmtt-8"> </span><span
1402 class="cmtt-8"> bytestream</span><span
1403 class="cmtt-8"> length</span><span
1404 class="cmtt-8"> ==</span><span
1405 class="cmtt-8"> 2</span><span
1406 class="cmtt-8"> bytes</span>
1407 <br class="fancyvrb" /><a
1408 id="x1-43064r11"></a><span
1409 class="cmr-6">11</span><span
1410 class="cmtt-8"> </span><span
1411 class="cmtt-8"> </span><span
1412 class="cmtt-8"> </span><span
1413 class="cmtt-8"> </span><span
1414 class="cmtt-8"> </span><span
1415 class="cmtt-8"> </span><span
1416 class="cmtt-8"> </span><span
1417 class="cmtt-8"> </span><span
1418 class="cmtt-8"> </span><span
1419 class="cmtt-8"> </span><span
1420 class="cmtt-8"> </span><span
1421 class="cmtt-8"> </span><span
1422 class="cmtt-8"> </span><span
1423 class="cmtt-8"> </span><span
1424 class="cmtt-8"> </span><span
1425 class="cmtt-8"> </span><span
1426 class="cmtt-8"> </span><span
1427 class="cmtt-8"> </span><span
1428 class="cmtt-8"> </span><span
1429 class="cmtt-8"> </span><span
1430 class="cmtt-8"> </span><span
1431 class="cmtt-8"> </span><span
1432 class="cmtt-8"> </span><span
1433 class="cmtt-8"> </span><span
1434 class="cmtt-8"> </span><span
1435 class="cmtt-8"> </span><span
1436 class="cmtt-8"> </span><span
1437 class="cmtt-8"> bit</span><span
1438 class="cmtt-8"> cursor</span><span
1439 class="cmtt-8"> ==</span><span
1440 class="cmtt-8"> 6</span>
1442 <!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
1443 <!--l. 156--><p class="noindent" >
1444 <div class="fancyvrb" id="fancyvrb5">
1446 id="x1-43066r1"></a><span
1447 class="cmr-6">1</span><span
1448 class="cmtt-8"> </span><span
1449 class="cmtt-8"> </span><span
1450 class="cmtt-8"> </span><span
1451 class="cmtt-8"> </span><span
1452 class="cmtt-8"> </span><span
1453 class="cmtt-8"> </span><span
1454 class="cmtt-8"> </span><span
1455 class="cmtt-8"> </span><span
1456 class="cmtt-8"> </span><span
1457 class="cmtt-8"> </span><span
1458 class="cmtt-8"> </span><span
1459 class="cmtt-8"> </span><span
1460 class="cmtt-8"> </span><span
1461 class="cmtt-8"> </span><span
1462 class="cmtt-8"> </span><span
1463 class="cmtt-8"> </span><span
1464 class="cmtt-8"> </span><span
1465 class="cmtt-8"> |</span>
1466 <br class="fancyvrb" /><a
1467 id="x1-43068r2"></a><span
1468 class="cmr-6">2</span><span
1469 class="cmtt-8"> </span><span
1470 class="cmtt-8"> </span><span
1471 class="cmtt-8"> </span><span
1472 class="cmtt-8"> </span><span
1473 class="cmtt-8"> </span><span
1474 class="cmtt-8"> </span><span
1475 class="cmtt-8"> </span><span
1476 class="cmtt-8"> </span><span
1477 class="cmtt-8"> </span><span
1478 class="cmtt-8"> </span><span
1479 class="cmtt-8"> </span><span
1480 class="cmtt-8"> </span><span
1481 class="cmtt-8"> </span><span
1482 class="cmtt-8"> </span><span
1483 class="cmtt-8"> </span><span
1484 class="cmtt-8"> </span><span
1485 class="cmtt-8"> </span><span
1486 class="cmtt-8"> V</span>
1487 <br class="fancyvrb" /><a
1488 id="x1-43070r3"></a><span
1489 class="cmr-6">3</span><span
1490 class="cmtt-8"> </span><span
1491 class="cmtt-8"> </span>
1492 <br class="fancyvrb" /><a
1493 id="x1-43072r4"></a><span
1494 class="cmr-6">4</span><span
1495 class="cmtt-8"> </span><span
1496 class="cmtt-8"> </span><span
1497 class="cmtt-8"> </span><span
1498 class="cmtt-8"> </span><span
1499 class="cmtt-8"> </span><span
1500 class="cmtt-8"> </span><span
1501 class="cmtt-8"> </span><span
1502 class="cmtt-8"> </span><span
1503 class="cmtt-8"> </span><span
1504 class="cmtt-8"> 7</span><span
1505 class="cmtt-8"> 6</span><span
1506 class="cmtt-8"> 5</span><span
1507 class="cmtt-8"> 4</span><span
1508 class="cmtt-8"> 3</span><span
1509 class="cmtt-8"> 2</span><span
1510 class="cmtt-8"> 1</span><span
1511 class="cmtt-8"> 0</span>
1512 <br class="fancyvrb" /><a
1513 id="x1-43074r5"></a><span
1514 class="cmr-6">5</span><span
1515 class="cmtt-8"> </span><span
1516 class="cmtt-8"> byte</span><span
1517 class="cmtt-8"> 0</span><span
1518 class="cmtt-8"> [1</span><span
1519 class="cmtt-8"> 1</span><span
1520 class="cmtt-8"> 1</span><span
1521 class="cmtt-8"> 1</span><span
1522 class="cmtt-8"> 1</span><span
1523 class="cmtt-8"> 1</span><span
1524 class="cmtt-8"> 0</span><span
1525 class="cmtt-8"> 0]</span>
1526 <br class="fancyvrb" /><a
1527 id="x1-43076r6"></a><span
1528 class="cmr-6">6</span><span
1529 class="cmtt-8"> </span><span
1530 class="cmtt-8"> byte</span><span
1531 class="cmtt-8"> 1</span><span
1532 class="cmtt-8"> [0</span><span
1533 class="cmtt-8"> 1</span><span
1534 class="cmtt-8"> 0</span><span
1535 class="cmtt-8"> 0</span><span
1536 class="cmtt-8"> 1</span><span
1537 class="cmtt-8"> 0</span><span
1538 class="cmtt-8"> 0</span><span
1539 class="cmtt-8"> 0]</span>
1540 <br class="fancyvrb" /><a
1541 id="x1-43078r7"></a><span
1542 class="cmr-6">7</span><span
1543 class="cmtt-8"> </span><span
1544 class="cmtt-8"> byte</span><span
1545 class="cmtt-8"> 2</span><span
1546 class="cmtt-8"> [1</span><span
1547 class="cmtt-8"> 1</span><span
1548 class="cmtt-8"> 0</span><span
1549 class="cmtt-8"> 0</span><span
1550 class="cmtt-8"> 1</span><span
1551 class="cmtt-8"> 1</span><span
1552 class="cmtt-8"> 1</span><span
1553 class="cmtt-8"> 0]</span>
1554 <br class="fancyvrb" /><a
1555 id="x1-43080r8"></a><span
1556 class="cmr-6">8</span><span
1557 class="cmtt-8"> </span><span
1558 class="cmtt-8"> byte</span><span
1559 class="cmtt-8"> 3</span><span
1560 class="cmtt-8"> [0</span><span
1561 class="cmtt-8"> 0</span><span
1562 class="cmtt-8"> 0</span><span
1563 class="cmtt-8"> 0</span><span
1564 class="cmtt-8"> 0</span><span
1565 class="cmtt-8"> 1</span><span
1566 class="cmtt-8"> 1</span><span
1567 class="cmtt-8"> 0]</span><span
1568 class="cmtt-8"> </span><span
1569 class="cmtt-8"> <-</span>
1570 <br class="fancyvrb" /><a
1571 id="x1-43082r9"></a><span
1572 class="cmr-6">9</span><span
1573 class="cmtt-8"> </span><span
1574 class="cmtt-8"> </span><span
1575 class="cmtt-8"> </span><span
1576 class="cmtt-8"> </span><span
1577 class="cmtt-8"> </span><span
1578 class="cmtt-8"> </span><span
1579 class="cmtt-8"> </span><span
1580 class="cmtt-8"> </span><span
1581 class="cmtt-8"> </span><span
1582 class="cmtt-8"> </span><span
1583 class="cmtt-8"> </span><span
1584 class="cmtt-8"> </span><span
1585 class="cmtt-8"> </span><span
1586 class="cmtt-8"> </span><span
1587 class="cmtt-8"> ...</span>
1588 <br class="fancyvrb" /><a
1589 id="x1-43084r10"></a><span
1590 class="cmr-6">10</span><span
1591 class="cmtt-8"> </span><span
1592 class="cmtt-8"> byte</span><span
1593 class="cmtt-8"> n</span><span
1594 class="cmtt-8"> [</span><span
1595 class="cmtt-8"> </span><span
1596 class="cmtt-8"> </span><span
1597 class="cmtt-8"> </span><span
1598 class="cmtt-8"> </span><span
1599 class="cmtt-8"> </span><span
1600 class="cmtt-8"> </span><span
1601 class="cmtt-8"> </span><span
1602 class="cmtt-8"> </span><span
1603 class="cmtt-8"> </span><span
1604 class="cmtt-8"> </span><span
1605 class="cmtt-8"> </span><span
1606 class="cmtt-8"> </span><span
1607 class="cmtt-8"> </span><span
1608 class="cmtt-8"> </span><span
1609 class="cmtt-8"> ]</span><span
1610 class="cmtt-8"> </span><span
1611 class="cmtt-8"> bytestream</span><span
1612 class="cmtt-8"> length</span><span
1613 class="cmtt-8"> ==</span><span
1614 class="cmtt-8"> 4</span><span
1615 class="cmtt-8"> bytes</span>
1616 <br class="fancyvrb" /><a
1617 id="x1-43086r11"></a><span
1618 class="cmr-6">11</span><span
1619 class="cmtt-8"> </span><span
1620 class="cmtt-8"> </span>
1622 <!--l. 173--><p class="noindent" >
1623 <h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a
1624 id="x1-440002.1.7"></a>decoding example</h5>
1625 <!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
1626 <!--l. 177--><p class="noindent" >
1627 <div class="fancyvrb" id="fancyvrb6">
1632 id="x1-44002r1"></a><span
1633 class="cmr-6">1</span><span
1634 class="cmtt-8"> </span><span
1635 class="cmtt-8"> </span><span
1636 class="cmtt-8"> </span><span
1637 class="cmtt-8"> </span><span
1638 class="cmtt-8"> </span><span
1639 class="cmtt-8"> </span><span
1640 class="cmtt-8"> </span><span
1641 class="cmtt-8"> </span><span
1642 class="cmtt-8"> </span><span
1643 class="cmtt-8"> </span><span
1644 class="cmtt-8"> </span><span
1645 class="cmtt-8"> </span><span
1646 class="cmtt-8"> </span><span
1647 class="cmtt-8"> </span><span
1648 class="cmtt-8"> </span><span
1649 class="cmtt-8"> </span><span
1650 class="cmtt-8"> </span><span
1651 class="cmtt-8"> </span><span
1652 class="cmtt-8"> </span><span
1653 class="cmtt-8"> </span><span
1654 class="cmtt-8"> </span><span
1655 class="cmtt-8"> </span><span
1656 class="cmtt-8"> </span><span
1657 class="cmtt-8"> |</span>
1658 <br class="fancyvrb" /><a
1659 id="x1-44004r2"></a><span
1660 class="cmr-6">2</span><span
1661 class="cmtt-8"> </span><span
1662 class="cmtt-8"> </span><span
1663 class="cmtt-8"> </span><span
1664 class="cmtt-8"> </span><span
1665 class="cmtt-8"> </span><span
1666 class="cmtt-8"> </span><span
1667 class="cmtt-8"> </span><span
1668 class="cmtt-8"> </span><span
1669 class="cmtt-8"> </span><span
1670 class="cmtt-8"> </span><span
1671 class="cmtt-8"> </span><span
1672 class="cmtt-8"> </span><span
1673 class="cmtt-8"> </span><span
1674 class="cmtt-8"> </span><span
1675 class="cmtt-8"> </span><span
1676 class="cmtt-8"> </span><span
1677 class="cmtt-8"> </span><span
1678 class="cmtt-8"> </span><span
1679 class="cmtt-8"> </span><span
1680 class="cmtt-8"> </span><span
1681 class="cmtt-8"> </span><span
1682 class="cmtt-8"> </span><span
1683 class="cmtt-8"> </span><span
1684 class="cmtt-8"> V</span>
1685 <br class="fancyvrb" /><a
1686 id="x1-44006r3"></a><span
1687 class="cmr-6">3</span><span
1688 class="cmtt-8"> </span><span
1689 class="cmtt-8"> </span>
1690 <br class="fancyvrb" /><a
1691 id="x1-44008r4"></a><span
1692 class="cmr-6">4</span><span
1693 class="cmtt-8"> </span><span
1694 class="cmtt-8"> </span><span
1695 class="cmtt-8"> </span><span
1696 class="cmtt-8"> </span><span
1697 class="cmtt-8"> </span><span
1698 class="cmtt-8"> </span><span
1699 class="cmtt-8"> </span><span
1700 class="cmtt-8"> </span><span
1701 class="cmtt-8"> </span><span
1702 class="cmtt-8"> 7</span><span
1703 class="cmtt-8"> 6</span><span
1704 class="cmtt-8"> 5</span><span
1705 class="cmtt-8"> 4</span><span
1706 class="cmtt-8"> 3</span><span
1707 class="cmtt-8"> 2</span><span
1708 class="cmtt-8"> 1</span><span
1709 class="cmtt-8"> 0</span>
1710 <br class="fancyvrb" /><a
1711 id="x1-44010r5"></a><span
1712 class="cmr-6">5</span><span
1713 class="cmtt-8"> </span><span
1714 class="cmtt-8"> byte</span><span
1715 class="cmtt-8"> 0</span><span
1716 class="cmtt-8"> [1</span><span
1717 class="cmtt-8"> 1</span><span
1718 class="cmtt-8"> 1</span><span
1719 class="cmtt-8"> 1</span><span
1720 class="cmtt-8"> 1</span><span
1721 class="cmtt-8"> 1</span><span
1722 class="cmtt-8"> 0</span><span
1723 class="cmtt-8"> 0]</span><span
1724 class="cmtt-8"> </span><span
1725 class="cmtt-8"> <-</span>
1726 <br class="fancyvrb" /><a
1727 id="x1-44012r6"></a><span
1728 class="cmr-6">6</span><span
1729 class="cmtt-8"> </span><span
1730 class="cmtt-8"> byte</span><span
1731 class="cmtt-8"> 1</span><span
1732 class="cmtt-8"> [0</span><span
1733 class="cmtt-8"> 1</span><span
1734 class="cmtt-8"> 0</span><span
1735 class="cmtt-8"> 0</span><span
1736 class="cmtt-8"> 1</span><span
1737 class="cmtt-8"> 0</span><span
1738 class="cmtt-8"> 0</span><span
1739 class="cmtt-8"> 0]</span>
1740 <br class="fancyvrb" /><a
1741 id="x1-44014r7"></a><span
1742 class="cmr-6">7</span><span
1743 class="cmtt-8"> </span><span
1744 class="cmtt-8"> byte</span><span
1745 class="cmtt-8"> 2</span><span
1746 class="cmtt-8"> [1</span><span
1747 class="cmtt-8"> 1</span><span
1748 class="cmtt-8"> 0</span><span
1749 class="cmtt-8"> 0</span><span
1750 class="cmtt-8"> 1</span><span
1751 class="cmtt-8"> 1</span><span
1752 class="cmtt-8"> 1</span><span
1753 class="cmtt-8"> 0]</span>
1754 <br class="fancyvrb" /><a
1755 id="x1-44016r8"></a><span
1756 class="cmr-6">8</span><span
1757 class="cmtt-8"> </span><span
1758 class="cmtt-8"> byte</span><span
1759 class="cmtt-8"> 3</span><span
1760 class="cmtt-8"> [0</span><span
1761 class="cmtt-8"> 0</span><span
1762 class="cmtt-8"> 0</span><span
1763 class="cmtt-8"> 0</span><span
1764 class="cmtt-8"> 0</span><span
1765 class="cmtt-8"> 1</span><span
1766 class="cmtt-8"> 1</span><span
1767 class="cmtt-8"> 0]</span><span
1768 class="cmtt-8"> </span><span
1769 class="cmtt-8"> bytestream</span><span
1770 class="cmtt-8"> length</span><span
1771 class="cmtt-8"> ==</span><span
1772 class="cmtt-8"> 4</span><span
1773 class="cmtt-8"> bytes</span>
1774 <br class="fancyvrb" /><a
1775 id="x1-44018r9"></a><span
1776 class="cmr-6">9</span><span
1777 class="cmtt-8"> </span><span
1778 class="cmtt-8"> </span>
1780 <!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
1781 are worth noting here:
1782 <ul class="itemize1">
1783 <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
1784 some other combination of bit-widths from the bitstream is well defined. There are
1785 no artificial alignment boundaries maintained in the bitstream.
1787 <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
1788 either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
1789 decode context.</li></ul>
1790 <!--l. 208--><p class="noindent" >
1791 <h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a
1792 id="x1-450002.1.8"></a>end-of-packet alignment</h5>
1793 <!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
1794 embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
1795 Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
1796 the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
1797 in the last byte of a packet.
1798 <!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
1799 should this unused space be read, it will return binary zeroes.
1800 <!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
1801 End-of-packet is not to be considered an error; it is merely a state indicating that there is
1802 insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
1803 normal mode of operation, and as such, decoders must handle reading past the end of a packet as
1804 a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
1805 also return ’end-of-packet’.
1809 <!--l. 233--><p class="noindent" >
1810 <h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a
1811 id="x1-460002.1.9"></a>reading zero bits</h5>
1812 <!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
1813 Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
1814 triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
1815 end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
1816 shall also fail with ’end-of-packet’.
1823 <h3 class="sectionHead"><span class="titlemark">3. </span> <a
1824 id="x1-470003"></a>Probability Model and Codebooks</h3>
1825 <!--l. 6--><p class="noindent" >
1826 <h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a
1827 id="x1-480003.1"></a>Overview</h4>
1828 <!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
1829 probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
1830 bitstream itself in the third header, the codec setup header. This packed configuration consists of
1831 multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
1832 compressed codewords as well as an optional lookup table of output vector values to which a
1833 decoded Huffman value is applied as an offset, generating the final decoded output corresponding
1834 to a given compressed codeword.
1835 <!--l. 18--><p class="noindent" >
1836 <h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a
1837 id="x1-490003.1.1"></a>Bitwise operation</h5>
1838 <!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
1839 and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
1840 read from the stream according to <a
1841 href="#x1-360002">Section 2</a>, “<a
1842 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
1843 <!--l. 27--><p class="noindent" >
1844 <h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a
1845 id="x1-500003.2"></a>Packed codebook format</h4>
1846 <!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
1847 eight bits. This is not universally true; see <a
1848 href="#x1-360002">Section 2</a>, “<a
1849 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
1850 relating to non-eight-bit bytes.
1854 <!--l. 34--><p class="noindent" >
1855 <h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a
1856 id="x1-510003.2.1"></a>codebook decode</h5>
1857 <!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
1858 <!--l. 38--><p class="noindent" >
1859 <div class="fancyvrb" id="fancyvrb7">
1861 id="x1-51002r1"></a><span
1862 class="cmr-6">1</span><span
1863 class="cmtt-8"> </span><span
1864 class="cmtt-8"> byte</span><span
1865 class="cmtt-8"> 0:</span><span
1866 class="cmtt-8"> [</span><span
1867 class="cmtt-8"> 0</span><span
1868 class="cmtt-8"> 1</span><span
1869 class="cmtt-8"> 0</span><span
1870 class="cmtt-8"> 0</span><span
1871 class="cmtt-8"> 0</span><span
1872 class="cmtt-8"> 0</span><span
1873 class="cmtt-8"> 1</span><span
1874 class="cmtt-8"> 0</span><span
1875 class="cmtt-8"> ]</span><span
1876 class="cmtt-8"> (0x42)</span>
1877 <br class="fancyvrb" /><a
1878 id="x1-51004r2"></a><span
1879 class="cmr-6">2</span><span
1880 class="cmtt-8"> </span><span
1881 class="cmtt-8"> byte</span><span
1882 class="cmtt-8"> 1:</span><span
1883 class="cmtt-8"> [</span><span
1884 class="cmtt-8"> 0</span><span
1885 class="cmtt-8"> 1</span><span
1886 class="cmtt-8"> 0</span><span
1887 class="cmtt-8"> 0</span><span
1888 class="cmtt-8"> 0</span><span
1889 class="cmtt-8"> 0</span><span
1890 class="cmtt-8"> 1</span><span
1891 class="cmtt-8"> 1</span><span
1892 class="cmtt-8"> ]</span><span
1893 class="cmtt-8"> (0x43)</span>
1894 <br class="fancyvrb" /><a
1895 id="x1-51006r3"></a><span
1896 class="cmr-6">3</span><span
1897 class="cmtt-8"> </span><span
1898 class="cmtt-8"> byte</span><span
1899 class="cmtt-8"> 2:</span><span
1900 class="cmtt-8"> [</span><span
1901 class="cmtt-8"> 0</span><span
1902 class="cmtt-8"> 1</span><span
1903 class="cmtt-8"> 0</span><span
1904 class="cmtt-8"> 1</span><span
1905 class="cmtt-8"> 0</span><span
1906 class="cmtt-8"> 1</span><span
1907 class="cmtt-8"> 1</span><span
1908 class="cmtt-8"> 0</span><span
1909 class="cmtt-8"> ]</span><span
1910 class="cmtt-8"> (0x56)</span>
1912 <!--l. 44--><p class="noindent" >16 bit <span
1913 class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span
1914 class="cmtt-12">[codebook_entries] </span>fields:
1915 <!--l. 46--><p class="noindent" >
1916 <div class="fancyvrb" id="fancyvrb8">
1918 id="x1-51008r1"></a><span
1919 class="cmr-6">1</span><span
1920 class="cmtt-8"> </span><span
1921 class="cmtt-8"> </span>
1922 <br class="fancyvrb" /><a
1923 id="x1-51010r2"></a><span
1924 class="cmr-6">2</span><span
1925 class="cmtt-8"> </span><span
1926 class="cmtt-8"> byte</span><span
1927 class="cmtt-8"> 3:</span><span
1928 class="cmtt-8"> [</span><span
1929 class="cmtt-8"> X</span><span
1930 class="cmtt-8"> X</span><span
1931 class="cmtt-8"> X</span><span
1932 class="cmtt-8"> X</span><span
1933 class="cmtt-8"> X</span><span
1934 class="cmtt-8"> X</span><span
1935 class="cmtt-8"> X</span><span
1936 class="cmtt-8"> X</span><span
1937 class="cmtt-8"> ]</span>
1938 <br class="fancyvrb" /><a
1939 id="x1-51012r3"></a><span
1940 class="cmr-6">3</span><span
1941 class="cmtt-8"> </span><span
1942 class="cmtt-8"> byte</span><span
1943 class="cmtt-8"> 4:</span><span
1944 class="cmtt-8"> [</span><span
1945 class="cmtt-8"> X</span><span
1946 class="cmtt-8"> X</span><span
1947 class="cmtt-8"> X</span><span
1948 class="cmtt-8"> X</span><span
1949 class="cmtt-8"> X</span><span
1950 class="cmtt-8"> X</span><span
1951 class="cmtt-8"> X</span><span
1952 class="cmtt-8"> X</span><span
1953 class="cmtt-8"> ]</span><span
1954 class="cmtt-8"> [codebook_dimensions]</span><span
1955 class="cmtt-8"> (16</span><span
1956 class="cmtt-8"> bit</span><span
1957 class="cmtt-8"> unsigned)</span>
1958 <br class="fancyvrb" /><a
1959 id="x1-51014r4"></a><span
1960 class="cmr-6">4</span><span
1961 class="cmtt-8"> </span><span
1962 class="cmtt-8"> </span>
1963 <br class="fancyvrb" /><a
1964 id="x1-51016r5"></a><span
1965 class="cmr-6">5</span><span
1966 class="cmtt-8"> </span><span
1967 class="cmtt-8"> byte</span><span
1968 class="cmtt-8"> 5:</span><span
1969 class="cmtt-8"> [</span><span
1970 class="cmtt-8"> X</span><span
1971 class="cmtt-8"> X</span><span
1972 class="cmtt-8"> X</span><span
1973 class="cmtt-8"> X</span><span
1974 class="cmtt-8"> X</span><span
1975 class="cmtt-8"> X</span><span
1976 class="cmtt-8"> X</span><span
1977 class="cmtt-8"> X</span><span
1978 class="cmtt-8"> ]</span>
1979 <br class="fancyvrb" /><a
1980 id="x1-51018r6"></a><span
1981 class="cmr-6">6</span><span
1982 class="cmtt-8"> </span><span
1983 class="cmtt-8"> byte</span><span
1984 class="cmtt-8"> 6:</span><span
1985 class="cmtt-8"> [</span><span
1986 class="cmtt-8"> X</span><span
1987 class="cmtt-8"> X</span><span
1988 class="cmtt-8"> X</span><span
1989 class="cmtt-8"> X</span><span
1990 class="cmtt-8"> X</span><span
1991 class="cmtt-8"> X</span><span
1992 class="cmtt-8"> X</span><span
1993 class="cmtt-8"> X</span><span
1994 class="cmtt-8"> ]</span>
1995 <br class="fancyvrb" /><a
1996 id="x1-51020r7"></a><span
1997 class="cmr-6">7</span><span
1998 class="cmtt-8"> </span><span
1999 class="cmtt-8"> byte</span><span
2000 class="cmtt-8"> 7:</span><span
2001 class="cmtt-8"> [</span><span
2002 class="cmtt-8"> X</span><span
2003 class="cmtt-8"> X</span><span
2004 class="cmtt-8"> X</span><span
2005 class="cmtt-8"> X</span><span
2006 class="cmtt-8"> X</span><span
2007 class="cmtt-8"> X</span><span
2008 class="cmtt-8"> X</span><span
2009 class="cmtt-8"> X</span><span
2010 class="cmtt-8"> ]</span><span
2011 class="cmtt-8"> [codebook_entries]</span><span
2012 class="cmtt-8"> (24</span><span
2013 class="cmtt-8"> bit</span><span
2014 class="cmtt-8"> unsigned)</span>
2015 <br class="fancyvrb" /><a
2016 id="x1-51022r8"></a><span
2017 class="cmr-6">8</span><span
2018 class="cmtt-8"> </span><span
2019 class="cmtt-8"> </span>
2021 <!--l. 57--><p class="noindent" >Next is the <span
2022 class="cmtt-12">[ordered] </span>bit flag:
2023 <!--l. 59--><p class="noindent" >
2024 <div class="fancyvrb" id="fancyvrb9">
2026 id="x1-51024r1"></a><span
2027 class="cmr-6">1</span><span
2028 class="cmtt-8"> </span><span
2029 class="cmtt-8"> </span>
2030 <br class="fancyvrb" /><a
2031 id="x1-51026r2"></a><span
2032 class="cmr-6">2</span><span
2033 class="cmtt-8"> </span><span
2034 class="cmtt-8"> byte</span><span
2035 class="cmtt-8"> 8:</span><span
2036 class="cmtt-8"> [</span><span
2037 class="cmtt-8"> </span><span
2038 class="cmtt-8"> </span><span
2039 class="cmtt-8"> </span><span
2040 class="cmtt-8"> </span><span
2041 class="cmtt-8"> </span><span
2042 class="cmtt-8"> </span><span
2043 class="cmtt-8"> </span><span
2044 class="cmtt-8"> </span><span
2045 class="cmtt-8"> </span><span
2046 class="cmtt-8"> </span><span
2047 class="cmtt-8"> </span><span
2048 class="cmtt-8"> </span><span
2049 class="cmtt-8"> </span><span
2050 class="cmtt-8"> </span><span
2051 class="cmtt-8"> X</span><span
2052 class="cmtt-8"> ]</span><span
2053 class="cmtt-8"> [ordered]</span><span
2054 class="cmtt-8"> (1</span><span
2055 class="cmtt-8"> bit)</span>
2056 <br class="fancyvrb" /><a
2057 id="x1-51028r3"></a><span
2058 class="cmr-6">3</span><span
2059 class="cmtt-8"> </span><span
2060 class="cmtt-8"> </span>
2062 <!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
2063 class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length.
2064 We now read the list of codeword lengths and store these lengths in the array
2066 class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span
2067 class="cmtt-12">[ordered] </span>flag
2069 <ul class="itemize1">
2070 <li class="itemize">If the <span
2071 class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
2072 needs to read each codeword length one-by-one.
2073 <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
2074 class="cmtt-12">[sparse] </span>flag. This flag determines
2075 whether or not the codebook contains unused entries that are not to be included in
2079 the codeword decode tree:
2080 <!--l. 82--><p class="noindent" >
2081 <div class="fancyvrb" id="fancyvrb10">
2083 id="x1-51030r1"></a><span
2084 class="cmr-6">1</span><span
2085 class="cmtt-8"> </span><span
2086 class="cmtt-8"> byte</span><span
2087 class="cmtt-8"> 8:</span><span
2088 class="cmtt-8"> [</span><span
2089 class="cmtt-8"> </span><span
2090 class="cmtt-8"> </span><span
2091 class="cmtt-8"> </span><span
2092 class="cmtt-8"> </span><span
2093 class="cmtt-8"> </span><span
2094 class="cmtt-8"> </span><span
2095 class="cmtt-8"> </span><span
2096 class="cmtt-8"> </span><span
2097 class="cmtt-8"> </span><span
2098 class="cmtt-8"> </span><span
2099 class="cmtt-8"> </span><span
2100 class="cmtt-8"> </span><span
2101 class="cmtt-8"> X</span><span
2102 class="cmtt-8"> 1</span><span
2103 class="cmtt-8"> ]</span><span
2104 class="cmtt-8"> [sparse]</span><span
2105 class="cmtt-8"> flag</span><span
2106 class="cmtt-8"> (1</span><span
2107 class="cmtt-8"> bit)</span>
2109 <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
2110 class="cmtt-12">[codebook_entries] </span>codebook entries:
2111 <!--l. 89--><p class="noindent" >
2112 <div class="fancyvrb" id="fancyvrb11">
2114 id="x1-51032r1"></a><span
2115 class="cmr-6">1</span><span
2116 class="cmtt-8"> </span><span
2117 class="cmtt-8"> </span>
2118 <br class="fancyvrb" /><a
2119 id="x1-51034r2"></a><span
2120 class="cmr-6">2</span><span
2121 class="cmtt-8"> </span><span
2122 class="cmtt-8"> </span><span
2123 class="cmtt-8"> </span><span
2124 class="cmtt-8"> 1)</span><span
2125 class="cmtt-8"> if([sparse]</span><span
2126 class="cmtt-8"> is</span><span
2127 class="cmtt-8"> set)</span><span
2128 class="cmtt-8"> </span><span
2129 class="cmsy-8">{</span>
2130 <br class="fancyvrb" /><a
2131 id="x1-51036r3"></a><span
2132 class="cmr-6">3</span><span
2133 class="cmtt-8"> </span><span
2134 class="cmtt-8"> </span>
2135 <br class="fancyvrb" /><a
2136 id="x1-51038r4"></a><span
2137 class="cmr-6">4</span><span
2138 class="cmtt-8"> </span><span
2139 class="cmtt-8"> </span><span
2140 class="cmtt-8"> </span><span
2141 class="cmtt-8"> </span><span
2142 class="cmtt-8"> </span><span
2143 class="cmtt-8"> </span><span
2144 class="cmtt-8"> </span><span
2145 class="cmtt-8"> </span><span
2146 class="cmtt-8"> </span><span
2147 class="cmtt-8"> </span><span
2148 class="cmtt-8"> 2)</span><span
2149 class="cmtt-8"> [flag]</span><span
2150 class="cmtt-8"> =</span><span
2151 class="cmtt-8"> read</span><span
2152 class="cmtt-8"> one</span><span
2153 class="cmtt-8"> bit;</span>
2154 <br class="fancyvrb" /><a
2155 id="x1-51040r5"></a><span
2156 class="cmr-6">5</span><span
2157 class="cmtt-8"> </span><span
2158 class="cmtt-8"> </span><span
2159 class="cmtt-8"> </span><span
2160 class="cmtt-8"> </span><span
2161 class="cmtt-8"> </span><span
2162 class="cmtt-8"> </span><span
2163 class="cmtt-8"> </span><span
2164 class="cmtt-8"> </span><span
2165 class="cmtt-8"> </span><span
2166 class="cmtt-8"> </span><span
2167 class="cmtt-8"> 3)</span><span
2168 class="cmtt-8"> if([flag]</span><span
2169 class="cmtt-8"> is</span><span
2170 class="cmtt-8"> set)</span><span
2171 class="cmtt-8"> </span><span
2172 class="cmsy-8">{</span>
2173 <br class="fancyvrb" /><a
2174 id="x1-51042r6"></a><span
2175 class="cmr-6">6</span><span
2176 class="cmtt-8"> </span><span
2177 class="cmtt-8"> </span>
2178 <br class="fancyvrb" /><a
2179 id="x1-51044r7"></a><span
2180 class="cmr-6">7</span><span
2181 class="cmtt-8"> </span><span
2182 class="cmtt-8"> </span><span
2183 class="cmtt-8"> </span><span
2184 class="cmtt-8"> </span><span
2185 class="cmtt-8"> </span><span
2186 class="cmtt-8"> </span><span
2187 class="cmtt-8"> </span><span
2188 class="cmtt-8"> </span><span
2189 class="cmtt-8"> </span><span
2190 class="cmtt-8"> </span><span
2191 class="cmtt-8"> </span><span
2192 class="cmtt-8"> </span><span
2193 class="cmtt-8"> </span><span
2194 class="cmtt-8"> </span><span
2195 class="cmtt-8"> </span><span
2196 class="cmtt-8"> 4)</span><span
2197 class="cmtt-8"> [length]</span><span
2198 class="cmtt-8"> =</span><span
2199 class="cmtt-8"> read</span><span
2200 class="cmtt-8"> a</span><span
2201 class="cmtt-8"> five</span><span
2202 class="cmtt-8"> bit</span><span
2203 class="cmtt-8"> unsigned</span><span
2204 class="cmtt-8"> integer;</span>
2205 <br class="fancyvrb" /><a
2206 id="x1-51046r8"></a><span
2207 class="cmr-6">8</span><span
2208 class="cmtt-8"> </span><span
2209 class="cmtt-8"> </span><span
2210 class="cmtt-8"> </span><span
2211 class="cmtt-8"> </span><span
2212 class="cmtt-8"> </span><span
2213 class="cmtt-8"> </span><span
2214 class="cmtt-8"> </span><span
2215 class="cmtt-8"> </span><span
2216 class="cmtt-8"> </span><span
2217 class="cmtt-8"> </span><span
2218 class="cmtt-8"> </span><span
2219 class="cmtt-8"> </span><span
2220 class="cmtt-8"> </span><span
2221 class="cmtt-8"> </span><span
2222 class="cmtt-8"> </span><span
2223 class="cmtt-8"> 5)</span><span
2224 class="cmtt-8"> codeword</span><span
2225 class="cmtt-8"> length</span><span
2226 class="cmtt-8"> for</span><span
2227 class="cmtt-8"> this</span><span
2228 class="cmtt-8"> entry</span><span
2229 class="cmtt-8"> is</span><span
2230 class="cmtt-8"> [length]+1;</span>
2231 <br class="fancyvrb" /><a
2232 id="x1-51048r9"></a><span
2233 class="cmr-6">9</span><span
2234 class="cmtt-8"> </span><span
2235 class="cmtt-8"> </span>
2236 <br class="fancyvrb" /><a
2237 id="x1-51050r10"></a><span
2238 class="cmr-6">10</span><span
2239 class="cmtt-8"> </span><span
2240 class="cmtt-8"> </span><span
2241 class="cmtt-8"> </span><span
2242 class="cmtt-8"> </span><span
2243 class="cmtt-8"> </span><span
2244 class="cmtt-8"> </span><span
2245 class="cmtt-8"> </span><span
2246 class="cmtt-8"> </span><span
2247 class="cmtt-8"> </span><span
2248 class="cmtt-8"> </span><span
2249 class="cmtt-8"> </span><span
2250 class="cmtt-8"> </span><span
2251 class="cmtt-8"> </span><span
2252 class="cmtt-8"> </span><span
2253 class="cmsy-8">}</span><span
2254 class="cmtt-8"> else</span><span
2255 class="cmtt-8"> </span><span
2256 class="cmsy-8">{</span>
2257 <br class="fancyvrb" /><a
2258 id="x1-51052r11"></a><span
2259 class="cmr-6">11</span><span
2260 class="cmtt-8"> </span><span
2261 class="cmtt-8"> </span>
2262 <br class="fancyvrb" /><a
2263 id="x1-51054r12"></a><span
2264 class="cmr-6">12</span><span
2265 class="cmtt-8"> </span><span
2266 class="cmtt-8"> </span><span
2267 class="cmtt-8"> </span><span
2268 class="cmtt-8"> </span><span
2269 class="cmtt-8"> </span><span
2270 class="cmtt-8"> </span><span
2271 class="cmtt-8"> </span><span
2272 class="cmtt-8"> </span><span
2273 class="cmtt-8"> </span><span
2274 class="cmtt-8"> </span><span
2275 class="cmtt-8"> </span><span
2276 class="cmtt-8"> </span><span
2277 class="cmtt-8"> </span><span
2278 class="cmtt-8"> </span><span
2279 class="cmtt-8"> </span><span
2280 class="cmtt-8"> 6)</span><span
2281 class="cmtt-8"> this</span><span
2282 class="cmtt-8"> entry</span><span
2283 class="cmtt-8"> is</span><span
2284 class="cmtt-8"> unused.</span><span
2285 class="cmtt-8"> </span><span
2286 class="cmtt-8"> mark</span><span
2287 class="cmtt-8"> it</span><span
2288 class="cmtt-8"> as</span><span
2289 class="cmtt-8"> such.</span>
2290 <br class="fancyvrb" /><a
2291 id="x1-51056r13"></a><span
2292 class="cmr-6">13</span><span
2293 class="cmtt-8"> </span><span
2294 class="cmtt-8"> </span>
2295 <br class="fancyvrb" /><a
2296 id="x1-51058r14"></a><span
2297 class="cmr-6">14</span><span
2298 class="cmtt-8"> </span><span
2299 class="cmtt-8"> </span><span
2300 class="cmtt-8"> </span><span
2301 class="cmtt-8"> </span><span
2302 class="cmtt-8"> </span><span
2303 class="cmtt-8"> </span><span
2304 class="cmtt-8"> </span><span
2305 class="cmtt-8"> </span><span
2306 class="cmtt-8"> </span><span
2307 class="cmtt-8"> </span><span
2308 class="cmtt-8"> </span><span
2309 class="cmtt-8"> </span><span
2310 class="cmtt-8"> </span><span
2311 class="cmtt-8"> </span><span
2312 class="cmsy-8">}</span>
2313 <br class="fancyvrb" /><a
2314 id="x1-51060r15"></a><span
2315 class="cmr-6">15</span><span
2316 class="cmtt-8"> </span><span
2317 class="cmtt-8"> </span>
2318 <br class="fancyvrb" /><a
2319 id="x1-51062r16"></a><span
2320 class="cmr-6">16</span><span
2321 class="cmtt-8"> </span><span
2322 class="cmtt-8"> </span><span
2323 class="cmtt-8"> </span><span
2324 class="cmtt-8"> </span><span
2325 class="cmtt-8"> </span><span
2326 class="cmtt-8"> </span><span
2327 class="cmtt-8"> </span><span
2328 class="cmsy-8">}</span><span
2329 class="cmtt-8"> else</span><span
2330 class="cmtt-8"> the</span><span
2331 class="cmtt-8"> sparse</span><span
2332 class="cmtt-8"> flag</span><span
2333 class="cmtt-8"> is</span><span
2334 class="cmtt-8"> not</span><span
2335 class="cmtt-8"> set</span><span
2336 class="cmtt-8"> </span><span
2337 class="cmsy-8">{</span>
2338 <br class="fancyvrb" /><a
2339 id="x1-51064r17"></a><span
2340 class="cmr-6">17</span><span
2341 class="cmtt-8"> </span><span
2342 class="cmtt-8"> </span>
2343 <br class="fancyvrb" /><a
2344 id="x1-51066r18"></a><span
2345 class="cmr-6">18</span><span
2346 class="cmtt-8"> </span><span
2347 class="cmtt-8"> </span><span
2348 class="cmtt-8"> </span><span
2349 class="cmtt-8"> </span><span
2350 class="cmtt-8"> </span><span
2351 class="cmtt-8"> </span><span
2352 class="cmtt-8"> </span><span
2353 class="cmtt-8"> </span><span
2354 class="cmtt-8"> </span><span
2355 class="cmtt-8"> 7)</span><span
2356 class="cmtt-8"> [length]</span><span
2357 class="cmtt-8"> =</span><span
2358 class="cmtt-8"> read</span><span
2359 class="cmtt-8"> a</span><span
2360 class="cmtt-8"> five</span><span
2361 class="cmtt-8"> bit</span><span
2362 class="cmtt-8"> unsigned</span><span
2363 class="cmtt-8"> integer;</span>
2364 <br class="fancyvrb" /><a
2365 id="x1-51068r19"></a><span
2366 class="cmr-6">19</span><span
2367 class="cmtt-8"> </span><span
2368 class="cmtt-8"> </span><span
2369 class="cmtt-8"> </span><span
2370 class="cmtt-8"> </span><span
2371 class="cmtt-8"> </span><span
2372 class="cmtt-8"> </span><span
2373 class="cmtt-8"> </span><span
2374 class="cmtt-8"> </span><span
2375 class="cmtt-8"> </span><span
2376 class="cmtt-8"> 8)</span><span
2377 class="cmtt-8"> the</span><span
2378 class="cmtt-8"> codeword</span><span
2379 class="cmtt-8"> length</span><span
2380 class="cmtt-8"> for</span><span
2381 class="cmtt-8"> this</span><span
2382 class="cmtt-8"> entry</span><span
2383 class="cmtt-8"> is</span><span
2384 class="cmtt-8"> [length]+1;</span>
2385 <br class="fancyvrb" /><a
2386 id="x1-51070r20"></a><span
2387 class="cmr-6">20</span><span
2388 class="cmtt-8"> </span><span
2389 class="cmtt-8"> </span>
2390 <br class="fancyvrb" /><a
2391 id="x1-51072r21"></a><span
2392 class="cmr-6">21</span><span
2393 class="cmtt-8"> </span><span
2394 class="cmtt-8"> </span><span
2395 class="cmtt-8"> </span><span
2396 class="cmtt-8"> </span><span
2397 class="cmtt-8"> </span><span
2398 class="cmtt-8"> </span><span
2399 class="cmtt-8"> </span><span
2400 class="cmsy-8">}</span>
2401 <br class="fancyvrb" /><a
2402 id="x1-51074r22"></a><span
2403 class="cmr-6">22</span><span
2404 class="cmtt-8"> </span><span
2405 class="cmtt-8"> </span>
2408 <li class="itemize">If the <span
2409 class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
2410 ascending length order. Rather than reading a length for every codeword, the
2411 encoder reads the number of codewords per length. That is, beginning at entry
2413 <!--l. 120--><p class="noindent" >
2414 <div class="fancyvrb" id="fancyvrb12">
2416 id="x1-51076r1"></a><span
2417 class="cmr-6">1</span><span
2418 class="cmtt-8"> </span><span
2419 class="cmtt-8"> </span><span
2420 class="cmtt-8"> </span><span
2421 class="cmtt-8"> 1)</span><span
2422 class="cmtt-8"> [current_entry]</span><span
2423 class="cmtt-8"> =</span><span
2424 class="cmtt-8"> 0;</span>
2425 <br class="fancyvrb" /><a
2426 id="x1-51078r2"></a><span
2427 class="cmr-6">2</span><span
2428 class="cmtt-8"> </span><span
2429 class="cmtt-8"> </span><span
2430 class="cmtt-8"> </span><span
2431 class="cmtt-8"> 2)</span><span
2432 class="cmtt-8"> [current_length]</span><span
2433 class="cmtt-8"> =</span><span
2434 class="cmtt-8"> read</span><span
2435 class="cmtt-8"> a</span><span
2436 class="cmtt-8"> five</span><span
2437 class="cmtt-8"> bit</span><span
2438 class="cmtt-8"> unsigned</span><span
2439 class="cmtt-8"> integer</span><span
2440 class="cmtt-8"> and</span><span
2441 class="cmtt-8"> add</span><span
2442 class="cmtt-8"> 1;</span>
2443 <br class="fancyvrb" /><a
2444 id="x1-51080r3"></a><span
2445 class="cmr-6">3</span><span
2446 class="cmtt-8"> </span><span
2447 class="cmtt-8"> </span><span
2448 class="cmtt-8"> </span><span
2449 class="cmtt-8"> 3)</span><span
2450 class="cmtt-8"> [number]</span><span
2451 class="cmtt-8"> =</span><span
2452 class="cmtt-8"> read</span><span
2453 class="cmtt-8"> </span><a
2454 href="#x1-1170009.2.1"><span
2455 class="cmtt-8">ilog</span></a><span
2456 class="cmtt-8">([codebook_entries]</span><span
2457 class="cmtt-8"> -</span><span
2458 class="cmtt-8"> [current_entry])</span><span
2459 class="cmtt-8"> bits</span><span
2460 class="cmtt-8"> as</span><span
2461 class="cmtt-8"> an</span><span
2462 class="cmtt-8"> unsigned</span><span
2463 class="cmtt-8"> integer</span>
2464 <br class="fancyvrb" /><a
2465 id="x1-51082r4"></a><span
2466 class="cmr-6">4</span><span
2467 class="cmtt-8"> </span><span
2468 class="cmtt-8"> </span><span
2469 class="cmtt-8"> </span><span
2470 class="cmtt-8"> 4)</span><span
2471 class="cmtt-8"> set</span><span
2472 class="cmtt-8"> the</span><span
2473 class="cmtt-8"> entries</span><span
2474 class="cmtt-8"> [current_entry]</span><span
2475 class="cmtt-8"> through</span><span
2476 class="cmtt-8"> [current_entry]+[number]-1,</span><span
2477 class="cmtt-8"> inclusive,</span>
2478 <br class="fancyvrb" /><a
2479 id="x1-51084r5"></a><span
2480 class="cmr-6">5</span><span
2481 class="cmtt-8"> </span><span
2482 class="cmtt-8"> </span><span
2483 class="cmtt-8"> </span><span
2484 class="cmtt-8"> </span><span
2485 class="cmtt-8"> </span><span
2486 class="cmtt-8"> of</span><span
2487 class="cmtt-8"> the</span><span
2488 class="cmtt-8"> [codebook_codeword_lengths]</span><span
2489 class="cmtt-8"> array</span><span
2490 class="cmtt-8"> to</span><span
2491 class="cmtt-8"> [current_length]</span>
2492 <br class="fancyvrb" /><a
2493 id="x1-51086r6"></a><span
2494 class="cmr-6">6</span><span
2495 class="cmtt-8"> </span><span
2496 class="cmtt-8"> </span><span
2497 class="cmtt-8"> </span><span
2498 class="cmtt-8"> 5)</span><span
2499 class="cmtt-8"> set</span><span
2500 class="cmtt-8"> [current_entry]</span><span
2501 class="cmtt-8"> to</span><span
2502 class="cmtt-8"> [number]</span><span
2503 class="cmtt-8"> +</span><span
2504 class="cmtt-8"> [current_entry]</span>
2505 <br class="fancyvrb" /><a
2506 id="x1-51088r7"></a><span
2507 class="cmr-6">7</span><span
2508 class="cmtt-8"> </span><span
2509 class="cmtt-8"> </span><span
2510 class="cmtt-8"> </span><span
2511 class="cmtt-8"> 6)</span><span
2512 class="cmtt-8"> increment</span><span
2513 class="cmtt-8"> [current_length]</span><span
2514 class="cmtt-8"> by</span><span
2515 class="cmtt-8"> 1</span>
2516 <br class="fancyvrb" /><a
2517 id="x1-51090r8"></a><span
2518 class="cmr-6">8</span><span
2519 class="cmtt-8"> </span><span
2520 class="cmtt-8"> </span><span
2521 class="cmtt-8"> </span><span
2522 class="cmtt-8"> 7)</span><span
2523 class="cmtt-8"> if</span><span
2524 class="cmtt-8"> [current_entry]</span><span
2525 class="cmtt-8"> is</span><span
2526 class="cmtt-8"> greater</span><span
2527 class="cmtt-8"> than</span><span
2528 class="cmtt-8"> [codebook_entries]</span><span
2529 class="cmtt-8"> ERROR</span><span
2530 class="cmtt-8"> CONDITION;</span>
2531 <br class="fancyvrb" /><a
2532 id="x1-51092r9"></a><span
2533 class="cmr-6">9</span><span
2534 class="cmtt-8"> </span><span
2535 class="cmtt-8"> </span><span
2536 class="cmtt-8"> </span><span
2537 class="cmtt-8"> </span><span
2538 class="cmtt-8"> </span><span
2539 class="cmtt-8"> the</span><span
2540 class="cmtt-8"> decoder</span><span
2541 class="cmtt-8"> will</span><span
2542 class="cmtt-8"> not</span><span
2543 class="cmtt-8"> be</span><span
2544 class="cmtt-8"> able</span><span
2545 class="cmtt-8"> to</span><span
2546 class="cmtt-8"> read</span><span
2547 class="cmtt-8"> this</span><span
2548 class="cmtt-8"> stream.</span>
2549 <br class="fancyvrb" /><a
2550 id="x1-51094r10"></a><span
2551 class="cmr-6">10</span><span
2552 class="cmtt-8"> </span><span
2553 class="cmtt-8"> </span><span
2554 class="cmtt-8"> </span><span
2555 class="cmtt-8"> 8)</span><span
2556 class="cmtt-8"> if</span><span
2557 class="cmtt-8"> [current_entry]</span><span
2558 class="cmtt-8"> is</span><span
2559 class="cmtt-8"> less</span><span
2560 class="cmtt-8"> than</span><span
2561 class="cmtt-8"> [codebook_entries],</span><span
2562 class="cmtt-8"> repeat</span><span
2563 class="cmtt-8"> process</span><span
2564 class="cmtt-8"> starting</span><span
2565 class="cmtt-8"> at</span><span
2566 class="cmtt-8"> 3)</span>
2567 <br class="fancyvrb" /><a
2568 id="x1-51096r11"></a><span
2569 class="cmr-6">11</span><span
2570 class="cmtt-8"> </span><span
2571 class="cmtt-8"> </span><span
2572 class="cmtt-8"> </span><span
2573 class="cmtt-8"> 9)</span><span
2574 class="cmtt-8"> done.</span>
2580 <!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
2581 I supports three lookup types:
2582 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
2584 class="enumerate-enumitem">No lookup
2585 </dd><dt class="enumerate-enumitem">
2587 class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ)
2588 </dd><dt class="enumerate-enumitem">
2590 class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl>
2591 <!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
2592 <div class="fancyvrb" id="fancyvrb13">
2594 id="x1-51101r1"></a><span
2595 class="cmr-6">1</span><span
2596 class="cmtt-8"> </span><span
2597 class="cmtt-8"> </span><span
2598 class="cmtt-8"> </span><span
2599 class="cmtt-8"> 1)</span><span
2600 class="cmtt-8"> [codebook_lookup_type]</span><span
2601 class="cmtt-8"> =</span><span
2602 class="cmtt-8"> read</span><span
2603 class="cmtt-8"> four</span><span
2604 class="cmtt-8"> bits</span><span
2605 class="cmtt-8"> as</span><span
2606 class="cmtt-8"> an</span><span
2607 class="cmtt-8"> unsigned</span><span
2608 class="cmtt-8"> integer</span>
2610 <!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
2611 class="cmtt-12">[codebook_lookup_type]</span>:
2612 <ul class="itemize1">
2613 <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
2615 <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
2616 be read. Lookup type one reads a list of values that are permuted in a set pattern to
2617 build a list of vectors, each vector of order <span
2618 class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup
2619 type two builds the same vector list, but reads each scalar for each vector explicitly,
2620 rather than building vectors from a smaller list of possible scalar values. Lookup
2621 decode proceeds as follows:
2622 <!--l. 168--><p class="noindent" >
2623 <div class="fancyvrb" id="fancyvrb14">
2625 id="x1-51103r1"></a><span
2626 class="cmr-6">1</span><span
2627 class="cmtt-8"> </span><span
2628 class="cmtt-8"> </span><span
2629 class="cmtt-8"> </span><span
2630 class="cmtt-8"> 1)</span><span
2631 class="cmtt-8"> [codebook_minimum_value]</span><span
2632 class="cmtt-8"> =</span><span
2633 class="cmtt-8"> </span><a
2634 href="#x1-1180009.2.2"><span
2635 class="cmtt-8">float32_unpack</span></a><span
2636 class="cmtt-8">(</span><span
2637 class="cmtt-8"> read</span><span
2638 class="cmtt-8"> 32</span><span
2639 class="cmtt-8"> bits</span><span
2640 class="cmtt-8"> as</span><span
2641 class="cmtt-8"> an</span><span
2642 class="cmtt-8"> unsigned</span><span
2643 class="cmtt-8"> integer)</span>
2644 <br class="fancyvrb" /><a
2645 id="x1-51105r2"></a><span
2646 class="cmr-6">2</span><span
2647 class="cmtt-8"> </span><span
2648 class="cmtt-8"> </span><span
2649 class="cmtt-8"> </span><span
2650 class="cmtt-8"> 2)</span><span
2651 class="cmtt-8"> [codebook_delta_value]</span><span
2652 class="cmtt-8"> =</span><span
2653 class="cmtt-8"> </span><a
2654 href="#x1-1180009.2.2"><span
2655 class="cmtt-8">float32_unpack</span></a><span
2656 class="cmtt-8">(</span><span
2657 class="cmtt-8"> read</span><span
2658 class="cmtt-8"> 32</span><span
2659 class="cmtt-8"> bits</span><span
2660 class="cmtt-8"> as</span><span
2661 class="cmtt-8"> an</span><span
2662 class="cmtt-8"> unsigned</span><span
2663 class="cmtt-8"> integer)</span>
2664 <br class="fancyvrb" /><a
2665 id="x1-51107r3"></a><span
2666 class="cmr-6">3</span><span
2667 class="cmtt-8"> </span><span
2668 class="cmtt-8"> </span><span
2669 class="cmtt-8"> </span><span
2670 class="cmtt-8"> 3)</span><span
2671 class="cmtt-8"> [codebook_value_bits]</span><span
2672 class="cmtt-8"> =</span><span
2673 class="cmtt-8"> read</span><span
2674 class="cmtt-8"> 4</span><span
2675 class="cmtt-8"> bits</span><span
2676 class="cmtt-8"> as</span><span
2677 class="cmtt-8"> an</span><span
2678 class="cmtt-8"> unsigned</span><span
2679 class="cmtt-8"> integer</span><span
2680 class="cmtt-8"> and</span><span
2681 class="cmtt-8"> add</span><span
2682 class="cmtt-8"> 1</span>
2683 <br class="fancyvrb" /><a
2684 id="x1-51109r4"></a><span
2685 class="cmr-6">4</span><span
2686 class="cmtt-8"> </span><span
2687 class="cmtt-8"> </span><span
2688 class="cmtt-8"> </span><span
2689 class="cmtt-8"> 4)</span><span
2690 class="cmtt-8"> [codebook_sequence_p]</span><span
2691 class="cmtt-8"> =</span><span
2692 class="cmtt-8"> read</span><span
2693 class="cmtt-8"> 1</span><span
2694 class="cmtt-8"> bit</span><span
2695 class="cmtt-8"> as</span><span
2696 class="cmtt-8"> a</span><span
2697 class="cmtt-8"> boolean</span><span
2698 class="cmtt-8"> flag</span>
2699 <br class="fancyvrb" /><a
2700 id="x1-51111r5"></a><span
2701 class="cmr-6">5</span><span
2702 class="cmtt-8"> </span><span
2703 class="cmtt-8"> </span>
2704 <br class="fancyvrb" /><a
2705 id="x1-51113r6"></a><span
2706 class="cmr-6">6</span><span
2707 class="cmtt-8"> </span><span
2708 class="cmtt-8"> </span><span
2709 class="cmtt-8"> </span><span
2710 class="cmtt-8"> if</span><span
2711 class="cmtt-8"> (</span><span
2712 class="cmtt-8"> [codebook_lookup_type]</span><span
2713 class="cmtt-8"> is</span><span
2714 class="cmtt-8"> 1</span><span
2715 class="cmtt-8"> )</span><span
2716 class="cmtt-8"> </span><span
2717 class="cmsy-8">{</span>
2718 <br class="fancyvrb" /><a
2719 id="x1-51115r7"></a><span
2720 class="cmr-6">7</span><span
2721 class="cmtt-8"> </span><span
2722 class="cmtt-8"> </span>
2723 <br class="fancyvrb" /><a
2724 id="x1-51117r8"></a><span
2725 class="cmr-6">8</span><span
2726 class="cmtt-8"> </span><span
2727 class="cmtt-8"> </span><span
2728 class="cmtt-8"> </span><span
2729 class="cmtt-8"> </span><span
2730 class="cmtt-8"> </span><span
2731 class="cmtt-8"> </span><span
2732 class="cmtt-8"> 5)</span><span
2733 class="cmtt-8"> [codebook_lookup_values]</span><span
2734 class="cmtt-8"> =</span><span
2735 class="cmtt-8"> </span><a
2736 href="#x1-1190009.2.3"><span
2737 class="cmtt-8">lookup1_values</span></a><span
2738 class="cmtt-8">([codebook_entries],</span><span
2739 class="cmtt-8"> [codebook_dimensions]</span><span
2740 class="cmtt-8"> )</span>
2741 <br class="fancyvrb" /><a
2742 id="x1-51119r9"></a><span
2743 class="cmr-6">9</span><span
2744 class="cmtt-8"> </span><span
2745 class="cmtt-8"> </span>
2746 <br class="fancyvrb" /><a
2747 id="x1-51121r10"></a><span
2748 class="cmr-6">10</span><span
2749 class="cmtt-8"> </span><span
2750 class="cmtt-8"> </span><span
2751 class="cmtt-8"> </span><span
2752 class="cmtt-8"> </span><span
2753 class="cmsy-8">}</span><span
2754 class="cmtt-8"> else</span><span
2755 class="cmtt-8"> </span><span
2756 class="cmsy-8">{</span>
2757 <br class="fancyvrb" /><a
2758 id="x1-51123r11"></a><span
2759 class="cmr-6">11</span><span
2760 class="cmtt-8"> </span><span
2761 class="cmtt-8"> </span>
2762 <br class="fancyvrb" /><a
2763 id="x1-51125r12"></a><span
2764 class="cmr-6">12</span><span
2765 class="cmtt-8"> </span><span
2766 class="cmtt-8"> </span><span
2767 class="cmtt-8"> </span><span
2768 class="cmtt-8"> </span><span
2769 class="cmtt-8"> </span><span
2770 class="cmtt-8"> </span><span
2771 class="cmtt-8"> 6)</span><span
2772 class="cmtt-8"> [codebook_lookup_values]</span><span
2773 class="cmtt-8"> =</span><span
2774 class="cmtt-8"> [codebook_entries]</span><span
2775 class="cmtt-8"> *</span><span
2776 class="cmtt-8"> [codebook_dimensions]</span>
2777 <br class="fancyvrb" /><a
2778 id="x1-51127r13"></a><span
2779 class="cmr-6">13</span><span
2780 class="cmtt-8"> </span><span
2781 class="cmtt-8"> </span>
2782 <br class="fancyvrb" /><a
2783 id="x1-51129r14"></a><span
2784 class="cmr-6">14</span><span
2785 class="cmtt-8"> </span><span
2786 class="cmtt-8"> </span><span
2787 class="cmtt-8"> </span><span
2788 class="cmtt-8"> </span><span
2789 class="cmsy-8">}</span>
2790 <br class="fancyvrb" /><a
2791 id="x1-51131r15"></a><span
2792 class="cmr-6">15</span><span
2793 class="cmtt-8"> </span><span
2794 class="cmtt-8"> </span>
2795 <br class="fancyvrb" /><a
2796 id="x1-51133r16"></a><span
2797 class="cmr-6">16</span><span
2798 class="cmtt-8"> </span><span
2799 class="cmtt-8"> </span><span
2800 class="cmtt-8"> </span><span
2801 class="cmtt-8"> 7)</span><span
2802 class="cmtt-8"> read</span><span
2803 class="cmtt-8"> a</span><span
2804 class="cmtt-8"> total</span><span
2805 class="cmtt-8"> of</span><span
2806 class="cmtt-8"> [codebook_lookup_values]</span><span
2807 class="cmtt-8"> unsigned</span><span
2808 class="cmtt-8"> integers</span><span
2809 class="cmtt-8"> of</span><span
2810 class="cmtt-8"> [codebook_value_bits]</span><span
2811 class="cmtt-8"> each;</span>
2815 <br class="fancyvrb" /><a
2816 id="x1-51135r17"></a><span
2817 class="cmr-6">17</span><span
2818 class="cmtt-8"> </span><span
2819 class="cmtt-8"> </span><span
2820 class="cmtt-8"> </span><span
2821 class="cmtt-8"> </span><span
2822 class="cmtt-8"> </span><span
2823 class="cmtt-8"> </span><span
2824 class="cmtt-8"> store</span><span
2825 class="cmtt-8"> these</span><span
2826 class="cmtt-8"> in</span><span
2827 class="cmtt-8"> order</span><span
2828 class="cmtt-8"> in</span><span
2829 class="cmtt-8"> the</span><span
2830 class="cmtt-8"> array</span><span
2831 class="cmtt-8"> [codebook_multiplicands]</span>
2834 <li class="itemize">A <span
2835 class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is
2836 not decodable by the specification in this document.
2838 <!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
2839 rendering the stream undecodable.
2840 <!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
2841 id="x1-520003.2.1"></a><span
2842 class="cmbx-12">Huffman decision tree representation</span></span>
2844 class="cmtt-12">[codebook_codeword_lengths] </span>array and <span
2845 class="cmtt-12">[codebook_entries] </span>value uniquely define the
2846 Huffman decision tree used for entropy decoding.
2847 <!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
2848 codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
2849 possible. Assume the following codeword length list:
2850 <!--l. 209--><p class="noindent" >
2851 <div class="fancyvrb" id="fancyvrb15">
2853 id="x1-52002r1"></a><span
2854 class="cmr-6">1</span><span
2855 class="cmtt-8"> </span><span
2856 class="cmtt-8"> entry</span><span
2857 class="cmtt-8"> 0:</span><span
2858 class="cmtt-8"> length</span><span
2859 class="cmtt-8"> 2</span>
2860 <br class="fancyvrb" /><a
2861 id="x1-52004r2"></a><span
2862 class="cmr-6">2</span><span
2863 class="cmtt-8"> </span><span
2864 class="cmtt-8"> entry</span><span
2865 class="cmtt-8"> 1:</span><span
2866 class="cmtt-8"> length</span><span
2867 class="cmtt-8"> 4</span>
2868 <br class="fancyvrb" /><a
2869 id="x1-52006r3"></a><span
2870 class="cmr-6">3</span><span
2871 class="cmtt-8"> </span><span
2872 class="cmtt-8"> entry</span><span
2873 class="cmtt-8"> 2:</span><span
2874 class="cmtt-8"> length</span><span
2875 class="cmtt-8"> 4</span>
2876 <br class="fancyvrb" /><a
2877 id="x1-52008r4"></a><span
2878 class="cmr-6">4</span><span
2879 class="cmtt-8"> </span><span
2880 class="cmtt-8"> entry</span><span
2881 class="cmtt-8"> 3:</span><span
2882 class="cmtt-8"> length</span><span
2883 class="cmtt-8"> 4</span>
2884 <br class="fancyvrb" /><a
2885 id="x1-52010r5"></a><span
2886 class="cmr-6">5</span><span
2887 class="cmtt-8"> </span><span
2888 class="cmtt-8"> entry</span><span
2889 class="cmtt-8"> 4:</span><span
2890 class="cmtt-8"> length</span><span
2891 class="cmtt-8"> 4</span>
2892 <br class="fancyvrb" /><a
2893 id="x1-52012r6"></a><span
2894 class="cmr-6">6</span><span
2895 class="cmtt-8"> </span><span
2896 class="cmtt-8"> entry</span><span
2897 class="cmtt-8"> 5:</span><span
2898 class="cmtt-8"> length</span><span
2899 class="cmtt-8"> 2</span>
2900 <br class="fancyvrb" /><a
2901 id="x1-52014r7"></a><span
2902 class="cmr-6">7</span><span
2903 class="cmtt-8"> </span><span
2904 class="cmtt-8"> entry</span><span
2905 class="cmtt-8"> 6:</span><span
2906 class="cmtt-8"> length</span><span
2907 class="cmtt-8"> 3</span>
2908 <br class="fancyvrb" /><a
2909 id="x1-52016r8"></a><span
2910 class="cmr-6">8</span><span
2911 class="cmtt-8"> </span><span
2912 class="cmtt-8"> entry</span><span
2913 class="cmtt-8"> 7:</span><span
2914 class="cmtt-8"> length</span><span
2915 class="cmtt-8"> 3</span>
2917 <!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
2918 in the following codeword list:
2919 <!--l. 223--><p class="noindent" >
2920 <div class="fancyvrb" id="fancyvrb16">
2922 id="x1-52018r1"></a><span
2923 class="cmr-6">1</span><span
2924 class="cmtt-8"> </span><span
2925 class="cmtt-8"> entry</span><span
2926 class="cmtt-8"> 0:</span><span
2927 class="cmtt-8"> length</span><span
2928 class="cmtt-8"> 2</span><span
2929 class="cmtt-8"> codeword</span><span
2930 class="cmtt-8"> 00</span>
2931 <br class="fancyvrb" /><a
2932 id="x1-52020r2"></a><span
2933 class="cmr-6">2</span><span
2934 class="cmtt-8"> </span><span
2935 class="cmtt-8"> entry</span><span
2936 class="cmtt-8"> 1:</span><span
2937 class="cmtt-8"> length</span><span
2938 class="cmtt-8"> 4</span><span
2939 class="cmtt-8"> codeword</span><span
2940 class="cmtt-8"> 0100</span>
2941 <br class="fancyvrb" /><a
2942 id="x1-52022r3"></a><span
2943 class="cmr-6">3</span><span
2944 class="cmtt-8"> </span><span
2945 class="cmtt-8"> entry</span><span
2946 class="cmtt-8"> 2:</span><span
2947 class="cmtt-8"> length</span><span
2948 class="cmtt-8"> 4</span><span
2949 class="cmtt-8"> codeword</span><span
2950 class="cmtt-8"> 0101</span>
2951 <br class="fancyvrb" /><a
2952 id="x1-52024r4"></a><span
2953 class="cmr-6">4</span><span
2954 class="cmtt-8"> </span><span
2955 class="cmtt-8"> entry</span><span
2956 class="cmtt-8"> 3:</span><span
2957 class="cmtt-8"> length</span><span
2958 class="cmtt-8"> 4</span><span
2959 class="cmtt-8"> codeword</span><span
2960 class="cmtt-8"> 0110</span>
2961 <br class="fancyvrb" /><a
2962 id="x1-52026r5"></a><span
2963 class="cmr-6">5</span><span
2964 class="cmtt-8"> </span><span
2965 class="cmtt-8"> entry</span><span
2966 class="cmtt-8"> 4:</span><span
2967 class="cmtt-8"> length</span><span
2968 class="cmtt-8"> 4</span><span
2969 class="cmtt-8"> codeword</span><span
2970 class="cmtt-8"> 0111</span>
2971 <br class="fancyvrb" /><a
2972 id="x1-52028r6"></a><span
2973 class="cmr-6">6</span><span
2974 class="cmtt-8"> </span><span
2975 class="cmtt-8"> entry</span><span
2976 class="cmtt-8"> 5:</span><span
2977 class="cmtt-8"> length</span><span
2978 class="cmtt-8"> 2</span><span
2979 class="cmtt-8"> codeword</span><span
2980 class="cmtt-8"> 10</span>
2981 <br class="fancyvrb" /><a
2982 id="x1-52030r7"></a><span
2983 class="cmr-6">7</span><span
2984 class="cmtt-8"> </span><span
2985 class="cmtt-8"> entry</span><span
2986 class="cmtt-8"> 6:</span><span
2987 class="cmtt-8"> length</span><span
2988 class="cmtt-8"> 3</span><span
2989 class="cmtt-8"> codeword</span><span
2990 class="cmtt-8"> 110</span>
2991 <br class="fancyvrb" /><a
2992 id="x1-52032r8"></a><span
2993 class="cmr-6">8</span><span
2994 class="cmtt-8"> </span><span
2995 class="cmtt-8"> entry</span><span
2996 class="cmtt-8"> 7:</span><span
2997 class="cmtt-8"> length</span><span
2998 class="cmtt-8"> 3</span><span
2999 class="cmtt-8"> codeword</span><span
3000 class="cmtt-8"> 111</span>
3005 <!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
3006 id="x1-530003.2.1"></a><span
3007 class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
3008 be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
3009 one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
3011 <!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
3012 numbers equivalent to the leaves numbered left-to-right:
3015 <!--l. 247--><p class="noindent" >
3017 <!--l. 248--><p class="noindent" ><img
3018 src="hufftree.png" alt="PIC"
3020 <br /> <div class="caption"
3021 ><span class="id">Figure 4: </span><span
3022 class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 -->
3024 <!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
3026 <!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
3027 In the above example, if codeword seven were eliminated, it’s clear that the tree is
3031 <!--l. 260--><p class="noindent" >
3033 <!--l. 261--><p class="noindent" ><img
3034 src="hufftree-under.png" alt="PIC"
3036 <br /> <div class="caption"
3037 ><span class="id">Figure 5: </span><span
3038 class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 -->
3040 <!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
3041 codeword is impossible. Both underspecified and overspecified trees are an error condition
3042 rendering the stream undecodable. Take special care that a codebook with a single used
3043 entry is handled properly; it consists of a single codework of zero bits and ’reading’
3044 a value out of such a codebook always returns the single used value and sinks zero
3046 <!--l. 274--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
3047 codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
3048 from the stream to decode to that entry number.
3052 <!--l. 281--><p class="noindent" ><span class="paragraphHead"><a
3053 id="x1-540003.2.1"></a><span
3054 class="cmbx-12">VQ lookup table vector representation</span></span>
3055 Unpacking the VQ lookup table vectors relies on the following values:
3056 <div class="fancyvrb" id="fancyvrb17">
3058 id="x1-54002r1"></a><span
3059 class="cmr-6">1</span><span
3060 class="cmtt-8"> </span><span
3061 class="cmtt-8"> the</span><span
3062 class="cmtt-8"> [codebook\_multiplicands]</span><span
3063 class="cmtt-8"> array</span>
3064 <br class="fancyvrb" /><a
3065 id="x1-54004r2"></a><span
3066 class="cmr-6">2</span><span
3067 class="cmtt-8"> </span><span
3068 class="cmtt-8"> [codebook\_minimum\_value]</span>
3069 <br class="fancyvrb" /><a
3070 id="x1-54006r3"></a><span
3071 class="cmr-6">3</span><span
3072 class="cmtt-8"> </span><span
3073 class="cmtt-8"> [codebook\_delta\_value]</span>
3074 <br class="fancyvrb" /><a
3075 id="x1-54008r4"></a><span
3076 class="cmr-6">4</span><span
3077 class="cmtt-8"> </span><span
3078 class="cmtt-8"> [codebook\_sequence\_p]</span>
3079 <br class="fancyvrb" /><a
3080 id="x1-54010r5"></a><span
3081 class="cmr-6">5</span><span
3082 class="cmtt-8"> </span><span
3083 class="cmtt-8"> [codebook\_lookup\_type]</span>
3084 <br class="fancyvrb" /><a
3085 id="x1-54012r6"></a><span
3086 class="cmr-6">6</span><span
3087 class="cmtt-8"> </span><span
3088 class="cmtt-8"> [codebook\_entries]</span>
3089 <br class="fancyvrb" /><a
3090 id="x1-54014r7"></a><span
3091 class="cmr-6">7</span><span
3092 class="cmtt-8"> </span><span
3093 class="cmtt-8"> [codebook\_dimensions]</span>
3094 <br class="fancyvrb" /><a
3095 id="x1-54016r8"></a><span
3096 class="cmr-6">8</span><span
3097 class="cmtt-8"> </span><span
3098 class="cmtt-8"> [codebook\_lookup\_values]</span>
3100 <!--l. 297--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to
3102 class="cmtt-12">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return
3103 during audio packet decode in a VQ context.
3104 <!--l. 302--><p class="noindent" ><span class="paragraphHead"><a
3105 id="x1-550003.2.1"></a><span
3106 class="cmbx-12">Vector value decode: Lookup type 1</span></span>
3107 Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of
3108 scalar values. Calculate (unpack) the final values of a codebook entry vector from
3109 the entries in <span
3110 class="cmtt-12">[codebook_multiplicands] </span>as follows (<span
3111 class="cmtt-12">[value_vector] </span>is the output
3112 vector representing the vector of values for entry number <span
3113 class="cmtt-12">[lookup_offset] </span>in this
3115 <!--l. 311--><p class="noindent" >
3116 <div class="fancyvrb" id="fancyvrb18">
3118 id="x1-55002r1"></a><span
3119 class="cmr-6">1</span><span
3120 class="cmtt-8"> </span><span
3121 class="cmtt-8"> </span><span
3122 class="cmtt-8"> </span><span
3123 class="cmtt-8"> 1)</span><span
3124 class="cmtt-8"> [last]</span><span
3125 class="cmtt-8"> =</span><span
3126 class="cmtt-8"> 0;</span>
3127 <br class="fancyvrb" /><a
3128 id="x1-55004r2"></a><span
3129 class="cmr-6">2</span><span
3130 class="cmtt-8"> </span><span
3131 class="cmtt-8"> </span><span
3132 class="cmtt-8"> </span><span
3133 class="cmtt-8"> 2)</span><span
3134 class="cmtt-8"> [index_divisor]</span><span
3135 class="cmtt-8"> =</span><span
3136 class="cmtt-8"> 1;</span>
3137 <br class="fancyvrb" /><a
3138 id="x1-55006r3"></a><span
3139 class="cmr-6">3</span><span
3140 class="cmtt-8"> </span><span
3141 class="cmtt-8"> </span><span
3142 class="cmtt-8"> </span><span
3143 class="cmtt-8"> 3)</span><span
3144 class="cmtt-8"> iterate</span><span
3145 class="cmtt-8"> [i]</span><span
3146 class="cmtt-8"> over</span><span
3147 class="cmtt-8"> the</span><span
3148 class="cmtt-8"> range</span><span
3149 class="cmtt-8"> 0</span><span
3150 class="cmtt-8"> ...</span><span
3151 class="cmtt-8"> [codebook_dimensions]-1</span><span
3152 class="cmtt-8"> (once</span><span
3153 class="cmtt-8"> for</span><span
3154 class="cmtt-8"> each</span><span
3155 class="cmtt-8"> scalar</span><span
3156 class="cmtt-8"> value</span><span
3157 class="cmtt-8"> in</span><span
3158 class="cmtt-8"> the</span><span
3159 class="cmtt-8"> value</span><span
3160 class="cmtt-8"> vector)</span><span
3161 class="cmtt-8"> </span><span
3162 class="cmsy-8">{</span>
3163 <br class="fancyvrb" /><a
3164 id="x1-55008r4"></a><span
3165 class="cmr-6">4</span><span
3166 class="cmtt-8"> </span><span
3167 class="cmtt-8"> </span>
3168 <br class="fancyvrb" /><a
3169 id="x1-55010r5"></a><span
3170 class="cmr-6">5</span><span
3171 class="cmtt-8"> </span><span
3172 class="cmtt-8"> </span><span
3173 class="cmtt-8"> </span><span
3174 class="cmtt-8"> </span><span
3175 class="cmtt-8"> </span><span
3176 class="cmtt-8"> </span><span
3177 class="cmtt-8"> </span><span
3178 class="cmtt-8"> </span><span
3179 class="cmtt-8"> 4)</span><span
3180 class="cmtt-8"> [multiplicand_offset]</span><span
3181 class="cmtt-8"> =</span><span
3182 class="cmtt-8"> (</span><span
3183 class="cmtt-8"> [lookup_offset]</span><span
3184 class="cmtt-8"> divided</span><span
3185 class="cmtt-8"> by</span><span
3186 class="cmtt-8"> [index_divisor]</span><span
3187 class="cmtt-8"> using</span><span
3188 class="cmtt-8"> integer</span>
3189 <br class="fancyvrb" /><a
3190 id="x1-55012r6"></a><span
3191 class="cmr-6">6</span><span
3192 class="cmtt-8"> </span><span
3193 class="cmtt-8"> </span><span
3194 class="cmtt-8"> </span><span
3195 class="cmtt-8"> </span><span
3196 class="cmtt-8"> </span><span
3197 class="cmtt-8"> </span><span
3198 class="cmtt-8"> </span><span
3199 class="cmtt-8"> </span><span
3200 class="cmtt-8"> </span><span
3201 class="cmtt-8"> </span><span
3202 class="cmtt-8"> </span><span
3203 class="cmtt-8"> division</span><span
3204 class="cmtt-8"> )</span><span
3205 class="cmtt-8"> integer</span><span
3206 class="cmtt-8"> modulo</span><span
3207 class="cmtt-8"> [codebook_lookup_values]</span>
3208 <br class="fancyvrb" /><a
3209 id="x1-55014r7"></a><span
3210 class="cmr-6">7</span><span
3211 class="cmtt-8"> </span><span
3212 class="cmtt-8"> </span>
3213 <br class="fancyvrb" /><a
3214 id="x1-55016r8"></a><span
3215 class="cmr-6">8</span><span
3216 class="cmtt-8"> </span><span
3217 class="cmtt-8"> </span><span
3218 class="cmtt-8"> </span><span
3219 class="cmtt-8"> </span><span
3220 class="cmtt-8"> </span><span
3221 class="cmtt-8"> </span><span
3222 class="cmtt-8"> </span><span
3223 class="cmtt-8"> </span><span
3224 class="cmtt-8"> 5)</span><span
3225 class="cmtt-8"> vector</span><span
3226 class="cmtt-8"> [value_vector]</span><span
3227 class="cmtt-8"> element</span><span
3228 class="cmtt-8"> [i]</span><span
3229 class="cmtt-8"> =</span>
3230 <br class="fancyvrb" /><a
3231 id="x1-55018r9"></a><span
3232 class="cmr-6">9</span><span
3233 class="cmtt-8"> </span><span
3234 class="cmtt-8"> </span><span
3235 class="cmtt-8"> </span><span
3236 class="cmtt-8"> </span><span
3237 class="cmtt-8"> </span><span
3238 class="cmtt-8"> </span><span
3239 class="cmtt-8"> </span><span
3240 class="cmtt-8"> </span><span
3241 class="cmtt-8"> </span><span
3242 class="cmtt-8"> </span><span
3243 class="cmtt-8"> </span><span
3244 class="cmtt-8"> </span><span
3245 class="cmtt-8"> </span><span
3246 class="cmtt-8"> (</span><span
3247 class="cmtt-8"> [codebook_multiplicands]</span><span
3248 class="cmtt-8"> array</span><span
3249 class="cmtt-8"> element</span><span
3250 class="cmtt-8"> number</span><span
3251 class="cmtt-8"> [multiplicand_offset]</span><span
3252 class="cmtt-8"> )</span><span
3253 class="cmtt-8"> *</span>
3254 <br class="fancyvrb" /><a
3255 id="x1-55020r10"></a><span
3256 class="cmr-6">10</span><span
3257 class="cmtt-8"> </span><span
3258 class="cmtt-8"> </span><span
3259 class="cmtt-8"> </span><span
3260 class="cmtt-8"> </span><span
3261 class="cmtt-8"> </span><span
3262 class="cmtt-8"> </span><span
3263 class="cmtt-8"> </span><span
3264 class="cmtt-8"> </span><span
3265 class="cmtt-8"> </span><span
3266 class="cmtt-8"> </span><span
3267 class="cmtt-8"> </span><span
3268 class="cmtt-8"> </span><span
3269 class="cmtt-8"> </span><span
3270 class="cmtt-8"> [codebook_delta_value]</span><span
3271 class="cmtt-8"> +</span><span
3272 class="cmtt-8"> [codebook_minimum_value]</span><span
3273 class="cmtt-8"> +</span><span
3274 class="cmtt-8"> [last];</span>
3275 <br class="fancyvrb" /><a
3276 id="x1-55022r11"></a><span
3277 class="cmr-6">11</span><span
3278 class="cmtt-8"> </span><span
3279 class="cmtt-8"> </span>
3280 <br class="fancyvrb" /><a
3281 id="x1-55024r12"></a><span
3282 class="cmr-6">12</span><span
3283 class="cmtt-8"> </span><span
3284 class="cmtt-8"> </span><span
3285 class="cmtt-8"> </span><span
3286 class="cmtt-8"> </span><span
3287 class="cmtt-8"> </span><span
3288 class="cmtt-8"> </span><span
3289 class="cmtt-8"> </span><span
3290 class="cmtt-8"> </span><span
3291 class="cmtt-8"> 6)</span><span
3292 class="cmtt-8"> if</span><span
3293 class="cmtt-8"> (</span><span
3294 class="cmtt-8"> [codebook_sequence_p]</span><span
3295 class="cmtt-8"> is</span><span
3296 class="cmtt-8"> set</span><span
3297 class="cmtt-8"> )</span><span
3298 class="cmtt-8"> then</span><span
3299 class="cmtt-8"> set</span><span
3300 class="cmtt-8"> [last]</span><span
3301 class="cmtt-8"> =</span><span
3302 class="cmtt-8"> vector</span><span
3303 class="cmtt-8"> [value_vector]</span><span
3304 class="cmtt-8"> element</span><span
3305 class="cmtt-8"> [i]</span>
3306 <br class="fancyvrb" /><a
3307 id="x1-55026r13"></a><span
3308 class="cmr-6">13</span><span
3309 class="cmtt-8"> </span><span
3310 class="cmtt-8"> </span>
3311 <br class="fancyvrb" /><a
3312 id="x1-55028r14"></a><span
3313 class="cmr-6">14</span><span
3314 class="cmtt-8"> </span><span
3315 class="cmtt-8"> </span><span
3316 class="cmtt-8"> </span><span
3317 class="cmtt-8"> </span><span
3318 class="cmtt-8"> </span><span
3319 class="cmtt-8"> </span><span
3320 class="cmtt-8"> </span><span
3321 class="cmtt-8"> </span><span
3322 class="cmtt-8"> 7)</span><span
3323 class="cmtt-8"> [index_divisor]</span><span
3324 class="cmtt-8"> =</span><span
3325 class="cmtt-8"> [index_divisor]</span><span
3326 class="cmtt-8"> *</span><span
3327 class="cmtt-8"> [codebook_lookup_values]</span>
3328 <br class="fancyvrb" /><a
3329 id="x1-55030r15"></a><span
3330 class="cmr-6">15</span><span
3331 class="cmtt-8"> </span><span
3332 class="cmtt-8"> </span>
3333 <br class="fancyvrb" /><a
3334 id="x1-55032r16"></a><span
3335 class="cmr-6">16</span><span
3336 class="cmtt-8"> </span><span
3337 class="cmtt-8"> </span><span
3338 class="cmtt-8"> </span><span
3339 class="cmtt-8"> </span><span
3340 class="cmtt-8"> </span><span
3341 class="cmtt-8"> </span><span
3342 class="cmtt-8"> </span><span
3343 class="cmsy-8">}</span>
3344 <br class="fancyvrb" /><a
3345 id="x1-55034r17"></a><span
3346 class="cmr-6">17</span><span
3347 class="cmtt-8"> </span><span
3348 class="cmtt-8"> </span>
3349 <br class="fancyvrb" /><a
3350 id="x1-55036r18"></a><span
3351 class="cmr-6">18</span><span
3352 class="cmtt-8"> </span><span
3353 class="cmtt-8"> </span><span
3354 class="cmtt-8"> </span><span
3355 class="cmtt-8"> 8)</span><span
3356 class="cmtt-8"> vector</span><span
3357 class="cmtt-8"> calculation</span><span
3358 class="cmtt-8"> completed.</span>
3363 <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
3364 id="x1-560003.2.1"></a><span
3365 class="cmbx-12">Vector value decode: Lookup type 2</span></span>
3366 Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set
3368 class="cmtt-12">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final
3369 values of a codebook entry vector from the entries in <span
3370 class="cmtt-12">[codebook_multiplicands] </span>as follows
3372 class="cmtt-12">[value_vector] </span>is the output vector representing the vector of values for entry number
3374 class="cmtt-12">[lookup_offset] </span>in this codebook):
3375 <!--l. 344--><p class="noindent" >
3376 <div class="fancyvrb" id="fancyvrb19">
3378 id="x1-56002r1"></a><span
3379 class="cmr-6">1</span><span
3380 class="cmtt-8"> </span><span
3381 class="cmtt-8"> </span><span
3382 class="cmtt-8"> </span><span
3383 class="cmtt-8"> 1)</span><span
3384 class="cmtt-8"> [last]</span><span
3385 class="cmtt-8"> =</span><span
3386 class="cmtt-8"> 0;</span>
3387 <br class="fancyvrb" /><a
3388 id="x1-56004r2"></a><span
3389 class="cmr-6">2</span><span
3390 class="cmtt-8"> </span><span
3391 class="cmtt-8"> </span><span
3392 class="cmtt-8"> </span><span
3393 class="cmtt-8"> 2)</span><span
3394 class="cmtt-8"> [multiplicand_offset]</span><span
3395 class="cmtt-8"> =</span><span
3396 class="cmtt-8"> [lookup_offset]</span><span
3397 class="cmtt-8"> *</span><span
3398 class="cmtt-8"> [codebook_dimensions]</span>
3399 <br class="fancyvrb" /><a
3400 id="x1-56006r3"></a><span
3401 class="cmr-6">3</span><span
3402 class="cmtt-8"> </span><span
3403 class="cmtt-8"> </span><span
3404 class="cmtt-8"> </span><span
3405 class="cmtt-8"> 3)</span><span
3406 class="cmtt-8"> iterate</span><span
3407 class="cmtt-8"> [i]</span><span
3408 class="cmtt-8"> over</span><span
3409 class="cmtt-8"> the</span><span
3410 class="cmtt-8"> range</span><span
3411 class="cmtt-8"> 0</span><span
3412 class="cmtt-8"> ...</span><span
3413 class="cmtt-8"> [codebook_dimensions]-1</span><span
3414 class="cmtt-8"> (once</span><span
3415 class="cmtt-8"> for</span><span
3416 class="cmtt-8"> each</span><span
3417 class="cmtt-8"> scalar</span><span
3418 class="cmtt-8"> value</span><span
3419 class="cmtt-8"> in</span><span
3420 class="cmtt-8"> the</span><span
3421 class="cmtt-8"> value</span><span
3422 class="cmtt-8"> vector)</span><span
3423 class="cmtt-8"> </span><span
3424 class="cmsy-8">{</span>
3425 <br class="fancyvrb" /><a
3426 id="x1-56008r4"></a><span
3427 class="cmr-6">4</span><span
3428 class="cmtt-8"> </span><span
3429 class="cmtt-8"> </span>
3430 <br class="fancyvrb" /><a
3431 id="x1-56010r5"></a><span
3432 class="cmr-6">5</span><span
3433 class="cmtt-8"> </span><span
3434 class="cmtt-8"> </span><span
3435 class="cmtt-8"> </span><span
3436 class="cmtt-8"> </span><span
3437 class="cmtt-8"> </span><span
3438 class="cmtt-8"> </span><span
3439 class="cmtt-8"> </span><span
3440 class="cmtt-8"> </span><span
3441 class="cmtt-8"> 4)</span><span
3442 class="cmtt-8"> vector</span><span
3443 class="cmtt-8"> [value_vector]</span><span
3444 class="cmtt-8"> element</span><span
3445 class="cmtt-8"> [i]</span><span
3446 class="cmtt-8"> =</span>
3447 <br class="fancyvrb" /><a
3448 id="x1-56012r6"></a><span
3449 class="cmr-6">6</span><span
3450 class="cmtt-8"> </span><span
3451 class="cmtt-8"> </span><span
3452 class="cmtt-8"> </span><span
3453 class="cmtt-8"> </span><span
3454 class="cmtt-8"> </span><span
3455 class="cmtt-8"> </span><span
3456 class="cmtt-8"> </span><span
3457 class="cmtt-8"> </span><span
3458 class="cmtt-8"> </span><span
3459 class="cmtt-8"> </span><span
3460 class="cmtt-8"> </span><span
3461 class="cmtt-8"> </span><span
3462 class="cmtt-8"> </span><span
3463 class="cmtt-8"> (</span><span
3464 class="cmtt-8"> [codebook_multiplicands]</span><span
3465 class="cmtt-8"> array</span><span
3466 class="cmtt-8"> element</span><span
3467 class="cmtt-8"> number</span><span
3468 class="cmtt-8"> [multiplicand_offset]</span><span
3469 class="cmtt-8"> )</span><span
3470 class="cmtt-8"> *</span>
3471 <br class="fancyvrb" /><a
3472 id="x1-56014r7"></a><span
3473 class="cmr-6">7</span><span
3474 class="cmtt-8"> </span><span
3475 class="cmtt-8"> </span><span
3476 class="cmtt-8"> </span><span
3477 class="cmtt-8"> </span><span
3478 class="cmtt-8"> </span><span
3479 class="cmtt-8"> </span><span
3480 class="cmtt-8"> </span><span
3481 class="cmtt-8"> </span><span
3482 class="cmtt-8"> </span><span
3483 class="cmtt-8"> </span><span
3484 class="cmtt-8"> </span><span
3485 class="cmtt-8"> </span><span
3486 class="cmtt-8"> </span><span
3487 class="cmtt-8"> [codebook_delta_value]</span><span
3488 class="cmtt-8"> +</span><span
3489 class="cmtt-8"> [codebook_minimum_value]</span><span
3490 class="cmtt-8"> +</span><span
3491 class="cmtt-8"> [last];</span>
3492 <br class="fancyvrb" /><a
3493 id="x1-56016r8"></a><span
3494 class="cmr-6">8</span><span
3495 class="cmtt-8"> </span><span
3496 class="cmtt-8"> </span>
3497 <br class="fancyvrb" /><a
3498 id="x1-56018r9"></a><span
3499 class="cmr-6">9</span><span
3500 class="cmtt-8"> </span><span
3501 class="cmtt-8"> </span><span
3502 class="cmtt-8"> </span><span
3503 class="cmtt-8"> </span><span
3504 class="cmtt-8"> </span><span
3505 class="cmtt-8"> </span><span
3506 class="cmtt-8"> </span><span
3507 class="cmtt-8"> </span><span
3508 class="cmtt-8"> 5)</span><span
3509 class="cmtt-8"> if</span><span
3510 class="cmtt-8"> (</span><span
3511 class="cmtt-8"> [codebook_sequence_p]</span><span
3512 class="cmtt-8"> is</span><span
3513 class="cmtt-8"> set</span><span
3514 class="cmtt-8"> )</span><span
3515 class="cmtt-8"> then</span><span
3516 class="cmtt-8"> set</span><span
3517 class="cmtt-8"> [last]</span><span
3518 class="cmtt-8"> =</span><span
3519 class="cmtt-8"> vector</span><span
3520 class="cmtt-8"> [value_vector]</span><span
3521 class="cmtt-8"> element</span><span
3522 class="cmtt-8"> [i]</span>
3523 <br class="fancyvrb" /><a
3524 id="x1-56020r10"></a><span
3525 class="cmr-6">10</span><span
3526 class="cmtt-8"> </span><span
3527 class="cmtt-8"> </span>
3528 <br class="fancyvrb" /><a
3529 id="x1-56022r11"></a><span
3530 class="cmr-6">11</span><span
3531 class="cmtt-8"> </span><span
3532 class="cmtt-8"> </span><span
3533 class="cmtt-8"> </span><span
3534 class="cmtt-8"> </span><span
3535 class="cmtt-8"> </span><span
3536 class="cmtt-8"> </span><span
3537 class="cmtt-8"> </span><span
3538 class="cmtt-8"> </span><span
3539 class="cmtt-8"> 6)</span><span
3540 class="cmtt-8"> increment</span><span
3541 class="cmtt-8"> [multiplicand_offset]</span>
3542 <br class="fancyvrb" /><a
3543 id="x1-56024r12"></a><span
3544 class="cmr-6">12</span><span
3545 class="cmtt-8"> </span><span
3546 class="cmtt-8"> </span>
3547 <br class="fancyvrb" /><a
3548 id="x1-56026r13"></a><span
3549 class="cmr-6">13</span><span
3550 class="cmtt-8"> </span><span
3551 class="cmtt-8"> </span><span
3552 class="cmtt-8"> </span><span
3553 class="cmtt-8"> </span><span
3554 class="cmtt-8"> </span><span
3555 class="cmtt-8"> </span><span
3556 class="cmtt-8"> </span><span
3557 class="cmsy-8">}</span>
3558 <br class="fancyvrb" /><a
3559 id="x1-56028r14"></a><span
3560 class="cmr-6">14</span><span
3561 class="cmtt-8"> </span><span
3562 class="cmtt-8"> </span>
3563 <br class="fancyvrb" /><a
3564 id="x1-56030r15"></a><span
3565 class="cmr-6">15</span><span
3566 class="cmtt-8"> </span><span
3567 class="cmtt-8"> </span><span
3568 class="cmtt-8"> </span><span
3569 class="cmtt-8"> 7)</span><span
3570 class="cmtt-8"> vector</span><span
3571 class="cmtt-8"> calculation</span><span
3572 class="cmtt-8"> completed.</span>
3574 <!--l. 370--><p class="noindent" >
3575 <h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a
3576 id="x1-570003.3"></a>Use of the codebook abstraction</h4>
3577 <!--l. 372--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a
3578 specific codebook reads a codeword from the bitstream, decoding it into an entry number, and
3579 then returns that entry number to the decoder (when used in a scalar entropy coding context), or
3580 uses that entry number as an offset into the VQ lookup table, returning a vector of values (when
3581 used in a context desiring a VQ value). Scalar or VQ context is always explicit; any
3582 call to the codebook mechanism requests either a scalar entry number or a lookup
3584 <!--l. 382--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting
3585 decode using a codebook of lookup type 0 in any context expecting a vector return
3586 value (even in a case where a vector of dimension one) is forbidden. If decoder setup
3587 or decode requests such an action, that is an error condition rendering the packet
3592 <!--l. 389--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
3593 next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
3594 codeword in the codebook. This process can be though of as logically walking the
3595 Huffman decode tree by reading one bit at a time from the bitstream, and using the
3596 bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
3597 branch (right in the above examples). Walking the tree finishes when the decode process
3598 hits a leaf in the decision tree; the result is the entry number corresponding to that
3599 leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
3601 <!--l. 401--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
3603 <!--l. 404--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup
3604 table. The value returned to the decoder is the vector of scalars corresponding to this
3612 <h3 class="sectionHead"><span class="titlemark">4. </span> <a
3613 id="x1-580004"></a>Codec Setup and Packet Decode</h3>
3614 <!--l. 7--><p class="noindent" >
3615 <h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a
3616 id="x1-590004.1"></a>Overview</h4>
3617 <!--l. 9--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
3618 of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
3619 process, which is provided in <a
3620 href="#x1-20001">Section 1</a>, “<a
3621 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
3622 href="#x1-360002">Section 2</a>,
3624 href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
3626 <!--l. 17--><p class="noindent" >
3627 <h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a
3628 id="x1-600004.2"></a>Header decode and decode setup</h4>
3629 <!--l. 19--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the
3630 identification header, the comments header, and the setup header. All are required for decode
3631 compliance. An end-of-packet condition during decoding the first or third header packet renders
3632 the stream undecodable. End-of-packet decoding the comment header is a non-fatal error
3634 <!--l. 26--><p class="noindent" >
3635 <h5 class="subsubsectionHead"><span class="titlemark">4.2.1. </span> <a
3636 id="x1-610004.2.1"></a>Common header decode</h5>
3637 <!--l. 28--><p class="noindent" >Each header packet begins with the same header fields.
3638 <!--l. 31--><p class="noindent" >
3639 <div class="fancyvrb" id="fancyvrb20">
3641 id="x1-61002r1"></a><span
3642 class="cmr-6">1</span><span
3643 class="cmtt-8"> </span><span
3644 class="cmtt-8"> </span><span
3645 class="cmtt-8"> </span><span
3646 class="cmtt-8"> 1)</span><span
3647 class="cmtt-8"> [packet_type]</span><span
3648 class="cmtt-8"> :</span><span
3649 class="cmtt-8"> 8</span><span
3650 class="cmtt-8"> bit</span><span
3651 class="cmtt-8"> value</span>
3652 <br class="fancyvrb" /><a
3653 id="x1-61004r2"></a><span
3654 class="cmr-6">2</span><span
3655 class="cmtt-8"> </span><span
3656 class="cmtt-8"> </span><span
3657 class="cmtt-8"> </span><span
3658 class="cmtt-8"> 2)</span><span
3659 class="cmtt-8"> 0x76,</span><span
3660 class="cmtt-8"> 0x6f,</span><span
3661 class="cmtt-8"> 0x72,</span><span
3662 class="cmtt-8"> 0x62,</span><span
3663 class="cmtt-8"> 0x69,</span><span
3664 class="cmtt-8"> 0x73:</span><span
3665 class="cmtt-8"> the</span><span
3666 class="cmtt-8"> characters</span><span
3667 class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
3668 class="cmtt-8"> as</span><span
3669 class="cmtt-8"> six</span><span
3670 class="cmtt-8"> octets</span>
3675 <!--l. 36--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
3676 header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
3677 single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
3679 <!--l. 44--><p class="noindent" >
3680 <h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a
3681 id="x1-620004.2.2"></a>Identification header</h5>
3682 <!--l. 46--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream
3683 definitively as Vorbis, and provide a few externally relevant pieces of information about the audio
3684 stream. The identification header is coded as follows:
3685 <!--l. 51--><p class="noindent" >
3686 <div class="fancyvrb" id="fancyvrb21">
3688 id="x1-62002r1"></a><span
3689 class="cmr-6">1</span><span
3690 class="cmtt-8"> </span><span
3691 class="cmtt-8"> </span><span
3692 class="cmtt-8"> 1)</span><span
3693 class="cmtt-8"> [vorbis_version]</span><span
3694 class="cmtt-8"> =</span><span
3695 class="cmtt-8"> read</span><span
3696 class="cmtt-8"> 32</span><span
3697 class="cmtt-8"> bits</span><span
3698 class="cmtt-8"> as</span><span
3699 class="cmtt-8"> unsigned</span><span
3700 class="cmtt-8"> integer</span>
3701 <br class="fancyvrb" /><a
3702 id="x1-62004r2"></a><span
3703 class="cmr-6">2</span><span
3704 class="cmtt-8"> </span><span
3705 class="cmtt-8"> </span><span
3706 class="cmtt-8"> 2)</span><span
3707 class="cmtt-8"> [audio_channels]</span><span
3708 class="cmtt-8"> =</span><span
3709 class="cmtt-8"> read</span><span
3710 class="cmtt-8"> 8</span><span
3711 class="cmtt-8"> bit</span><span
3712 class="cmtt-8"> integer</span><span
3713 class="cmtt-8"> as</span><span
3714 class="cmtt-8"> unsigned</span>
3715 <br class="fancyvrb" /><a
3716 id="x1-62006r3"></a><span
3717 class="cmr-6">3</span><span
3718 class="cmtt-8"> </span><span
3719 class="cmtt-8"> </span><span
3720 class="cmtt-8"> 3)</span><span
3721 class="cmtt-8"> [audio_sample_rate]</span><span
3722 class="cmtt-8"> =</span><span
3723 class="cmtt-8"> read</span><span
3724 class="cmtt-8"> 32</span><span
3725 class="cmtt-8"> bits</span><span
3726 class="cmtt-8"> as</span><span
3727 class="cmtt-8"> unsigned</span><span
3728 class="cmtt-8"> integer</span>
3729 <br class="fancyvrb" /><a
3730 id="x1-62008r4"></a><span
3731 class="cmr-6">4</span><span
3732 class="cmtt-8"> </span><span
3733 class="cmtt-8"> </span><span
3734 class="cmtt-8"> 4)</span><span
3735 class="cmtt-8"> [bitrate_maximum]</span><span
3736 class="cmtt-8"> =</span><span
3737 class="cmtt-8"> read</span><span
3738 class="cmtt-8"> 32</span><span
3739 class="cmtt-8"> bits</span><span
3740 class="cmtt-8"> as</span><span
3741 class="cmtt-8"> signed</span><span
3742 class="cmtt-8"> integer</span>
3743 <br class="fancyvrb" /><a
3744 id="x1-62010r5"></a><span
3745 class="cmr-6">5</span><span
3746 class="cmtt-8"> </span><span
3747 class="cmtt-8"> </span><span
3748 class="cmtt-8"> 5)</span><span
3749 class="cmtt-8"> [bitrate_nominal]</span><span
3750 class="cmtt-8"> =</span><span
3751 class="cmtt-8"> read</span><span
3752 class="cmtt-8"> 32</span><span
3753 class="cmtt-8"> bits</span><span
3754 class="cmtt-8"> as</span><span
3755 class="cmtt-8"> signed</span><span
3756 class="cmtt-8"> integer</span>
3757 <br class="fancyvrb" /><a
3758 id="x1-62012r6"></a><span
3759 class="cmr-6">6</span><span
3760 class="cmtt-8"> </span><span
3761 class="cmtt-8"> </span><span
3762 class="cmtt-8"> 6)</span><span
3763 class="cmtt-8"> [bitrate_minimum]</span><span
3764 class="cmtt-8"> =</span><span
3765 class="cmtt-8"> read</span><span
3766 class="cmtt-8"> 32</span><span
3767 class="cmtt-8"> bits</span><span
3768 class="cmtt-8"> as</span><span
3769 class="cmtt-8"> signed</span><span
3770 class="cmtt-8"> integer</span>
3771 <br class="fancyvrb" /><a
3772 id="x1-62014r7"></a><span
3773 class="cmr-6">7</span><span
3774 class="cmtt-8"> </span><span
3775 class="cmtt-8"> </span><span
3776 class="cmtt-8"> 7)</span><span
3777 class="cmtt-8"> [blocksize_0]</span><span
3778 class="cmtt-8"> =</span><span
3779 class="cmtt-8"> 2</span><span
3780 class="cmtt-8"> exponent</span><span
3781 class="cmtt-8"> (read</span><span
3782 class="cmtt-8"> 4</span><span
3783 class="cmtt-8"> bits</span><span
3784 class="cmtt-8"> as</span><span
3785 class="cmtt-8"> unsigned</span><span
3786 class="cmtt-8"> integer)</span>
3787 <br class="fancyvrb" /><a
3788 id="x1-62016r8"></a><span
3789 class="cmr-6">8</span><span
3790 class="cmtt-8"> </span><span
3791 class="cmtt-8"> </span><span
3792 class="cmtt-8"> 8)</span><span
3793 class="cmtt-8"> [blocksize_1]</span><span
3794 class="cmtt-8"> =</span><span
3795 class="cmtt-8"> 2</span><span
3796 class="cmtt-8"> exponent</span><span
3797 class="cmtt-8"> (read</span><span
3798 class="cmtt-8"> 4</span><span
3799 class="cmtt-8"> bits</span><span
3800 class="cmtt-8"> as</span><span
3801 class="cmtt-8"> unsigned</span><span
3802 class="cmtt-8"> integer)</span>
3803 <br class="fancyvrb" /><a
3804 id="x1-62018r9"></a><span
3805 class="cmr-6">9</span><span
3806 class="cmtt-8"> </span><span
3807 class="cmtt-8"> </span><span
3808 class="cmtt-8"> 9)</span><span
3809 class="cmtt-8"> [framing_flag]</span><span
3810 class="cmtt-8"> =</span><span
3811 class="cmtt-8"> read</span><span
3812 class="cmtt-8"> one</span><span
3813 class="cmtt-8"> bit</span>
3815 <!--l. 63--><p class="noindent" ><span
3816 class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
3818 class="cmtt-12">[audio_channels] </span>and <span
3819 class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final
3820 blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
3821 class="cmtt-12">[blocksize_0]</span>
3822 must be less than or equal to <span
3823 class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet
3824 any of these conditions renders a stream undecodable.
3825 <!--l. 71--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
3826 considerably off in purely VBR streams. The fields are meaningful only when greater than
3828 <ul class="itemize1">
3829 <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
3830 fixed-rate bitstream
3832 <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
3837 <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
3839 <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
3840 <!--l. 85--><p class="noindent" >
3841 <h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a
3842 id="x1-630004.2.3"></a>Comment header</h5>
3843 <!--l. 86--><p class="noindent" >Comment header decode and data specification is covered in <a
3844 href="#x1-810005">Section 5</a>, “<a
3845 href="#x1-810005">comment field and
3846 header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
3847 <!--l. 90--><p class="noindent" >
3848 <h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a
3849 id="x1-640004.2.4"></a>Setup header</h5>
3850 <!--l. 92--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
3853 <!--l. 94--><p class="noindent" >
3855 <!--l. 95--><p class="noindent" ><img
3856 src="components.png" alt="PIC"
3858 <br /> <div class="caption"
3859 ><span class="id">Figure 6: </span><span
3860 class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-640016 -->
3862 <!--l. 100--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
3863 header contains, in order, the lists of codebook configurations, time-domain transform
3864 configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
3865 mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
3866 decode proceeds in the following order:
3867 <!--l. 108--><p class="noindent" ><span class="paragraphHead"><a
3868 id="x1-650004.2.4"></a><span
3869 class="cmbx-12">Codebooks</span></span>
3873 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3875 class="enumerate-enumitem"><span
3876 class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
3877 </dd><dt class="enumerate-enumitem">
3879 class="enumerate-enumitem">Decode <span
3880 class="cmtt-12">[vorbis_codebook_count] </span>codebooks in order as defined in <a
3881 href="#x1-470003">Section 3</a>,
3883 href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
3884 of codebook configurations <span
3885 class="cmtt-12">[vorbis_codebook_configurations]</span>.</dd></dl>
3886 <!--l. 120--><p class="noindent" ><span class="paragraphHead"><a
3887 id="x1-660004.2.4"></a><span
3888 class="cmbx-12">Time domain transforms</span></span>
3889 These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must
3890 be read to maintain bitstream sync.
3891 <!--l. 127--><p class="noindent" >
3892 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3894 class="enumerate-enumitem"><span
3895 class="cmtt-12">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one
3896 </dd><dt class="enumerate-enumitem">
3898 class="enumerate-enumitem">read <span
3899 class="cmtt-12">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is
3900 nonzero, this is an error condition and the stream is undecodable.</dd></dl>
3901 <!--l. 133--><p class="noindent" ><span class="paragraphHead"><a
3902 id="x1-670004.2.4"></a><span
3903 class="cmbx-12">Floors</span></span>
3904 Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate
3906 <!--l. 139--><p class="noindent" >
3907 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3909 class="enumerate-enumitem"><span
3910 class="cmtt-12">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one
3911 </dd><dt class="enumerate-enumitem">
3913 class="enumerate-enumitem">For each <span
3914 class="cmtt-12">[i] </span>of <span
3915 class="cmtt-12">[vorbis_floor_count] </span>floor numbers:
3916 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3918 class="enumerate-enumitem">read the floor type: vector <span
3919 class="cmtt-12">[vorbis_floor_types] </span>element <span
3920 class="cmtt-12">[i] </span>= read 16 bits
3922 </dd><dt class="enumerate-enumitem">
3924 class="enumerate-enumitem">If the floor type is zero, decode the floor configuration as defined in <a
3925 href="#x1-890006">Section 6</a>,
3927 href="#x1-890006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
3928 class="cmtt-12">[i] </span>of the floor
3929 configuration array <span
3930 class="cmtt-12">[vorbis_floor_configurations]</span>.
3934 </dd><dt class="enumerate-enumitem">
3936 class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a
3937 href="#x1-950007">Section 7</a>,
3939 href="#x1-950007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
3940 class="cmtt-12">[i] </span>of the floor
3941 configuration array <span
3942 class="cmtt-12">[vorbis_floor_configurations]</span>.
3943 </dd><dt class="enumerate-enumitem">
3945 class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR
3948 <!--l. 157--><p class="noindent" ><span class="paragraphHead"><a
3949 id="x1-680004.2.4"></a><span
3950 class="cmbx-12">Residues</span></span>
3951 Vorbis uses three residue types; header decode of each type is identical.
3952 <!--l. 163--><p class="noindent" >
3953 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3955 class="enumerate-enumitem"><span
3956 class="cmtt-12">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one
3957 </dd><dt class="enumerate-enumitem">
3959 class="enumerate-enumitem">For each of <span
3960 class="cmtt-12">[vorbis_residue_count] </span>residue numbers:
3961 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3963 class="enumerate-enumitem">read the residue type; vector <span
3964 class="cmtt-12">[vorbis_residue_types] </span>element <span
3965 class="cmtt-12">[i] </span>= read 16
3966 bits as unsigned integer
3967 </dd><dt class="enumerate-enumitem">
3969 class="enumerate-enumitem">If the residue type is zero, one or two, decode the residue configuration as defined
3971 href="#x1-1020008">Section 8</a>, “<a
3972 href="#x1-1020008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
3973 class="cmtt-12">[i] </span>of
3974 the residue configuration array <span
3975 class="cmtt-12">[vorbis_residue_configurations]</span>.
3976 </dd><dt class="enumerate-enumitem">
3978 class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR
3981 <!--l. 177--><p class="noindent" ><span class="paragraphHead"><a
3982 id="x1-690004.2.4"></a><span
3983 class="cmbx-12">Mappings</span></span>
3984 Mappings are used to set up specific pipelines for encoding multichannel audio with varying
3985 channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
3990 <!--l. 188--><p class="noindent" >
3991 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
3993 class="enumerate-enumitem"><span
3994 class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
3995 </dd><dt class="enumerate-enumitem">
3997 class="enumerate-enumitem">For each <span
3998 class="cmtt-12">[i] </span>of <span
3999 class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers:
4000 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4002 class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
4003 the mapping type in Vorbis I.
4004 </dd><dt class="enumerate-enumitem">
4006 class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable
4007 </dd><dt class="enumerate-enumitem">
4009 class="enumerate-enumitem">If the mapping type is zero:
4010 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4012 class="enumerate-enumitem">read 1 bit as a boolean flag
4013 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4015 class="enumerate-enumitem">if set, <span
4016 class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer
4018 </dd><dt class="enumerate-enumitem">
4020 class="enumerate-enumitem">if unset, <span
4021 class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</dd></dl>
4022 </dd><dt class="enumerate-enumitem">
4024 class="enumerate-enumitem">read 1 bit as a boolean flag
4025 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4027 class="enumerate-enumitem">if set, square polar channel mapping is in use:
4028 <ul class="itemize1">
4029 <li class="itemize"><span
4030 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned
4033 <li class="itemize">for <span
4034 class="cmtt-12">[j] </span>each of <span
4035 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps:
4036 <ul class="itemize2">
4037 <li class="itemize">vector <span
4038 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
4039 class="cmtt-12">[j]</span>= read
4041 href="#x1-1170009.2.1">ilog</a>(<span
4042 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
4044 <li class="itemize">vector <span
4045 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
4046 class="cmtt-12">[j]</span>= read
4048 href="#x1-1170009.2.1">ilog</a>(<span
4049 class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer
4054 <li class="itemize">the numbers read in the above two steps are channel numbers
4055 representing the channel to treat as magnitude and the channel
4056 to treat as angle, respectively. If for any coupling step the
4057 angle channel number equals the magnitude channel number, the
4058 magnitude channel number is greater than <span
4059 class="cmtt-12">[audio_channels]</span>-1, or
4060 the angle channel is greater than <span
4061 class="cmtt-12">[audio_channels]</span>-1, the stream
4062 is undecodable.</li></ul>
4064 </dd><dt class="enumerate-enumitem">
4066 class="enumerate-enumitem">if unset, <span
4067 class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= 0</dd></dl>
4068 </dd><dt class="enumerate-enumitem">
4070 class="enumerate-enumitem">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
4071 </dd><dt class="enumerate-enumitem">
4073 class="enumerate-enumitem">if <span
4074 class="cmtt-12">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex
4075 settings. For each <span
4076 class="cmtt-12">[j] </span>of <span
4077 class="cmtt-12">[audio_channels] </span>channels:
4078 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4080 class="enumerate-enumitem">vector <span
4081 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4082 class="cmtt-12">[j] </span>= read 4 bits as unsigned
4084 </dd><dt class="enumerate-enumitem">
4086 class="enumerate-enumitem">if the value is greater than the highest numbered submap
4088 class="cmtt-12">[vorbis_mapping_submaps] </span>- 1), this in an error condition rendering
4089 the stream undecodable</dd></dl>
4090 </dd><dt class="enumerate-enumitem">
4092 class="enumerate-enumitem">for each submap <span
4093 class="cmtt-12">[j] </span>of <span
4094 class="cmtt-12">[vorbis_mapping_submaps] </span>submaps, read the floor and
4095 residue numbers for use in decoding that submap:
4096 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4098 class="enumerate-enumitem">read and discard 8 bits (the unused time configuration placeholder)
4099 </dd><dt class="enumerate-enumitem">
4101 class="enumerate-enumitem">read 8 bits as unsigned integer for the floor number; save in vector
4103 class="cmtt-12">[vorbis_mapping_submap_floor] </span>element <span
4104 class="cmtt-12">[j]</span>
4105 </dd><dt class="enumerate-enumitem">
4107 class="enumerate-enumitem">verify the floor number is not greater than the highest number floor
4108 configured for the bitstream. If it is, the bitstream is undecodable
4109 </dd><dt class="enumerate-enumitem">
4111 class="enumerate-enumitem">read 8 bits as unsigned integer for the residue number; save in vector
4113 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
4114 class="cmtt-12">[j]</span>
4118 </dd><dt class="enumerate-enumitem">
4120 class="enumerate-enumitem">verify the residue number is not greater than the highest number residue
4121 configured for the bitstream. If it is, the bitstream is undecodable</dd></dl>
4122 </dd><dt class="enumerate-enumitem">
4124 class="enumerate-enumitem">save this mapping configuration in slot <span
4125 class="cmtt-12">[i] </span>of the mapping configuration array
4127 class="cmtt-12">[vorbis_mapping_configurations]</span>.</dd></dl>
4130 <!--l. 247--><p class="noindent" ><span class="paragraphHead"><a
4131 id="x1-700004.2.4"></a><span
4132 class="cmbx-12">Modes</span></span>
4133 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4135 class="enumerate-enumitem"><span
4136 class="cmtt-12">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one
4137 </dd><dt class="enumerate-enumitem">
4139 class="enumerate-enumitem">For each of <span
4140 class="cmtt-12">[vorbis_mode_count] </span>mode numbers:
4141 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4143 class="enumerate-enumitem"><span
4144 class="cmtt-12">[vorbis_mode_blockflag] </span>= read 1 bit
4145 </dd><dt class="enumerate-enumitem">
4147 class="enumerate-enumitem"><span
4148 class="cmtt-12">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer
4149 </dd><dt class="enumerate-enumitem">
4151 class="enumerate-enumitem"><span
4152 class="cmtt-12">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer
4153 </dd><dt class="enumerate-enumitem">
4155 class="enumerate-enumitem"><span
4156 class="cmtt-12">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer
4157 </dd><dt class="enumerate-enumitem">
4159 class="enumerate-enumitem">verify ranges; zero is the only legal value in
4161 class="cmtt-12">[vorbis_mode_windowtype] </span>and <span
4162 class="cmtt-12">[vorbis_mode_transformtype]</span>.
4164 class="cmtt-12">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping
4165 in use. Any illegal values render the stream undecodable.
4166 </dd><dt class="enumerate-enumitem">
4168 class="enumerate-enumitem">save this mode configuration in slot <span
4169 class="cmtt-12">[i] </span>of the mode configuration array
4171 class="cmtt-12">[vorbis_mode_configurations]</span>.</dd></dl>
4172 </dd><dt class="enumerate-enumitem">
4174 class="enumerate-enumitem">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not
4175 decodable.</dd></dl>
4179 <!--l. 268--><p class="noindent" >After reading mode descriptions, setup header decode is complete.
4180 <!--l. 277--><p class="noindent" >
4181 <h4 class="subsectionHead"><span class="titlemark">4.3. </span> <a
4182 id="x1-710004.3"></a>Audio packet decode and synthesis</h4>
4183 <!--l. 279--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
4184 audio packet decode is to read and verify the packet type. <span
4185 class="cmti-12">A non-audio packet when audio is</span>
4187 class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
4189 class="cmti-12">packet and not attempt decoding it to audio</span>.
4190 <!--l. 286--><p class="noindent" >
4191 <h5 class="subsubsectionHead"><span class="titlemark">4.3.1. </span> <a
4192 id="x1-720004.3.1"></a>packet type, mode and window decode</h5>
4193 <!--l. 289--><p class="noindent" >
4194 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4196 class="enumerate-enumitem">read 1 bit <span
4197 class="cmtt-12">[packet_type]</span>; check that packet type is 0 (audio)
4198 </dd><dt class="enumerate-enumitem">
4200 class="enumerate-enumitem">read <a
4201 href="#x1-1170009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span
4202 class="cmtt-12">[mode_number]</span>
4203 </dd><dt class="enumerate-enumitem">
4205 class="enumerate-enumitem">decode blocksize <span
4206 class="cmtt-12">[n] </span>is equal to <span
4207 class="cmtt-12">[blocksize_0] </span>if <span
4208 class="cmtt-12">[vorbis_mode_blockflag] </span>is 0,
4210 class="cmtt-12">[n] </span>is equal to <span
4211 class="cmtt-12">[blocksize_1]</span>.
4212 </dd><dt class="enumerate-enumitem">
4214 class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse
4216 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4218 class="enumerate-enumitem">if this is a long window (the <span
4219 class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is
4221 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4223 class="enumerate-enumitem">read 1 bit for <span
4224 class="cmtt-12">[previous_window_flag]</span>
4225 </dd><dt class="enumerate-enumitem">
4227 class="enumerate-enumitem">read 1 bit for <span
4228 class="cmtt-12">[next_window_flag]</span>
4232 </dd><dt class="enumerate-enumitem">
4234 class="enumerate-enumitem">if <span
4235 class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will
4236 be a hybrid window for lapping with a short block. See <a
4237 href="#paragraph.1" >paragraph <a
4238 href="#x1-260001.3.2">1.3.2</a></a>,
4240 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4241 overlapping dissimilar windows. Else, the left half window will have normal
4243 </dd><dt class="enumerate-enumitem">
4245 class="enumerate-enumitem">if <span
4246 class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be
4247 a hybrid window for lapping with a short block. See <a
4248 href="#x1-260001.3.2">paragraph 1.3.2</a>,
4250 href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
4251 overlapping dissimilar windows. Else, the left right window will have normal
4252 long shape.</dd></dl>
4253 </dd><dt class="enumerate-enumitem">
4255 class="enumerate-enumitem">if this is a short window, the window is always the same short-window
4258 <!--l. 321--><p class="noindent" >Vorbis windows all use the slope function <span
4259 class="cmmi-12">y </span>= sin(<img
4260 src="Vorbis_I_spec1x.png" alt="π2" class="frac" align="middle"> <span
4261 class="cmsy-10x-x-120">∗</span> sin <sup><span
4262 class="cmr-8">2</span></sup>((<span
4263 class="cmmi-12">x </span>+ 0<span
4264 class="cmmi-12">.</span>5)<span
4265 class="cmmi-12">∕n </span><span
4266 class="cmsy-10x-x-120">∗ </span><span
4267 class="cmmi-12">π</span>)), where <span
4268 class="cmmi-12">n </span>is window
4270 class="cmmi-12">x </span>ranges 0<span
4271 class="cmmi-12">…</span><span
4272 class="cmmi-12">n</span><span
4273 class="cmsy-10x-x-120">− </span>1, but dissimilar lapping requirements can affect overall shape. Window
4274 generation proceeds as follows:
4275 <!--l. 327--><p class="noindent" >
4276 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4278 class="enumerate-enumitem"><span
4279 class="cmtt-12">[window_center] </span>= <span
4280 class="cmtt-12">[n] </span>/ 2
4281 </dd><dt class="enumerate-enumitem">
4283 class="enumerate-enumitem">if (<span
4284 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4285 class="cmtt-12">[previous_window_flag] </span>is not set)
4287 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4289 class="enumerate-enumitem"><span
4290 class="cmtt-12">[left_window_start] </span>= <span
4291 class="cmtt-12">[n]</span>/4 - <span
4292 class="cmtt-12">[blocksize_0]</span>/4
4293 </dd><dt class="enumerate-enumitem">
4295 class="enumerate-enumitem"><span
4296 class="cmtt-12">[left_window_end] </span>= <span
4297 class="cmtt-12">[n]</span>/4 + <span
4298 class="cmtt-12">[blocksize_0]</span>/4
4299 </dd><dt class="enumerate-enumitem">
4301 class="enumerate-enumitem"><span
4302 class="cmtt-12">[left_n] </span>= <span
4303 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4304 <!--l. 336--><p class="noindent" >else
4305 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4307 class="enumerate-enumitem"><span
4308 class="cmtt-12">[left_window_start] </span>= 0
4309 </dd><dt class="enumerate-enumitem">
4311 class="enumerate-enumitem"><span
4312 class="cmtt-12">[left_window_end] </span>= <span
4313 class="cmtt-12">[window_center]</span>
4317 </dd><dt class="enumerate-enumitem">
4319 class="enumerate-enumitem"><span
4320 class="cmtt-12">[left_n] </span>= <span
4321 class="cmtt-12">[n]</span>/2</dd></dl>
4322 </dd><dt class="enumerate-enumitem">
4324 class="enumerate-enumitem">if (<span
4325 class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
4326 class="cmtt-12">[next_window_flag] </span>is not set) then
4327 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4329 class="enumerate-enumitem"><span
4330 class="cmtt-12">[right_window_start] </span>= <span
4331 class="cmtt-12">[n]*3</span>/4 - <span
4332 class="cmtt-12">[blocksize_0]</span>/4
4333 </dd><dt class="enumerate-enumitem">
4335 class="enumerate-enumitem"><span
4336 class="cmtt-12">[right_window_end] </span>= <span
4337 class="cmtt-12">[n]*3</span>/4 + <span
4338 class="cmtt-12">[blocksize_0]</span>/4
4339 </dd><dt class="enumerate-enumitem">
4341 class="enumerate-enumitem"><span
4342 class="cmtt-12">[right_n] </span>= <span
4343 class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
4344 <!--l. 352--><p class="noindent" >else
4345 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4347 class="enumerate-enumitem"><span
4348 class="cmtt-12">[right_window_start] </span>= <span
4349 class="cmtt-12">[window_center]</span>
4350 </dd><dt class="enumerate-enumitem">
4352 class="enumerate-enumitem"><span
4353 class="cmtt-12">[right_window_end] </span>= <span
4354 class="cmtt-12">[n]</span>
4355 </dd><dt class="enumerate-enumitem">
4357 class="enumerate-enumitem"><span
4358 class="cmtt-12">[right_n] </span>= <span
4359 class="cmtt-12">[n]</span>/2</dd></dl>
4360 </dd><dt class="enumerate-enumitem">
4362 class="enumerate-enumitem">window from range 0 ... <span
4363 class="cmtt-12">[left_window_start]</span>-1 inclusive is zero
4364 </dd><dt class="enumerate-enumitem">
4366 class="enumerate-enumitem">for <span
4367 class="cmtt-12">[i] </span>in range <span
4368 class="cmtt-12">[left_window_start] </span>... <span
4369 class="cmtt-12">[left_window_end]</span>-1, window(<span
4370 class="cmtt-12">[i]</span>) =
4372 src="Vorbis_I_spec2x.png" alt="π
4373 2" class="frac" align="middle"> <span
4374 class="cmsy-10x-x-120">∗</span> sin <sup><span
4375 class="cmr-8">2</span></sup>( (<span
4376 class="cmtt-12">[i]</span>-<span
4377 class="cmtt-12">[left_window_start]</span>+0.5) / <span
4378 class="cmtt-12">[left_n] </span><span
4379 class="cmsy-10x-x-120">∗</span><img
4380 src="Vorbis_I_spec3x.png" alt="π
4381 2" class="frac" align="middle">) )
4382 </dd><dt class="enumerate-enumitem">
4384 class="enumerate-enumitem">window from range <span
4385 class="cmtt-12">[left_window_end] </span>... <span
4386 class="cmtt-12">[right_window_start]</span>-1 inclusive is
4388 </dd><dt class="enumerate-enumitem">
4390 class="enumerate-enumitem">for <span
4391 class="cmtt-12">[i] </span>in range <span
4392 class="cmtt-12">[right_window_start] </span>... <span
4393 class="cmtt-12">[right_window_end]</span>-1, window(<span
4394 class="cmtt-12">[i]</span>) =
4396 src="Vorbis_I_spec4x.png" alt="π
4397 2" class="frac" align="middle"> <span
4398 class="cmsy-10x-x-120">∗</span> sin <sup><span
4399 class="cmr-8">2</span></sup>( (<span
4400 class="cmtt-12">[i]</span>-<span
4401 class="cmtt-12">[right_window_start]</span>+0.5) / <span
4402 class="cmtt-12">[right_n] </span><span
4403 class="cmsy-10x-x-120">∗</span><img
4404 src="Vorbis_I_spec5x.png" alt="π
4405 2" class="frac" align="middle"> + <img
4406 src="Vorbis_I_spec6x.png" alt="π
4407 2" class="frac" align="middle">) )
4408 </dd><dt class="enumerate-enumitem">
4410 class="enumerate-enumitem">window from range <span
4411 class="cmtt-12">[right_window_start] </span>... <span
4412 class="cmtt-12">[n]</span>-1 is zero</dd></dl>
4413 <!--l. 368--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this
4414 packet from the stream. An end of packet condition past this point is to be considered a possible
4419 <!--l. 375--><p class="noindent" >
4420 <h5 class="subsubsectionHead"><span class="titlemark">4.3.2. </span> <a
4421 id="x1-730004.3.2"></a>floor curve decode</h5>
4422 <!--l. 377--><p class="noindent" >From this point on, we assume out decode context is using mode number <span
4423 class="cmtt-12">[mode_number]</span>
4424 from configuration array <span
4425 class="cmtt-12">[vorbis_mode_configurations] </span>and the map number
4427 class="cmtt-12">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration
4429 class="cmtt-12">[vorbis_mapping_configurations]</span>.
4430 <!--l. 384--><p class="noindent" >Floor curves are decoded one-by-one in channel order.
4431 <!--l. 386--><p class="noindent" >For each floor <span
4432 class="cmtt-12">[i] </span>of <span
4433 class="cmtt-12">[audio_channels]</span>
4434 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4436 class="enumerate-enumitem"><span
4437 class="cmtt-12">[submap_number] </span>= element <span
4438 class="cmtt-12">[i] </span>of vector [vorbis_mapping_mux]
4439 </dd><dt class="enumerate-enumitem">
4441 class="enumerate-enumitem"><span
4442 class="cmtt-12">[floor_number] </span>= element <span
4443 class="cmtt-12">[submap_number] </span>of vector [vorbis_submap_floor]
4444 </dd><dt class="enumerate-enumitem">
4446 class="enumerate-enumitem">if the floor type of this floor (vector
4448 class="cmtt-12">[vorbis_floor_types] </span>element <span
4449 class="cmtt-12">[floor_number]</span>) is zero then decode the floor for
4451 class="cmtt-12">[i] </span>according to the <a
4452 href="#x1-930006.2.2">subsubsection 6.2.2</a>, “<a
4453 href="#x1-930006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
4454 </dd><dt class="enumerate-enumitem">
4456 class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span
4457 class="cmtt-12">[i] </span>according to the
4459 href="#x1-1000007.2.2">paragraph 7.2.2</a>, “<a
4460 href="#x1-1000007.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
4461 </dd><dt class="enumerate-enumitem">
4463 class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis
4464 </dd><dt class="enumerate-enumitem">
4466 class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span
4467 class="cmtt-12">[no_residue] </span>element <span
4468 class="cmtt-12">[i] </span>to true,
4469 else set vector <span
4470 class="cmtt-12">[no_residue] </span>element <span
4471 class="cmtt-12">[i] </span>to false</dd></dl>
4472 <!--l. 406--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
4473 output vectors and skipping to the add/overlap output stage.
4474 <!--l. 412--><p class="noindent" >
4475 <h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a
4476 id="x1-740004.3.3"></a>nonzero vector propagate</h5>
4477 <!--l. 414--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
4478 that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
4479 coded in the stream, save for one complication. If some vectors are used and some are not,
4483 channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
4485 <!--l. 421--><p class="noindent" >for each <span
4486 class="cmtt-12">[i] </span>from 0 ... <span
4487 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1
4488 <!--l. 424--><p class="noindent" >
4489 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4491 class="enumerate-enumitem">if either <span
4492 class="cmtt-12">[no_residue] </span>entry for channel (<span
4493 class="cmtt-12">[vorbis_mapping_magnitude] </span>element
4495 class="cmtt-12">[i]</span>) or channel (<span
4496 class="cmtt-12">[vorbis_mapping_angle] </span>element <span
4497 class="cmtt-12">[i]</span>) are set to false, then both
4498 must be set to false. Note that an ’unused’ floor has no decoded floor information; it
4499 is important that this is remembered at floor curve synthesis time.</dd></dl>
4500 <!--l. 436--><p class="noindent" >
4501 <h5 class="subsubsectionHead"><span class="titlemark">4.3.4. </span> <a
4502 id="x1-750004.3.4"></a>residue decode</h5>
4503 <!--l. 438--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap
4505 <!--l. 441--><p class="noindent" >for each submap <span
4506 class="cmtt-12">[i] </span>in order from 0 ... <span
4507 class="cmtt-12">[vorbis_mapping_submaps]</span>-1
4508 <!--l. 444--><p class="noindent" >
4509 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4511 class="enumerate-enumitem"><span
4512 class="cmtt-12">[ch] </span>= 0
4513 </dd><dt class="enumerate-enumitem">
4515 class="enumerate-enumitem">for each channel <span
4516 class="cmtt-12">[j] </span>in order from 0 ... <span
4517 class="cmtt-12">[audio_channels] </span>- 1
4518 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4520 class="enumerate-enumitem">if channel <span
4521 class="cmtt-12">[j] </span>in submap <span
4522 class="cmtt-12">[i] </span>(vector <span
4523 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4524 class="cmtt-12">[j] </span>is equal to
4526 class="cmtt-12">[i]</span>)
4527 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4529 class="enumerate-enumitem">if vector <span
4530 class="cmtt-12">[no_residue] </span>element <span
4531 class="cmtt-12">[j] </span>is true
4532 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4534 class="enumerate-enumitem">vector <span
4535 class="cmtt-12">[do_not_decode_flag] </span>element <span
4536 class="cmtt-12">[ch] </span>is set</dd></dl>
4537 <!--l. 453--><p class="noindent" >else
4538 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4540 class="enumerate-enumitem">vector <span
4541 class="cmtt-12">[do_not_decode_flag] </span>element <span
4542 class="cmtt-12">[ch] </span>is unset</dd></dl>
4543 </dd><dt class="enumerate-enumitem">
4545 class="enumerate-enumitem">increment <span
4546 class="cmtt-12">[ch]</span></dd></dl>
4551 </dd><dt class="enumerate-enumitem">
4553 class="enumerate-enumitem"><span
4554 class="cmtt-12">[residue_number] </span>= vector <span
4555 class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span
4556 class="cmtt-12">[i]</span>
4557 </dd><dt class="enumerate-enumitem">
4559 class="enumerate-enumitem"><span
4560 class="cmtt-12">[residue_type] </span>= vector <span
4561 class="cmtt-12">[vorbis_residue_types] </span>element <span
4562 class="cmtt-12">[residue_number]</span>
4563 </dd><dt class="enumerate-enumitem">
4565 class="enumerate-enumitem">decode <span
4566 class="cmtt-12">[ch] </span>vectors using residue <span
4567 class="cmtt-12">[residue_number]</span>, according to type <span
4568 class="cmtt-12">[residue_type]</span>,
4569 also passing vector <span
4570 class="cmtt-12">[do_not_decode_flag] </span>to indicate which vectors in the bundle should
4571 not be decoded. Correct per-vector decode length is <span
4572 class="cmtt-12">[n]</span>/2.
4573 </dd><dt class="enumerate-enumitem">
4575 class="enumerate-enumitem"><span
4576 class="cmtt-12">[ch] </span>= 0
4577 </dd><dt class="enumerate-enumitem">
4579 class="enumerate-enumitem">for each channel <span
4580 class="cmtt-12">[j] </span>in order from 0 ... <span
4581 class="cmtt-12">[audio_channels]</span>
4582 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4584 class="enumerate-enumitem">if channel <span
4585 class="cmtt-12">[j] </span>is in submap <span
4586 class="cmtt-12">[i] </span>(vector <span
4587 class="cmtt-12">[vorbis_mapping_mux] </span>element <span
4588 class="cmtt-12">[j] </span>is equal
4590 class="cmtt-12">[i]</span>)
4591 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4593 class="enumerate-enumitem">residue vector for channel <span
4594 class="cmtt-12">[j] </span>is set to decoded residue vector <span
4595 class="cmtt-12">[ch]</span>
4596 </dd><dt class="enumerate-enumitem">
4598 class="enumerate-enumitem">increment <span
4599 class="cmtt-12">[ch]</span></dd></dl>
4602 <!--l. 480--><p class="noindent" >
4603 <h5 class="subsubsectionHead"><span class="titlemark">4.3.5. </span> <a
4604 id="x1-760004.3.5"></a>inverse coupling</h5>
4605 <!--l. 482--><p class="noindent" >for each <span
4606 class="cmtt-12">[i] </span>from <span
4607 class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 descending to 0
4608 <!--l. 485--><p class="noindent" >
4609 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4611 class="enumerate-enumitem"><span
4612 class="cmtt-12">[magnitude_vector] </span>= the residue vector for channel (vector
4614 class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
4615 class="cmtt-12">[i]</span>)
4616 </dd><dt class="enumerate-enumitem">
4618 class="enumerate-enumitem"><span
4619 class="cmtt-12">[angle_vector] </span>= the residue vector for channel (vector <span
4620 class="cmtt-12">[vorbis_mapping_angle]</span>
4625 class="cmtt-12">[i]</span>)
4626 </dd><dt class="enumerate-enumitem">
4628 class="enumerate-enumitem">for each scalar value <span
4629 class="cmtt-12">[M] </span>in vector <span
4630 class="cmtt-12">[magnitude_vector] </span>and the corresponding scalar value
4632 class="cmtt-12">[A] </span>in vector <span
4633 class="cmtt-12">[angle_vector]</span>:
4634 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4636 class="enumerate-enumitem">if (<span
4637 class="cmtt-12">[M] </span>is greater than zero)
4638 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4640 class="enumerate-enumitem">if (<span
4641 class="cmtt-12">[A] </span>is greater than zero)
4642 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4644 class="enumerate-enumitem"><span
4645 class="cmtt-12">[new_M] </span>= <span
4646 class="cmtt-12">[M]</span>
4647 </dd><dt class="enumerate-enumitem">
4649 class="enumerate-enumitem"><span
4650 class="cmtt-12">[new_A] </span>= <span
4651 class="cmtt-12">[M]</span>-<span
4652 class="cmtt-12">[A]</span></dd></dl>
4653 <!--l. 498--><p class="noindent" >else
4654 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4656 class="enumerate-enumitem"><span
4657 class="cmtt-12">[new_A] </span>= <span
4658 class="cmtt-12">[M]</span>
4659 </dd><dt class="enumerate-enumitem">
4661 class="enumerate-enumitem"><span
4662 class="cmtt-12">[new_M] </span>= <span
4663 class="cmtt-12">[M]</span>+<span
4664 class="cmtt-12">[A]</span></dd></dl>
4666 <!--l. 505--><p class="noindent" >else
4667 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4669 class="enumerate-enumitem">if (<span
4670 class="cmtt-12">[A] </span>is greater than zero)
4671 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4673 class="enumerate-enumitem"><span
4674 class="cmtt-12">[new_M] </span>= <span
4675 class="cmtt-12">[M]</span>
4676 </dd><dt class="enumerate-enumitem">
4678 class="enumerate-enumitem"><span
4679 class="cmtt-12">[new_A] </span>= <span
4680 class="cmtt-12">[M]</span>+<span
4681 class="cmtt-12">[A]</span></dd></dl>
4682 <!--l. 512--><p class="noindent" >else
4683 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
4685 class="enumerate-enumitem"><span
4686 class="cmtt-12">[new_A] </span>= <span
4687 class="cmtt-12">[M]</span>
4688 </dd><dt class="enumerate-enumitem">
4690 class="enumerate-enumitem"><span
4691 class="cmtt-12">[new_M] </span>= <span
4692 class="cmtt-12">[M]</span>-<span
4693 class="cmtt-12">[A]</span></dd></dl>
4695 </dd><dt class="enumerate-enumitem">
4697 class="enumerate-enumitem">set scalar value <span
4698 class="cmtt-12">[M] </span>in vector <span
4699 class="cmtt-12">[magnitude_vector] </span>to <span
4700 class="cmtt-12">[new_M]</span>
4704 </dd><dt class="enumerate-enumitem">
4706 class="enumerate-enumitem">set scalar value <span
4707 class="cmtt-12">[A] </span>in vector <span
4708 class="cmtt-12">[angle_vector] </span>to <span
4709 class="cmtt-12">[new_A]</span></dd></dl>
4711 <!--l. 529--><p class="noindent" >
4712 <h5 class="subsubsectionHead"><span class="titlemark">4.3.6. </span> <a
4713 id="x1-770004.3.6"></a>dot product</h5>
4714 <!--l. 531--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
4715 packet type. Note that the vector synthesis length for floor computation is <span
4716 class="cmtt-12">[n]</span>/2.
4717 <!--l. 535--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
4718 channel’s residue vector. The result is the dot product of the floor and residue vectors for
4719 each channel; the produced vectors are the length <span
4720 class="cmtt-12">[n]</span>/2 audio spectrum for each
4722 <!--l. 543--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
4723 implementation might be to assume that a 32 bit fixed-point representation for floor and
4724 residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
4725 in all cases because it happens to mostly work with the current Xiph.Org reference
4727 <!--l. 550--><p class="noindent" >However, floor vector values can span <span
4728 class="cmsy-10x-x-120">∼</span>140dB (<span
4729 class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
4730 vector should represent a minimum of 120dB (<span
4731 class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
4732 bit PCM device. For the residue vector to represent full scale if the floor is nailed
4734 class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
4735 full scale if the floor is nailed at 0dB, it must be able to represent <span
4736 class="cmsy-10x-x-120">−</span>140dB to +0dB.
4737 Thus, in order to handle full range dynamics, a residue vector may span <span
4738 class="cmsy-10x-x-120">−</span>140dB to
4739 +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
4740 residue vector must be able to represent a 48 bit range and the dot product must
4741 be able to handle an effective 48 bit times 24 bit multiplication. This range may be
4742 achieved using large (64 bit or larger) integers, or implementing a movable binary point
4744 <!--l. 567--><p class="noindent" >
4745 <h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a
4746 id="x1-780004.3.7"></a>inverse MDCT</h5>
4747 <!--l. 569--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an
4751 inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is
4752 available in <span class="cite">[<a
4753 href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described
4755 <!--l. 576--><p class="noindent" >
4756 <h5 class="subsubsectionHead"><span class="titlemark">4.3.8. </span> <a
4757 id="x1-790004.3.8"></a>overlap_add</h5>
4758 <!--l. 578--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
4759 window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
4760 current window (as illustrated in <a
4761 href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a
4762 href="#x1-260001.3.2">Window shape decode (long windows
4763 only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
4764 is finished data to be returned by the decoder. This data spans from the center of
4765 the previous window to the center of the current window. In the case of same-sized
4766 windows, the amount of data to return is one-half block consisting of and only of the
4767 overlapped portions. When overlapping a short and long window, much of the returned
4768 range does not actually overlap. This does not damage transform orthogonality. Pay
4769 attention however to returning the correct data range; the amount of data to be returned
4771 <!--l. 592--><p class="noindent" >
4772 <div class="fancyvrb" id="fancyvrb22">
4774 id="x1-79002r1"></a><span
4775 class="cmr-6">1</span><span
4776 class="cmtt-8"> </span><span
4777 class="cmtt-8"> window\_blocksize(previous\_window)/4+window\_blocksize(current\_window)/4</span>
4779 <!--l. 596--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
4780 windowsize/2-1, inclusive) of the current window.
4781 <!--l. 599--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
4782 encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
4783 PCM output offset is ’0’ (as no data has been returned yet).
4784 <!--l. 606--><p class="noindent" >
4785 <h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a
4786 id="x1-800004.3.9"></a>output channel order</h5>
4787 <!--l. 608--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
4788 implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the
4789 specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for
4793 greater-than-eight channels remains ’left to the implementation’.
4794 <!--l. 614--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a
4795 decoder to produce output with channels in any order. Any such decoder should explicitly
4796 document channel reordering behavior.
4797 <!--l. 620--><p class="noindent" >
4798 <dl class="description"><dt class="description">
4800 class="cmssbx-10x-x-120">one channel</span> </dt><dd
4801 class="description">the stream is monophonic
4802 </dd><dt class="description">
4804 class="cmssbx-10x-x-120">two channels</span> </dt><dd
4805 class="description">the stream is stereo. channel order: left, right
4806 </dd><dt class="description">
4808 class="cmssbx-10x-x-120">three channels</span> </dt><dd
4809 class="description">the stream is a 1d-surround encoding. channel order: left, center, right
4810 </dd><dt class="description">
4812 class="cmssbx-10x-x-120">four channels</span> </dt><dd
4813 class="description">the stream is quadraphonic surround. channel order: front left, front right,
4814 rear left, rear right
4815 </dd><dt class="description">
4817 class="cmssbx-10x-x-120">five channels</span> </dt><dd
4818 class="description">the stream is five-channel surround. channel order: front left, center, front
4819 right, rear left, rear right
4820 </dd><dt class="description">
4822 class="cmssbx-10x-x-120">six channels</span> </dt><dd
4823 class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear
4824 left, rear right, LFE
4825 </dd><dt class="description">
4827 class="cmssbx-10x-x-120">seven channels</span> </dt><dd
4828 class="description">the stream is 6.1 surround. channel order: front left, center, front right,
4829 side left, side right, rear center, LFE
4830 </dd><dt class="description">
4832 class="cmssbx-10x-x-120">eight channels</span> </dt><dd
4833 class="description">the stream is 7.1 surround. channel order: front left, center, front right,
4834 side left, side right, rear left, rear right, LFE
4835 </dd><dt class="description">
4837 class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd
4838 class="description">channel use and order is defined by the application
4840 <!--l. 656--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
4841 channel mappings (such as three and four channel <a
4842 href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
4843 mappings other than mapping 0.
4850 <h3 class="sectionHead"><span class="titlemark">5. </span> <a
4851 id="x1-810005"></a>comment field and header specification</h3>
4852 <!--l. 6--><p class="noindent" >
4853 <h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a
4854 id="x1-820005.1"></a>Overview</h4>
4855 <!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
4856 bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
4857 belongs in a separate logical bitstream (usually an XML stream type) that provides greater
4858 structure and machine parseability.
4859 <!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
4860 a CDR. It should be a little information to remember the disc by and explain it to others; a
4861 short, to-the-point text note that need not only be a couple words, but isn’t going to be more
4862 than a short paragraph. The essentials, in other words, whatever they turn out to be,
4864 <!--l. 21--><p class="noindent" >
4866 <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
4867 class="cmti-12">“I’m Still Around”</span>, opening
4868 for Moxy Früvous, 1997.</div>
4869 <!--l. 29--><p class="noindent" >
4870 <h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a
4871 id="x1-830005.2"></a>Comment encoding</h4>
4872 <!--l. 31--><p class="noindent" >
4873 <h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a
4874 id="x1-840005.2.1"></a>Structure</h5>
4875 <!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
4876 bounded to 2<sup><span
4877 class="cmr-8">32</span></sup> <span
4878 class="cmsy-10x-x-120">− </span>1 and the length of each vector is limited to 2<sup><span
4879 class="cmr-8">32</span></sup> <span
4880 class="cmsy-10x-x-120">− </span>1 bytes. The vector length is
4884 encoded; the vector contents themselves are not null terminated. In addition to the vector list,
4885 there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
4886 example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
4888 <!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
4889 packing conventions of the vorbis codec. However, since data in the comment header
4890 is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
4892 <!--l. 46--><p class="noindent" >The comment header is decoded as follows:
4893 <!--l. 48--><p class="noindent" >
4894 <div class="fancyvrb" id="fancyvrb23">
4896 id="x1-84002r1"></a><span
4897 class="cmr-6">1</span><span
4898 class="cmtt-8"> </span><span
4899 class="cmtt-8"> </span><span
4900 class="cmtt-8"> </span><span
4901 class="cmtt-8"> 1)</span><span
4902 class="cmtt-8"> [vendor\_length]</span><span
4903 class="cmtt-8"> =</span><span
4904 class="cmtt-8"> read</span><span
4905 class="cmtt-8"> an</span><span
4906 class="cmtt-8"> unsigned</span><span
4907 class="cmtt-8"> integer</span><span
4908 class="cmtt-8"> of</span><span
4909 class="cmtt-8"> 32</span><span
4910 class="cmtt-8"> bits</span>
4911 <br class="fancyvrb" /><a
4912 id="x1-84004r2"></a><span
4913 class="cmr-6">2</span><span
4914 class="cmtt-8"> </span><span
4915 class="cmtt-8"> </span><span
4916 class="cmtt-8"> </span><span
4917 class="cmtt-8"> 2)</span><span
4918 class="cmtt-8"> [vendor\_string]</span><span
4919 class="cmtt-8"> =</span><span
4920 class="cmtt-8"> read</span><span
4921 class="cmtt-8"> a</span><span
4922 class="cmtt-8"> UTF-8</span><span
4923 class="cmtt-8"> vector</span><span
4924 class="cmtt-8"> as</span><span
4925 class="cmtt-8"> [vendor\_length]</span><span
4926 class="cmtt-8"> octets</span>
4927 <br class="fancyvrb" /><a
4928 id="x1-84006r3"></a><span
4929 class="cmr-6">3</span><span
4930 class="cmtt-8"> </span><span
4931 class="cmtt-8"> </span><span
4932 class="cmtt-8"> </span><span
4933 class="cmtt-8"> 3)</span><span
4934 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4935 class="cmtt-8"> =</span><span
4936 class="cmtt-8"> read</span><span
4937 class="cmtt-8"> an</span><span
4938 class="cmtt-8"> unsigned</span><span
4939 class="cmtt-8"> integer</span><span
4940 class="cmtt-8"> of</span><span
4941 class="cmtt-8"> 32</span><span
4942 class="cmtt-8"> bits</span>
4943 <br class="fancyvrb" /><a
4944 id="x1-84008r4"></a><span
4945 class="cmr-6">4</span><span
4946 class="cmtt-8"> </span><span
4947 class="cmtt-8"> </span><span
4948 class="cmtt-8"> </span><span
4949 class="cmtt-8"> 4)</span><span
4950 class="cmtt-8"> iterate</span><span
4951 class="cmtt-8"> [user\_comment\_list\_length]</span><span
4952 class="cmtt-8"> times</span><span
4953 class="cmtt-8"> {</span>
4954 <br class="fancyvrb" /><a
4955 id="x1-84010r5"></a><span
4956 class="cmr-6">5</span><span
4957 class="cmtt-8"> </span><span
4958 class="cmtt-8"> </span><span
4959 class="cmtt-8"> </span><span
4960 class="cmtt-8"> </span><span
4961 class="cmtt-8"> </span><span
4962 class="cmtt-8"> </span><span
4963 class="cmtt-8"> </span><span
4964 class="cmtt-8"> </span><span
4965 class="cmtt-8"> 5)</span><span
4966 class="cmtt-8"> [length]</span><span
4967 class="cmtt-8"> =</span><span
4968 class="cmtt-8"> read</span><span
4969 class="cmtt-8"> an</span><span
4970 class="cmtt-8"> unsigned</span><span
4971 class="cmtt-8"> integer</span><span
4972 class="cmtt-8"> of</span><span
4973 class="cmtt-8"> 32</span><span
4974 class="cmtt-8"> bits</span>
4975 <br class="fancyvrb" /><a
4976 id="x1-84012r6"></a><span
4977 class="cmr-6">6</span><span
4978 class="cmtt-8"> </span><span
4979 class="cmtt-8"> </span><span
4980 class="cmtt-8"> </span><span
4981 class="cmtt-8"> </span><span
4982 class="cmtt-8"> </span><span
4983 class="cmtt-8"> </span><span
4984 class="cmtt-8"> </span><span
4985 class="cmtt-8"> </span><span
4986 class="cmtt-8"> 6)</span><span
4987 class="cmtt-8"> this</span><span
4988 class="cmtt-8"> iteration’s</span><span
4989 class="cmtt-8"> user</span><span
4990 class="cmtt-8"> comment</span><span
4991 class="cmtt-8"> =</span><span
4992 class="cmtt-8"> read</span><span
4993 class="cmtt-8"> a</span><span
4994 class="cmtt-8"> UTF-8</span><span
4995 class="cmtt-8"> vector</span><span
4996 class="cmtt-8"> as</span><span
4997 class="cmtt-8"> [length]</span><span
4998 class="cmtt-8"> octets</span>
4999 <br class="fancyvrb" /><a
5000 id="x1-84014r7"></a><span
5001 class="cmr-6">7</span><span
5002 class="cmtt-8"> </span><span
5003 class="cmtt-8"> </span><span
5004 class="cmtt-8"> </span><span
5005 class="cmtt-8"> </span><span
5006 class="cmtt-8"> </span><span
5007 class="cmtt-8"> </span><span
5008 class="cmtt-8"> }</span>
5009 <br class="fancyvrb" /><a
5010 id="x1-84016r8"></a><span
5011 class="cmr-6">8</span><span
5012 class="cmtt-8"> </span><span
5013 class="cmtt-8"> </span><span
5014 class="cmtt-8"> </span><span
5015 class="cmtt-8"> 7)</span><span
5016 class="cmtt-8"> [framing\_bit]</span><span
5017 class="cmtt-8"> =</span><span
5018 class="cmtt-8"> read</span><span
5019 class="cmtt-8"> a</span><span
5020 class="cmtt-8"> single</span><span
5021 class="cmtt-8"> bit</span><span
5022 class="cmtt-8"> as</span><span
5023 class="cmtt-8"> boolean</span>
5024 <br class="fancyvrb" /><a
5025 id="x1-84018r9"></a><span
5026 class="cmr-6">9</span><span
5027 class="cmtt-8"> </span><span
5028 class="cmtt-8"> </span><span
5029 class="cmtt-8"> </span><span
5030 class="cmtt-8"> 8)</span><span
5031 class="cmtt-8"> if</span><span
5032 class="cmtt-8"> (</span><span
5033 class="cmtt-8"> [framing\_bit]</span><span
5034 class="cmtt-8"> unset</span><span
5035 class="cmtt-8"> or</span><span
5036 class="cmtt-8"> end-of-packet</span><span
5037 class="cmtt-8"> )</span><span
5038 class="cmtt-8"> then</span><span
5039 class="cmtt-8"> ERROR</span>
5040 <br class="fancyvrb" /><a
5041 id="x1-84020r10"></a><span
5042 class="cmr-6">10</span><span
5043 class="cmtt-8"> </span><span
5044 class="cmtt-8"> </span><span
5045 class="cmtt-8"> </span><span
5046 class="cmtt-8"> 9)</span><span
5047 class="cmtt-8"> done.</span>
5049 <!--l. 64--><p class="noindent" >
5050 <h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a
5051 id="x1-850005.2.2"></a>Content vector format</h5>
5052 <!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is,
5053 comment fields consist of a field name and a corresponding value and look like:
5054 <!--l. 70--><p class="noindent" >
5056 <!--l. 71--><p class="noindent" >
5057 <div class="fancyvrb" id="fancyvrb24">
5059 id="x1-85002r1"></a><span
5060 class="cmr-6">1</span><span
5061 class="cmtt-8"> </span><span
5062 class="cmtt-8"> comment[0]="ARTIST=me";</span>
5063 <br class="fancyvrb" /><a
5064 id="x1-85004r2"></a><span
5065 class="cmr-6">2</span><span
5066 class="cmtt-8"> </span><span
5067 class="cmtt-8"> comment[1]="TITLE=the</span><span
5068 class="cmtt-8"> sound</span><span
5069 class="cmtt-8"> of</span><span
5070 class="cmtt-8"> Vorbis";</span>
5076 <!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
5077 excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
5078 ASCII 0x61 through 0x7A inclusive (characters a-z).
5079 <!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
5080 terminate the field name.
5081 <!--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
5083 <!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
5084 id="x1-860005.2.2"></a><span
5085 class="cmbx-12">Field names</span></span>
5086 Below is a proposed, minimal list of standard field names with a description of intended use. No
5087 single or group of field names is mandatory; a comment header may contain one, all or none of
5088 the names in this list.
5089 <!--l. 99--><p class="noindent" >
5090 <dl class="description"><dt class="description">
5092 class="cmssbx-10x-x-120">TITLE</span> </dt><dd
5093 class="description">Track/Work name
5094 </dd><dt class="description">
5096 class="cmssbx-10x-x-120">VERSION</span> </dt><dd
5097 class="description">The version field may be used to differentiate multiple versions of the same
5098 track title in a single collection. (e.g. remix info)
5099 </dd><dt class="description">
5101 class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
5102 class="description">The collection name to which this track belongs
5103 </dd><dt class="description">
5105 class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
5106 class="description">The track number of this piece if part of a specific larger collection or
5108 </dd><dt class="description">
5110 class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
5111 class="description">The artist generally considered responsible for the work. In popular music this is
5112 usually the performing band or singer. For classical music it would be the composer.
5113 For an audio book it would be the author of the original text.
5114 </dd><dt class="description">
5116 class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
5117 class="description">The artist(s) who performed the work. In classical music this would be the
5118 conductor, orchestra, soloists. In an audio book it would be the actor who did the
5119 reading. In popular music this is typically the same as the ARTIST and is omitted.
5120 </dd><dt class="description">
5122 class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
5123 class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
5124 </dd><dt class="description">
5129 class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
5130 class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to
5131 a license such as a Creative
5132 Commons license (”www.creativecommons.org/blahblah/license.html”) or the EFF
5133 Open Audio License (’distributed under the terms of the Open Audio License. see
5134 http://www.eff.org/IP/Open_licenses/eff_oal.html for details’), etc.
5135 </dd><dt class="description">
5137 class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
5138 class="description">Name of the organization producing the track (i.e. the ’record label’)
5139 </dd><dt class="description">
5141 class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
5142 class="description">A short text description of the contents
5143 </dd><dt class="description">
5145 class="cmssbx-10x-x-120">GENRE</span> </dt><dd
5146 class="description">A short text indication of music genre
5147 </dd><dt class="description">
5149 class="cmssbx-10x-x-120">DATE</span> </dt><dd
5150 class="description">Date the track was recorded
5151 </dd><dt class="description">
5153 class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
5154 class="description">Location where track was recorded
5155 </dd><dt class="description">
5157 class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
5158 class="description">Contact information for the creators or distributors of the track. This could
5159 be a URL, an email address, the physical address of the producing label.
5160 </dd><dt class="description">
5162 class="cmssbx-10x-x-120">ISRC</span> </dt><dd
5163 class="description">International Standard Recording Code for the track; see <a
5164 href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for
5165 more information on ISRC numbers.
5167 <!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
5168 id="x1-870005.2.2"></a><span
5169 class="cmbx-12">Implications</span></span>
5170 Field names should not be ’internationalized’; this is a concession to simplicity not
5171 an attempt to exclude the majority of the world that doesn’t speak English. Field
5173 class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
5175 <!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
5176 the field name is bounded in a known way. Thus we also have the length of the field
5178 <!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
5179 use of comment fields should be clear through context at this point. Abuse will be
5184 <!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
5185 to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
5186 tags here to help with standardization.
5187 <!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
5188 example, assume a track was recorded by three well know artists; the following is permissible,
5190 <!--l. 183--><p class="noindent" >
5192 <!--l. 184--><p class="noindent" >
5193 <div class="fancyvrb" id="fancyvrb25">
5195 id="x1-87002r1"></a><span
5196 class="cmr-6">1</span><span
5197 class="cmtt-8"> </span><span
5198 class="cmtt-8"> ARTIST=Dizzy</span><span
5199 class="cmtt-8"> Gillespie</span>
5200 <br class="fancyvrb" /><a
5201 id="x1-87004r2"></a><span
5202 class="cmr-6">2</span><span
5203 class="cmtt-8"> </span><span
5204 class="cmtt-8"> ARTIST=Sonny</span><span
5205 class="cmtt-8"> Rollins</span>
5206 <br class="fancyvrb" /><a
5207 id="x1-87006r3"></a><span
5208 class="cmr-6">3</span><span
5209 class="cmtt-8"> </span><span
5210 class="cmtt-8"> ARTIST=Sonny</span><span
5211 class="cmtt-8"> Stitt</span>
5214 <!--l. 197--><p class="noindent" >
5215 <h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a
5216 id="x1-880005.2.3"></a>Encoding</h5>
5217 <!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
5218 first bitstream header packet, it is not generally the only packet on the second page and may not
5219 be restricted to within the second bitstream page. The length of the comment header packet is
5220 (practically) unbounded. The comment header packet is not optional; it must be present in the
5221 bitstream even if it is effectively empty.
5222 <!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
5223 renders least-significant-bit of the word to be coded into the least significant available bit of the
5224 current bitstream octet first):
5225 <!--l. 213--><p class="noindent" >
5226 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5228 class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets)
5229 </dd><dt class="enumerate-enumitem">
5231 class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of
5232 string, not null terminated)
5236 </dd><dt class="enumerate-enumitem">
5238 class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields)
5239 </dd><dt class="enumerate-enumitem">
5241 class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span
5242 class="cmmi-12">> </span>0; 32 bit unsigned quantity
5243 specifying number of octets)
5244 </dd><dt class="enumerate-enumitem">
5246 class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
5247 end of string, not null terminated)
5248 </dd><dt class="enumerate-enumitem">
5250 class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span
5251 class="cmmi-12">> </span>1...)...
5253 <!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
5255 class="cmtt-12">vorbis/lib/info.c</span>, <span
5256 class="cmtt-12">_vorbis_pack_comment() </span>and <span
5257 class="cmtt-12">_vorbis_unpack_comment()</span>.
5264 <h3 class="sectionHead"><span class="titlemark">6. </span> <a
5265 id="x1-890006"></a>Floor type 0 setup and decode</h3>
5266 <!--l. 6--><p class="noindent" >
5267 <h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a
5268 id="x1-900006.1"></a>Overview</h4>
5269 <!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral
5270 Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency
5271 response of the LSP filter. This representation is equivalent to a traditional all-pole infinite
5272 impulse response filter as would be used in linear predictive coding; LSP representation may be
5273 converted to LPC representation and vice-versa.
5274 <!--l. 18--><p class="noindent" >
5275 <h4 class="subsectionHead"><span class="titlemark">6.2. </span> <a
5276 id="x1-910006.2"></a>Floor 0 format</h4>
5277 <!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in
5278 coding/decoding the LSP filter coefficient values used by each frame.
5279 <!--l. 24--><p class="noindent" >
5280 <h5 class="subsubsectionHead"><span class="titlemark">6.2.1. </span> <a
5281 id="x1-920006.2.1"></a>header decode</h5>
5282 <!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third
5283 packet). configuration decode proceeds as follows:
5284 <!--l. 30--><p class="noindent" >
5285 <div class="fancyvrb" id="fancyvrb26">
5287 id="x1-92002r1"></a><span
5288 class="cmr-6">1</span><span
5289 class="cmtt-8"> </span><span
5290 class="cmtt-8"> </span><span
5291 class="cmtt-8"> </span><span
5292 class="cmtt-8"> 1)</span><span
5293 class="cmtt-8"> [floor0_order]</span><span
5294 class="cmtt-8"> =</span><span
5295 class="cmtt-8"> read</span><span
5296 class="cmtt-8"> an</span><span
5297 class="cmtt-8"> unsigned</span><span
5298 class="cmtt-8"> integer</span><span
5299 class="cmtt-8"> of</span><span
5300 class="cmtt-8"> 8</span><span
5301 class="cmtt-8"> bits</span>
5302 <br class="fancyvrb" /><a
5303 id="x1-92004r2"></a><span
5304 class="cmr-6">2</span><span
5305 class="cmtt-8"> </span><span
5306 class="cmtt-8"> </span><span
5307 class="cmtt-8"> </span><span
5308 class="cmtt-8"> 2)</span><span
5309 class="cmtt-8"> [floor0_rate]</span><span
5310 class="cmtt-8"> =</span><span
5311 class="cmtt-8"> read</span><span
5312 class="cmtt-8"> an</span><span
5313 class="cmtt-8"> unsigned</span><span
5314 class="cmtt-8"> integer</span><span
5315 class="cmtt-8"> of</span><span
5316 class="cmtt-8"> 16</span><span
5317 class="cmtt-8"> bits</span>
5318 <br class="fancyvrb" /><a
5319 id="x1-92006r3"></a><span
5320 class="cmr-6">3</span><span
5321 class="cmtt-8"> </span><span
5322 class="cmtt-8"> </span><span
5323 class="cmtt-8"> </span><span
5324 class="cmtt-8"> 3)</span><span
5325 class="cmtt-8"> [floor0_bark_map_size]</span><span
5326 class="cmtt-8"> =</span><span
5327 class="cmtt-8"> read</span><span
5328 class="cmtt-8"> an</span><span
5329 class="cmtt-8"> unsigned</span><span
5330 class="cmtt-8"> integer</span><span
5331 class="cmtt-8"> of</span><span
5332 class="cmtt-8"> 16</span><span
5333 class="cmtt-8"> bits</span>
5334 <br class="fancyvrb" /><a
5335 id="x1-92008r4"></a><span
5336 class="cmr-6">4</span><span
5337 class="cmtt-8"> </span><span
5338 class="cmtt-8"> </span><span
5339 class="cmtt-8"> </span><span
5340 class="cmtt-8"> 4)</span><span
5341 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5342 class="cmtt-8"> =</span><span
5343 class="cmtt-8"> read</span><span
5344 class="cmtt-8"> an</span><span
5345 class="cmtt-8"> unsigned</span><span
5346 class="cmtt-8"> integer</span><span
5347 class="cmtt-8"> of</span><span
5348 class="cmtt-8"> six</span><span
5349 class="cmtt-8"> bits</span>
5350 <br class="fancyvrb" /><a
5351 id="x1-92010r5"></a><span
5352 class="cmr-6">5</span><span
5353 class="cmtt-8"> </span><span
5354 class="cmtt-8"> </span><span
5355 class="cmtt-8"> </span><span
5356 class="cmtt-8"> 5)</span><span
5357 class="cmtt-8"> [floor0_amplitude_offset]</span><span
5358 class="cmtt-8"> =</span><span
5359 class="cmtt-8"> read</span><span
5360 class="cmtt-8"> an</span><span
5361 class="cmtt-8"> unsigned</span><span
5362 class="cmtt-8"> integer</span><span
5363 class="cmtt-8"> of</span><span
5364 class="cmtt-8"> eight</span><span
5365 class="cmtt-8"> bits</span>
5366 <br class="fancyvrb" /><a
5367 id="x1-92012r6"></a><span
5368 class="cmr-6">6</span><span
5369 class="cmtt-8"> </span><span
5370 class="cmtt-8"> </span><span
5371 class="cmtt-8"> </span><span
5372 class="cmtt-8"> 6)</span><span
5373 class="cmtt-8"> [floor0_number_of_books]</span><span
5374 class="cmtt-8"> =</span><span
5375 class="cmtt-8"> read</span><span
5376 class="cmtt-8"> an</span><span
5377 class="cmtt-8"> unsigned</span><span
5378 class="cmtt-8"> integer</span><span
5379 class="cmtt-8"> of</span><span
5380 class="cmtt-8"> four</span><span
5381 class="cmtt-8"> bits</span><span
5382 class="cmtt-8"> and</span><span
5383 class="cmtt-8"> add</span><span
5384 class="cmtt-8"> 1</span>
5385 <br class="fancyvrb" /><a
5386 id="x1-92014r7"></a><span
5387 class="cmr-6">7</span><span
5388 class="cmtt-8"> </span><span
5389 class="cmtt-8"> </span><span
5390 class="cmtt-8"> </span><span
5391 class="cmtt-8"> 7)</span><span
5392 class="cmtt-8"> array</span><span
5393 class="cmtt-8"> [floor0_book_list]</span><span
5394 class="cmtt-8"> =</span><span
5395 class="cmtt-8"> read</span><span
5396 class="cmtt-8"> a</span><span
5397 class="cmtt-8"> list</span><span
5398 class="cmtt-8"> of</span><span
5399 class="cmtt-8"> [floor0_number_of_books]</span><span
5400 class="cmtt-8"> unsigned</span><span
5401 class="cmtt-8"> integers</span><span
5402 class="cmtt-8"> of</span><span
5403 class="cmtt-8"> eight</span><span
5404 class="cmtt-8"> bits</span><span
5405 class="cmtt-8"> each;</span>
5410 <!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
5411 In addition, any element of the array <span
5412 class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum
5413 codebook number for this bitstream is an error condition that also renders the stream
5415 <!--l. 48--><p class="noindent" >
5416 <h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a
5417 id="x1-930006.2.2"></a>packet decode</h5>
5418 <!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve
5420 class="cmtt-12">[floor0_order] </span>LSP coefficient values from the bitstream, and then
5421 computing the floor curve, which is defined as the frequency response of the decoded LSP
5423 <!--l. 56--><p class="noindent" >Packet decode proceeds as follows:
5424 <div class="fancyvrb" id="fancyvrb27">
5426 id="x1-93002r1"></a><span
5427 class="cmr-6">1</span><span
5428 class="cmtt-8"> </span><span
5429 class="cmtt-8"> </span><span
5430 class="cmtt-8"> </span><span
5431 class="cmtt-8"> 1)</span><span
5432 class="cmtt-8"> [amplitude]</span><span
5433 class="cmtt-8"> =</span><span
5434 class="cmtt-8"> read</span><span
5435 class="cmtt-8"> an</span><span
5436 class="cmtt-8"> unsigned</span><span
5437 class="cmtt-8"> integer</span><span
5438 class="cmtt-8"> of</span><span
5439 class="cmtt-8"> [floor0_amplitude_bits]</span><span
5440 class="cmtt-8"> bits</span>
5441 <br class="fancyvrb" /><a
5442 id="x1-93004r2"></a><span
5443 class="cmr-6">2</span><span
5444 class="cmtt-8"> </span><span
5445 class="cmtt-8"> </span><span
5446 class="cmtt-8"> </span><span
5447 class="cmtt-8"> 2)</span><span
5448 class="cmtt-8"> if</span><span
5449 class="cmtt-8"> (</span><span
5450 class="cmtt-8"> [amplitude]</span><span
5451 class="cmtt-8"> is</span><span
5452 class="cmtt-8"> greater</span><span
5453 class="cmtt-8"> than</span><span
5454 class="cmtt-8"> zero</span><span
5455 class="cmtt-8"> )</span><span
5456 class="cmtt-8"> </span><span
5457 class="cmsy-8">{</span>
5458 <br class="fancyvrb" /><a
5459 id="x1-93006r3"></a><span
5460 class="cmr-6">3</span><span
5461 class="cmtt-8"> </span><span
5462 class="cmtt-8"> </span><span
5463 class="cmtt-8"> </span><span
5464 class="cmtt-8"> </span><span
5465 class="cmtt-8"> </span><span
5466 class="cmtt-8"> </span><span
5467 class="cmtt-8"> </span><span
5468 class="cmtt-8"> </span><span
5469 class="cmtt-8"> 3)</span><span
5470 class="cmtt-8"> [coefficients]</span><span
5471 class="cmtt-8"> is</span><span
5472 class="cmtt-8"> an</span><span
5473 class="cmtt-8"> empty,</span><span
5474 class="cmtt-8"> zero</span><span
5475 class="cmtt-8"> length</span><span
5476 class="cmtt-8"> vector</span>
5477 <br class="fancyvrb" /><a
5478 id="x1-93008r4"></a><span
5479 class="cmr-6">4</span><span
5480 class="cmtt-8"> </span><span
5481 class="cmtt-8"> </span><span
5482 class="cmtt-8"> </span><span
5483 class="cmtt-8"> </span><span
5484 class="cmtt-8"> </span><span
5485 class="cmtt-8"> </span><span
5486 class="cmtt-8"> </span><span
5487 class="cmtt-8"> </span><span
5488 class="cmtt-8"> 4)</span><span
5489 class="cmtt-8"> [booknumber]</span><span
5490 class="cmtt-8"> =</span><span
5491 class="cmtt-8"> read</span><span
5492 class="cmtt-8"> an</span><span
5493 class="cmtt-8"> unsigned</span><span
5494 class="cmtt-8"> integer</span><span
5495 class="cmtt-8"> of</span><span
5496 class="cmtt-8"> </span><a
5497 href="#x1-1170009.2.1"><span
5498 class="cmtt-8">ilog</span></a><span
5499 class="cmtt-8">(</span><span
5500 class="cmtt-8"> [floor0_number_of_books]</span><span
5501 class="cmtt-8"> )</span><span
5502 class="cmtt-8"> bits</span>
5503 <br class="fancyvrb" /><a
5504 id="x1-93010r5"></a><span
5505 class="cmr-6">5</span><span
5506 class="cmtt-8"> </span><span
5507 class="cmtt-8"> </span><span
5508 class="cmtt-8"> </span><span
5509 class="cmtt-8"> </span><span
5510 class="cmtt-8"> </span><span
5511 class="cmtt-8"> </span><span
5512 class="cmtt-8"> </span><span
5513 class="cmtt-8"> </span><span
5514 class="cmtt-8"> 5)</span><span
5515 class="cmtt-8"> if</span><span
5516 class="cmtt-8"> (</span><span
5517 class="cmtt-8"> [booknumber]</span><span
5518 class="cmtt-8"> is</span><span
5519 class="cmtt-8"> greater</span><span
5520 class="cmtt-8"> than</span><span
5521 class="cmtt-8"> the</span><span
5522 class="cmtt-8"> highest</span><span
5523 class="cmtt-8"> number</span><span
5524 class="cmtt-8"> decode</span><span
5525 class="cmtt-8"> codebook</span><span
5526 class="cmtt-8"> )</span><span
5527 class="cmtt-8"> then</span><span
5528 class="cmtt-8"> packet</span><span
5529 class="cmtt-8"> is</span><span
5530 class="cmtt-8"> undecodable</span>
5531 <br class="fancyvrb" /><a
5532 id="x1-93012r6"></a><span
5533 class="cmr-6">6</span><span
5534 class="cmtt-8"> </span><span
5535 class="cmtt-8"> </span><span
5536 class="cmtt-8"> </span><span
5537 class="cmtt-8"> </span><span
5538 class="cmtt-8"> </span><span
5539 class="cmtt-8"> </span><span
5540 class="cmtt-8"> </span><span
5541 class="cmtt-8"> </span><span
5542 class="cmtt-8"> 6)</span><span
5543 class="cmtt-8"> [last]</span><span
5544 class="cmtt-8"> =</span><span
5545 class="cmtt-8"> zero;</span>
5546 <br class="fancyvrb" /><a
5547 id="x1-93014r7"></a><span
5548 class="cmr-6">7</span><span
5549 class="cmtt-8"> </span><span
5550 class="cmtt-8"> </span><span
5551 class="cmtt-8"> </span><span
5552 class="cmtt-8"> </span><span
5553 class="cmtt-8"> </span><span
5554 class="cmtt-8"> </span><span
5555 class="cmtt-8"> </span><span
5556 class="cmtt-8"> </span><span
5557 class="cmtt-8"> 7)</span><span
5558 class="cmtt-8"> vector</span><span
5559 class="cmtt-8"> [temp_vector]</span><span
5560 class="cmtt-8"> =</span><span
5561 class="cmtt-8"> read</span><span
5562 class="cmtt-8"> vector</span><span
5563 class="cmtt-8"> from</span><span
5564 class="cmtt-8"> bitstream</span><span
5565 class="cmtt-8"> using</span><span
5566 class="cmtt-8"> codebook</span><span
5567 class="cmtt-8"> number</span><span
5568 class="cmtt-8"> [floor0_book_list]</span><span
5569 class="cmtt-8"> element</span><span
5570 class="cmtt-8"> [booknumber]</span><span
5571 class="cmtt-8"> in</span><span
5572 class="cmtt-8"> VQ</span><span
5573 class="cmtt-8"> context.</span>
5574 <br class="fancyvrb" /><a
5575 id="x1-93016r8"></a><span
5576 class="cmr-6">8</span><span
5577 class="cmtt-8"> </span><span
5578 class="cmtt-8"> </span><span
5579 class="cmtt-8"> </span><span
5580 class="cmtt-8"> </span><span
5581 class="cmtt-8"> </span><span
5582 class="cmtt-8"> </span><span
5583 class="cmtt-8"> </span><span
5584 class="cmtt-8"> </span><span
5585 class="cmtt-8"> 8)</span><span
5586 class="cmtt-8"> add</span><span
5587 class="cmtt-8"> the</span><span
5588 class="cmtt-8"> scalar</span><span
5589 class="cmtt-8"> value</span><span
5590 class="cmtt-8"> [last]</span><span
5591 class="cmtt-8"> to</span><span
5592 class="cmtt-8"> each</span><span
5593 class="cmtt-8"> scalar</span><span
5594 class="cmtt-8"> in</span><span
5595 class="cmtt-8"> vector</span><span
5596 class="cmtt-8"> [temp_vector]</span>
5597 <br class="fancyvrb" /><a
5598 id="x1-93018r9"></a><span
5599 class="cmr-6">9</span><span
5600 class="cmtt-8"> </span><span
5601 class="cmtt-8"> </span><span
5602 class="cmtt-8"> </span><span
5603 class="cmtt-8"> </span><span
5604 class="cmtt-8"> </span><span
5605 class="cmtt-8"> </span><span
5606 class="cmtt-8"> </span><span
5607 class="cmtt-8"> </span><span
5608 class="cmtt-8"> 9)</span><span
5609 class="cmtt-8"> [last]</span><span
5610 class="cmtt-8"> =</span><span
5611 class="cmtt-8"> the</span><span
5612 class="cmtt-8"> value</span><span
5613 class="cmtt-8"> of</span><span
5614 class="cmtt-8"> the</span><span
5615 class="cmtt-8"> last</span><span
5616 class="cmtt-8"> scalar</span><span
5617 class="cmtt-8"> in</span><span
5618 class="cmtt-8"> vector</span><span
5619 class="cmtt-8"> [temp_vector]</span>
5620 <br class="fancyvrb" /><a
5621 id="x1-93020r10"></a><span
5622 class="cmr-6">10</span><span
5623 class="cmtt-8"> </span><span
5624 class="cmtt-8"> </span><span
5625 class="cmtt-8"> </span><span
5626 class="cmtt-8"> </span><span
5627 class="cmtt-8"> </span><span
5628 class="cmtt-8"> </span><span
5629 class="cmtt-8"> </span><span
5630 class="cmtt-8"> 10)</span><span
5631 class="cmtt-8"> concatenate</span><span
5632 class="cmtt-8"> [temp_vector]</span><span
5633 class="cmtt-8"> onto</span><span
5634 class="cmtt-8"> the</span><span
5635 class="cmtt-8"> end</span><span
5636 class="cmtt-8"> of</span><span
5637 class="cmtt-8"> the</span><span
5638 class="cmtt-8"> [coefficients]</span><span
5639 class="cmtt-8"> vector</span>
5640 <br class="fancyvrb" /><a
5641 id="x1-93022r11"></a><span
5642 class="cmr-6">11</span><span
5643 class="cmtt-8"> </span><span
5644 class="cmtt-8"> </span><span
5645 class="cmtt-8"> </span><span
5646 class="cmtt-8"> </span><span
5647 class="cmtt-8"> </span><span
5648 class="cmtt-8"> </span><span
5649 class="cmtt-8"> </span><span
5650 class="cmtt-8"> 11)</span><span
5651 class="cmtt-8"> if</span><span
5652 class="cmtt-8"> (length</span><span
5653 class="cmtt-8"> of</span><span
5654 class="cmtt-8"> vector</span><span
5655 class="cmtt-8"> [coefficients]</span><span
5656 class="cmtt-8"> is</span><span
5657 class="cmtt-8"> less</span><span
5658 class="cmtt-8"> than</span><span
5659 class="cmtt-8"> [floor0_order],</span><span
5660 class="cmtt-8"> continue</span><span
5661 class="cmtt-8"> at</span><span
5662 class="cmtt-8"> step</span><span
5663 class="cmtt-8"> 6</span>
5664 <br class="fancyvrb" /><a
5665 id="x1-93024r12"></a><span
5666 class="cmr-6">12</span><span
5667 class="cmtt-8"> </span><span
5668 class="cmtt-8"> </span>
5669 <br class="fancyvrb" /><a
5670 id="x1-93026r13"></a><span
5671 class="cmr-6">13</span><span
5672 class="cmtt-8"> </span><span
5673 class="cmtt-8"> </span><span
5674 class="cmtt-8"> </span><span
5675 class="cmtt-8"> </span><span
5676 class="cmtt-8"> </span><span
5677 class="cmtt-8"> </span><span
5678 class="cmtt-8"> </span><span
5679 class="cmsy-8">}</span>
5680 <br class="fancyvrb" /><a
5681 id="x1-93028r14"></a><span
5682 class="cmr-6">14</span><span
5683 class="cmtt-8"> </span><span
5684 class="cmtt-8"> </span>
5685 <br class="fancyvrb" /><a
5686 id="x1-93030r15"></a><span
5687 class="cmr-6">15</span><span
5688 class="cmtt-8"> </span><span
5689 class="cmtt-8"> </span><span
5690 class="cmtt-8"> 12)</span><span
5691 class="cmtt-8"> done.</span>
5692 <br class="fancyvrb" /><a
5693 id="x1-93032r16"></a><span
5694 class="cmr-6">16</span><span
5695 class="cmtt-8"> </span><span
5696 class="cmtt-8"> </span>
5698 <!--l. 76--><p class="noindent" >Take note of the following properties of decode:
5699 <ul class="itemize1">
5700 <li class="itemize">An <span
5701 class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
5702 is unused in this frame (the output of the channel will be all-zeroes in synthesis).
5703 Several later stages of decode don’t occur for an unused channel.
5705 <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
5706 if end-of-packet is reached during any read operation above, floor decode is to return
5707 ’unused’ status as if the <span
5708 class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
5710 <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
5711 href="#x1-1170009.2.1">ilog</a>(
5716 class="cmtt-12">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct
5717 and values greater than the maximum possible book value are reserved.
5719 <li class="itemize">The number of scalars read into the vector <span
5720 class="cmtt-12">[coefficients] </span>may be greater
5722 class="cmtt-12">[floor0_order]</span>, the number actually required for curve computation. For
5723 example, if the VQ codebook used for the floor currently being decoded has a
5725 class="cmtt-12">[codebook_dimensions] </span>value of three and <span
5726 class="cmtt-12">[floor0_order] </span>is ten, the only way to
5727 fill all the needed scalars in <span
5728 class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
5729 as four vectors of three scalars each. This is not an error condition, and care must
5730 be taken not to allow a buffer overflow in decode. The extra values are not used and
5731 may be ignored or discarded.</li></ul>
5732 <!--l. 104--><p class="noindent" >
5733 <h5 class="subsubsectionHead"><span class="titlemark">6.2.3. </span> <a
5734 id="x1-940006.2.3"></a>curve computation</h5>
5735 <!--l. 106--><p class="noindent" >Given an <span
5736 class="cmtt-12">[amplitude] </span>integer and <span
5737 class="cmtt-12">[coefficients] </span>vector from packet decode as well as
5738 the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and
5739 [floor0_amplitude_offset] values from floor setup, and an output vector size <span
5740 class="cmtt-12">[n] </span>specified by the
5741 decode process, we compute a floor output vector.
5742 <!--l. 113--><p class="noindent" >If the value <span
5743 class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span
5744 class="cmtt-12">[n] </span>vector with all-zero
5745 scalars. Otherwise, begin by assuming the following definitions for the given vector to be
5747 <center class="par-math-display" >
5749 src="Vorbis_I_spec7x.png" alt=" {
5750 min (floor0_bark_map_size − 1,foobar ) for i ∈ [0,n − 1 ]
5751 mapi = − 1 for i = n
5752 " class="par-math-display" ></center>
5753 <!--l. 128--><p class="nopar" >
5754 <!--l. 130--><p class="noindent" >where
5755 <center class="par-math-display" >
5757 src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋
5758 (floor0_rate ⋅ i) floor0_bark_map_size
5759 foobar = bark -------2n------- ⋅-bark(.5 ⋅ floor0_rate-)
5760 " class="par-math-display" ></center>
5764 <!--l. 137--><p class="nopar" >
5765 <!--l. 139--><p class="noindent" >and
5766 <center class="par-math-display" >
5768 src="Vorbis_I_spec9x.png" alt=" 2
5769 bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x )
5770 " class="par-math-display" ></center>
5771 <!--l. 143--><p class="nopar" >
5772 <!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
5773 result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
5775 class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
5777 <!--l. 151--><p class="noindent" >
5778 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5780 class="enumerate-enumitem"><span
5781 class="cmtt-12">[i] </span>= 0
5782 </dd><dt class="enumerate-enumitem">
5784 class="enumerate-enumitem"><span
5785 class="cmtt-12">[</span><span
5786 class="cmmi-12">ω</span><span
5787 class="cmtt-12">] </span>= <span
5788 class="cmmi-12">π </span>* map element <span
5789 class="cmtt-12">[i] </span>/ <span
5790 class="cmtt-12">[floor0_bark_map_size]</span>
5791 </dd><dt class="enumerate-enumitem">
5793 class="enumerate-enumitem">if ( <span
5794 class="cmtt-12">[floor0_order] </span>is odd )
5795 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5797 class="enumerate-enumitem">calculate <span
5798 class="cmtt-12">[p] </span>and <span
5799 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5800 <center class="math-display" >
5802 src="Vorbis_I_spec10x.png" alt=" floor0_order−3
5804 p = (1 − cos ω) 4(cos([coefficients ]2j+1) − cosω )
5805 floor0_order−1 j=0
5807 q = -- 4(cos([coefficients ]2j) − cosω )2
5812 " class="math-display" ></center>
5815 <!--l. 162--><p class="noindent" >else <span
5816 class="cmtt-12">[floor0_order] </span>is even
5817 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
5819 class="enumerate-enumitem">calculate <span
5820 class="cmtt-12">[p] </span>and <span
5821 class="cmtt-12">[q] </span>according to: <div class="eqnarray">
5822 <center class="math-display" >
5824 src="Vorbis_I_spec11x.png" alt=" floor0_order−2
5825 (1-−-cosω-) ∏2 2
5826 p = 2 4(cos([coefficients ]2j+1) − cosω)
5828 floor0_∏o2rder−-2
5829 q = (1-+-cosω-) 4(cos([coefficients ]2j) − cos ω)2
5831 " class="math-display" ></center>
5834 </dd><dt class="enumerate-enumitem">
5836 class="enumerate-enumitem">calculate <span
5837 class="cmtt-12">[linear_floor_value] </span>according to:
5838 <center class="math-display" >
5840 src="Vorbis_I_spec12x.png" alt=" ( ( ))
5841 exp .11512925 amplitude---⋅ floor0_amplitute_√offset---− floor0_amplitude_offset
5842 (2floor0_amplitude_bits − 1) p + q
5843 " class="math-display" ></center>
5844 <!--l. 177--><p class="nopar" >
5845 </dd><dt class="enumerate-enumitem">
5847 class="enumerate-enumitem"><span
5848 class="cmtt-12">[iteration_condition] </span>= map element <span
5849 class="cmtt-12">[i]</span>
5853 </dd><dt class="enumerate-enumitem">
5855 class="enumerate-enumitem"><span
5856 class="cmtt-12">[output] </span>element <span
5857 class="cmtt-12">[i] </span>= <span
5858 class="cmtt-12">[linear_floor_value]</span>
5859 </dd><dt class="enumerate-enumitem">
5861 class="enumerate-enumitem">increment <span
5862 class="cmtt-12">[i]</span>
5863 </dd><dt class="enumerate-enumitem">
5865 class="enumerate-enumitem">if ( map element <span
5866 class="cmtt-12">[i] </span>is equal to <span
5867 class="cmtt-12">[iteration_condition] </span>) continue at step
5869 </dd><dt class="enumerate-enumitem">
5871 class="enumerate-enumitem">if ( <span
5872 class="cmtt-12">[i] </span>is less than <span
5873 class="cmtt-12">[n] </span>) continue at step 2
5874 </dd><dt class="enumerate-enumitem">
5876 class="enumerate-enumitem">done</dd></dl>
5883 <h3 class="sectionHead"><span class="titlemark">7. </span> <a
5884 id="x1-950007"></a>Floor type 1 setup and decode</h3>
5885 <!--l. 6--><p class="noindent" >
5886 <h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a
5887 id="x1-960007.1"></a>Overview</h4>
5888 <!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
5889 curve. The representation plots this curve mechanically on a linear frequency axis and a
5890 logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
5892 <!--l. 16--><p class="noindent" >
5893 <h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a
5894 id="x1-970007.2"></a>Floor 1 format</h4>
5895 <!--l. 18--><p class="noindent" >
5896 <h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a
5897 id="x1-980007.2.1"></a>model</h5>
5898 <!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
5899 floor curve using iterative prediction in a process roughly equivalent to the following simplified
5901 <ul class="itemize1">
5902 <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
5903 where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
5906 <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
5907 produces a y˙new value at that point computed from the existing line’s y value at
5908 x˙new (as plotted by the line) and a difference value decoded from the bitstream
5914 <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
5915 x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
5916 y˙new represents no change to the amplitude value at x˙new so that later refinement
5917 is additionally bounded at x˙new.
5919 <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
5920 at floor 1 initialization time. Computation is completed at the end of the x value list.
5922 <!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
5923 representing typical configuration:
5924 <!--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
5925 in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
5926 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
5927 example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
5928 way, beginning with the first line:
5931 <!--l. 59--><p class="noindent" >
5933 <!--l. 60--><p class="noindent" ><img
5934 src="floor1-1.png" alt="PIC"
5936 <br /> <div class="caption"
5937 ><span class="id">Figure 7: </span><span
5938 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980017 -->
5940 <!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
5944 <!--l. 67--><p class="noindent" >
5946 <!--l. 68--><p class="noindent" ><img
5947 src="floor1-2.png" alt="PIC"
5949 <br /> <div class="caption"
5950 ><span class="id">Figure 8: </span><span
5951 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980028 -->
5953 <!--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
5954 further refinement. From here on, the pattern should be clear; we complete the floor computation
5961 <!--l. 76--><p class="noindent" >
5963 <!--l. 77--><p class="noindent" ><img
5964 src="floor1-3.png" alt="PIC"
5966 <br /> <div class="caption"
5967 ><span class="id">Figure 9: </span><span
5968 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980039 -->
5972 <!--l. 81--><p class="noindent" >
5974 <!--l. 82--><p class="noindent" ><img
5975 src="floor1-4.png" alt="PIC"
5977 <br /> <div class="caption"
5978 ><span class="id">Figure 10: </span><span
5979 class="content">graph of example floor</span></div><!--tex4ht:label?: x1-9800410 -->
5981 <!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual
5982 decode, as described later. The actual algorithm splits Y value computation and line plotting
5983 into two steps with modifications to the above algorithm to eliminate noise accumulation
5984 through integer roundoff/truncation.
5985 <!--l. 94--><p class="noindent" >
5986 <h5 class="subsubsectionHead"><span class="titlemark">7.2.2. </span> <a
5987 id="x1-990007.2.2"></a>header decode</h5>
5988 <!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
5989 during packet decode and synthesis). This list is split into partitions, and each partition is
5990 assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
5991 partition or partition class.
5992 <!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
5993 the partition class encodes at once), a ’subclass’ value representing the number of
5994 alternate entropy books the partition class may use in representing Y values, the list of
5995 [subclass] books and a master book used to encode which alternate books were chosen
5996 for representation in a given packet. The master/subclass mechanism is meant to be
5997 used as a flexible representation cascade while still using codebooks only in a scalar
6002 <!--l. 112--><p class="noindent" >
6003 <div class="fancyvrb" id="fancyvrb28">
6005 id="x1-99002r1"></a><span
6006 class="cmr-6">1</span><span
6007 class="cmtt-8"> </span><span
6008 class="cmtt-8"> </span>
6009 <br class="fancyvrb" /><a
6010 id="x1-99004r2"></a><span
6011 class="cmr-6">2</span><span
6012 class="cmtt-8"> </span><span
6013 class="cmtt-8"> </span><span
6014 class="cmtt-8"> </span><span
6015 class="cmtt-8"> 1)</span><span
6016 class="cmtt-8"> [floor1_partitions]</span><span
6017 class="cmtt-8"> =</span><span
6018 class="cmtt-8"> read</span><span
6019 class="cmtt-8"> 5</span><span
6020 class="cmtt-8"> bits</span><span
6021 class="cmtt-8"> as</span><span
6022 class="cmtt-8"> unsigned</span><span
6023 class="cmtt-8"> integer</span>
6024 <br class="fancyvrb" /><a
6025 id="x1-99006r3"></a><span
6026 class="cmr-6">3</span><span
6027 class="cmtt-8"> </span><span
6028 class="cmtt-8"> </span><span
6029 class="cmtt-8"> </span><span
6030 class="cmtt-8"> 2)</span><span
6031 class="cmtt-8"> [maximum_class]</span><span
6032 class="cmtt-8"> =</span><span
6033 class="cmtt-8"> -1</span>
6034 <br class="fancyvrb" /><a
6035 id="x1-99008r4"></a><span
6036 class="cmr-6">4</span><span
6037 class="cmtt-8"> </span><span
6038 class="cmtt-8"> </span><span
6039 class="cmtt-8"> </span><span
6040 class="cmtt-8"> 3)</span><span
6041 class="cmtt-8"> iterate</span><span
6042 class="cmtt-8"> [i]</span><span
6043 class="cmtt-8"> over</span><span
6044 class="cmtt-8"> the</span><span
6045 class="cmtt-8"> range</span><span
6046 class="cmtt-8"> 0</span><span
6047 class="cmtt-8"> ...</span><span
6048 class="cmtt-8"> [floor1_partitions]-1</span><span
6049 class="cmtt-8"> </span><span
6050 class="cmsy-8">{</span>
6051 <br class="fancyvrb" /><a
6052 id="x1-99010r5"></a><span
6053 class="cmr-6">5</span><span
6054 class="cmtt-8"> </span><span
6055 class="cmtt-8"> </span>
6056 <br class="fancyvrb" /><a
6057 id="x1-99012r6"></a><span
6058 class="cmr-6">6</span><span
6059 class="cmtt-8"> </span><span
6060 class="cmtt-8"> </span><span
6061 class="cmtt-8"> </span><span
6062 class="cmtt-8"> </span><span
6063 class="cmtt-8"> </span><span
6064 class="cmtt-8"> </span><span
6065 class="cmtt-8"> </span><span
6066 class="cmtt-8"> </span><span
6067 class="cmtt-8"> </span><span
6068 class="cmtt-8"> 4)</span><span
6069 class="cmtt-8"> vector</span><span
6070 class="cmtt-8"> [floor1_partition_class_list]</span><span
6071 class="cmtt-8"> element</span><span
6072 class="cmtt-8"> [i]</span><span
6073 class="cmtt-8"> =</span><span
6074 class="cmtt-8"> read</span><span
6075 class="cmtt-8"> 4</span><span
6076 class="cmtt-8"> bits</span><span
6077 class="cmtt-8"> as</span><span
6078 class="cmtt-8"> unsigned</span><span
6079 class="cmtt-8"> integer</span>
6080 <br class="fancyvrb" /><a
6081 id="x1-99014r7"></a><span
6082 class="cmr-6">7</span><span
6083 class="cmtt-8"> </span><span
6084 class="cmtt-8"> </span>
6085 <br class="fancyvrb" /><a
6086 id="x1-99016r8"></a><span
6087 class="cmr-6">8</span><span
6088 class="cmtt-8"> </span><span
6089 class="cmtt-8"> </span><span
6090 class="cmtt-8"> </span><span
6091 class="cmtt-8"> </span><span
6092 class="cmtt-8"> </span><span
6093 class="cmtt-8"> </span><span
6094 class="cmtt-8"> </span><span
6095 class="cmsy-8">}</span>
6096 <br class="fancyvrb" /><a
6097 id="x1-99018r9"></a><span
6098 class="cmr-6">9</span><span
6099 class="cmtt-8"> </span><span
6100 class="cmtt-8"> </span>
6101 <br class="fancyvrb" /><a
6102 id="x1-99020r10"></a><span
6103 class="cmr-6">10</span><span
6104 class="cmtt-8"> </span><span
6105 class="cmtt-8"> </span><span
6106 class="cmtt-8"> </span><span
6107 class="cmtt-8"> 5)</span><span
6108 class="cmtt-8"> [maximum_class]</span><span
6109 class="cmtt-8"> =</span><span
6110 class="cmtt-8"> largest</span><span
6111 class="cmtt-8"> integer</span><span
6112 class="cmtt-8"> scalar</span><span
6113 class="cmtt-8"> value</span><span
6114 class="cmtt-8"> in</span><span
6115 class="cmtt-8"> vector</span><span
6116 class="cmtt-8"> [floor1_partition_class_list]</span>
6117 <br class="fancyvrb" /><a
6118 id="x1-99022r11"></a><span
6119 class="cmr-6">11</span><span
6120 class="cmtt-8"> </span><span
6121 class="cmtt-8"> </span><span
6122 class="cmtt-8"> </span><span
6123 class="cmtt-8"> 6)</span><span
6124 class="cmtt-8"> iterate</span><span
6125 class="cmtt-8"> [i]</span><span
6126 class="cmtt-8"> over</span><span
6127 class="cmtt-8"> the</span><span
6128 class="cmtt-8"> range</span><span
6129 class="cmtt-8"> 0</span><span
6130 class="cmtt-8"> ...</span><span
6131 class="cmtt-8"> [maximum_class]</span><span
6132 class="cmtt-8"> </span><span
6133 class="cmsy-8">{</span>
6134 <br class="fancyvrb" /><a
6135 id="x1-99024r12"></a><span
6136 class="cmr-6">12</span><span
6137 class="cmtt-8"> </span><span
6138 class="cmtt-8"> </span>
6139 <br class="fancyvrb" /><a
6140 id="x1-99026r13"></a><span
6141 class="cmr-6">13</span><span
6142 class="cmtt-8"> </span><span
6143 class="cmtt-8"> </span><span
6144 class="cmtt-8"> </span><span
6145 class="cmtt-8"> </span><span
6146 class="cmtt-8"> </span><span
6147 class="cmtt-8"> </span><span
6148 class="cmtt-8"> </span><span
6149 class="cmtt-8"> </span><span
6150 class="cmtt-8"> </span><span
6151 class="cmtt-8"> 7)</span><span
6152 class="cmtt-8"> vector</span><span
6153 class="cmtt-8"> [floor1_class_dimensions]</span><span
6154 class="cmtt-8"> element</span><span
6155 class="cmtt-8"> [i]</span><span
6156 class="cmtt-8"> =</span><span
6157 class="cmtt-8"> read</span><span
6158 class="cmtt-8"> 3</span><span
6159 class="cmtt-8"> bits</span><span
6160 class="cmtt-8"> as</span><span
6161 class="cmtt-8"> unsigned</span><span
6162 class="cmtt-8"> integer</span><span
6163 class="cmtt-8"> and</span><span
6164 class="cmtt-8"> add</span><span
6165 class="cmtt-8"> 1</span>
6166 <br class="fancyvrb" /><a
6167 id="x1-99028r14"></a><span
6168 class="cmr-6">14</span><span
6169 class="cmtt-8"> </span><span
6170 class="cmtt-8">  8)</span><span
6171 class="cmtt-8"> vector</span><span
6172 class="cmtt-8"> [floor1_class_subclasses]</span><span
6173 class="cmtt-8"> element</span><span
6174 class="cmtt-8"> [i]</span><span
6175 class="cmtt-8"> =</span><span
6176 class="cmtt-8"> read</span><span
6177 class="cmtt-8"> 2</span><span
6178 class="cmtt-8"> bits</span><span
6179 class="cmtt-8"> as</span><span
6180 class="cmtt-8"> unsigned</span><span
6181 class="cmtt-8"> integer</span>
6182 <br class="fancyvrb" /><a
6183 id="x1-99030r15"></a><span
6184 class="cmr-6">15</span><span
6185 class="cmtt-8"> </span><span
6186 class="cmtt-8"> </span><span
6187 class="cmtt-8"> </span><span
6188 class="cmtt-8"> </span><span
6189 class="cmtt-8"> </span><span
6190 class="cmtt-8"> </span><span
6191 class="cmtt-8"> </span><span
6192 class="cmtt-8"> </span><span
6193 class="cmtt-8"> </span><span
6194 class="cmtt-8"> 9)</span><span
6195 class="cmtt-8"> if</span><span
6196 class="cmtt-8"> (</span><span
6197 class="cmtt-8"> vector</span><span
6198 class="cmtt-8"> [floor1_class_subclasses]</span><span
6199 class="cmtt-8"> element</span><span
6200 class="cmtt-8"> [i]</span><span
6201 class="cmtt-8"> is</span><span
6202 class="cmtt-8"> nonzero</span><span
6203 class="cmtt-8"> )</span><span
6204 class="cmtt-8"> </span><span
6205 class="cmsy-8">{</span>
6206 <br class="fancyvrb" /><a
6207 id="x1-99032r16"></a><span
6208 class="cmr-6">16</span><span
6209 class="cmtt-8"> </span><span
6210 class="cmtt-8"> </span>
6211 <br class="fancyvrb" /><a
6212 id="x1-99034r17"></a><span
6213 class="cmr-6">17</span><span
6214 class="cmtt-8"> </span><span
6215 class="cmtt-8"> </span><span
6216 class="cmtt-8"> </span><span
6217 class="cmtt-8"> </span><span
6218 class="cmtt-8"> </span><span
6219 class="cmtt-8"> </span><span
6220 class="cmtt-8"> </span><span
6221 class="cmtt-8"> </span><span
6222 class="cmtt-8"> </span><span
6223 class="cmtt-8"> </span><span
6224 class="cmtt-8"> </span><span
6225 class="cmtt-8"> </span><span
6226 class="cmtt-8"> </span><span
6227 class="cmtt-8"> </span><span
6228 class="cmtt-8"> 10)</span><span
6229 class="cmtt-8"> vector</span><span
6230 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6231 class="cmtt-8"> element</span><span
6232 class="cmtt-8"> [i]</span><span
6233 class="cmtt-8"> =</span><span
6234 class="cmtt-8"> read</span><span
6235 class="cmtt-8"> 8</span><span
6236 class="cmtt-8"> bits</span><span
6237 class="cmtt-8"> as</span><span
6238 class="cmtt-8"> unsigned</span><span
6239 class="cmtt-8"> integer</span>
6240 <br class="fancyvrb" /><a
6241 id="x1-99036r18"></a><span
6242 class="cmr-6">18</span><span
6243 class="cmtt-8"> </span><span
6244 class="cmtt-8"> </span>
6245 <br class="fancyvrb" /><a
6246 id="x1-99038r19"></a><span
6247 class="cmr-6">19</span><span
6248 class="cmtt-8"> </span><span
6249 class="cmtt-8"> </span><span
6250 class="cmtt-8"> </span><span
6251 class="cmtt-8"> </span><span
6252 class="cmtt-8"> </span><span
6253 class="cmtt-8"> </span><span
6254 class="cmtt-8"> </span><span
6255 class="cmtt-8"> </span><span
6256 class="cmtt-8"> </span><span
6257 class="cmtt-8"> </span><span
6258 class="cmtt-8"> </span><span
6259 class="cmtt-8"> </span><span
6260 class="cmtt-8"> </span><span
6261 class="cmsy-8">}</span>
6262 <br class="fancyvrb" /><a
6263 id="x1-99040r20"></a><span
6264 class="cmr-6">20</span><span
6265 class="cmtt-8"> </span><span
6266 class="cmtt-8"> </span>
6267 <br class="fancyvrb" /><a
6268 id="x1-99042r21"></a><span
6269 class="cmr-6">21</span><span
6270 class="cmtt-8"> </span><span
6271 class="cmtt-8"> </span><span
6272 class="cmtt-8"> </span><span
6273 class="cmtt-8"> </span><span
6274 class="cmtt-8"> </span><span
6275 class="cmtt-8"> </span><span
6276 class="cmtt-8"> </span><span
6277 class="cmtt-8"> </span><span
6278 class="cmtt-8"> 11)</span><span
6279 class="cmtt-8"> iterate</span><span
6280 class="cmtt-8"> [j]</span><span
6281 class="cmtt-8"> over</span><span
6282 class="cmtt-8"> the</span><span
6283 class="cmtt-8"> range</span><span
6284 class="cmtt-8"> 0</span><span
6285 class="cmtt-8"> ...</span><span
6286 class="cmtt-8"> (2</span><span
6287 class="cmtt-8"> exponent</span><span
6288 class="cmtt-8"> [floor1_class_subclasses]</span><span
6289 class="cmtt-8"> element</span><span
6290 class="cmtt-8"> [i])</span><span
6291 class="cmtt-8"> -</span><span
6292 class="cmtt-8"> 1</span><span
6293 class="cmtt-8"> </span><span
6294 class="cmsy-8">{</span>
6295 <br class="fancyvrb" /><a
6296 id="x1-99044r22"></a><span
6297 class="cmr-6">22</span><span
6298 class="cmtt-8"> </span><span
6299 class="cmtt-8"> </span>
6300 <br class="fancyvrb" /><a
6301 id="x1-99046r23"></a><span
6302 class="cmr-6">23</span><span
6303 class="cmtt-8"> </span><span
6304 class="cmtt-8"> </span><span
6305 class="cmtt-8"> </span><span
6306 class="cmtt-8"> </span><span
6307 class="cmtt-8"> </span><span
6308 class="cmtt-8"> </span><span
6309 class="cmtt-8"> </span><span
6310 class="cmtt-8"> </span><span
6311 class="cmtt-8"> </span><span
6312 class="cmtt-8"> </span><span
6313 class="cmtt-8"> </span><span
6314 class="cmtt-8"> </span><span
6315 class="cmtt-8"> </span><span
6316 class="cmtt-8"> </span><span
6317 class="cmtt-8"> 12)</span><span
6318 class="cmtt-8"> array</span><span
6319 class="cmtt-8"> [floor1_subclass_books]</span><span
6320 class="cmtt-8"> element</span><span
6321 class="cmtt-8"> [i],[j]</span><span
6322 class="cmtt-8"> =</span>
6323 <br class="fancyvrb" /><a
6324 id="x1-99048r24"></a><span
6325 class="cmr-6">24</span><span
6326 class="cmtt-8"> </span><span
6327 class="cmtt-8"> </span><span
6328 class="cmtt-8"> </span><span
6329 class="cmtt-8"> </span><span
6330 class="cmtt-8"> </span><span
6331 class="cmtt-8"> </span><span
6332 class="cmtt-8"> </span><span
6333 class="cmtt-8"> </span><span
6334 class="cmtt-8"> </span><span
6335 class="cmtt-8"> </span><span
6336 class="cmtt-8"> </span><span
6337 class="cmtt-8"> </span><span
6338 class="cmtt-8"> </span><span
6339 class="cmtt-8"> </span><span
6340 class="cmtt-8"> </span><span
6341 class="cmtt-8"> </span><span
6342 class="cmtt-8"> </span><span
6343 class="cmtt-8"> </span><span
6344 class="cmtt-8"> read</span><span
6345 class="cmtt-8"> 8</span><span
6346 class="cmtt-8"> bits</span><span
6347 class="cmtt-8"> as</span><span
6348 class="cmtt-8"> unsigned</span><span
6349 class="cmtt-8"> integer</span><span
6350 class="cmtt-8"> and</span><span
6351 class="cmtt-8"> subtract</span><span
6352 class="cmtt-8"> one</span>
6353 <br class="fancyvrb" /><a
6354 id="x1-99050r25"></a><span
6355 class="cmr-6">25</span><span
6356 class="cmtt-8"> </span><span
6357 class="cmtt-8"> </span><span
6358 class="cmtt-8"> </span><span
6359 class="cmtt-8"> </span><span
6360 class="cmtt-8"> </span><span
6361 class="cmtt-8"> </span><span
6362 class="cmtt-8"> </span><span
6363 class="cmtt-8"> </span><span
6364 class="cmtt-8"> </span><span
6365 class="cmtt-8"> </span><span
6366 class="cmtt-8"> </span><span
6367 class="cmtt-8"> </span><span
6368 class="cmtt-8"> </span><span
6369 class="cmsy-8">}</span>
6370 <br class="fancyvrb" /><a
6371 id="x1-99052r26"></a><span
6372 class="cmr-6">26</span><span
6373 class="cmtt-8"> </span><span
6374 class="cmtt-8"> </span><span
6375 class="cmtt-8"> </span><span
6376 class="cmtt-8"> </span><span
6377 class="cmtt-8"> </span><span
6378 class="cmtt-8"> </span><span
6379 class="cmtt-8"> </span><span
6380 class="cmtt-8"> </span><span
6381 class="cmsy-8">}</span>
6382 <br class="fancyvrb" /><a
6383 id="x1-99054r27"></a><span
6384 class="cmr-6">27</span><span
6385 class="cmtt-8"> </span><span
6386 class="cmtt-8"> </span>
6387 <br class="fancyvrb" /><a
6388 id="x1-99056r28"></a><span
6389 class="cmr-6">28</span><span
6390 class="cmtt-8"> </span><span
6391 class="cmtt-8"> </span><span
6392 class="cmtt-8"> 13)</span><span
6393 class="cmtt-8"> [floor1_multiplier]</span><span
6394 class="cmtt-8"> =</span><span
6395 class="cmtt-8"> read</span><span
6396 class="cmtt-8"> 2</span><span
6397 class="cmtt-8"> bits</span><span
6398 class="cmtt-8"> as</span><span
6399 class="cmtt-8"> unsigned</span><span
6400 class="cmtt-8"> integer</span><span
6401 class="cmtt-8"> and</span><span
6402 class="cmtt-8"> add</span><span
6403 class="cmtt-8"> one</span>
6404 <br class="fancyvrb" /><a
6405 id="x1-99058r29"></a><span
6406 class="cmr-6">29</span><span
6407 class="cmtt-8"> </span><span
6408 class="cmtt-8"> </span><span
6409 class="cmtt-8"> 14)</span><span
6410 class="cmtt-8"> [rangebits]</span><span
6411 class="cmtt-8"> =</span><span
6412 class="cmtt-8"> read</span><span
6413 class="cmtt-8"> 4</span><span
6414 class="cmtt-8"> bits</span><span
6415 class="cmtt-8"> as</span><span
6416 class="cmtt-8"> unsigned</span><span
6417 class="cmtt-8"> integer</span>
6418 <br class="fancyvrb" /><a
6419 id="x1-99060r30"></a><span
6420 class="cmr-6">30</span><span
6421 class="cmtt-8"> </span><span
6422 class="cmtt-8"> </span><span
6423 class="cmtt-8"> 15)</span><span
6424 class="cmtt-8"> vector</span><span
6425 class="cmtt-8"> [floor1_X_list]</span><span
6426 class="cmtt-8"> element</span><span
6427 class="cmtt-8"> [0]</span><span
6428 class="cmtt-8"> =</span><span
6429 class="cmtt-8"> 0</span>
6430 <br class="fancyvrb" /><a
6431 id="x1-99062r31"></a><span
6432 class="cmr-6">31</span><span
6433 class="cmtt-8"> </span><span
6434 class="cmtt-8"> </span><span
6435 class="cmtt-8"> 16)</span><span
6436 class="cmtt-8"> vector</span><span
6437 class="cmtt-8"> [floor1_X_list]</span><span
6438 class="cmtt-8"> element</span><span
6439 class="cmtt-8"> [1]</span><span
6440 class="cmtt-8"> =</span><span
6441 class="cmtt-8"> 2</span><span
6442 class="cmtt-8"> exponent</span><span
6443 class="cmtt-8"> [rangebits];</span>
6444 <br class="fancyvrb" /><a
6445 id="x1-99064r32"></a><span
6446 class="cmr-6">32</span><span
6447 class="cmtt-8"> </span><span
6448 class="cmtt-8"> </span><span
6449 class="cmtt-8"> 17)</span><span
6450 class="cmtt-8"> [floor1_values]</span><span
6451 class="cmtt-8"> =</span><span
6452 class="cmtt-8"> 2</span>
6453 <br class="fancyvrb" /><a
6454 id="x1-99066r33"></a><span
6455 class="cmr-6">33</span><span
6456 class="cmtt-8"> </span><span
6457 class="cmtt-8"> </span><span
6458 class="cmtt-8"> 18)</span><span
6459 class="cmtt-8"> iterate</span><span
6460 class="cmtt-8"> [i]</span><span
6461 class="cmtt-8"> over</span><span
6462 class="cmtt-8"> the</span><span
6463 class="cmtt-8"> range</span><span
6464 class="cmtt-8"> 0</span><span
6465 class="cmtt-8"> ...</span><span
6466 class="cmtt-8"> [floor1_partitions]-1</span><span
6467 class="cmtt-8"> </span><span
6468 class="cmsy-8">{</span>
6469 <br class="fancyvrb" /><a
6470 id="x1-99068r34"></a><span
6471 class="cmr-6">34</span><span
6472 class="cmtt-8"> </span><span
6473 class="cmtt-8"> </span>
6474 <br class="fancyvrb" /><a
6475 id="x1-99070r35"></a><span
6476 class="cmr-6">35</span><span
6477 class="cmtt-8"> </span><span
6478 class="cmtt-8"> </span><span
6479 class="cmtt-8"> </span><span
6480 class="cmtt-8"> </span><span
6481 class="cmtt-8"> </span><span
6482 class="cmtt-8"> </span><span
6483 class="cmtt-8"> </span><span
6484 class="cmtt-8"> </span><span
6485 class="cmtt-8"> 19)</span><span
6486 class="cmtt-8"> [current_class_number]</span><span
6487 class="cmtt-8"> =</span><span
6488 class="cmtt-8"> vector</span><span
6489 class="cmtt-8"> [floor1_partition_class_list]</span><span
6490 class="cmtt-8"> element</span><span
6491 class="cmtt-8"> [i]</span>
6492 <br class="fancyvrb" /><a
6493 id="x1-99072r36"></a><span
6494 class="cmr-6">36</span><span
6495 class="cmtt-8"> </span><span
6496 class="cmtt-8"> </span><span
6497 class="cmtt-8"> </span><span
6498 class="cmtt-8"> </span><span
6499 class="cmtt-8"> </span><span
6500 class="cmtt-8"> </span><span
6501 class="cmtt-8"> </span><span
6502 class="cmtt-8"> </span><span
6503 class="cmtt-8"> 20)</span><span
6504 class="cmtt-8"> iterate</span><span
6505 class="cmtt-8"> [j]</span><span
6506 class="cmtt-8"> over</span><span
6507 class="cmtt-8"> the</span><span
6508 class="cmtt-8"> range</span><span
6509 class="cmtt-8"> 0</span><span
6510 class="cmtt-8"> ...</span><span
6511 class="cmtt-8"> ([floor1_class_dimensions]</span><span
6512 class="cmtt-8"> element</span><span
6513 class="cmtt-8"> [current_class_number])-1</span><span
6514 class="cmtt-8"> </span><span
6515 class="cmsy-8">{</span>
6516 <br class="fancyvrb" /><a
6517 id="x1-99074r37"></a><span
6518 class="cmr-6">37</span><span
6519 class="cmtt-8"> </span><span
6520 class="cmtt-8"> </span><span
6521 class="cmtt-8"> </span><span
6522 class="cmtt-8"> </span><span
6523 class="cmtt-8"> </span><span
6524 class="cmtt-8"> </span><span
6525 class="cmtt-8"> </span><span
6526 class="cmtt-8"> </span><span
6527 class="cmtt-8"> </span><span
6528 class="cmtt-8"> </span><span
6529 class="cmtt-8"> </span><span
6530 class="cmtt-8"> </span><span
6531 class="cmtt-8"> </span><span
6532 class="cmtt-8"> </span><span
6533 class="cmtt-8"> 21)</span><span
6534 class="cmtt-8"> vector</span><span
6535 class="cmtt-8"> [floor1_X_list]</span><span
6536 class="cmtt-8"> element</span><span
6537 class="cmtt-8"> ([floor1_values])</span><span
6538 class="cmtt-8"> =</span>
6539 <br class="fancyvrb" /><a
6540 id="x1-99076r38"></a><span
6541 class="cmr-6">38</span><span
6542 class="cmtt-8"> </span><span
6543 class="cmtt-8"> </span><span
6544 class="cmtt-8"> </span><span
6545 class="cmtt-8"> </span><span
6546 class="cmtt-8"> </span><span
6547 class="cmtt-8"> </span><span
6548 class="cmtt-8"> </span><span
6549 class="cmtt-8"> </span><span
6550 class="cmtt-8"> </span><span
6551 class="cmtt-8"> </span><span
6552 class="cmtt-8"> </span><span
6553 class="cmtt-8"> </span><span
6554 class="cmtt-8"> </span><span
6555 class="cmtt-8"> </span><span
6556 class="cmtt-8"> </span><span
6557 class="cmtt-8"> </span><span
6558 class="cmtt-8"> </span><span
6559 class="cmtt-8"> </span><span
6560 class="cmtt-8"> read</span><span
6561 class="cmtt-8"> [rangebits]</span><span
6562 class="cmtt-8"> bits</span><span
6563 class="cmtt-8"> as</span><span
6564 class="cmtt-8"> unsigned</span><span
6565 class="cmtt-8"> integer</span>
6566 <br class="fancyvrb" /><a
6567 id="x1-99078r39"></a><span
6568 class="cmr-6">39</span><span
6569 class="cmtt-8"> </span><span
6570 class="cmtt-8"> </span><span
6571 class="cmtt-8"> </span><span
6572 class="cmtt-8"> </span><span
6573 class="cmtt-8"> </span><span
6574 class="cmtt-8"> </span><span
6575 class="cmtt-8"> </span><span
6576 class="cmtt-8"> </span><span
6577 class="cmtt-8"> </span><span
6578 class="cmtt-8"> </span><span
6579 class="cmtt-8"> </span><span
6580 class="cmtt-8"> </span><span
6581 class="cmtt-8"> </span><span
6582 class="cmtt-8"> </span><span
6583 class="cmtt-8"> 22)</span><span
6584 class="cmtt-8"> increment</span><span
6585 class="cmtt-8"> [floor1_values]</span><span
6586 class="cmtt-8"> by</span><span
6587 class="cmtt-8"> one</span>
6588 <br class="fancyvrb" /><a
6589 id="x1-99080r40"></a><span
6590 class="cmr-6">40</span><span
6591 class="cmtt-8"> </span><span
6592 class="cmtt-8"> </span><span
6593 class="cmtt-8"> </span><span
6594 class="cmtt-8"> </span><span
6595 class="cmtt-8"> </span><span
6596 class="cmtt-8"> </span><span
6597 class="cmtt-8"> </span><span
6598 class="cmtt-8"> </span><span
6599 class="cmtt-8"> </span><span
6600 class="cmtt-8"> </span><span
6601 class="cmtt-8"> </span><span
6602 class="cmtt-8"> </span><span
6603 class="cmtt-8"> </span><span
6604 class="cmsy-8">}</span>
6605 <br class="fancyvrb" /><a
6606 id="x1-99082r41"></a><span
6607 class="cmr-6">41</span><span
6608 class="cmtt-8"> </span><span
6609 class="cmtt-8"> </span><span
6610 class="cmtt-8"> </span><span
6611 class="cmtt-8"> </span><span
6612 class="cmtt-8"> </span><span
6613 class="cmtt-8"> </span><span
6614 class="cmtt-8"> </span><span
6615 class="cmsy-8">}</span>
6616 <br class="fancyvrb" /><a
6617 id="x1-99084r42"></a><span
6618 class="cmr-6">42</span><span
6619 class="cmtt-8"> </span><span
6620 class="cmtt-8"> </span>
6621 <br class="fancyvrb" /><a
6622 id="x1-99086r43"></a><span
6623 class="cmr-6">43</span><span
6624 class="cmtt-8"> </span><span
6625 class="cmtt-8"> </span><span
6626 class="cmtt-8"> 23)</span><span
6627 class="cmtt-8"> done</span>
6629 <!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
6630 setup renders a stream undecodable. In addition, a <span
6631 class="cmtt-12">[floor1_class_masterbooks] </span>or
6633 class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook
6634 configured in this stream is an error condition that renders the stream undecodable. All vector
6635 [floor1_x_list] element values must be unique within the vector; a non-unique value renders the
6637 <!--l. 167--><p class="noindent" ><span class="paragraphHead"><a
6638 id="x1-1000007.2.2"></a><span
6639 class="cmbx-12">packet decode</span></span>
6643 Packet decode begins by checking the <span
6644 class="cmtt-12">[nonzero] </span>flag:
6645 <!--l. 171--><p class="noindent" >
6646 <div class="fancyvrb" id="fancyvrb29">
6648 id="x1-100002r1"></a><span
6649 class="cmr-6">1</span><span
6650 class="cmtt-8"> </span><span
6651 class="cmtt-8"> </span><span
6652 class="cmtt-8"> </span><span
6653 class="cmtt-8"> 1)</span><span
6654 class="cmtt-8"> [nonzero]</span><span
6655 class="cmtt-8"> =</span><span
6656 class="cmtt-8"> read</span><span
6657 class="cmtt-8"> 1</span><span
6658 class="cmtt-8"> bit</span><span
6659 class="cmtt-8"> as</span><span
6660 class="cmtt-8"> boolean</span>
6662 <!--l. 175--><p class="noindent" >If <span
6663 class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
6664 Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
6665 this frame. (A return status of ’unused’ is different from decoding a floor that has all
6666 points set to minimum representation amplitude, which happens to be approximately
6668 <!--l. 183--><p class="noindent" >Assuming <span
6669 class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
6670 <!--l. 185--><p class="noindent" >
6671 <div class="fancyvrb" id="fancyvrb30">
6673 id="x1-100004r1"></a><span
6674 class="cmr-6">1</span><span
6675 class="cmtt-8"> </span><span
6676 class="cmtt-8"> </span><span
6677 class="cmtt-8"> </span><span
6678 class="cmtt-8"> 1)</span><span
6679 class="cmtt-8"> [range]</span><span
6680 class="cmtt-8"> =</span><span
6681 class="cmtt-8"> vector</span><span
6682 class="cmtt-8"> </span><span
6683 class="cmsy-8">{</span><span
6684 class="cmtt-8"> 256,</span><span
6685 class="cmtt-8"> 128,</span><span
6686 class="cmtt-8"> 86,</span><span
6687 class="cmtt-8"> 64</span><span
6688 class="cmtt-8"> </span><span
6689 class="cmsy-8">}</span><span
6690 class="cmtt-8"> element</span><span
6691 class="cmtt-8"> ([floor1_multiplier]-1)</span>
6692 <br class="fancyvrb" /><a
6693 id="x1-100006r2"></a><span
6694 class="cmr-6">2</span><span
6695 class="cmtt-8"> </span><span
6696 class="cmtt-8"> </span><span
6697 class="cmtt-8"> </span><span
6698 class="cmtt-8"> 2)</span><span
6699 class="cmtt-8"> vector</span><span
6700 class="cmtt-8"> [floor1_Y]</span><span
6701 class="cmtt-8"> element</span><span
6702 class="cmtt-8"> [0]</span><span
6703 class="cmtt-8"> =</span><span
6704 class="cmtt-8"> read</span><span
6705 class="cmtt-8"> </span><a
6706 href="#x1-1170009.2.1"><span
6707 class="cmtt-8">ilog</span></a><span
6708 class="cmtt-8">([range]-1)</span><span
6709 class="cmtt-8"> bits</span><span
6710 class="cmtt-8"> as</span><span
6711 class="cmtt-8"> unsigned</span><span
6712 class="cmtt-8"> integer</span>
6713 <br class="fancyvrb" /><a
6714 id="x1-100008r3"></a><span
6715 class="cmr-6">3</span><span
6716 class="cmtt-8"> </span><span
6717 class="cmtt-8"> </span><span
6718 class="cmtt-8"> </span><span
6719 class="cmtt-8"> 3)</span><span
6720 class="cmtt-8"> vector</span><span
6721 class="cmtt-8"> [floor1_Y]</span><span
6722 class="cmtt-8"> element</span><span
6723 class="cmtt-8"> [1]</span><span
6724 class="cmtt-8"> =</span><span
6725 class="cmtt-8"> read</span><span
6726 class="cmtt-8"> </span><a
6727 href="#x1-1170009.2.1"><span
6728 class="cmtt-8">ilog</span></a><span
6729 class="cmtt-8">([range]-1)</span><span
6730 class="cmtt-8"> bits</span><span
6731 class="cmtt-8"> as</span><span
6732 class="cmtt-8"> unsigned</span><span
6733 class="cmtt-8"> integer</span>
6734 <br class="fancyvrb" /><a
6735 id="x1-100010r4"></a><span
6736 class="cmr-6">4</span><span
6737 class="cmtt-8"> </span><span
6738 class="cmtt-8"> </span><span
6739 class="cmtt-8"> </span><span
6740 class="cmtt-8"> 4)</span><span
6741 class="cmtt-8"> [offset]</span><span
6742 class="cmtt-8"> =</span><span
6743 class="cmtt-8"> 2;</span>
6744 <br class="fancyvrb" /><a
6745 id="x1-100012r5"></a><span
6746 class="cmr-6">5</span><span
6747 class="cmtt-8"> </span><span
6748 class="cmtt-8"> </span><span
6749 class="cmtt-8"> </span><span
6750 class="cmtt-8"> 5)</span><span
6751 class="cmtt-8"> iterate</span><span
6752 class="cmtt-8"> [i]</span><span
6753 class="cmtt-8"> over</span><span
6754 class="cmtt-8"> the</span><span
6755 class="cmtt-8"> range</span><span
6756 class="cmtt-8"> 0</span><span
6757 class="cmtt-8"> ...</span><span
6758 class="cmtt-8"> [floor1_partitions]-1</span><span
6759 class="cmtt-8"> </span><span
6760 class="cmsy-8">{</span>
6761 <br class="fancyvrb" /><a
6762 id="x1-100014r6"></a><span
6763 class="cmr-6">6</span><span
6764 class="cmtt-8"> </span><span
6765 class="cmtt-8"> </span>
6766 <br class="fancyvrb" /><a
6767 id="x1-100016r7"></a><span
6768 class="cmr-6">7</span><span
6769 class="cmtt-8"> </span><span
6770 class="cmtt-8"> </span><span
6771 class="cmtt-8"> </span><span
6772 class="cmtt-8"> </span><span
6773 class="cmtt-8"> </span><span
6774 class="cmtt-8"> </span><span
6775 class="cmtt-8"> </span><span
6776 class="cmtt-8"> </span><span
6777 class="cmtt-8"> 6)</span><span
6778 class="cmtt-8"> [class]</span><span
6779 class="cmtt-8"> =</span><span
6780 class="cmtt-8"> vector</span><span
6781 class="cmtt-8"> [floor1_partition_class]</span><span
6782 class="cmtt-8"> </span><span
6783 class="cmtt-8"> element</span><span
6784 class="cmtt-8"> [i]</span>
6785 <br class="fancyvrb" /><a
6786 id="x1-100018r8"></a><span
6787 class="cmr-6">8</span><span
6788 class="cmtt-8"> </span><span
6789 class="cmtt-8"> </span><span
6790 class="cmtt-8"> </span><span
6791 class="cmtt-8"> </span><span
6792 class="cmtt-8"> </span><span
6793 class="cmtt-8"> </span><span
6794 class="cmtt-8"> </span><span
6795 class="cmtt-8"> </span><span
6796 class="cmtt-8"> 7)</span><span
6797 class="cmtt-8"> [cdim]</span><span
6798 class="cmtt-8"> </span><span
6799 class="cmtt-8"> =</span><span
6800 class="cmtt-8"> vector</span><span
6801 class="cmtt-8"> [floor1_class_dimensions]</span><span
6802 class="cmtt-8"> element</span><span
6803 class="cmtt-8"> [class]</span>
6804 <br class="fancyvrb" /><a
6805 id="x1-100020r9"></a><span
6806 class="cmr-6">9</span><span
6807 class="cmtt-8"> </span><span
6808 class="cmtt-8"> </span><span
6809 class="cmtt-8"> </span><span
6810 class="cmtt-8"> </span><span
6811 class="cmtt-8"> </span><span
6812 class="cmtt-8"> </span><span
6813 class="cmtt-8"> </span><span
6814 class="cmtt-8"> </span><span
6815 class="cmtt-8"> 8)</span><span
6816 class="cmtt-8"> [cbits]</span><span
6817 class="cmtt-8"> =</span><span
6818 class="cmtt-8"> vector</span><span
6819 class="cmtt-8"> [floor1_class_subclasses]</span><span
6820 class="cmtt-8"> element</span><span
6821 class="cmtt-8"> [class]</span>
6822 <br class="fancyvrb" /><a
6823 id="x1-100022r10"></a><span
6824 class="cmr-6">10</span><span
6825 class="cmtt-8"> </span><span
6826 class="cmtt-8"> </span><span
6827 class="cmtt-8"> </span><span
6828 class="cmtt-8"> </span><span
6829 class="cmtt-8"> </span><span
6830 class="cmtt-8"> </span><span
6831 class="cmtt-8"> </span><span
6832 class="cmtt-8"> </span><span
6833 class="cmtt-8"> 9)</span><span
6834 class="cmtt-8"> [csub]</span><span
6835 class="cmtt-8"> </span><span
6836 class="cmtt-8"> =</span><span
6837 class="cmtt-8"> (2</span><span
6838 class="cmtt-8"> exponent</span><span
6839 class="cmtt-8"> [cbits])-1</span>
6840 <br class="fancyvrb" /><a
6841 id="x1-100024r11"></a><span
6842 class="cmr-6">11</span><span
6843 class="cmtt-8"> </span><span
6844 class="cmtt-8"> </span><span
6845 class="cmtt-8"> </span><span
6846 class="cmtt-8"> </span><span
6847 class="cmtt-8"> </span><span
6848 class="cmtt-8"> </span><span
6849 class="cmtt-8"> </span><span
6850 class="cmtt-8"> 10)</span><span
6851 class="cmtt-8"> [cval]</span><span
6852 class="cmtt-8"> </span><span
6853 class="cmtt-8"> =</span><span
6854 class="cmtt-8"> 0</span>
6855 <br class="fancyvrb" /><a
6856 id="x1-100026r12"></a><span
6857 class="cmr-6">12</span><span
6858 class="cmtt-8"> </span><span
6859 class="cmtt-8"> </span><span
6860 class="cmtt-8"> </span><span
6861 class="cmtt-8"> </span><span
6862 class="cmtt-8"> </span><span
6863 class="cmtt-8"> </span><span
6864 class="cmtt-8"> </span><span
6865 class="cmtt-8"> 11)</span><span
6866 class="cmtt-8"> if</span><span
6867 class="cmtt-8"> (</span><span
6868 class="cmtt-8"> [cbits]</span><span
6869 class="cmtt-8"> is</span><span
6870 class="cmtt-8"> greater</span><span
6871 class="cmtt-8"> than</span><span
6872 class="cmtt-8"> zero</span><span
6873 class="cmtt-8"> )</span><span
6874 class="cmtt-8"> </span><span
6875 class="cmsy-8">{</span>
6876 <br class="fancyvrb" /><a
6877 id="x1-100028r13"></a><span
6878 class="cmr-6">13</span><span
6879 class="cmtt-8"> </span><span
6880 class="cmtt-8"> </span>
6881 <br class="fancyvrb" /><a
6882 id="x1-100030r14"></a><span
6883 class="cmr-6">14</span><span
6884 class="cmtt-8"> </span><span
6885 class="cmtt-8"> </span><span
6886 class="cmtt-8"> </span><span
6887 class="cmtt-8"> </span><span
6888 class="cmtt-8"> </span><span
6889 class="cmtt-8"> </span><span
6890 class="cmtt-8"> </span><span
6891 class="cmtt-8"> </span><span
6892 class="cmtt-8"> </span><span
6893 class="cmtt-8"> </span><span
6894 class="cmtt-8"> </span><span
6895 class="cmtt-8"> </span><span
6896 class="cmtt-8"> </span><span
6897 class="cmtt-8"> </span><span
6898 class="cmtt-8"> 12)</span><span
6899 class="cmtt-8"> [cval]</span><span
6900 class="cmtt-8"> =</span><span
6901 class="cmtt-8"> read</span><span
6902 class="cmtt-8"> from</span><span
6903 class="cmtt-8"> packet</span><span
6904 class="cmtt-8"> using</span><span
6905 class="cmtt-8"> codebook</span><span
6906 class="cmtt-8"> number</span>
6907 <br class="fancyvrb" /><a
6908 id="x1-100032r15"></a><span
6909 class="cmr-6">15</span><span
6910 class="cmtt-8"> </span><span
6911 class="cmtt-8"> </span><span
6912 class="cmtt-8"> </span><span
6913 class="cmtt-8"> </span><span
6914 class="cmtt-8"> </span><span
6915 class="cmtt-8"> </span><span
6916 class="cmtt-8"> </span><span
6917 class="cmtt-8"> </span><span
6918 class="cmtt-8"> </span><span
6919 class="cmtt-8"> </span><span
6920 class="cmtt-8"> </span><span
6921 class="cmtt-8"> </span><span
6922 class="cmtt-8"> </span><span
6923 class="cmtt-8"> </span><span
6924 class="cmtt-8"> </span><span
6925 class="cmtt-8"> </span><span
6926 class="cmtt-8"> </span><span
6927 class="cmtt-8"> </span><span
6928 class="cmtt-8"> (vector</span><span
6929 class="cmtt-8"> [floor1_class_masterbooks]</span><span
6930 class="cmtt-8"> element</span><span
6931 class="cmtt-8"> [class])</span><span
6932 class="cmtt-8"> in</span><span
6933 class="cmtt-8"> scalar</span><span
6934 class="cmtt-8"> context</span>
6935 <br class="fancyvrb" /><a
6936 id="x1-100034r16"></a><span
6937 class="cmr-6">16</span><span
6938 class="cmtt-8"> </span><span
6939 class="cmtt-8"> </span><span
6940 class="cmtt-8"> </span><span
6941 class="cmtt-8"> </span><span
6942 class="cmtt-8"> </span><span
6943 class="cmtt-8"> </span><span
6944 class="cmtt-8"> </span><span
6945 class="cmtt-8"> </span><span
6946 class="cmtt-8"> </span><span
6947 class="cmtt-8"> </span><span
6948 class="cmtt-8"> </span><span
6949 class="cmtt-8"> </span><span
6950 class="cmsy-8">}</span>
6951 <br class="fancyvrb" /><a
6952 id="x1-100036r17"></a><span
6953 class="cmr-6">17</span><span
6954 class="cmtt-8"> </span><span
6955 class="cmtt-8"> </span>
6956 <br class="fancyvrb" /><a
6957 id="x1-100038r18"></a><span
6958 class="cmr-6">18</span><span
6959 class="cmtt-8"> </span><span
6960 class="cmtt-8"> </span><span
6961 class="cmtt-8"> </span><span
6962 class="cmtt-8"> </span><span
6963 class="cmtt-8"> </span><span
6964 class="cmtt-8"> </span><span
6965 class="cmtt-8"> </span><span
6966 class="cmtt-8"> 13)</span><span
6967 class="cmtt-8"> iterate</span><span
6968 class="cmtt-8"> [j]</span><span
6969 class="cmtt-8"> over</span><span
6970 class="cmtt-8"> the</span><span
6971 class="cmtt-8"> range</span><span
6972 class="cmtt-8"> 0</span><span
6973 class="cmtt-8"> ...</span><span
6974 class="cmtt-8"> [cdim]-1</span><span
6975 class="cmtt-8"> </span><span
6976 class="cmsy-8">{</span>
6977 <br class="fancyvrb" /><a
6978 id="x1-100040r19"></a><span
6979 class="cmr-6">19</span><span
6980 class="cmtt-8"> </span><span
6981 class="cmtt-8"> </span>
6982 <br class="fancyvrb" /><a
6983 id="x1-100042r20"></a><span
6984 class="cmr-6">20</span><span
6985 class="cmtt-8"> </span><span
6986 class="cmtt-8"> </span><span
6987 class="cmtt-8"> </span><span
6988 class="cmtt-8"> </span><span
6989 class="cmtt-8"> </span><span
6990 class="cmtt-8"> </span><span
6991 class="cmtt-8"> </span><span
6992 class="cmtt-8"> </span><span
6993 class="cmtt-8"> </span><span
6994 class="cmtt-8"> </span><span
6995 class="cmtt-8"> </span><span
6996 class="cmtt-8"> </span><span
6997 class="cmtt-8"> </span><span
6998 class="cmtt-8"> </span><span
6999 class="cmtt-8"> 14)</span><span
7000 class="cmtt-8"> [book]</span><span
7001 class="cmtt-8"> =</span><span
7002 class="cmtt-8"> array</span><span
7003 class="cmtt-8"> [floor1_subclass_books]</span><span
7004 class="cmtt-8"> element</span><span
7005 class="cmtt-8"> [class],([cval]</span><span
7006 class="cmtt-8"> bitwise</span><span
7007 class="cmtt-8"> AND</span><span
7008 class="cmtt-8"> [csub])</span>
7009 <br class="fancyvrb" /><a
7010 id="x1-100044r21"></a><span
7011 class="cmr-6">21</span><span
7012 class="cmtt-8"> </span><span
7013 class="cmtt-8"> </span><span
7014 class="cmtt-8"> </span><span
7015 class="cmtt-8"> </span><span
7016 class="cmtt-8"> </span><span
7017 class="cmtt-8"> </span><span
7018 class="cmtt-8"> </span><span
7019 class="cmtt-8"> </span><span
7020 class="cmtt-8"> </span><span
7021 class="cmtt-8"> </span><span
7022 class="cmtt-8"> </span><span
7023 class="cmtt-8"> </span><span
7024 class="cmtt-8"> </span><span
7025 class="cmtt-8"> </span><span
7026 class="cmtt-8"> 15)</span><span
7027 class="cmtt-8"> [cval]</span><span
7028 class="cmtt-8"> =</span><span
7029 class="cmtt-8"> [cval]</span><span
7030 class="cmtt-8"> right</span><span
7031 class="cmtt-8"> shifted</span><span
7032 class="cmtt-8"> [cbits]</span><span
7033 class="cmtt-8"> bits</span>
7034 <br class="fancyvrb" /><a
7035 id="x1-100046r22"></a><span
7036 class="cmr-6">22</span><span
7037 class="cmtt-8"> </span><span
7038 class="cmtt-8">  </span><span
7039 class="cmtt-8"> </span><span
7040 class="cmtt-8"> </span><span
7041 class="cmtt-8"> </span><span
7042 class="cmtt-8"> </span><span
7043 class="cmtt-8"> 16)</span><span
7044 class="cmtt-8"> if</span><span
7045 class="cmtt-8"> (</span><span
7046 class="cmtt-8"> [book]</span><span
7047 class="cmtt-8"> is</span><span
7048 class="cmtt-8"> not</span><span
7049 class="cmtt-8"> less</span><span
7050 class="cmtt-8"> than</span><span
7051 class="cmtt-8"> zero</span><span
7052 class="cmtt-8"> )</span><span
7053 class="cmtt-8"> </span><span
7054 class="cmsy-8">{</span>
7055 <br class="fancyvrb" /><a
7056 id="x1-100048r23"></a><span
7057 class="cmr-6">23</span><span
7058 class="cmtt-8"> </span><span
7059 class="cmtt-8"> </span>
7060 <br class="fancyvrb" /><a
7061 id="x1-100050r24"></a><span
7062 class="cmr-6">24</span><span
7063 class="cmtt-8"> </span><span
7064 class="cmtt-8">  </span><span
7065 class="cmtt-8"> </span><span
7066 class="cmtt-8"> </span><span
7067 class="cmtt-8"> </span><span
7068 class="cmtt-8"> </span><span
7069 class="cmtt-8"> </span><span
7070 class="cmtt-8"> </span><span
7071 class="cmtt-8"> </span><span
7072 class="cmtt-8"> </span><span
7073 class="cmtt-8"> </span><span
7074 class="cmtt-8"> </span><span
7075 class="cmtt-8"> 17)</span><span
7076 class="cmtt-8"> vector</span><span
7077 class="cmtt-8"> [floor1_Y]</span><span
7078 class="cmtt-8"> element</span><span
7079 class="cmtt-8"> ([j]+[offset])</span><span
7080 class="cmtt-8"> =</span><span
7081 class="cmtt-8"> read</span><span
7082 class="cmtt-8"> from</span><span
7083 class="cmtt-8"> packet</span><span
7084 class="cmtt-8"> using</span><span
7085 class="cmtt-8"> codebook</span>
7086 <br class="fancyvrb" /><a
7087 id="x1-100052r25"></a><span
7088 class="cmr-6">25</span><span
7089 class="cmtt-8"> </span><span
7090 class="cmtt-8"> </span><span
7091 class="cmtt-8"> </span><span
7092 class="cmtt-8"> </span><span
7093 class="cmtt-8"> </span><span
7094 class="cmtt-8"> </span><span
7095 class="cmtt-8"> </span><span
7096 class="cmtt-8"> </span><span
7097 class="cmtt-8"> </span><span
7098 class="cmtt-8"> </span><span
7099 class="cmtt-8"> </span><span
7100 class="cmtt-8"> </span><span
7101 class="cmtt-8"> </span><span
7102 class="cmtt-8"> </span><span
7103 class="cmtt-8"> </span><span
7104 class="cmtt-8"> </span><span
7105 class="cmtt-8"> </span><span
7106 class="cmtt-8"> </span><span
7107 class="cmtt-8"> </span><span
7108 class="cmtt-8"> </span><span
7109 class="cmtt-8"> </span><span
7110 class="cmtt-8"> </span><span
7111 class="cmtt-8"> </span><span
7112 class="cmtt-8"> </span><span
7113 class="cmtt-8"> [book]</span><span
7114 class="cmtt-8"> in</span><span
7115 class="cmtt-8"> scalar</span><span
7116 class="cmtt-8"> context</span>
7117 <br class="fancyvrb" /><a
7118 id="x1-100054r26"></a><span
7119 class="cmr-6">26</span><span
7120 class="cmtt-8"> </span><span
7121 class="cmtt-8"> </span>
7122 <br class="fancyvrb" /><a
7123 id="x1-100056r27"></a><span
7124 class="cmr-6">27</span><span
7125 class="cmtt-8"> </span><span
7126 class="cmtt-8"> </span><span
7127 class="cmtt-8"> </span><span
7128 class="cmtt-8"> </span><span
7129 class="cmtt-8"> </span><span
7130 class="cmtt-8"> </span><span
7131 class="cmtt-8"> </span><span
7132 class="cmtt-8"> </span><span
7133 class="cmtt-8"> </span><span
7134 class="cmtt-8"> </span><span
7135 class="cmtt-8"> </span><span
7136 class="cmtt-8"> </span><span
7137 class="cmtt-8"> </span><span
7138 class="cmtt-8"> </span><span
7139 class="cmtt-8"> </span><span
7140 class="cmtt-8"> </span><span
7141 class="cmtt-8"> </span><span
7142 class="cmtt-8"> </span><span
7143 class="cmtt-8"> </span><span
7144 class="cmsy-8">}</span><span
7145 class="cmtt-8"> else</span><span
7146 class="cmtt-8"> [book]</span><span
7147 class="cmtt-8"> is</span><span
7148 class="cmtt-8"> less</span><span
7149 class="cmtt-8"> than</span><span
7150 class="cmtt-8"> zero</span><span
7151 class="cmtt-8"> </span><span
7152 class="cmsy-8">{</span>
7153 <br class="fancyvrb" /><a
7154 id="x1-100058r28"></a><span
7155 class="cmr-6">28</span><span
7156 class="cmtt-8"> </span><span
7157 class="cmtt-8"> </span>
7158 <br class="fancyvrb" /><a
7159 id="x1-100060r29"></a><span
7160 class="cmr-6">29</span><span
7161 class="cmtt-8"> </span><span
7162 class="cmtt-8">  </span><span
7163 class="cmtt-8"> </span><span
7164 class="cmtt-8"> </span><span
7165 class="cmtt-8"> </span><span
7166 class="cmtt-8"> </span><span
7167 class="cmtt-8"> </span><span
7168 class="cmtt-8"> </span><span
7169 class="cmtt-8"> </span><span
7170 class="cmtt-8"> </span><span
7171 class="cmtt-8"> </span><span
7172 class="cmtt-8"> </span><span
7173 class="cmtt-8"> 18)</span><span
7174 class="cmtt-8"> vector</span><span
7175 class="cmtt-8"> [floor1_Y]</span><span
7176 class="cmtt-8"> element</span><span
7177 class="cmtt-8"> ([j]+[offset])</span><span
7178 class="cmtt-8"> =</span><span
7179 class="cmtt-8"> 0</span>
7180 <br class="fancyvrb" /><a
7181 id="x1-100062r30"></a><span
7182 class="cmr-6">30</span><span
7183 class="cmtt-8"> </span><span
7184 class="cmtt-8"> </span>
7185 <br class="fancyvrb" /><a
7186 id="x1-100064r31"></a><span
7187 class="cmr-6">31</span><span
7188 class="cmtt-8"> </span><span
7189 class="cmtt-8"> </span><span
7190 class="cmtt-8"> </span><span
7191 class="cmtt-8"> </span><span
7192 class="cmtt-8"> </span><span
7193 class="cmtt-8"> </span><span
7194 class="cmtt-8"> </span><span
7195 class="cmtt-8"> </span><span
7196 class="cmtt-8"> </span><span
7197 class="cmtt-8"> </span><span
7198 class="cmtt-8"> </span><span
7199 class="cmtt-8"> </span><span
7200 class="cmtt-8"> </span><span
7201 class="cmtt-8"> </span><span
7202 class="cmtt-8"> </span><span
7203 class="cmtt-8"> </span><span
7204 class="cmtt-8"> </span><span
7205 class="cmtt-8"> </span><span
7206 class="cmtt-8"> </span><span
7207 class="cmsy-8">}</span>
7208 <br class="fancyvrb" /><a
7209 id="x1-100066r32"></a><span
7210 class="cmr-6">32</span><span
7211 class="cmtt-8"> </span><span
7212 class="cmtt-8"> </span><span
7213 class="cmtt-8"> </span><span
7214 class="cmtt-8"> </span><span
7215 class="cmtt-8"> </span><span
7216 class="cmtt-8"> </span><span
7217 class="cmtt-8"> </span><span
7218 class="cmtt-8"> </span><span
7219 class="cmtt-8"> </span><span
7220 class="cmtt-8"> </span><span
7221 class="cmtt-8"> </span><span
7222 class="cmtt-8"> </span><span
7223 class="cmsy-8">}</span>
7224 <br class="fancyvrb" /><a
7225 id="x1-100068r33"></a><span
7226 class="cmr-6">33</span><span
7227 class="cmtt-8"> </span><span
7228 class="cmtt-8"> </span>
7229 <br class="fancyvrb" /><a
7230 id="x1-100070r34"></a><span
7231 class="cmr-6">34</span><span
7232 class="cmtt-8"> </span><span
7233 class="cmtt-8"> </span><span
7234 class="cmtt-8"> </span><span
7235 class="cmtt-8"> </span><span
7236 class="cmtt-8"> </span><span
7237 class="cmtt-8"> </span><span
7238 class="cmtt-8"> </span><span
7239 class="cmtt-8"> 19)</span><span
7240 class="cmtt-8"> [offset]</span><span
7241 class="cmtt-8"> =</span><span
7242 class="cmtt-8"> [offset]</span><span
7243 class="cmtt-8"> +</span><span
7244 class="cmtt-8"> [cdim]</span>
7245 <br class="fancyvrb" /><a
7246 id="x1-100072r35"></a><span
7247 class="cmr-6">35</span><span
7248 class="cmtt-8"> </span><span
7249 class="cmtt-8"> </span>
7250 <br class="fancyvrb" /><a
7251 id="x1-100074r36"></a><span
7252 class="cmr-6">36</span><span
7253 class="cmtt-8"> </span><span
7254 class="cmtt-8"> </span><span
7255 class="cmtt-8"> </span><span
7256 class="cmtt-8"> </span><span
7257 class="cmtt-8"> </span><span
7258 class="cmtt-8"> </span><span
7259 class="cmtt-8"> </span><span
7260 class="cmsy-8">}</span>
7261 <br class="fancyvrb" /><a
7262 id="x1-100076r37"></a><span
7263 class="cmr-6">37</span><span
7264 class="cmtt-8"> </span><span
7265 class="cmtt-8"> </span>
7266 <br class="fancyvrb" /><a
7267 id="x1-100078r38"></a><span
7268 class="cmr-6">38</span><span
7269 class="cmtt-8"> </span><span
7270 class="cmtt-8"> </span><span
7271 class="cmtt-8"> 20)</span><span
7272 class="cmtt-8"> done</span>
7277 <!--l. 226--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
7278 end-of-packet is reached during any read operation above, floor decode is to return ’unused’
7279 status as if the <span
7280 class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
7281 <!--l. 232--><p class="noindent" >Vector <span
7282 class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
7283 <!--l. 237--><p class="noindent" ><span class="paragraphHead"><a
7284 id="x1-1010007.2.2"></a><span
7285 class="cmbx-12">curve computation</span></span>
7286 Curve computation is split into two logical steps; the first step derives final Y amplitude values
7287 from the encoded, wrapped difference values taken from the bitstream. The second step
7288 plots the curve lines. Also, although zero-difference values are used in the iterative
7289 prediction to find final Y values, these points are conditionally skipped during final
7290 line computation in step two. Skipping zero-difference values allows a smoother line
7292 <!--l. 247--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations,
7293 implementors are warned to follow the details closely. Deviation from implementing a strictly
7294 equivalent algorithm can result in serious decoding errors.
7295 <!--l. 253--><p class="noindent" >
7296 <dl class="description"><dt class="description">
7298 class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd
7299 class="description">
7300 <!--l. 255--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference
7301 values, then apply to line prediction.
7302 <!--l. 258--><p class="noindent" >
7303 <div class="fancyvrb" id="fancyvrb31">
7305 id="x1-101002r1"></a><span
7306 class="cmr-6">1</span><span
7307 class="cmtt-8"> </span><span
7308 class="cmtt-8"> </span><span
7309 class="cmtt-8"> </span><span
7310 class="cmtt-8"> 1)</span><span
7311 class="cmtt-8"> [range]</span><span
7312 class="cmtt-8"> =</span><span
7313 class="cmtt-8"> vector</span><span
7314 class="cmtt-8"> </span><span
7315 class="cmsy-8">{</span><span
7316 class="cmtt-8"> 256,</span><span
7317 class="cmtt-8"> 128,</span><span
7318 class="cmtt-8"> 86,</span><span
7319 class="cmtt-8"> 64</span><span
7320 class="cmtt-8"> </span><span
7321 class="cmsy-8">}</span><span
7322 class="cmtt-8"> element</span><span
7323 class="cmtt-8"> ([floor1_multiplier]-1)</span>
7324 <br class="fancyvrb" /><a
7325 id="x1-101004r2"></a><span
7326 class="cmr-6">2</span><span
7327 class="cmtt-8"> </span><span
7328 class="cmtt-8"> </span><span
7329 class="cmtt-8"> </span><span
7330 class="cmtt-8"> 2)</span><span
7331 class="cmtt-8"> vector</span><span
7332 class="cmtt-8"> [floor1_step2_flag]</span><span
7333 class="cmtt-8"> element</span><span
7334 class="cmtt-8"> [0]</span><span
7335 class="cmtt-8"> =</span><span
7336 class="cmtt-8"> set</span>
7337 <br class="fancyvrb" /><a
7338 id="x1-101006r3"></a><span
7339 class="cmr-6">3</span><span
7340 class="cmtt-8"> </span><span
7341 class="cmtt-8"> </span><span
7342 class="cmtt-8"> </span><span
7343 class="cmtt-8"> 3)</span><span
7344 class="cmtt-8"> vector</span><span
7345 class="cmtt-8"> [floor1_step2_flag]</span><span
7346 class="cmtt-8"> element</span><span
7347 class="cmtt-8"> [1]</span><span
7348 class="cmtt-8"> =</span><span
7349 class="cmtt-8"> set</span>
7350 <br class="fancyvrb" /><a
7351 id="x1-101008r4"></a><span
7352 class="cmr-6">4</span><span
7353 class="cmtt-8"> </span><span
7354 class="cmtt-8"> </span><span
7355 class="cmtt-8"> </span><span
7356 class="cmtt-8"> 4)</span><span
7357 class="cmtt-8"> vector</span><span
7358 class="cmtt-8"> [floor1_final_Y]</span><span
7359 class="cmtt-8"> element</span><span
7360 class="cmtt-8"> [0]</span><span
7361 class="cmtt-8"> =</span><span
7362 class="cmtt-8"> vector</span><span
7363 class="cmtt-8"> [floor1_Y]</span><span
7364 class="cmtt-8"> element</span><span
7365 class="cmtt-8"> [0]</span>
7366 <br class="fancyvrb" /><a
7367 id="x1-101010r5"></a><span
7368 class="cmr-6">5</span><span
7369 class="cmtt-8"> </span><span
7370 class="cmtt-8"> </span><span
7371 class="cmtt-8"> </span><span
7372 class="cmtt-8"> 5)</span><span
7373 class="cmtt-8"> vector</span><span
7374 class="cmtt-8"> [floor1_final_Y]</span><span
7375 class="cmtt-8"> element</span><span
7376 class="cmtt-8"> [1]</span><span
7377 class="cmtt-8"> =</span><span
7378 class="cmtt-8"> vector</span><span
7379 class="cmtt-8"> [floor1_Y]</span><span
7380 class="cmtt-8"> element</span><span
7381 class="cmtt-8"> [1]</span>
7382 <br class="fancyvrb" /><a
7383 id="x1-101012r6"></a><span
7384 class="cmr-6">6</span><span
7385 class="cmtt-8"> </span><span
7386 class="cmtt-8"> </span><span
7387 class="cmtt-8"> </span><span
7388 class="cmtt-8"> 6)</span><span
7389 class="cmtt-8"> iterate</span><span
7390 class="cmtt-8"> [i]</span><span
7391 class="cmtt-8"> over</span><span
7392 class="cmtt-8"> the</span><span
7393 class="cmtt-8"> range</span><span
7394 class="cmtt-8"> 2</span><span
7395 class="cmtt-8"> ...</span><span
7396 class="cmtt-8"> [floor1_values]-1</span><span
7397 class="cmtt-8"> </span><span
7398 class="cmsy-8">{</span>
7399 <br class="fancyvrb" /><a
7400 id="x1-101014r7"></a><span
7401 class="cmr-6">7</span><span
7402 class="cmtt-8"> </span><span
7403 class="cmtt-8"> </span>
7404 <br class="fancyvrb" /><a
7405 id="x1-101016r8"></a><span
7406 class="cmr-6">8</span><span
7407 class="cmtt-8"> </span><span
7408 class="cmtt-8"> </span><span
7409 class="cmtt-8"> </span><span
7410 class="cmtt-8"> </span><span
7411 class="cmtt-8"> </span><span
7412 class="cmtt-8"> </span><span
7413 class="cmtt-8"> </span><span
7414 class="cmtt-8"> </span><span
7415 class="cmtt-8"> 7)</span><span
7416 class="cmtt-8"> [low_neighbor_offset]</span><span
7417 class="cmtt-8"> =</span><span
7418 class="cmtt-8"> </span><a
7419 href="#x1-1200009.2.4"><span
7420 class="cmtt-8">low_neighbor</span></a><span
7421 class="cmtt-8">([floor1_X_list],[i])</span>
7422 <br class="fancyvrb" /><a
7423 id="x1-101018r9"></a><span
7424 class="cmr-6">9</span><span
7425 class="cmtt-8"> </span><span
7426 class="cmtt-8"> </span><span
7427 class="cmtt-8"> </span><span
7428 class="cmtt-8"> </span><span
7429 class="cmtt-8"> </span><span
7430 class="cmtt-8"> </span><span
7431 class="cmtt-8"> </span><span
7432 class="cmtt-8"> </span><span
7433 class="cmtt-8"> 8)</span><span
7434 class="cmtt-8"> [high_neighbor_offset]</span><span
7435 class="cmtt-8"> =</span><span
7436 class="cmtt-8"> </span><a
7437 href="#x1-1210009.2.5"><span
7438 class="cmtt-8">high_neighbor</span></a><span
7439 class="cmtt-8">([floor1_X_list],[i])</span>
7440 <br class="fancyvrb" /><a
7441 id="x1-101020r10"></a><span
7442 class="cmr-6">10</span><span
7443 class="cmtt-8"> </span><span
7444 class="cmtt-8"> </span>
7445 <br class="fancyvrb" /><a
7446 id="x1-101022r11"></a><span
7447 class="cmr-6">11</span><span
7448 class="cmtt-8"> </span><span
7449 class="cmtt-8"> </span><span
7450 class="cmtt-8"> </span><span
7451 class="cmtt-8"> </span><span
7452 class="cmtt-8"> </span><span
7453 class="cmtt-8"> </span><span
7454 class="cmtt-8"> </span><span
7455 class="cmtt-8"> </span><span
7456 class="cmtt-8"> 9)</span><span
7457 class="cmtt-8"> [predicted]</span><span
7458 class="cmtt-8"> =</span><span
7459 class="cmtt-8"> </span><a
7460 href="#x1-1220009.2.6"><span
7461 class="cmtt-8">render_point</span></a><span
7462 class="cmtt-8">(</span><span
7463 class="cmtt-8"> vector</span><span
7464 class="cmtt-8"> [floor1_X_list]</span><span
7465 class="cmtt-8"> element</span><span
7466 class="cmtt-8"> [low_neighbor_offset],</span>
7467 <br class="fancyvrb" /><a
7468 id="x1-101024r12"></a><span
7469 class="cmr-6">12</span><span
7470 class="cmtt-8"> </span><span
7471 class="cmtt-8">  </span><span
7472 class="cmtt-8"> </span><span
7473 class="cmtt-8"> </span><span
7474 class="cmtt-8"> </span><span
7475 class="cmtt-8"> </span><span
7476 class="cmtt-8"> </span><span
7477 class="cmtt-8"> vector</span><span
7478 class="cmtt-8"> [floor1_final_Y]</span><span
7479 class="cmtt-8"> element</span><span
7480 class="cmtt-8"> [low_neighbor_offset],</span>
7481 <br class="fancyvrb" /><a
7482 id="x1-101026r13"></a><span
7483 class="cmr-6">13</span><span
7484 class="cmtt-8"> </span><span
7485 class="cmtt-8"> </span><span
7486 class="cmtt-8"> </span><span
7487 class="cmtt-8"> </span><span
7488 class="cmtt-8"> </span><span
7489 class="cmtt-8"> </span><span
7490 class="cmtt-8"> </span><span
7491 class="cmtt-8"> </span><span
7492 class="cmtt-8"> </span><span
7493 class="cmtt-8"> </span><span
7494 class="cmtt-8"> </span><span
7495 class="cmtt-8"> </span><span
7496 class="cmtt-8"> </span><span
7497 class="cmtt-8"> </span><span
7498 class="cmtt-8"> </span><span
7499 class="cmtt-8"> </span><span
7500 class="cmtt-8"> </span><span
7501 class="cmtt-8"> </span><span
7502 class="cmtt-8"> </span><span
7503 class="cmtt-8"> </span><span
7504 class="cmtt-8"> </span><span
7505 class="cmtt-8"> </span><span
7506 class="cmtt-8"> </span><span
7507 class="cmtt-8"> </span><span
7508 class="cmtt-8"> </span><span
7509 class="cmtt-8"> </span><span
7510 class="cmtt-8"> </span><span
7511 class="cmtt-8"> </span><span
7512 class="cmtt-8"> </span><span
7513 class="cmtt-8"> </span><span
7514 class="cmtt-8"> </span><span
7515 class="cmtt-8"> </span><span
7516 class="cmtt-8"> </span><span
7517 class="cmtt-8"> </span><span
7518 class="cmtt-8"> </span><span
7519 class="cmtt-8"> </span><span
7520 class="cmtt-8"> </span><span
7521 class="cmtt-8"> </span><span
7522 class="cmtt-8"> </span><span
7523 class="cmtt-8"> vector</span><span
7524 class="cmtt-8"> [floor1_X_list]</span><span
7525 class="cmtt-8"> element</span><span
7526 class="cmtt-8"> [high_neighbor_offset],</span>
7527 <br class="fancyvrb" /><a
7528 id="x1-101028r14"></a><span
7529 class="cmr-6">14</span><span
7530 class="cmtt-8"> </span><span
7531 class="cmtt-8">  </span><span
7532 class="cmtt-8"> </span><span
7533 class="cmtt-8"> </span><span
7534 class="cmtt-8"> </span><span
7535 class="cmtt-8"> </span><span
7536 class="cmtt-8"> </span><span
7537 class="cmtt-8"> vector</span><span
7538 class="cmtt-8"> [floor1_final_Y]</span><span
7539 class="cmtt-8"> element</span><span
7540 class="cmtt-8"> [high_neighbor_offset],</span>
7541 <br class="fancyvrb" /><a
7542 id="x1-101030r15"></a><span
7543 class="cmr-6">15</span><span
7544 class="cmtt-8"> </span><span
7545 class="cmtt-8"> </span><span
7546 class="cmtt-8"> </span><span
7547 class="cmtt-8"> </span><span
7548 class="cmtt-8"> </span><span
7549 class="cmtt-8"> </span><span
7550 class="cmtt-8"> </span><span
7551 class="cmtt-8"> </span><span
7552 class="cmtt-8"> </span><span
7553 class="cmtt-8"> </span><span
7554 class="cmtt-8"> </span><span
7555 class="cmtt-8"> </span><span
7556 class="cmtt-8"> </span><span
7557 class="cmtt-8"> </span><span
7558 class="cmtt-8"> </span><span
7559 class="cmtt-8"> </span><span
7560 class="cmtt-8"> </span><span
7561 class="cmtt-8"> </span><span
7562 class="cmtt-8"> </span><span
7563 class="cmtt-8"> </span><span
7564 class="cmtt-8"> </span><span
7565 class="cmtt-8"> </span><span
7566 class="cmtt-8"> </span><span
7567 class="cmtt-8"> </span><span
7568 class="cmtt-8"> </span><span
7569 class="cmtt-8"> </span><span
7570 class="cmtt-8"> </span><span
7571 class="cmtt-8"> </span><span
7572 class="cmtt-8"> </span><span
7573 class="cmtt-8"> </span><span
7574 class="cmtt-8"> </span><span
7575 class="cmtt-8"> </span><span
7576 class="cmtt-8"> </span><span
7577 class="cmtt-8"> </span><span
7578 class="cmtt-8"> </span><span
7579 class="cmtt-8"> </span><span
7580 class="cmtt-8"> </span><span
7581 class="cmtt-8"> </span><span
7582 class="cmtt-8"> </span><span
7583 class="cmtt-8"> vector</span><span
7584 class="cmtt-8"> [floor1_X_list]</span><span
7585 class="cmtt-8"> element</span><span
7586 class="cmtt-8"> [i]</span><span
7587 class="cmtt-8"> )</span>
7588 <br class="fancyvrb" /><a
7589 id="x1-101032r16"></a><span
7590 class="cmr-6">16</span><span
7591 class="cmtt-8"> </span><span
7592 class="cmtt-8"> </span>
7593 <br class="fancyvrb" /><a
7594 id="x1-101034r17"></a><span
7595 class="cmr-6">17</span><span
7596 class="cmtt-8"> </span><span
7597 class="cmtt-8"> </span><span
7598 class="cmtt-8"> </span><span
7599 class="cmtt-8"> </span><span
7600 class="cmtt-8"> </span><span
7601 class="cmtt-8"> </span><span
7602 class="cmtt-8"> </span><span
7603 class="cmtt-8"> 10)</span><span
7604 class="cmtt-8"> [val]</span><span
7605 class="cmtt-8"> =</span><span
7606 class="cmtt-8"> vector</span><span
7607 class="cmtt-8"> [floor1_Y]</span><span
7608 class="cmtt-8"> element</span><span
7609 class="cmtt-8"> [i]</span>
7610 <br class="fancyvrb" /><a
7611 id="x1-101036r18"></a><span
7612 class="cmr-6">18</span><span
7613 class="cmtt-8"> </span><span
7614 class="cmtt-8"> </span><span
7615 class="cmtt-8"> </span><span
7616 class="cmtt-8"> </span><span
7617 class="cmtt-8"> </span><span
7618 class="cmtt-8"> </span><span
7619 class="cmtt-8"> </span><span
7620 class="cmtt-8"> 11)</span><span
7621 class="cmtt-8"> [highroom]</span><span
7622 class="cmtt-8"> =</span><span
7623 class="cmtt-8"> [range]</span><span
7624 class="cmtt-8"> -</span><span
7625 class="cmtt-8"> [predicted]</span>
7626 <br class="fancyvrb" /><a
7627 id="x1-101038r19"></a><span
7628 class="cmr-6">19</span><span
7629 class="cmtt-8"> </span><span
7630 class="cmtt-8"> </span><span
7631 class="cmtt-8"> </span><span
7632 class="cmtt-8"> </span><span
7633 class="cmtt-8"> </span><span
7634 class="cmtt-8"> </span><span
7635 class="cmtt-8"> </span><span
7636 class="cmtt-8"> 12)</span><span
7637 class="cmtt-8"> [lowroom]</span><span
7638 class="cmtt-8"> </span><span
7639 class="cmtt-8"> =</span><span
7640 class="cmtt-8"> [predicted]</span>
7641 <br class="fancyvrb" /><a
7642 id="x1-101040r20"></a><span
7643 class="cmr-6">20</span><span
7644 class="cmtt-8"> </span><span
7645 class="cmtt-8"> </span><span
7646 class="cmtt-8"> </span><span
7647 class="cmtt-8"> </span><span
7648 class="cmtt-8"> </span><span
7649 class="cmtt-8"> </span><span
7650 class="cmtt-8"> </span><span
7651 class="cmtt-8"> 13)</span><span
7652 class="cmtt-8"> if</span><span
7653 class="cmtt-8"> (</span><span
7654 class="cmtt-8"> [highroom]</span><span
7655 class="cmtt-8"> is</span><span
7656 class="cmtt-8"> less</span><span
7657 class="cmtt-8"> than</span><span
7658 class="cmtt-8"> [lowroom]</span><span
7659 class="cmtt-8"> )</span><span
7660 class="cmtt-8"> </span><span
7661 class="cmsy-8">{</span>
7662 <br class="fancyvrb" /><a
7663 id="x1-101042r21"></a><span
7664 class="cmr-6">21</span><span
7665 class="cmtt-8"> </span><span
7666 class="cmtt-8"> </span>
7667 <br class="fancyvrb" /><a
7668 id="x1-101044r22"></a><span
7669 class="cmr-6">22</span><span
7670 class="cmtt-8"> </span><span
7671 class="cmtt-8"> </span><span
7672 class="cmtt-8"> </span><span
7673 class="cmtt-8"> </span><span
7674 class="cmtt-8"> </span><span
7675 class="cmtt-8"> </span><span
7676 class="cmtt-8"> </span><span
7677 class="cmtt-8"> </span><span
7678 class="cmtt-8"> </span><span
7679 class="cmtt-8"> </span><span
7680 class="cmtt-8"> </span><span
7681 class="cmtt-8"> </span><span
7682 class="cmtt-8"> </span><span
7683 class="cmtt-8"> 14)</span><span
7684 class="cmtt-8"> [room]</span><span
7685 class="cmtt-8"> =</span><span
7686 class="cmtt-8"> [highroom]</span><span
7687 class="cmtt-8"> *</span><span
7688 class="cmtt-8"> 2</span>
7692 <br class="fancyvrb" /><a
7693 id="x1-101046r23"></a><span
7694 class="cmr-6">23</span><span
7695 class="cmtt-8"> </span><span
7696 class="cmtt-8"> </span>
7697 <br class="fancyvrb" /><a
7698 id="x1-101048r24"></a><span
7699 class="cmr-6">24</span><span
7700 class="cmtt-8"> </span><span
7701 class="cmtt-8"> </span><span
7702 class="cmtt-8"> </span><span
7703 class="cmtt-8"> </span><span
7704 class="cmtt-8"> </span><span
7705 class="cmtt-8"> </span><span
7706 class="cmtt-8"> </span><span
7707 class="cmtt-8"> </span><span
7708 class="cmtt-8"> </span><span
7709 class="cmtt-8"> </span><span
7710 class="cmtt-8"> </span><span
7711 class="cmtt-8"> </span><span
7712 class="cmsy-8">}</span><span
7713 class="cmtt-8"> else</span><span
7714 class="cmtt-8"> [highroom]</span><span
7715 class="cmtt-8"> is</span><span
7716 class="cmtt-8"> not</span><span
7717 class="cmtt-8"> less</span><span
7718 class="cmtt-8"> than</span><span
7719 class="cmtt-8"> [lowroom]</span><span
7720 class="cmtt-8"> </span><span
7721 class="cmsy-8">{</span>
7722 <br class="fancyvrb" /><a
7723 id="x1-101050r25"></a><span
7724 class="cmr-6">25</span><span
7725 class="cmtt-8"> </span><span
7726 class="cmtt-8"> </span>
7727 <br class="fancyvrb" /><a
7728 id="x1-101052r26"></a><span
7729 class="cmr-6">26</span><span
7730 class="cmtt-8"> </span><span
7731 class="cmtt-8"> </span><span
7732 class="cmtt-8"> </span><span
7733 class="cmtt-8"> </span><span
7734 class="cmtt-8"> </span><span
7735 class="cmtt-8"> </span><span
7736 class="cmtt-8"> </span><span
7737 class="cmtt-8"> </span><span
7738 class="cmtt-8"> </span><span
7739 class="cmtt-8"> </span><span
7740 class="cmtt-8"> </span><span
7741 class="cmtt-8"> </span><span
7742 class="cmtt-8"> </span><span
7743 class="cmtt-8"> 15)</span><span
7744 class="cmtt-8"> [room]</span><span
7745 class="cmtt-8"> =</span><span
7746 class="cmtt-8"> [lowroom]</span><span
7747 class="cmtt-8"> *</span><span
7748 class="cmtt-8"> 2</span>
7749 <br class="fancyvrb" /><a
7750 id="x1-101054r27"></a><span
7751 class="cmr-6">27</span><span
7752 class="cmtt-8"> </span><span
7753 class="cmtt-8"> </span>
7754 <br class="fancyvrb" /><a
7755 id="x1-101056r28"></a><span
7756 class="cmr-6">28</span><span
7757 class="cmtt-8"> </span><span
7758 class="cmtt-8"> </span><span
7759 class="cmtt-8"> </span><span
7760 class="cmtt-8"> </span><span
7761 class="cmtt-8"> </span><span
7762 class="cmtt-8"> </span><span
7763 class="cmtt-8"> </span><span
7764 class="cmtt-8"> </span><span
7765 class="cmtt-8"> </span><span
7766 class="cmtt-8"> </span><span
7767 class="cmtt-8"> </span><span
7768 class="cmtt-8"> </span><span
7769 class="cmsy-8">}</span>
7770 <br class="fancyvrb" /><a
7771 id="x1-101058r29"></a><span
7772 class="cmr-6">29</span><span
7773 class="cmtt-8"> </span><span
7774 class="cmtt-8"> </span>
7775 <br class="fancyvrb" /><a
7776 id="x1-101060r30"></a><span
7777 class="cmr-6">30</span><span
7778 class="cmtt-8"> </span><span
7779 class="cmtt-8"> </span><span
7780 class="cmtt-8"> </span><span
7781 class="cmtt-8"> </span><span
7782 class="cmtt-8"> </span><span
7783 class="cmtt-8"> </span><span
7784 class="cmtt-8"> </span><span
7785 class="cmtt-8"> 16)</span><span
7786 class="cmtt-8"> if</span><span
7787 class="cmtt-8"> (</span><span
7788 class="cmtt-8"> [val]</span><span
7789 class="cmtt-8"> is</span><span
7790 class="cmtt-8"> nonzero</span><span
7791 class="cmtt-8"> )</span><span
7792 class="cmtt-8"> </span><span
7793 class="cmsy-8">{</span>
7794 <br class="fancyvrb" /><a
7795 id="x1-101062r31"></a><span
7796 class="cmr-6">31</span><span
7797 class="cmtt-8"> </span><span
7798 class="cmtt-8"> </span>
7799 <br class="fancyvrb" /><a
7800 id="x1-101064r32"></a><span
7801 class="cmr-6">32</span><span
7802 class="cmtt-8"> </span><span
7803 class="cmtt-8"> </span><span
7804 class="cmtt-8"> </span><span
7805 class="cmtt-8"> </span><span
7806 class="cmtt-8"> </span><span
7807 class="cmtt-8"> </span><span
7808 class="cmtt-8"> </span><span
7809 class="cmtt-8"> </span><span
7810 class="cmtt-8"> </span><span
7811 class="cmtt-8"> </span><span
7812 class="cmtt-8"> </span><span
7813 class="cmtt-8"> </span><span
7814 class="cmtt-8"> </span><span
7815 class="cmtt-8"> 17)</span><span
7816 class="cmtt-8"> vector</span><span
7817 class="cmtt-8"> [floor1_step2_flag]</span><span
7818 class="cmtt-8"> element</span><span
7819 class="cmtt-8"> [low_neighbor_offset]</span><span
7820 class="cmtt-8"> =</span><span
7821 class="cmtt-8"> set</span>
7822 <br class="fancyvrb" /><a
7823 id="x1-101066r33"></a><span
7824 class="cmr-6">33</span><span
7825 class="cmtt-8"> </span><span
7826 class="cmtt-8"> </span><span
7827 class="cmtt-8"> </span><span
7828 class="cmtt-8"> </span><span
7829 class="cmtt-8"> </span><span
7830 class="cmtt-8"> </span><span
7831 class="cmtt-8"> </span><span
7832 class="cmtt-8"> </span><span
7833 class="cmtt-8"> </span><span
7834 class="cmtt-8"> </span><span
7835 class="cmtt-8"> </span><span
7836 class="cmtt-8"> </span><span
7837 class="cmtt-8"> </span><span
7838 class="cmtt-8"> 18)</span><span
7839 class="cmtt-8"> vector</span><span
7840 class="cmtt-8"> [floor1_step2_flag]</span><span
7841 class="cmtt-8"> element</span><span
7842 class="cmtt-8"> [high_neighbor_offset]</span><span
7843 class="cmtt-8"> =</span><span
7844 class="cmtt-8"> set</span>
7845 <br class="fancyvrb" /><a
7846 id="x1-101068r34"></a><span
7847 class="cmr-6">34</span><span
7848 class="cmtt-8"> </span><span
7849 class="cmtt-8"> </span><span
7850 class="cmtt-8"> </span><span
7851 class="cmtt-8"> </span><span
7852 class="cmtt-8"> </span><span
7853 class="cmtt-8"> </span><span
7854 class="cmtt-8"> </span><span
7855 class="cmtt-8"> </span><span
7856 class="cmtt-8"> </span><span
7857 class="cmtt-8"> </span><span
7858 class="cmtt-8"> </span><span
7859 class="cmtt-8"> </span><span
7860 class="cmtt-8"> </span><span
7861 class="cmtt-8"> 19)</span><span
7862 class="cmtt-8"> vector</span><span
7863 class="cmtt-8"> [floor1_step2_flag]</span><span
7864 class="cmtt-8"> element</span><span
7865 class="cmtt-8"> [i]</span><span
7866 class="cmtt-8"> =</span><span
7867 class="cmtt-8"> set</span>
7868 <br class="fancyvrb" /><a
7869 id="x1-101070r35"></a><span
7870 class="cmr-6">35</span><span
7871 class="cmtt-8"> </span><span
7872 class="cmtt-8"> </span><span
7873 class="cmtt-8"> </span><span
7874 class="cmtt-8"> </span><span
7875 class="cmtt-8"> </span><span
7876 class="cmtt-8"> </span><span
7877 class="cmtt-8"> </span><span
7878 class="cmtt-8"> </span><span
7879 class="cmtt-8"> </span><span
7880 class="cmtt-8"> </span><span
7881 class="cmtt-8"> </span><span
7882 class="cmtt-8"> </span><span
7883 class="cmtt-8"> </span><span
7884 class="cmtt-8"> 20)</span><span
7885 class="cmtt-8"> if</span><span
7886 class="cmtt-8"> (</span><span
7887 class="cmtt-8"> [val]</span><span
7888 class="cmtt-8"> is</span><span
7889 class="cmtt-8"> greater</span><span
7890 class="cmtt-8"> than</span><span
7891 class="cmtt-8"> or</span><span
7892 class="cmtt-8"> equal</span><span
7893 class="cmtt-8"> to</span><span
7894 class="cmtt-8"> [room]</span><span
7895 class="cmtt-8"> )</span><span
7896 class="cmtt-8"> </span><span
7897 class="cmsy-8">{</span>
7898 <br class="fancyvrb" /><a
7899 id="x1-101072r36"></a><span
7900 class="cmr-6">36</span><span
7901 class="cmtt-8"> </span><span
7902 class="cmtt-8"> </span>
7903 <br class="fancyvrb" /><a
7904 id="x1-101074r37"></a><span
7905 class="cmr-6">37</span><span
7906 class="cmtt-8"> </span><span
7907 class="cmtt-8"> </span><span
7908 class="cmtt-8"> </span><span
7909 class="cmtt-8"> </span><span
7910 class="cmtt-8"> </span><span
7911 class="cmtt-8"> </span><span
7912 class="cmtt-8"> </span><span
7913 class="cmtt-8"> </span><span
7914 class="cmtt-8"> </span><span
7915 class="cmtt-8"> </span><span
7916 class="cmtt-8"> </span><span
7917 class="cmtt-8"> </span><span
7918 class="cmtt-8"> </span><span
7919 class="cmtt-8"> </span><span
7920 class="cmtt-8"> </span><span
7921 class="cmtt-8"> </span><span
7922 class="cmtt-8"> </span><span
7923 class="cmtt-8"> </span><span
7924 class="cmtt-8"> </span><span
7925 class="cmtt-8"> 21)</span><span
7926 class="cmtt-8"> if</span><span
7927 class="cmtt-8"> (</span><span
7928 class="cmtt-8"> [highroom]</span><span
7929 class="cmtt-8"> is</span><span
7930 class="cmtt-8"> greater</span><span
7931 class="cmtt-8"> than</span><span
7932 class="cmtt-8"> [lowroom]</span><span
7933 class="cmtt-8"> )</span><span
7934 class="cmtt-8"> </span><span
7935 class="cmsy-8">{</span>
7936 <br class="fancyvrb" /><a
7937 id="x1-101076r38"></a><span
7938 class="cmr-6">38</span><span
7939 class="cmtt-8"> </span><span
7940 class="cmtt-8"> </span>
7941 <br class="fancyvrb" /><a
7942 id="x1-101078r39"></a><span
7943 class="cmr-6">39</span><span
7944 class="cmtt-8"> </span><span
7945 class="cmtt-8"> </span><span
7946 class="cmtt-8"> </span><span
7947 class="cmtt-8"> </span><span
7948 class="cmtt-8"> </span><span
7949 class="cmtt-8"> </span><span
7950 class="cmtt-8"> </span><span
7951 class="cmtt-8"> </span><span
7952 class="cmtt-8"> </span><span
7953 class="cmtt-8"> </span><span
7954 class="cmtt-8"> </span><span
7955 class="cmtt-8"> </span><span
7956 class="cmtt-8"> </span><span
7957 class="cmtt-8"> </span><span
7958 class="cmtt-8"> </span><span
7959 class="cmtt-8"> </span><span
7960 class="cmtt-8"> </span><span
7961 class="cmtt-8"> </span><span
7962 class="cmtt-8"> </span><span
7963 class="cmtt-8"> </span><span
7964 class="cmtt-8"> </span><span
7965 class="cmtt-8"> </span><span
7966 class="cmtt-8"> </span><span
7967 class="cmtt-8"> </span><span
7968 class="cmtt-8"> </span><span
7969 class="cmtt-8"> 22)</span><span
7970 class="cmtt-8"> vector</span><span
7971 class="cmtt-8"> [floor1_final_Y]</span><span
7972 class="cmtt-8"> element</span><span
7973 class="cmtt-8"> [i]</span><span
7974 class="cmtt-8"> =</span><span
7975 class="cmtt-8"> [val]</span><span
7976 class="cmtt-8"> -</span><span
7977 class="cmtt-8"> [lowroom]</span><span
7978 class="cmtt-8"> +</span><span
7979 class="cmtt-8"> [predicted]</span>
7980 <br class="fancyvrb" /><a
7981 id="x1-101080r40"></a><span
7982 class="cmr-6">40</span><span
7983 class="cmtt-8"> </span><span
7984 class="cmtt-8"> </span>
7985 <br class="fancyvrb" /><a
7986 id="x1-101082r41"></a><span
7987 class="cmr-6">41</span><span
7988 class="cmtt-8"> </span><span
7989 class="cmtt-8">  </span><span
7990 class="cmtt-8"> </span><span
7991 class="cmtt-8"> </span><span
7992 class="cmtt-8"> </span><span
7993 class="cmtt-8"> </span><span
7994 class="cmtt-8"> </span><span
7995 class="cmtt-8"> </span><span
7996 class="cmsy-8">}</span><span
7997 class="cmtt-8"> else</span><span
7998 class="cmtt-8"> [highroom]</span><span
7999 class="cmtt-8"> is</span><span
8000 class="cmtt-8"> not</span><span
8001 class="cmtt-8"> greater</span><span
8002 class="cmtt-8"> than</span><span
8003 class="cmtt-8"> [lowroom]</span><span
8004 class="cmtt-8"> </span><span
8005 class="cmsy-8">{</span>
8006 <br class="fancyvrb" /><a
8007 id="x1-101084r42"></a><span
8008 class="cmr-6">42</span><span
8009 class="cmtt-8"> </span><span
8010 class="cmtt-8"> </span>
8011 <br class="fancyvrb" /><a
8012 id="x1-101086r43"></a><span
8013 class="cmr-6">43</span><span
8014 class="cmtt-8"> </span><span
8015 class="cmtt-8"> </span><span
8016 class="cmtt-8"> </span><span
8017 class="cmtt-8"> </span><span
8018 class="cmtt-8"> </span><span
8019 class="cmtt-8"> </span><span
8020 class="cmtt-8"> </span><span
8021 class="cmtt-8"> </span><span
8022 class="cmtt-8"> </span><span
8023 class="cmtt-8"> </span><span
8024 class="cmtt-8"> </span><span
8025 class="cmtt-8"> </span><span
8026 class="cmtt-8"> </span><span
8027 class="cmtt-8"> </span><span
8028 class="cmtt-8"> </span><span
8029 class="cmtt-8"> </span><span
8030 class="cmtt-8"> </span><span
8031 class="cmtt-8"> </span><span
8032 class="cmtt-8"> </span><span
8033 class="cmtt-8"> </span><span
8034 class="cmtt-8"> </span><span
8035 class="cmtt-8"> </span><span
8036 class="cmtt-8"> </span><span
8037 class="cmtt-8"> </span><span
8038 class="cmtt-8"> </span><span
8039 class="cmtt-8"> 23)</span><span
8040 class="cmtt-8"> vector</span><span
8041 class="cmtt-8"> [floor1_final_Y]</span><span
8042 class="cmtt-8"> element</span><span
8043 class="cmtt-8"> [i]</span><span
8044 class="cmtt-8"> =</span><span
8045 class="cmtt-8"> [predicted]</span><span
8046 class="cmtt-8"> -</span><span
8047 class="cmtt-8"> [val]</span><span
8048 class="cmtt-8"> +</span><span
8049 class="cmtt-8"> [highroom]</span><span
8050 class="cmtt-8"> -</span><span
8051 class="cmtt-8"> 1</span>
8052 <br class="fancyvrb" /><a
8053 id="x1-101088r44"></a><span
8054 class="cmr-6">44</span><span
8055 class="cmtt-8"> </span><span
8056 class="cmtt-8"> </span>
8057 <br class="fancyvrb" /><a
8058 id="x1-101090r45"></a><span
8059 class="cmr-6">45</span><span
8060 class="cmtt-8"> </span><span
8061 class="cmtt-8"> </span><span
8062 class="cmtt-8"> </span><span
8063 class="cmtt-8"> </span><span
8064 class="cmtt-8"> </span><span
8065 class="cmtt-8"> </span><span
8066 class="cmtt-8"> </span><span
8067 class="cmtt-8"> </span><span
8068 class="cmtt-8"> </span><span
8069 class="cmtt-8"> </span><span
8070 class="cmtt-8"> </span><span
8071 class="cmtt-8"> </span><span
8072 class="cmtt-8"> </span><span
8073 class="cmtt-8"> </span><span
8074 class="cmtt-8"> </span><span
8075 class="cmtt-8"> </span><span
8076 class="cmtt-8"> </span><span
8077 class="cmtt-8"> </span><span
8078 class="cmtt-8"> </span><span
8079 class="cmtt-8"> </span><span
8080 class="cmtt-8"> </span><span
8081 class="cmtt-8"> </span><span
8082 class="cmtt-8"> </span><span
8083 class="cmtt-8"> </span><span
8084 class="cmsy-8">}</span>
8085 <br class="fancyvrb" /><a
8086 id="x1-101092r46"></a><span
8087 class="cmr-6">46</span><span
8088 class="cmtt-8"> </span><span
8089 class="cmtt-8"> </span>
8090 <br class="fancyvrb" /><a
8091 id="x1-101094r47"></a><span
8092 class="cmr-6">47</span><span
8093 class="cmtt-8"> </span><span
8094 class="cmtt-8"> </span><span
8095 class="cmtt-8"> </span><span
8096 class="cmtt-8"> </span><span
8097 class="cmtt-8"> </span><span
8098 class="cmtt-8"> </span><span
8099 class="cmtt-8"> </span><span
8100 class="cmtt-8"> </span><span
8101 class="cmtt-8"> </span><span
8102 class="cmtt-8"> </span><span
8103 class="cmtt-8"> </span><span
8104 class="cmtt-8"> </span><span
8105 class="cmtt-8"> </span><span
8106 class="cmtt-8"> </span><span
8107 class="cmtt-8"> </span><span
8108 class="cmtt-8"> </span><span
8109 class="cmtt-8"> </span><span
8110 class="cmtt-8"> </span><span
8111 class="cmsy-8">}</span><span
8112 class="cmtt-8"> else</span><span
8113 class="cmtt-8"> [val]</span><span
8114 class="cmtt-8"> is</span><span
8115 class="cmtt-8"> less</span><span
8116 class="cmtt-8"> than</span><span
8117 class="cmtt-8"> [room]</span><span
8118 class="cmtt-8"> </span><span
8119 class="cmsy-8">{</span>
8120 <br class="fancyvrb" /><a
8121 id="x1-101096r48"></a><span
8122 class="cmr-6">48</span><span
8123 class="cmtt-8"> </span><span
8124 class="cmtt-8"> </span>
8125 <br class="fancyvrb" /><a
8126 id="x1-101098r49"></a><span
8127 class="cmr-6">49</span><span
8128 class="cmtt-8"> </span><span
8129 class="cmtt-8">  </span><span
8130 class="cmtt-8"> </span><span
8131 class="cmtt-8"> 24)</span><span
8132 class="cmtt-8"> if</span><span
8133 class="cmtt-8"> ([val]</span><span
8134 class="cmtt-8"> is</span><span
8135 class="cmtt-8"> odd)</span><span
8136 class="cmtt-8"> </span><span
8137 class="cmsy-8">{</span>
8138 <br class="fancyvrb" /><a
8139 id="x1-101100r50"></a><span
8140 class="cmr-6">50</span><span
8141 class="cmtt-8"> </span><span
8142 class="cmtt-8"> </span>
8143 <br class="fancyvrb" /><a
8144 id="x1-101102r51"></a><span
8145 class="cmr-6">51</span><span
8146 class="cmtt-8"> </span><span
8147 class="cmtt-8"> </span><span
8148 class="cmtt-8"> </span><span
8149 class="cmtt-8"> </span><span
8150 class="cmtt-8"> </span><span
8151 class="cmtt-8"> </span><span
8152 class="cmtt-8"> </span><span
8153 class="cmtt-8"> </span><span
8154 class="cmtt-8"> </span><span
8155 class="cmtt-8"> </span><span
8156 class="cmtt-8"> </span><span
8157 class="cmtt-8"> </span><span
8158 class="cmtt-8"> </span><span
8159 class="cmtt-8"> </span><span
8160 class="cmtt-8"> </span><span
8161 class="cmtt-8"> </span><span
8162 class="cmtt-8"> </span><span
8163 class="cmtt-8"> </span><span
8164 class="cmtt-8"> </span><span
8165 class="cmtt-8"> </span><span
8166 class="cmtt-8"> </span><span
8167 class="cmtt-8"> </span><span
8168 class="cmtt-8"> </span><span
8169 class="cmtt-8"> </span><span
8170 class="cmtt-8"> </span><span
8171 class="cmtt-8"> 25)</span><span
8172 class="cmtt-8"> vector</span><span
8173 class="cmtt-8"> [floor1_final_Y]</span><span
8174 class="cmtt-8"> element</span><span
8175 class="cmtt-8"> [i]</span><span
8176 class="cmtt-8"> =</span>
8177 <br class="fancyvrb" /><a
8178 id="x1-101104r52"></a><span
8179 class="cmr-6">52</span><span
8180 class="cmtt-8"> </span><span
8181 class="cmtt-8"> </span><span
8182 class="cmtt-8"> </span><span
8183 class="cmtt-8"> </span><span
8184 class="cmtt-8"> </span><span
8185 class="cmtt-8"> </span><span
8186 class="cmtt-8"> </span><span
8187 class="cmtt-8"> </span><span
8188 class="cmtt-8"> </span><span
8189 class="cmtt-8"> </span><span
8190 class="cmtt-8"> </span><span
8191 class="cmtt-8"> </span><span
8192 class="cmtt-8"> </span><span
8193 class="cmtt-8"> </span><span
8194 class="cmtt-8"> </span><span
8195 class="cmtt-8"> </span><span
8196 class="cmtt-8"> </span><span
8197 class="cmtt-8"> </span><span
8198 class="cmtt-8"> </span><span
8199 class="cmtt-8"> </span><span
8200 class="cmtt-8"> </span><span
8201 class="cmtt-8"> </span><span
8202 class="cmtt-8"> </span><span
8203 class="cmtt-8"> </span><span
8204 class="cmtt-8"> </span><span
8205 class="cmtt-8"> </span><span
8206 class="cmtt-8"> </span><span
8207 class="cmtt-8"> </span><span
8208 class="cmtt-8"> </span><span
8209 class="cmtt-8"> [predicted]</span><span
8210 class="cmtt-8"> -</span><span
8211 class="cmtt-8"> (([val]</span><span
8212 class="cmtt-8"> +</span><span
8213 class="cmtt-8"> 1)</span><span
8214 class="cmtt-8"> divided</span><span
8215 class="cmtt-8"> by</span><span
8216 class="cmtt-8"> </span><span
8217 class="cmtt-8"> 2</span><span
8218 class="cmtt-8"> using</span><span
8219 class="cmtt-8"> integer</span><span
8220 class="cmtt-8"> division)</span>
8221 <br class="fancyvrb" /><a
8222 id="x1-101106r53"></a><span
8223 class="cmr-6">53</span><span
8224 class="cmtt-8"> </span><span
8225 class="cmtt-8"> </span>
8226 <br class="fancyvrb" /><a
8227 id="x1-101108r54"></a><span
8228 class="cmr-6">54</span><span
8229 class="cmtt-8"> </span><span
8230 class="cmtt-8"> </span><span
8231 class="cmtt-8"> </span><span
8232 class="cmtt-8"> </span><span
8233 class="cmtt-8"> </span><span
8234 class="cmtt-8"> </span><span
8235 class="cmtt-8"> </span><span
8236 class="cmtt-8"> </span><span
8237 class="cmtt-8"> </span><span
8238 class="cmtt-8"> </span><span
8239 class="cmtt-8"> </span><span
8240 class="cmtt-8"> </span><span
8241 class="cmtt-8"> </span><span
8242 class="cmtt-8"> </span><span
8243 class="cmtt-8"> </span><span
8244 class="cmtt-8"> </span><span
8245 class="cmtt-8"> </span><span
8246 class="cmtt-8"> </span><span
8247 class="cmtt-8"> </span><span
8248 class="cmtt-8"> </span><span
8249 class="cmtt-8"> </span><span
8250 class="cmtt-8"> </span><span
8251 class="cmtt-8"> </span><span
8252 class="cmtt-8"> </span><span
8253 class="cmsy-8">}</span><span
8254 class="cmtt-8"> else</span><span
8255 class="cmtt-8"> [val]</span><span
8256 class="cmtt-8"> is</span><span
8257 class="cmtt-8"> even</span><span
8258 class="cmtt-8"> </span><span
8259 class="cmsy-8">{</span>
8260 <br class="fancyvrb" /><a
8261 id="x1-101110r55"></a><span
8262 class="cmr-6">55</span><span
8263 class="cmtt-8"> </span><span
8264 class="cmtt-8"> </span>
8265 <br class="fancyvrb" /><a
8266 id="x1-101112r56"></a><span
8267 class="cmr-6">56</span><span
8268 class="cmtt-8"> </span><span
8269 class="cmtt-8"> </span><span
8270 class="cmtt-8"> </span><span
8271 class="cmtt-8"> </span><span
8272 class="cmtt-8"> </span><span
8273 class="cmtt-8"> </span><span
8274 class="cmtt-8"> </span><span
8275 class="cmtt-8"> </span><span
8276 class="cmtt-8"> </span><span
8277 class="cmtt-8"> </span><span
8278 class="cmtt-8"> </span><span
8279 class="cmtt-8"> </span><span
8280 class="cmtt-8"> </span><span
8281 class="cmtt-8"> </span><span
8282 class="cmtt-8"> </span><span
8283 class="cmtt-8"> </span><span
8284 class="cmtt-8"> </span><span
8285 class="cmtt-8"> </span><span
8286 class="cmtt-8"> </span><span
8287 class="cmtt-8"> </span><span
8288 class="cmtt-8"> </span><span
8289 class="cmtt-8"> </span><span
8290 class="cmtt-8"> </span><span
8291 class="cmtt-8"> </span><span
8292 class="cmtt-8"> </span><span
8293 class="cmtt-8"> 26)</span><span
8294 class="cmtt-8"> vector</span><span
8295 class="cmtt-8"> [floor1_final_Y]</span><span
8296 class="cmtt-8"> element</span><span
8297 class="cmtt-8"> [i]</span><span
8298 class="cmtt-8"> =</span>
8299 <br class="fancyvrb" /><a
8300 id="x1-101114r57"></a><span
8301 class="cmr-6">57</span><span
8302 class="cmtt-8"> </span><span
8303 class="cmtt-8"> </span><span
8304 class="cmtt-8"> </span><span
8305 class="cmtt-8"> </span><span
8306 class="cmtt-8"> </span><span
8307 class="cmtt-8"> </span><span
8308 class="cmtt-8"> </span><span
8309 class="cmtt-8"> </span><span
8310 class="cmtt-8"> </span><span
8311 class="cmtt-8"> </span><span
8312 class="cmtt-8"> </span><span
8313 class="cmtt-8"> </span><span
8314 class="cmtt-8"> </span><span
8315 class="cmtt-8"> </span><span
8316 class="cmtt-8"> </span><span
8317 class="cmtt-8"> </span><span
8318 class="cmtt-8"> </span><span
8319 class="cmtt-8"> </span><span
8320 class="cmtt-8"> </span><span
8321 class="cmtt-8"> </span><span
8322 class="cmtt-8"> </span><span
8323 class="cmtt-8"> </span><span
8324 class="cmtt-8"> </span><span
8325 class="cmtt-8"> </span><span
8326 class="cmtt-8"> </span><span
8327 class="cmtt-8"> </span><span
8328 class="cmtt-8"> </span><span
8329 class="cmtt-8"> </span><span
8330 class="cmtt-8"> </span><span
8331 class="cmtt-8"> [predicted]</span><span
8332 class="cmtt-8"> +</span><span
8333 class="cmtt-8"> ([val]</span><span
8334 class="cmtt-8"> /</span><span
8335 class="cmtt-8"> 2</span><span
8336 class="cmtt-8"> using</span><span
8337 class="cmtt-8"> integer</span><span
8338 class="cmtt-8"> division)</span>
8339 <br class="fancyvrb" /><a
8340 id="x1-101116r58"></a><span
8341 class="cmr-6">58</span><span
8342 class="cmtt-8"> </span><span
8343 class="cmtt-8"> </span>
8344 <br class="fancyvrb" /><a
8345 id="x1-101118r59"></a><span
8346 class="cmr-6">59</span><span
8347 class="cmtt-8"> </span><span
8348 class="cmtt-8"> </span><span
8349 class="cmtt-8"> </span><span
8350 class="cmtt-8"> </span><span
8351 class="cmtt-8"> </span><span
8352 class="cmtt-8"> </span><span
8353 class="cmtt-8"> </span><span
8354 class="cmtt-8"> </span><span
8355 class="cmtt-8"> </span><span
8356 class="cmtt-8"> </span><span
8357 class="cmtt-8"> </span><span
8358 class="cmtt-8"> </span><span
8359 class="cmtt-8"> </span><span
8360 class="cmtt-8"> </span><span
8361 class="cmtt-8"> </span><span
8362 class="cmtt-8"> </span><span
8363 class="cmtt-8"> </span><span
8364 class="cmtt-8"> </span><span
8365 class="cmtt-8"> </span><span
8366 class="cmtt-8"> </span><span
8367 class="cmtt-8"> </span><span
8368 class="cmtt-8"> </span><span
8369 class="cmtt-8"> </span><span
8370 class="cmtt-8"> </span><span
8371 class="cmsy-8">}</span>
8372 <br class="fancyvrb" /><a
8373 id="x1-101120r60"></a><span
8374 class="cmr-6">60</span><span
8375 class="cmtt-8"> </span><span
8376 class="cmtt-8"> </span>
8377 <br class="fancyvrb" /><a
8378 id="x1-101122r61"></a><span
8379 class="cmr-6">61</span><span
8380 class="cmtt-8"> </span><span
8381 class="cmtt-8"> </span><span
8382 class="cmtt-8"> </span><span
8383 class="cmtt-8"> </span><span
8384 class="cmtt-8"> </span><span
8385 class="cmtt-8"> </span><span
8386 class="cmtt-8"> </span><span
8387 class="cmtt-8"> </span><span
8388 class="cmtt-8"> </span><span
8389 class="cmtt-8"> </span><span
8390 class="cmtt-8"> </span><span
8391 class="cmtt-8"> </span><span
8392 class="cmtt-8"> </span><span
8393 class="cmtt-8"> </span><span
8394 class="cmtt-8"> </span><span
8395 class="cmtt-8"> </span><span
8396 class="cmtt-8"> </span><span
8397 class="cmtt-8"> </span><span
8398 class="cmsy-8">}</span>
8399 <br class="fancyvrb" /><a
8400 id="x1-101124r62"></a><span
8401 class="cmr-6">62</span><span
8402 class="cmtt-8"> </span><span
8403 class="cmtt-8"> </span>
8404 <br class="fancyvrb" /><a
8405 id="x1-101126r63"></a><span
8406 class="cmr-6">63</span><span
8407 class="cmtt-8"> </span><span
8408 class="cmtt-8"> </span><span
8409 class="cmtt-8"> </span><span
8410 class="cmtt-8"> </span><span
8411 class="cmtt-8"> </span><span
8412 class="cmtt-8"> </span><span
8413 class="cmtt-8"> </span><span
8414 class="cmtt-8"> </span><span
8415 class="cmtt-8"> </span><span
8416 class="cmtt-8"> </span><span
8417 class="cmtt-8"> </span><span
8418 class="cmtt-8"> </span><span
8419 class="cmsy-8">}</span><span
8420 class="cmtt-8"> else</span><span
8421 class="cmtt-8"> [val]</span><span
8422 class="cmtt-8"> is</span><span
8423 class="cmtt-8"> zero</span><span
8424 class="cmtt-8"> </span><span
8425 class="cmsy-8">{</span>
8426 <br class="fancyvrb" /><a
8427 id="x1-101128r64"></a><span
8428 class="cmr-6">64</span><span
8429 class="cmtt-8"> </span><span
8430 class="cmtt-8"> </span>
8431 <br class="fancyvrb" /><a
8432 id="x1-101130r65"></a><span
8433 class="cmr-6">65</span><span
8434 class="cmtt-8"> </span><span
8435 class="cmtt-8"> </span><span
8436 class="cmtt-8"> </span><span
8437 class="cmtt-8"> </span><span
8438 class="cmtt-8"> </span><span
8439 class="cmtt-8"> </span><span
8440 class="cmtt-8"> </span><span
8441 class="cmtt-8"> </span><span
8442 class="cmtt-8"> </span><span
8443 class="cmtt-8"> </span><span
8444 class="cmtt-8"> </span><span
8445 class="cmtt-8"> </span><span
8446 class="cmtt-8"> </span><span
8447 class="cmtt-8"> 27)</span><span
8448 class="cmtt-8"> vector</span><span
8449 class="cmtt-8"> [floor1_step2_flag]</span><span
8450 class="cmtt-8"> element</span><span
8451 class="cmtt-8"> [i]</span><span
8452 class="cmtt-8"> =</span><span
8453 class="cmtt-8"> unset</span>
8454 <br class="fancyvrb" /><a
8455 id="x1-101132r66"></a><span
8456 class="cmr-6">66</span><span
8457 class="cmtt-8"> </span><span
8458 class="cmtt-8"> </span><span
8459 class="cmtt-8"> </span><span
8460 class="cmtt-8"> </span><span
8461 class="cmtt-8"> </span><span
8462 class="cmtt-8"> </span><span
8463 class="cmtt-8"> </span><span
8464 class="cmtt-8"> </span><span
8465 class="cmtt-8"> </span><span
8466 class="cmtt-8"> </span><span
8467 class="cmtt-8"> </span><span
8468 class="cmtt-8"> </span><span
8469 class="cmtt-8"> </span><span
8470 class="cmtt-8"> 28)</span><span
8471 class="cmtt-8"> vector</span><span
8472 class="cmtt-8"> [floor1_final_Y]</span><span
8473 class="cmtt-8"> element</span><span
8474 class="cmtt-8"> [i]</span><span
8475 class="cmtt-8"> =</span><span
8476 class="cmtt-8"> [predicted]</span>
8477 <br class="fancyvrb" /><a
8478 id="x1-101134r67"></a><span
8479 class="cmr-6">67</span><span
8480 class="cmtt-8"> </span><span
8481 class="cmtt-8"> </span>
8482 <br class="fancyvrb" /><a
8483 id="x1-101136r68"></a><span
8484 class="cmr-6">68</span><span
8485 class="cmtt-8"> </span><span
8486 class="cmtt-8"> </span><span
8487 class="cmtt-8"> </span><span
8488 class="cmtt-8"> </span><span
8489 class="cmtt-8"> </span><span
8490 class="cmtt-8"> </span><span
8491 class="cmtt-8"> </span><span
8492 class="cmtt-8"> </span><span
8493 class="cmtt-8"> </span><span
8494 class="cmtt-8"> </span><span
8495 class="cmtt-8"> </span><span
8496 class="cmtt-8"> </span><span
8497 class="cmsy-8">}</span>
8498 <br class="fancyvrb" /><a
8499 id="x1-101138r69"></a><span
8500 class="cmr-6">69</span><span
8501 class="cmtt-8"> </span><span
8502 class="cmtt-8"> </span>
8503 <br class="fancyvrb" /><a
8504 id="x1-101140r70"></a><span
8505 class="cmr-6">70</span><span
8506 class="cmtt-8"> </span><span
8507 class="cmtt-8"> </span><span
8508 class="cmtt-8"> </span><span
8509 class="cmtt-8"> </span><span
8510 class="cmtt-8"> </span><span
8511 class="cmtt-8"> </span><span
8512 class="cmtt-8"> </span><span
8513 class="cmsy-8">}</span>
8514 <br class="fancyvrb" /><a
8515 id="x1-101142r71"></a><span
8516 class="cmr-6">71</span><span
8517 class="cmtt-8"> </span><span
8518 class="cmtt-8"> </span>
8519 <br class="fancyvrb" /><a
8520 id="x1-101144r72"></a><span
8521 class="cmr-6">72</span><span
8522 class="cmtt-8"> </span><span
8523 class="cmtt-8"> </span><span
8524 class="cmtt-8"> 29)</span><span
8525 class="cmtt-8"> done</span>
8526 <br class="fancyvrb" /><a
8527 id="x1-101146r73"></a><span
8528 class="cmr-6">73</span><span
8529 class="cmtt-8"> </span><span
8530 class="cmtt-8"> </span>
8532 </dd><dt class="description">
8534 class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
8535 class="description">
8536 <!--l. 338--><p class="noindent" >Curve synthesis generates a return vector <span
8537 class="cmtt-12">[floor] </span>of length <span
8538 class="cmtt-12">[n] </span>(where <span
8539 class="cmtt-12">[n] </span>is provided by
8540 the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
8542 class="cmtt-12">[floor1_X_list]</span>, <span
8543 class="cmtt-12">[floor1_final_Y] </span>and <span
8544 class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as
8545 [floor1_multiplier] and [floor1_values] values.
8549 <!--l. 345--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
8550 class="cmtt-12">[floor1_X_list]</span>, <span
8551 class="cmtt-12">[floor1_final_Y] </span>and
8553 class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span
8554 class="cmtt-12">[floor1_X_list]’</span>, <span
8555 class="cmtt-12">[floor1_final_Y]’</span>
8557 class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
8559 class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span
8560 class="cmtt-12">[floor1_X_list] </span>and then apply the same
8561 permutation to elements of the other two vectors so that the X, Y and step2_flag values
8563 <!--l. 355--><p class="noindent" >Then compute the final curve in one pass:
8564 <!--l. 357--><p class="noindent" >
8565 <div class="fancyvrb" id="fancyvrb32">
8567 id="x1-101148r1"></a><span
8568 class="cmr-6">1</span><span
8569 class="cmtt-8"> </span><span
8570 class="cmtt-8"> </span><span
8571 class="cmtt-8"> </span><span
8572 class="cmtt-8"> 1)</span><span
8573 class="cmtt-8"> [hx]</span><span
8574 class="cmtt-8"> =</span><span
8575 class="cmtt-8"> 0</span>
8576 <br class="fancyvrb" /><a
8577 id="x1-101150r2"></a><span
8578 class="cmr-6">2</span><span
8579 class="cmtt-8"> </span><span
8580 class="cmtt-8"> </span><span
8581 class="cmtt-8"> </span><span
8582 class="cmtt-8"> 2)</span><span
8583 class="cmtt-8"> [lx]</span><span
8584 class="cmtt-8"> =</span><span
8585 class="cmtt-8"> 0</span>
8586 <br class="fancyvrb" /><a
8587 id="x1-101152r3"></a><span
8588 class="cmr-6">3</span><span
8589 class="cmtt-8"> </span><span
8590 class="cmtt-8"> </span><span
8591 class="cmtt-8"> </span><span
8592 class="cmtt-8"> 3)</span><span
8593 class="cmtt-8"> [ly]</span><span
8594 class="cmtt-8"> =</span><span
8595 class="cmtt-8"> vector</span><span
8596 class="cmtt-8"> [floor1_final_Y]’</span><span
8597 class="cmtt-8"> element</span><span
8598 class="cmtt-8"> [0]</span><span
8599 class="cmtt-8"> *</span><span
8600 class="cmtt-8"> [floor1_multiplier]</span>
8601 <br class="fancyvrb" /><a
8602 id="x1-101154r4"></a><span
8603 class="cmr-6">4</span><span
8604 class="cmtt-8"> </span><span
8605 class="cmtt-8"> </span><span
8606 class="cmtt-8"> </span><span
8607 class="cmtt-8"> 4)</span><span
8608 class="cmtt-8"> iterate</span><span
8609 class="cmtt-8"> [i]</span><span
8610 class="cmtt-8"> over</span><span
8611 class="cmtt-8"> the</span><span
8612 class="cmtt-8"> range</span><span
8613 class="cmtt-8"> 1</span><span
8614 class="cmtt-8"> ...</span><span
8615 class="cmtt-8"> [floor1_values]-1</span><span
8616 class="cmtt-8"> </span><span
8617 class="cmsy-8">{</span>
8618 <br class="fancyvrb" /><a
8619 id="x1-101156r5"></a><span
8620 class="cmr-6">5</span><span
8621 class="cmtt-8"> </span><span
8622 class="cmtt-8"> </span>
8623 <br class="fancyvrb" /><a
8624 id="x1-101158r6"></a><span
8625 class="cmr-6">6</span><span
8626 class="cmtt-8"> </span><span
8627 class="cmtt-8"> </span><span
8628 class="cmtt-8"> </span><span
8629 class="cmtt-8"> </span><span
8630 class="cmtt-8"> </span><span
8631 class="cmtt-8"> </span><span
8632 class="cmtt-8"> </span><span
8633 class="cmtt-8"> </span><span
8634 class="cmtt-8"> 5)</span><span
8635 class="cmtt-8"> if</span><span
8636 class="cmtt-8"> (</span><span
8637 class="cmtt-8"> [floor1_step2_flag]’</span><span
8638 class="cmtt-8"> element</span><span
8639 class="cmtt-8"> [i]</span><span
8640 class="cmtt-8"> is</span><span
8641 class="cmtt-8"> set</span><span
8642 class="cmtt-8"> )</span><span
8643 class="cmtt-8"> </span><span
8644 class="cmsy-8">{</span>
8645 <br class="fancyvrb" /><a
8646 id="x1-101160r7"></a><span
8647 class="cmr-6">7</span><span
8648 class="cmtt-8"> </span><span
8649 class="cmtt-8"> </span>
8650 <br class="fancyvrb" /><a
8651 id="x1-101162r8"></a><span
8652 class="cmr-6">8</span><span
8653 class="cmtt-8"> </span><span
8654 class="cmtt-8"> </span><span
8655 class="cmtt-8"> </span><span
8656 class="cmtt-8"> </span><span
8657 class="cmtt-8"> </span><span
8658 class="cmtt-8"> </span><span
8659 class="cmtt-8"> </span><span
8660 class="cmtt-8"> </span><span
8661 class="cmtt-8"> </span><span
8662 class="cmtt-8"> </span><span
8663 class="cmtt-8"> </span><span
8664 class="cmtt-8"> </span><span
8665 class="cmtt-8"> </span><span
8666 class="cmtt-8"> </span><span
8667 class="cmtt-8"> 6)</span><span
8668 class="cmtt-8"> [hy]</span><span
8669 class="cmtt-8"> =</span><span
8670 class="cmtt-8"> [floor1_final_Y]’</span><span
8671 class="cmtt-8"> element</span><span
8672 class="cmtt-8"> [i]</span><span
8673 class="cmtt-8"> *</span><span
8674 class="cmtt-8"> [floor1_multiplier]</span>
8675 <br class="fancyvrb" /><a
8676 id="x1-101164r9"></a><span
8677 class="cmr-6">9</span><span
8678 class="cmtt-8"> </span><span
8679 class="cmtt-8"> </span><span
8680 class="cmtt-8">  </span><span
8681 class="cmtt-8"> </span><span
8682 class="cmtt-8"> </span><span
8683 class="cmtt-8"> </span><span
8684 class="cmtt-8"> </span><span
8685 class="cmtt-8"> 7)</span><span
8686 class="cmtt-8"> [hx]</span><span
8687 class="cmtt-8"> =</span><span
8688 class="cmtt-8"> [floor1_X_list]’</span><span
8689 class="cmtt-8"> element</span><span
8690 class="cmtt-8"> [i]</span>
8691 <br class="fancyvrb" /><a
8692 id="x1-101166r10"></a><span
8693 class="cmr-6">10</span><span
8694 class="cmtt-8"> </span><span
8695 class="cmtt-8"> </span><span
8696 class="cmtt-8"> </span><span
8697 class="cmtt-8"> </span><span
8698 class="cmtt-8"> </span><span
8699 class="cmtt-8"> </span><span
8700 class="cmtt-8"> </span><span
8701 class="cmtt-8"> </span><span
8702 class="cmtt-8"> </span><span
8703 class="cmtt-8"> </span><span
8704 class="cmtt-8"> </span><span
8705 class="cmtt-8"> </span><span
8706 class="cmtt-8"> </span><span
8707 class="cmtt-8"> </span><span
8708 class="cmtt-8"> 8)</span><span
8709 class="cmtt-8"> </span><a
8710 href="#x1-1230009.2.7"><span
8711 class="cmtt-8">render_line</span></a><span
8712 class="cmtt-8">(</span><span
8713 class="cmtt-8"> [lx],</span><span
8714 class="cmtt-8"> [ly],</span><span
8715 class="cmtt-8"> [hx],</span><span
8716 class="cmtt-8"> [hy],</span><span
8717 class="cmtt-8"> [floor]</span><span
8718 class="cmtt-8"> )</span>
8719 <br class="fancyvrb" /><a
8720 id="x1-101168r11"></a><span
8721 class="cmr-6">11</span><span
8722 class="cmtt-8"> </span><span
8723 class="cmtt-8"> </span><span
8724 class="cmtt-8"> </span><span
8725 class="cmtt-8"> </span><span
8726 class="cmtt-8"> </span><span
8727 class="cmtt-8"> </span><span
8728 class="cmtt-8"> </span><span
8729 class="cmtt-8"> </span><span
8730 class="cmtt-8"> </span><span
8731 class="cmtt-8"> </span><span
8732 class="cmtt-8"> </span><span
8733 class="cmtt-8"> </span><span
8734 class="cmtt-8"> </span><span
8735 class="cmtt-8"> </span><span
8736 class="cmtt-8"> 9)</span><span
8737 class="cmtt-8"> [lx]</span><span
8738 class="cmtt-8"> =</span><span
8739 class="cmtt-8"> [hx]</span>
8740 <br class="fancyvrb" /><a
8741 id="x1-101170r12"></a><span
8742 class="cmr-6">12</span><span
8743 class="cmtt-8"> </span><span
8744 class="cmtt-8">  </span><span
8745 class="cmtt-8"> </span><span
8746 class="cmtt-8"> </span><span
8747 class="cmtt-8"> </span><span
8748 class="cmtt-8"> 10)</span><span
8749 class="cmtt-8"> [ly]</span><span
8750 class="cmtt-8"> =</span><span
8751 class="cmtt-8"> [hy]</span>
8752 <br class="fancyvrb" /><a
8753 id="x1-101172r13"></a><span
8754 class="cmr-6">13</span><span
8755 class="cmtt-8"> </span><span
8756 class="cmtt-8"> </span><span
8757 class="cmtt-8"> </span><span
8758 class="cmtt-8"> </span><span
8759 class="cmtt-8"> </span><span
8760 class="cmtt-8"> </span><span
8761 class="cmtt-8"> </span><span
8762 class="cmtt-8"> </span><span
8763 class="cmtt-8"> </span><span
8764 class="cmtt-8"> </span><span
8765 class="cmtt-8"> </span><span
8766 class="cmtt-8"> </span><span
8767 class="cmsy-8">}</span>
8768 <br class="fancyvrb" /><a
8769 id="x1-101174r14"></a><span
8770 class="cmr-6">14</span><span
8771 class="cmtt-8"> </span><span
8772 class="cmtt-8"> </span><span
8773 class="cmtt-8"> </span><span
8774 class="cmtt-8"> </span><span
8775 class="cmtt-8"> </span><span
8776 class="cmtt-8"> </span><span
8777 class="cmtt-8"> </span><span
8778 class="cmsy-8">}</span>
8779 <br class="fancyvrb" /><a
8780 id="x1-101176r15"></a><span
8781 class="cmr-6">15</span><span
8782 class="cmtt-8"> </span><span
8783 class="cmtt-8"> </span>
8784 <br class="fancyvrb" /><a
8785 id="x1-101178r16"></a><span
8786 class="cmr-6">16</span><span
8787 class="cmtt-8"> </span><span
8788 class="cmtt-8"> </span><span
8789 class="cmtt-8"> 11)</span><span
8790 class="cmtt-8"> if</span><span
8791 class="cmtt-8"> (</span><span
8792 class="cmtt-8"> [hx]</span><span
8793 class="cmtt-8"> is</span><span
8794 class="cmtt-8"> less</span><span
8795 class="cmtt-8"> than</span><span
8796 class="cmtt-8"> [n]</span><span
8797 class="cmtt-8"> )</span><span
8798 class="cmtt-8"> </span><span
8799 class="cmsy-8">{</span>
8800 <br class="fancyvrb" /><a
8801 id="x1-101180r17"></a><span
8802 class="cmr-6">17</span><span
8803 class="cmtt-8"> </span><span
8804 class="cmtt-8"> </span>
8805 <br class="fancyvrb" /><a
8806 id="x1-101182r18"></a><span
8807 class="cmr-6">18</span><span
8808 class="cmtt-8"> </span><span
8809 class="cmtt-8"> </span><span
8810 class="cmtt-8"> </span><span
8811 class="cmtt-8"> </span><span
8812 class="cmtt-8"> </span><span
8813 class="cmtt-8"> </span><span
8814 class="cmtt-8"> </span><span
8815 class="cmtt-8"> </span><span
8816 class="cmtt-8"> </span><span
8817 class="cmtt-8"> 12)</span><span
8818 class="cmtt-8"> </span><a
8819 href="#x1-1230009.2.7"><span
8820 class="cmtt-8">render_line</span></a><span
8821 class="cmtt-8">(</span><span
8822 class="cmtt-8"> [hx],</span><span
8823 class="cmtt-8"> [hy],</span><span
8824 class="cmtt-8"> [n],</span><span
8825 class="cmtt-8"> [hy],</span><span
8826 class="cmtt-8"> [floor]</span><span
8827 class="cmtt-8"> )</span>
8828 <br class="fancyvrb" /><a
8829 id="x1-101184r19"></a><span
8830 class="cmr-6">19</span><span
8831 class="cmtt-8"> </span><span
8832 class="cmtt-8"> </span>
8833 <br class="fancyvrb" /><a
8834 id="x1-101186r20"></a><span
8835 class="cmr-6">20</span><span
8836 class="cmtt-8"> </span><span
8837 class="cmtt-8"> </span><span
8838 class="cmtt-8"> </span><span
8839 class="cmtt-8"> </span><span
8840 class="cmtt-8"> </span><span
8841 class="cmtt-8"> </span><span
8842 class="cmtt-8"> </span><span
8843 class="cmsy-8">}</span>
8844 <br class="fancyvrb" /><a
8845 id="x1-101188r21"></a><span
8846 class="cmr-6">21</span><span
8847 class="cmtt-8"> </span><span
8848 class="cmtt-8"> </span>
8849 <br class="fancyvrb" /><a
8850 id="x1-101190r22"></a><span
8851 class="cmr-6">22</span><span
8852 class="cmtt-8"> </span><span
8853 class="cmtt-8"> </span><span
8854 class="cmtt-8"> 13)</span><span
8855 class="cmtt-8"> if</span><span
8856 class="cmtt-8"> (</span><span
8857 class="cmtt-8"> [hx]</span><span
8858 class="cmtt-8"> is</span><span
8859 class="cmtt-8"> greater</span><span
8860 class="cmtt-8"> than</span><span
8861 class="cmtt-8"> [n]</span><span
8862 class="cmtt-8"> )</span><span
8863 class="cmtt-8"> </span><span
8864 class="cmsy-8">{</span>
8865 <br class="fancyvrb" /><a
8866 id="x1-101192r23"></a><span
8867 class="cmr-6">23</span><span
8868 class="cmtt-8"> </span><span
8869 class="cmtt-8"> </span>
8870 <br class="fancyvrb" /><a
8871 id="x1-101194r24"></a><span
8872 class="cmr-6">24</span><span
8873 class="cmtt-8"> </span><span
8874 class="cmtt-8"> </span><span
8875 class="cmtt-8"> </span><span
8876 class="cmtt-8"> </span><span
8877 class="cmtt-8"> </span><span
8878 class="cmtt-8"> </span><span
8879 class="cmtt-8"> </span><span
8880 class="cmtt-8"> </span><span
8881 class="cmtt-8"> </span><span
8882 class="cmtt-8"> </span><span
8883 class="cmtt-8"> </span><span
8884 class="cmtt-8"> </span><span
8885 class="cmtt-8"> </span><span
8886 class="cmtt-8"> 14)</span><span
8887 class="cmtt-8"> truncate</span><span
8888 class="cmtt-8"> vector</span><span
8889 class="cmtt-8"> [floor]</span><span
8890 class="cmtt-8"> to</span><span
8891 class="cmtt-8"> [n]</span><span
8892 class="cmtt-8"> elements</span>
8893 <br class="fancyvrb" /><a
8894 id="x1-101196r25"></a><span
8895 class="cmr-6">25</span><span
8896 class="cmtt-8"> </span><span
8897 class="cmtt-8"> </span>
8898 <br class="fancyvrb" /><a
8899 id="x1-101198r26"></a><span
8900 class="cmr-6">26</span><span
8901 class="cmtt-8"> </span><span
8902 class="cmtt-8"> </span><span
8903 class="cmtt-8"> </span><span
8904 class="cmtt-8"> </span><span
8905 class="cmtt-8"> </span><span
8906 class="cmtt-8"> </span><span
8907 class="cmtt-8"> </span><span
8908 class="cmsy-8">}</span>
8909 <br class="fancyvrb" /><a
8910 id="x1-101200r27"></a><span
8911 class="cmr-6">27</span><span
8912 class="cmtt-8"> </span><span
8913 class="cmtt-8"> </span>
8914 <br class="fancyvrb" /><a
8915 id="x1-101202r28"></a><span
8916 class="cmr-6">28</span><span
8917 class="cmtt-8"> </span><span
8918 class="cmtt-8"> </span><span
8919 class="cmtt-8"> 15)</span><span
8920 class="cmtt-8"> for</span><span
8921 class="cmtt-8"> each</span><span
8922 class="cmtt-8"> scalar</span><span
8923 class="cmtt-8"> in</span><span
8924 class="cmtt-8"> vector</span><span
8925 class="cmtt-8"> [floor],</span><span
8926 class="cmtt-8"> perform</span><span
8927 class="cmtt-8"> a</span><span
8928 class="cmtt-8"> lookup</span><span
8929 class="cmtt-8"> substitution</span><span
8930 class="cmtt-8"> using</span>
8931 <br class="fancyvrb" /><a
8932 id="x1-101204r29"></a><span
8933 class="cmr-6">29</span><span
8934 class="cmtt-8"> </span><span
8935 class="cmtt-8"> </span><span
8936 class="cmtt-8"> </span><span
8937 class="cmtt-8"> </span><span
8938 class="cmtt-8"> </span><span
8939 class="cmtt-8"> </span><span
8940 class="cmtt-8"> the</span><span
8941 class="cmtt-8"> scalar</span><span
8942 class="cmtt-8"> value</span><span
8943 class="cmtt-8"> from</span><span
8944 class="cmtt-8"> [floor]</span><span
8945 class="cmtt-8"> as</span><span
8946 class="cmtt-8"> an</span><span
8947 class="cmtt-8"> offset</span><span
8948 class="cmtt-8"> into</span><span
8949 class="cmtt-8"> the</span><span
8950 class="cmtt-8"> vector</span><span
8951 class="cmtt-8"> </span><a
8952 href="#x1-12500010.1"><span
8953 class="cmtt-8">[floor1_inverse_dB_static_table]</span></a>
8954 <br class="fancyvrb" /><a
8955 id="x1-101206r30"></a><span
8956 class="cmr-6">30</span><span
8957 class="cmtt-8"> </span><span
8958 class="cmtt-8"> </span>
8959 <br class="fancyvrb" /><a
8960 id="x1-101208r31"></a><span
8961 class="cmr-6">31</span><span
8962 class="cmtt-8"> </span><span
8963 class="cmtt-8"> </span><span
8964 class="cmtt-8"> 16)</span><span
8965 class="cmtt-8"> done</span>
8966 <br class="fancyvrb" /><a
8967 id="x1-101210r32"></a><span
8968 class="cmr-6">32</span><span
8969 class="cmtt-8"> </span><span
8970 class="cmtt-8"> </span>
8976 <h3 class="sectionHead"><span class="titlemark">8. </span> <a
8977 id="x1-1020008"></a>Residue setup and decode</h3>
8978 <!--l. 6--><p class="noindent" >
8979 <h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a
8980 id="x1-1030008.1"></a>Overview</h4>
8981 <!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame
8982 after the encoder subtracts the floor curve and performs any channel coupling. A residue vector
8983 may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel
8984 coupling. The exact semantic content of the vector does not matter to the residue
8986 <!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the
8987 bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three
8988 different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding
8990 <!--l. 23--><p class="noindent" >
8991 <h4 class="subsectionHead"><span class="titlemark">8.2. </span> <a
8992 id="x1-1040008.2"></a>Residue format</h4>
8993 <!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
8994 chunk, encodes the chunk classifications and finally encodes the chunks themselves
8995 using the the specific VQ arrangement defined for each selected classification. The
8996 exact interleaving and partitioning vary by residue encoding number, however the
8997 high-level process used to classify and encode the residue vector is the same in all three
8999 <!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
9000 the moment exactly how a partition is encoded and simply trusting that it is, is as
9002 <ul class="itemize1">
9003 <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
9004 specified. If we have a vector size of <span
9005 class="cmti-12">n</span>, a partition size <span
9006 class="cmti-12">residue</span><span
9007 class="cmti-12">_partition</span><span
9008 class="cmti-12">_size</span>,
9009 and a total of <span
9010 class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded
9015 class="cmti-12">n</span>/<span
9016 class="cmti-12">residue</span><span
9017 class="cmti-12">_partition</span><span
9018 class="cmti-12">_size</span>*<span
9019 class="cmti-12">ch</span>. It is important to note that the integer division
9020 truncates. In the below example, we assume an example <span
9021 class="cmti-12">residue</span><span
9022 class="cmti-12">_partition</span><span
9023 class="cmti-12">_size </span>of 8.
9025 <li class="itemize">Each partition in each vector has a classification number that specifies which of
9026 multiple configured VQ codebook setups are used to decode that partition. The
9027 classification numbers of each partition can be thought of as forming a vector in
9028 their own right, as in the illustration below. Just as the residue vectors are coded
9029 in grouped partitions to increase encoding efficiency, the classification vector is also
9030 partitioned into chunks. The integer elements of each scalar in a classification chunk
9031 are built into a single scalar that represents the classification numbers in that chunk.
9032 In the below example, the classification codeword encodes two classification numbers.
9034 <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
9035 the residue vector, but more often efficient codebook design dictates that each vector
9036 is encoded as the additive sum of several passes through the residue vector using
9037 more than one VQ codebook. Thus, each residue value potentially accumulates values
9038 from multiple decode passes. The classification value associated with a partition is
9039 the same in each pass, thus the classification codeword is coded only in the first pass.
9043 <!--l. 70--><p class="noindent" >
9045 <!--l. 71--><p class="noindent" ><img
9046 src="residue-pack.png" alt="PIC"
9048 <br /> <div class="caption"
9049 ><span class="id">Figure 11: </span><span
9050 class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10400111 -->
9052 <!--l. 77--><p class="noindent" >
9053 <h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a
9054 id="x1-1050008.3"></a>residue 0</h4>
9055 <!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
9056 partition encoding (visually treated as a black box–or cyan box or brown box–in the above
9058 <!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
9062 encode a partition in a specific pass. The dimension of the codebook need not be the same in
9063 multiple passes, however the partition size must be an even multiple of the codebook
9065 <!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
9066 codebook sizes of 8, 4, 2 and 1:
9067 <!--l. 92--><p class="noindent" >
9068 <div class="fancyvrb" id="fancyvrb33">
9070 id="x1-105002r1"></a><span
9071 class="cmr-6">1</span><span
9072 class="cmtt-8"> </span><span
9073 class="cmtt-8"> </span>
9074 <br class="fancyvrb" /><a
9075 id="x1-105004r2"></a><span
9076 class="cmr-6">2</span><span
9077 class="cmtt-8"> </span><span
9078 class="cmtt-8"> </span><span
9079 class="cmtt-8"> </span><span
9080 class="cmtt-8"> </span><span
9081 class="cmtt-8"> </span><span
9082 class="cmtt-8"> </span><span
9083 class="cmtt-8"> </span><span
9084 class="cmtt-8"> </span><span
9085 class="cmtt-8"> </span><span
9086 class="cmtt-8"> </span><span
9087 class="cmtt-8"> </span><span
9088 class="cmtt-8"> </span><span
9089 class="cmtt-8"> </span><span
9090 class="cmtt-8"> original</span><span
9091 class="cmtt-8"> residue</span><span
9092 class="cmtt-8"> vector:</span><span
9093 class="cmtt-8"> [</span><span
9094 class="cmtt-8"> 0</span><span
9095 class="cmtt-8"> 1</span><span
9096 class="cmtt-8"> 2</span><span
9097 class="cmtt-8"> 3</span><span
9098 class="cmtt-8"> 4</span><span
9099 class="cmtt-8"> 5</span><span
9100 class="cmtt-8"> 6</span><span
9101 class="cmtt-8"> 7</span><span
9102 class="cmtt-8"> ]</span>
9103 <br class="fancyvrb" /><a
9104 id="x1-105006r3"></a><span
9105 class="cmr-6">3</span><span
9106 class="cmtt-8"> </span><span
9107 class="cmtt-8"> </span>
9108 <br class="fancyvrb" /><a
9109 id="x1-105008r4"></a><span
9110 class="cmr-6">4</span><span
9111 class="cmtt-8"> </span><span
9112 class="cmtt-8"> codebook</span><span
9113 class="cmtt-8"> dimensions</span><span
9114 class="cmtt-8"> =</span><span
9115 class="cmtt-8"> 8</span><span
9116 class="cmtt-8"> </span><span
9117 class="cmtt-8"> encoded</span><span
9118 class="cmtt-8"> as:</span><span
9119 class="cmtt-8"> [</span><span
9120 class="cmtt-8"> 0</span><span
9121 class="cmtt-8"> 1</span><span
9122 class="cmtt-8"> 2</span><span
9123 class="cmtt-8"> 3</span><span
9124 class="cmtt-8"> 4</span><span
9125 class="cmtt-8"> 5</span><span
9126 class="cmtt-8"> 6</span><span
9127 class="cmtt-8"> 7</span><span
9128 class="cmtt-8"> ]</span>
9129 <br class="fancyvrb" /><a
9130 id="x1-105010r5"></a><span
9131 class="cmr-6">5</span><span
9132 class="cmtt-8"> </span><span
9133 class="cmtt-8"> </span>
9134 <br class="fancyvrb" /><a
9135 id="x1-105012r6"></a><span
9136 class="cmr-6">6</span><span
9137 class="cmtt-8"> </span><span
9138 class="cmtt-8"> codebook</span><span
9139 class="cmtt-8"> dimensions</span><span
9140 class="cmtt-8"> =</span><span
9141 class="cmtt-8"> 4</span><span
9142 class="cmtt-8"> </span><span
9143 class="cmtt-8"> encoded</span><span
9144 class="cmtt-8"> as:</span><span
9145 class="cmtt-8"> [</span><span
9146 class="cmtt-8"> 0</span><span
9147 class="cmtt-8"> 2</span><span
9148 class="cmtt-8"> 4</span><span
9149 class="cmtt-8"> 6</span><span
9150 class="cmtt-8"> ],</span><span
9151 class="cmtt-8"> [</span><span
9152 class="cmtt-8"> 1</span><span
9153 class="cmtt-8"> 3</span><span
9154 class="cmtt-8"> 5</span><span
9155 class="cmtt-8"> 7</span><span
9156 class="cmtt-8"> ]</span>
9157 <br class="fancyvrb" /><a
9158 id="x1-105014r7"></a><span
9159 class="cmr-6">7</span><span
9160 class="cmtt-8"> </span><span
9161 class="cmtt-8"> </span>
9162 <br class="fancyvrb" /><a
9163 id="x1-105016r8"></a><span
9164 class="cmr-6">8</span><span
9165 class="cmtt-8"> </span><span
9166 class="cmtt-8"> codebook</span><span
9167 class="cmtt-8"> dimensions</span><span
9168 class="cmtt-8"> =</span><span
9169 class="cmtt-8"> 2</span><span
9170 class="cmtt-8"> </span><span
9171 class="cmtt-8"> encoded</span><span
9172 class="cmtt-8"> as:</span><span
9173 class="cmtt-8"> [</span><span
9174 class="cmtt-8"> 0</span><span
9175 class="cmtt-8"> 4</span><span
9176 class="cmtt-8"> ],</span><span
9177 class="cmtt-8"> [</span><span
9178 class="cmtt-8"> 1</span><span
9179 class="cmtt-8"> 5</span><span
9180 class="cmtt-8"> ],</span><span
9181 class="cmtt-8"> [</span><span
9182 class="cmtt-8"> 2</span><span
9183 class="cmtt-8"> 6</span><span
9184 class="cmtt-8"> ],</span><span
9185 class="cmtt-8"> [</span><span
9186 class="cmtt-8"> 3</span><span
9187 class="cmtt-8"> 7</span><span
9188 class="cmtt-8"> ]</span>
9189 <br class="fancyvrb" /><a
9190 id="x1-105018r9"></a><span
9191 class="cmr-6">9</span><span
9192 class="cmtt-8"> </span><span
9193 class="cmtt-8"> </span>
9194 <br class="fancyvrb" /><a
9195 id="x1-105020r10"></a><span
9196 class="cmr-6">10</span><span
9197 class="cmtt-8"> </span><span
9198 class="cmtt-8"> codebook</span><span
9199 class="cmtt-8"> dimensions</span><span
9200 class="cmtt-8"> =</span><span
9201 class="cmtt-8"> 1</span><span
9202 class="cmtt-8"> </span><span
9203 class="cmtt-8"> encoded</span><span
9204 class="cmtt-8"> as:</span><span
9205 class="cmtt-8"> [</span><span
9206 class="cmtt-8"> 0</span><span
9207 class="cmtt-8"> ],</span><span
9208 class="cmtt-8"> [</span><span
9209 class="cmtt-8"> 1</span><span
9210 class="cmtt-8"> ],</span><span
9211 class="cmtt-8"> [</span><span
9212 class="cmtt-8"> 2</span><span
9213 class="cmtt-8"> ],</span><span
9214 class="cmtt-8"> [</span><span
9215 class="cmtt-8"> 3</span><span
9216 class="cmtt-8"> ],</span><span
9217 class="cmtt-8"> [</span><span
9218 class="cmtt-8"> 4</span><span
9219 class="cmtt-8"> ],</span><span
9220 class="cmtt-8"> [</span><span
9221 class="cmtt-8"> 5</span><span
9222 class="cmtt-8"> ],</span><span
9223 class="cmtt-8"> [</span><span
9224 class="cmtt-8"> 6</span><span
9225 class="cmtt-8"> ],</span><span
9226 class="cmtt-8"> [</span><span
9227 class="cmtt-8"> 7</span><span
9228 class="cmtt-8"> ]</span>
9229 <br class="fancyvrb" /><a
9230 id="x1-105022r11"></a><span
9231 class="cmr-6">11</span><span
9232 class="cmtt-8"> </span><span
9233 class="cmtt-8"> </span>
9235 <!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
9236 restricted to a power of two.
9237 <!--l. 111--><p class="noindent" >
9238 <h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a
9239 id="x1-1060008.4"></a>residue 1</h4>
9240 <!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As
9241 with residue 0, however, partition length must be an integer multiple of the codebook dimension,
9242 although dimension may vary from pass to pass.
9243 <!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
9244 codebook sizes of 8, 4, 2 and 1:
9245 <!--l. 121--><p class="noindent" >
9246 <div class="fancyvrb" id="fancyvrb34">
9248 id="x1-106002r1"></a><span
9249 class="cmr-6">1</span><span
9250 class="cmtt-8"> </span><span
9251 class="cmtt-8"> </span>
9252 <br class="fancyvrb" /><a
9253 id="x1-106004r2"></a><span
9254 class="cmr-6">2</span><span
9255 class="cmtt-8"> </span><span
9256 class="cmtt-8"> </span><span
9257 class="cmtt-8"> </span><span
9258 class="cmtt-8"> </span><span
9259 class="cmtt-8"> </span><span
9260 class="cmtt-8"> </span><span
9261 class="cmtt-8"> </span><span
9262 class="cmtt-8"> </span><span
9263 class="cmtt-8"> </span><span
9264 class="cmtt-8"> </span><span
9265 class="cmtt-8"> </span><span
9266 class="cmtt-8"> </span><span
9267 class="cmtt-8"> </span><span
9268 class="cmtt-8"> original</span><span
9269 class="cmtt-8"> residue</span><span
9270 class="cmtt-8"> vector:</span><span
9271 class="cmtt-8"> [</span><span
9272 class="cmtt-8"> 0</span><span
9273 class="cmtt-8"> 1</span><span
9274 class="cmtt-8"> 2</span><span
9275 class="cmtt-8"> 3</span><span
9276 class="cmtt-8"> 4</span><span
9277 class="cmtt-8"> 5</span><span
9278 class="cmtt-8"> 6</span><span
9279 class="cmtt-8"> 7</span><span
9280 class="cmtt-8"> ]</span>
9281 <br class="fancyvrb" /><a
9282 id="x1-106006r3"></a><span
9283 class="cmr-6">3</span><span
9284 class="cmtt-8"> </span><span
9285 class="cmtt-8"> </span>
9286 <br class="fancyvrb" /><a
9287 id="x1-106008r4"></a><span
9288 class="cmr-6">4</span><span
9289 class="cmtt-8"> </span><span
9290 class="cmtt-8"> codebook</span><span
9291 class="cmtt-8"> dimensions</span><span
9292 class="cmtt-8"> =</span><span
9293 class="cmtt-8"> 8</span><span
9294 class="cmtt-8"> </span><span
9295 class="cmtt-8"> encoded</span><span
9296 class="cmtt-8"> as:</span><span
9297 class="cmtt-8"> [</span><span
9298 class="cmtt-8"> 0</span><span
9299 class="cmtt-8"> 1</span><span
9300 class="cmtt-8"> 2</span><span
9301 class="cmtt-8"> 3</span><span
9302 class="cmtt-8"> 4</span><span
9303 class="cmtt-8"> 5</span><span
9304 class="cmtt-8"> 6</span><span
9305 class="cmtt-8"> 7</span><span
9306 class="cmtt-8"> ]</span>
9307 <br class="fancyvrb" /><a
9308 id="x1-106010r5"></a><span
9309 class="cmr-6">5</span><span
9310 class="cmtt-8"> </span><span
9311 class="cmtt-8"> </span>
9312 <br class="fancyvrb" /><a
9313 id="x1-106012r6"></a><span
9314 class="cmr-6">6</span><span
9315 class="cmtt-8"> </span><span
9316 class="cmtt-8"> codebook</span><span
9317 class="cmtt-8"> dimensions</span><span
9318 class="cmtt-8"> =</span><span
9319 class="cmtt-8"> 4</span><span
9320 class="cmtt-8"> </span><span
9321 class="cmtt-8"> encoded</span><span
9322 class="cmtt-8"> as:</span><span
9323 class="cmtt-8"> [</span><span
9324 class="cmtt-8"> 0</span><span
9325 class="cmtt-8"> 1</span><span
9326 class="cmtt-8"> 2</span><span
9327 class="cmtt-8"> 3</span><span
9328 class="cmtt-8"> ],</span><span
9329 class="cmtt-8"> [</span><span
9330 class="cmtt-8"> 4</span><span
9331 class="cmtt-8"> 5</span><span
9332 class="cmtt-8"> 6</span><span
9333 class="cmtt-8"> 7</span><span
9334 class="cmtt-8"> ]</span>
9335 <br class="fancyvrb" /><a
9336 id="x1-106014r7"></a><span
9337 class="cmr-6">7</span><span
9338 class="cmtt-8"> </span><span
9339 class="cmtt-8"> </span>
9340 <br class="fancyvrb" /><a
9341 id="x1-106016r8"></a><span
9342 class="cmr-6">8</span><span
9343 class="cmtt-8"> </span><span
9344 class="cmtt-8"> codebook</span><span
9345 class="cmtt-8"> dimensions</span><span
9346 class="cmtt-8"> =</span><span
9347 class="cmtt-8"> 2</span><span
9348 class="cmtt-8"> </span><span
9349 class="cmtt-8"> encoded</span><span
9350 class="cmtt-8"> as:</span><span
9351 class="cmtt-8"> [</span><span
9352 class="cmtt-8"> 0</span><span
9353 class="cmtt-8"> 1</span><span
9354 class="cmtt-8"> ],</span><span
9355 class="cmtt-8"> [</span><span
9356 class="cmtt-8"> 2</span><span
9357 class="cmtt-8"> 3</span><span
9358 class="cmtt-8"> ],</span><span
9359 class="cmtt-8"> [</span><span
9360 class="cmtt-8"> 4</span><span
9361 class="cmtt-8"> 5</span><span
9362 class="cmtt-8"> ],</span><span
9363 class="cmtt-8"> [</span><span
9364 class="cmtt-8"> 6</span><span
9365 class="cmtt-8"> 7</span><span
9366 class="cmtt-8"> ]</span>
9367 <br class="fancyvrb" /><a
9368 id="x1-106018r9"></a><span
9369 class="cmr-6">9</span><span
9370 class="cmtt-8"> </span><span
9371 class="cmtt-8"> </span>
9372 <br class="fancyvrb" /><a
9373 id="x1-106020r10"></a><span
9374 class="cmr-6">10</span><span
9375 class="cmtt-8"> </span><span
9376 class="cmtt-8"> codebook</span><span
9377 class="cmtt-8"> dimensions</span><span
9378 class="cmtt-8"> =</span><span
9379 class="cmtt-8"> 1</span><span
9380 class="cmtt-8"> </span><span
9381 class="cmtt-8"> encoded</span><span
9382 class="cmtt-8"> as:</span><span
9383 class="cmtt-8"> [</span><span
9384 class="cmtt-8"> 0</span><span
9385 class="cmtt-8"> ],</span><span
9386 class="cmtt-8"> [</span><span
9387 class="cmtt-8"> 1</span><span
9388 class="cmtt-8"> ],</span><span
9389 class="cmtt-8"> [</span><span
9390 class="cmtt-8"> 2</span><span
9391 class="cmtt-8"> ],</span><span
9392 class="cmtt-8"> [</span><span
9393 class="cmtt-8"> 3</span><span
9394 class="cmtt-8"> ],</span><span
9395 class="cmtt-8"> [</span><span
9396 class="cmtt-8"> 4</span><span
9397 class="cmtt-8"> ],</span><span
9398 class="cmtt-8"> [</span><span
9399 class="cmtt-8"> 5</span><span
9400 class="cmtt-8"> ],</span><span
9401 class="cmtt-8"> [</span><span
9402 class="cmtt-8"> 6</span><span
9403 class="cmtt-8"> ],</span><span
9404 class="cmtt-8"> [</span><span
9405 class="cmtt-8"> 7</span><span
9406 class="cmtt-8"> ]</span>
9407 <br class="fancyvrb" /><a
9408 id="x1-106022r11"></a><span
9409 class="cmr-6">11</span><span
9410 class="cmtt-8"> </span><span
9411 class="cmtt-8"> </span>
9416 <!--l. 137--><p class="noindent" >
9417 <h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a
9418 id="x1-1070008.5"></a>residue 2</h4>
9419 <!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
9420 passed-in vectors as in residue type 1, the <span
9421 class="cmti-12">ch </span>passed in vectors of length <span
9422 class="cmti-12">n </span>are first interleaved
9423 and flattened into a single vector of length <span
9424 class="cmti-12">ch</span>*<span
9425 class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
9426 is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
9427 residue type 1 and type 2 are equivalent.
9430 <!--l. 147--><p class="noindent" >
9432 <!--l. 148--><p class="noindent" ><img
9433 src="residue2.png" alt="PIC"
9435 <br /> <div class="caption"
9436 ><span class="id">Figure 12: </span><span
9437 class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10700112 -->
9439 <!--l. 153--><p class="noindent" >
9440 <h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a
9441 id="x1-1080008.6"></a>Residue decode</h4>
9442 <!--l. 155--><p class="noindent" >
9443 <h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a
9444 id="x1-1090008.6.1"></a>header decode</h5>
9445 <!--l. 157--><p class="noindent" >Header decode for all three residue types is identical.
9446 <div class="fancyvrb" id="fancyvrb35">
9448 id="x1-109002r1"></a><span
9449 class="cmr-6">1</span><span
9450 class="cmtt-8"> </span><span
9451 class="cmtt-8"> </span><span
9452 class="cmtt-8"> </span><span
9453 class="cmtt-8"> 1)</span><span
9454 class="cmtt-8"> [residue\_begin]</span><span
9455 class="cmtt-8"> =</span><span
9456 class="cmtt-8"> read</span><span
9457 class="cmtt-8"> 24</span><span
9458 class="cmtt-8"> bits</span><span
9459 class="cmtt-8"> as</span><span
9460 class="cmtt-8"> unsigned</span><span
9461 class="cmtt-8"> integer</span>
9462 <br class="fancyvrb" /><a
9463 id="x1-109004r2"></a><span
9464 class="cmr-6">2</span><span
9465 class="cmtt-8"> </span><span
9466 class="cmtt-8"> </span><span
9467 class="cmtt-8"> </span><span
9468 class="cmtt-8"> 2)</span><span
9469 class="cmtt-8"> [residue\_end]</span><span
9470 class="cmtt-8"> =</span><span
9471 class="cmtt-8"> read</span><span
9472 class="cmtt-8"> 24</span><span
9473 class="cmtt-8"> bits</span><span
9474 class="cmtt-8"> as</span><span
9475 class="cmtt-8"> unsigned</span><span
9476 class="cmtt-8"> integer</span>
9477 <br class="fancyvrb" /><a
9478 id="x1-109006r3"></a><span
9479 class="cmr-6">3</span><span
9480 class="cmtt-8"> </span><span
9481 class="cmtt-8"> </span><span
9482 class="cmtt-8"> </span><span
9483 class="cmtt-8"> 3)</span><span
9484 class="cmtt-8"> [residue\_partition\_size]</span><span
9485 class="cmtt-8"> =</span><span
9486 class="cmtt-8"> read</span><span
9487 class="cmtt-8"> 24</span><span
9488 class="cmtt-8"> bits</span><span
9489 class="cmtt-8"> as</span><span
9490 class="cmtt-8"> unsigned</span><span
9491 class="cmtt-8"> integer</span><span
9492 class="cmtt-8"> and</span><span
9493 class="cmtt-8"> add</span><span
9494 class="cmtt-8"> one</span>
9495 <br class="fancyvrb" /><a
9496 id="x1-109008r4"></a><span
9497 class="cmr-6">4</span><span
9498 class="cmtt-8"> </span><span
9499 class="cmtt-8"> </span><span
9500 class="cmtt-8"> </span><span
9501 class="cmtt-8"> 4)</span><span
9502 class="cmtt-8"> [residue\_classifications]</span><span
9503 class="cmtt-8"> =</span><span
9504 class="cmtt-8"> read</span><span
9505 class="cmtt-8"> 6</span><span
9506 class="cmtt-8"> bits</span><span
9507 class="cmtt-8"> as</span><span
9508 class="cmtt-8"> unsigned</span><span
9509 class="cmtt-8"> integer</span><span
9510 class="cmtt-8"> and</span><span
9511 class="cmtt-8"> add</span><span
9512 class="cmtt-8"> one</span>
9516 <br class="fancyvrb" /><a
9517 id="x1-109010r5"></a><span
9518 class="cmr-6">5</span><span
9519 class="cmtt-8"> </span><span
9520 class="cmtt-8"> </span><span
9521 class="cmtt-8"> </span><span
9522 class="cmtt-8"> 5)</span><span
9523 class="cmtt-8"> [residue\_classbook]</span><span
9524 class="cmtt-8"> =</span><span
9525 class="cmtt-8"> read</span><span
9526 class="cmtt-8"> 8</span><span
9527 class="cmtt-8"> bits</span><span
9528 class="cmtt-8"> as</span><span
9529 class="cmtt-8"> unsigned</span><span
9530 class="cmtt-8"> integer</span>
9532 <!--l. 166--><p class="noindent" ><span
9533 class="cmtt-12">[residue_begin] </span>and <span
9534 class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is
9535 actually coded; it implements akin to a bandpass where, for coding purposes, the vector
9536 effectively begins at element <span
9537 class="cmtt-12">[residue_begin] </span>and ends at <span
9538 class="cmtt-12">[residue_end]</span>. Preceding and
9539 following values in the unpacked vectors are zeroed. Note that for residue type 2, these
9540 values as well as <span
9541 class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the
9542 individual vectors before interleave. <span
9543 class="cmtt-12">[residue_partition_size] </span>is as explained above,
9545 class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can
9547 class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification
9548 codewords. The number of dimensions in book <span
9549 class="cmtt-12">[residue_classbook] </span>determines how
9550 many classification values are grouped into a single classification codeword. Note that
9551 the number of entries and dimensions in book <span
9552 class="cmtt-12">[residue_classbook]</span>, along with
9554 class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification
9556 class="cmtt-12">[residue_classifications]</span>ˆ<span
9557 class="cmtt-12">[residue_classbook]</span>.dimensions exceeds
9559 class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
9560 <!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
9562 <!--l. 193--><p class="noindent" >
9563 <div class="fancyvrb" id="fancyvrb36">
9565 id="x1-109012r1"></a><span
9566 class="cmr-6">1</span><span
9567 class="cmtt-8"> </span><span
9568 class="cmtt-8"> </span><span
9569 class="cmtt-8"> </span><span
9570 class="cmtt-8"> 1)</span><span
9571 class="cmtt-8"> iterate</span><span
9572 class="cmtt-8"> [i]</span><span
9573 class="cmtt-8"> over</span><span
9574 class="cmtt-8"> the</span><span
9575 class="cmtt-8"> range</span><span
9576 class="cmtt-8"> 0</span><span
9577 class="cmtt-8"> ...</span><span
9578 class="cmtt-8"> [residue\_classifications]-1</span><span
9579 class="cmtt-8"> {</span>
9580 <br class="fancyvrb" /><a
9581 id="x1-109014r2"></a><span
9582 class="cmr-6">2</span><span
9583 class="cmtt-8"> </span><span
9584 class="cmtt-8"> </span>
9585 <br class="fancyvrb" /><a
9586 id="x1-109016r3"></a><span
9587 class="cmr-6">3</span><span
9588 class="cmtt-8"> </span><span
9589 class="cmtt-8"> </span><span
9590 class="cmtt-8"> </span><span
9591 class="cmtt-8"> </span><span
9592 class="cmtt-8"> </span><span
9593 class="cmtt-8"> </span><span
9594 class="cmtt-8"> </span><span
9595 class="cmtt-8"> </span><span
9596 class="cmtt-8"> 2)</span><span
9597 class="cmtt-8"> [high\_bits]</span><span
9598 class="cmtt-8"> =</span><span
9599 class="cmtt-8"> 0</span>
9600 <br class="fancyvrb" /><a
9601 id="x1-109018r4"></a><span
9602 class="cmr-6">4</span><span
9603 class="cmtt-8"> </span><span
9604 class="cmtt-8"> </span><span
9605 class="cmtt-8"> </span><span
9606 class="cmtt-8"> </span><span
9607 class="cmtt-8"> </span><span
9608 class="cmtt-8"> </span><span
9609 class="cmtt-8"> </span><span
9610 class="cmtt-8"> </span><span
9611 class="cmtt-8"> 3)</span><span
9612 class="cmtt-8"> [low\_bits]</span><span
9613 class="cmtt-8"> =</span><span
9614 class="cmtt-8"> read</span><span
9615 class="cmtt-8"> 3</span><span
9616 class="cmtt-8"> bits</span><span
9617 class="cmtt-8"> as</span><span
9618 class="cmtt-8"> unsigned</span><span
9619 class="cmtt-8"> integer</span>
9620 <br class="fancyvrb" /><a
9621 id="x1-109020r5"></a><span
9622 class="cmr-6">5</span><span
9623 class="cmtt-8"> </span><span
9624 class="cmtt-8"> </span><span
9625 class="cmtt-8"> </span><span
9626 class="cmtt-8"> </span><span
9627 class="cmtt-8"> </span><span
9628 class="cmtt-8"> </span><span
9629 class="cmtt-8"> </span><span
9630 class="cmtt-8"> </span><span
9631 class="cmtt-8"> 4)</span><span
9632 class="cmtt-8"> [bitflag]</span><span
9633 class="cmtt-8"> =</span><span
9634 class="cmtt-8"> read</span><span
9635 class="cmtt-8"> one</span><span
9636 class="cmtt-8"> bit</span><span
9637 class="cmtt-8"> as</span><span
9638 class="cmtt-8"> boolean</span>
9639 <br class="fancyvrb" /><a
9640 id="x1-109022r6"></a><span
9641 class="cmr-6">6</span><span
9642 class="cmtt-8"> </span><span
9643 class="cmtt-8"> </span><span
9644 class="cmtt-8"> </span><span
9645 class="cmtt-8"> </span><span
9646 class="cmtt-8"> </span><span
9647 class="cmtt-8"> </span><span
9648 class="cmtt-8"> </span><span
9649 class="cmtt-8"> </span><span
9650 class="cmtt-8"> 5)</span><span
9651 class="cmtt-8"> if</span><span
9652 class="cmtt-8"> (</span><span
9653 class="cmtt-8"> [bitflag]</span><span
9654 class="cmtt-8"> is</span><span
9655 class="cmtt-8"> set</span><span
9656 class="cmtt-8"> )</span><span
9657 class="cmtt-8"> then</span><span
9658 class="cmtt-8"> [high\_bits]</span><span
9659 class="cmtt-8"> =</span><span
9660 class="cmtt-8"> read</span><span
9661 class="cmtt-8"> five</span><span
9662 class="cmtt-8"> bits</span><span
9663 class="cmtt-8"> as</span><span
9664 class="cmtt-8"> unsigned</span><span
9665 class="cmtt-8"> integer</span>
9666 <br class="fancyvrb" /><a
9667 id="x1-109024r7"></a><span
9668 class="cmr-6">7</span><span
9669 class="cmtt-8"> </span><span
9670 class="cmtt-8"> </span><span
9671 class="cmtt-8"> </span><span
9672 class="cmtt-8"> </span><span
9673 class="cmtt-8"> </span><span
9674 class="cmtt-8"> </span><span
9675 class="cmtt-8"> </span><span
9676 class="cmtt-8"> </span><span
9677 class="cmtt-8"> 6)</span><span
9678 class="cmtt-8"> vector</span><span
9679 class="cmtt-8"> [residue\_cascade]</span><span
9680 class="cmtt-8"> element</span><span
9681 class="cmtt-8"> [i]</span><span
9682 class="cmtt-8"> =</span><span
9683 class="cmtt-8"> [high\_bits]</span><span
9684 class="cmtt-8"> *</span><span
9685 class="cmtt-8"> 8</span><span
9686 class="cmtt-8"> +</span><span
9687 class="cmtt-8"> [low\_bits]</span>
9688 <br class="fancyvrb" /><a
9689 id="x1-109026r8"></a><span
9690 class="cmr-6">8</span><span
9691 class="cmtt-8"> </span><span
9692 class="cmtt-8"> </span><span
9693 class="cmtt-8"> </span><span
9694 class="cmtt-8"> </span><span
9695 class="cmtt-8"> </span><span
9696 class="cmtt-8"> </span><span
9697 class="cmtt-8"> }</span>
9698 <br class="fancyvrb" /><a
9699 id="x1-109028r9"></a><span
9700 class="cmr-6">9</span><span
9701 class="cmtt-8"> </span><span
9702 class="cmtt-8"> </span><span
9703 class="cmtt-8"> </span><span
9704 class="cmtt-8"> 7)</span><span
9705 class="cmtt-8"> done</span>
9707 <!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
9708 bitmap. We loop over the possible codebook classifications and the maximum possible number of
9709 encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
9711 <!--l. 211--><p class="noindent" >
9712 <div class="fancyvrb" id="fancyvrb37">
9714 id="x1-109030r1"></a><span
9715 class="cmr-6">1</span><span
9716 class="cmtt-8"> </span><span
9717 class="cmtt-8"> </span><span
9718 class="cmtt-8"> </span><span
9719 class="cmtt-8"> 1)</span><span
9720 class="cmtt-8"> iterate</span><span
9721 class="cmtt-8"> [i]</span><span
9722 class="cmtt-8"> over</span><span
9723 class="cmtt-8"> the</span><span
9724 class="cmtt-8"> range</span><span
9725 class="cmtt-8"> 0</span><span
9726 class="cmtt-8"> ...</span><span
9727 class="cmtt-8"> [residue\_classifications]-1</span><span
9728 class="cmtt-8"> {</span>
9729 <br class="fancyvrb" /><a
9730 id="x1-109032r2"></a><span
9731 class="cmr-6">2</span><span
9732 class="cmtt-8"> </span><span
9733 class="cmtt-8"> </span>
9734 <br class="fancyvrb" /><a
9735 id="x1-109034r3"></a><span
9736 class="cmr-6">3</span><span
9737 class="cmtt-8"> </span><span
9738 class="cmtt-8"> </span><span
9739 class="cmtt-8"> </span><span
9740 class="cmtt-8"> </span><span
9741 class="cmtt-8"> </span><span
9742 class="cmtt-8"> </span><span
9743 class="cmtt-8"> </span><span
9744 class="cmtt-8"> </span><span
9745 class="cmtt-8"> 2)</span><span
9746 class="cmtt-8"> iterate</span><span
9747 class="cmtt-8"> [j]</span><span
9748 class="cmtt-8"> over</span><span
9749 class="cmtt-8"> the</span><span
9750 class="cmtt-8"> range</span><span
9751 class="cmtt-8"> 0</span><span
9752 class="cmtt-8"> ...</span><span
9753 class="cmtt-8"> 7</span><span
9754 class="cmtt-8"> {</span>
9755 <br class="fancyvrb" /><a
9756 id="x1-109036r4"></a><span
9757 class="cmr-6">4</span><span
9758 class="cmtt-8"> </span><span
9759 class="cmtt-8"> </span>
9760 <br class="fancyvrb" /><a
9761 id="x1-109038r5"></a><span
9762 class="cmr-6">5</span><span
9763 class="cmtt-8"> </span><span
9764 class="cmtt-8"> </span><span
9765 class="cmtt-8"> </span><span
9766 class="cmtt-8"> </span><span
9767 class="cmtt-8"> </span><span
9768 class="cmtt-8"> </span><span
9769 class="cmtt-8"> </span><span
9770 class="cmtt-8"> </span><span
9771 class="cmtt-8"> </span><span
9772 class="cmtt-8"> </span><span
9773 class="cmtt-8"> </span><span
9774 class="cmtt-8"> </span><span
9775 class="cmtt-8"> </span><span
9776 class="cmtt-8"> 3)</span><span
9777 class="cmtt-8"> if</span><span
9778 class="cmtt-8"> (</span><span
9779 class="cmtt-8"> vector</span><span
9780 class="cmtt-8"> [residue\_cascade]</span><span
9781 class="cmtt-8"> element</span><span
9782 class="cmtt-8"> [i]</span><span
9783 class="cmtt-8"> bit</span><span
9784 class="cmtt-8"> [j]</span><span
9785 class="cmtt-8"> is</span><span
9786 class="cmtt-8"> set</span><span
9787 class="cmtt-8"> )</span><span
9788 class="cmtt-8"> {</span>
9789 <br class="fancyvrb" /><a
9790 id="x1-109040r6"></a><span
9791 class="cmr-6">6</span><span
9792 class="cmtt-8"> </span><span
9793 class="cmtt-8"> </span>
9794 <br class="fancyvrb" /><a
9795 id="x1-109042r7"></a><span
9796 class="cmr-6">7</span><span
9797 class="cmtt-8"> </span><span
9798 class="cmtt-8"> </span><span
9799 class="cmtt-8"> </span><span
9800 class="cmtt-8"> </span><span
9801 class="cmtt-8"> </span><span
9802 class="cmtt-8"> </span><span
9803 class="cmtt-8"> </span><span
9804 class="cmtt-8"> </span><span
9805 class="cmtt-8"> </span><span
9806 class="cmtt-8"> </span><span
9807 class="cmtt-8"> </span><span
9808 class="cmtt-8"> </span><span
9809 class="cmtt-8"> </span><span
9810 class="cmtt-8"> </span><span
9811 class="cmtt-8"> </span><span
9812 class="cmtt-8"> </span><span
9813 class="cmtt-8"> </span><span
9814 class="cmtt-8"> </span><span
9815 class="cmtt-8"> 4)</span><span
9816 class="cmtt-8"> array</span><span
9817 class="cmtt-8"> [residue\_books]</span><span
9818 class="cmtt-8"> element</span><span
9819 class="cmtt-8"> [i][j]</span><span
9820 class="cmtt-8"> =</span><span
9821 class="cmtt-8"> read</span><span
9822 class="cmtt-8"> 8</span><span
9823 class="cmtt-8"> bits</span><span
9824 class="cmtt-8"> as</span><span
9825 class="cmtt-8"> unsigned</span><span
9826 class="cmtt-8"> integer</span>
9827 <br class="fancyvrb" /><a
9828 id="x1-109044r8"></a><span
9829 class="cmr-6">8</span><span
9830 class="cmtt-8"> </span><span
9831 class="cmtt-8"> </span>
9832 <br class="fancyvrb" /><a
9833 id="x1-109046r9"></a><span
9834 class="cmr-6">9</span><span
9835 class="cmtt-8"> </span><span
9836 class="cmtt-8"> </span><span
9837 class="cmtt-8"> </span><span
9838 class="cmtt-8"> </span><span
9839 class="cmtt-8"> </span><span
9840 class="cmtt-8"> </span><span
9841 class="cmtt-8"> </span><span
9842 class="cmtt-8"> </span><span
9843 class="cmtt-8"> </span><span
9844 class="cmtt-8"> </span><span
9845 class="cmtt-8"> </span><span
9846 class="cmtt-8"> </span><span
9847 class="cmtt-8"> </span><span
9848 class="cmtt-8"> </span><span
9849 class="cmtt-8"> </span><span
9850 class="cmtt-8"> </span><span
9851 class="cmtt-8"> }</span><span
9852 class="cmtt-8"> else</span><span
9853 class="cmtt-8"> {</span>
9857 <br class="fancyvrb" /><a
9858 id="x1-109048r10"></a><span
9859 class="cmr-6">10</span><span
9860 class="cmtt-8"> </span><span
9861 class="cmtt-8"> </span>
9862 <br class="fancyvrb" /><a
9863 id="x1-109050r11"></a><span
9864 class="cmr-6">11</span><span
9865 class="cmtt-8"> </span><span
9866 class="cmtt-8"> </span><span
9867 class="cmtt-8"> </span><span
9868 class="cmtt-8"> </span><span
9869 class="cmtt-8"> </span><span
9870 class="cmtt-8"> </span><span
9871 class="cmtt-8"> </span><span
9872 class="cmtt-8"> </span><span
9873 class="cmtt-8"> </span><span
9874 class="cmtt-8"> </span><span
9875 class="cmtt-8"> </span><span
9876 class="cmtt-8"> </span><span
9877 class="cmtt-8"> </span><span
9878 class="cmtt-8"> </span><span
9879 class="cmtt-8"> </span><span
9880 class="cmtt-8"> </span><span
9881 class="cmtt-8"> </span><span
9882 class="cmtt-8"> </span><span
9883 class="cmtt-8"> 5)</span><span
9884 class="cmtt-8"> array</span><span
9885 class="cmtt-8"> [residue\_books]</span><span
9886 class="cmtt-8"> element</span><span
9887 class="cmtt-8"> [i][j]</span><span
9888 class="cmtt-8"> =</span><span
9889 class="cmtt-8"> unused</span>
9890 <br class="fancyvrb" /><a
9891 id="x1-109052r12"></a><span
9892 class="cmr-6">12</span><span
9893 class="cmtt-8"> </span><span
9894 class="cmtt-8"> </span>
9895 <br class="fancyvrb" /><a
9896 id="x1-109054r13"></a><span
9897 class="cmr-6">13</span><span
9898 class="cmtt-8"> </span><span
9899 class="cmtt-8"> </span><span
9900 class="cmtt-8"> </span><span
9901 class="cmtt-8"> </span><span
9902 class="cmtt-8"> </span><span
9903 class="cmtt-8"> </span><span
9904 class="cmtt-8"> </span><span
9905 class="cmtt-8"> </span><span
9906 class="cmtt-8"> </span><span
9907 class="cmtt-8"> </span><span
9908 class="cmtt-8"> </span><span
9909 class="cmtt-8"> </span><span
9910 class="cmtt-8"> </span><span
9911 class="cmtt-8"> </span><span
9912 class="cmtt-8"> </span><span
9913 class="cmtt-8"> </span><span
9914 class="cmtt-8"> }</span>
9915 <br class="fancyvrb" /><a
9916 id="x1-109056r14"></a><span
9917 class="cmr-6">14</span><span
9918 class="cmtt-8"> </span><span
9919 class="cmtt-8"> </span><span
9920 class="cmtt-8"> </span><span
9921 class="cmtt-8"> </span><span
9922 class="cmtt-8"> </span><span
9923 class="cmtt-8"> </span><span
9924 class="cmtt-8"> </span><span
9925 class="cmtt-8"> </span><span
9926 class="cmtt-8"> </span><span
9927 class="cmtt-8"> </span><span
9928 class="cmtt-8"> </span><span
9929 class="cmtt-8"> }</span>
9930 <br class="fancyvrb" /><a
9931 id="x1-109058r15"></a><span
9932 class="cmr-6">15</span><span
9933 class="cmtt-8"> </span><span
9934 class="cmtt-8"> </span><span
9935 class="cmtt-8"> </span><span
9936 class="cmtt-8"> </span><span
9937 class="cmtt-8"> </span><span
9938 class="cmtt-8"> </span><span
9939 class="cmtt-8"> </span><span
9940 class="cmtt-8"> }</span>
9941 <br class="fancyvrb" /><a
9942 id="x1-109060r16"></a><span
9943 class="cmr-6">16</span><span
9944 class="cmtt-8"> </span><span
9945 class="cmtt-8"> </span>
9946 <br class="fancyvrb" /><a
9947 id="x1-109062r17"></a><span
9948 class="cmr-6">17</span><span
9949 class="cmtt-8"> </span><span
9950 class="cmtt-8"> </span><span
9951 class="cmtt-8"> </span><span
9952 class="cmtt-8"> 6)</span><span
9953 class="cmtt-8"> done</span>
9955 <!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable.
9956 In addition, any codebook number greater than the maximum numbered codebook
9957 set up in this stream also renders the stream undecodable. All codebooks in array
9958 [residue_books] are required to have a value mapping. The presence of codebook in array
9959 [residue_books] without a value mapping (maptype equals zero) renders the stream
9961 <!--l. 241--><p class="noindent" >
9962 <h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a
9963 id="x1-1100008.6.2"></a>packet decode</h5>
9964 <!--l. 243--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
9965 decode can be built out of the format 1 decode process. Thus we describe first the decode
9966 infrastructure identical to all three formats.
9967 <!--l. 248--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
9968 vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
9969 decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
9970 decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
9971 allocated and zeroed.
9972 <!--l. 255--><p class="noindent" >Depending on the values of <span
9973 class="cmtt-12">[residue_begin] </span>and <span
9974 class="cmtt-12">[residue_end]</span>, it is obvious that the
9975 encoded portion of a residue vector may be the entire possible residue vector or some other strict
9976 subset of the actual residue vector size with zero padding at either uncoded end. However, it is
9977 also possible to set <span
9978 class="cmtt-12">[residue_begin] </span>and <span
9979 class="cmtt-12">[residue_end] </span>to specify a range partially or wholly
9980 beyond the maximum vector size. Before beginning residue decode, limit <span
9981 class="cmtt-12">[residue_begin]</span>
9983 class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that
9984 the number of vectors being encoded, <span
9985 class="cmtt-12">[ch] </span>is provided by the higher level decoding
9987 <!--l. 269--><p class="noindent" >
9988 <div class="fancyvrb" id="fancyvrb38">
9990 id="x1-110002r1"></a><span
9991 class="cmr-6">1</span><span
9992 class="cmtt-8"> </span><span
9993 class="cmtt-8"> </span><span
9994 class="cmtt-8"> </span><span
9995 class="cmtt-8"> 1)</span><span
9996 class="cmtt-8"> [actual\_size]</span><span
9997 class="cmtt-8"> =</span><span
9998 class="cmtt-8"> current</span><span
9999 class="cmtt-8"> blocksize/2;</span>
10000 <br class="fancyvrb" /><a
10001 id="x1-110004r2"></a><span
10002 class="cmr-6">2</span><span
10003 class="cmtt-8"> </span><span
10004 class="cmtt-8"> </span><span
10005 class="cmtt-8"> </span><span
10006 class="cmtt-8"> 2)</span><span
10007 class="cmtt-8"> if</span><span
10008 class="cmtt-8"> residue</span><span
10009 class="cmtt-8"> encoding</span><span
10010 class="cmtt-8"> is</span><span
10011 class="cmtt-8"> format</span><span
10012 class="cmtt-8"> 2</span>
10013 <br class="fancyvrb" /><a
10014 id="x1-110006r3"></a><span
10015 class="cmr-6">3</span><span
10016 class="cmtt-8"> </span><span
10017 class="cmtt-8"> </span><span
10018 class="cmtt-8"> </span><span
10019 class="cmtt-8"> </span><span
10020 class="cmtt-8"> </span><span
10021 class="cmtt-8"> </span><span
10022 class="cmtt-8"> </span><span
10023 class="cmtt-8"> </span><span
10024 class="cmtt-8"> 3)</span><span
10025 class="cmtt-8"> [actual\_size]</span><span
10026 class="cmtt-8"> =</span><span
10027 class="cmtt-8"> [actual\_size]</span><span
10028 class="cmtt-8"> *</span><span
10029 class="cmtt-8"> [ch];</span>
10033 <br class="fancyvrb" /><a
10034 id="x1-110008r4"></a><span
10035 class="cmr-6">4</span><span
10036 class="cmtt-8"> </span><span
10037 class="cmtt-8"> </span><span
10038 class="cmtt-8"> </span><span
10039 class="cmtt-8"> 4)</span><span
10040 class="cmtt-8"> [limit\_residue\_begin]</span><span
10041 class="cmtt-8"> =</span><span
10042 class="cmtt-8"> maximum</span><span
10043 class="cmtt-8"> of</span><span
10044 class="cmtt-8"> ([residue\_begin],[actual\_size]);</span>
10045 <br class="fancyvrb" /><a
10046 id="x1-110010r5"></a><span
10047 class="cmr-6">5</span><span
10048 class="cmtt-8"> </span><span
10049 class="cmtt-8"> </span><span
10050 class="cmtt-8"> </span><span
10051 class="cmtt-8"> 5)</span><span
10052 class="cmtt-8"> [limit\_residue\_end]</span><span
10053 class="cmtt-8"> =</span><span
10054 class="cmtt-8"> maximum</span><span
10055 class="cmtt-8"> of</span><span
10056 class="cmtt-8"> ([residue\_end],[actual\_size]);</span>
10058 <!--l. 277--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
10059 <!--l. 280--><p class="noindent" >
10060 <div class="fancyvrb" id="fancyvrb39">
10062 id="x1-110012r1"></a><span
10063 class="cmr-6">1</span><span
10064 class="cmtt-8"> </span><span
10065 class="cmtt-8"> </span><span
10066 class="cmtt-8"> </span><span
10067 class="cmtt-8"> 1)</span><span
10068 class="cmtt-8"> [classwords\_per\_codeword]</span><span
10069 class="cmtt-8"> =</span><span
10070 class="cmtt-8"> [codebook\_dimensions]</span><span
10071 class="cmtt-8"> value</span><span
10072 class="cmtt-8"> of</span><span
10073 class="cmtt-8"> codebook</span><span
10074 class="cmtt-8"> [residue\_classbook]</span>
10075 <br class="fancyvrb" /><a
10076 id="x1-110014r2"></a><span
10077 class="cmr-6">2</span><span
10078 class="cmtt-8"> </span><span
10079 class="cmtt-8"> </span><span
10080 class="cmtt-8"> </span><span
10081 class="cmtt-8"> 2)</span><span
10082 class="cmtt-8"> [n\_to\_read]</span><span
10083 class="cmtt-8"> =</span><span
10084 class="cmtt-8"> [limit\_residue\_end]</span><span
10085 class="cmtt-8"> -</span><span
10086 class="cmtt-8"> [limit\_residue\_begin]</span>
10087 <br class="fancyvrb" /><a
10088 id="x1-110016r3"></a><span
10089 class="cmr-6">3</span><span
10090 class="cmtt-8"> </span><span
10091 class="cmtt-8"> </span><span
10092 class="cmtt-8"> </span><span
10093 class="cmtt-8"> 3)</span><span
10094 class="cmtt-8"> [partitions\_to\_read]</span><span
10095 class="cmtt-8"> =</span><span
10096 class="cmtt-8"> [n\_to\_read]</span><span
10097 class="cmtt-8"> /</span><span
10098 class="cmtt-8"> [residue\_partition\_size]</span>
10100 <!--l. 286--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
10101 <div class="fancyvrb" id="fancyvrb40">
10103 id="x1-110018r1"></a><span
10104 class="cmr-6">1</span><span
10105 class="cmtt-8"> </span><span
10106 class="cmtt-8"> </span><span
10107 class="cmtt-8"> </span><span
10108 class="cmtt-8"> 1)</span><span
10109 class="cmtt-8"> allocate</span><span
10110 class="cmtt-8"> and</span><span
10111 class="cmtt-8"> zero</span><span
10112 class="cmtt-8"> all</span><span
10113 class="cmtt-8"> vectors</span><span
10114 class="cmtt-8"> that</span><span
10115 class="cmtt-8"> will</span><span
10116 class="cmtt-8"> be</span><span
10117 class="cmtt-8"> returned.</span>
10118 <br class="fancyvrb" /><a
10119 id="x1-110020r2"></a><span
10120 class="cmr-6">2</span><span
10121 class="cmtt-8"> </span><span
10122 class="cmtt-8"> </span><span
10123 class="cmtt-8"> </span><span
10124 class="cmtt-8"> 2)</span><span
10125 class="cmtt-8"> if</span><span
10126 class="cmtt-8"> ([n\_to\_read]</span><span
10127 class="cmtt-8"> is</span><span
10128 class="cmtt-8"> zero),</span><span
10129 class="cmtt-8"> stop;</span><span
10130 class="cmtt-8"> there</span><span
10131 class="cmtt-8"> is</span><span
10132 class="cmtt-8"> no</span><span
10133 class="cmtt-8"> residue</span><span
10134 class="cmtt-8"> to</span><span
10135 class="cmtt-8"> decode.</span>
10136 <br class="fancyvrb" /><a
10137 id="x1-110022r3"></a><span
10138 class="cmr-6">3</span><span
10139 class="cmtt-8"> </span><span
10140 class="cmtt-8"> </span><span
10141 class="cmtt-8"> </span><span
10142 class="cmtt-8"> 3)</span><span
10143 class="cmtt-8"> iterate</span><span
10144 class="cmtt-8"> [pass]</span><span
10145 class="cmtt-8"> over</span><span
10146 class="cmtt-8"> the</span><span
10147 class="cmtt-8"> range</span><span
10148 class="cmtt-8"> 0</span><span
10149 class="cmtt-8"> ...</span><span
10150 class="cmtt-8"> 7</span><span
10151 class="cmtt-8"> {</span>
10152 <br class="fancyvrb" /><a
10153 id="x1-110024r4"></a><span
10154 class="cmr-6">4</span><span
10155 class="cmtt-8"> </span><span
10156 class="cmtt-8"> </span>
10157 <br class="fancyvrb" /><a
10158 id="x1-110026r5"></a><span
10159 class="cmr-6">5</span><span
10160 class="cmtt-8"> </span><span
10161 class="cmtt-8"> </span><span
10162 class="cmtt-8"> </span><span
10163 class="cmtt-8"> </span><span
10164 class="cmtt-8"> </span><span
10165 class="cmtt-8"> </span><span
10166 class="cmtt-8"> </span><span
10167 class="cmtt-8"> </span><span
10168 class="cmtt-8"> 4)</span><span
10169 class="cmtt-8"> [partition\_count]</span><span
10170 class="cmtt-8"> =</span><span
10171 class="cmtt-8"> 0</span>
10172 <br class="fancyvrb" /><a
10173 id="x1-110028r6"></a><span
10174 class="cmr-6">6</span><span
10175 class="cmtt-8"> </span><span
10176 class="cmtt-8"> </span>
10177 <br class="fancyvrb" /><a
10178 id="x1-110030r7"></a><span
10179 class="cmr-6">7</span><span
10180 class="cmtt-8"> </span><span
10181 class="cmtt-8"> </span><span
10182 class="cmtt-8"> </span><span
10183 class="cmtt-8"> </span><span
10184 class="cmtt-8"> </span><span
10185 class="cmtt-8"> </span><span
10186 class="cmtt-8"> </span><span
10187 class="cmtt-8"> </span><span
10188 class="cmtt-8"> 5)</span><span
10189 class="cmtt-8"> while</span><span
10190 class="cmtt-8"> [partition\_count]</span><span
10191 class="cmtt-8"> is</span><span
10192 class="cmtt-8"> less</span><span
10193 class="cmtt-8"> than</span><span
10194 class="cmtt-8"> [partitions\_to\_read]</span>
10195 <br class="fancyvrb" /><a
10196 id="x1-110032r8"></a><span
10197 class="cmr-6">8</span><span
10198 class="cmtt-8"> </span><span
10199 class="cmtt-8"> </span>
10200 <br class="fancyvrb" /><a
10201 id="x1-110034r9"></a><span
10202 class="cmr-6">9</span><span
10203 class="cmtt-8"> </span><span
10204 class="cmtt-8"> </span><span
10205 class="cmtt-8"> </span><span
10206 class="cmtt-8"> </span><span
10207 class="cmtt-8"> </span><span
10208 class="cmtt-8"> </span><span
10209 class="cmtt-8"> </span><span
10210 class="cmtt-8"> </span><span
10211 class="cmtt-8"> </span><span
10212 class="cmtt-8"> </span><span
10213 class="cmtt-8"> </span><span
10214 class="cmtt-8"> </span><span
10215 class="cmtt-8"> </span><span
10216 class="cmtt-8"> 6)</span><span
10217 class="cmtt-8"> if</span><span
10218 class="cmtt-8"> ([pass]</span><span
10219 class="cmtt-8"> is</span><span
10220 class="cmtt-8"> zero)</span><span
10221 class="cmtt-8"> {</span>
10222 <br class="fancyvrb" /><a
10223 id="x1-110036r10"></a><span
10224 class="cmr-6">10</span><span
10225 class="cmtt-8"> </span><span
10226 class="cmtt-8"> </span>
10227 <br class="fancyvrb" /><a
10228 id="x1-110038r11"></a><span
10229 class="cmr-6">11</span><span
10230 class="cmtt-8"> </span><span
10231 class="cmtt-8"> </span><span
10232 class="cmtt-8"> </span><span
10233 class="cmtt-8"> </span><span
10234 class="cmtt-8"> </span><span
10235 class="cmtt-8"> </span><span
10236 class="cmtt-8"> </span><span
10237 class="cmtt-8"> </span><span
10238 class="cmtt-8"> </span><span
10239 class="cmtt-8"> </span><span
10240 class="cmtt-8"> </span><span
10241 class="cmtt-8"> </span><span
10242 class="cmtt-8"> </span><span
10243 class="cmtt-8"> </span><span
10244 class="cmtt-8"> </span><span
10245 class="cmtt-8"> </span><span
10246 class="cmtt-8"> </span><span
10247 class="cmtt-8"> </span><span
10248 class="cmtt-8"> 7)</span><span
10249 class="cmtt-8"> iterate</span><span
10250 class="cmtt-8"> [j]</span><span
10251 class="cmtt-8"> over</span><span
10252 class="cmtt-8"> the</span><span
10253 class="cmtt-8"> range</span><span
10254 class="cmtt-8"> 0</span><span
10255 class="cmtt-8"> ..</span><span
10256 class="cmtt-8"> [ch]-1</span><span
10257 class="cmtt-8"> {</span>
10258 <br class="fancyvrb" /><a
10259 id="x1-110040r12"></a><span
10260 class="cmr-6">12</span><span
10261 class="cmtt-8"> </span><span
10262 class="cmtt-8"> </span>
10263 <br class="fancyvrb" /><a
10264 id="x1-110042r13"></a><span
10265 class="cmr-6">13</span><span
10266 class="cmtt-8"> </span><span
10267 class="cmtt-8"> </span><span
10268 class="cmtt-8"> </span><span
10269 class="cmtt-8"> </span><span
10270 class="cmtt-8"> </span><span
10271 class="cmtt-8"> </span><span
10272 class="cmtt-8"> </span><span
10273 class="cmtt-8"> </span><span
10274 class="cmtt-8"> </span><span
10275 class="cmtt-8"> </span><span
10276 class="cmtt-8"> </span><span
10277 class="cmtt-8"> </span><span
10278 class="cmtt-8"> </span><span
10279 class="cmtt-8"> </span><span
10280 class="cmtt-8"> </span><span
10281 class="cmtt-8"> </span><span
10282 class="cmtt-8"> </span><span
10283 class="cmtt-8"> </span><span
10284 class="cmtt-8"> </span><span
10285 class="cmtt-8"> </span><span
10286 class="cmtt-8"> </span><span
10287 class="cmtt-8"> </span><span
10288 class="cmtt-8"> </span><span
10289 class="cmtt-8"> 8)</span><span
10290 class="cmtt-8"> if</span><span
10291 class="cmtt-8"> vector</span><span
10292 class="cmtt-8"> [j]</span><span
10293 class="cmtt-8"> is</span><span
10294 class="cmtt-8"> not</span><span
10295 class="cmtt-8"> marked</span><span
10296 class="cmtt-8"> ’do</span><span
10297 class="cmtt-8"> not</span><span
10298 class="cmtt-8"> decode’</span><span
10299 class="cmtt-8"> {</span>
10300 <br class="fancyvrb" /><a
10301 id="x1-110044r14"></a><span
10302 class="cmr-6">14</span><span
10303 class="cmtt-8"> </span><span
10304 class="cmtt-8"> </span>
10305 <br class="fancyvrb" /><a
10306 id="x1-110046r15"></a><span
10307 class="cmr-6">15</span><span
10308 class="cmtt-8"> </span><span
10309 class="cmtt-8"> </span><span
10310 class="cmtt-8"> </span><span
10311 class="cmtt-8"> </span><span
10312 class="cmtt-8"> </span><span
10313 class="cmtt-8"> </span><span
10314 class="cmtt-8"> </span><span
10315 class="cmtt-8"> </span><span
10316 class="cmtt-8"> </span><span
10317 class="cmtt-8"> </span><span
10318 class="cmtt-8"> </span><span
10319 class="cmtt-8"> </span><span
10320 class="cmtt-8"> </span><span
10321 class="cmtt-8"> </span><span
10322 class="cmtt-8"> </span><span
10323 class="cmtt-8"> </span><span
10324 class="cmtt-8"> </span><span
10325 class="cmtt-8"> </span><span
10326 class="cmtt-8"> </span><span
10327 class="cmtt-8"> </span><span
10328 class="cmtt-8"> </span><span
10329 class="cmtt-8"> </span><span
10330 class="cmtt-8"> </span><span
10331 class="cmtt-8"> </span><span
10332 class="cmtt-8"> </span><span
10333 class="cmtt-8"> </span><span
10334 class="cmtt-8"> </span><span
10335 class="cmtt-8"> </span><span
10336 class="cmtt-8"> 9)</span><span
10337 class="cmtt-8"> [temp]</span><span
10338 class="cmtt-8"> =</span><span
10339 class="cmtt-8"> read</span><span
10340 class="cmtt-8"> from</span><span
10341 class="cmtt-8"> packet</span><span
10342 class="cmtt-8"> using</span><span
10343 class="cmtt-8"> codebook</span><span
10344 class="cmtt-8"> [residue\_classbook]</span><span
10345 class="cmtt-8"> in</span><span
10346 class="cmtt-8"> scalar</span><span
10347 class="cmtt-8"> context</span>
10348 <br class="fancyvrb" /><a
10349 id="x1-110048r16"></a><span
10350 class="cmr-6">16</span><span
10351 class="cmtt-8"> </span><span
10352 class="cmtt-8"> </span><span
10353 class="cmtt-8"> </span><span
10354 class="cmtt-8"> </span><span
10355 class="cmtt-8"> </span><span
10356 class="cmtt-8"> </span><span
10357 class="cmtt-8"> </span><span
10358 class="cmtt-8"> </span><span
10359 class="cmtt-8"> </span><span
10360 class="cmtt-8"> </span><span
10361 class="cmtt-8"> </span><span
10362 class="cmtt-8"> </span><span
10363 class="cmtt-8"> </span><span
10364 class="cmtt-8"> </span><span
10365 class="cmtt-8"> </span><span
10366 class="cmtt-8"> </span><span
10367 class="cmtt-8"> </span><span
10368 class="cmtt-8"> </span><span
10369 class="cmtt-8"> </span><span
10370 class="cmtt-8"> </span><span
10371 class="cmtt-8"> </span><span
10372 class="cmtt-8"> </span><span
10373 class="cmtt-8"> </span><span
10374 class="cmtt-8"> </span><span
10375 class="cmtt-8"> </span><span
10376 class="cmtt-8"> </span><span
10377 class="cmtt-8"> </span><span
10378 class="cmtt-8"> 10)</span><span
10379 class="cmtt-8"> iterate</span><span
10380 class="cmtt-8"> [i]</span><span
10381 class="cmtt-8"> descending</span><span
10382 class="cmtt-8"> over</span><span
10383 class="cmtt-8"> the</span><span
10384 class="cmtt-8"> range</span><span
10385 class="cmtt-8"> [classwords\_per\_codeword]-1</span><span
10386 class="cmtt-8"> ...</span><span
10387 class="cmtt-8"> 0</span><span
10388 class="cmtt-8"> {</span>
10389 <br class="fancyvrb" /><a
10390 id="x1-110050r17"></a><span
10391 class="cmr-6">17</span><span
10392 class="cmtt-8"> </span><span
10393 class="cmtt-8"> </span>
10394 <br class="fancyvrb" /><a
10395 id="x1-110052r18"></a><span
10396 class="cmr-6">18</span><span
10397 class="cmtt-8"> </span><span
10398 class="cmtt-8"> </span><span
10399 class="cmtt-8"> </span><span
10400 class="cmtt-8"> </span><span
10401 class="cmtt-8"> </span><span
10402 class="cmtt-8"> </span><span
10403 class="cmtt-8"> </span><span
10404 class="cmtt-8"> </span><span
10405 class="cmtt-8"> </span><span
10406 class="cmtt-8"> </span><span
10407 class="cmtt-8"> </span><span
10408 class="cmtt-8"> </span><span
10409 class="cmtt-8"> </span><span
10410 class="cmtt-8"> </span><span
10411 class="cmtt-8"> </span><span
10412 class="cmtt-8"> </span><span
10413 class="cmtt-8"> </span><span
10414 class="cmtt-8"> </span><span
10415 class="cmtt-8"> </span><span
10416 class="cmtt-8"> </span><span
10417 class="cmtt-8"> </span><span
10418 class="cmtt-8"> </span><span
10419 class="cmtt-8"> </span><span
10420 class="cmtt-8"> </span><span
10421 class="cmtt-8"> </span><span
10422 class="cmtt-8"> </span><span
10423 class="cmtt-8"> </span><span
10424 class="cmtt-8"> </span><span
10425 class="cmtt-8"> </span><span
10426 class="cmtt-8"> </span><span
10427 class="cmtt-8"> </span><span
10428 class="cmtt-8"> </span><span
10429 class="cmtt-8"> 11)</span><span
10430 class="cmtt-8"> array</span><span
10431 class="cmtt-8"> [classifications]</span><span
10432 class="cmtt-8"> element</span><span
10433 class="cmtt-8"> [j],([i]+[partition\_count])</span><span
10434 class="cmtt-8"> =</span>
10435 <br class="fancyvrb" /><a
10436 id="x1-110054r19"></a><span
10437 class="cmr-6">19</span><span
10438 class="cmtt-8"> </span><span
10439 class="cmtt-8"> </span><span
10440 class="cmtt-8"> </span><span
10441 class="cmtt-8"> </span><span
10442 class="cmtt-8"> </span><span
10443 class="cmtt-8"> </span><span
10444 class="cmtt-8"> </span><span
10445 class="cmtt-8"> </span><span
10446 class="cmtt-8"> </span><span
10447 class="cmtt-8"> </span><span
10448 class="cmtt-8"> </span><span
10449 class="cmtt-8"> </span><span
10450 class="cmtt-8"> </span><span
10451 class="cmtt-8"> </span><span
10452 class="cmtt-8"> </span><span
10453 class="cmtt-8"> </span><span
10454 class="cmtt-8"> </span><span
10455 class="cmtt-8"> </span><span
10456 class="cmtt-8"> </span><span
10457 class="cmtt-8"> </span><span
10458 class="cmtt-8"> </span><span
10459 class="cmtt-8"> </span><span
10460 class="cmtt-8"> </span><span
10461 class="cmtt-8"> </span><span
10462 class="cmtt-8"> </span><span
10463 class="cmtt-8"> </span><span
10464 class="cmtt-8"> </span><span
10465 class="cmtt-8"> </span><span
10466 class="cmtt-8"> </span><span
10467 class="cmtt-8"> </span><span
10468 class="cmtt-8"> </span><span
10469 class="cmtt-8"> </span><span
10470 class="cmtt-8"> </span><span
10471 class="cmtt-8"> </span><span
10472 class="cmtt-8"> </span><span
10473 class="cmtt-8"> </span><span
10474 class="cmtt-8"> [temp]</span><span
10475 class="cmtt-8"> integer</span><span
10476 class="cmtt-8"> modulo</span><span
10477 class="cmtt-8"> [residue\_classifications]</span>
10478 <br class="fancyvrb" /><a
10479 id="x1-110056r20"></a><span
10480 class="cmr-6">20</span><span
10481 class="cmtt-8"> </span><span
10482 class="cmtt-8"> </span><span
10483 class="cmtt-8"> </span><span
10484 class="cmtt-8"> </span><span
10485 class="cmtt-8"> </span><span
10486 class="cmtt-8"> </span><span
10487 class="cmtt-8"> </span><span
10488 class="cmtt-8"> </span><span
10489 class="cmtt-8"> </span><span
10490 class="cmtt-8"> </span><span
10491 class="cmtt-8"> </span><span
10492 class="cmtt-8"> </span><span
10493 class="cmtt-8"> </span><span
10494 class="cmtt-8"> </span><span
10495 class="cmtt-8"> </span><span
10496 class="cmtt-8"> </span><span
10497 class="cmtt-8"> </span><span
10498 class="cmtt-8"> </span><span
10499 class="cmtt-8"> </span><span
10500 class="cmtt-8"> </span><span
10501 class="cmtt-8"> </span><span
10502 class="cmtt-8"> </span><span
10503 class="cmtt-8"> </span><span
10504 class="cmtt-8"> </span><span
10505 class="cmtt-8"> </span><span
10506 class="cmtt-8"> </span><span
10507 class="cmtt-8"> </span><span
10508 class="cmtt-8"> </span><span
10509 class="cmtt-8"> </span><span
10510 class="cmtt-8"> </span><span
10511 class="cmtt-8"> </span><span
10512 class="cmtt-8"> </span><span
10513 class="cmtt-8"> 12)</span><span
10514 class="cmtt-8"> [temp]</span><span
10515 class="cmtt-8"> =</span><span
10516 class="cmtt-8"> [temp]</span><span
10517 class="cmtt-8"> /</span><span
10518 class="cmtt-8"> [residue\_classifications]</span><span
10519 class="cmtt-8"> using</span><span
10520 class="cmtt-8"> integer</span><span
10521 class="cmtt-8"> division</span>
10522 <br class="fancyvrb" /><a
10523 id="x1-110058r21"></a><span
10524 class="cmr-6">21</span><span
10525 class="cmtt-8"> </span><span
10526 class="cmtt-8"> </span>
10527 <br class="fancyvrb" /><a
10528 id="x1-110060r22"></a><span
10529 class="cmr-6">22</span><span
10530 class="cmtt-8"> </span><span
10531 class="cmtt-8"> </span><span
10532 class="cmtt-8"> </span><span
10533 class="cmtt-8"> </span><span
10534 class="cmtt-8"> </span><span
10535 class="cmtt-8"> </span><span
10536 class="cmtt-8"> </span><span
10537 class="cmtt-8"> </span><span
10538 class="cmtt-8"> </span><span
10539 class="cmtt-8"> </span><span
10540 class="cmtt-8"> </span><span
10541 class="cmtt-8"> </span><span
10542 class="cmtt-8"> </span><span
10543 class="cmtt-8"> </span><span
10544 class="cmtt-8"> </span><span
10545 class="cmtt-8"> </span><span
10546 class="cmtt-8"> </span><span
10547 class="cmtt-8"> </span><span
10548 class="cmtt-8"> </span><span
10549 class="cmtt-8"> </span><span
10550 class="cmtt-8"> </span><span
10551 class="cmtt-8"> </span><span
10552 class="cmtt-8"> </span><span
10553 class="cmtt-8"> </span><span
10554 class="cmtt-8"> </span><span
10555 class="cmtt-8"> </span><span
10556 class="cmtt-8"> </span><span
10557 class="cmtt-8"> </span><span
10558 class="cmtt-8"> </span><span
10559 class="cmtt-8"> </span><span
10560 class="cmtt-8"> </span><span
10561 class="cmtt-8"> }</span>
10562 <br class="fancyvrb" /><a
10563 id="x1-110062r23"></a><span
10564 class="cmr-6">23</span><span
10565 class="cmtt-8"> </span><span
10566 class="cmtt-8"> </span>
10567 <br class="fancyvrb" /><a
10568 id="x1-110064r24"></a><span
10569 class="cmr-6">24</span><span
10570 class="cmtt-8"> </span><span
10571 class="cmtt-8"> </span><span
10572 class="cmtt-8"> </span><span
10573 class="cmtt-8"> </span><span
10574 class="cmtt-8"> </span><span
10575 class="cmtt-8"> </span><span
10576 class="cmtt-8"> </span><span
10577 class="cmtt-8"> </span><span
10578 class="cmtt-8"> </span><span
10579 class="cmtt-8"> </span><span
10580 class="cmtt-8"> </span><span
10581 class="cmtt-8"> </span><span
10582 class="cmtt-8"> </span><span
10583 class="cmtt-8"> </span><span
10584 class="cmtt-8"> </span><span
10585 class="cmtt-8"> </span><span
10586 class="cmtt-8"> </span><span
10587 class="cmtt-8"> </span><span
10588 class="cmtt-8"> </span><span
10589 class="cmtt-8"> </span><span
10590 class="cmtt-8"> </span><span
10591 class="cmtt-8"> </span><span
10592 class="cmtt-8"> </span><span
10593 class="cmtt-8"> </span><span
10594 class="cmtt-8"> </span><span
10595 class="cmtt-8"> </span><span
10596 class="cmtt-8"> }</span>
10597 <br class="fancyvrb" /><a
10598 id="x1-110066r25"></a><span
10599 class="cmr-6">25</span><span
10600 class="cmtt-8"> </span><span
10601 class="cmtt-8"> </span>
10602 <br class="fancyvrb" /><a
10603 id="x1-110068r26"></a><span
10604 class="cmr-6">26</span><span
10605 class="cmtt-8"> </span><span
10606 class="cmtt-8"> </span><span
10607 class="cmtt-8"> </span><span
10608 class="cmtt-8"> </span><span
10609 class="cmtt-8"> </span><span
10610 class="cmtt-8"> </span><span
10611 class="cmtt-8"> </span><span
10612 class="cmtt-8"> </span><span
10613 class="cmtt-8"> </span><span
10614 class="cmtt-8"> </span><span
10615 class="cmtt-8"> </span><span
10616 class="cmtt-8"> </span><span
10617 class="cmtt-8"> </span><span
10618 class="cmtt-8"> </span><span
10619 class="cmtt-8"> </span><span
10620 class="cmtt-8"> </span><span
10621 class="cmtt-8"> </span><span
10622 class="cmtt-8"> </span><span
10623 class="cmtt-8"> </span><span
10624 class="cmtt-8"> </span><span
10625 class="cmtt-8"> </span><span
10626 class="cmtt-8"> }</span>
10627 <br class="fancyvrb" /><a
10628 id="x1-110070r27"></a><span
10629 class="cmr-6">27</span><span
10630 class="cmtt-8"> </span><span
10631 class="cmtt-8"> </span>
10632 <br class="fancyvrb" /><a
10633 id="x1-110072r28"></a><span
10634 class="cmr-6">28</span><span
10635 class="cmtt-8"> </span><span
10636 class="cmtt-8"> </span><span
10637 class="cmtt-8"> </span><span
10638 class="cmtt-8"> </span><span
10639 class="cmtt-8"> </span><span
10640 class="cmtt-8"> </span><span
10641 class="cmtt-8"> </span><span
10642 class="cmtt-8"> </span><span
10643 class="cmtt-8"> </span><span
10644 class="cmtt-8"> </span><span
10645 class="cmtt-8"> </span><span
10646 class="cmtt-8"> </span><span
10647 class="cmtt-8"> </span><span
10648 class="cmtt-8"> </span><span
10649 class="cmtt-8"> </span><span
10650 class="cmtt-8"> </span><span
10651 class="cmtt-8"> }</span>
10652 <br class="fancyvrb" /><a
10653 id="x1-110074r29"></a><span
10654 class="cmr-6">29</span><span
10655 class="cmtt-8"> </span><span
10656 class="cmtt-8"> </span>
10657 <br class="fancyvrb" /><a
10658 id="x1-110076r30"></a><span
10659 class="cmr-6">30</span><span
10660 class="cmtt-8"> </span><span
10661 class="cmtt-8"> </span><span
10662 class="cmtt-8"> </span><span
10663 class="cmtt-8"> </span><span
10664 class="cmtt-8"> </span><span
10665 class="cmtt-8"> </span><span
10666 class="cmtt-8"> </span><span
10667 class="cmtt-8"> </span><span
10668 class="cmtt-8"> </span><span
10669 class="cmtt-8"> </span><span
10670 class="cmtt-8"> </span><span
10671 class="cmtt-8"> </span><span
10672 class="cmtt-8"> 13)</span><span
10673 class="cmtt-8"> iterate</span><span
10674 class="cmtt-8"> [i]</span><span
10675 class="cmtt-8"> over</span><span
10676 class="cmtt-8"> the</span><span
10677 class="cmtt-8"> range</span><span
10678 class="cmtt-8"> 0</span><span
10679 class="cmtt-8"> ..</span><span
10680 class="cmtt-8"> ([classwords\_per\_codeword]</span><span
10681 class="cmtt-8"> -</span><span
10682 class="cmtt-8"> 1)</span><span
10683 class="cmtt-8"> while</span><span
10684 class="cmtt-8"> [partition\_count]</span>
10685 <br class="fancyvrb" /><a
10686 id="x1-110078r31"></a><span
10687 class="cmr-6">31</span><span
10688 class="cmtt-8"> </span><span
10689 class="cmtt-8"> </span><span
10690 class="cmtt-8"> </span><span
10691 class="cmtt-8"> </span><span
10692 class="cmtt-8"> </span><span
10693 class="cmtt-8"> </span><span
10694 class="cmtt-8"> </span><span
10695 class="cmtt-8"> </span><span
10696 class="cmtt-8"> </span><span
10697 class="cmtt-8"> </span><span
10698 class="cmtt-8"> </span><span
10699 class="cmtt-8"> </span><span
10700 class="cmtt-8"> </span><span
10701 class="cmtt-8"> </span><span
10702 class="cmtt-8"> </span><span
10703 class="cmtt-8"> </span><span
10704 class="cmtt-8"> is</span><span
10705 class="cmtt-8"> also</span><span
10706 class="cmtt-8"> less</span><span
10707 class="cmtt-8"> than</span><span
10708 class="cmtt-8"> [partitions\_to\_read]</span><span
10709 class="cmtt-8"> {</span>
10710 <br class="fancyvrb" /><a
10711 id="x1-110080r32"></a><span
10712 class="cmr-6">32</span><span
10713 class="cmtt-8"> </span><span
10714 class="cmtt-8"> </span>
10715 <br class="fancyvrb" /><a
10716 id="x1-110082r33"></a><span
10717 class="cmr-6">33</span><span
10718 class="cmtt-8"> </span><span
10719 class="cmtt-8"> </span><span
10720 class="cmtt-8"> </span><span
10721 class="cmtt-8"> </span><span
10722 class="cmtt-8"> </span><span
10723 class="cmtt-8"> </span><span
10724 class="cmtt-8"> </span><span
10725 class="cmtt-8"> </span><span
10726 class="cmtt-8"> </span><span
10727 class="cmtt-8"> </span><span
10728 class="cmtt-8"> </span><span
10729 class="cmtt-8"> </span><span
10730 class="cmtt-8"> </span><span
10731 class="cmtt-8"> </span><span
10732 class="cmtt-8"> </span><span
10733 class="cmtt-8"> </span><span
10734 class="cmtt-8"> </span><span
10735 class="cmtt-8"> </span><span
10736 class="cmtt-8"> 14)</span><span
10737 class="cmtt-8"> iterate</span><span
10738 class="cmtt-8"> [j]</span><span
10739 class="cmtt-8"> over</span><span
10740 class="cmtt-8"> the</span><span
10741 class="cmtt-8"> range</span><span
10742 class="cmtt-8"> 0</span><span
10743 class="cmtt-8"> ..</span><span
10744 class="cmtt-8"> [ch]-1</span><span
10745 class="cmtt-8"> {</span>
10746 <br class="fancyvrb" /><a
10747 id="x1-110084r34"></a><span
10748 class="cmr-6">34</span><span
10749 class="cmtt-8"> </span><span
10750 class="cmtt-8"> </span>
10751 <br class="fancyvrb" /><a
10752 id="x1-110086r35"></a><span
10753 class="cmr-6">35</span><span
10754 class="cmtt-8"> </span><span
10755 class="cmtt-8"> </span><span
10756 class="cmtt-8"> </span><span
10757 class="cmtt-8"> </span><span
10758 class="cmtt-8"> </span><span
10759 class="cmtt-8"> </span><span
10760 class="cmtt-8"> </span><span
10761 class="cmtt-8"> </span><span
10762 class="cmtt-8"> </span><span
10763 class="cmtt-8"> </span><span
10764 class="cmtt-8"> </span><span
10765 class="cmtt-8"> </span><span
10766 class="cmtt-8"> </span><span
10767 class="cmtt-8"> </span><span
10768 class="cmtt-8"> </span><span
10769 class="cmtt-8"> </span><span
10770 class="cmtt-8"> </span><span
10771 class="cmtt-8"> </span><span
10772 class="cmtt-8"> </span><span
10773 class="cmtt-8"> </span><span
10774 class="cmtt-8"> </span><span
10775 class="cmtt-8"> </span><span
10776 class="cmtt-8"> </span><span
10777 class="cmtt-8"> 15)</span><span
10778 class="cmtt-8"> if</span><span
10779 class="cmtt-8"> vector</span><span
10780 class="cmtt-8"> [j]</span><span
10781 class="cmtt-8"> is</span><span
10782 class="cmtt-8"> not</span><span
10783 class="cmtt-8"> marked</span><span
10784 class="cmtt-8"> ’do</span><span
10785 class="cmtt-8"> not</span><span
10786 class="cmtt-8"> decode’</span><span
10787 class="cmtt-8"> {</span>
10788 <br class="fancyvrb" /><a
10789 id="x1-110088r36"></a><span
10790 class="cmr-6">36</span><span
10791 class="cmtt-8"> </span><span
10792 class="cmtt-8"> </span>
10793 <br class="fancyvrb" /><a
10794 id="x1-110090r37"></a><span
10795 class="cmr-6">37</span><span
10796 class="cmtt-8"> </span><span
10797 class="cmtt-8"> </span><span
10798 class="cmtt-8"> </span><span
10799 class="cmtt-8"> </span><span
10800 class="cmtt-8"> </span><span
10801 class="cmtt-8"> </span><span
10802 class="cmtt-8"> </span><span
10803 class="cmtt-8"> </span><span
10804 class="cmtt-8"> </span><span
10805 class="cmtt-8"> </span><span
10806 class="cmtt-8"> </span><span
10807 class="cmtt-8"> </span><span
10808 class="cmtt-8"> </span><span
10809 class="cmtt-8"> </span><span
10810 class="cmtt-8"> </span><span
10811 class="cmtt-8"> </span><span
10812 class="cmtt-8"> </span><span
10813 class="cmtt-8"> </span><span
10814 class="cmtt-8"> </span><span
10815 class="cmtt-8"> </span><span
10816 class="cmtt-8"> </span><span
10817 class="cmtt-8"> </span><span
10818 class="cmtt-8"> </span><span
10819 class="cmtt-8"> </span><span
10820 class="cmtt-8"> </span><span
10821 class="cmtt-8"> </span><span
10822 class="cmtt-8"> </span><span
10823 class="cmtt-8"> </span><span
10824 class="cmtt-8"> 16)</span><span
10825 class="cmtt-8"> [vqclass]</span><span
10826 class="cmtt-8"> =</span><span
10827 class="cmtt-8"> array</span><span
10828 class="cmtt-8"> [classifications]</span><span
10829 class="cmtt-8"> element</span><span
10830 class="cmtt-8"> [j],[partition\_count]</span>
10831 <br class="fancyvrb" /><a
10832 id="x1-110092r38"></a><span
10833 class="cmr-6">38</span><span
10834 class="cmtt-8"> </span><span
10835 class="cmtt-8"> </span><span
10836 class="cmtt-8"> </span><span
10837 class="cmtt-8"> </span><span
10838 class="cmtt-8"> </span><span
10839 class="cmtt-8"> </span><span
10840 class="cmtt-8"> </span><span
10841 class="cmtt-8"> </span><span
10842 class="cmtt-8"> </span><span
10843 class="cmtt-8"> </span><span
10844 class="cmtt-8"> </span><span
10845 class="cmtt-8"> </span><span
10846 class="cmtt-8"> </span><span
10847 class="cmtt-8"> </span><span
10848 class="cmtt-8"> </span><span
10849 class="cmtt-8"> </span><span
10850 class="cmtt-8"> </span><span
10851 class="cmtt-8"> </span><span
10852 class="cmtt-8"> </span><span
10853 class="cmtt-8"> </span><span
10854 class="cmtt-8"> </span><span
10855 class="cmtt-8"> </span><span
10856 class="cmtt-8"> </span><span
10857 class="cmtt-8"> </span><span
10858 class="cmtt-8"> </span><span
10859 class="cmtt-8"> </span><span
10860 class="cmtt-8"> </span><span
10861 class="cmtt-8"> </span><span
10862 class="cmtt-8"> 17)</span><span
10863 class="cmtt-8"> [vqbook]</span><span
10864 class="cmtt-8"> =</span><span
10865 class="cmtt-8"> array</span><span
10866 class="cmtt-8"> [residue\_books]</span><span
10867 class="cmtt-8"> element</span><span
10868 class="cmtt-8"> [vqclass],[pass]</span>
10869 <br class="fancyvrb" /><a
10870 id="x1-110094r39"></a><span
10871 class="cmr-6">39</span><span
10872 class="cmtt-8"> </span><span
10873 class="cmtt-8"> </span><span
10874 class="cmtt-8"> </span><span
10875 class="cmtt-8"> </span><span
10876 class="cmtt-8"> </span><span
10877 class="cmtt-8"> </span><span
10878 class="cmtt-8"> </span><span
10879 class="cmtt-8"> </span><span
10880 class="cmtt-8"> </span><span
10881 class="cmtt-8"> </span><span
10882 class="cmtt-8"> </span><span
10883 class="cmtt-8"> </span><span
10884 class="cmtt-8"> </span><span
10885 class="cmtt-8"> </span><span
10886 class="cmtt-8"> </span><span
10887 class="cmtt-8"> </span><span
10888 class="cmtt-8"> </span><span
10889 class="cmtt-8"> </span><span
10890 class="cmtt-8"> </span><span
10891 class="cmtt-8"> </span><span
10892 class="cmtt-8"> </span><span
10893 class="cmtt-8"> </span><span
10894 class="cmtt-8"> </span><span
10895 class="cmtt-8"> </span><span
10896 class="cmtt-8"> </span><span
10897 class="cmtt-8"> </span><span
10898 class="cmtt-8"> </span><span
10899 class="cmtt-8"> </span><span
10900 class="cmtt-8"> 18)</span><span
10901 class="cmtt-8"> if</span><span
10902 class="cmtt-8"> ([vqbook]</span><span
10903 class="cmtt-8"> is</span><span
10904 class="cmtt-8"> not</span><span
10905 class="cmtt-8"> ’unused’)</span><span
10906 class="cmtt-8"> {</span>
10907 <br class="fancyvrb" /><a
10908 id="x1-110096r40"></a><span
10909 class="cmr-6">40</span><span
10910 class="cmtt-8"> </span><span
10911 class="cmtt-8"> </span>
10912 <br class="fancyvrb" /><a
10913 id="x1-110098r41"></a><span
10914 class="cmr-6">41</span><span
10915 class="cmtt-8"> </span><span
10916 class="cmtt-8"> </span><span
10917 class="cmtt-8"> </span><span
10918 class="cmtt-8"> </span><span
10919 class="cmtt-8"> </span><span
10920 class="cmtt-8"> </span><span
10921 class="cmtt-8"> </span><span
10922 class="cmtt-8"> </span><span
10923 class="cmtt-8"> </span><span
10924 class="cmtt-8"> </span><span
10925 class="cmtt-8"> </span><span
10926 class="cmtt-8"> </span><span
10927 class="cmtt-8"> </span><span
10928 class="cmtt-8"> </span><span
10929 class="cmtt-8"> </span><span
10930 class="cmtt-8"> </span><span
10931 class="cmtt-8"> </span><span
10932 class="cmtt-8"> </span><span
10933 class="cmtt-8"> </span><span
10934 class="cmtt-8"> </span><span
10935 class="cmtt-8"> </span><span
10936 class="cmtt-8"> </span><span
10937 class="cmtt-8"> </span><span
10938 class="cmtt-8"> </span><span
10939 class="cmtt-8"> </span><span
10940 class="cmtt-8"> </span><span
10941 class="cmtt-8"> </span><span
10942 class="cmtt-8"> </span><span
10943 class="cmtt-8"> </span><span
10944 class="cmtt-8"> </span><span
10945 class="cmtt-8"> </span><span
10946 class="cmtt-8"> </span><span
10947 class="cmtt-8"> </span><span
10948 class="cmtt-8"> 19)</span><span
10949 class="cmtt-8"> decode</span><span
10950 class="cmtt-8"> partition</span><span
10951 class="cmtt-8"> into</span><span
10952 class="cmtt-8"> output</span><span
10953 class="cmtt-8"> vector</span><span
10954 class="cmtt-8"> number</span><span
10955 class="cmtt-8"> [j],</span><span
10956 class="cmtt-8"> starting</span><span
10957 class="cmtt-8"> at</span><span
10958 class="cmtt-8"> scalar</span>
10959 <br class="fancyvrb" /><a
10960 id="x1-110100r42"></a><span
10961 class="cmr-6">42</span><span
10962 class="cmtt-8"> </span><span
10963 class="cmtt-8"> </span><span
10964 class="cmtt-8"> </span><span
10965 class="cmtt-8"> </span><span
10966 class="cmtt-8"> </span><span
10967 class="cmtt-8"> </span><span
10968 class="cmtt-8"> </span><span
10969 class="cmtt-8"> </span><span
10970 class="cmtt-8"> </span><span
10971 class="cmtt-8"> </span><span
10972 class="cmtt-8"> </span><span
10973 class="cmtt-8"> </span><span
10974 class="cmtt-8"> </span><span
10975 class="cmtt-8"> </span><span
10976 class="cmtt-8"> </span><span
10977 class="cmtt-8"> </span><span
10978 class="cmtt-8"> </span><span
10979 class="cmtt-8"> </span><span
10980 class="cmtt-8"> </span><span
10981 class="cmtt-8"> </span><span
10982 class="cmtt-8"> </span><span
10983 class="cmtt-8"> </span><span
10984 class="cmtt-8"> </span><span
10985 class="cmtt-8"> </span><span
10986 class="cmtt-8"> </span><span
10987 class="cmtt-8"> </span><span
10988 class="cmtt-8"> </span><span
10989 class="cmtt-8"> </span><span
10990 class="cmtt-8"> </span><span
10991 class="cmtt-8"> </span><span
10992 class="cmtt-8"> </span><span
10993 class="cmtt-8"> </span><span
10994 class="cmtt-8"> </span><span
10995 class="cmtt-8"> </span><span
10996 class="cmtt-8"> </span><span
10997 class="cmtt-8"> </span><span
10998 class="cmtt-8"> </span><span
10999 class="cmtt-8"> offset</span><span
11000 class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span
11001 class="cmtt-8"> using</span>
11002 <br class="fancyvrb" /><a
11003 id="x1-110102r43"></a><span
11004 class="cmr-6">43</span><span
11005 class="cmtt-8"> </span><span
11006 class="cmtt-8"> </span><span
11007 class="cmtt-8"> </span><span
11008 class="cmtt-8"> </span><span
11009 class="cmtt-8"> </span><span
11010 class="cmtt-8"> </span><span
11011 class="cmtt-8"> </span><span
11012 class="cmtt-8"> </span><span
11013 class="cmtt-8"> </span><span
11014 class="cmtt-8"> </span><span
11015 class="cmtt-8"> </span><span
11016 class="cmtt-8"> </span><span
11017 class="cmtt-8"> </span><span
11018 class="cmtt-8"> </span><span
11019 class="cmtt-8"> </span><span
11020 class="cmtt-8"> </span><span
11021 class="cmtt-8"> </span><span
11022 class="cmtt-8"> </span><span
11023 class="cmtt-8"> </span><span
11024 class="cmtt-8"> </span><span
11025 class="cmtt-8"> </span><span
11026 class="cmtt-8"> </span><span
11027 class="cmtt-8"> </span><span
11028 class="cmtt-8"> </span><span
11029 class="cmtt-8"> </span><span
11030 class="cmtt-8"> </span><span
11031 class="cmtt-8"> </span><span
11032 class="cmtt-8"> </span><span
11033 class="cmtt-8"> </span><span
11034 class="cmtt-8"> </span><span
11035 class="cmtt-8"> </span><span
11036 class="cmtt-8"> </span><span
11037 class="cmtt-8"> </span><span
11038 class="cmtt-8"> </span><span
11039 class="cmtt-8"> </span><span
11040 class="cmtt-8"> </span><span
11041 class="cmtt-8"> </span><span
11042 class="cmtt-8"> codebook</span><span
11043 class="cmtt-8"> number</span><span
11044 class="cmtt-8"> [vqbook]</span><span
11045 class="cmtt-8"> in</span><span
11046 class="cmtt-8"> VQ</span><span
11047 class="cmtt-8"> context</span>
11048 <br class="fancyvrb" /><a
11049 id="x1-110104r44"></a><span
11050 class="cmr-6">44</span><span
11051 class="cmtt-8"> </span><span
11052 class="cmtt-8"> </span><span
11053 class="cmtt-8"> </span><span
11054 class="cmtt-8"> </span><span
11055 class="cmtt-8"> </span><span
11056 class="cmtt-8"> </span><span
11057 class="cmtt-8"> </span><span
11058 class="cmtt-8"> </span><span
11059 class="cmtt-8"> </span><span
11060 class="cmtt-8"> </span><span
11061 class="cmtt-8"> </span><span
11062 class="cmtt-8"> </span><span
11063 class="cmtt-8"> </span><span
11064 class="cmtt-8"> </span><span
11065 class="cmtt-8"> </span><span
11066 class="cmtt-8"> </span><span
11067 class="cmtt-8"> </span><span
11068 class="cmtt-8"> </span><span
11069 class="cmtt-8"> </span><span
11070 class="cmtt-8"> </span><span
11071 class="cmtt-8"> </span><span
11072 class="cmtt-8"> </span><span
11073 class="cmtt-8"> </span><span
11074 class="cmtt-8"> </span><span
11075 class="cmtt-8"> </span><span
11076 class="cmtt-8"> </span><span
11077 class="cmtt-8"> </span><span
11078 class="cmtt-8"> }</span>
11082 <br class="fancyvrb" /><a
11083 id="x1-110106r45"></a><span
11084 class="cmr-6">45</span><span
11085 class="cmtt-8"> </span><span
11086 class="cmtt-8"> </span><span
11087 class="cmtt-8"> </span><span
11088 class="cmtt-8"> </span><span
11089 class="cmtt-8"> </span><span
11090 class="cmtt-8"> </span><span
11091 class="cmtt-8"> </span><span
11092 class="cmtt-8"> </span><span
11093 class="cmtt-8"> </span><span
11094 class="cmtt-8"> </span><span
11095 class="cmtt-8"> </span><span
11096 class="cmtt-8"> </span><span
11097 class="cmtt-8"> </span><span
11098 class="cmtt-8"> </span><span
11099 class="cmtt-8"> </span><span
11100 class="cmtt-8"> </span><span
11101 class="cmtt-8"> </span><span
11102 class="cmtt-8"> </span><span
11103 class="cmtt-8"> </span><span
11104 class="cmtt-8"> </span><span
11105 class="cmtt-8"> </span><span
11106 class="cmtt-8"> </span><span
11107 class="cmtt-8"> }</span>
11108 <br class="fancyvrb" /><a
11109 id="x1-110108r46"></a><span
11110 class="cmr-6">46</span><span
11111 class="cmtt-8"> </span><span
11112 class="cmtt-8"> </span>
11113 <br class="fancyvrb" /><a
11114 id="x1-110110r47"></a><span
11115 class="cmr-6">47</span><span
11116 class="cmtt-8"> </span><span
11117 class="cmtt-8"> </span><span
11118 class="cmtt-8"> </span><span
11119 class="cmtt-8"> </span><span
11120 class="cmtt-8"> </span><span
11121 class="cmtt-8"> </span><span
11122 class="cmtt-8"> </span><span
11123 class="cmtt-8"> </span><span
11124 class="cmtt-8"> </span><span
11125 class="cmtt-8"> </span><span
11126 class="cmtt-8"> </span><span
11127 class="cmtt-8"> </span><span
11128 class="cmtt-8"> </span><span
11129 class="cmtt-8"> </span><span
11130 class="cmtt-8"> </span><span
11131 class="cmtt-8"> </span><span
11132 class="cmtt-8"> </span><span
11133 class="cmtt-8"> </span><span
11134 class="cmtt-8"> 20)</span><span
11135 class="cmtt-8"> increment</span><span
11136 class="cmtt-8"> [partition\_count]</span><span
11137 class="cmtt-8"> by</span><span
11138 class="cmtt-8"> one</span>
11139 <br class="fancyvrb" /><a
11140 id="x1-110112r48"></a><span
11141 class="cmr-6">48</span><span
11142 class="cmtt-8"> </span><span
11143 class="cmtt-8"> </span>
11144 <br class="fancyvrb" /><a
11145 id="x1-110114r49"></a><span
11146 class="cmr-6">49</span><span
11147 class="cmtt-8"> </span><span
11148 class="cmtt-8"> </span><span
11149 class="cmtt-8"> </span><span
11150 class="cmtt-8"> </span><span
11151 class="cmtt-8"> </span><span
11152 class="cmtt-8"> </span><span
11153 class="cmtt-8"> </span><span
11154 class="cmtt-8"> </span><span
11155 class="cmtt-8"> </span><span
11156 class="cmtt-8"> </span><span
11157 class="cmtt-8"> </span><span
11158 class="cmtt-8"> </span><span
11159 class="cmtt-8"> </span><span
11160 class="cmtt-8"> </span><span
11161 class="cmtt-8"> </span><span
11162 class="cmtt-8"> </span><span
11163 class="cmtt-8"> }</span>
11164 <br class="fancyvrb" /><a
11165 id="x1-110116r50"></a><span
11166 class="cmr-6">50</span><span
11167 class="cmtt-8"> </span><span
11168 class="cmtt-8"> </span><span
11169 class="cmtt-8"> </span><span
11170 class="cmtt-8"> </span><span
11171 class="cmtt-8"> </span><span
11172 class="cmtt-8"> </span><span
11173 class="cmtt-8"> </span><span
11174 class="cmtt-8"> </span><span
11175 class="cmtt-8"> </span><span
11176 class="cmtt-8"> </span><span
11177 class="cmtt-8"> </span><span
11178 class="cmtt-8"> }</span>
11179 <br class="fancyvrb" /><a
11180 id="x1-110118r51"></a><span
11181 class="cmr-6">51</span><span
11182 class="cmtt-8"> </span><span
11183 class="cmtt-8"> </span><span
11184 class="cmtt-8"> </span><span
11185 class="cmtt-8"> </span><span
11186 class="cmtt-8"> </span><span
11187 class="cmtt-8"> </span><span
11188 class="cmtt-8"> }</span>
11189 <br class="fancyvrb" /><a
11190 id="x1-110120r52"></a><span
11191 class="cmr-6">52</span><span
11192 class="cmtt-8"> </span><span
11193 class="cmtt-8"> </span>
11194 <br class="fancyvrb" /><a
11195 id="x1-110122r53"></a><span
11196 class="cmr-6">53</span><span
11197 class="cmtt-8"> </span><span
11198 class="cmtt-8"> </span><span
11199 class="cmtt-8"> 21)</span><span
11200 class="cmtt-8"> done</span>
11201 <br class="fancyvrb" /><a
11202 id="x1-110124r54"></a><span
11203 class="cmr-6">54</span><span
11204 class="cmtt-8"> </span><span
11205 class="cmtt-8"> </span>
11207 <!--l. 344--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
11208 Decode returns the result of vector decode up to that point.
11209 <!--l. 350--><p class="noindent" >
11210 <h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a
11211 id="x1-1110008.6.3"></a>format 0 specifics</h5>
11212 <!--l. 352--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
11213 section. The following pseudocode presents the same algorithm. Assume:
11214 <ul class="itemize1">
11215 <li class="itemize"><span
11216 class="cmtt-12">[n] </span>is the value in <span
11217 class="cmtt-12">[residue_partition_size]</span>
11219 <li class="itemize"><span
11220 class="cmtt-12">[v] </span>is the residue vector
11222 <li class="itemize"><span
11223 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
11224 <!--l. 363--><p class="noindent" >
11225 <div class="fancyvrb" id="fancyvrb41">
11227 id="x1-111002r1"></a><span
11228 class="cmr-6">1</span><span
11229 class="cmtt-8"> </span><span
11230 class="cmtt-8"> </span><span
11231 class="cmtt-8"> 1)</span><span
11232 class="cmtt-8"> [step]</span><span
11233 class="cmtt-8"> =</span><span
11234 class="cmtt-8"> [n]</span><span
11235 class="cmtt-8"> /</span><span
11236 class="cmtt-8"> [codebook\_dimensions]</span>
11237 <br class="fancyvrb" /><a
11238 id="x1-111004r2"></a><span
11239 class="cmr-6">2</span><span
11240 class="cmtt-8"> </span><span
11241 class="cmtt-8"> </span><span
11242 class="cmtt-8"> 2)</span><span
11243 class="cmtt-8"> iterate</span><span
11244 class="cmtt-8"> [i]</span><span
11245 class="cmtt-8"> over</span><span
11246 class="cmtt-8"> the</span><span
11247 class="cmtt-8"> range</span><span
11248 class="cmtt-8"> 0</span><span
11249 class="cmtt-8"> ...</span><span
11250 class="cmtt-8"> [step]-1</span><span
11251 class="cmtt-8"> {</span>
11252 <br class="fancyvrb" /><a
11253 id="x1-111006r3"></a><span
11254 class="cmr-6">3</span><span
11255 class="cmtt-8"> </span><span
11256 class="cmtt-8"> </span>
11257 <br class="fancyvrb" /><a
11258 id="x1-111008r4"></a><span
11259 class="cmr-6">4</span><span
11260 class="cmtt-8"> </span><span
11261 class="cmtt-8"> </span><span
11262 class="cmtt-8"> </span><span
11263 class="cmtt-8"> </span><span
11264 class="cmtt-8"> </span><span
11265 class="cmtt-8"> </span><span
11266 class="cmtt-8"> </span><span
11267 class="cmtt-8"> 3)</span><span
11268 class="cmtt-8"> vector</span><span
11269 class="cmtt-8"> [entry\_temp]</span><span
11270 class="cmtt-8"> =</span><span
11271 class="cmtt-8"> read</span><span
11272 class="cmtt-8"> vector</span><span
11273 class="cmtt-8"> from</span><span
11274 class="cmtt-8"> packet</span><span
11275 class="cmtt-8"> using</span><span
11276 class="cmtt-8"> current</span><span
11277 class="cmtt-8"> codebook</span><span
11278 class="cmtt-8"> in</span><span
11279 class="cmtt-8"> VQ</span><span
11280 class="cmtt-8"> context</span>
11281 <br class="fancyvrb" /><a
11282 id="x1-111010r5"></a><span
11283 class="cmr-6">5</span><span
11284 class="cmtt-8"> </span><span
11285 class="cmtt-8"> </span><span
11286 class="cmtt-8"> </span><span
11287 class="cmtt-8"> </span><span
11288 class="cmtt-8"> </span><span
11289 class="cmtt-8"> </span><span
11290 class="cmtt-8"> </span><span
11291 class="cmtt-8"> 4)</span><span
11292 class="cmtt-8"> iterate</span><span
11293 class="cmtt-8"> [j]</span><span
11294 class="cmtt-8"> over</span><span
11295 class="cmtt-8"> the</span><span
11296 class="cmtt-8"> range</span><span
11297 class="cmtt-8"> 0</span><span
11298 class="cmtt-8"> ...</span><span
11299 class="cmtt-8"> [codebook\_dimensions]-1</span><span
11300 class="cmtt-8"> {</span>
11301 <br class="fancyvrb" /><a
11302 id="x1-111012r6"></a><span
11303 class="cmr-6">6</span><span
11304 class="cmtt-8"> </span><span
11305 class="cmtt-8"> </span>
11306 <br class="fancyvrb" /><a
11307 id="x1-111014r7"></a><span
11308 class="cmr-6">7</span><span
11309 class="cmtt-8"> </span><span
11310 class="cmtt-8"> </span><span
11311 class="cmtt-8"> </span><span
11312 class="cmtt-8"> </span><span
11313 class="cmtt-8"> </span><span
11314 class="cmtt-8"> </span><span
11315 class="cmtt-8"> </span><span
11316 class="cmtt-8"> </span><span
11317 class="cmtt-8"> </span><span
11318 class="cmtt-8"> </span><span
11319 class="cmtt-8"> </span><span
11320 class="cmtt-8"> </span><span
11321 class="cmtt-8"> 5)</span><span
11322 class="cmtt-8"> vector</span><span
11323 class="cmtt-8"> [v]</span><span
11324 class="cmtt-8"> element</span><span
11325 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
11326 class="cmtt-8"> =</span>
11327 <br class="fancyvrb" /><a
11328 id="x1-111016r8"></a><span
11329 class="cmr-6">8</span><span
11330 class="cmtt-8"> </span><span
11331 class="cmtt-8">  </span><span
11332 class="cmtt-8"> </span><span
11333 class="cmtt-8"> </span><span
11334 class="cmtt-8"> </span><span
11335 class="cmtt-8"> </span><span
11336 class="cmtt-8"> </span><span
11337 class="cmtt-8"> </span><span
11338 class="cmtt-8"> </span><span
11339 class="cmtt-8"> vector</span><span
11340 class="cmtt-8"> [v]</span><span
11341 class="cmtt-8"> element</span><span
11342 class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
11343 class="cmtt-8"> +</span>
11344 <br class="fancyvrb" /><a
11345 id="x1-111018r9"></a><span
11346 class="cmr-6">9</span><span
11347 class="cmtt-8"> </span><span
11348 class="cmtt-8"> </span><span
11349 class="cmtt-8"> </span><span
11350 class="cmtt-8"> </span><span
11351 class="cmtt-8"> </span><span
11352 class="cmtt-8"> </span><span
11353 class="cmtt-8"> </span><span
11354 class="cmtt-8"> </span><span
11355 class="cmtt-8"> </span><span
11356 class="cmtt-8"> </span><span
11357 class="cmtt-8"> </span><span
11358 class="cmtt-8"> </span><span
11359 class="cmtt-8"> </span><span
11360 class="cmtt-8"> </span><span
11361 class="cmtt-8"> </span><span
11362 class="cmtt-8"> </span><span
11363 class="cmtt-8"> </span><span
11364 class="cmtt-8"> vector</span><span
11365 class="cmtt-8"> [entry\_temp]</span><span
11366 class="cmtt-8"> element</span><span
11367 class="cmtt-8"> [j]</span>
11368 <br class="fancyvrb" /><a
11369 id="x1-111020r10"></a><span
11370 class="cmr-6">10</span><span
11371 class="cmtt-8"> </span><span
11372 class="cmtt-8"> </span>
11373 <br class="fancyvrb" /><a
11374 id="x1-111022r11"></a><span
11375 class="cmr-6">11</span><span
11376 class="cmtt-8"> </span><span
11377 class="cmtt-8"> </span><span
11378 class="cmtt-8"> </span><span
11379 class="cmtt-8"> </span><span
11380 class="cmtt-8"> </span><span
11381 class="cmtt-8"> </span><span
11382 class="cmtt-8"> </span><span
11383 class="cmtt-8"> </span><span
11384 class="cmtt-8"> </span><span
11385 class="cmtt-8"> </span><span
11386 class="cmtt-8"> }</span>
11387 <br class="fancyvrb" /><a
11388 id="x1-111024r12"></a><span
11389 class="cmr-6">12</span><span
11390 class="cmtt-8"> </span><span
11391 class="cmtt-8"> </span>
11392 <br class="fancyvrb" /><a
11393 id="x1-111026r13"></a><span
11394 class="cmr-6">13</span><span
11395 class="cmtt-8"> </span><span
11396 class="cmtt-8"> </span><span
11397 class="cmtt-8"> </span><span
11398 class="cmtt-8"> </span><span
11399 class="cmtt-8"> </span><span
11400 class="cmtt-8"> }</span>
11401 <br class="fancyvrb" /><a
11402 id="x1-111028r14"></a><span
11403 class="cmr-6">14</span><span
11404 class="cmtt-8"> </span><span
11405 class="cmtt-8"> </span>
11406 <br class="fancyvrb" /><a
11407 id="x1-111030r15"></a><span
11408 class="cmr-6">15</span><span
11409 class="cmtt-8"> </span><span
11410 class="cmtt-8"> </span><span
11411 class="cmtt-8"> </span><span
11412 class="cmtt-8"> 6)</span><span
11413 class="cmtt-8"> done</span>
11414 <br class="fancyvrb" /><a
11415 id="x1-111032r16"></a><span
11416 class="cmr-6">16</span><span
11417 class="cmtt-8"> </span><span
11418 class="cmtt-8"> </span>
11423 <!--l. 384--><p class="noindent" >
11424 <h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a
11425 id="x1-1120008.6.4"></a>format 1 specifics</h5>
11426 <!--l. 386--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
11427 section. The following pseudocode presents the same algorithm. Assume:
11428 <ul class="itemize1">
11429 <li class="itemize"><span
11430 class="cmtt-12">[n] </span>is the value in <span
11431 class="cmtt-12">[residue_partition_size]</span>
11433 <li class="itemize"><span
11434 class="cmtt-12">[v] </span>is the residue vector
11436 <li class="itemize"><span
11437 class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
11438 <!--l. 398--><p class="noindent" >
11439 <div class="fancyvrb" id="fancyvrb42">
11441 id="x1-112002r1"></a><span
11442 class="cmr-6">1</span><span
11443 class="cmtt-8"> </span><span
11444 class="cmtt-8"> </span><span
11445 class="cmtt-8"> 1)</span><span
11446 class="cmtt-8"> [i]</span><span
11447 class="cmtt-8"> =</span><span
11448 class="cmtt-8"> 0</span>
11449 <br class="fancyvrb" /><a
11450 id="x1-112004r2"></a><span
11451 class="cmr-6">2</span><span
11452 class="cmtt-8"> </span><span
11453 class="cmtt-8"> </span><span
11454 class="cmtt-8"> 2)</span><span
11455 class="cmtt-8"> vector</span><span
11456 class="cmtt-8"> [entry\_temp]</span><span
11457 class="cmtt-8"> =</span><span
11458 class="cmtt-8"> read</span><span
11459 class="cmtt-8"> vector</span><span
11460 class="cmtt-8"> from</span><span
11461 class="cmtt-8"> packet</span><span
11462 class="cmtt-8"> using</span><span
11463 class="cmtt-8"> current</span><span
11464 class="cmtt-8"> codebook</span><span
11465 class="cmtt-8"> in</span><span
11466 class="cmtt-8"> VQ</span><span
11467 class="cmtt-8"> context</span>
11468 <br class="fancyvrb" /><a
11469 id="x1-112006r3"></a><span
11470 class="cmr-6">3</span><span
11471 class="cmtt-8"> </span><span
11472 class="cmtt-8"> </span><span
11473 class="cmtt-8"> 3)</span><span
11474 class="cmtt-8"> iterate</span><span
11475 class="cmtt-8"> [j]</span><span
11476 class="cmtt-8"> over</span><span
11477 class="cmtt-8"> the</span><span
11478 class="cmtt-8"> range</span><span
11479 class="cmtt-8"> 0</span><span
11480 class="cmtt-8"> ...</span><span
11481 class="cmtt-8"> [codebook\_dimensions]-1</span><span
11482 class="cmtt-8"> {</span>
11483 <br class="fancyvrb" /><a
11484 id="x1-112008r4"></a><span
11485 class="cmr-6">4</span><span
11486 class="cmtt-8"> </span><span
11487 class="cmtt-8"> </span>
11488 <br class="fancyvrb" /><a
11489 id="x1-112010r5"></a><span
11490 class="cmr-6">5</span><span
11491 class="cmtt-8"> </span><span
11492 class="cmtt-8"> </span><span
11493 class="cmtt-8"> </span><span
11494 class="cmtt-8"> </span><span
11495 class="cmtt-8"> </span><span
11496 class="cmtt-8"> </span><span
11497 class="cmtt-8"> </span><span
11498 class="cmtt-8"> 4)</span><span
11499 class="cmtt-8"> vector</span><span
11500 class="cmtt-8"> [v]</span><span
11501 class="cmtt-8"> element</span><span
11502 class="cmtt-8"> ([offset]+[i])</span><span
11503 class="cmtt-8"> =</span>
11504 <br class="fancyvrb" /><a
11505 id="x1-112012r6"></a><span
11506 class="cmr-6">6</span><span
11507 class="cmtt-8"> </span><span
11508 class="cmtt-8">  </span><span
11509 class="cmtt-8"> </span><span
11510 class="cmtt-8"> vector</span><span
11511 class="cmtt-8"> [v]</span><span
11512 class="cmtt-8"> element</span><span
11513 class="cmtt-8"> ([offset]+[i])</span><span
11514 class="cmtt-8"> +</span>
11515 <br class="fancyvrb" /><a
11516 id="x1-112014r7"></a><span
11517 class="cmr-6">7</span><span
11518 class="cmtt-8"> </span><span
11519 class="cmtt-8"> </span><span
11520 class="cmtt-8"> </span><span
11521 class="cmtt-8"> </span><span
11522 class="cmtt-8"> </span><span
11523 class="cmtt-8"> </span><span
11524 class="cmtt-8"> </span><span
11525 class="cmtt-8"> </span><span
11526 class="cmtt-8"> </span><span
11527 class="cmtt-8"> </span><span
11528 class="cmtt-8"> </span><span
11529 class="cmtt-8"> vector</span><span
11530 class="cmtt-8"> [entry\_temp]</span><span
11531 class="cmtt-8"> element</span><span
11532 class="cmtt-8"> [j]</span>
11533 <br class="fancyvrb" /><a
11534 id="x1-112016r8"></a><span
11535 class="cmr-6">8</span><span
11536 class="cmtt-8"> </span><span
11537 class="cmtt-8"> </span><span
11538 class="cmtt-8"> </span><span
11539 class="cmtt-8"> </span><span
11540 class="cmtt-8"> </span><span
11541 class="cmtt-8"> </span><span
11542 class="cmtt-8"> </span><span
11543 class="cmtt-8"> 5)</span><span
11544 class="cmtt-8"> increment</span><span
11545 class="cmtt-8"> [i]</span>
11546 <br class="fancyvrb" /><a
11547 id="x1-112018r9"></a><span
11548 class="cmr-6">9</span><span
11549 class="cmtt-8"> </span><span
11550 class="cmtt-8"> </span>
11551 <br class="fancyvrb" /><a
11552 id="x1-112020r10"></a><span
11553 class="cmr-6">10</span><span
11554 class="cmtt-8"> </span><span
11555 class="cmtt-8"> </span><span
11556 class="cmtt-8"> </span><span
11557 class="cmtt-8"> </span><span
11558 class="cmtt-8"> </span><span
11559 class="cmtt-8"> }</span>
11560 <br class="fancyvrb" /><a
11561 id="x1-112022r11"></a><span
11562 class="cmr-6">11</span><span
11563 class="cmtt-8"> </span><span
11564 class="cmtt-8"> </span>
11565 <br class="fancyvrb" /><a
11566 id="x1-112024r12"></a><span
11567 class="cmr-6">12</span><span
11568 class="cmtt-8"> </span><span
11569 class="cmtt-8"> </span><span
11570 class="cmtt-8"> </span><span
11571 class="cmtt-8"> 6)</span><span
11572 class="cmtt-8"> if</span><span
11573 class="cmtt-8"> (</span><span
11574 class="cmtt-8"> [i]</span><span
11575 class="cmtt-8"> is</span><span
11576 class="cmtt-8"> less</span><span
11577 class="cmtt-8"> than</span><span
11578 class="cmtt-8"> [n]</span><span
11579 class="cmtt-8"> )</span><span
11580 class="cmtt-8"> continue</span><span
11581 class="cmtt-8"> at</span><span
11582 class="cmtt-8"> step</span><span
11583 class="cmtt-8"> 2</span>
11584 <br class="fancyvrb" /><a
11585 id="x1-112026r13"></a><span
11586 class="cmr-6">13</span><span
11587 class="cmtt-8"> </span><span
11588 class="cmtt-8"> </span><span
11589 class="cmtt-8"> </span><span
11590 class="cmtt-8"> 7)</span><span
11591 class="cmtt-8"> done</span>
11593 <!--l. 416--><p class="noindent" >
11594 <h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a
11595 id="x1-1130008.6.5"></a>format 2 specifics</h5>
11596 <!--l. 418--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
11597 additional post-decode step after a normal format 1 decode.
11601 <!--l. 421--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
11602 ’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
11603 the vectors are decoded. We then request normal format 1 to decode a single vector
11604 representing all output channels, rather than a vector for each channel. After decode,
11605 deinterleave the vector into independent vectors, one for each output channel. That
11607 <!--l. 429--><p class="noindent" >
11608 <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
11610 class="enumerate-enumitem">If all vectors 0 through <span
11611 class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
11613 class="cmtt-12">[v]</span>of length <span
11614 class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
11616 </dd><dt class="enumerate-enumitem">
11618 class="enumerate-enumitem">Rather than performing format 1 decode to produce <span
11619 class="cmti-12">ch </span>vectors of length <span
11620 class="cmti-12">n </span>each, call
11621 format 1 decode to produce a single vector <span
11622 class="cmtt-12">[v] </span>of length <span
11623 class="cmti-12">ch*n</span>.
11624 </dd><dt class="enumerate-enumitem">
11626 class="enumerate-enumitem">Post decode: Deinterleave the single vector <span
11627 class="cmtt-12">[v] </span>returned by format 1 decode as
11628 described above into <span
11629 class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
11631 <div class="fancyvrb" id="fancyvrb43">
11633 id="x1-113005r1"></a><span
11634 class="cmr-6">1</span><span
11635 class="cmtt-8"> </span><span
11636 class="cmtt-8"> </span><span
11637 class="cmtt-8"> </span><span
11638 class="cmtt-8"> 1)</span><span
11639 class="cmtt-8"> iterate</span><span
11640 class="cmtt-8"> [i]</span><span
11641 class="cmtt-8"> over</span><span
11642 class="cmtt-8"> the</span><span
11643 class="cmtt-8"> range</span><span
11644 class="cmtt-8"> 0</span><span
11645 class="cmtt-8"> ...</span><span
11646 class="cmtt-8"> [n]-1</span><span
11647 class="cmtt-8"> {</span>
11648 <br class="fancyvrb" /><a
11649 id="x1-113007r2"></a><span
11650 class="cmr-6">2</span><span
11651 class="cmtt-8"> </span><span
11652 class="cmtt-8"> </span>
11653 <br class="fancyvrb" /><a
11654 id="x1-113009r3"></a><span
11655 class="cmr-6">3</span><span
11656 class="cmtt-8"> </span><span
11657 class="cmtt-8"> </span><span
11658 class="cmtt-8"> </span><span
11659 class="cmtt-8"> </span><span
11660 class="cmtt-8"> </span><span
11661 class="cmtt-8"> </span><span
11662 class="cmtt-8"> </span><span
11663 class="cmtt-8"> </span><span
11664 class="cmtt-8"> 2)</span><span
11665 class="cmtt-8"> iterate</span><span
11666 class="cmtt-8"> [j]</span><span
11667 class="cmtt-8"> over</span><span
11668 class="cmtt-8"> the</span><span
11669 class="cmtt-8"> range</span><span
11670 class="cmtt-8"> 0</span><span
11671 class="cmtt-8"> ...</span><span
11672 class="cmtt-8"> [ch]-1</span><span
11673 class="cmtt-8"> {</span>
11674 <br class="fancyvrb" /><a
11675 id="x1-113011r4"></a><span
11676 class="cmr-6">4</span><span
11677 class="cmtt-8"> </span><span
11678 class="cmtt-8"> </span>
11679 <br class="fancyvrb" /><a
11680 id="x1-113013r5"></a><span
11681 class="cmr-6">5</span><span
11682 class="cmtt-8"> </span><span
11683 class="cmtt-8"> </span><span
11684 class="cmtt-8"> </span><span
11685 class="cmtt-8"> </span><span
11686 class="cmtt-8"> </span><span
11687 class="cmtt-8"> </span><span
11688 class="cmtt-8"> </span><span
11689 class="cmtt-8"> </span><span
11690 class="cmtt-8"> </span><span
11691 class="cmtt-8"> </span><span
11692 class="cmtt-8"> </span><span
11693 class="cmtt-8"> </span><span
11694 class="cmtt-8"> </span><span
11695 class="cmtt-8"> 3)</span><span
11696 class="cmtt-8"> output</span><span
11697 class="cmtt-8"> vector</span><span
11698 class="cmtt-8"> number</span><span
11699 class="cmtt-8"> [j]</span><span
11700 class="cmtt-8"> element</span><span
11701 class="cmtt-8"> [i]</span><span
11702 class="cmtt-8"> =</span><span
11703 class="cmtt-8"> vector</span><span
11704 class="cmtt-8"> [v]</span><span
11705 class="cmtt-8"> element</span><span
11706 class="cmtt-8"> ([i]</span><span
11707 class="cmtt-8"> *</span><span
11708 class="cmtt-8"> [ch]</span><span
11709 class="cmtt-8"> +</span><span
11710 class="cmtt-8"> [j])</span>
11711 <br class="fancyvrb" /><a
11712 id="x1-113015r6"></a><span
11713 class="cmr-6">6</span><span
11714 class="cmtt-8"> </span><span
11715 class="cmtt-8"> </span>
11716 <br class="fancyvrb" /><a
11717 id="x1-113017r7"></a><span
11718 class="cmr-6">7</span><span
11719 class="cmtt-8"> </span><span
11720 class="cmtt-8"> </span><span
11721 class="cmtt-8"> </span><span
11722 class="cmtt-8"> </span><span
11723 class="cmtt-8"> </span><span
11724 class="cmtt-8"> </span><span
11725 class="cmtt-8"> </span><span
11726 class="cmtt-8"> </span><span
11727 class="cmtt-8"> </span><span
11728 class="cmtt-8"> </span><span
11729 class="cmtt-8"> </span><span
11730 class="cmtt-8"> }</span>
11731 <br class="fancyvrb" /><a
11732 id="x1-113019r8"></a><span
11733 class="cmr-6">8</span><span
11734 class="cmtt-8"> </span><span
11735 class="cmtt-8"> </span><span
11736 class="cmtt-8"> </span><span
11737 class="cmtt-8"> </span><span
11738 class="cmtt-8"> </span><span
11739 class="cmtt-8"> </span><span
11740 class="cmtt-8"> }</span>
11741 <br class="fancyvrb" /><a
11742 id="x1-113021r9"></a><span
11743 class="cmr-6">9</span><span
11744 class="cmtt-8"> </span><span
11745 class="cmtt-8"> </span>
11746 <br class="fancyvrb" /><a
11747 id="x1-113023r10"></a><span
11748 class="cmr-6">10</span><span
11749 class="cmtt-8"> </span><span
11750 class="cmtt-8"> </span><span
11751 class="cmtt-8"> </span><span
11752 class="cmtt-8"> 4)</span><span
11753 class="cmtt-8"> done</span>
11762 <h3 class="sectionHead"><span class="titlemark">9. </span> <a
11763 id="x1-1140009"></a>Helper equations</h3>
11764 <!--l. 6--><p class="noindent" >
11765 <h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a
11766 id="x1-1150009.1"></a>Overview</h4>
11767 <!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than
11768 cluttering up the main specification documents, they are defined here and referenced where
11770 <!--l. 13--><p class="noindent" >
11771 <h4 class="subsectionHead"><span class="titlemark">9.2. </span> <a
11772 id="x1-1160009.2"></a>Functions</h4>
11773 <!--l. 15--><p class="noindent" >
11774 <h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a
11775 id="x1-1170009.2.1"></a>ilog</h5>
11776 <!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
11777 two’s complement integer value <span
11778 class="cmtt-12">[x]</span>. Values of <span
11779 class="cmtt-12">[x] </span>less than zero are defined to return
11781 <!--l. 20--><p class="noindent" >
11782 <div class="fancyvrb" id="fancyvrb44">
11784 id="x1-117002r1"></a><span
11785 class="cmr-6">1</span><span
11786 class="cmtt-8"> </span><span
11787 class="cmtt-8"> </span><span
11788 class="cmtt-8"> </span><span
11789 class="cmtt-8"> 1)</span><span
11790 class="cmtt-8"> [return\_value]</span><span
11791 class="cmtt-8"> =</span><span
11792 class="cmtt-8"> 0;</span>
11793 <br class="fancyvrb" /><a
11794 id="x1-117004r2"></a><span
11795 class="cmr-6">2</span><span
11796 class="cmtt-8"> </span><span
11797 class="cmtt-8"> </span><span
11798 class="cmtt-8"> </span><span
11799 class="cmtt-8"> 2)</span><span
11800 class="cmtt-8"> if</span><span
11801 class="cmtt-8"> (</span><span
11802 class="cmtt-8"> [x]</span><span
11803 class="cmtt-8"> is</span><span
11804 class="cmtt-8"> greater</span><span
11805 class="cmtt-8"> than</span><span
11806 class="cmtt-8"> zero</span><span
11807 class="cmtt-8"> )</span><span
11808 class="cmtt-8"> {</span>
11809 <br class="fancyvrb" /><a
11810 id="x1-117006r3"></a><span
11811 class="cmr-6">3</span><span
11812 class="cmtt-8"> </span><span
11813 class="cmtt-8"> </span>
11814 <br class="fancyvrb" /><a
11815 id="x1-117008r4"></a><span
11816 class="cmr-6">4</span><span
11817 class="cmtt-8"> </span><span
11818 class="cmtt-8"> </span><span
11819 class="cmtt-8"> </span><span
11820 class="cmtt-8"> </span><span
11821 class="cmtt-8"> </span><span
11822 class="cmtt-8"> </span><span
11823 class="cmtt-8"> </span><span
11824 class="cmtt-8"> </span><span
11825 class="cmtt-8"> 3)</span><span
11826 class="cmtt-8"> increment</span><span
11827 class="cmtt-8"> [return\_value];</span>
11828 <br class="fancyvrb" /><a
11829 id="x1-117010r5"></a><span
11830 class="cmr-6">5</span><span
11831 class="cmtt-8"> </span><span
11832 class="cmtt-8"> </span><span
11833 class="cmtt-8"> </span><span
11834 class="cmtt-8"> </span><span
11835 class="cmtt-8"> </span><span
11836 class="cmtt-8"> </span><span
11837 class="cmtt-8"> </span><span
11838 class="cmtt-8"> </span><span
11839 class="cmtt-8"> 4)</span><span
11840 class="cmtt-8"> logical</span><span
11841 class="cmtt-8"> shift</span><span
11842 class="cmtt-8"> [x]</span><span
11843 class="cmtt-8"> one</span><span
11844 class="cmtt-8"> bit</span><span
11845 class="cmtt-8"> to</span><span
11846 class="cmtt-8"> the</span><span
11847 class="cmtt-8"> right,</span><span
11848 class="cmtt-8"> padding</span><span
11849 class="cmtt-8"> the</span><span
11850 class="cmtt-8"> MSb</span><span
11851 class="cmtt-8"> with</span><span
11852 class="cmtt-8"> zero</span>
11853 <br class="fancyvrb" /><a
11854 id="x1-117012r6"></a><span
11855 class="cmr-6">6</span><span
11856 class="cmtt-8"> </span><span
11857 class="cmtt-8"> </span><span
11858 class="cmtt-8"> </span><span
11859 class="cmtt-8"> </span><span
11860 class="cmtt-8"> </span><span
11861 class="cmtt-8"> </span><span
11862 class="cmtt-8"> </span><span
11863 class="cmtt-8"> </span><span
11864 class="cmtt-8"> 5)</span><span
11865 class="cmtt-8"> repeat</span><span
11866 class="cmtt-8"> at</span><span
11867 class="cmtt-8"> step</span><span
11868 class="cmtt-8"> 2)</span>
11869 <br class="fancyvrb" /><a
11870 id="x1-117014r7"></a><span
11871 class="cmr-6">7</span><span
11872 class="cmtt-8"> </span><span
11873 class="cmtt-8"> </span>
11874 <br class="fancyvrb" /><a
11875 id="x1-117016r8"></a><span
11876 class="cmr-6">8</span><span
11877 class="cmtt-8"> </span><span
11878 class="cmtt-8"> </span><span
11879 class="cmtt-8"> </span><span
11880 class="cmtt-8"> </span><span
11881 class="cmtt-8"> </span><span
11882 class="cmtt-8"> </span><span
11883 class="cmtt-8"> }</span>
11884 <br class="fancyvrb" /><a
11885 id="x1-117018r9"></a><span
11886 class="cmr-6">9</span><span
11887 class="cmtt-8"> </span><span
11888 class="cmtt-8"> </span>
11889 <br class="fancyvrb" /><a
11890 id="x1-117020r10"></a><span
11891 class="cmr-6">10</span><span
11892 class="cmtt-8"> </span><span
11893 class="cmtt-8"> </span><span
11894 class="cmtt-8"> </span><span
11895 class="cmtt-8"> </span><span
11896 class="cmtt-8"> 6)</span><span
11897 class="cmtt-8"> done</span>
11902 <!--l. 33--><p class="noindent" >Examples:
11903 <ul class="itemize1">
11904 <li class="itemize">ilog(0) = 0;
11906 <li class="itemize">ilog(1) = 1;
11908 <li class="itemize">ilog(2) = 2;
11910 <li class="itemize">ilog(3) = 2;
11912 <li class="itemize">ilog(4) = 3;
11914 <li class="itemize">ilog(7) = 3;
11916 <li class="itemize">ilog(negative number) = 0;</li></ul>
11917 <!--l. 48--><p class="noindent" >
11918 <h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a
11919 id="x1-1180009.2.2"></a>float32_unpack</h5>
11920 <!--l. 50--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis
11921 codebook float value into the representation used by the decoder for floating point numbers. For
11922 purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
11924 <!--l. 56--><p class="noindent" >
11925 <div class="fancyvrb" id="fancyvrb45">
11927 id="x1-118002r1"></a><span
11928 class="cmr-6">1</span><span
11929 class="cmtt-8"> </span><span
11930 class="cmtt-8"> </span><span
11931 class="cmtt-8"> </span><span
11932 class="cmtt-8"> 1)</span><span
11933 class="cmtt-8"> [mantissa]</span><span
11934 class="cmtt-8"> =</span><span
11935 class="cmtt-8"> [x]</span><span
11936 class="cmtt-8"> bitwise</span><span
11937 class="cmtt-8"> AND</span><span
11938 class="cmtt-8"> 0x1fffff</span><span
11939 class="cmtt-8"> (unsigned</span><span
11940 class="cmtt-8"> result)</span>
11941 <br class="fancyvrb" /><a
11942 id="x1-118004r2"></a><span
11943 class="cmr-6">2</span><span
11944 class="cmtt-8"> </span><span
11945 class="cmtt-8"> </span><span
11946 class="cmtt-8"> </span><span
11947 class="cmtt-8"> 2)</span><span
11948 class="cmtt-8"> [sign]</span><span
11949 class="cmtt-8"> =</span><span
11950 class="cmtt-8"> [x]</span><span
11951 class="cmtt-8"> bitwise</span><span
11952 class="cmtt-8"> AND</span><span
11953 class="cmtt-8"> 0x80000000</span><span
11954 class="cmtt-8"> (unsigned</span><span
11955 class="cmtt-8"> result)</span>
11956 <br class="fancyvrb" /><a
11957 id="x1-118006r3"></a><span
11958 class="cmr-6">3</span><span
11959 class="cmtt-8"> </span><span
11960 class="cmtt-8"> </span><span
11961 class="cmtt-8"> </span><span
11962 class="cmtt-8"> 3)</span><span
11963 class="cmtt-8"> [exponent]</span><span
11964 class="cmtt-8"> =</span><span
11965 class="cmtt-8"> (</span><span
11966 class="cmtt-8"> [x]</span><span
11967 class="cmtt-8"> bitwise</span><span
11968 class="cmtt-8"> AND</span><span
11969 class="cmtt-8"> 0x7fe00000)</span><span
11970 class="cmtt-8"> shifted</span><span
11971 class="cmtt-8"> right</span><span
11972 class="cmtt-8"> 21</span><span
11973 class="cmtt-8"> bits</span><span
11974 class="cmtt-8"> (unsigned</span><span
11975 class="cmtt-8"> result)</span>
11976 <br class="fancyvrb" /><a
11977 id="x1-118008r4"></a><span
11978 class="cmr-6">4</span><span
11979 class="cmtt-8"> </span><span
11980 class="cmtt-8"> </span><span
11981 class="cmtt-8"> </span><span
11982 class="cmtt-8"> 4)</span><span
11983 class="cmtt-8"> if</span><span
11984 class="cmtt-8"> (</span><span
11985 class="cmtt-8"> [sign]</span><span
11986 class="cmtt-8"> is</span><span
11987 class="cmtt-8"> nonzero</span><span
11988 class="cmtt-8"> )</span><span
11989 class="cmtt-8"> then</span><span
11990 class="cmtt-8"> negate</span><span
11991 class="cmtt-8"> [mantissa]</span>
11992 <br class="fancyvrb" /><a
11993 id="x1-118010r5"></a><span
11994 class="cmr-6">5</span><span
11995 class="cmtt-8"> </span><span
11996 class="cmtt-8"> </span><span
11997 class="cmtt-8"> </span><span
11998 class="cmtt-8"> 5)</span><span
11999 class="cmtt-8"> return</span><span
12000 class="cmtt-8"> [mantissa]</span><span
12001 class="cmtt-8"> *</span><span
12002 class="cmtt-8"> (</span><span
12003 class="cmtt-8"> 2</span><span
12004 class="cmtt-8"> ^</span><span
12005 class="cmtt-8"> (</span><span
12006 class="cmtt-8"> [exponent]</span><span
12007 class="cmtt-8"> -</span><span
12008 class="cmtt-8"> 788</span><span
12009 class="cmtt-8"> )</span><span
12010 class="cmtt-8"> )</span>
12015 <!--l. 66--><p class="noindent" >
12016 <h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a
12017 id="x1-1190009.2.3"></a>lookup1_values</h5>
12018 <!--l. 68--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the
12019 correct length of the value index for a codebook VQ lookup table of lookup type 1.
12020 The values on this list are permuted to construct the VQ vector lookup table of size
12022 class="cmtt-12">[codebook_entries]</span>.
12023 <!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
12025 class="cmtt-12">[return_value] </span>to the power of <span
12026 class="cmtt-12">[codebook_dimensions] </span>is less than or equal to
12028 class="cmtt-12">[codebook_entries]</span>’.
12029 <!--l. 81--><p class="noindent" >
12030 <h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a
12031 id="x1-1200009.2.4"></a>low_neighbor</h5>
12032 <!--l. 83--><p class="noindent" >”low_neighbor(v,x)” finds the position <span
12033 class="cmtt-12">n </span>in vector <span
12034 class="cmtt-12">[v] </span>of the greatest value scalar element for
12036 class="cmtt-12">n </span>is less than <span
12037 class="cmtt-12">[x] </span>and vector <span
12038 class="cmtt-12">[v] </span>element <span
12039 class="cmtt-12">n </span>is less than vector <span
12040 class="cmtt-12">[v] </span>element
12042 class="cmtt-12">[x]</span>.
12043 <!--l. 88--><p class="noindent" >
12044 <h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a
12045 id="x1-1210009.2.5"></a>high_neighbor</h5>
12046 <!--l. 90--><p class="noindent" >”high_neighbor(v,x)” finds the position <span
12047 class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
12049 class="cmtt-12">n </span>is less than <span
12050 class="cmtt-12">[x] </span>and vector <span
12051 class="cmtt-12">[v] </span>element <span
12052 class="cmtt-12">n </span>is greater than vector <span
12053 class="cmtt-12">[v] </span>element
12055 class="cmtt-12">[x]</span>.
12056 <!--l. 97--><p class="noindent" >
12057 <h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a
12058 id="x1-1220009.2.6"></a>render_point</h5>
12059 <!--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
12060 x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
12061 calculating intervening values along the line.
12065 <!--l. 104--><p class="noindent" >
12066 <div class="fancyvrb" id="fancyvrb46">
12068 id="x1-122002r1"></a><span
12069 class="cmr-6">1</span><span
12070 class="cmtt-8"> </span><span
12071 class="cmtt-8"> </span><span
12072 class="cmtt-8"> </span><span
12073 class="cmtt-8"> 1)</span><span
12074 class="cmtt-8"> </span><span
12075 class="cmtt-8"> [dy]</span><span
12076 class="cmtt-8"> =</span><span
12077 class="cmtt-8"> [y1]</span><span
12078 class="cmtt-8"> -</span><span
12079 class="cmtt-8"> [y0]</span>
12080 <br class="fancyvrb" /><a
12081 id="x1-122004r2"></a><span
12082 class="cmr-6">2</span><span
12083 class="cmtt-8"> </span><span
12084 class="cmtt-8"> </span><span
12085 class="cmtt-8"> </span><span
12086 class="cmtt-8"> 2)</span><span
12087 class="cmtt-8"> [adx]</span><span
12088 class="cmtt-8"> =</span><span
12089 class="cmtt-8"> [x1]</span><span
12090 class="cmtt-8"> -</span><span
12091 class="cmtt-8"> [x0]</span>
12092 <br class="fancyvrb" /><a
12093 id="x1-122006r3"></a><span
12094 class="cmr-6">3</span><span
12095 class="cmtt-8"> </span><span
12096 class="cmtt-8"> </span><span
12097 class="cmtt-8"> </span><span
12098 class="cmtt-8"> 3)</span><span
12099 class="cmtt-8"> [ady]</span><span
12100 class="cmtt-8"> =</span><span
12101 class="cmtt-8"> absolute</span><span
12102 class="cmtt-8"> value</span><span
12103 class="cmtt-8"> of</span><span
12104 class="cmtt-8"> [dy]</span>
12105 <br class="fancyvrb" /><a
12106 id="x1-122008r4"></a><span
12107 class="cmr-6">4</span><span
12108 class="cmtt-8"> </span><span
12109 class="cmtt-8"> </span><span
12110 class="cmtt-8"> </span><span
12111 class="cmtt-8"> 4)</span><span
12112 class="cmtt-8"> [err]</span><span
12113 class="cmtt-8"> =</span><span
12114 class="cmtt-8"> [ady]</span><span
12115 class="cmtt-8"> *</span><span
12116 class="cmtt-8"> ([X]</span><span
12117 class="cmtt-8"> -</span><span
12118 class="cmtt-8"> [x0])</span>
12119 <br class="fancyvrb" /><a
12120 id="x1-122010r5"></a><span
12121 class="cmr-6">5</span><span
12122 class="cmtt-8"> </span><span
12123 class="cmtt-8"> </span><span
12124 class="cmtt-8"> </span><span
12125 class="cmtt-8"> 5)</span><span
12126 class="cmtt-8"> [off]</span><span
12127 class="cmtt-8"> =</span><span
12128 class="cmtt-8"> [err]</span><span
12129 class="cmtt-8"> /</span><span
12130 class="cmtt-8"> [adx]</span><span
12131 class="cmtt-8"> using</span><span
12132 class="cmtt-8"> integer</span><span
12133 class="cmtt-8"> division</span>
12134 <br class="fancyvrb" /><a
12135 id="x1-122012r6"></a><span
12136 class="cmr-6">6</span><span
12137 class="cmtt-8"> </span><span
12138 class="cmtt-8"> </span><span
12139 class="cmtt-8"> </span><span
12140 class="cmtt-8"> 6)</span><span
12141 class="cmtt-8"> if</span><span
12142 class="cmtt-8"> (</span><span
12143 class="cmtt-8"> [dy]</span><span
12144 class="cmtt-8"> is</span><span
12145 class="cmtt-8"> less</span><span
12146 class="cmtt-8"> than</span><span
12147 class="cmtt-8"> zero</span><span
12148 class="cmtt-8"> )</span><span
12149 class="cmtt-8"> {</span>
12150 <br class="fancyvrb" /><a
12151 id="x1-122014r7"></a><span
12152 class="cmr-6">7</span><span
12153 class="cmtt-8"> </span><span
12154 class="cmtt-8"> </span>
12155 <br class="fancyvrb" /><a
12156 id="x1-122016r8"></a><span
12157 class="cmr-6">8</span><span
12158 class="cmtt-8"> </span><span
12159 class="cmtt-8"> </span><span
12160 class="cmtt-8"> </span><span
12161 class="cmtt-8"> </span><span
12162 class="cmtt-8"> </span><span
12163 class="cmtt-8"> </span><span
12164 class="cmtt-8"> </span><span
12165 class="cmtt-8"> </span><span
12166 class="cmtt-8"> 7)</span><span
12167 class="cmtt-8"> [Y]</span><span
12168 class="cmtt-8"> =</span><span
12169 class="cmtt-8"> [y0]</span><span
12170 class="cmtt-8"> -</span><span
12171 class="cmtt-8"> [off]</span>
12172 <br class="fancyvrb" /><a
12173 id="x1-122018r9"></a><span
12174 class="cmr-6">9</span><span
12175 class="cmtt-8"> </span><span
12176 class="cmtt-8"> </span>
12177 <br class="fancyvrb" /><a
12178 id="x1-122020r10"></a><span
12179 class="cmr-6">10</span><span
12180 class="cmtt-8"> </span><span
12181 class="cmtt-8"> </span><span
12182 class="cmtt-8"> </span><span
12183 class="cmtt-8"> </span><span
12184 class="cmtt-8"> </span><span
12185 class="cmtt-8"> </span><span
12186 class="cmtt-8"> }</span><span
12187 class="cmtt-8"> else</span><span
12188 class="cmtt-8"> {</span>
12189 <br class="fancyvrb" /><a
12190 id="x1-122022r11"></a><span
12191 class="cmr-6">11</span><span
12192 class="cmtt-8"> </span><span
12193 class="cmtt-8"> </span>
12194 <br class="fancyvrb" /><a
12195 id="x1-122024r12"></a><span
12196 class="cmr-6">12</span><span
12197 class="cmtt-8"> </span><span
12198 class="cmtt-8"> </span><span
12199 class="cmtt-8"> </span><span
12200 class="cmtt-8"> </span><span
12201 class="cmtt-8"> </span><span
12202 class="cmtt-8"> </span><span
12203 class="cmtt-8"> </span><span
12204 class="cmtt-8"> </span><span
12205 class="cmtt-8"> 8)</span><span
12206 class="cmtt-8"> [Y]</span><span
12207 class="cmtt-8"> =</span><span
12208 class="cmtt-8"> [y0]</span><span
12209 class="cmtt-8"> +</span><span
12210 class="cmtt-8"> [off]</span>
12211 <br class="fancyvrb" /><a
12212 id="x1-122026r13"></a><span
12213 class="cmr-6">13</span><span
12214 class="cmtt-8"> </span><span
12215 class="cmtt-8"> </span>
12216 <br class="fancyvrb" /><a
12217 id="x1-122028r14"></a><span
12218 class="cmr-6">14</span><span
12219 class="cmtt-8"> </span><span
12220 class="cmtt-8"> </span><span
12221 class="cmtt-8"> </span><span
12222 class="cmtt-8"> </span><span
12223 class="cmtt-8"> </span><span
12224 class="cmtt-8"> </span><span
12225 class="cmtt-8"> }</span>
12226 <br class="fancyvrb" /><a
12227 id="x1-122030r15"></a><span
12228 class="cmr-6">15</span><span
12229 class="cmtt-8"> </span><span
12230 class="cmtt-8"> </span>
12231 <br class="fancyvrb" /><a
12232 id="x1-122032r16"></a><span
12233 class="cmr-6">16</span><span
12234 class="cmtt-8"> </span><span
12235 class="cmtt-8"> </span><span
12236 class="cmtt-8"> </span><span
12237 class="cmtt-8"> 9)</span><span
12238 class="cmtt-8"> done</span>
12240 <!--l. 125--><p class="noindent" >
12241 <h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a
12242 id="x1-1230009.2.7"></a>render_line</h5>
12243 <!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)”
12244 to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
12245 been relevant elsewhere, but here we must define integer division as rounding division of both
12246 positive and negative numbers toward zero.
12247 <!--l. 134--><p class="noindent" >
12248 <div class="fancyvrb" id="fancyvrb47">
12250 id="x1-123002r1"></a><span
12251 class="cmr-6">1</span><span
12252 class="cmtt-8"> </span><span
12253 class="cmtt-8"> </span><span
12254 class="cmtt-8"> </span><span
12255 class="cmtt-8"> 1)</span><span
12256 class="cmtt-8"> </span><span
12257 class="cmtt-8"> </span><span
12258 class="cmtt-8"> [dy]</span><span
12259 class="cmtt-8"> =</span><span
12260 class="cmtt-8"> [y1]</span><span
12261 class="cmtt-8"> -</span><span
12262 class="cmtt-8"> [y0]</span>
12263 <br class="fancyvrb" /><a
12264 id="x1-123004r2"></a><span
12265 class="cmr-6">2</span><span
12266 class="cmtt-8"> </span><span
12267 class="cmtt-8"> </span><span
12268 class="cmtt-8"> </span><span
12269 class="cmtt-8"> 2)</span><span
12270 class="cmtt-8"> </span><span
12271 class="cmtt-8"> [adx]</span><span
12272 class="cmtt-8"> =</span><span
12273 class="cmtt-8"> [x1]</span><span
12274 class="cmtt-8"> -</span><span
12275 class="cmtt-8"> [x0]</span>
12276 <br class="fancyvrb" /><a
12277 id="x1-123006r3"></a><span
12278 class="cmr-6">3</span><span
12279 class="cmtt-8"> </span><span
12280 class="cmtt-8"> </span><span
12281 class="cmtt-8"> </span><span
12282 class="cmtt-8"> 3)</span><span
12283 class="cmtt-8"> </span><span
12284 class="cmtt-8"> [ady]</span><span
12285 class="cmtt-8"> =</span><span
12286 class="cmtt-8"> absolute</span><span
12287 class="cmtt-8"> value</span><span
12288 class="cmtt-8"> of</span><span
12289 class="cmtt-8"> [dy]</span>
12290 <br class="fancyvrb" /><a
12291 id="x1-123008r4"></a><span
12292 class="cmr-6">4</span><span
12293 class="cmtt-8"> </span><span
12294 class="cmtt-8"> </span><span
12295 class="cmtt-8"> </span><span
12296 class="cmtt-8"> 4)</span><span
12297 class="cmtt-8"> [base]</span><span
12298 class="cmtt-8"> =</span><span
12299 class="cmtt-8"> [dy]</span><span
12300 class="cmtt-8"> /</span><span
12301 class="cmtt-8"> [adx]</span><span
12302 class="cmtt-8"> using</span><span
12303 class="cmtt-8"> integer</span><span
12304 class="cmtt-8"> division</span>
12305 <br class="fancyvrb" /><a
12306 id="x1-123010r5"></a><span
12307 class="cmr-6">5</span><span
12308 class="cmtt-8"> </span><span
12309 class="cmtt-8"> </span><span
12310 class="cmtt-8"> </span><span
12311 class="cmtt-8"> 5)</span><span
12312 class="cmtt-8"> </span><span
12313 class="cmtt-8"> </span><span
12314 class="cmtt-8"> </span><span
12315 class="cmtt-8"> [x]</span><span
12316 class="cmtt-8"> =</span><span
12317 class="cmtt-8"> [x0]</span>
12318 <br class="fancyvrb" /><a
12319 id="x1-123012r6"></a><span
12320 class="cmr-6">6</span><span
12321 class="cmtt-8"> </span><span
12322 class="cmtt-8"> </span><span
12323 class="cmtt-8"> </span><span
12324 class="cmtt-8"> 6)</span><span
12325 class="cmtt-8"> </span><span
12326 class="cmtt-8"> </span><span
12327 class="cmtt-8"> </span><span
12328 class="cmtt-8"> [y]</span><span
12329 class="cmtt-8"> =</span><span
12330 class="cmtt-8"> [y0]</span>
12331 <br class="fancyvrb" /><a
12332 id="x1-123014r7"></a><span
12333 class="cmr-6">7</span><span
12334 class="cmtt-8"> </span><span
12335 class="cmtt-8"> </span><span
12336 class="cmtt-8"> </span><span
12337 class="cmtt-8"> 7)</span><span
12338 class="cmtt-8"> </span><span
12339 class="cmtt-8"> [err]</span><span
12340 class="cmtt-8"> =</span><span
12341 class="cmtt-8"> 0</span>
12342 <br class="fancyvrb" /><a
12343 id="x1-123016r8"></a><span
12344 class="cmr-6">8</span><span
12345 class="cmtt-8"> </span><span
12346 class="cmtt-8"> </span>
12347 <br class="fancyvrb" /><a
12348 id="x1-123018r9"></a><span
12349 class="cmr-6">9</span><span
12350 class="cmtt-8"> </span><span
12351 class="cmtt-8"> </span><span
12352 class="cmtt-8"> </span><span
12353 class="cmtt-8"> 8)</span><span
12354 class="cmtt-8"> if</span><span
12355 class="cmtt-8"> (</span><span
12356 class="cmtt-8"> [dy]</span><span
12357 class="cmtt-8"> is</span><span
12358 class="cmtt-8"> less</span><span
12359 class="cmtt-8"> than</span><span
12360 class="cmtt-8"> 0</span><span
12361 class="cmtt-8"> )</span><span
12362 class="cmtt-8"> {</span>
12363 <br class="fancyvrb" /><a
12364 id="x1-123020r10"></a><span
12365 class="cmr-6">10</span><span
12366 class="cmtt-8"> </span><span
12367 class="cmtt-8"> </span>
12368 <br class="fancyvrb" /><a
12369 id="x1-123022r11"></a><span
12370 class="cmr-6">11</span><span
12371 class="cmtt-8"> </span><span
12372 class="cmtt-8"> </span><span
12373 class="cmtt-8"> </span><span
12374 class="cmtt-8"> </span><span
12375 class="cmtt-8"> </span><span
12376 class="cmtt-8"> </span><span
12377 class="cmtt-8"> </span><span
12378 class="cmtt-8"> </span><span
12379 class="cmtt-8"> </span><span
12380 class="cmtt-8"> 9)</span><span
12381 class="cmtt-8"> [sy]</span><span
12382 class="cmtt-8"> =</span><span
12383 class="cmtt-8"> [base]</span><span
12384 class="cmtt-8"> -</span><span
12385 class="cmtt-8"> 1</span>
12386 <br class="fancyvrb" /><a
12387 id="x1-123024r12"></a><span
12388 class="cmr-6">12</span><span
12389 class="cmtt-8"> </span><span
12390 class="cmtt-8"> </span>
12391 <br class="fancyvrb" /><a
12392 id="x1-123026r13"></a><span
12393 class="cmr-6">13</span><span
12394 class="cmtt-8"> </span><span
12395 class="cmtt-8"> </span><span
12396 class="cmtt-8"> </span><span
12397 class="cmtt-8"> </span><span
12398 class="cmtt-8"> </span><span
12399 class="cmtt-8"> </span><span
12400 class="cmtt-8"> }</span><span
12401 class="cmtt-8"> else</span><span
12402 class="cmtt-8"> {</span>
12403 <br class="fancyvrb" /><a
12404 id="x1-123028r14"></a><span
12405 class="cmr-6">14</span><span
12406 class="cmtt-8"> </span><span
12407 class="cmtt-8"> </span>
12408 <br class="fancyvrb" /><a
12409 id="x1-123030r15"></a><span
12410 class="cmr-6">15</span><span
12411 class="cmtt-8"> </span><span
12412 class="cmtt-8"> </span><span
12413 class="cmtt-8"> </span><span
12414 class="cmtt-8"> </span><span
12415 class="cmtt-8"> </span><span
12416 class="cmtt-8"> </span><span
12417 class="cmtt-8"> </span><span
12418 class="cmtt-8"> </span><span
12419 class="cmtt-8"> 10)</span><span
12420 class="cmtt-8"> [sy]</span><span
12421 class="cmtt-8"> =</span><span
12422 class="cmtt-8"> [base]</span><span
12423 class="cmtt-8"> +</span><span
12424 class="cmtt-8"> 1</span>
12425 <br class="fancyvrb" /><a
12426 id="x1-123032r16"></a><span
12427 class="cmr-6">16</span><span
12428 class="cmtt-8"> </span><span
12429 class="cmtt-8"> </span>
12430 <br class="fancyvrb" /><a
12431 id="x1-123034r17"></a><span
12432 class="cmr-6">17</span><span
12433 class="cmtt-8"> </span><span
12434 class="cmtt-8"> </span><span
12435 class="cmtt-8"> </span><span
12436 class="cmtt-8"> </span><span
12437 class="cmtt-8"> </span><span
12438 class="cmtt-8"> </span><span
12439 class="cmtt-8"> }</span>
12440 <br class="fancyvrb" /><a
12441 id="x1-123036r18"></a><span
12442 class="cmr-6">18</span><span
12443 class="cmtt-8"> </span><span
12444 class="cmtt-8"> </span>
12445 <br class="fancyvrb" /><a
12446 id="x1-123038r19"></a><span
12447 class="cmr-6">19</span><span
12448 class="cmtt-8"> </span><span
12449 class="cmtt-8"> </span><span
12450 class="cmtt-8"> 11)</span><span
12451 class="cmtt-8"> [ady]</span><span
12452 class="cmtt-8"> =</span><span
12453 class="cmtt-8"> [ady]</span><span
12454 class="cmtt-8"> -</span><span
12455 class="cmtt-8"> (absolute</span><span
12456 class="cmtt-8"> value</span><span
12457 class="cmtt-8"> of</span><span
12458 class="cmtt-8"> [base])</span><span
12459 class="cmtt-8"> *</span><span
12460 class="cmtt-8"> [adx]</span>
12461 <br class="fancyvrb" /><a
12462 id="x1-123040r20"></a><span
12463 class="cmr-6">20</span><span
12464 class="cmtt-8"> </span><span
12465 class="cmtt-8"> </span><span
12466 class="cmtt-8"> 12)</span><span
12467 class="cmtt-8"> vector</span><span
12468 class="cmtt-8"> [v]</span><span
12469 class="cmtt-8"> element</span><span
12470 class="cmtt-8"> [x]</span><span
12471 class="cmtt-8"> =</span><span
12472 class="cmtt-8"> [y]</span>
12473 <br class="fancyvrb" /><a
12474 id="x1-123042r21"></a><span
12475 class="cmr-6">21</span><span
12476 class="cmtt-8"> </span><span
12477 class="cmtt-8"> </span>
12478 <br class="fancyvrb" /><a
12479 id="x1-123044r22"></a><span
12480 class="cmr-6">22</span><span
12481 class="cmtt-8"> </span><span
12482 class="cmtt-8"> </span><span
12483 class="cmtt-8"> 13)</span><span
12484 class="cmtt-8"> iterate</span><span
12485 class="cmtt-8"> [x]</span><span
12486 class="cmtt-8"> over</span><span
12487 class="cmtt-8"> the</span><span
12488 class="cmtt-8"> range</span><span
12489 class="cmtt-8"> [x0]+1</span><span
12490 class="cmtt-8"> ...</span><span
12491 class="cmtt-8"> [x1]-1</span><span
12492 class="cmtt-8"> {</span>
12496 <br class="fancyvrb" /><a
12497 id="x1-123046r23"></a><span
12498 class="cmr-6">23</span><span
12499 class="cmtt-8"> </span><span
12500 class="cmtt-8"> </span>
12501 <br class="fancyvrb" /><a
12502 id="x1-123048r24"></a><span
12503 class="cmr-6">24</span><span
12504 class="cmtt-8"> </span><span
12505 class="cmtt-8"> </span><span
12506 class="cmtt-8"> </span><span
12507 class="cmtt-8"> </span><span
12508 class="cmtt-8"> </span><span
12509 class="cmtt-8"> </span><span
12510 class="cmtt-8"> </span><span
12511 class="cmtt-8"> </span><span
12512 class="cmtt-8"> 14)</span><span
12513 class="cmtt-8"> [err]</span><span
12514 class="cmtt-8"> =</span><span
12515 class="cmtt-8"> [err]</span><span
12516 class="cmtt-8"> +</span><span
12517 class="cmtt-8"> [ady];</span>
12518 <br class="fancyvrb" /><a
12519 id="x1-123050r25"></a><span
12520 class="cmr-6">25</span><span
12521 class="cmtt-8"> </span><span
12522 class="cmtt-8"> </span><span
12523 class="cmtt-8"> </span><span
12524 class="cmtt-8"> </span><span
12525 class="cmtt-8"> </span><span
12526 class="cmtt-8"> </span><span
12527 class="cmtt-8"> </span><span
12528 class="cmtt-8"> </span><span
12529 class="cmtt-8"> 15)</span><span
12530 class="cmtt-8"> if</span><span
12531 class="cmtt-8"> (</span><span
12532 class="cmtt-8"> [err]</span><span
12533 class="cmtt-8"> >=</span><span
12534 class="cmtt-8"> [adx]</span><span
12535 class="cmtt-8"> )</span><span
12536 class="cmtt-8"> {</span>
12537 <br class="fancyvrb" /><a
12538 id="x1-123052r26"></a><span
12539 class="cmr-6">26</span><span
12540 class="cmtt-8"> </span><span
12541 class="cmtt-8"> </span>
12542 <br class="fancyvrb" /><a
12543 id="x1-123054r27"></a><span
12544 class="cmr-6">27</span><span
12545 class="cmtt-8"> </span><span
12546 class="cmtt-8"> </span><span
12547 class="cmtt-8"> </span><span
12548 class="cmtt-8"> </span><span
12549 class="cmtt-8"> </span><span
12550 class="cmtt-8"> </span><span
12551 class="cmtt-8"> </span><span
12552 class="cmtt-8"> </span><span
12553 class="cmtt-8"> </span><span
12554 class="cmtt-8"> </span><span
12555 class="cmtt-8"> </span><span
12556 class="cmtt-8"> </span><span
12557 class="cmtt-8"> </span><span
12558 class="cmtt-8"> </span><span
12559 class="cmtt-8"> 16)</span><span
12560 class="cmtt-8"> [err]</span><span
12561 class="cmtt-8"> =</span><span
12562 class="cmtt-8"> [err]</span><span
12563 class="cmtt-8"> -</span><span
12564 class="cmtt-8"> [adx]</span>
12565 <br class="fancyvrb" /><a
12566 id="x1-123056r28"></a><span
12567 class="cmr-6">28</span><span
12568 class="cmtt-8"> </span><span
12569 class="cmtt-8"> </span><span
12570 class="cmtt-8"> </span><span
12571 class="cmtt-8"> </span><span
12572 class="cmtt-8"> </span><span
12573 class="cmtt-8"> </span><span
12574 class="cmtt-8"> </span><span
12575 class="cmtt-8"> </span><span
12576 class="cmtt-8"> </span><span
12577 class="cmtt-8"> </span><span
12578 class="cmtt-8"> </span><span
12579 class="cmtt-8"> </span><span
12580 class="cmtt-8"> </span><span
12581 class="cmtt-8"> </span><span
12582 class="cmtt-8"> 17)</span><span
12583 class="cmtt-8"> </span><span
12584 class="cmtt-8"> </span><span
12585 class="cmtt-8"> [y]</span><span
12586 class="cmtt-8"> =</span><span
12587 class="cmtt-8"> [y]</span><span
12588 class="cmtt-8"> +</span><span
12589 class="cmtt-8"> [sy]</span>
12590 <br class="fancyvrb" /><a
12591 id="x1-123058r29"></a><span
12592 class="cmr-6">29</span><span
12593 class="cmtt-8"> </span><span
12594 class="cmtt-8"> </span>
12595 <br class="fancyvrb" /><a
12596 id="x1-123060r30"></a><span
12597 class="cmr-6">30</span><span
12598 class="cmtt-8"> </span><span
12599 class="cmtt-8"> </span><span
12600 class="cmtt-8"> </span><span
12601 class="cmtt-8"> </span><span
12602 class="cmtt-8"> </span><span
12603 class="cmtt-8"> </span><span
12604 class="cmtt-8"> </span><span
12605 class="cmtt-8"> </span><span
12606 class="cmtt-8"> </span><span
12607 class="cmtt-8"> </span><span
12608 class="cmtt-8"> </span><span
12609 class="cmtt-8"> </span><span
12610 class="cmtt-8"> }</span><span
12611 class="cmtt-8"> else</span><span
12612 class="cmtt-8"> {</span>
12613 <br class="fancyvrb" /><a
12614 id="x1-123062r31"></a><span
12615 class="cmr-6">31</span><span
12616 class="cmtt-8"> </span><span
12617 class="cmtt-8"> </span>
12618 <br class="fancyvrb" /><a
12619 id="x1-123064r32"></a><span
12620 class="cmr-6">32</span><span
12621 class="cmtt-8"> </span><span
12622 class="cmtt-8"> </span><span
12623 class="cmtt-8"> </span><span
12624 class="cmtt-8"> </span><span
12625 class="cmtt-8"> </span><span
12626 class="cmtt-8"> </span><span
12627 class="cmtt-8"> </span><span
12628 class="cmtt-8"> </span><span
12629 class="cmtt-8"> </span><span
12630 class="cmtt-8"> </span><span
12631 class="cmtt-8"> </span><span
12632 class="cmtt-8"> </span><span
12633 class="cmtt-8"> </span><span
12634 class="cmtt-8"> </span><span
12635 class="cmtt-8"> 18)</span><span
12636 class="cmtt-8"> [y]</span><span
12637 class="cmtt-8"> =</span><span
12638 class="cmtt-8"> [y]</span><span
12639 class="cmtt-8"> +</span><span
12640 class="cmtt-8"> [base]</span>
12641 <br class="fancyvrb" /><a
12642 id="x1-123066r33"></a><span
12643 class="cmr-6">33</span><span
12644 class="cmtt-8"> </span><span
12645 class="cmtt-8"> </span>
12646 <br class="fancyvrb" /><a
12647 id="x1-123068r34"></a><span
12648 class="cmr-6">34</span><span
12649 class="cmtt-8"> </span><span
12650 class="cmtt-8"> </span><span
12651 class="cmtt-8"> </span><span
12652 class="cmtt-8"> </span><span
12653 class="cmtt-8"> </span><span
12654 class="cmtt-8"> </span><span
12655 class="cmtt-8"> </span><span
12656 class="cmtt-8"> </span><span
12657 class="cmtt-8"> </span><span
12658 class="cmtt-8"> </span><span
12659 class="cmtt-8"> </span><span
12660 class="cmtt-8"> </span><span
12661 class="cmtt-8"> }</span>
12662 <br class="fancyvrb" /><a
12663 id="x1-123070r35"></a><span
12664 class="cmr-6">35</span><span
12665 class="cmtt-8"> </span><span
12666 class="cmtt-8"> </span>
12667 <br class="fancyvrb" /><a
12668 id="x1-123072r36"></a><span
12669 class="cmr-6">36</span><span
12670 class="cmtt-8"> </span><span
12671 class="cmtt-8"> </span><span
12672 class="cmtt-8"> </span><span
12673 class="cmtt-8"> </span><span
12674 class="cmtt-8"> </span><span
12675 class="cmtt-8"> </span><span
12676 class="cmtt-8"> </span><span
12677 class="cmtt-8"> </span><span
12678 class="cmtt-8"> 19)</span><span
12679 class="cmtt-8"> vector</span><span
12680 class="cmtt-8"> [v]</span><span
12681 class="cmtt-8"> element</span><span
12682 class="cmtt-8"> [x]</span><span
12683 class="cmtt-8"> =</span><span
12684 class="cmtt-8"> [y]</span>
12685 <br class="fancyvrb" /><a
12686 id="x1-123074r37"></a><span
12687 class="cmr-6">37</span><span
12688 class="cmtt-8"> </span><span
12689 class="cmtt-8"> </span>
12690 <br class="fancyvrb" /><a
12691 id="x1-123076r38"></a><span
12692 class="cmr-6">38</span><span
12693 class="cmtt-8"> </span><span
12694 class="cmtt-8"> </span><span
12695 class="cmtt-8"> </span><span
12696 class="cmtt-8"> </span><span
12697 class="cmtt-8"> </span><span
12698 class="cmtt-8"> </span><span
12699 class="cmtt-8"> }</span>
12707 <h3 class="sectionHead"><span class="titlemark">10. </span> <a
12708 id="x1-12400010"></a>Tables</h3>
12709 <!--l. 6--><p class="noindent" >
12710 <h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a
12711 id="x1-12500010.1"></a>floor1_inverse_dB_table</h4>
12712 <!--l. 8--><p class="noindent" >The vector <span
12713 class="cmtt-12">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consiting of the
12714 following values (read left to right then top to bottom):
12715 <!--l. 12--><p class="noindent" >
12716 <div class="fancyvrb" id="fancyvrb48">
12718 id="x1-125002r1"></a><span
12719 class="cmr-6">1</span><span
12720 class="cmtt-8"> </span><span
12721 class="cmtt-8"> </span><span
12722 class="cmtt-8"> </span><span
12723 class="cmtt-8"> 1.0649863e-07,</span><span
12724 class="cmtt-8"> 1.1341951e-07,</span><span
12725 class="cmtt-8"> 1.2079015e-07,</span><span
12726 class="cmtt-8"> 1.2863978e-07,</span>
12727 <br class="fancyvrb" /><a
12728 id="x1-125004r2"></a><span
12729 class="cmr-6">2</span><span
12730 class="cmtt-8"> </span><span
12731 class="cmtt-8"> </span><span
12732 class="cmtt-8"> </span><span
12733 class="cmtt-8"> 1.3699951e-07,</span><span
12734 class="cmtt-8"> 1.4590251e-07,</span><span
12735 class="cmtt-8"> 1.5538408e-07,</span><span
12736 class="cmtt-8"> 1.6548181e-07,</span>
12737 <br class="fancyvrb" /><a
12738 id="x1-125006r3"></a><span
12739 class="cmr-6">3</span><span
12740 class="cmtt-8"> </span><span
12741 class="cmtt-8"> </span><span
12742 class="cmtt-8"> </span><span
12743 class="cmtt-8"> 1.7623575e-07,</span><span
12744 class="cmtt-8"> 1.8768855e-07,</span><span
12745 class="cmtt-8"> 1.9988561e-07,</span><span
12746 class="cmtt-8"> 2.1287530e-07,</span>
12747 <br class="fancyvrb" /><a
12748 id="x1-125008r4"></a><span
12749 class="cmr-6">4</span><span
12750 class="cmtt-8"> </span><span
12751 class="cmtt-8"> </span><span
12752 class="cmtt-8"> </span><span
12753 class="cmtt-8"> 2.2670913e-07,</span><span
12754 class="cmtt-8"> 2.4144197e-07,</span><span
12755 class="cmtt-8"> 2.5713223e-07,</span><span
12756 class="cmtt-8"> 2.7384213e-07,</span>
12757 <br class="fancyvrb" /><a
12758 id="x1-125010r5"></a><span
12759 class="cmr-6">5</span><span
12760 class="cmtt-8"> </span><span
12761 class="cmtt-8"> </span><span
12762 class="cmtt-8"> </span><span
12763 class="cmtt-8"> 2.9163793e-07,</span><span
12764 class="cmtt-8"> 3.1059021e-07,</span><span
12765 class="cmtt-8"> 3.3077411e-07,</span><span
12766 class="cmtt-8"> 3.5226968e-07,</span>
12767 <br class="fancyvrb" /><a
12768 id="x1-125012r6"></a><span
12769 class="cmr-6">6</span><span
12770 class="cmtt-8"> </span><span
12771 class="cmtt-8"> </span><span
12772 class="cmtt-8"> </span><span
12773 class="cmtt-8"> 3.7516214e-07,</span><span
12774 class="cmtt-8"> 3.9954229e-07,</span><span
12775 class="cmtt-8"> 4.2550680e-07,</span><span
12776 class="cmtt-8"> 4.5315863e-07,</span>
12777 <br class="fancyvrb" /><a
12778 id="x1-125014r7"></a><span
12779 class="cmr-6">7</span><span
12780 class="cmtt-8"> </span><span
12781 class="cmtt-8"> </span><span
12782 class="cmtt-8"> </span><span
12783 class="cmtt-8"> 4.8260743e-07,</span><span
12784 class="cmtt-8"> 5.1396998e-07,</span><span
12785 class="cmtt-8"> 5.4737065e-07,</span><span
12786 class="cmtt-8"> 5.8294187e-07,</span>
12787 <br class="fancyvrb" /><a
12788 id="x1-125016r8"></a><span
12789 class="cmr-6">8</span><span
12790 class="cmtt-8"> </span><span
12791 class="cmtt-8"> </span><span
12792 class="cmtt-8"> </span><span
12793 class="cmtt-8"> 6.2082472e-07,</span><span
12794 class="cmtt-8"> 6.6116941e-07,</span><span
12795 class="cmtt-8"> 7.0413592e-07,</span><span
12796 class="cmtt-8"> 7.4989464e-07,</span>
12797 <br class="fancyvrb" /><a
12798 id="x1-125018r9"></a><span
12799 class="cmr-6">9</span><span
12800 class="cmtt-8"> </span><span
12801 class="cmtt-8"> </span><span
12802 class="cmtt-8"> </span><span
12803 class="cmtt-8"> 7.9862701e-07,</span><span
12804 class="cmtt-8"> 8.5052630e-07,</span><span
12805 class="cmtt-8"> 9.0579828e-07,</span><span
12806 class="cmtt-8"> 9.6466216e-07,</span>
12807 <br class="fancyvrb" /><a
12808 id="x1-125020r10"></a><span
12809 class="cmr-6">10</span><span
12810 class="cmtt-8"> </span><span
12811 class="cmtt-8"> </span><span
12812 class="cmtt-8"> </span><span
12813 class="cmtt-8"> 1.0273513e-06,</span><span
12814 class="cmtt-8"> 1.0941144e-06,</span><span
12815 class="cmtt-8"> 1.1652161e-06,</span><span
12816 class="cmtt-8"> 1.2409384e-06,</span>
12817 <br class="fancyvrb" /><a
12818 id="x1-125022r11"></a><span
12819 class="cmr-6">11</span><span
12820 class="cmtt-8"> </span><span
12821 class="cmtt-8"> </span><span
12822 class="cmtt-8"> </span><span
12823 class="cmtt-8"> 1.3215816e-06,</span><span
12824 class="cmtt-8"> 1.4074654e-06,</span><span
12825 class="cmtt-8"> 1.4989305e-06,</span><span
12826 class="cmtt-8"> 1.5963394e-06,</span>
12827 <br class="fancyvrb" /><a
12828 id="x1-125024r12"></a><span
12829 class="cmr-6">12</span><span
12830 class="cmtt-8"> </span><span
12831 class="cmtt-8"> </span><span
12832 class="cmtt-8"> </span><span
12833 class="cmtt-8"> 1.7000785e-06,</span><span
12834 class="cmtt-8"> 1.8105592e-06,</span><span
12835 class="cmtt-8"> 1.9282195e-06,</span><span
12836 class="cmtt-8"> 2.0535261e-06,</span>
12837 <br class="fancyvrb" /><a
12838 id="x1-125026r13"></a><span
12839 class="cmr-6">13</span><span
12840 class="cmtt-8"> </span><span
12841 class="cmtt-8"> </span><span
12842 class="cmtt-8"> </span><span
12843 class="cmtt-8"> 2.1869758e-06,</span><span
12844 class="cmtt-8"> 2.3290978e-06,</span><span
12845 class="cmtt-8"> 2.4804557e-06,</span><span
12846 class="cmtt-8"> 2.6416497e-06,</span>
12847 <br class="fancyvrb" /><a
12848 id="x1-125028r14"></a><span
12849 class="cmr-6">14</span><span
12850 class="cmtt-8"> </span><span
12851 class="cmtt-8"> </span><span
12852 class="cmtt-8"> </span><span
12853 class="cmtt-8"> 2.8133190e-06,</span><span
12854 class="cmtt-8"> 2.9961443e-06,</span><span
12855 class="cmtt-8"> 3.1908506e-06,</span><span
12856 class="cmtt-8"> 3.3982101e-06,</span>
12857 <br class="fancyvrb" /><a
12858 id="x1-125030r15"></a><span
12859 class="cmr-6">15</span><span
12860 class="cmtt-8"> </span><span
12861 class="cmtt-8"> </span><span
12862 class="cmtt-8"> </span><span
12863 class="cmtt-8"> 3.6190449e-06,</span><span
12864 class="cmtt-8"> 3.8542308e-06,</span><span
12865 class="cmtt-8"> 4.1047004e-06,</span><span
12866 class="cmtt-8"> 4.3714470e-06,</span>
12867 <br class="fancyvrb" /><a
12868 id="x1-125032r16"></a><span
12869 class="cmr-6">16</span><span
12870 class="cmtt-8"> </span><span
12871 class="cmtt-8"> </span><span
12872 class="cmtt-8"> </span><span
12873 class="cmtt-8"> 4.6555282e-06,</span><span
12874 class="cmtt-8"> 4.9580707e-06,</span><span
12875 class="cmtt-8"> 5.2802740e-06,</span><span
12876 class="cmtt-8"> 5.6234160e-06,</span>
12877 <br class="fancyvrb" /><a
12878 id="x1-125034r17"></a><span
12879 class="cmr-6">17</span><span
12880 class="cmtt-8"> </span><span
12881 class="cmtt-8"> </span><span
12882 class="cmtt-8"> </span><span
12883 class="cmtt-8"> 5.9888572e-06,</span><span
12884 class="cmtt-8"> 6.3780469e-06,</span><span
12885 class="cmtt-8"> 6.7925283e-06,</span><span
12886 class="cmtt-8"> 7.2339451e-06,</span>
12887 <br class="fancyvrb" /><a
12888 id="x1-125036r18"></a><span
12889 class="cmr-6">18</span><span
12890 class="cmtt-8"> </span><span
12891 class="cmtt-8"> </span><span
12892 class="cmtt-8"> </span><span
12893 class="cmtt-8"> 7.7040476e-06,</span><span
12894 class="cmtt-8"> 8.2047000e-06,</span><span
12895 class="cmtt-8"> 8.7378876e-06,</span><span
12896 class="cmtt-8"> 9.3057248e-06,</span>
12897 <br class="fancyvrb" /><a
12898 id="x1-125038r19"></a><span
12899 class="cmr-6">19</span><span
12900 class="cmtt-8"> </span><span
12901 class="cmtt-8"> </span><span
12902 class="cmtt-8"> </span><span
12903 class="cmtt-8"> 9.9104632e-06,</span><span
12904 class="cmtt-8"> 1.0554501e-05,</span><span
12905 class="cmtt-8"> 1.1240392e-05,</span><span
12906 class="cmtt-8"> 1.1970856e-05,</span>
12907 <br class="fancyvrb" /><a
12908 id="x1-125040r20"></a><span
12909 class="cmr-6">20</span><span
12910 class="cmtt-8"> </span><span
12911 class="cmtt-8"> </span><span
12912 class="cmtt-8"> </span><span
12913 class="cmtt-8"> 1.2748789e-05,</span><span
12914 class="cmtt-8"> 1.3577278e-05,</span><span
12915 class="cmtt-8"> 1.4459606e-05,</span><span
12916 class="cmtt-8"> 1.5399272e-05,</span>
12917 <br class="fancyvrb" /><a
12918 id="x1-125042r21"></a><span
12919 class="cmr-6">21</span><span
12920 class="cmtt-8"> </span><span
12921 class="cmtt-8"> </span><span
12922 class="cmtt-8"> </span><span
12923 class="cmtt-8"> 1.6400004e-05,</span><span
12924 class="cmtt-8"> 1.7465768e-05,</span><span
12925 class="cmtt-8"> 1.8600792e-05,</span><span
12926 class="cmtt-8"> 1.9809576e-05,</span>
12927 <br class="fancyvrb" /><a
12928 id="x1-125044r22"></a><span
12929 class="cmr-6">22</span><span
12930 class="cmtt-8"> </span><span
12931 class="cmtt-8"> </span><span
12932 class="cmtt-8"> </span><span
12933 class="cmtt-8"> 2.1096914e-05,</span><span
12934 class="cmtt-8"> 2.2467911e-05,</span><span
12935 class="cmtt-8"> 2.3928002e-05,</span><span
12936 class="cmtt-8"> 2.5482978e-05,</span>
12937 <br class="fancyvrb" /><a
12938 id="x1-125046r23"></a><span
12939 class="cmr-6">23</span><span
12940 class="cmtt-8"> </span><span
12941 class="cmtt-8"> </span><span
12942 class="cmtt-8"> </span><span
12943 class="cmtt-8"> 2.7139006e-05,</span><span
12944 class="cmtt-8"> 2.8902651e-05,</span><span
12945 class="cmtt-8"> 3.0780908e-05,</span><span
12946 class="cmtt-8"> 3.2781225e-05,</span>
12947 <br class="fancyvrb" /><a
12948 id="x1-125048r24"></a><span
12949 class="cmr-6">24</span><span
12950 class="cmtt-8"> </span><span
12951 class="cmtt-8"> </span><span
12952 class="cmtt-8"> </span><span
12953 class="cmtt-8"> 3.4911534e-05,</span><span
12954 class="cmtt-8"> 3.7180282e-05,</span><span
12955 class="cmtt-8"> 3.9596466e-05,</span><span
12956 class="cmtt-8"> 4.2169667e-05,</span>
12957 <br class="fancyvrb" /><a
12958 id="x1-125050r25"></a><span
12959 class="cmr-6">25</span><span
12960 class="cmtt-8"> </span><span
12961 class="cmtt-8"> </span><span
12962 class="cmtt-8"> </span><span
12963 class="cmtt-8"> 4.4910090e-05,</span><span
12964 class="cmtt-8"> 4.7828601e-05,</span><span
12965 class="cmtt-8"> 5.0936773e-05,</span><span
12966 class="cmtt-8"> 5.4246931e-05,</span>
12967 <br class="fancyvrb" /><a
12968 id="x1-125052r26"></a><span
12969 class="cmr-6">26</span><span
12970 class="cmtt-8"> </span><span
12971 class="cmtt-8"> </span><span
12972 class="cmtt-8"> </span><span
12973 class="cmtt-8"> 5.7772202e-05,</span><span
12974 class="cmtt-8"> 6.1526565e-05,</span><span
12975 class="cmtt-8"> 6.5524908e-05,</span><span
12976 class="cmtt-8"> 6.9783085e-05,</span>
12977 <br class="fancyvrb" /><a
12978 id="x1-125054r27"></a><span
12979 class="cmr-6">27</span><span
12980 class="cmtt-8"> </span><span
12981 class="cmtt-8"> </span><span
12982 class="cmtt-8"> </span><span
12983 class="cmtt-8"> 7.4317983e-05,</span><span
12984 class="cmtt-8"> 7.9147585e-05,</span><span
12985 class="cmtt-8"> 8.4291040e-05,</span><span
12986 class="cmtt-8"> 8.9768747e-05,</span>
12987 <br class="fancyvrb" /><a
12988 id="x1-125056r28"></a><span
12989 class="cmr-6">28</span><span
12990 class="cmtt-8"> </span><span
12991 class="cmtt-8"> </span><span
12992 class="cmtt-8"> </span><span
12993 class="cmtt-8"> 9.5602426e-05,</span><span
12994 class="cmtt-8"> 0.00010181521,</span><span
12995 class="cmtt-8"> 0.00010843174,</span><span
12996 class="cmtt-8"> 0.00011547824,</span>
12997 <br class="fancyvrb" /><a
12998 id="x1-125058r29"></a><span
12999 class="cmr-6">29</span><span
13000 class="cmtt-8"> </span><span
13001 class="cmtt-8"> </span><span
13002 class="cmtt-8"> </span><span
13003 class="cmtt-8"> 0.00012298267,</span><span
13004 class="cmtt-8"> 0.00013097477,</span><span
13005 class="cmtt-8"> 0.00013948625,</span><span
13006 class="cmtt-8"> 0.00014855085,</span>
13007 <br class="fancyvrb" /><a
13008 id="x1-125060r30"></a><span
13009 class="cmr-6">30</span><span
13010 class="cmtt-8"> </span><span
13011 class="cmtt-8"> </span><span
13012 class="cmtt-8"> </span><span
13013 class="cmtt-8"> 0.00015820453,</span><span
13014 class="cmtt-8"> 0.00016848555,</span><span
13015 class="cmtt-8"> 0.00017943469,</span><span
13016 class="cmtt-8"> 0.00019109536,</span>
13017 <br class="fancyvrb" /><a
13018 id="x1-125062r31"></a><span
13019 class="cmr-6">31</span><span
13020 class="cmtt-8"> </span><span
13021 class="cmtt-8"> </span><span
13022 class="cmtt-8"> </span><span
13023 class="cmtt-8"> 0.00020351382,</span><span
13024 class="cmtt-8"> 0.00021673929,</span><span
13025 class="cmtt-8"> 0.00023082423,</span><span
13026 class="cmtt-8"> 0.00024582449,</span>
13027 <br class="fancyvrb" /><a
13028 id="x1-125064r32"></a><span
13029 class="cmr-6">32</span><span
13030 class="cmtt-8"> </span><span
13031 class="cmtt-8"> </span><span
13032 class="cmtt-8"> </span><span
13033 class="cmtt-8"> 0.00026179955,</span><span
13034 class="cmtt-8"> 0.00027881276,</span><span
13035 class="cmtt-8"> 0.00029693158,</span><span
13036 class="cmtt-8"> 0.00031622787,</span>
13037 <br class="fancyvrb" /><a
13038 id="x1-125066r33"></a><span
13039 class="cmr-6">33</span><span
13040 class="cmtt-8"> </span><span
13041 class="cmtt-8"> </span><span
13042 class="cmtt-8"> </span><span
13043 class="cmtt-8"> 0.00033677814,</span><span
13044 class="cmtt-8"> 0.00035866388,</span><span
13045 class="cmtt-8"> 0.00038197188,</span><span
13046 class="cmtt-8"> 0.00040679456,</span>
13047 <br class="fancyvrb" /><a
13048 id="x1-125068r34"></a><span
13049 class="cmr-6">34</span><span
13050 class="cmtt-8"> </span><span
13051 class="cmtt-8"> </span><span
13052 class="cmtt-8"> </span><span
13053 class="cmtt-8"> 0.00043323036,</span><span
13054 class="cmtt-8"> 0.00046138411,</span><span
13055 class="cmtt-8"> 0.00049136745,</span><span
13056 class="cmtt-8"> 0.00052329927,</span>
13057 <br class="fancyvrb" /><a
13058 id="x1-125070r35"></a><span
13059 class="cmr-6">35</span><span
13060 class="cmtt-8"> </span><span
13061 class="cmtt-8"> </span><span
13062 class="cmtt-8"> </span><span
13063 class="cmtt-8"> 0.00055730621,</span><span
13064 class="cmtt-8"> 0.00059352311,</span><span
13065 class="cmtt-8"> 0.00063209358,</span><span
13066 class="cmtt-8"> 0.00067317058,</span>
13067 <br class="fancyvrb" /><a
13068 id="x1-125072r36"></a><span
13069 class="cmr-6">36</span><span
13070 class="cmtt-8"> </span><span
13071 class="cmtt-8"> </span><span
13072 class="cmtt-8"> </span><span
13073 class="cmtt-8"> 0.00071691700,</span><span
13074 class="cmtt-8"> 0.00076350630,</span><span
13075 class="cmtt-8"> 0.00081312324,</span><span
13076 class="cmtt-8"> 0.00086596457,</span>
13077 <br class="fancyvrb" /><a
13078 id="x1-125074r37"></a><span
13079 class="cmr-6">37</span><span
13080 class="cmtt-8"> </span><span
13081 class="cmtt-8"> </span><span
13082 class="cmtt-8"> </span><span
13083 class="cmtt-8"> 0.00092223983,</span><span
13084 class="cmtt-8"> 0.00098217216,</span><span
13085 class="cmtt-8"> 0.0010459992,</span><span
13086 class="cmtt-8"> </span><span
13087 class="cmtt-8"> 0.0011139742,</span>
13088 <br class="fancyvrb" /><a
13089 id="x1-125076r38"></a><span
13090 class="cmr-6">38</span><span
13091 class="cmtt-8"> </span><span
13092 class="cmtt-8"> </span><span
13093 class="cmtt-8"> </span><span
13094 class="cmtt-8"> 0.0011863665,</span><span
13095 class="cmtt-8"> </span><span
13096 class="cmtt-8"> 0.0012634633,</span><span
13097 class="cmtt-8"> </span><span
13098 class="cmtt-8"> 0.0013455702,</span><span
13099 class="cmtt-8"> </span><span
13100 class="cmtt-8"> 0.0014330129,</span>
13101 <br class="fancyvrb" /><a
13102 id="x1-125078r39"></a><span
13103 class="cmr-6">39</span><span
13104 class="cmtt-8"> </span><span
13105 class="cmtt-8"> </span><span
13106 class="cmtt-8"> </span><span
13107 class="cmtt-8"> 0.0015261382,</span><span
13108 class="cmtt-8"> </span><span
13109 class="cmtt-8"> 0.0016253153,</span><span
13110 class="cmtt-8"> </span><span
13111 class="cmtt-8"> 0.0017309374,</span><span
13112 class="cmtt-8"> </span><span
13113 class="cmtt-8"> 0.0018434235,</span>
13114 <br class="fancyvrb" /><a
13115 id="x1-125080r40"></a><span
13116 class="cmr-6">40</span><span
13117 class="cmtt-8"> </span><span
13118 class="cmtt-8"> </span><span
13119 class="cmtt-8"> </span><span
13120 class="cmtt-8"> 0.0019632195,</span><span
13121 class="cmtt-8"> </span><span
13122 class="cmtt-8"> 0.0020908006,</span><span
13123 class="cmtt-8"> </span><span
13124 class="cmtt-8"> 0.0022266726,</span><span
13125 class="cmtt-8"> </span><span
13126 class="cmtt-8"> 0.0023713743,</span>
13127 <br class="fancyvrb" /><a
13128 id="x1-125082r41"></a><span
13129 class="cmr-6">41</span><span
13130 class="cmtt-8"> </span><span
13131 class="cmtt-8"> </span><span
13132 class="cmtt-8"> </span><span
13133 class="cmtt-8"> 0.0025254795,</span><span
13134 class="cmtt-8"> </span><span
13135 class="cmtt-8"> 0.0026895994,</span><span
13136 class="cmtt-8"> </span><span
13137 class="cmtt-8"> 0.0028643847,</span><span
13138 class="cmtt-8"> </span><span
13139 class="cmtt-8"> 0.0030505286,</span>
13140 <br class="fancyvrb" /><a
13141 id="x1-125084r42"></a><span
13142 class="cmr-6">42</span><span
13143 class="cmtt-8"> </span><span
13144 class="cmtt-8"> </span><span
13145 class="cmtt-8"> </span><span
13146 class="cmtt-8"> 0.0032487691,</span><span
13147 class="cmtt-8"> </span><span
13148 class="cmtt-8"> 0.0034598925,</span><span
13149 class="cmtt-8"> </span><span
13150 class="cmtt-8"> 0.0036847358,</span><span
13151 class="cmtt-8"> </span><span
13152 class="cmtt-8"> 0.0039241906,</span>
13156 <br class="fancyvrb" /><a
13157 id="x1-125086r43"></a><span
13158 class="cmr-6">43</span><span
13159 class="cmtt-8"> </span><span
13160 class="cmtt-8"> </span><span
13161 class="cmtt-8"> </span><span
13162 class="cmtt-8"> 0.0041792066,</span><span
13163 class="cmtt-8"> </span><span
13164 class="cmtt-8"> 0.0044507950,</span><span
13165 class="cmtt-8"> </span><span
13166 class="cmtt-8"> 0.0047400328,</span><span
13167 class="cmtt-8"> </span><span
13168 class="cmtt-8"> 0.0050480668,</span>
13169 <br class="fancyvrb" /><a
13170 id="x1-125088r44"></a><span
13171 class="cmr-6">44</span><span
13172 class="cmtt-8"> </span><span
13173 class="cmtt-8"> </span><span
13174 class="cmtt-8"> </span><span
13175 class="cmtt-8"> 0.0053761186,</span><span
13176 class="cmtt-8"> </span><span
13177 class="cmtt-8"> 0.0057254891,</span><span
13178 class="cmtt-8"> </span><span
13179 class="cmtt-8"> 0.0060975636,</span><span
13180 class="cmtt-8"> </span><span
13181 class="cmtt-8"> 0.0064938176,</span>
13182 <br class="fancyvrb" /><a
13183 id="x1-125090r45"></a><span
13184 class="cmr-6">45</span><span
13185 class="cmtt-8"> </span><span
13186 class="cmtt-8"> </span><span
13187 class="cmtt-8"> </span><span
13188 class="cmtt-8"> 0.0069158225,</span><span
13189 class="cmtt-8"> </span><span
13190 class="cmtt-8"> 0.0073652516,</span><span
13191 class="cmtt-8"> </span><span
13192 class="cmtt-8"> 0.0078438871,</span><span
13193 class="cmtt-8"> </span><span
13194 class="cmtt-8"> 0.0083536271,</span>
13195 <br class="fancyvrb" /><a
13196 id="x1-125092r46"></a><span
13197 class="cmr-6">46</span><span
13198 class="cmtt-8"> </span><span
13199 class="cmtt-8"> </span><span
13200 class="cmtt-8"> </span><span
13201 class="cmtt-8"> 0.0088964928,</span><span
13202 class="cmtt-8"> </span><span
13203 class="cmtt-8"> 0.009474637,</span><span
13204 class="cmtt-8"> </span><span
13205 class="cmtt-8"> </span><span
13206 class="cmtt-8"> 0.010090352,</span><span
13207 class="cmtt-8"> </span><span
13208 class="cmtt-8"> </span><span
13209 class="cmtt-8"> 0.010746080,</span>
13210 <br class="fancyvrb" /><a
13211 id="x1-125094r47"></a><span
13212 class="cmr-6">47</span><span
13213 class="cmtt-8"> </span><span
13214 class="cmtt-8"> </span><span
13215 class="cmtt-8"> </span><span
13216 class="cmtt-8"> 0.011444421,</span><span
13217 class="cmtt-8"> </span><span
13218 class="cmtt-8"> </span><span
13219 class="cmtt-8"> 0.012188144,</span><span
13220 class="cmtt-8"> </span><span
13221 class="cmtt-8"> </span><span
13222 class="cmtt-8"> 0.012980198,</span><span
13223 class="cmtt-8"> </span><span
13224 class="cmtt-8"> </span><span
13225 class="cmtt-8"> 0.013823725,</span>
13226 <br class="fancyvrb" /><a
13227 id="x1-125096r48"></a><span
13228 class="cmr-6">48</span><span
13229 class="cmtt-8"> </span><span
13230 class="cmtt-8"> </span><span
13231 class="cmtt-8"> </span><span
13232 class="cmtt-8"> 0.014722068,</span><span
13233 class="cmtt-8"> </span><span
13234 class="cmtt-8"> </span><span
13235 class="cmtt-8"> 0.015678791,</span><span
13236 class="cmtt-8"> </span><span
13237 class="cmtt-8"> </span><span
13238 class="cmtt-8"> 0.016697687,</span><span
13239 class="cmtt-8"> </span><span
13240 class="cmtt-8"> </span><span
13241 class="cmtt-8"> 0.017782797,</span>
13242 <br class="fancyvrb" /><a
13243 id="x1-125098r49"></a><span
13244 class="cmr-6">49</span><span
13245 class="cmtt-8"> </span><span
13246 class="cmtt-8"> </span><span
13247 class="cmtt-8"> </span><span
13248 class="cmtt-8"> 0.018938423,</span><span
13249 class="cmtt-8"> </span><span
13250 class="cmtt-8"> </span><span
13251 class="cmtt-8"> 0.020169149,</span><span
13252 class="cmtt-8"> </span><span
13253 class="cmtt-8"> </span><span
13254 class="cmtt-8"> 0.021479854,</span><span
13255 class="cmtt-8"> </span><span
13256 class="cmtt-8"> </span><span
13257 class="cmtt-8"> 0.022875735,</span>
13258 <br class="fancyvrb" /><a
13259 id="x1-125100r50"></a><span
13260 class="cmr-6">50</span><span
13261 class="cmtt-8"> </span><span
13262 class="cmtt-8"> </span><span
13263 class="cmtt-8"> </span><span
13264 class="cmtt-8"> 0.024362330,</span><span
13265 class="cmtt-8"> </span><span
13266 class="cmtt-8"> </span><span
13267 class="cmtt-8"> 0.025945531,</span><span
13268 class="cmtt-8"> </span><span
13269 class="cmtt-8"> </span><span
13270 class="cmtt-8"> 0.027631618,</span><span
13271 class="cmtt-8"> </span><span
13272 class="cmtt-8"> </span><span
13273 class="cmtt-8"> 0.029427276,</span>
13274 <br class="fancyvrb" /><a
13275 id="x1-125102r51"></a><span
13276 class="cmr-6">51</span><span
13277 class="cmtt-8"> </span><span
13278 class="cmtt-8"> </span><span
13279 class="cmtt-8"> </span><span
13280 class="cmtt-8"> 0.031339626,</span><span
13281 class="cmtt-8"> </span><span
13282 class="cmtt-8"> </span><span
13283 class="cmtt-8"> 0.033376252,</span><span
13284 class="cmtt-8"> </span><span
13285 class="cmtt-8"> </span><span
13286 class="cmtt-8"> 0.035545228,</span><span
13287 class="cmtt-8"> </span><span
13288 class="cmtt-8"> </span><span
13289 class="cmtt-8"> 0.037855157,</span>
13290 <br class="fancyvrb" /><a
13291 id="x1-125104r52"></a><span
13292 class="cmr-6">52</span><span
13293 class="cmtt-8"> </span><span
13294 class="cmtt-8"> </span><span
13295 class="cmtt-8"> </span><span
13296 class="cmtt-8"> 0.040315199,</span><span
13297 class="cmtt-8"> </span><span
13298 class="cmtt-8"> </span><span
13299 class="cmtt-8"> 0.042935108,</span><span
13300 class="cmtt-8"> </span><span
13301 class="cmtt-8"> </span><span
13302 class="cmtt-8"> 0.045725273,</span><span
13303 class="cmtt-8"> </span><span
13304 class="cmtt-8"> </span><span
13305 class="cmtt-8"> 0.048696758,</span>
13306 <br class="fancyvrb" /><a
13307 id="x1-125106r53"></a><span
13308 class="cmr-6">53</span><span
13309 class="cmtt-8"> </span><span
13310 class="cmtt-8"> </span><span
13311 class="cmtt-8"> </span><span
13312 class="cmtt-8"> 0.051861348,</span><span
13313 class="cmtt-8"> </span><span
13314 class="cmtt-8"> </span><span
13315 class="cmtt-8"> 0.055231591,</span><span
13316 class="cmtt-8"> </span><span
13317 class="cmtt-8"> </span><span
13318 class="cmtt-8"> 0.058820850,</span><span
13319 class="cmtt-8"> </span><span
13320 class="cmtt-8"> </span><span
13321 class="cmtt-8"> 0.062643361,</span>
13322 <br class="fancyvrb" /><a
13323 id="x1-125108r54"></a><span
13324 class="cmr-6">54</span><span
13325 class="cmtt-8"> </span><span
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13327 class="cmtt-8"> </span><span
13328 class="cmtt-8"> 0.066714279,</span><span
13329 class="cmtt-8"> </span><span
13330 class="cmtt-8"> </span><span
13331 class="cmtt-8"> 0.071049749,</span><span
13332 class="cmtt-8"> </span><span
13333 class="cmtt-8"> </span><span
13334 class="cmtt-8"> 0.075666962,</span><span
13335 class="cmtt-8"> </span><span
13336 class="cmtt-8"> </span><span
13337 class="cmtt-8"> 0.080584227,</span>
13338 <br class="fancyvrb" /><a
13339 id="x1-125110r55"></a><span
13340 class="cmr-6">55</span><span
13341 class="cmtt-8"> </span><span
13342 class="cmtt-8"> </span><span
13343 class="cmtt-8"> </span><span
13344 class="cmtt-8"> 0.085821044,</span><span
13345 class="cmtt-8"> </span><span
13346 class="cmtt-8"> </span><span
13347 class="cmtt-8"> 0.091398179,</span><span
13348 class="cmtt-8"> </span><span
13349 class="cmtt-8"> </span><span
13350 class="cmtt-8"> 0.097337747,</span><span
13351 class="cmtt-8"> </span><span
13352 class="cmtt-8"> </span><span
13353 class="cmtt-8"> 0.10366330,</span>
13354 <br class="fancyvrb" /><a
13355 id="x1-125112r56"></a><span
13356 class="cmr-6">56</span><span
13357 class="cmtt-8"> </span><span
13358 class="cmtt-8"> </span><span
13359 class="cmtt-8"> </span><span
13360 class="cmtt-8"> 0.11039993,</span><span
13361 class="cmtt-8"> </span><span
13362 class="cmtt-8"> </span><span
13363 class="cmtt-8"> </span><span
13364 class="cmtt-8"> 0.11757434,</span><span
13365 class="cmtt-8"> </span><span
13366 class="cmtt-8"> </span><span
13367 class="cmtt-8"> </span><span
13368 class="cmtt-8"> 0.12521498,</span><span
13369 class="cmtt-8"> </span><span
13370 class="cmtt-8"> </span><span
13371 class="cmtt-8"> </span><span
13372 class="cmtt-8"> 0.13335215,</span>
13373 <br class="fancyvrb" /><a
13374 id="x1-125114r57"></a><span
13375 class="cmr-6">57</span><span
13376 class="cmtt-8"> </span><span
13377 class="cmtt-8"> </span><span
13378 class="cmtt-8"> </span><span
13379 class="cmtt-8"> 0.14201813,</span><span
13380 class="cmtt-8"> </span><span
13381 class="cmtt-8"> </span><span
13382 class="cmtt-8"> </span><span
13383 class="cmtt-8"> 0.15124727,</span><span
13384 class="cmtt-8"> </span><span
13385 class="cmtt-8"> </span><span
13386 class="cmtt-8"> </span><span
13387 class="cmtt-8"> 0.16107617,</span><span
13388 class="cmtt-8"> </span><span
13389 class="cmtt-8"> </span><span
13390 class="cmtt-8"> </span><span
13391 class="cmtt-8"> 0.17154380,</span>
13392 <br class="fancyvrb" /><a
13393 id="x1-125116r58"></a><span
13394 class="cmr-6">58</span><span
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13397 class="cmtt-8"> </span><span
13398 class="cmtt-8"> 0.18269168,</span><span
13399 class="cmtt-8"> </span><span
13400 class="cmtt-8"> </span><span
13401 class="cmtt-8"> </span><span
13402 class="cmtt-8"> 0.19456402,</span><span
13403 class="cmtt-8"> </span><span
13404 class="cmtt-8"> </span><span
13405 class="cmtt-8"> </span><span
13406 class="cmtt-8"> 0.20720788,</span><span
13407 class="cmtt-8"> </span><span
13408 class="cmtt-8"> </span><span
13409 class="cmtt-8"> </span><span
13410 class="cmtt-8"> 0.22067342,</span>
13411 <br class="fancyvrb" /><a
13412 id="x1-125118r59"></a><span
13413 class="cmr-6">59</span><span
13414 class="cmtt-8"> </span><span
13415 class="cmtt-8"> </span><span
13416 class="cmtt-8"> </span><span
13417 class="cmtt-8"> 0.23501402,</span><span
13418 class="cmtt-8"> </span><span
13419 class="cmtt-8"> </span><span
13420 class="cmtt-8"> </span><span
13421 class="cmtt-8"> 0.25028656,</span><span
13422 class="cmtt-8"> </span><span
13423 class="cmtt-8"> </span><span
13424 class="cmtt-8"> </span><span
13425 class="cmtt-8"> 0.26655159,</span><span
13426 class="cmtt-8"> </span><span
13427 class="cmtt-8"> </span><span
13428 class="cmtt-8"> </span><span
13429 class="cmtt-8"> 0.28387361,</span>
13430 <br class="fancyvrb" /><a
13431 id="x1-125120r60"></a><span
13432 class="cmr-6">60</span><span
13433 class="cmtt-8"> </span><span
13434 class="cmtt-8"> </span><span
13435 class="cmtt-8"> </span><span
13436 class="cmtt-8"> 0.30232132,</span><span
13437 class="cmtt-8"> </span><span
13438 class="cmtt-8"> </span><span
13439 class="cmtt-8"> </span><span
13440 class="cmtt-8"> 0.32196786,</span><span
13441 class="cmtt-8"> </span><span
13442 class="cmtt-8"> </span><span
13443 class="cmtt-8"> </span><span
13444 class="cmtt-8"> 0.34289114,</span><span
13445 class="cmtt-8"> </span><span
13446 class="cmtt-8"> </span><span
13447 class="cmtt-8"> </span><span
13448 class="cmtt-8"> 0.36517414,</span>
13449 <br class="fancyvrb" /><a
13450 id="x1-125122r61"></a><span
13451 class="cmr-6">61</span><span
13452 class="cmtt-8"> </span><span
13453 class="cmtt-8"> </span><span
13454 class="cmtt-8"> </span><span
13455 class="cmtt-8"> 0.38890521,</span><span
13456 class="cmtt-8"> </span><span
13457 class="cmtt-8"> </span><span
13458 class="cmtt-8"> </span><span
13459 class="cmtt-8"> 0.41417847,</span><span
13460 class="cmtt-8"> </span><span
13461 class="cmtt-8"> </span><span
13462 class="cmtt-8"> </span><span
13463 class="cmtt-8"> 0.44109412,</span><span
13464 class="cmtt-8"> </span><span
13465 class="cmtt-8"> </span><span
13466 class="cmtt-8"> </span><span
13467 class="cmtt-8"> 0.46975890,</span>
13468 <br class="fancyvrb" /><a
13469 id="x1-125124r62"></a><span
13470 class="cmr-6">62</span><span
13471 class="cmtt-8"> </span><span
13472 class="cmtt-8"> </span><span
13473 class="cmtt-8"> </span><span
13474 class="cmtt-8"> 0.50028648,</span><span
13475 class="cmtt-8"> </span><span
13476 class="cmtt-8"> </span><span
13477 class="cmtt-8"> </span><span
13478 class="cmtt-8"> 0.53279791,</span><span
13479 class="cmtt-8"> </span><span
13480 class="cmtt-8"> </span><span
13481 class="cmtt-8"> </span><span
13482 class="cmtt-8"> 0.56742212,</span><span
13483 class="cmtt-8"> </span><span
13484 class="cmtt-8"> </span><span
13485 class="cmtt-8"> </span><span
13486 class="cmtt-8"> 0.60429640,</span>
13487 <br class="fancyvrb" /><a
13488 id="x1-125126r63"></a><span
13489 class="cmr-6">63</span><span
13490 class="cmtt-8"> </span><span
13491 class="cmtt-8"> </span><span
13492 class="cmtt-8"> </span><span
13493 class="cmtt-8"> 0.64356699,</span><span
13494 class="cmtt-8"> </span><span
13495 class="cmtt-8"> </span><span
13496 class="cmtt-8"> </span><span
13497 class="cmtt-8"> 0.68538959,</span><span
13498 class="cmtt-8"> </span><span
13499 class="cmtt-8"> </span><span
13500 class="cmtt-8"> </span><span
13501 class="cmtt-8"> 0.72993007,</span><span
13502 class="cmtt-8"> </span><span
13503 class="cmtt-8"> </span><span
13504 class="cmtt-8"> </span><span
13505 class="cmtt-8"> 0.77736504,</span>
13506 <br class="fancyvrb" /><a
13507 id="x1-125128r64"></a><span
13508 class="cmr-6">64</span><span
13509 class="cmtt-8"> </span><span
13510 class="cmtt-8"> </span><span
13511 class="cmtt-8"> </span><span
13512 class="cmtt-8"> 0.82788260,</span><span
13513 class="cmtt-8"> </span><span
13514 class="cmtt-8"> </span><span
13515 class="cmtt-8"> </span><span
13516 class="cmtt-8"> 0.88168307,</span><span
13517 class="cmtt-8"> </span><span
13518 class="cmtt-8"> </span><span
13519 class="cmtt-8"> </span><span
13520 class="cmtt-8"> 0.9389798,</span><span
13521 class="cmtt-8"> </span><span
13522 class="cmtt-8"> </span><span
13523 class="cmtt-8"> </span><span
13524 class="cmtt-8"> </span><span
13525 class="cmtt-8"> 1.</span>
13533 <h3 class="sectionHead"><span class="titlemark">A. </span> <a
13534 id="x1-126000A"></a>Embedding Vorbis into an Ogg stream</h3>
13535 <!--l. 6--><p class="noindent" >
13536 <h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a
13537 id="x1-127000A.1"></a>Overview</h4>
13538 <!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
13539 compressed audio packet data into file form.
13540 <!--l. 12--><p class="noindent" >The <a
13541 href="#x1-20001">Section 1</a>, “<a
13542 href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of
13543 Vorbis audio packets.
13544 <!--l. 15--><p class="noindent" >The <a
13545 href="oggstream.html" >Ogg bitstream overview</a> and <a
13546 href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
13547 descriptions of Ogg transport streams. This specification document assumes a working
13548 knowledge of the concepts covered in these named backround documents. Please read them
13550 <!--l. 22--><p class="noindent" >
13551 <h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a
13552 id="x1-128000A.1.1"></a>Restrictions</h5>
13553 <!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
13554 streams in degenerate, unmultiplexed form only. That is:
13555 <ul class="itemize1">
13556 <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
13558 <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
13561 <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
13567 <!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
13568 types into a multi-stream Ogg file. At the time this document was written, Ogg was
13569 becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
13570 audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
13571 within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
13572 implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
13573 stream (naturally, application authors are encouraged to support full multiplexed Ogg
13575 <!--l. 55--><p class="noindent" >
13576 <h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a
13577 id="x1-129000A.1.2"></a>MIME type</h5>
13578 <!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and
13579 applications should use <span
13580 class="cmtt-12">application/ogg</span>, while visual media should use <span
13581 class="cmtt-12">video/ogg</span>, and audio
13583 class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP
13584 encapsulated Vorbis should use <span
13585 class="cmtt-12">audio/vorbis </span>+ <span
13586 class="cmtt-12">audio/vorbis-config</span>.
13587 <!--l. 65--><p class="noindent" >
13588 <h4 class="subsectionHead"><span class="titlemark">A.2. </span> <a
13589 id="x1-130000A.2"></a>Encapsulation</h4>
13590 <!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
13591 <ul class="itemize1">
13592 <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
13593 as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
13594 results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
13597 <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
13599 <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
13600 more pages beginning on the second page of the logical stream. However many pages
13601 they span, the third header packet finishes the page on which it ends. The next (first
13602 audio) packet must begin on a fresh page.
13607 <li class="itemize">The granule position of these first pages containing only headers is zero.
13609 <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
13611 <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
13613 <li class="itemize">The last page is marked ’end of stream’ in the page flags.
13615 <li class="itemize">Vorbis packets may span page boundaries.
13617 <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
13618 samples (per channel; a stereo stream’s granule position does not increment at twice
13619 the speed of a mono stream).
13621 <li class="itemize">The granule position of a page represents the end PCM sample position of the last
13623 class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
13624 returned by decode, not an internal sample awaiting lapping with a subsequent block.
13625 A page that is entirely spanned by a single packet (that completes on a subsequent
13626 page) has no granule position, and the granule position is set to ’-1’.
13627 <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
13628 necessarily the middle sample from that block. If, eg, the current Vorbis packet
13629 encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
13630 decodable sample from the current packet be at position (3*long_block_length/4) -
13631 (short_block_length/4).
13633 <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
13634 started at position zero. Although the granule position belongs to the last completed
13635 packet on the page and a valid granule position must be positive, by inference it may
13636 indicate that the PCM position of the beginning of audio is positive or negative.
13637 <ul class="itemize2">
13638 <li class="itemize">A positive starting value simply indicates that this stream begins at some
13639 positive time offset, potentially within a larger program. This is a common case
13640 when connecting to the middle of broadcast stream.
13642 <li class="itemize">A negative value indicates that output samples preceeding time zero should be
13646 discarded during decoding; this technique is used to allow sample-granularity
13647 editing of the stream start time of already-encoded Vorbis streams. The number
13648 of samples to be discarded must not exceed the overlap-add span of the first two
13651 <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
13652 second finished audio packet must flush the page on which it appears and the
13653 third packet begin a fresh page. This allows the decoder to always be able to
13654 perform PCM position adjustments before needing to return any PCM data from
13655 synthesis, resulting in correct positioning information without any aditional seeking
13657 <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
13658 id="x1-131000A.2"></a><span
13659 class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return
13660 incorrect positioning information for seeking operations at the very beginning of the
13663 <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the
13664 final packet would normally return is used to end the stream on other than even frame
13665 boundaries. The difference between the actual available data returned and the
13666 declared amount indicates how many trailing samples to discard from the decoding
13672 <h3 class="sectionHead"><span class="titlemark">B. </span> <a
13673 id="x1-132000B"></a>Vorbis encapsulation in RTP</h3>
13674 <!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
13675 class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
13676 how to embed Vorbis audio in an RTP stream.
13683 <h3 class="likesectionHead"><a
13684 id="x1-133000B"></a>Colophon</h3>
13685 <!--l. 6--><p class="noindent" ><img
13686 src="Vorbis_I_spec13x.png" alt="PIC" class="graphics"><!--tex4ht:graphics
13687 name="Vorbis_I_spec13x.png" src="xifish.pdf"
13689 <!--l. 10--><p class="noindent" >Ogg is a <a
13690 href="http://www.xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from
13691 corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
13693 href="http://www.xiph.org/about.html" >About the Xiph.Org Foundation</a> for details.
13694 <!--l. 17--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and
13695 Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.Org
13696 Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification
13697 and certify specification compliance.
13698 <!--l. 23--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
13699 does not restrict third parties from distributing independent implementations of Vorbis software
13700 under other licenses.
13701 <!--l. 28--><p class="noindent" >Ogg, Vorbis, Xiph.Org Foundation and their logos are trademarks (tm) of the <a
13702 href="http://www.xiph.org/" >Xiph.Org
13703 Foundation</a>. These pages are copyright (C) 1994-2007 Xiph.Org Foundation. All rights
13705 <!--l. 33--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span
13706 class="E">E</span>X</span></span>.
13710 <h3 class="likesectionHead"><a
13711 id="x1-134000B"></a>References</h3>
13712 <!--l. 125--><p class="noindent" >
13713 <div class="thebibliography">
13714 <p class="bibitem" ><span class="biblabel">
13715 [1]<span class="bibsp">   </span></span><a
13716 id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
13717 B. Edler, The use of multirate filter banks for coding of high quality digital audio,
13719 href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span
13720 class="cmtt-12">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.