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diff --git a/vorbis/doc/Vorbis_I_spec.html b/vorbis/doc/Vorbis_I_spec.html new file mode 100644 index 0000000..629b2fb --- /dev/null +++ b/vorbis/doc/Vorbis_I_spec.html @@ -0,0 +1,13243 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Vorbis I specification</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)"> +<meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)"> +<!-- html --> +<meta name="src" content="Vorbis_I_spec.tex"> +<meta name="date" content="2015-02-27 13:18:00"> +<link rel="stylesheet" type="text/css" href="Vorbis_I_spec.css"> +</head><body +> +<div class="maketitle"> + + + + + + + +<h2 class="titleHead">Vorbis I specification</h2> +<div class="author" ><span +class="cmr-17">Xiph.Org Foundation</span></div><br /> +<div class="date" ><span +class="cmr-17">February 27, 2015</span></div> +</div> +<h3 class="likesectionHead"><a + id="x1-1000"></a>Contents</h3> +<div class="tableofcontents"> + <span class="sectionToc" >1 <a +href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span> +<br />  <span class="subsectionToc" >1.1 <a +href="#x1-30001.1" id="QQ2-1-3">Overview</a></span> +<br />   <span class="subsubsectionToc" >1.1.1 <a +href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span> +<br />   <span class="subsubsectionToc" >1.1.2 <a +href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span> +<br />   <span class="subsubsectionToc" >1.1.3 <a +href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span> +<br />   <span class="subsubsectionToc" >1.1.4 <a +href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span> +<br />   <span class="subsubsectionToc" >1.1.5 <a +href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span> +<br />   <span class="subsubsectionToc" >1.1.6 <a +href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span> +<br />  <span class="subsectionToc" >1.2 <a +href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span> +<br />   <span class="subsubsectionToc" >1.2.1 <a +href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span> +<br />   <span class="subsubsectionToc" >1.2.2 <a +href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span> +<br />   <span class="subsubsectionToc" >1.2.3 <a +href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span> + + + +<br />   <span class="subsubsectionToc" >1.2.4 <a +href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span> +<br />   <span class="subsubsectionToc" >1.2.5 <a +href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span> +<br />   <span class="subsubsectionToc" >1.2.6 <a +href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span> +<br />  <span class="subsectionToc" >1.3 <a +href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span> +<br />   <span class="subsubsectionToc" >1.3.1 <a +href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span> +<br />   <span class="subsubsectionToc" >1.3.2 <a +href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span> +<br /> <span class="sectionToc" >2 <a +href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span> +<br />  <span class="subsectionToc" >2.1 <a +href="#x1-370002.1" id="QQ2-1-40">Overview</a></span> +<br />   <span class="subsubsectionToc" >2.1.1 <a +href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span> +<br />   <span class="subsubsectionToc" >2.1.2 <a +href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span> +<br />   <span class="subsubsectionToc" >2.1.3 <a +href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span> +<br />   <span class="subsubsectionToc" >2.1.4 <a +href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span> +<br />   <span class="subsubsectionToc" >2.1.5 <a +href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span> +<br />   <span class="subsubsectionToc" >2.1.6 <a +href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span> +<br />   <span class="subsubsectionToc" >2.1.7 <a +href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span> +<br />   <span class="subsubsectionToc" >2.1.8 <a +href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span> +<br />   <span class="subsubsectionToc" >2.1.9 <a +href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span> +<br /> <span class="sectionToc" >3 <a +href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span> +<br />  <span class="subsectionToc" >3.1 <a +href="#x1-480003.1" id="QQ2-1-51">Overview</a></span> +<br />   <span class="subsubsectionToc" >3.1.1 <a +href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span> +<br />  <span class="subsectionToc" >3.2 <a +href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span> +<br />   <span class="subsubsectionToc" >3.2.1 <a +href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span> +<br />  <span class="subsectionToc" >3.3 <a +href="#x1-580003.3" id="QQ2-1-63">Use of the codebook abstraction</a></span> +<br /> <span class="sectionToc" >4 <a +href="#x1-590004" id="QQ2-1-64">Codec Setup and Packet Decode</a></span> +<br />  <span class="subsectionToc" >4.1 <a +href="#x1-600004.1" id="QQ2-1-65">Overview</a></span> +<br />  <span class="subsectionToc" >4.2 <a +href="#x1-610004.2" id="QQ2-1-66">Header decode and decode setup</a></span> +<br />   <span class="subsubsectionToc" >4.2.1 <a +href="#x1-620004.2.1" id="QQ2-1-67">Common header decode</a></span> +<br />   <span class="subsubsectionToc" >4.2.2 <a +href="#x1-630004.2.2" id="QQ2-1-68">Identification header</a></span> +<br />   <span class="subsubsectionToc" >4.2.3 <a +href="#x1-640004.2.3" id="QQ2-1-69">Comment header</a></span> + + + +<br />   <span class="subsubsectionToc" >4.2.4 <a +href="#x1-650004.2.4" id="QQ2-1-70">Setup header</a></span> +<br />  <span class="subsectionToc" >4.3 <a +href="#x1-720004.3" id="QQ2-1-78">Audio packet decode and synthesis</a></span> +<br />   <span class="subsubsectionToc" >4.3.1 <a +href="#x1-730004.3.1" id="QQ2-1-79">packet type, mode and window decode</a></span> +<br />   <span class="subsubsectionToc" >4.3.2 <a +href="#x1-740004.3.2" id="QQ2-1-80">floor curve decode</a></span> +<br />   <span class="subsubsectionToc" >4.3.3 <a +href="#x1-750004.3.3" id="QQ2-1-81">nonzero vector propagate</a></span> +<br />   <span class="subsubsectionToc" >4.3.4 <a +href="#x1-760004.3.4" id="QQ2-1-82">residue decode</a></span> +<br />   <span class="subsubsectionToc" >4.3.5 <a +href="#x1-770004.3.5" id="QQ2-1-83">inverse coupling</a></span> +<br />   <span class="subsubsectionToc" >4.3.6 <a +href="#x1-780004.3.6" id="QQ2-1-84">dot product</a></span> +<br />   <span class="subsubsectionToc" >4.3.7 <a +href="#x1-790004.3.7" id="QQ2-1-85">inverse MDCT</a></span> +<br />   <span class="subsubsectionToc" >4.3.8 <a +href="#x1-800004.3.8" id="QQ2-1-86">overlap_add</a></span> +<br />   <span class="subsubsectionToc" >4.3.9 <a +href="#x1-810004.3.9" id="QQ2-1-87">output channel order</a></span> +<br /> <span class="sectionToc" >5 <a +href="#x1-820005" id="QQ2-1-88">comment field and header specification</a></span> +<br />  <span class="subsectionToc" >5.1 <a +href="#x1-830005.1" id="QQ2-1-89">Overview</a></span> +<br />  <span class="subsectionToc" >5.2 <a +href="#x1-840005.2" id="QQ2-1-90">Comment encoding</a></span> +<br />   <span class="subsubsectionToc" >5.2.1 <a +href="#x1-850005.2.1" id="QQ2-1-91">Structure</a></span> +<br />   <span class="subsubsectionToc" >5.2.2 <a +href="#x1-860005.2.2" id="QQ2-1-92">Content vector format</a></span> +<br />   <span class="subsubsectionToc" >5.2.3 <a +href="#x1-890005.2.3" id="QQ2-1-95">Encoding</a></span> +<br /> <span class="sectionToc" >6 <a +href="#x1-900006" id="QQ2-1-96">Floor type 0 setup and decode</a></span> +<br />  <span class="subsectionToc" >6.1 <a +href="#x1-910006.1" id="QQ2-1-97">Overview</a></span> +<br />  <span class="subsectionToc" >6.2 <a +href="#x1-920006.2" id="QQ2-1-98">Floor 0 format</a></span> +<br />   <span class="subsubsectionToc" >6.2.1 <a +href="#x1-930006.2.1" id="QQ2-1-99">header decode</a></span> +<br />   <span class="subsubsectionToc" >6.2.2 <a +href="#x1-940006.2.2" id="QQ2-1-100">packet decode</a></span> +<br />   <span class="subsubsectionToc" >6.2.3 <a +href="#x1-950006.2.3" id="QQ2-1-101">curve computation</a></span> +<br /> <span class="sectionToc" >7 <a +href="#x1-970007" id="QQ2-1-103">Floor type 1 setup and decode</a></span> +<br />  <span class="subsectionToc" >7.1 <a +href="#x1-980007.1" id="QQ2-1-104">Overview</a></span> +<br />  <span class="subsectionToc" >7.2 <a +href="#x1-990007.2" id="QQ2-1-105">Floor 1 format</a></span> +<br />   <span class="subsubsectionToc" >7.2.1 <a +href="#x1-1000007.2.1" id="QQ2-1-106">model</a></span> +<br />   <span class="subsubsectionToc" >7.2.2 <a +href="#x1-1010007.2.2" id="QQ2-1-111">header decode</a></span> +<br />   <span class="subsubsectionToc" >7.2.3 <a +href="#x1-1020007.2.3" id="QQ2-1-112">packet decode</a></span> + + + +<br />   <span class="subsubsectionToc" >7.2.4 <a +href="#x1-1030007.2.4" id="QQ2-1-113">curve computation</a></span> +<br /> <span class="sectionToc" >8 <a +href="#x1-1040008" id="QQ2-1-114">Residue setup and decode</a></span> +<br />  <span class="subsectionToc" >8.1 <a +href="#x1-1050008.1" id="QQ2-1-115">Overview</a></span> +<br />  <span class="subsectionToc" >8.2 <a +href="#x1-1060008.2" id="QQ2-1-116">Residue format</a></span> +<br />  <span class="subsectionToc" >8.3 <a +href="#x1-1070008.3" id="QQ2-1-118">residue 0</a></span> +<br />  <span class="subsectionToc" >8.4 <a +href="#x1-1080008.4" id="QQ2-1-119">residue 1</a></span> +<br />  <span class="subsectionToc" >8.5 <a +href="#x1-1090008.5" id="QQ2-1-120">residue 2</a></span> +<br />  <span class="subsectionToc" >8.6 <a +href="#x1-1100008.6" id="QQ2-1-122">Residue decode</a></span> +<br />   <span class="subsubsectionToc" >8.6.1 <a +href="#x1-1110008.6.1" id="QQ2-1-123">header decode</a></span> +<br />   <span class="subsubsectionToc" >8.6.2 <a +href="#x1-1120008.6.2" id="QQ2-1-124">packet decode</a></span> +<br />   <span class="subsubsectionToc" >8.6.3 <a +href="#x1-1130008.6.3" id="QQ2-1-125">format 0 specifics</a></span> +<br />   <span class="subsubsectionToc" >8.6.4 <a +href="#x1-1140008.6.4" id="QQ2-1-126">format 1 specifics</a></span> +<br />   <span class="subsubsectionToc" >8.6.5 <a +href="#x1-1150008.6.5" id="QQ2-1-127">format 2 specifics</a></span> +<br /> <span class="sectionToc" >9 <a +href="#x1-1160009" id="QQ2-1-128">Helper equations</a></span> +<br />  <span class="subsectionToc" >9.1 <a +href="#x1-1170009.1" id="QQ2-1-129">Overview</a></span> +<br />  <span class="subsectionToc" >9.2 <a +href="#x1-1180009.2" id="QQ2-1-130">Functions</a></span> +<br />   <span class="subsubsectionToc" >9.2.1 <a +href="#x1-1190009.2.1" id="QQ2-1-131">ilog</a></span> +<br />   <span class="subsubsectionToc" >9.2.2 <a +href="#x1-1200009.2.2" id="QQ2-1-132">float32_unpack</a></span> +<br />   <span class="subsubsectionToc" >9.2.3 <a +href="#x1-1210009.2.3" id="QQ2-1-133">lookup1_values</a></span> +<br />   <span class="subsubsectionToc" >9.2.4 <a +href="#x1-1220009.2.4" id="QQ2-1-134">low_neighbor</a></span> +<br />   <span class="subsubsectionToc" >9.2.5 <a +href="#x1-1230009.2.5" id="QQ2-1-135">high_neighbor</a></span> +<br />   <span class="subsubsectionToc" >9.2.6 <a +href="#x1-1240009.2.6" id="QQ2-1-136">render_point</a></span> +<br />   <span class="subsubsectionToc" >9.2.7 <a +href="#x1-1250009.2.7" id="QQ2-1-137">render_line</a></span> +<br /> <span class="sectionToc" >10 <a +href="#x1-12600010" id="QQ2-1-138">Tables</a></span> +<br />  <span class="subsectionToc" >10.1 <a +href="#x1-12700010.1" id="QQ2-1-139">floor1_inverse_dB_table</a></span> +<br /> <span class="sectionToc" >A <a +href="#x1-128000A" id="QQ2-1-140">Embedding Vorbis into an Ogg stream</a></span> +<br />  <span class="subsectionToc" >A.1 <a +href="#x1-129000A.1" id="QQ2-1-141">Overview</a></span> +<br />   <span class="subsubsectionToc" >A.1.1 <a +href="#x1-130000A.1.1" id="QQ2-1-142">Restrictions</a></span> +<br />   <span class="subsubsectionToc" >A.1.2 <a +href="#x1-131000A.1.2" id="QQ2-1-143">MIME type</a></span> + + + +<br />  <span class="subsectionToc" >A.2 <a +href="#x1-132000A.2" id="QQ2-1-144">Encapsulation</a></span> +<br /> <span class="sectionToc" >B <a +href="#x1-134000B" id="QQ2-1-146">Vorbis encapsulation in RTP</a></span> +</div> + + + +<h3 class="sectionHead"><span class="titlemark">1. </span> <a + id="x1-20001"></a>Introduction and Description</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">1.1. </span> <a + id="x1-30001.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit +specification appears beginning in <a +href="#x1-590004">section 4</a>, “<a +href="#x1-590004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later +sections assume a high-level understanding of the Vorbis decode process, which is provided +here. +<!--l. 15--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.1. </span> <a + id="x1-40001.1.1"></a>Application</h5> +<!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder +flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At +the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same +league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT +rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower +and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel +representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255 +discrete channels). +<!--l. 29--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.2. </span> <a + id="x1-50001.1.2"></a>Classification</h5> +<!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete +Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in +Vorbis II to offer better transient response and reproduction using a transform better suited to +localized time events. + + + +<!--l. 37--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.3. </span> <a + id="x1-60001.1.3"></a>Assumptions</h5> +<!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple, +low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does +require more working memory as Vorbis has no static probability model; the vector codebooks +used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis +bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to +which they are pre-decoded into a cache is the dominant factor in decoder memory +usage. +<!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it +is solely a method of accepting input audio, dividing it into individual frames and +compressing these frames into raw, unformatted ’packets’. The decoder then accepts +these raw packets in sequence, decodes them, synthesizes audio frames from them, and +reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form +variable bit rate (VBR) codec and packets have no minimum size, maximum size, or +fixed/expected size. Packets are designed that they may be truncated (or padded) +and remain decodable; this is not to be considered an error condition and is used +extensively in bitrate management in peeling. Both the transport mechanism and +decoder must allow that a packet may be any size, or end before or after packet decode +expects. +<!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form +framing, sync, positioning and error correction in accordance with these design assumptions, such +as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this +document, we will assume that Vorbis is to be embedded in an Ogg stream specifically, +although this is by no means a requirement or fundamental assumption in the Vorbis +design. +<!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a +href="#x1-128000A">section A</a>, +“<a +href="#x1-128000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”. +<!--l. 77--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.4. </span> <a + id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5> +<!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple +decades of continuous encoder improvement before running out of room within the codec +specification. For these reasons, configurable aspects of codec setup intentionally lean toward the +extreme of forward adaptive. + + + +<!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis +developer to keep in mind) is that the entire probability model of the codec, the Huffman and +VQ codebooks, is packed into the bitstream header along with extensive CODEC setup +parameters (often several hundred fields). This makes it impossible, as it would be with +MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin +decode at any frame in the stream without having previously fetched the codec setup +header. +<!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a + id="x1-80001.1.4"></a><span +class="cmbx-12">Note:</span></span> Vorbis <span +class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec +has been initialized/setup with the setup headers. +<!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream +headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less +is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion). +<!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is +an unusual design and thus causes some amount of complaint among engineers as this runs +against current design trends (and also points out limitations in some existing software/interface +designs, such as Windows’ ACM codec framework). However, we find that it does not +fundamentally limit Vorbis’ suitable application space. +<!--l. 115--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.5. </span> <a + id="x1-90001.1.5"></a>Format Specification</h5> +<!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets +that are correctly decoded by the reference Vorbis decoder described below may be considered +a proper Vorbis encoder. A decoder must faithfully and completely implement the +specification defined below (except where noted) to be considered a proper Vorbis +decoder. +<!--l. 123--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.1.6. </span> <a + id="x1-100001.1.6"></a>Hardware Profile</h5> + + + +<!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an +embedded design. For this reason, embedded designs are allowed to deviate in limited ways from +the ‘full’ decode specification yet still be certified compliant. These optional omissions are +labelled in the spec where relevant. +<!--l. 131--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">1.2. </span> <a + id="x1-110001.2"></a>Decoder Configuration</h4> +<!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that +perform specific functions in the decode pipeline. Each different component instance of a specific +type is semantically interchangeable; decoder configuration consists both of internal component +configuration, as well as arrangement of specific instances into a decode pipeline. Componentry +arrangement is roughly as follows: +<div class="center" +> +<!--l. 141--><p class="noindent" > + +<!--l. 142--><p class="noindent" ><img +src="components.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 1: </span><span +class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-110011 --> +</div> +<!--l. 146--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.2.1. </span> <a + id="x1-120001.2.1"></a>Global Config</h5> +<!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis +version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other +configuration is in the context of specific components. +<!--l. 152--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.2.2. </span> <a + id="x1-130001.2.2"></a>Mode</h5> + + + +<!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many +modes. +<!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible +methods with the intention of choosing a method best suited to that frame. Different +modes are, e.g. how frame size is changed from frame to frame. The mode number of a +frame serves as a top level configuration switch for all other specific aspects of frame +decode. +<!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis +window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping +number. The mapping number specifies which mapping configuration instance to use for low-level +packet decode and synthesis. +<!--l. 171--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.2.3. </span> <a + id="x1-140001.2.3"></a>Mapping</h5> +<!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets +of channel vectors together for grouped encoding and decoding. These submaps are +not references to external components; the submap list is internal and specific to a +mapping. +<!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors +within a mapping. The submap functions as a last layer of indirection such that specific special +floor or residue settings can be applied not only to all the vectors in a given mode, but also +specific vectors in a specific mode. Each submap specifies the proper floor and residue +instance number to use for decoding that submap’s spectral floor and spectral residue +vectors. +<!--l. 186--><p class="noindent" >As an example: +<!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth +channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a +full-spectrum version of it as with the other channels. The submapping mechanism can be used +to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only +representation to the bass channel, thus saving space. In this example, channels 0-4 belong to +submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which +uses a bass-only representation. + + + +<!--l. 199--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.2.4. </span> <a + id="x1-150001.2.4"></a>Floor</h5> +<!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution +representation of the audio spectrum for the given channel in the current frame, generally used +akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has +historically used it as a unit-baseline for spectral resolution. +<!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB +amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear +interpolated representation on a dB amplitude scale and linear frequency scale. The two floors +are semantically interchangeable in encoding/decoding. However, floor type 1 provides more +stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and +high bitrate modes. Floor 1 is also considerably less expensive to decode than floor +0. +<!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis +encoder past Xiph.Org’s own beta 4 makes use of floor 0. +<!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy +coding to save space. For this reason, a floor configuration generally refers to multiple +codebooks in the codebook component list. Entropy coding is thus provided as an +abstraction, and each floor instance may choose from any and all available codebooks when +coding/decoding. +<!--l. 230--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.2.5. </span> <a + id="x1-160001.2.5"></a>Residue</h5> +<!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been +subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector +quantization according to one of three specific packing/coding algorithms numbered +0 through 2. The packing algorithm details are configured by residue instance. As +with the floor components, the final VQ/entropy encoding is provided by external +codebook instances and each residue instance may choose from any and all available +codebooks. +<!--l. 241--><p class="noindent" > + + + +<h5 class="subsubsectionHead"><span class="titlemark">1.2.6. </span> <a + id="x1-170001.2.6"></a>Codebooks</h5> +<!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use +the entropy-decoded integer value as an offset into an index of output value vectors, returning +the indicated vector of values. +<!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree +representation. This tree is tightly packed using one of several methods, depending on whether +codeword lengths are ordered or unordered, or the tree is sparse. +<!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly, +the vector index is encoded as a single list of values of possible values that are then permuted +into a list of n-dimensional rows (lattice VQ). +<!--l. 260--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">1.3. </span> <a + id="x1-180001.3"></a>High-level Decode Process</h4> +<!--l. 262--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.3.1. </span> <a + id="x1-190001.3.1"></a>Decode Setup</h5> +<!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the +stream to be decoded. Vorbis uses three header packets; all are required, in-order, by +this specification. Once set up, decode may begin at any audio packet belonging to +the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio +packets. +<!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup +header. +<!--l. 274--><p class="noindent" ><span class="paragraphHead"><a + id="x1-200001.3.1"></a><span +class="cmbx-12">Identification Header</span></span> +The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio +characteristics of the stream such as sample rate and number of channels. + + + +<!--l. 279--><p class="noindent" ><span class="paragraphHead"><a + id="x1-210001.3.1"></a><span +class="cmbx-12">Comment Header</span></span> +The comment header includes user text comments (“tags”) and a vendor string for the +application/library that produced the bitstream. The encoding and proper use of the comment +header is described in <a +href="#x1-820005">section 5</a>, “<a +href="#x1-820005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”. +<!--l. 284--><p class="noindent" ><span class="paragraphHead"><a + id="x1-220001.3.1"></a><span +class="cmbx-12">Setup Header</span></span> +The setup header includes extensive CODEC setup information as well as the complete VQ and +Huffman codebooks needed for decode. +<!--l. 289--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">1.3.2. </span> <a + id="x1-230001.3.2"></a>Decode Procedure</h5> +<!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same. + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">decode packet type flag + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">decode mode number + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">decode window shape (long windows only) + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">decode floor + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem">decode residue into residue vectors + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem">inverse channel coupling of residue vectors + </dd><dt class="enumerate-enumitem"> + 7. </dt><dd +class="enumerate-enumitem">generate floor curve from decoded floor data + </dd><dt class="enumerate-enumitem"> + 8. </dt><dd +class="enumerate-enumitem">compute dot product of floor and residue, producing audio spectrum vector + </dd><dt class="enumerate-enumitem"> + 9. </dt><dd +class="enumerate-enumitem">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis + I + + + + </dd><dt class="enumerate-enumitem"> + 10. </dt><dd +class="enumerate-enumitem">overlap/add left-hand output of transform with right-hand output of previous frame + </dd><dt class="enumerate-enumitem"> + 11. </dt><dd +class="enumerate-enumitem">store right hand-data from transform of current frame for future lapping + </dd><dt class="enumerate-enumitem"> + 12. </dt><dd +class="enumerate-enumitem">if not first frame, return results of overlap/add as audio result of current frame</dd></dl> +<!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can +take advantage of symmetries in the MDCT to store the right-hand transform data of a partial +MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before +overlap/add with the next frame. This optimization produces entirely equivalent output and is +naturally perfectly legal. The decoder must be <span +class="cmti-12">entirely mathematically equivalent </span>to the +specification, it need not be a literal semantic implementation. +<!--l. 317--><p class="noindent" ><span class="paragraphHead"><a + id="x1-240001.3.2"></a><span +class="cmbx-12">Packet type decode</span></span> +Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis +headers described above. The fourth packet type marks an audio packet. All other packet types +are reserved; packets marked with a reserved type should be ignored. +<!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of +audio packet decode is to read and verify the packet type; <span +class="cmti-12">a non-audio packet when audio is</span> +<span +class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span> +<span +class="cmti-12">packet and not attempt decoding it to audio</span>. +<!--l. 334--><p class="noindent" ><span class="paragraphHead"><a + id="x1-250001.3.2"></a><span +class="cmbx-12">Mode decode</span></span> +Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of +which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct +offset into the mode instance index. +<!--l. 341--><p class="noindent" ><span class="paragraphHead"><a + id="x1-260001.3.2"></a><span +class="cmbx-12">Window shape decode (long windows only)</span></span> +Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I, +legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis +handles channels as independent vectors and these frame sizes are in samples per +channel. + + + +<!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next, +avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed +according to MDCT requirements, overlapped 50% with the output of the previous frame and +added. The window shape assures seamless reconstruction. +<!--l. 354--><p class="noindent" >This is easy to visualize in the case of equal sized-windows: +<div class="center" +> +<!--l. 356--><p class="noindent" > + +<!--l. 357--><p class="noindent" ><img +src="window1.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 2: </span><span +class="content">overlap of two equal-sized windows</span></div><!--tex4ht:label?: x1-260012 --> +</div> +<!--l. 361--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows: +<div class="center" +> +<!--l. 364--><p class="noindent" > + +<!--l. 365--><p class="noindent" ><img +src="window2.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 3: </span><span +class="content">overlap of a long and a short window</span></div><!--tex4ht:label?: x1-260023 --> +</div> +<!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for +seamless lapping as above. It is possible to correctly infer window shape to be applied to the +current window from knowing the sizes of the current, previous and next window. It is legal for a +decoder to use this method. However, in the case of a long window (short windows require no +modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although +not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to +the point of lapping entirely independently of any other packet, allowing easier abstraction of +decode layers as well as allowing a greater level of easy parallelism in encode and +decode. +<!--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 +href="#XSporer/Brandenburg/Edler">1</a>]</span>. +Vorbis windows all use the slope function +<center class="math-display" > +<img +src="Vorbis_I_spec0x.png" alt="y = sin (.5 * π sin2((x + .5)∕n * π)). + + + +" class="math-display" ></center> +<!--l. 385--><p class="nopar" > +<!--l. 389--><p class="noindent" ><span class="paragraphHead"><a + id="x1-270001.3.2"></a><span +class="cmbx-12">floor decode</span></span> +Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that +specifies which floor configuration to use. All floors are decoded before residue decode +begins. +<!--l. 395--><p class="noindent" ><span class="paragraphHead"><a + id="x1-280001.3.2"></a><span +class="cmbx-12">residue decode</span></span> +Although the number of residue vectors equals the number of channels, channel coupling may +mean that the raw residue vectors extracted during decode do not map directly to specific +channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or +angle. The coupling relationships are described in the codec setup and may differ from frame to +frame, due to different mode numbers. +<!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from +submap 0 through n-1. This differs from floors which are coded using a configuration provided by +submap number, but are coded individually in channel order. +<!--l. 411--><p class="noindent" ><span class="paragraphHead"><a + id="x1-290001.3.2"></a><span +class="cmbx-12">inverse channel coupling</span></span> +A detailed discussion of stereo in the Vorbis codec can be found in the document +<a +href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo +coupling, but the stereo document also gives a good overview of the generic coupling +mechanism. +<!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a +pair at a time in the order and using the vectors specified in the current mapping +configuration. The decoupling operation is the same for all pairs, converting square polar +representation (where one vector is magnitude and the second angle) back to Cartesian +representation. +<!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors +represent the fine spectral detail of each output channel. + + + +<!--l. 432--><p class="noindent" ><span class="paragraphHead"><a + id="x1-300001.3.2"></a><span +class="cmbx-12">generate floor curve</span></span> +The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to +generate the output curve when the floor data is decoded from the raw packet, or it +can be generated after inverse coupling and applied to the spectral residue directly, +combining generation and the dot product into one step and eliminating some working +space. +<!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied +(dot product) by the linear-range, linear-domain spectral residue. +<!--l. 447--><p class="noindent" ><span class="paragraphHead"><a + id="x1-310001.3.2"></a><span +class="cmbx-12">compute floor/residue dot product</span></span> +This step is straightforward; for each output channel, the decoder multiplies the floor curve and +residue vectors element by element, producing the finished audio spectrum of each +channel. +<!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point +implementation might be to assume that a 32 bit fixed-point representation for floor and +residue and direct multiplication of the vectors is sufficient for acceptable spectral depth +in all cases because it happens to mostly work with the current Xiph.Org reference +encoder. +<!--l. 462--><p class="noindent" >However, floor vector values can span <span +class="cmsy-10x-x-120">~</span>140dB (<span +class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum +vector should represent a minimum of 120dB (<span +class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16 +bit PCM device. For the residue vector to represent full scale if the floor is nailed +to <span +class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach +full scale if the floor is nailed at 0dB, it must be able to represent <span +class="cmsy-10x-x-120">-</span>140dB to +0dB. +Thus, in order to handle full range dynamics, a residue vector may span <span +class="cmsy-10x-x-120">-</span>140dB to ++140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the +residue vector must be able to represent a 48 bit range and the dot product must +be able to handle an effective 48 bit times 24 bit multiplication. This range may be +achieved using large (64 bit or larger) integers, or implementing a movable binary point +representation. +<!--l. 479--><p class="noindent" ><span class="paragraphHead"><a + id="x1-320001.3.2"></a><span +class="cmbx-12">inverse monolithic transform (MDCT)</span></span> +The audio spectrum is converted back into time domain PCM audio via an inverse Modified +Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in +<span class="cite">[<a +href="#XSporer/Brandenburg/Edler">1</a>]</span>. +<!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be + + + +lapped with surrounding frames using an appropriate window (such as the Vorbis window) before +the MDCT can be considered orthogonal. +<!--l. 492--><p class="noindent" ><span class="paragraphHead"><a + id="x1-330001.3.2"></a><span +class="cmbx-12">overlap/add data</span></span> +Windowed MDCT output is overlapped and added with the right hand data of the previous +window such that the 3/4 point of the previous window is aligned with the 1/4 point of the +current window (as illustrated in the window overlap diagram). At this point, the audio data +between the center of the previous frame and the center of the current frame is now finished and +ready to be returned. +<!--l. 501--><p class="noindent" ><span class="paragraphHead"><a + id="x1-340001.3.2"></a><span +class="cmbx-12">cache right hand data</span></span> +The decoder must cache the right hand portion of the current frame to be lapped with the left +hand portion of the next frame. +<!--l. 507--><p class="noindent" ><span class="paragraphHead"><a + id="x1-350001.3.2"></a><span +class="cmbx-12">return finished audio data</span></span> +The overlapped portion produced from overlapping the previous and current frame data +is finished data to be returned by the decoder. This data spans from the center of +the previous window to the center of the current window. In the case of same-sized +windows, the amount of data to return is one-half block consisting of and only of the +overlapped portions. When overlapping a short and long window, much of the returned +range is not actually overlap. This does not damage transform orthogonality. Pay +attention however to returning the correct data range; the amount of data to be returned +is: +<!--l. 519--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb1"><a + id="x1-35002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span></div> +<!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window. +<!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The +encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper +PCM output offset is ’0’ (as no data has been returned yet). + + + + + + +<h3 class="sectionHead"><span class="titlemark">2. </span> <a + id="x1-360002"></a>Bitpacking Convention</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a + id="x1-370002.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary +integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the +encoder and then read one-by-one in the same monotonically increasing order by the decoder. +Most current binary storage arrangements group bits into a native word size of eight bits +(octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis +bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual +representation in fixed-width words. +<!--l. 19--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a + id="x1-380002.1.1"></a>octets, bytes and words</h5> +<!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits. +This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used. +For purposes of the bitpacking convention, a byte implies the native, smallest integer +storage representation offered by a platform. On modern platforms, this is generally +assumed to be eight bits (not necessarily because of the processor but because of the +filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental +atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest +size. +<!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word +to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis +bitpacking convention is still well defined for any native byte size; Vorbis uses the native +bit-width of a given storage system. This document assumes that a byte is one octet for purposes +of example. +<!--l. 39--><p class="noindent" > + + + +<h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a + id="x1-390002.1.2"></a>bit order</h5> +<!--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 +storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the +opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span +class="cmmi-12">n </span>(<span +class="cmmi-12">n </span>= 7 in an +octet) for the MSb. +<!--l. 50--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a + id="x1-400002.1.3"></a>byte order</h5> +<!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the +common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the +highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in +which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed +endian’). +<!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not +word, level, thus host word ordering is of a concern only during optimization when writing high +performance code that operates on a word of storage at a time rather than by byte. +Logically, bytes are always coded and decoded in order from byte zero through byte +<span +class="cmmi-12">n</span>. +<!--l. 68--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a + id="x1-410002.1.4"></a>coding bits into byte sequences</h5> +<!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits +wide, into packets. These integer fields are not aligned to the boundaries of the byte +representation; the next field is written at the bit position at which the previous field +ends. +<!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical +bitstream first, followed by next least significant bit, etc, until the requested number of bits +have been coded. When packing the bits into bytes, the encoder begins by placing +the LSb of the integer to be written into the least significant unused bit position of +the destination byte, followed by the next-least significant bit of the source integer +and so on up to the requested number of bits. When all bits of the destination byte +have been filled, encoding continues by zeroing all bits of the next byte and writing +the next bit into the bit position 0 of that byte. Decoding follows the same process + + + +as encoding, but by reading bits from the byte stream and reassembling them into +integers. +<!--l. 90--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a + id="x1-420002.1.5"></a>signedness</h5> +<!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder +given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent +either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The +encoder and decoder are responsible for knowing if fields are to be treated as signed or +unsigned. +<!--l. 101--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a + id="x1-430002.1.6"></a>coding example</h5> +<!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result: +<!--l. 106--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb2"><a + id="x1-43002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> |</span><br class="fancyvrb" /><a + id="x1-43004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> V</span><br class="fancyvrb" /><a + id="x1-43006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-43008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-43010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> <-</span><br class="fancyvrb" /><a + id="x1-43012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span> +<br class="fancyvrb" /><a + id="x1-43014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-43016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-43018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ...</span><br class="fancyvrb" /><a + id="x1-43020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> n</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bytestream</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> byte</span><br class="fancyvrb" /><a + id="x1-43022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]: +<!--l. 123--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb3"><a + id="x1-43024r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> |</span><br class="fancyvrb" /><a + id="x1-43026r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> V</span><br class="fancyvrb" /><a + id="x1-43028r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-43030r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-43032r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> <-</span><br class="fancyvrb" /><a + id="x1-43034r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span> +<br class="fancyvrb" /><a + id="x1-43036r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-43038r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-43040r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ...</span><br class="fancyvrb" /><a + id="x1-43042r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> n</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bytestream</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> byte</span></div> +<!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]: +<!--l. 139--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb4"><a + id="x1-43044r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> |</span><br class="fancyvrb" /><a + id="x1-43046r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> V</span><br class="fancyvrb" /><a + id="x1-43048r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-43050r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-43052r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> [1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><br class="fancyvrb" /><a + id="x1-43054r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> <-</span><br class="fancyvrb" /><a + id="x1-43056r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span> +<br class="fancyvrb" /><a + id="x1-43058r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-43060r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ...</span><br class="fancyvrb" /><a + id="x1-43062r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> n</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bytestream</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> bytes</span><br class="fancyvrb" /><a + id="x1-43064r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> cursor</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 6</span></div> +<!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]: +<!--l. 156--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb5"><a + id="x1-43066r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> |</span><br class="fancyvrb" /><a + id="x1-43068r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> V</span><br class="fancyvrb" /><a + id="x1-43070r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-43072r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-43074r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> [1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><br class="fancyvrb" /><a + id="x1-43076r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span> +<br class="fancyvrb" /><a + id="x1-43078r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> [1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0]</span><br class="fancyvrb" /><a + id="x1-43080r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> <-</span><br class="fancyvrb" /><a + id="x1-43082r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ...</span><br class="fancyvrb" /><a + id="x1-43084r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> n</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bytestream</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bytes</span><br class="fancyvrb" /><a + id="x1-43086r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> + + + +<!--l. 173--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a + id="x1-440002.1.7"></a>decoding example</h5> +<!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example: +<!--l. 177--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb6"><a + id="x1-44002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> |</span><br class="fancyvrb" /><a + id="x1-44004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> V</span><br class="fancyvrb" /><a + id="x1-44006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-44008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-44010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> [1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> <-</span> +<br class="fancyvrb" /><a + id="x1-44012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0]</span><br class="fancyvrb" /><a + id="x1-44014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> [1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0]</span><br class="fancyvrb" /><a + id="x1-44016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> [0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> bytestream</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> ==</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bytes</span><br class="fancyvrb" /><a + id="x1-44018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things +are worth noting here: + <ul class="itemize1"> + <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading + some other combination of bit-widths from the bitstream is well defined. There are + no artificial alignment boundaries maintained in the bitstream. + </li> + <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted + either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on + decode context.</li></ul> +<!--l. 208--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a + id="x1-450002.1.8"></a>end-of-packet alignment</h5> +<!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are +embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream. +Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often, +the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space +in the last byte of a packet. +<!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus, +should this unused space be read, it will return binary zeroes. +<!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition. +End-of-packet is not to be considered an error; it is merely a state indicating that there is +insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a + + + +normal mode of operation, and as such, decoders must handle reading past the end of a packet as +a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall +also return ’end-of-packet’. +<!--l. 233--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a + id="x1-460002.1.9"></a>reading zero bits</h5> +<!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor. +Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not +triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an +end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’ +shall also fail with ’end-of-packet’. + + + + + + +<h3 class="sectionHead"><span class="titlemark">3. </span> <a + id="x1-470003"></a>Probability Model and Codebooks</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a + id="x1-480003.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured +probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the +bitstream itself in the third header, the codec setup header. This packed configuration consists of +multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding +compressed codewords as well as an optional lookup table of output vector values to which a +decoded Huffman value is applied as an offset, generating the final decoded output corresponding +to a given compressed codeword. +<!--l. 18--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a + id="x1-490003.1.1"></a>Bitwise operation</h5> +<!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves +and the codewords they decode are unrolled from a packet as a series of arbitrary-width values +read from the stream according to <a +href="#x1-360002">section 2</a>, “<a +href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”. +<!--l. 27--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a + id="x1-500003.2"></a>Packed codebook format</h4> +<!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is +eight bits. This is not universally true; see <a +href="#x1-360002">section 2</a>, “<a +href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion +relating to non-eight-bit bytes. + + + +<!--l. 34--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a + id="x1-510003.2.1"></a>codebook decode</h5> +<!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342: +<!--l. 38--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb7"><a + id="x1-51002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 0:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> (0x42)</span><br class="fancyvrb" /><a + id="x1-51004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 1:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> (0x43)</span><br class="fancyvrb" /><a + id="x1-51006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 2:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> (0x56)</span></div> +<!--l. 44--><p class="noindent" >16 bit <span +class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span +class="cmtt-12">[codebook_entries] </span>fields: +<!--l. 46--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb8"><a + id="x1-51008r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51010r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 3:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-51012r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 4:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> [codebook_dimensions]</span><span +class="cmtt-8"> (16</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a + id="x1-51014r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-51016r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 5:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-51018r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 6:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-51020r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 7:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> [codebook_entries]</span><span +class="cmtt-8"> (24</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> unsigned)</span><br class="fancyvrb" /><a + id="x1-51022r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 57--><p class="noindent" >Next is the <span +class="cmtt-12">[ordered] </span>bit flag: +<!--l. 59--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb9"><a + id="x1-51024r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51026r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 8:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> [ordered]</span><span +class="cmtt-8"> (1</span><span +class="cmtt-8"> bit)</span><br class="fancyvrb" /><a + id="x1-51028r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 65--><p class="noindent" >Each entry, numbering a total of <span +class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length. +We now read the list of codeword lengths and store these lengths in the array +<span +class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span +class="cmtt-12">[ordered] </span>flag +is set or unset. + <ul class="itemize1"> + <li class="itemize">If the <span +class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder + needs to read each codeword length one-by-one. + <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span +class="cmtt-12">[sparse] </span>flag. This flag determines + whether or not the codebook contains unused entries that are not to be included in + the codeword decode tree: + <!--l. 82--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb10"><a + id="x1-51030r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> byte</span><span +class="cmtt-8"> 8:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> X</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ]</span><span +class="cmtt-8"> [sparse]</span><span +class="cmtt-8"> flag</span><span +class="cmtt-8"> (1</span><span +class="cmtt-8"> bit)</span></div> + <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span +class="cmtt-12">[codebook_entries] </span>codebook entries: + <!--l. 89--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb11"><a + id="x1-51032r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51034r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> if([sparse]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set)</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-51036r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51038r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [flag]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> one</span><span +class="cmtt-8"> bit;</span><br class="fancyvrb" /><a + id="x1-51040r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> if([flag]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set)</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-51042r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-51044r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> five</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer;</span><br class="fancyvrb" /><a + id="x1-51046r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> for</span><span +class="cmtt-8"> this</span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a + id="x1-51048r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-51050r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-51052r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51054r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> this</span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> unused.</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> mark</span><span +class="cmtt-8"> it</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> such.</span><br class="fancyvrb" /><a + id="x1-51056r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51058r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-51060r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51062r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> sparse</span><span +class="cmtt-8"> flag</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> + <br class="fancyvrb" /><a + id="x1-51064r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51066r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> five</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer;</span><br class="fancyvrb" /><a + id="x1-51068r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> for</span><span +class="cmtt-8"> this</span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> [length]+1;</span><br class="fancyvrb" /><a + id="x1-51070r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51072r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-51074r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> + + + + </li> + <li class="itemize">If the <span +class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in + ascending length order. Rather than reading a length for every codeword, the + encoder reads the number of codewords per length. That is, beginning at entry + zero: + <!--l. 120--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb12"><a + id="x1-51076r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [current_entry]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0;</span><br class="fancyvrb" /><a + id="x1-51078r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [current_length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> five</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> 1;</span> + <br class="fancyvrb" /><a + id="x1-51080r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [number]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> </span><a +href="#x1-1190009.2.1"><span +class="cmtt-8">ilog</span></a><span +class="cmtt-8">([codebook_entries]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [current_entry])</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> + <br class="fancyvrb" /><a + id="x1-51082r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> entries</span><span +class="cmtt-8"> [current_entry]</span><span +class="cmtt-8"> through</span><span +class="cmtt-8"> [current_entry]+[number]-1,</span><span +class="cmtt-8"> inclusive,</span> + <br class="fancyvrb" /><a + id="x1-51084r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> [codebook_codeword_lengths]</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> [current_length]</span> + <br class="fancyvrb" /><a + id="x1-51086r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> [current_entry]</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> [number]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [current_entry]</span><br class="fancyvrb" /><a + id="x1-51088r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [current_length]</span><span +class="cmtt-8"> by</span><span +class="cmtt-8"> 1</span> + <br class="fancyvrb" /><a + id="x1-51090r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> [current_entry]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [codebook_entries]</span><span +class="cmtt-8"> ERROR</span><span +class="cmtt-8"> CONDITION;</span><br class="fancyvrb" /><a + id="x1-51092r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> decoder</span><span +class="cmtt-8"> will</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> be</span><span +class="cmtt-8"> able</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> this</span><span +class="cmtt-8"> stream.</span> + <br class="fancyvrb" /><a + id="x1-51094r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> [current_entry]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [codebook_entries],</span><span +class="cmtt-8"> repeat</span><span +class="cmtt-8"> process</span><span +class="cmtt-8"> starting</span><span +class="cmtt-8"> at</span><span +class="cmtt-8"> 3)</span><br class="fancyvrb" /><a + id="x1-51096r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> done.</span></div> + </li></ul> +<!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis +I supports three lookup types: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">No lookup + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ) + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl> +<!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer: +<div class="fancyvrb" id="fancyvrb13"><a + id="x1-51101r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [codebook_lookup_type]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> four</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span></div> +<!--l. 154--><p class="noindent" >Codebook decode precedes according to <span +class="cmtt-12">[codebook_lookup_type]</span>: + <ul class="itemize1"> + <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode. + </li> + <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to + be read. Lookup type one reads a list of values that are permuted in a set pattern to + build a list of vectors, each vector of order <span +class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup + type two builds the same vector list, but reads each scalar for each vector explicitly, + rather than building vectors from a smaller list of possible scalar values. Lookup + decode proceeds as follows: + <!--l. 168--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb14"><a + id="x1-51103r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [codebook_minimum_value]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1200009.2.2"><span +class="cmtt-8">float32_unpack</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer)</span> + <br class="fancyvrb" /><a + id="x1-51105r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [codebook_delta_value]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1200009.2.2"><span +class="cmtt-8">float32_unpack</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer)</span> + <br class="fancyvrb" /><a + id="x1-51107r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [codebook_value_bits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> 1</span><br class="fancyvrb" /><a + id="x1-51109r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [codebook_sequence_p]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> boolean</span><span +class="cmtt-8"> flag</span><br class="fancyvrb" /><a + id="x1-51111r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + + + + <br class="fancyvrb" /><a + id="x1-51113r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [codebook_lookup_type]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-51115r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51117r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [codebook_lookup_values]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1210009.2.3"><span +class="cmtt-8">lookup1_values</span></a><span +class="cmtt-8">([codebook_entries],</span><span +class="cmtt-8"> [codebook_dimensions]</span><span +class="cmtt-8"> )</span> + <br class="fancyvrb" /><a + id="x1-51119r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51121r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-51123r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51125r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [codebook_lookup_values]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [codebook_entries]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [codebook_dimensions]</span><br class="fancyvrb" /><a + id="x1-51127r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-51129r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-51131r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-51133r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> total</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [codebook_lookup_values]</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integers</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [codebook_value_bits]</span><span +class="cmtt-8"> each;</span> + <br class="fancyvrb" /><a + id="x1-51135r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> store</span><span +class="cmtt-8"> these</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> order</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [codebook_multiplicands]</span></div> + </li> + <li class="itemize">A <span +class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is + not decodable by the specification in this document. + </li></ul> +<!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition +rendering the stream undecodable. +<!--l. 198--><p class="noindent" ><span class="paragraphHead"><a + id="x1-520003.2.1"></a><span +class="cmbx-12">Huffman decision tree representation</span></span> +The <span +class="cmtt-12">[codebook_codeword_lengths] </span>array and <span +class="cmtt-12">[codebook_entries] </span>value uniquely define the +Huffman decision tree used for entropy decoding. +<!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused +codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword +possible. Assume the following codeword length list: +<!--l. 209--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb15"><a + id="x1-52002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 0:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 2</span><br class="fancyvrb" /><a + id="x1-52004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 1:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><br class="fancyvrb" /><a + id="x1-52006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 2:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><br class="fancyvrb" /><a + id="x1-52008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 3:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><br class="fancyvrb" /><a + id="x1-52010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 4:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><br class="fancyvrb" /><a + id="x1-52012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 5:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 2</span> +<br class="fancyvrb" /><a + id="x1-52014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 6:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 3</span><br class="fancyvrb" /><a + id="x1-52016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 7:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 3</span></div> +<!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results +in the following codeword list: +<!--l. 223--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb16"><a + id="x1-52018r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 0:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 00</span><br class="fancyvrb" /><a + id="x1-52020r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 1:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 0100</span><br class="fancyvrb" /><a + id="x1-52022r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 2:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 0101</span><br class="fancyvrb" /><a + id="x1-52024r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 3:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 0110</span> +<br class="fancyvrb" /><a + id="x1-52026r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 4:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 0111</span><br class="fancyvrb" /><a + id="x1-52028r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 5:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 10</span><br class="fancyvrb" /><a + id="x1-52030r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 6:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 110</span><br class="fancyvrb" /><a + id="x1-52032r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> entry</span><span +class="cmtt-8"> 7:</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> codeword</span><span +class="cmtt-8"> 111</span></div> +<!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a + id="x1-530003.2.1"></a><span +class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to +be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero, +one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost +bit is the MSb. +<!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry +numbers equivalent to the leaves numbered left-to-right: + + + +<div class="center" +> +<!--l. 247--><p class="noindent" > + +<!--l. 248--><p class="noindent" ><img +src="hufftree.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 4: </span><span +class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 --> +</div> +<!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost +possible position. +<!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list. +In the above example, if codeword seven were eliminated, it’s clear that the tree is +unfinished: +<div class="center" +> +<!--l. 260--><p class="noindent" > + +<!--l. 261--><p class="noindent" ><img +src="hufftree-under.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 5: </span><span +class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 --> +</div> +<!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth +codeword is impossible. Both underspecified and overspecified trees are an error condition +rendering the stream undecodable. +<!--l. 271--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no +codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read +from the stream to decode to that entry number. +<!--l. 276--><p class="noindent" ><span class="paragraphHead"><a + id="x1-540003.2.1"></a><span +class="cmbx-12">Errata 20150226: Single entry codebooks</span></span> +A ’single-entry codebook’ is a codebook with one active codeword entry. A single-entry codebook +may be either a fully populated codebook with only one declared entry, or a sparse codebook +with only one entry marked used. The Vorbis I spec provides no means to specify a codeword +length of zero, and as a result, a single-entry codebook is inherently malformed because it is +underpopulated. The original specification did not address directly the matter of single-entry +codebooks; they were implicitly illegal as it was not possible to write such a codebook with a +valid tree structure. + + + +<!--l. 288--><p class="noindent" >In r14811 of the libvorbis reference implementation, Xiph added an additional check to the +codebook implementation to reject underpopulated Huffman trees. This change led to the +discovery of single-entry books used ’in the wild’ when the new, stricter checks rejected a number +of apparently working streams. +<!--l. 294--><p class="noindent" >In order to minimize breakage of deployed (if technically erroneous) streams, r16073 of the +reference implementation explicitly special-cased single-entry codebooks to tolerate the +single-entry case. Commit r16073 also added the following to the specification: +<!--l. 303--><p class="noindent" >“<span class="sout">Take special care that a codebook with a single used entry is handled properly; it consists of a +single codework of zero bits and reading a value out of such a codebook always returns the single +used value and sinks zero bits. </span>” +<!--l. 305--><p class="noindent" >The intent was to clarify the spec and codify current practice. However, this addition is +erroneously at odds with the intent of preserving usability of existing streams using single-entry +codebooks, disagrees with the code changes that reinstated decoding, and does not address how +single-entry codebooks should be encoded. +<!--l. 311--><p class="noindent" >As such, the above addition made in r16037 is struck from the specification and replaced by the +following: +<!--l. 330--><p class="noindent" > + <div class="quote"> + <!--l. 330--><p class="noindent" >It is possible to declare a Vorbis codebook containing a single codework + entry. A single-entry codebook may be either a fully populated codebook with + <span +class="cmtt-12">[codebook_entries] </span>set to 1, or a sparse codebook marking only one entry + used. Note that it is not possible to also encode a <span +class="cmtt-12">[codeword_length] </span>of zero + for the single used codeword, as the unsigned value written to the stream + is <span +class="cmtt-12">[codeword_length]-1</span>. Instead, encoder implementations should indicate a + <span +class="cmtt-12">[codeword_length] </span>of 1 and ’write’ the codeword to a stream during audio + encoding by writing a single zero bit. + <!--l. 330--><p class="noindent" >Decoder implementations shall reject a codebook if it contains only one used + entry and the encoded <span +class="cmtt-12">[codeword_length] </span>of that entry is not 1. ’Reading’ a + value from single-entry codebook always returns the single used codeword value + and sinks one bit. Decoders should tolerate that the bit read from the stream + be ’1’ instead of ’0’; both values shall return the single used codeword.</div> +<!--l. 332--><p class="noindent" ><span class="paragraphHead"><a + id="x1-550003.2.1"></a><span +class="cmbx-12">VQ lookup table vector representation</span></span> +Unpacking the VQ lookup table vectors relies on the following values: + + + +<div class="fancyvrb" id="fancyvrb17"><a + id="x1-55002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> [codebook\_multiplicands]</span><span +class="cmtt-8"> array</span><br class="fancyvrb" /><a + id="x1-55004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_minimum\_value]</span><br class="fancyvrb" /><a + id="x1-55006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_delta\_value]</span><br class="fancyvrb" /><a + id="x1-55008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_sequence\_p]</span> +<br class="fancyvrb" /><a + id="x1-55010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_lookup\_type]</span><br class="fancyvrb" /><a + id="x1-55012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_entries]</span><br class="fancyvrb" /><a + id="x1-55014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_dimensions]</span><br class="fancyvrb" /><a + id="x1-55016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook\_lookup\_values]</span></div> +<!--l. 348--><p class="noindent" >Decoding (unpacking) a specific vector in the vector lookup table proceeds according to +<span +class="cmtt-12">[codebook_lookup_type]</span>. The unpacked vector values are what a codebook would return +during audio packet decode in a VQ context. +<!--l. 353--><p class="noindent" ><span class="paragraphHead"><a + id="x1-560003.2.1"></a><span +class="cmbx-12">Vector value decode: Lookup type 1</span></span> +Lookup type one specifies a lattice VQ lookup table built algorithmically from a list of +scalar values. Calculate (unpack) the final values of a codebook entry vector from +the entries in <span +class="cmtt-12">[codebook_multiplicands] </span>as follows (<span +class="cmtt-12">[value_vector] </span>is the output +vector representing the vector of values for entry number <span +class="cmtt-12">[lookup_offset] </span>in this +codebook): +<!--l. 362--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb18"><a + id="x1-56002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0;</span><br class="fancyvrb" /><a + id="x1-56004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [index_divisor]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 1;</span><br class="fancyvrb" /><a + id="x1-56006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [codebook_dimensions]-1</span><span +class="cmtt-8"> (once</span><span +class="cmtt-8"> for</span><span +class="cmtt-8"> each</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> vector)</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-56008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-56010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [multiplicand_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [lookup_offset]</span><span +class="cmtt-8"> divided</span><span +class="cmtt-8"> by</span><span +class="cmtt-8"> [index_divisor]</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-56012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> division</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> modulo</span><span +class="cmtt-8"> [codebook_lookup_values]</span><br class="fancyvrb" /><a + id="x1-56014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-56016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [value_vector]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span> +<br class="fancyvrb" /><a + id="x1-56018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [codebook_multiplicands]</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [multiplicand_offset]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> *</span> +<br class="fancyvrb" /><a + id="x1-56020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook_delta_value]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [codebook_minimum_value]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [last];</span><br class="fancyvrb" /><a + id="x1-56022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-56024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [codebook_sequence_p]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [value_vector]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><br class="fancyvrb" /><a + id="x1-56026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-56028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [index_divisor]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [index_divisor]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [codebook_lookup_values]</span><br class="fancyvrb" /><a + id="x1-56030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-56032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-56034r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-56036r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> calculation</span><span +class="cmtt-8"> completed.</span></div> +<!--l. 385--><p class="noindent" ><span class="paragraphHead"><a + id="x1-570003.2.1"></a><span +class="cmbx-12">Vector value decode: Lookup type 2</span></span> +Lookup type two specifies a VQ lookup table in which each scalar in each vector is explicitly set +by the <span +class="cmtt-12">[codebook_multiplicands] </span>array in a one-to-one mapping. Calculate [unpack] the final +values of a codebook entry vector from the entries in <span +class="cmtt-12">[codebook_multiplicands] </span>as follows +(<span +class="cmtt-12">[value_vector] </span>is the output vector representing the vector of values for entry number +<span +class="cmtt-12">[lookup_offset] </span>in this codebook): +<!--l. 395--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb19"><a + id="x1-57002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0;</span><br class="fancyvrb" /><a + id="x1-57004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [multiplicand_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [lookup_offset]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [codebook_dimensions]</span> +<br class="fancyvrb" /><a + id="x1-57006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [codebook_dimensions]-1</span><span +class="cmtt-8"> (once</span><span +class="cmtt-8"> for</span><span +class="cmtt-8"> each</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> vector)</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-57008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-57010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [value_vector]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><br class="fancyvrb" /><a + id="x1-57012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [codebook_multiplicands]</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [multiplicand_offset]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> *</span> +<br class="fancyvrb" /><a + id="x1-57014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [codebook_delta_value]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [codebook_minimum_value]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [last];</span><br class="fancyvrb" /><a + id="x1-57016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-57018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [codebook_sequence_p]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [value_vector]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><br class="fancyvrb" /><a + id="x1-57020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-57022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [multiplicand_offset]</span><br class="fancyvrb" /><a + id="x1-57024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-57026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-57028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-57030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> calculation</span><span +class="cmtt-8"> completed.</span></div> + + + +<!--l. 421--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a + id="x1-580003.3"></a>Use of the codebook abstraction</h4> +<!--l. 423--><p class="noindent" >The decoder uses the codebook abstraction much as it does the bit-unpacking convention; a +specific codebook reads a codeword from the bitstream, decoding it into an entry number, and +then returns that entry number to the decoder (when used in a scalar entropy coding context), or +uses that entry number as an offset into the VQ lookup table, returning a vector of values (when +used in a context desiring a VQ value). Scalar or VQ context is always explicit; any +call to the codebook mechanism requests either a scalar entry number or a lookup +vector. +<!--l. 433--><p class="noindent" >Note that VQ lookup type zero indicates that there is no lookup table; requesting +decode using a codebook of lookup type 0 in any context expecting a vector return +value (even in a case where a vector of dimension one) is forbidden. If decoder setup +or decode requests such an action, that is an error condition rendering the packet +undecodable. +<!--l. 440--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the +next codeword in the bitstream. The decoder reads bits until the accumulated bits match a +codeword in the codebook. This process can be though of as logically walking the +Huffman decode tree by reading one bit at a time from the bitstream, and using the +bit as a decision boolean to take the 0 branch (left in the above examples) or the 1 +branch (right in the above examples). Walking the tree finishes when the decode process +hits a leaf in the decision tree; the result is the entry number corresponding to that +leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the +decoder. +<!--l. 452--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return +value. +<!--l. 455--><p class="noindent" >When used in a VQ context, the codeword entry number is used as an offset into the VQ lookup +table. The value returned to the decoder is the vector of scalars corresponding to this +offset. + + + + + + +<h3 class="sectionHead"><span class="titlemark">4. </span> <a + id="x1-590004"></a>Codec Setup and Packet Decode</h3> +<!--l. 7--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a + id="x1-600004.1"></a>Overview</h4> +<!--l. 9--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification +of Vorbis I. This document assumes a high-level understanding of the Vorbis decode +process, which is provided in <a +href="#x1-20001">section 1</a>, “<a +href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a +href="#x1-360002">section 2</a>, +“<a +href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream +packets. +<!--l. 17--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a + id="x1-610004.2"></a>Header decode and decode setup</h4> +<!--l. 19--><p class="noindent" >A Vorbis bitstream begins with three header packets. The header packets are, in order, the +identification header, the comments header, and the setup header. All are required for decode +compliance. An end-of-packet condition during decoding the first or third header packet renders +the stream undecodable. End-of-packet decoding the comment header is a non-fatal error +condition. +<!--l. 26--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.2.1. </span> <a + id="x1-620004.2.1"></a>Common header decode</h5> +<!--l. 28--><p class="noindent" >Each header packet begins with the same header fields. +<!--l. 31--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb20"><a + id="x1-62002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [packet_type]</span><span +class="cmtt-8"> :</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> value</span><br class="fancyvrb" /><a + id="x1-62004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> 0x76,</span><span +class="cmtt-8"> 0x6f,</span><span +class="cmtt-8"> 0x72,</span><span +class="cmtt-8"> 0x62,</span><span +class="cmtt-8"> 0x69,</span><span +class="cmtt-8"> 0x73:</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> characters</span><span +class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> six</span><span +class="cmtt-8"> octets</span></div> +<!--l. 36--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment +header type 3 and the setup header type 5 (these types are all odd as a packet with a leading +single bit of ’0’ is an audio packet). The packets must occur in the order of identification, + + + +comment, setup. +<!--l. 44--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a + id="x1-630004.2.2"></a>Identification header</h5> +<!--l. 46--><p class="noindent" >The identification header is a short header of only a few fields used to declare the stream +definitively as Vorbis, and provide a few externally relevant pieces of information about the audio +stream. The identification header is coded as follows: +<!--l. 51--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb21"><a + id="x1-63002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [vorbis_version]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-63004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [audio_channels]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span> +<br class="fancyvrb" /><a + id="x1-63006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [audio_sample_rate]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-63008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [bitrate_maximum]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> signed</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-63010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [bitrate_nominal]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> signed</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-63012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [bitrate_minimum]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> signed</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-63014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [blocksize_0]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> exponent</span><span +class="cmtt-8"> (read</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer)</span><br class="fancyvrb" /><a + id="x1-63016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> [blocksize_1]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> exponent</span><span +class="cmtt-8"> (read</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer)</span> +<br class="fancyvrb" /><a + id="x1-63018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [framing_flag]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> one</span><span +class="cmtt-8"> bit</span></div> +<!--l. 63--><p class="noindent" ><span +class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both +<span +class="cmtt-12">[audio_channels] </span>and <span +class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final +blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span +class="cmtt-12">[blocksize_0]</span> +must be less than or equal to <span +class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet +any of these conditions renders a stream undecodable. +<!--l. 71--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be +considerably off in purely VBR streams. The fields are meaningful only when greater than +zero. + <ul class="itemize1"> + <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly + fixed-rate bitstream + </li> + <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate + </li> + <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits + </li> + <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul> + + + +<!--l. 85--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a + id="x1-640004.2.3"></a>Comment header</h5> +<!--l. 86--><p class="noindent" >Comment header decode and data specification is covered in <a +href="#x1-820005">section 5</a>, “<a +href="#x1-820005">comment field and +header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”. +<!--l. 90--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a + id="x1-650004.2.4"></a>Setup header</h5> +<!--l. 92--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree: +<div class="center" +> +<!--l. 94--><p class="noindent" > + +<!--l. 95--><p class="noindent" ><img +src="components.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 6: </span><span +class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-650016 --> +</div> +<!--l. 100--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup +header contains, in order, the lists of codebook configurations, time-domain transform +configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel +mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header +decode proceeds in the following order: +<!--l. 108--><p class="noindent" ><span class="paragraphHead"><a + id="x1-660004.2.4"></a><span +class="cmbx-12">Codebooks</span></span> + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">Decode <span +class="cmtt-12">[vorbis_codebook_count] </span>codebooks in order as defined in <a +href="#x1-470003">section 3</a>, + “<a +href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array + of codebook configurations <span +class="cmtt-12">[vorbis_codebook_configurations]</span>.</dd></dl> + + + +<!--l. 120--><p class="noindent" ><span class="paragraphHead"><a + id="x1-670004.2.4"></a><span +class="cmbx-12">Time domain transforms</span></span> +These hooks are placeholders in Vorbis I. Nevertheless, the configuration placeholder values must +be read to maintain bitstream sync. +<!--l. 127--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_time_count] </span>= read 6 bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">read <span +class="cmtt-12">[vorbis_time_count] </span>16 bit values; each value should be zero. If any value is + nonzero, this is an error condition and the stream is undecodable.</dd></dl> +<!--l. 133--><p class="noindent" ><span class="paragraphHead"><a + id="x1-680004.2.4"></a><span +class="cmbx-12">Floors</span></span> +Vorbis uses two floor types; header decode is handed to the decode abstraction of the appropriate +type. +<!--l. 139--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_floor_count] </span>= read 6 bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">For each <span +class="cmtt-12">[i] </span>of <span +class="cmtt-12">[vorbis_floor_count] </span>floor numbers: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">read the floor type: vector <span +class="cmtt-12">[vorbis_floor_types] </span>element <span +class="cmtt-12">[i] </span>= read 16 bits + as unsigned integer + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem">If the floor type is zero, decode the floor configuration as defined in <a +href="#x1-900006">section 6</a>, + “<a +href="#x1-900006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span +class="cmtt-12">[i] </span>of the floor + configuration array <span +class="cmtt-12">[vorbis_floor_configurations]</span>. + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a +href="#x1-970007">section 7</a>, + “<a +href="#x1-970007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span +class="cmtt-12">[i] </span>of the floor + configuration array <span +class="cmtt-12">[vorbis_floor_configurations]</span>. + </dd><dt class="enumerate-enumitem"> + d) </dt><dd +class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR + CONDITION</dd></dl> + + + + </dd></dl> +<!--l. 157--><p class="noindent" ><span class="paragraphHead"><a + id="x1-690004.2.4"></a><span +class="cmbx-12">Residues</span></span> +Vorbis uses three residue types; header decode of each type is identical. +<!--l. 163--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_residue_count] </span>= read 6 bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">For each of <span +class="cmtt-12">[vorbis_residue_count] </span>residue numbers: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">read the residue type; vector <span +class="cmtt-12">[vorbis_residue_types] </span>element <span +class="cmtt-12">[i] </span>= read 16 + bits as unsigned integer + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem">If the residue type is zero, one or two, decode the residue configuration as defined + in <a +href="#x1-1040008">section 8</a>, “<a +href="#x1-1040008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span +class="cmtt-12">[i] </span>of + the residue configuration array <span +class="cmtt-12">[vorbis_residue_configurations]</span>. + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR + CONDITION</dd></dl> + </dd></dl> +<!--l. 177--><p class="noindent" ><span class="paragraphHead"><a + id="x1-700004.2.4"></a><span +class="cmbx-12">Mappings</span></span> +Mappings are used to set up specific pipelines for encoding multichannel audio with varying +channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM +channel mappings. +<!--l. 188--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">For each <span +class="cmtt-12">[i] </span>of <span +class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers: + + + + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save + the mapping type in Vorbis I. + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem">If the mapping type is zero: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">read 1 bit as a boolean flag + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">if set, <span +class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer + and add one + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem">if unset, <span +class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</dd></dl> + </dd><dt class="enumerate-enumitem"> + ii. </dt><dd +class="enumerate-enumitem">read 1 bit as a boolean flag + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">if set, square polar channel mapping is in use: + <ul class="itemize1"> + <li class="itemize"><span +class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned + integer and add one + </li> + <li class="itemize">for <span +class="cmtt-12">[j] </span>each of <span +class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps: + <ul class="itemize2"> + <li class="itemize">vector <span +class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span +class="cmtt-12">[j]</span>= read + <a +href="#x1-1190009.2.1">ilog</a>(<span +class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer + </li> + <li class="itemize">vector <span +class="cmtt-12">[vorbis_mapping_angle] </span>element <span +class="cmtt-12">[j]</span>= read + <a +href="#x1-1190009.2.1">ilog</a>(<span +class="cmtt-12">[audio_channels] </span>- 1) bits as unsigned integer + </li> + <li class="itemize">the numbers read in the above two steps are channel numbers + representing the channel to treat as magnitude and the channel + to treat as angle, respectively. If for any coupling step the + angle channel number equals the magnitude channel number, the + magnitude channel number is greater than <span +class="cmtt-12">[audio_channels]</span>-1, or + the angle channel is greater than <span +class="cmtt-12">[audio_channels]</span>-1, the stream + is undecodable.</li></ul> + + + + </li></ul> + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem">if unset, <span +class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= 0</dd></dl> + </dd><dt class="enumerate-enumitem"> + iii. </dt><dd +class="enumerate-enumitem">read 2 bits (reserved field); if the value is nonzero, the stream is undecodable + </dd><dt class="enumerate-enumitem"> + iv. </dt><dd +class="enumerate-enumitem">if <span +class="cmtt-12">[vorbis_mapping_submaps] </span>is greater than one, we read channel multiplex + settings. For each <span +class="cmtt-12">[j] </span>of <span +class="cmtt-12">[audio_channels] </span>channels: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">vector <span +class="cmtt-12">[vorbis_mapping_mux] </span>element <span +class="cmtt-12">[j] </span>= read 4 bits as unsigned + integer + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem">if the value is greater than the highest numbered submap + (<span +class="cmtt-12">[vorbis_mapping_submaps] </span>- 1), this in an error condition rendering + the stream undecodable</dd></dl> + </dd><dt class="enumerate-enumitem"> + v. </dt><dd +class="enumerate-enumitem">for each submap <span +class="cmtt-12">[j] </span>of <span +class="cmtt-12">[vorbis_mapping_submaps] </span>submaps, read the floor and + residue numbers for use in decoding that submap: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">read and discard 8 bits (the unused time configuration placeholder) + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem">read 8 bits as unsigned integer for the floor number; save in vector + <span +class="cmtt-12">[vorbis_mapping_submap_floor] </span>element <span +class="cmtt-12">[j]</span> + </dd><dt class="enumerate-enumitem"> + C. </dt><dd +class="enumerate-enumitem">verify the floor number is not greater than the highest number floor + configured for the bitstream. If it is, the bitstream is undecodable + </dd><dt class="enumerate-enumitem"> + D. </dt><dd +class="enumerate-enumitem">read 8 bits as unsigned integer for the residue number; save in vector + <span +class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span +class="cmtt-12">[j]</span> + </dd><dt class="enumerate-enumitem"> + E. </dt><dd +class="enumerate-enumitem">verify the residue number is not greater than the highest number residue + configured for the bitstream. If it is, the bitstream is undecodable</dd></dl> + </dd><dt class="enumerate-enumitem"> + vi. </dt><dd +class="enumerate-enumitem">save this mapping configuration in slot <span +class="cmtt-12">[i] </span>of the mapping configuration array + <span +class="cmtt-12">[vorbis_mapping_configurations]</span>.</dd></dl> + </dd></dl> + + + + </dd></dl> +<!--l. 247--><p class="noindent" ><span class="paragraphHead"><a + id="x1-710004.2.4"></a><span +class="cmbx-12">Modes</span></span> + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mode_count] </span>= read 6 bits as unsigned integer and add one + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">For each of <span +class="cmtt-12">[vorbis_mode_count] </span>mode numbers: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mode_blockflag] </span>= read 1 bit + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mode_windowtype] </span>= read 16 bits as unsigned integer + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mode_transformtype] </span>= read 16 bits as unsigned integer + </dd><dt class="enumerate-enumitem"> + d) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[vorbis_mode_mapping] </span>= read 8 bits as unsigned integer + </dd><dt class="enumerate-enumitem"> + e) </dt><dd +class="enumerate-enumitem">verify ranges; zero is the only legal value in + Vorbis I for <span +class="cmtt-12">[vorbis_mode_windowtype] </span>and <span +class="cmtt-12">[vorbis_mode_transformtype]</span>. + <span +class="cmtt-12">[vorbis_mode_mapping] </span>must not be greater than the highest number mapping + in use. Any illegal values render the stream undecodable. + </dd><dt class="enumerate-enumitem"> + f) </dt><dd +class="enumerate-enumitem">save this mode configuration in slot <span +class="cmtt-12">[i] </span>of the mode configuration array + <span +class="cmtt-12">[vorbis_mode_configurations]</span>.</dd></dl> + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">read 1 bit as a framing flag. If unset, a framing error occurred and the stream is not + decodable.</dd></dl> +<!--l. 268--><p class="noindent" >After reading mode descriptions, setup header decode is complete. +<!--l. 277--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">4.3. </span> <a + id="x1-720004.3"></a>Audio packet decode and synthesis</h4> + + + +<!--l. 279--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of +audio packet decode is to read and verify the packet type. <span +class="cmti-12">A non-audio packet when audio is</span> +<span +class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span> +<span +class="cmti-12">packet and not attempt decoding it to audio</span>. +<!--l. 286--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.1. </span> <a + id="x1-730004.3.1"></a>packet type, mode and window decode</h5> +<!--l. 289--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">read 1 bit <span +class="cmtt-12">[packet_type]</span>; check that packet type is 0 (audio) + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">read <a +href="#x1-1190009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span +class="cmtt-12">[mode_number]</span> + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">decode blocksize <span +class="cmtt-12">[n] </span>is equal to <span +class="cmtt-12">[blocksize_0] </span>if <span +class="cmtt-12">[vorbis_mode_blockflag] </span>is 0, + else <span +class="cmtt-12">[n] </span>is equal to <span +class="cmtt-12">[blocksize_1]</span>. + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse + MDCT: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">if this is a long window (the <span +class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is + set): + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">read 1 bit for <span +class="cmtt-12">[previous_window_flag]</span> + </dd><dt class="enumerate-enumitem"> + ii. </dt><dd +class="enumerate-enumitem">read 1 bit for <span +class="cmtt-12">[next_window_flag]</span> + </dd><dt class="enumerate-enumitem"> + iii. </dt><dd +class="enumerate-enumitem">if <span +class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will + be a hybrid window for lapping with a short block. See <a +href="#paragraph.1" >paragraph <a +href="#x1-260001.3.2">1.3.2</a></a>, + “<a +href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of + overlapping dissimilar windows. Else, the left half window will have normal + long shape. + </dd><dt class="enumerate-enumitem"> + iv. </dt><dd +class="enumerate-enumitem">if <span +class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be + a hybrid window for lapping with a short block. See <a +href="#x1-260001.3.2">paragraph 1.3.2</a>, + + + + “<a +href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of + overlapping dissimilar windows. Else, the left right window will have normal + long shape.</dd></dl> + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem">if this is a short window, the window is always the same short-window + shape.</dd></dl> + </dd></dl> +<!--l. 321--><p class="noindent" >Vorbis windows all use the slope function <span +class="cmmi-12">y </span>= sin(<img +src="Vorbis_I_spec1x.png" alt="π +2" class="frac" align="middle"> <span +class="cmsy-10x-x-120">*</span> sin <sup><span +class="cmr-8">2</span></sup>((<span +class="cmmi-12">x </span>+ 0<span +class="cmmi-12">.</span>5)<span +class="cmmi-12">∕n </span><span +class="cmsy-10x-x-120">* </span><span +class="cmmi-12">π</span>)), where <span +class="cmmi-12">n </span>is window +size and <span +class="cmmi-12">x </span>ranges 0<span +class="cmmi-12">…</span><span +class="cmmi-12">n</span><span +class="cmsy-10x-x-120">- </span>1, but dissimilar lapping requirements can affect overall shape. Window +generation proceeds as follows: +<!--l. 327--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[window_center] </span>= <span +class="cmtt-12">[n] </span>/ 2 + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">if (<span +class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span +class="cmtt-12">[previous_window_flag] </span>is not set) + then + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_window_start] </span>= <span +class="cmtt-12">[n]</span>/4 - <span +class="cmtt-12">[blocksize_0]</span>/4 + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_window_end] </span>= <span +class="cmtt-12">[n]</span>/4 + <span +class="cmtt-12">[blocksize_0]</span>/4 + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_n] </span>= <span +class="cmtt-12">[blocksize_0]</span>/2</dd></dl> + <!--l. 336--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_window_start] </span>= 0 + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_window_end] </span>= <span +class="cmtt-12">[window_center]</span> + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[left_n] </span>= <span +class="cmtt-12">[n]</span>/2</dd></dl> + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">if (<span +class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span +class="cmtt-12">[next_window_flag] </span>is not set) then + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_window_start] </span>= <span +class="cmtt-12">[n]*3</span>/4 - <span +class="cmtt-12">[blocksize_0]</span>/4 + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_window_end] </span>= <span +class="cmtt-12">[n]*3</span>/4 + <span +class="cmtt-12">[blocksize_0]</span>/4 + + + + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_n] </span>= <span +class="cmtt-12">[blocksize_0]</span>/2</dd></dl> + <!--l. 352--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_window_start] </span>= <span +class="cmtt-12">[window_center]</span> + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_window_end] </span>= <span +class="cmtt-12">[n]</span> + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[right_n] </span>= <span +class="cmtt-12">[n]</span>/2</dd></dl> + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">window from range 0 ... <span +class="cmtt-12">[left_window_start]</span>-1 inclusive is zero + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem">for <span +class="cmtt-12">[i] </span>in range <span +class="cmtt-12">[left_window_start] </span>... <span +class="cmtt-12">[left_window_end]</span>-1, window(<span +class="cmtt-12">[i]</span>) = + sin(<img +src="Vorbis_I_spec2x.png" alt="π +2" class="frac" align="middle"> <span +class="cmsy-10x-x-120">*</span> sin <sup><span +class="cmr-8">2</span></sup>( (<span +class="cmtt-12">[i]</span>-<span +class="cmtt-12">[left_window_start]</span>+0.5) / <span +class="cmtt-12">[left_n] </span><span +class="cmsy-10x-x-120">*</span><img +src="Vorbis_I_spec3x.png" alt="π +2" class="frac" align="middle">) ) + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem">window from range <span +class="cmtt-12">[left_window_end] </span>... <span +class="cmtt-12">[right_window_start]</span>-1 inclusive is + one + </dd><dt class="enumerate-enumitem"> + 7. </dt><dd +class="enumerate-enumitem">for <span +class="cmtt-12">[i] </span>in range <span +class="cmtt-12">[right_window_start] </span>... <span +class="cmtt-12">[right_window_end]</span>-1, window(<span +class="cmtt-12">[i]</span>) = + sin(<img +src="Vorbis_I_spec4x.png" alt="π2" class="frac" align="middle"> <span +class="cmsy-10x-x-120">*</span> sin <sup><span +class="cmr-8">2</span></sup>( (<span +class="cmtt-12">[i]</span>-<span +class="cmtt-12">[right_window_start]</span>+0.5) / <span +class="cmtt-12">[right_n] </span><span +class="cmsy-10x-x-120">*</span><img +src="Vorbis_I_spec5x.png" alt="π2" class="frac" align="middle"> + <img +src="Vorbis_I_spec6x.png" alt="π2" class="frac" align="middle">) ) + </dd><dt class="enumerate-enumitem"> + 8. </dt><dd +class="enumerate-enumitem">window from range <span +class="cmtt-12">[right_window_start] </span>... <span +class="cmtt-12">[n]</span>-1 is zero</dd></dl> +<!--l. 368--><p class="noindent" >An end-of-packet condition up to this point should be considered an error that discards this +packet from the stream. An end of packet condition past this point is to be considered a possible +nominal occurrence. +<!--l. 375--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.2. </span> <a + id="x1-740004.3.2"></a>floor curve decode</h5> +<!--l. 377--><p class="noindent" >From this point on, we assume out decode context is using mode number <span +class="cmtt-12">[mode_number]</span> +from configuration array <span +class="cmtt-12">[vorbis_mode_configurations] </span>and the map number +<span +class="cmtt-12">[vorbis_mode_mapping] </span>(specified by the current mode) taken from the mapping configuration +array <span +class="cmtt-12">[vorbis_mapping_configurations]</span>. +<!--l. 384--><p class="noindent" >Floor curves are decoded one-by-one in channel order. + + + +<!--l. 386--><p class="noindent" >For each floor <span +class="cmtt-12">[i] </span>of <span +class="cmtt-12">[audio_channels]</span> + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[submap_number] </span>= element <span +class="cmtt-12">[i] </span>of vector [vorbis_mapping_mux] + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[floor_number] </span>= element <span +class="cmtt-12">[submap_number] </span>of vector [vorbis_submap_floor] + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">if the floor type of this floor (vector + <span +class="cmtt-12">[vorbis_floor_types] </span>element <span +class="cmtt-12">[floor_number]</span>) is zero then decode the floor for + channel <span +class="cmtt-12">[i] </span>according to the <a +href="#x1-940006.2.2">subsubsection 6.2.2</a>, “<a +href="#x1-940006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>” + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span +class="cmtt-12">[i] </span>according to the + <a +href="#x1-1020007.2.3">subsubsection 7.2.3</a>, “<a +href="#x1-1020007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>” + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span +class="cmtt-12">[no_residue] </span>element <span +class="cmtt-12">[i] </span>to true, + else set vector <span +class="cmtt-12">[no_residue] </span>element <span +class="cmtt-12">[i] </span>to false</dd></dl> +<!--l. 406--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel +output vectors and skipping to the add/overlap output stage. +<!--l. 412--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a + id="x1-750004.3.3"></a>nonzero vector propagate</h5> +<!--l. 414--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that +that final output vector is all-zero values (and the floor is zero). The residue for that vector is not +coded in the stream, save for one complication. If some vectors are used and some are not, +channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed +vectors. +<!--l. 421--><p class="noindent" >for each <span +class="cmtt-12">[i] </span>from 0 ... <span +class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 +<!--l. 424--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">if either <span +class="cmtt-12">[no_residue] </span>entry for channel (<span +class="cmtt-12">[vorbis_mapping_magnitude] </span>element + <span +class="cmtt-12">[i]</span>) or channel (<span +class="cmtt-12">[vorbis_mapping_angle] </span>element <span +class="cmtt-12">[i]</span>) are set to false, then both + must be set to false. Note that an ’unused’ floor has no decoded floor information; it + + + + is important that this is remembered at floor curve synthesis time.</dd></dl> +<!--l. 436--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.4. </span> <a + id="x1-760004.3.4"></a>residue decode</h5> +<!--l. 438--><p class="noindent" >Unlike floors, which are decoded in channel order, the residue vectors are decoded in submap +order. +<!--l. 441--><p class="noindent" >for each submap <span +class="cmtt-12">[i] </span>in order from 0 ... <span +class="cmtt-12">[vorbis_mapping_submaps]</span>-1 +<!--l. 444--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[ch] </span>= 0 + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">for each channel <span +class="cmtt-12">[j] </span>in order from 0 ... <span +class="cmtt-12">[audio_channels] </span>- 1 + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">if channel <span +class="cmtt-12">[j] </span>in submap <span +class="cmtt-12">[i] </span>(vector <span +class="cmtt-12">[vorbis_mapping_mux] </span>element <span +class="cmtt-12">[j] </span>is equal to + <span +class="cmtt-12">[i]</span>) + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">if vector <span +class="cmtt-12">[no_residue] </span>element <span +class="cmtt-12">[j] </span>is true + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">vector <span +class="cmtt-12">[do_not_decode_flag] </span>element <span +class="cmtt-12">[ch] </span>is set</dd></dl> + <!--l. 453--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem">vector <span +class="cmtt-12">[do_not_decode_flag] </span>element <span +class="cmtt-12">[ch] </span>is unset</dd></dl> + </dd><dt class="enumerate-enumitem"> + ii. </dt><dd +class="enumerate-enumitem">increment <span +class="cmtt-12">[ch]</span></dd></dl> + </dd></dl> + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[residue_number] </span>= vector <span +class="cmtt-12">[vorbis_mapping_submap_residue] </span>element <span +class="cmtt-12">[i]</span> + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[residue_type] </span>= vector <span +class="cmtt-12">[vorbis_residue_types] </span>element <span +class="cmtt-12">[residue_number]</span> + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem">decode <span +class="cmtt-12">[ch] </span>vectors using residue <span +class="cmtt-12">[residue_number]</span>, according to type <span +class="cmtt-12">[residue_type]</span>, + + + + also passing vector <span +class="cmtt-12">[do_not_decode_flag] </span>to indicate which vectors in the bundle should + not be decoded. Correct per-vector decode length is <span +class="cmtt-12">[n]</span>/2. + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[ch] </span>= 0 + </dd><dt class="enumerate-enumitem"> + 7. </dt><dd +class="enumerate-enumitem">for each channel <span +class="cmtt-12">[j] </span>in order from 0 ... <span +class="cmtt-12">[audio_channels]</span> + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">if channel <span +class="cmtt-12">[j] </span>is in submap <span +class="cmtt-12">[i] </span>(vector <span +class="cmtt-12">[vorbis_mapping_mux] </span>element <span +class="cmtt-12">[j] </span>is equal + to <span +class="cmtt-12">[i]</span>) + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">residue vector for channel <span +class="cmtt-12">[j] </span>is set to decoded residue vector <span +class="cmtt-12">[ch]</span> + </dd><dt class="enumerate-enumitem"> + ii. </dt><dd +class="enumerate-enumitem">increment <span +class="cmtt-12">[ch]</span></dd></dl> + </dd></dl> + </dd></dl> +<!--l. 480--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.5. </span> <a + id="x1-770004.3.5"></a>inverse coupling</h5> +<!--l. 482--><p class="noindent" >for each <span +class="cmtt-12">[i] </span>from <span +class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1 descending to 0 +<!--l. 485--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[magnitude_vector] </span>= the residue vector for channel (vector + <span +class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span +class="cmtt-12">[i]</span>) + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[angle_vector] </span>= the residue vector for channel (vector <span +class="cmtt-12">[vorbis_mapping_angle]</span> + element <span +class="cmtt-12">[i]</span>) + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">for each scalar value <span +class="cmtt-12">[M] </span>in vector <span +class="cmtt-12">[magnitude_vector] </span>and the corresponding scalar value + <span +class="cmtt-12">[A] </span>in vector <span +class="cmtt-12">[angle_vector]</span>: + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">if (<span +class="cmtt-12">[M] </span>is greater than zero) + + + + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">if (<span +class="cmtt-12">[A] </span>is greater than zero) + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_M] </span>= <span +class="cmtt-12">[M]</span> + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_A] </span>= <span +class="cmtt-12">[M]</span>-<span +class="cmtt-12">[A]</span></dd></dl> + <!--l. 498--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_A] </span>= <span +class="cmtt-12">[M]</span> + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_M] </span>= <span +class="cmtt-12">[M]</span>+<span +class="cmtt-12">[A]</span></dd></dl> + </dd></dl> + <!--l. 505--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + i. </dt><dd +class="enumerate-enumitem">if (<span +class="cmtt-12">[A] </span>is greater than zero) + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_M] </span>= <span +class="cmtt-12">[M]</span> + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_A] </span>= <span +class="cmtt-12">[M]</span>+<span +class="cmtt-12">[A]</span></dd></dl> + <!--l. 512--><p class="noindent" >else + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + A. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_A] </span>= <span +class="cmtt-12">[M]</span> + </dd><dt class="enumerate-enumitem"> + B. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[new_M] </span>= <span +class="cmtt-12">[M]</span>-<span +class="cmtt-12">[A]</span></dd></dl> + </dd></dl> + </dd><dt class="enumerate-enumitem"> + b) </dt><dd +class="enumerate-enumitem">set scalar value <span +class="cmtt-12">[M] </span>in vector <span +class="cmtt-12">[magnitude_vector] </span>to <span +class="cmtt-12">[new_M]</span> + </dd><dt class="enumerate-enumitem"> + c) </dt><dd +class="enumerate-enumitem">set scalar value <span +class="cmtt-12">[A] </span>in vector <span +class="cmtt-12">[angle_vector] </span>to <span +class="cmtt-12">[new_A]</span></dd></dl> + </dd></dl> + + + +<!--l. 529--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.6. </span> <a + id="x1-780004.3.6"></a>dot product</h5> +<!--l. 531--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to +packet type. Note that the vector synthesis length for floor computation is <span +class="cmtt-12">[n]</span>/2. +<!--l. 535--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that +channel’s residue vector. The result is the dot product of the floor and residue vectors for +each channel; the produced vectors are the length <span +class="cmtt-12">[n]</span>/2 audio spectrum for each +channel. +<!--l. 543--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point +implementation might be to assume that a 32 bit fixed-point representation for floor and +residue and direct multiplication of the vectors is sufficient for acceptable spectral depth +in all cases because it happens to mostly work with the current Xiph.Org reference +encoder. +<!--l. 550--><p class="noindent" >However, floor vector values can span <span +class="cmsy-10x-x-120">~</span>140dB (<span +class="cmsy-10x-x-120">~</span>24 bits unsigned), and the audio spectrum +vector should represent a minimum of 120dB (<span +class="cmsy-10x-x-120">~</span>21 bits with sign), even when output is to a 16 +bit PCM device. For the residue vector to represent full scale if the floor is nailed +to <span +class="cmsy-10x-x-120">-</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach +full scale if the floor is nailed at 0dB, it must be able to represent <span +class="cmsy-10x-x-120">-</span>140dB to +0dB. +Thus, in order to handle full range dynamics, a residue vector may span <span +class="cmsy-10x-x-120">-</span>140dB to ++140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the +residue vector must be able to represent a 48 bit range and the dot product must +be able to handle an effective 48 bit times 24 bit multiplication. This range may be +achieved using large (64 bit or larger) integers, or implementing a movable binary point +representation. +<!--l. 567--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a + id="x1-790004.3.7"></a>inverse MDCT</h5> +<!--l. 569--><p class="noindent" >Convert the audio spectrum vector of each channel back into time domain PCM audio via an +inverse Modified Discrete Cosine Transform (MDCT). A detailed description of the MDCT is +available in <span class="cite">[<a +href="#XSporer/Brandenburg/Edler">1</a>]</span>. The window function used for the MDCT is the function described +earlier. + + + +<!--l. 576--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.8. </span> <a + id="x1-800004.3.8"></a>overlap_add</h5> +<!--l. 578--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous +window such that the 3/4 point of the previous window is aligned with the 1/4 point of the +current window (as illustrated in <a +href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a +href="#x1-260001.3.2">Window shape decode (long windows +only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data +is finished data to be returned by the decoder. This data spans from the center of +the previous window to the center of the current window. In the case of same-sized +windows, the amount of data to return is one-half block consisting of and only of the +overlapped portions. When overlapping a short and long window, much of the returned +range does not actually overlap. This does not damage transform orthogonality. Pay +attention however to returning the correct data range; the amount of data to be returned +is: +<!--l. 592--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb22"><a + id="x1-80002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span></div> +<!--l. 596--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element +windowsize/2-1, inclusive) of the current window. +<!--l. 599--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The +encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper +PCM output offset is ’0’ (as no data has been returned yet). +<!--l. 606--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a + id="x1-810004.3.9"></a>output channel order</h5> +<!--l. 608--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is +implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the +specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for +greater-than-eight channels remains ’left to the implementation’. +<!--l. 614--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a +decoder to produce output with channels in any order. Any such decoder should explicitly +document channel reordering behavior. +<!--l. 620--><p class="noindent" > + <dl class="description"><dt class="description"> +<span +class="cmssbx-10x-x-120">one channel</span> </dt><dd +class="description">the stream is monophonic + + + + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">two channels</span> </dt><dd +class="description">the stream is stereo. channel order: left, right + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">three channels</span> </dt><dd +class="description">the stream is a 1d-surround encoding. channel order: left, center, right + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">four channels</span> </dt><dd +class="description">the stream is quadraphonic surround. channel order: front left, front right, + rear left, rear right + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">five channels</span> </dt><dd +class="description">the stream is five-channel surround. channel order: front left, center, front + right, rear left, rear right + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">six channels</span> </dt><dd +class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear + left, rear right, LFE + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">seven channels</span> </dt><dd +class="description">the stream is 6.1 surround. channel order: front left, center, front right, + side left, side right, rear center, LFE + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">eight channels</span> </dt><dd +class="description">the stream is 7.1 surround. channel order: front left, center, front right, + side left, side right, rear left, rear right, LFE + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd +class="description">channel use and order is defined by the application + </dd></dl> +<!--l. 656--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future +channel mappings (such as three and four channel <a +href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel +mappings other than mapping 0. + + + + + + +<h3 class="sectionHead"><span class="titlemark">5. </span> <a + id="x1-820005"></a>comment field and header specification</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a + id="x1-830005.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis +bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata +belongs in a separate logical bitstream (usually an XML stream type) that provides greater +structure and machine parseability. +<!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of +a CDR. It should be a little information to remember the disc by and explain it to others; a +short, to-the-point text note that need not only be a couple words, but isn’t going to be more +than a short paragraph. The essentials, in other words, whatever they turn out to be, +eg: +<!--l. 21--><p class="noindent" > + <div class="quote"> + <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span +class="cmti-12">“I’m Still Around”</span>, opening + for Moxy Früvous, 1997.</div> +<!--l. 29--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a + id="x1-840005.2"></a>Comment encoding</h4> +<!--l. 31--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a + id="x1-850005.2.1"></a>Structure</h5> +<!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is +bounded to 2<sup><span +class="cmr-8">32</span></sup> <span +class="cmsy-10x-x-120">- </span>1 and the length of each vector is limited to 2<sup><span +class="cmr-8">32</span></sup> <span +class="cmsy-10x-x-120">- </span>1 bytes. The vector length is + + + +encoded; the vector contents themselves are not null terminated. In addition to the vector list, +there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For +example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I +20020717”. +<!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit +packing conventions of the vorbis codec. However, since data in the comment header +is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned +integers. +<!--l. 46--><p class="noindent" >The comment header is decoded as follows: +<!--l. 48--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb23"><a + id="x1-85002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [vendor\_length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-85004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [vendor\_string]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> UTF-8</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> [vendor\_length]</span><span +class="cmtt-8"> octets</span> +<br class="fancyvrb" /><a + id="x1-85006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [user\_comment\_list\_length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-85008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [user\_comment\_list\_length]</span><span +class="cmtt-8"> times</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-85010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [length]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 32</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-85012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> this</span><span +class="cmtt-8"> iteration’s</span><span +class="cmtt-8"> user</span><span +class="cmtt-8"> comment</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> UTF-8</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> [length]</span><span +class="cmtt-8"> octets</span> +<br class="fancyvrb" /><a + id="x1-85014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-85016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [framing\_bit]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> single</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> boolean</span><br class="fancyvrb" /><a + id="x1-85018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [framing\_bit]</span><span +class="cmtt-8"> unset</span><span +class="cmtt-8"> or</span><span +class="cmtt-8"> end-of-packet</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> ERROR</span><br class="fancyvrb" /><a + id="x1-85020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> done.</span></div> +<!--l. 64--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a + id="x1-860005.2.2"></a>Content vector format</h5> +<!--l. 66--><p class="noindent" >The comment vectors are structured similarly to a UNIX environment variable. That is, +comment fields consist of a field name and a corresponding value and look like: +<!--l. 70--><p class="noindent" > + <div class="quote"> + <!--l. 71--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb24"><a + id="x1-86002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> comment[0]="ARTIST=me";</span><br class="fancyvrb" /><a + id="x1-86004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> comment[1]="TITLE=the</span><span +class="cmtt-8"> sound</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> Vorbis";</span></div> + </div> +<!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’) +excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to +ASCII 0x61 through 0x7A inclusive (characters a-z). +<!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to +terminate the field name. +<!--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 +field. + + + +<!--l. 91--><p class="noindent" ><span class="paragraphHead"><a + id="x1-870005.2.2"></a><span +class="cmbx-12">Field names</span></span> +Below is a proposed, minimal list of standard field names with a description of intended use. No +single or group of field names is mandatory; a comment header may contain one, all or none of +the names in this list. +<!--l. 99--><p class="noindent" > + <dl class="description"><dt class="description"> +<span +class="cmssbx-10x-x-120">TITLE</span> </dt><dd +class="description">Track/Work name + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">VERSION</span> </dt><dd +class="description">The version field may be used to differentiate multiple versions of the same + track title in a single collection. (e.g. remix info) + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">ALBUM</span> </dt><dd +class="description">The collection name to which this track belongs + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd +class="description">The track number of this piece if part of a specific larger collection or + album + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">ARTIST</span> </dt><dd +class="description">The artist generally considered responsible for the work. In popular music this is + usually the performing band or singer. For classical music it would be the composer. + For an audio book it would be the author of the original text. + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd +class="description">The artist(s) who performed the work. In classical music this would be the + conductor, orchestra, soloists. In an audio book it would be the actor who did the + reading. In popular music this is typically the same as the ARTIST and is omitted. + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd +class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’ + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">LICENSE</span> </dt><dd +class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to + a license such as a Creative + Commons license (”www.creativecommons.org/blahblah/license.html”) or the EFF + Open Audio License (’distributed under the terms of the Open Audio License. see + http://www.eff.org/IP/Open_licenses/eff_oal.html for details’), etc. + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd +class="description">Name of the organization producing the track (i.e. the ’record label’) + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd +class="description">A short text description of the contents + </dd><dt class="description"> + + + +<span +class="cmssbx-10x-x-120">GENRE</span> </dt><dd +class="description">A short text indication of music genre + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">DATE</span> </dt><dd +class="description">Date the track was recorded + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">LOCATION</span> </dt><dd +class="description">Location where track was recorded + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">CONTACT</span> </dt><dd +class="description">Contact information for the creators or distributors of the track. This could + be a URL, an email address, the physical address of the producing label. + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">ISRC</span> </dt><dd +class="description">International Standard Recording Code for the track; see <a +href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for + more information on ISRC numbers. + </dd></dl> +<!--l. 158--><p class="noindent" ><span class="paragraphHead"><a + id="x1-880005.2.2"></a><span +class="cmbx-12">Implications</span></span> +Field names should not be ’internationalized’; this is a concession to simplicity not +an attempt to exclude the majority of the world that doesn’t speak English. Field +<span +class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any +language. +<!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that +the field name is bounded in a known way. Thus we also have the length of the field +contents. +<!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper +use of comment fields should be clear through context at this point. Abuse will be +discouraged. +<!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort +to avoid arbitrarily polluting the common namespace. We will generally collect the more useful +tags here to help with standardization. +<!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an +example, assume a track was recorded by three well know artists; the following is permissible, +and encouraged: +<!--l. 183--><p class="noindent" > + <div class="quote"> + <!--l. 184--><p class="noindent" > + + + + <div class="fancyvrb" id="fancyvrb25"><a + id="x1-88002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ARTIST=Dizzy</span><span +class="cmtt-8"> Gillespie</span><br class="fancyvrb" /><a + id="x1-88004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ARTIST=Sonny</span><span +class="cmtt-8"> Rollins</span><br class="fancyvrb" /><a + id="x1-88006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> ARTIST=Sonny</span><span +class="cmtt-8"> Stitt</span></div> + </div> +<!--l. 197--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a + id="x1-890005.2.3"></a>Encoding</h5> +<!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the +first bitstream header packet, it is not generally the only packet on the second page and may not +be restricted to within the second bitstream page. The length of the comment header packet is +(practically) unbounded. The comment header packet is not optional; it must be present in the +bitstream even if it is effectively empty. +<!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which +renders least-significant-bit of the word to be coded into the least significant available bit of the +current bitstream octet first): +<!--l. 213--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets) + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of + string, not null terminated) + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields) + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span +class="cmmi-12">> </span>0; 32 bit unsigned quantity + specifying number of octets) + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to + end of string, not null terminated) + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span +class="cmmi-12">> </span>1...)... + </dd></dl> +<!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found +in <span +class="cmtt-12">vorbis/lib/info.c</span>, <span +class="cmtt-12">_vorbis_pack_comment() </span>and <span +class="cmtt-12">_vorbis_unpack_comment()</span>. + + + + + + + + + +<h3 class="sectionHead"><span class="titlemark">6. </span> <a + id="x1-900006"></a>Floor type 0 setup and decode</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a + id="x1-910006.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately known as Line Spectral +Frequency or LSF) representation to encode a smooth spectral envelope curve as the frequency +response of the LSP filter. This representation is equivalent to a traditional all-pole infinite +impulse response filter as would be used in linear predictive coding; LSP representation may be +converted to LPC representation and vice-versa. +<!--l. 18--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">6.2. </span> <a + id="x1-920006.2"></a>Floor 0 format</h4> +<!--l. 20--><p class="noindent" >Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in +coding/decoding the LSP filter coefficient values used by each frame. +<!--l. 24--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">6.2.1. </span> <a + id="x1-930006.2.1"></a>header decode</h5> +<!--l. 26--><p class="noindent" >Configuration information for instances of floor zero decodes from the codec setup header (third +packet). configuration decode proceeds as follows: +<!--l. 30--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb26"><a + id="x1-93002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [floor0_order]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-93004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [floor0_rate]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 16</span><span +class="cmtt-8"> bits</span> +<br class="fancyvrb" /><a + id="x1-93006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [floor0_bark_map_size]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> 16</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-93008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [floor0_amplitude_bits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> six</span><span +class="cmtt-8"> bits</span> +<br class="fancyvrb" /><a + id="x1-93010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [floor0_amplitude_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> eight</span><span +class="cmtt-8"> bits</span> +<br class="fancyvrb" /><a + id="x1-93012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [floor0_number_of_books]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> four</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> 1</span> +<br class="fancyvrb" /><a + id="x1-93014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [floor0_book_list]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> list</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [floor0_number_of_books]</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integers</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> eight</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> each;</span></div> + + + +<!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable. +In addition, any element of the array <span +class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum +codebook number for this bitstream is an error condition that also renders the stream +undecodable. +<!--l. 48--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a + id="x1-940006.2.2"></a>packet decode</h5> +<!--l. 50--><p class="noindent" >Extracting a floor0 curve from an audio packet consists of first decoding the curve +amplitude and <span +class="cmtt-12">[floor0_order] </span>LSP coefficient values from the bitstream, and then +computing the floor curve, which is defined as the frequency response of the decoded LSP +filter. +<!--l. 56--><p class="noindent" >Packet decode proceeds as follows: +<div class="fancyvrb" id="fancyvrb27"><a + id="x1-94002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [amplitude]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [floor0_amplitude_bits]</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-94004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [amplitude]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-94006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [coefficients]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> empty,</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> length</span><span +class="cmtt-8"> vector</span><br class="fancyvrb" /><a + id="x1-94008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [booknumber]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> </span><a +href="#x1-1190009.2.1"><span +class="cmtt-8">ilog</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> [floor0_number_of_books]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> bits</span> +<br class="fancyvrb" /><a + id="x1-94010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [booknumber]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> highest</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> decode</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> undecodable</span><br class="fancyvrb" /><a + id="x1-94012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> zero;</span> +<br class="fancyvrb" /><a + id="x1-94014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [temp_vector]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> bitstream</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [floor0_book_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [booknumber]</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> VQ</span><span +class="cmtt-8"> context.</span> +<br class="fancyvrb" /><a + id="x1-94016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> each</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [temp_vector]</span><br class="fancyvrb" /><a + id="x1-94018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [last]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> last</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [temp_vector]</span> +<br class="fancyvrb" /><a + id="x1-94020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> concatenate</span><span +class="cmtt-8"> [temp_vector]</span><span +class="cmtt-8"> onto</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> end</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> [coefficients]</span><span +class="cmtt-8"> vector</span> +<br class="fancyvrb" /><a + id="x1-94022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (length</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [coefficients]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [floor0_order],</span><span +class="cmtt-8"> continue</span><span +class="cmtt-8"> at</span><span +class="cmtt-8"> step</span><span +class="cmtt-8"> 6</span><br class="fancyvrb" /><a + id="x1-94024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-94026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-94028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-94030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> done.</span><br class="fancyvrb" /><a + id="x1-94032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 76--><p class="noindent" >Take note of the following properties of decode: + <ul class="itemize1"> + <li class="itemize">An <span +class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel + is unused in this frame (the output of the channel will be all-zeroes in synthesis). + Several later stages of decode don’t occur for an unused channel. + </li> + <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence; + if end-of-packet is reached during any read operation above, floor decode is to return + ’unused’ status as if the <span +class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode. + </li> + <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a +href="#x1-1190009.2.1">ilog</a>( + <span +class="cmtt-12">[floor0_number_of_books] </span>- 1 ) bits. Nevertheless, the above specification is correct + and values greater than the maximum possible book value are reserved. + </li> + <li class="itemize">The number of scalars read into the vector <span +class="cmtt-12">[coefficients] </span>may be greater + than <span +class="cmtt-12">[floor0_order]</span>, the number actually required for curve computation. For + example, if the VQ codebook used for the floor currently being decoded has a + <span +class="cmtt-12">[codebook_dimensions] </span>value of three and <span +class="cmtt-12">[floor0_order] </span>is ten, the only way to + + + + fill all the needed scalars in <span +class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars + as four vectors of three scalars each. This is not an error condition, and care must + be taken not to allow a buffer overflow in decode. The extra values are not used and + may be ignored or discarded.</li></ul> +<!--l. 104--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">6.2.3. </span> <a + id="x1-950006.2.3"></a>curve computation</h5> +<!--l. 106--><p class="noindent" >Given an <span +class="cmtt-12">[amplitude] </span>integer and <span +class="cmtt-12">[coefficients] </span>vector from packet decode as well as +the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and +[floor0_amplitude_offset] values from floor setup, and an output vector size <span +class="cmtt-12">[n] </span>specified by the +decode process, we compute a floor output vector. +<!--l. 113--><p class="noindent" >If the value <span +class="cmtt-12">[amplitude] </span>is zero, the return value is a length <span +class="cmtt-12">[n] </span>vector with all-zero +scalars. Otherwise, begin by assuming the following definitions for the given vector to be +synthesized: +<center class="par-math-display" > +<img +src="Vorbis_I_spec7x.png" alt=" { +map = min (floor0_bark_map_size - 1,f oobar) for i ∈ [0, n - 1] + i - 1 for i = n +" class="par-math-display" ></center> +<!--l. 128--><p class="nopar" > +<!--l. 130--><p class="noindent" >where +<center class="par-math-display" > +<img +src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋ + ( floor0_rate--⋅ i) floor0_bark_map_size---- +f oobar = bark 2n ⋅ bark(.5 ⋅ floor0_rate ) +" class="par-math-display" ></center> +<!--l. 137--><p class="nopar" > +<!--l. 139--><p class="noindent" >and +<center class="par-math-display" > +<img +src="Vorbis_I_spec9x.png" alt=" 2 +bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x ) + .0001x +" class="par-math-display" ></center> +<!--l. 143--><p class="nopar" > +<!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the +result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output +LSP curve <span +class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last +step: +<!--l. 151--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[i] </span>= 0 + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[</span><span +class="cmmi-12">ω</span><span +class="cmtt-12">] </span>= <span +class="cmmi-12">π </span>* map element <span +class="cmtt-12">[i] </span>/ <span +class="cmtt-12">[floor0_bark_map_size]</span> + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">if ( <span +class="cmtt-12">[floor0_order] </span>is odd ) + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">calculate <span +class="cmtt-12">[p] </span>and <span +class="cmtt-12">[q] </span>according to: <div class="eqnarray"> + <center class="math-display" > + <img +src="Vorbis_I_spec10x.png" alt=" floor0∏_2order-3 +p = (1 - cos2ω) 4(cos([coefficients ]2j+1) - cosω )2 + j=0 + floor0_order-1 + 1 ∏2 2 +q = 4- 4(cos([coefficients ]2j) - cosω ) + j=0 + " class="math-display" ></center> + </div> + </dd></dl> + <!--l. 162--><p class="noindent" >else <span +class="cmtt-12">[floor0_order] </span>is even + + + + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + a) </dt><dd +class="enumerate-enumitem">calculate <span +class="cmtt-12">[p] </span>and <span +class="cmtt-12">[q] </span>according to: <div class="eqnarray"> + <center class="math-display" > + <img +src="Vorbis_I_spec11x.png" alt=" floor0_order-2 + (1 - cosω ) ---∏2----- +p = ----------- 4(cos([coefficients ]2j+1) - cosω)2 + 2 j=0 + floor0_order--2 + (1-+-cosω-) ∏2 2 +q = 2 4(cos([coefficients ]2j) - cos ω) + j=0 + " class="math-display" ></center> + </div> + </dd></dl> + </dd><dt class="enumerate-enumitem"> + 4. </dt><dd +class="enumerate-enumitem">calculate <span +class="cmtt-12">[linear_floor_value] </span>according to: + <center class="math-display" > + <img +src="Vorbis_I_spec12x.png" alt=" ( ( )) + amplitude---⋅ floor0_amplitute_offset--- +exp .11512925 (2floor0_amplitude_bits - 1)√p--+-q - floor0_amplitude_offset + " class="math-display" ></center> + <!--l. 177--><p class="nopar" > + </dd><dt class="enumerate-enumitem"> + 5. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[iteration_condition] </span>= map element <span +class="cmtt-12">[i]</span> + </dd><dt class="enumerate-enumitem"> + 6. </dt><dd +class="enumerate-enumitem"><span +class="cmtt-12">[output] </span>element <span +class="cmtt-12">[i] </span>= <span +class="cmtt-12">[linear_floor_value]</span> + </dd><dt class="enumerate-enumitem"> + 7. </dt><dd +class="enumerate-enumitem">increment <span +class="cmtt-12">[i]</span> + </dd><dt class="enumerate-enumitem"> + 8. </dt><dd +class="enumerate-enumitem">if ( map element <span +class="cmtt-12">[i] </span>is equal to <span +class="cmtt-12">[iteration_condition] </span>) continue at step + + + + 5 + </dd><dt class="enumerate-enumitem"> + 9. </dt><dd +class="enumerate-enumitem">if ( <span +class="cmtt-12">[i] </span>is less than <span +class="cmtt-12">[n] </span>) continue at step 2 + </dd><dt class="enumerate-enumitem"> + 10. </dt><dd +class="enumerate-enumitem">done</dd></dl> +<!--l. 187--><p class="noindent" ><span class="paragraphHead"><a + id="x1-960006.2.3"></a><span +class="cmbx-12">Errata 20150227: Bark scale computation</span></span> +Due to a typo when typesetting this version of the specification from the original HTML +document, the Bark scale computation previously erroneously read: +<center class="par-math-display" > +<img +src="Vorbis_I_spec13x.png" alt=" 2 +bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x ) +" class="par-math-display" ></center> +<!--l. 195--><p class="nopar" > +<!--l. 197--><p class="noindent" >Note that the last parenthesis is misplaced. This document now uses the correct equation as it +appeared in the original HTML spec document: +<center class="par-math-display" > +<img +src="Vorbis_I_spec14x.png" alt="bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x2 ) + .0001x +" class="par-math-display" ></center> +<!--l. 201--><p class="nopar" > + + + + + + +<h3 class="sectionHead"><span class="titlemark">7. </span> <a + id="x1-970007"></a>Floor type 1 setup and decode</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a + id="x1-980007.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope +curve. The representation plots this curve mechanically on a linear frequency axis and a +logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s +algorithm. +<!--l. 16--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a + id="x1-990007.2"></a>Floor 1 format</h4> +<!--l. 18--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a + id="x1-1000007.2.1"></a>model</h5> +<!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a +floor curve using iterative prediction in a process roughly equivalent to the following simplified +description: + <ul class="itemize1"> + <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1 + where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be + computed. + </li> + <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and + produces a y˙new value at that point computed from the existing line’s y value at + x˙new (as plotted by the line) and a difference value decoded from the bitstream + packet. + + + + </li> + <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to + x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if + y˙new represents no change to the amplitude value at x˙new so that later refinement + is additionally bounded at x˙new. + </li> + <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header + at floor 1 initialization time. Computation is completed at the end of the x value list. + </li></ul> +<!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than +representing typical configuration: +<!--l. 51--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values +in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0, +128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an +example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following +way, beginning with the first line: +<div class="center" +> +<!--l. 59--><p class="noindent" > + +<!--l. 60--><p class="noindent" ><img +src="floor1-1.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 7: </span><span +class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000017 --> +</div> +<!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32 +and 96: +<div class="center" +> +<!--l. 67--><p class="noindent" > + +<!--l. 68--><p class="noindent" ><img +src="floor1-2.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 8: </span><span +class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000028 --> +</div> +<!--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 +further refinement. From here on, the pattern should be clear; we complete the floor computation +as follows: + + + +<div class="center" +> +<!--l. 76--><p class="noindent" > + +<!--l. 77--><p class="noindent" ><img +src="floor1-3.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 9: </span><span +class="content">graph of example floor</span></div><!--tex4ht:label?: x1-1000039 --> +</div> +<div class="center" +> +<!--l. 81--><p class="noindent" > + +<!--l. 82--><p class="noindent" ><img +src="floor1-4.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 10: </span><span +class="content">graph of example floor</span></div><!--tex4ht:label?: x1-10000410 --> +</div> +<!--l. 86--><p class="noindent" >A more efficient algorithm with carefully defined integer rounding behavior is used for actual +decode, as described later. The actual algorithm splits Y value computation and line plotting +into two steps with modifications to the above algorithm to eliminate noise accumulation +through integer roundoff/truncation. +<!--l. 94--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">7.2.2. </span> <a + id="x1-1010007.2.2"></a>header decode</h5> +<!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order +during packet decode and synthesis). This list is split into partitions, and each partition is +assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit +partition or partition class. +<!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which +the partition class encodes at once), a ’subclass’ value representing the number of +alternate entropy books the partition class may use in representing Y values, the list of +[subclass] books and a master book used to encode which alternate books were chosen +for representation in a given packet. The master/subclass mechanism is meant to be +used as a flexible representation cascade while still using codebooks only in a scalar +context. + + + +<!--l. 112--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb28"><a + id="x1-101002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [floor1_partitions]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-101006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [maximum_class]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> -1</span><br class="fancyvrb" /><a + id="x1-101008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [floor1_partitions]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-101010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_partition_class_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-101014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-101018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-101020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [maximum_class]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> largest</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_partition_class_list]</span><br class="fancyvrb" /><a + id="x1-101022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [maximum_class]</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-101024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_dimensions]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> 1</span> +<br class="fancyvrb" /><a + id="x1-101028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  8)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_subclasses]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-101030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_subclasses]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> nonzero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-101032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-101034r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_masterbooks]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-101036r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101038r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-101040r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-101042r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> (2</span><span +class="cmtt-8"> exponent</span><span +class="cmtt-8"> [floor1_class_subclasses]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i])</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-101044r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-101046r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [floor1_subclass_books]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i],[j]</span><span +class="cmtt-8"> =</span><br class="fancyvrb" /><a + id="x1-101048r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> subtract</span><span +class="cmtt-8"> one</span><br class="fancyvrb" /><a + id="x1-101050r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span> +<br class="fancyvrb" /><a + id="x1-101052r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-101054r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101056r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> [floor1_multiplier]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> one</span><br class="fancyvrb" /><a + id="x1-101058r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> [rangebits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-101060r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-101062r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [1]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> exponent</span><span +class="cmtt-8"> [rangebits];</span> +<br class="fancyvrb" /><a + id="x1-101064r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 17)</span><span +class="cmtt-8"> [floor1_values]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><br class="fancyvrb" /><a + id="x1-101066r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 18)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [floor1_partitions]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-101068r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101070r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 19)</span><span +class="cmtt-8"> [current_class_number]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_partition_class_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span> +<br class="fancyvrb" /><a + id="x1-101072r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 20)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> ([floor1_class_dimensions]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [current_class_number])-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> +<br class="fancyvrb" /><a + id="x1-101074r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 21)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([floor1_values])</span><span +class="cmtt-8"> =</span><br class="fancyvrb" /><a + id="x1-101076r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> [rangebits]</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-101078r39"></a><span +class="cmr-6">39</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 22)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [floor1_values]</span><span +class="cmtt-8"> by</span><span +class="cmtt-8"> one</span><br class="fancyvrb" /><a + id="x1-101080r40"></a><span +class="cmr-6">40</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-101082r41"></a><span +class="cmr-6">41</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-101084r42"></a><span +class="cmr-6">42</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-101086r43"></a><span +class="cmr-6">43</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 23)</span><span +class="cmtt-8"> done</span></div> +<!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during +setup renders a stream undecodable. In addition, a <span +class="cmtt-12">[floor1_class_masterbooks] </span>or +<span +class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook +configured in this stream is an error condition that renders the stream undecodable. Vector +[floor1_x_list] is limited to a maximum length of 65 elements; a setup indicating more than 65 +total elements (including elements 0 and 1 set prior to the read loop) renders the stream +undecodable. All vector [floor1_x_list] element values must be unique within the vector; a +non-unique value renders the stream undecodable. +<!--l. 170--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">7.2.3. </span> <a + id="x1-1020007.2.3"></a>packet decode</h5> +<!--l. 172--><p class="noindent" >Packet decode begins by checking the <span +class="cmtt-12">[nonzero] </span>flag: +<!--l. 174--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb29"><a + id="x1-102002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [nonzero]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> boolean</span></div> +<!--l. 178--><p class="noindent" >If <span +class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame. +Decode immediately returns a status indicating this floor curve (and thus this channel) is unused +this frame. (A return status of ’unused’ is different from decoding a floor that has all +points set to minimum representation amplitude, which happens to be approximately +-140dB). +<!--l. 186--><p class="noindent" >Assuming <span +class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows: +<!--l. 188--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb30"><a + id="x1-102004r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [range]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><span +class="cmtt-8"> 256,</span><span +class="cmtt-8"> 128,</span><span +class="cmtt-8"> 86,</span><span +class="cmtt-8"> 64</span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([floor1_multiplier]-1)</span> + + + +<br class="fancyvrb" /><a + id="x1-102006r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> </span><a +href="#x1-1190009.2.1"><span +class="cmtt-8">ilog</span></a><span +class="cmtt-8">([range]-1)</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-102008r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [1]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> </span><a +href="#x1-1190009.2.1"><span +class="cmtt-8">ilog</span></a><span +class="cmtt-8">([range]-1)</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-102010r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2;</span><br class="fancyvrb" /><a + id="x1-102012r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [floor1_partitions]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-102014r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-102016r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [class]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_partition_class]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><br class="fancyvrb" /><a + id="x1-102018r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [cdim]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_dimensions]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [class]</span> +<br class="fancyvrb" /><a + id="x1-102020r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> [cbits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_class_subclasses]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [class]</span><br class="fancyvrb" /><a + id="x1-102022r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [csub]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> (2</span><span +class="cmtt-8"> exponent</span><span +class="cmtt-8"> [cbits])-1</span><br class="fancyvrb" /><a + id="x1-102024r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> [cval]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span> +<br class="fancyvrb" /><a + id="x1-102026r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [cbits]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-102028r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102030r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> [cval]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> number</span> +<br class="fancyvrb" /><a + id="x1-102032r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (vector</span><span +class="cmtt-8"> [floor1_class_masterbooks]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [class])</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> context</span> +<br class="fancyvrb" /><a + id="x1-102034r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-102036r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102038r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [cdim]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-102040r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-102042r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> [book]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [floor1_subclass_books]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [class],([cval]</span><span +class="cmtt-8"> bitwise</span><span +class="cmtt-8"> AND</span><span +class="cmtt-8"> [csub])</span> +<br class="fancyvrb" /><a + id="x1-102044r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> [cval]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [cval]</span><span +class="cmtt-8"> right</span><span +class="cmtt-8"> shifted</span><span +class="cmtt-8"> [cbits]</span><span +class="cmtt-8"> bits</span><br class="fancyvrb" /><a + id="x1-102046r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [book]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-102048r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-102050r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 17)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([j]+[offset])</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> codebook</span><br class="fancyvrb" /><a + id="x1-102052r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [book]</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> context</span> +<br class="fancyvrb" /><a + id="x1-102054r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102056r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [book]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-102058r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102060r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 18)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([j]+[offset])</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span> +<br class="fancyvrb" /><a + id="x1-102062r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102064r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-102066r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-102068r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102070r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 19)</span><span +class="cmtt-8"> [offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [offset]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [cdim]</span><br class="fancyvrb" /><a + id="x1-102072r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102074r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-102076r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-102078r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 20)</span><span +class="cmtt-8"> done</span></div> +<!--l. 229--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if +end-of-packet is reached during any read operation above, floor decode is to return ’unused’ +status as if the <span +class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode. +<!--l. 235--><p class="noindent" >Vector <span +class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis. +<!--l. 240--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">7.2.4. </span> <a + id="x1-1030007.2.4"></a>curve computation</h5> +<!--l. 242--><p class="noindent" >Curve computation is split into two logical steps; the first step derives final Y amplitude values +from the encoded, wrapped difference values taken from the bitstream. The second step +plots the curve lines. Also, although zero-difference values are used in the iterative +prediction to find final Y values, these points are conditionally skipped during final +line computation in step two. Skipping zero-difference values allows a smoother line +fit. +<!--l. 250--><p class="noindent" >Although some aspects of the below algorithm look like inconsequential optimizations, +implementors are warned to follow the details closely. Deviation from implementing a strictly +equivalent algorithm can result in serious decoding errors. +<!--l. 255--><p class="noindent" ><span +class="cmti-12">Additional note: </span>Although <span +class="cmtt-12">[floor1_final_Y] </span>values in the prediction loop and at the end of +step 1 are inherently limited by the prediction algorithm to [0, <span +class="cmtt-12">[range]</span>), it is possible to abuse +the setup and codebook machinery to produce negative or over-range results. We suggest that +decoder implementations guard the values in vector <span +class="cmtt-12">[floor1_final_Y] </span>by clamping each +element to [0, <span +class="cmtt-12">[range]</span>) after step 1. Variants of this suggestion are acceptable as valid floor1 +setups cannot produce out of range values. +<!--l. 266--><p class="noindent" > + <dl class="description"><dt class="description"> +<span +class="cmssbx-10x-x-120">step 1: amplitude value synthesis</span> </dt><dd +class="description"> + <!--l. 268--><p class="noindent" >Unwrap the always-positive-or-zero values read from the packet into +/- difference + + + + values, then apply to line prediction. + <!--l. 271--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb31"><a + id="x1-103002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [range]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><span +class="cmtt-8"> 256,</span><span +class="cmtt-8"> 128,</span><span +class="cmtt-8"> 86,</span><span +class="cmtt-8"> 64</span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([floor1_multiplier]-1)</span><br class="fancyvrb" /><a + id="x1-103004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> set</span> + <br class="fancyvrb" /><a + id="x1-103006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [1]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> set</span><br class="fancyvrb" /><a + id="x1-103008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span> + <br class="fancyvrb" /><a + id="x1-103010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [1]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [1]</span><br class="fancyvrb" /><a + id="x1-103012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [floor1_values]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [low_neighbor_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1220009.2.4"><span +class="cmtt-8">low_neighbor</span></a><span +class="cmtt-8">([floor1_X_list],[i])</span><br class="fancyvrb" /><a + id="x1-103018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> [high_neighbor_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1230009.2.5"><span +class="cmtt-8">high_neighbor</span></a><span +class="cmtt-8">([floor1_X_list],[i])</span> + <br class="fancyvrb" /><a + id="x1-103020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [predicted]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> </span><a +href="#x1-1240009.2.6"><span +class="cmtt-8">render_point</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [low_neighbor_offset],</span> + <br class="fancyvrb" /><a + id="x1-103024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [low_neighbor_offset],</span> + <br class="fancyvrb" /><a + id="x1-103026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [high_neighbor_offset],</span> + <br class="fancyvrb" /><a + id="x1-103028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [high_neighbor_offset],</span> + <br class="fancyvrb" /><a + id="x1-103030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_X_list]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> )</span><br class="fancyvrb" /><a + id="x1-103032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103034r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span> + <br class="fancyvrb" /><a + id="x1-103036r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [range]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a + id="x1-103038r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [predicted]</span> + <br class="fancyvrb" /><a + id="x1-103040r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103042r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103044r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> [room]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> 2</span><br class="fancyvrb" /><a + id="x1-103046r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103048r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103050r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103052r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> [room]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> 2</span><br class="fancyvrb" /><a + id="x1-103054r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103056r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103058r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103060r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> nonzero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103062r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103064r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 17)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [low_neighbor_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> set</span> + <br class="fancyvrb" /><a + id="x1-103066r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 18)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [high_neighbor_offset]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> set</span> + <br class="fancyvrb" /><a + id="x1-103068r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 19)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> set</span><br class="fancyvrb" /><a + id="x1-103070r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 20)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> or</span><span +class="cmtt-8"> equal</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> [room]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span> + <br class="fancyvrb" /><a + id="x1-103072r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103074r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 21)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103076r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103078r39"></a><span +class="cmr-6">39</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 22)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [predicted]</span> + <br class="fancyvrb" /><a + id="x1-103080r40"></a><span +class="cmr-6">40</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103082r41"></a><span +class="cmr-6">41</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [lowroom]</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103084r42"></a><span +class="cmr-6">42</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103086r43"></a><span +class="cmr-6">43</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 23)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [predicted]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [highroom]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> 1</span> + <br class="fancyvrb" /><a + id="x1-103088r44"></a><span +class="cmr-6">44</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103090r45"></a><span +class="cmr-6">45</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103092r46"></a><span +class="cmr-6">46</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103094r47"></a><span +class="cmr-6">47</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [room]</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103096r48"></a><span +class="cmr-6">48</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103098r49"></a><span +class="cmr-6">49</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 24)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> ([val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> odd)</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103100r50"></a><span +class="cmr-6">50</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103102r51"></a><span +class="cmr-6">51</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 25)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span> + <br class="fancyvrb" /><a + id="x1-103104r52"></a><span +class="cmr-6">52</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [predicted]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> (([val]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> divided</span><span +class="cmtt-8"> by</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> division)</span><br class="fancyvrb" /><a + id="x1-103106r53"></a><span +class="cmr-6">53</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103108r54"></a><span +class="cmr-6">54</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> even</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103110r55"></a><span +class="cmr-6">55</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103112r56"></a><span +class="cmr-6">56</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 26)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span> + <br class="fancyvrb" /><a + id="x1-103114r57"></a><span +class="cmr-6">57</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [predicted]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> ([val]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> division)</span><br class="fancyvrb" /><a + id="x1-103116r58"></a><span +class="cmr-6">58</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103118r59"></a><span +class="cmr-6">59</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103120r60"></a><span +class="cmr-6">60</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103122r61"></a><span +class="cmr-6">61</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103124r62"></a><span +class="cmr-6">62</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103126r63"></a><span +class="cmr-6">63</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> [val]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103128r64"></a><span +class="cmr-6">64</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103130r65"></a><span +class="cmr-6">65</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 27)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_step2_flag]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> unset</span> + <br class="fancyvrb" /><a + id="x1-103132r66"></a><span +class="cmr-6">66</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 28)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [predicted]</span><br class="fancyvrb" /><a + id="x1-103134r67"></a><span +class="cmr-6">67</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103136r68"></a><span +class="cmr-6">68</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103138r69"></a><span +class="cmr-6">69</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103140r70"></a><span +class="cmr-6">70</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103142r71"></a><span +class="cmr-6">71</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103144r72"></a><span +class="cmr-6">72</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 29)</span><span +class="cmtt-8"> done</span><br class="fancyvrb" /><a + id="x1-103146r73"></a><span +class="cmr-6">73</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> + </dd><dt class="description"> +<span +class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd +class="description"> + <!--l. 351--><p class="noindent" >Curve synthesis generates a return vector <span +class="cmtt-12">[floor] </span>of length <span +class="cmtt-12">[n] </span>(where <span +class="cmtt-12">[n] </span>is provided by + the decode process calling to floor decode). Floor 1 curve synthesis makes use of the + <span +class="cmtt-12">[floor1_X_list]</span>, <span +class="cmtt-12">[floor1_final_Y] </span>and <span +class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as + [floor1_multiplier] and [floor1_values] values. + <!--l. 358--><p class="noindent" >Decode begins by sorting the scalars from vectors <span +class="cmtt-12">[floor1_X_list]</span>, <span +class="cmtt-12">[floor1_final_Y] </span>and + <span +class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span +class="cmtt-12">[floor1_X_list]’</span>, <span +class="cmtt-12">[floor1_final_Y]’</span> + and <span +class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in + <span +class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span +class="cmtt-12">[floor1_X_list] </span>and then apply the same + permutation to elements of the other two vectors so that the X, Y and step2_flag values + still match. + <!--l. 368--><p class="noindent" >Then compute the final curve in one pass: + <!--l. 370--><p class="noindent" > + <div class="fancyvrb" id="fancyvrb32"><a + id="x1-103148r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [hx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-103150r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [lx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-103152r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [ly]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor1_final_Y]’</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [0]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [floor1_multiplier]</span> + <br class="fancyvrb" /><a + id="x1-103154r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [floor1_values]-1</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103156r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103158r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [floor1_step2_flag]’</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103160r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-103162r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> [hy]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [floor1_final_Y]’</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [floor1_multiplier]</span><br class="fancyvrb" /><a + id="x1-103164r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [hx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [floor1_X_list]’</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span> + <br class="fancyvrb" /><a + id="x1-103166r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> </span><a +href="#x1-1250009.2.7"><span +class="cmtt-8">render_line</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> [lx],</span><span +class="cmtt-8"> [ly],</span><span +class="cmtt-8"> [hx],</span><span +class="cmtt-8"> [hy],</span><span +class="cmtt-8"> [floor]</span><span +class="cmtt-8"> )</span><br class="fancyvrb" /><a + id="x1-103168r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [lx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [hx]</span><br class="fancyvrb" /><a + id="x1-103170r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> [ly]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [hy]</span> + <br class="fancyvrb" /><a + id="x1-103172r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103174r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103176r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103178r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [hx]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [n]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103180r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103182r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> </span><a +href="#x1-1250009.2.7"><span +class="cmtt-8">render_line</span></a><span +class="cmtt-8">(</span><span +class="cmtt-8"> [hx],</span><span +class="cmtt-8"> [hy],</span><span +class="cmtt-8"> [n],</span><span +class="cmtt-8"> [hy],</span><span +class="cmtt-8"> [floor]</span><span +class="cmtt-8"> )</span> + <br class="fancyvrb" /><a + id="x1-103184r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103186r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103188r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103190r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [hx]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [n]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> </span><span +class="cmsy-8">{</span><br class="fancyvrb" /><a + id="x1-103192r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103194r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> truncate</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor]</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> [n]</span><span +class="cmtt-8"> elements</span> + <br class="fancyvrb" /><a + id="x1-103196r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103198r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmsy-8">}</span><br class="fancyvrb" /><a + id="x1-103200r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103202r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> for</span><span +class="cmtt-8"> each</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [floor],</span><span +class="cmtt-8"> perform</span><span +class="cmtt-8"> a</span><span +class="cmtt-8"> lookup</span><span +class="cmtt-8"> substitution</span><span +class="cmtt-8"> using</span> + + + + <br class="fancyvrb" /><a + id="x1-103204r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> [floor]</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> an</span><span +class="cmtt-8"> offset</span><span +class="cmtt-8"> into</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> </span><a +href="#x1-12700010.1"><span +class="cmtt-8">[floor1_inverse_dB_static_table]</span></a><br class="fancyvrb" /><a + id="x1-103206r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-103208r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> done</span><br class="fancyvrb" /><a + id="x1-103210r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> + </dd></dl> + + + +<h3 class="sectionHead"><span class="titlemark">8. </span> <a + id="x1-1040008"></a>Residue setup and decode</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a + id="x1-1050008.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >A residue vector represents the fine detail of the audio spectrum of one channel in an audio frame +after the encoder subtracts the floor curve and performs any channel coupling. A residue vector +may represent spectral lines, spectral magnitude, spectral phase or hybrids as mixed by channel +coupling. The exact semantic content of the vector does not matter to the residue +abstraction. +<!--l. 15--><p class="noindent" >Whatever the exact qualities, the Vorbis residue abstraction codes the residue vectors into the +bitstream packet, and then reconstructs the vectors during decode. Vorbis makes use of three +different encoding variants (numbered 0, 1 and 2) of the same basic vector encoding +abstraction. +<!--l. 23--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.2. </span> <a + id="x1-1060008.2"></a>Residue format</h4> +<!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each +chunk, encodes the chunk classifications and finally encodes the chunks themselves +using the the specific VQ arrangement defined for each selected classification. The +exact interleaving and partitioning vary by residue encoding number, however the +high-level process used to classify and encode the residue vector is the same in all three +variants. +<!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for +the moment exactly how a partition is encoded and simply trusting that it is, is as +follows: + <ul class="itemize1"> + <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration + specified. If we have a vector size of <span +class="cmti-12">n</span>, a partition size <span +class="cmti-12">residue</span><span +class="cmti-12">_partition</span><span +class="cmti-12">_size</span>, + and a total of <span +class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded + + + + is <span +class="cmti-12">n</span>/<span +class="cmti-12">residue</span><span +class="cmti-12">_partition</span><span +class="cmti-12">_size</span>*<span +class="cmti-12">ch</span>. It is important to note that the integer division + truncates. In the below example, we assume an example <span +class="cmti-12">residue</span><span +class="cmti-12">_partition</span><span +class="cmti-12">_size </span>of 8. + </li> + <li class="itemize">Each partition in each vector has a classification number that specifies which of + multiple configured VQ codebook setups are used to decode that partition. The + classification numbers of each partition can be thought of as forming a vector in + their own right, as in the illustration below. Just as the residue vectors are coded + in grouped partitions to increase encoding efficiency, the classification vector is also + partitioned into chunks. The integer elements of each scalar in a classification chunk + are built into a single scalar that represents the classification numbers in that chunk. + In the below example, the classification codeword encodes two classification numbers. + </li> + <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through + the residue vector, but more often efficient codebook design dictates that each vector + is encoded as the additive sum of several passes through the residue vector using + more than one VQ codebook. Thus, each residue value potentially accumulates values + from multiple decode passes. The classification value associated with a partition is + the same in each pass, thus the classification codeword is coded only in the first pass. + </li></ul> +<div class="center" +> +<!--l. 70--><p class="noindent" > + +<!--l. 71--><p class="noindent" ><img +src="residue-pack.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 11: </span><span +class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10600111 --> +</div> +<!--l. 77--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a + id="x1-1070008.3"></a>residue 0</h4> +<!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during +partition encoding (visually treated as a black box–or cyan box or brown box–in the above +figure). +<!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to + + + +encode a partition in a specific pass. The dimension of the codebook need not be the same in +multiple passes, however the partition size must be an even multiple of the codebook +dimension. +<!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using +codebook sizes of 8, 4, 2 and 1: +<!--l. 92--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb33"><a + id="x1-107002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-107004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> original</span><span +class="cmtt-8"> residue</span><span +class="cmtt-8"> vector:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-107006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-107008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-107010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-107012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-107014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-107016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span> +<br class="fancyvrb" /><a + id="x1-107018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-107020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-107022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is +restricted to a power of two. +<!--l. 111--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a + id="x1-1080008.4"></a>residue 1</h4> +<!--l. 113--><p class="noindent" >Residue 1 does not interleave VQ encoding. It represents partition vector scalars in order. As +with residue 0, however, partition length must be an integer multiple of the codebook dimension, +although dimension may vary from pass to pass. +<!--l. 118--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using +codebook sizes of 8, 4, 2 and 1: +<!--l. 121--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb34"><a + id="x1-108002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-108004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> original</span><span +class="cmtt-8"> residue</span><span +class="cmtt-8"> vector:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-108006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-108008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-108010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-108012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-108014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-108016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span> +<br class="fancyvrb" /><a + id="x1-108018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-108020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> dimensions</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> encoded</span><span +class="cmtt-8"> as:</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 1</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 4</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 5</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> ],</span><span +class="cmtt-8"> [</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> ]</span><br class="fancyvrb" /><a + id="x1-108022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 137--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a + id="x1-1090008.5"></a>residue 2</h4> +<!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple +passed-in vectors as in residue type 1, the <span +class="cmti-12">ch </span>passed in vectors of length <span +class="cmti-12">n </span>are first interleaved +and flattened into a single vector of length <span +class="cmti-12">ch</span>*<span +class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding +is as in type 1 with decode interleave reversed. If operating on a single vector to begin with, +residue type 1 and type 2 are equivalent. + + + +<div class="center" +> +<!--l. 147--><p class="noindent" > + +<!--l. 148--><p class="noindent" ><img +src="residue2.png" alt="PIC" +> +<br /> <div class="caption" +><span class="id">Figure 12: </span><span +class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10900112 --> +</div> +<!--l. 153--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a + id="x1-1100008.6"></a>Residue decode</h4> +<!--l. 155--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a + id="x1-1110008.6.1"></a>header decode</h5> +<!--l. 157--><p class="noindent" >Header decode for all three residue types is identical. +<div class="fancyvrb" id="fancyvrb35"><a + id="x1-111002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [residue\_begin]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 24</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-111004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [residue\_end]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 24</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-111006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [residue\_partition\_size]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 24</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> one</span> +<br class="fancyvrb" /><a + id="x1-111008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [residue\_classifications]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 6</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> add</span><span +class="cmtt-8"> one</span><br class="fancyvrb" /><a + id="x1-111010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [residue\_classbook]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span></div> +<!--l. 166--><p class="noindent" ><span +class="cmtt-12">[residue_begin] </span>and <span +class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is +actually coded; it implements akin to a bandpass where, for coding purposes, the vector +effectively begins at element <span +class="cmtt-12">[residue_begin] </span>and ends at <span +class="cmtt-12">[residue_end]</span>. Preceding and +following values in the unpacked vectors are zeroed. Note that for residue type 2, these +values as well as <span +class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the +individual vectors before interleave. <span +class="cmtt-12">[residue_partition_size] </span>is as explained above, +<span +class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can +belong and <span +class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification +codewords. The number of dimensions in book <span +class="cmtt-12">[residue_classbook] </span>determines how +many classification values are grouped into a single classification codeword. Note that +the number of entries and dimensions in book <span +class="cmtt-12">[residue_classbook]</span>, along with +<span +class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification +codewords. If <span +class="cmtt-12">[residue_classifications]</span>ˆ<span +class="cmtt-12">[residue_classbook]</span>.dimensions exceeds +<span +class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable. + + + +<!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which +passes. +<!--l. 193--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb36"><a + id="x1-111012r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [residue\_classifications]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-111014r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111016r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [high\_bits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span> +<br class="fancyvrb" /><a + id="x1-111018r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [low\_bits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 3</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-111020r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [bitflag]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> one</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> boolean</span> +<br class="fancyvrb" /><a + id="x1-111022r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [bitflag]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> [high\_bits]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> five</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span> +<br class="fancyvrb" /><a + id="x1-111024r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [residue\_cascade]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [high\_bits]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [low\_bits]</span><br class="fancyvrb" /><a + id="x1-111026r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-111028r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> done</span></div> +<!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade +bitmap. We loop over the possible codebook classifications and the maximum possible number of +encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight +bits): +<!--l. 211--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb37"><a + id="x1-111030r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [residue\_classifications]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-111032r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111034r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-111036r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111038r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [residue\_cascade]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> set</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-111040r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-111042r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [residue\_books]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i][j]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> 8</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> as</span><span +class="cmtt-8"> unsigned</span><span +class="cmtt-8"> integer</span><br class="fancyvrb" /><a + id="x1-111044r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111046r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-111048r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-111050r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [residue\_books]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i][j]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> unused</span><br class="fancyvrb" /><a + id="x1-111052r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111054r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-111056r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-111058r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-111060r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-111062r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> done</span></div> +<!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable. +In addition, any codebook number greater than the maximum numbered codebook +set up in this stream also renders the stream undecodable. All codebooks in array +[residue_books] are required to have a value mapping. The presence of codebook in array +[residue_books] without a value mapping (maptype equals zero) renders the stream +undecodable. +<!--l. 241--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a + id="x1-1120008.6.2"></a>packet decode</h5> +<!--l. 243--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet +decode can be built out of the format 1 decode process. Thus we describe first the decode +infrastructure identical to all three formats. +<!--l. 248--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of +vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be +decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’, +decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are +allocated and zeroed. +<!--l. 255--><p class="noindent" >Depending on the values of <span +class="cmtt-12">[residue_begin] </span>and <span +class="cmtt-12">[residue_end]</span>, it is obvious that the +encoded portion of a residue vector may be the entire possible residue vector or some other strict +subset of the actual residue vector size with zero padding at either uncoded end. However, it is + + + +also possible to set <span +class="cmtt-12">[residue_begin] </span>and <span +class="cmtt-12">[residue_end] </span>to specify a range partially or wholly +beyond the maximum vector size. Before beginning residue decode, limit <span +class="cmtt-12">[residue_begin]</span> +and <span +class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that +the number of vectors being encoded, <span +class="cmtt-12">[ch] </span>is provided by the higher level decoding +process. +<!--l. 269--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb38"><a + id="x1-112002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [actual\_size]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> current</span><span +class="cmtt-8"> blocksize/2;</span><br class="fancyvrb" /><a + id="x1-112004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> residue</span><span +class="cmtt-8"> encoding</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> format</span><span +class="cmtt-8"> 2</span> +<br class="fancyvrb" /><a + id="x1-112006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [actual\_size]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [actual\_size]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [ch];</span><br class="fancyvrb" /><a + id="x1-112008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [limit\_residue\_begin]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> minimum</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> ([residue\_begin],[actual\_size]);</span> +<br class="fancyvrb" /><a + id="x1-112010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [limit\_residue\_end]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> minimum</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> ([residue\_end],[actual\_size]);</span></div> +<!--l. 277--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process: +<!--l. 280--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb39"><a + id="x1-112012r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [classwords\_per\_codeword]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [codebook\_dimensions]</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> [residue\_classbook]</span> +<br class="fancyvrb" /><a + id="x1-112014r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [n\_to\_read]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [limit\_residue\_end]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [limit\_residue\_begin]</span><br class="fancyvrb" /><a + id="x1-112016r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [partitions\_to\_read]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [n\_to\_read]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> [residue\_partition\_size]</span></div> +<!--l. 286--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document. +<div class="fancyvrb" id="fancyvrb40"><a + id="x1-112018r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> allocate</span><span +class="cmtt-8"> and</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> all</span><span +class="cmtt-8"> vectors</span><span +class="cmtt-8"> that</span><span +class="cmtt-8"> will</span><span +class="cmtt-8"> be</span><span +class="cmtt-8"> returned.</span><br class="fancyvrb" /><a + id="x1-112020r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> ([n\_to\_read]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> zero),</span><span +class="cmtt-8"> stop;</span><span +class="cmtt-8"> there</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> no</span><span +class="cmtt-8"> residue</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> decode.</span> +<br class="fancyvrb" /><a + id="x1-112022r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [pass]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> 7</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-112024r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112026r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [partition\_count]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-112028r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-112030r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> while</span><span +class="cmtt-8"> [partition\_count]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [partitions\_to\_read]</span><br class="fancyvrb" /><a + id="x1-112032r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112034r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> ([pass]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> zero)</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-112036r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-112038r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ..</span><span +class="cmtt-8"> [ch]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-112040r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112042r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> marked</span><span +class="cmtt-8"> ’do</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> decode’</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-112044r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112046r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [temp]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> [residue\_classbook]</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> scalar</span><span +class="cmtt-8"> context</span> +<br class="fancyvrb" /><a + id="x1-112048r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> descending</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> [classwords\_per\_codeword]-1</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-112050r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112052r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [classifications]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [j],([i]+[partition\_count])</span><span +class="cmtt-8"> =</span> +<br class="fancyvrb" /><a + id="x1-112054r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [temp]</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> modulo</span><span +class="cmtt-8"> [residue\_classifications]</span> +<br class="fancyvrb" /><a + id="x1-112056r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> [temp]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [temp]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> [residue\_classifications]</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> division</span><br class="fancyvrb" /><a + id="x1-112058r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-112060r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112062r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112064r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112066r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112068r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112070r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112072r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112074r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-112076r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ..</span><span +class="cmtt-8"> ([classwords\_per\_codeword]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> while</span><span +class="cmtt-8"> [partition\_count]</span> +<br class="fancyvrb" /><a + id="x1-112078r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> also</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [partitions\_to\_read]</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-112080r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112082r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ..</span><span +class="cmtt-8"> [ch]-1</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-112084r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112086r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> marked</span><span +class="cmtt-8"> ’do</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> decode’</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-112088r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-112090r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> [vqclass]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [classifications]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [j],[partition\_count]</span> +<br class="fancyvrb" /><a + id="x1-112092r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 17)</span><span +class="cmtt-8"> [vqbook]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> array</span><span +class="cmtt-8"> [residue\_books]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [vqclass],[pass]</span><br class="fancyvrb" /><a + id="x1-112094r39"></a><span +class="cmr-6">39</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 18)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> ([vqbook]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> not</span><span +class="cmtt-8"> ’unused’)</span><span +class="cmtt-8"> {</span> +<br class="fancyvrb" /><a + id="x1-112096r40"></a><span +class="cmr-6">40</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112098r41"></a><span +class="cmr-6">41</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 19)</span><span +class="cmtt-8"> decode</span><span +class="cmtt-8"> partition</span><span +class="cmtt-8"> into</span><span +class="cmtt-8"> output</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [j],</span><span +class="cmtt-8"> starting</span><span +class="cmtt-8"> at</span><span +class="cmtt-8"> scalar</span> +<br class="fancyvrb" /><a + id="x1-112100r42"></a><span +class="cmr-6">42</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> offset</span><span +class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span +class="cmtt-8"> using</span> +<br class="fancyvrb" /><a + id="x1-112102r43"></a><span +class="cmr-6">43</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [vqbook]</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> VQ</span><span +class="cmtt-8"> context</span><br class="fancyvrb" /><a + id="x1-112104r44"></a><span +class="cmr-6">44</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112106r45"></a><span +class="cmr-6">45</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span> +<br class="fancyvrb" /><a + id="x1-112108r46"></a><span +class="cmr-6">46</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112110r47"></a><span +class="cmr-6">47</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 20)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [partition\_count]</span><span +class="cmtt-8"> by</span><span +class="cmtt-8"> one</span><br class="fancyvrb" /><a + id="x1-112112r48"></a><span +class="cmr-6">48</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112114r49"></a><span +class="cmr-6">49</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112116r50"></a><span +class="cmr-6">50</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112118r51"></a><span +class="cmr-6">51</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-112120r52"></a><span +class="cmr-6">52</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-112122r53"></a><span +class="cmr-6">53</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 21)</span><span +class="cmtt-8"> done</span><br class="fancyvrb" /><a + id="x1-112124r54"></a><span +class="cmr-6">54</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 344--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence. +Decode returns the result of vector decode up to that point. +<!--l. 350--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a + id="x1-1130008.6.3"></a>format 0 specifics</h5> +<!--l. 352--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’ +section. The following pseudocode presents the same algorithm. Assume: + + + + <ul class="itemize1"> + <li class="itemize"><span +class="cmtt-12">[n] </span>is the value in <span +class="cmtt-12">[residue_partition_size]</span> + </li> + <li class="itemize"><span +class="cmtt-12">[v] </span>is the residue vector + </li> + <li class="itemize"><span +class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul> +<!--l. 363--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb41"><a + id="x1-113002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [step]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [n]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> [codebook\_dimensions]</span><br class="fancyvrb" /><a + id="x1-113004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [step]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-113006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-113008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [entry\_temp]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> current</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> VQ</span><span +class="cmtt-8"> context</span> +<br class="fancyvrb" /><a + id="x1-113010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [codebook\_dimensions]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-113012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-113014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span +class="cmtt-8"> =</span> +<br class="fancyvrb" /><a + id="x1-113016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span +class="cmtt-8"> +</span><br class="fancyvrb" /><a + id="x1-113018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [entry\_temp]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [j]</span><br class="fancyvrb" /><a + id="x1-113020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-113022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-113024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-113026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-113028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-113030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> done</span><br class="fancyvrb" /><a + id="x1-113032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span></div> +<!--l. 384--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a + id="x1-1140008.6.4"></a>format 1 specifics</h5> +<!--l. 386--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’ +section. The following pseudocode presents the same algorithm. Assume: + <ul class="itemize1"> + <li class="itemize"><span +class="cmtt-12">[n] </span>is the value in <span +class="cmtt-12">[residue_partition_size]</span> + </li> + <li class="itemize"><span +class="cmtt-12">[v] </span>is the residue vector + </li> + <li class="itemize"><span +class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul> +<!--l. 398--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb42"><a + id="x1-114002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-114004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [entry\_temp]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> read</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> from</span><span +class="cmtt-8"> packet</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> current</span><span +class="cmtt-8"> codebook</span><span +class="cmtt-8"> in</span><span +class="cmtt-8"> VQ</span><span +class="cmtt-8"> context</span> +<br class="fancyvrb" /><a + id="x1-114006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [codebook\_dimensions]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-114008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-114010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([offset]+[i])</span><span +class="cmtt-8"> =</span> +<br class="fancyvrb" /><a + id="x1-114012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8">  </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([offset]+[i])</span><span +class="cmtt-8"> +</span><br class="fancyvrb" /><a + id="x1-114014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [entry\_temp]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [j]</span><br class="fancyvrb" /><a + id="x1-114016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [i]</span><br class="fancyvrb" /><a + id="x1-114018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-114020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-114022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-114024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> [n]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> continue</span><span +class="cmtt-8"> at</span><span +class="cmtt-8"> step</span><span +class="cmtt-8"> 2</span><br class="fancyvrb" /><a + id="x1-114026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> done</span></div> +<!--l. 416--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a + id="x1-1150008.6.5"></a>format 2 specifics</h5> + + + +<!--l. 418--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an +additional post-decode step after a normal format 1 decode. +<!--l. 421--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked +’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all +the vectors are decoded. We then request normal format 1 to decode a single vector +representing all output channels, rather than a vector for each channel. After decode, +deinterleave the vector into independent vectors, one for each output channel. That +is: +<!--l. 429--><p class="noindent" > + <dl class="enumerate-enumitem"><dt class="enumerate-enumitem"> + 1. </dt><dd +class="enumerate-enumitem">If all vectors 0 through <span +class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single + vector <span +class="cmtt-12">[v]</span>of length <span +class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode + step. + </dd><dt class="enumerate-enumitem"> + 2. </dt><dd +class="enumerate-enumitem">Rather than performing format 1 decode to produce <span +class="cmti-12">ch </span>vectors of length <span +class="cmti-12">n </span>each, call + format 1 decode to produce a single vector <span +class="cmtt-12">[v] </span>of length <span +class="cmti-12">ch*n</span>. + </dd><dt class="enumerate-enumitem"> + 3. </dt><dd +class="enumerate-enumitem">Post decode: Deinterleave the single vector <span +class="cmtt-12">[v] </span>returned by format 1 decode as + described above into <span +class="cmti-12">ch </span>independent vectors, one for each outputchannel, according + to: + <div class="fancyvrb" id="fancyvrb43"><a + id="x1-115005r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [n]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-115007r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-115009r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [ch]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-115011r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> + <br class="fancyvrb" /><a + id="x1-115013r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> output</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> number</span><span +class="cmtt-8"> [j]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [i]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> ([i]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [ch]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [j])</span><br class="fancyvrb" /><a + id="x1-115015r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-115017r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-115019r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-115021r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-115023r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> done</span></div> + </dd></dl> + + + + + + +<h3 class="sectionHead"><span class="titlemark">9. </span> <a + id="x1-1160009"></a>Helper equations</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a + id="x1-1170009.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >The equations below are used in multiple places by the Vorbis codec specification. Rather than +cluttering up the main specification documents, they are defined here and referenced where +appropriate. +<!--l. 13--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">9.2. </span> <a + id="x1-1180009.2"></a>Functions</h4> +<!--l. 15--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a + id="x1-1190009.2.1"></a>ilog</h5> +<!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the +two’s complement integer value <span +class="cmtt-12">[x]</span>. Values of <span +class="cmtt-12">[x] </span>less than zero are defined to return +zero. +<!--l. 20--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb44"><a + id="x1-119002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [return\_value]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0;</span><br class="fancyvrb" /><a + id="x1-119004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> greater</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-119006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-119008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> increment</span><span +class="cmtt-8"> [return\_value];</span> +<br class="fancyvrb" /><a + id="x1-119010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> logical</span><span +class="cmtt-8"> shift</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> one</span><span +class="cmtt-8"> bit</span><span +class="cmtt-8"> to</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> right,</span><span +class="cmtt-8"> padding</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> MSb</span><span +class="cmtt-8"> with</span><span +class="cmtt-8"> zero</span><br class="fancyvrb" /><a + id="x1-119012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> repeat</span><span +class="cmtt-8"> at</span><span +class="cmtt-8"> step</span><span +class="cmtt-8"> 2)</span><br class="fancyvrb" /><a + id="x1-119014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-119016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-119018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-119020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> done</span></div> +<!--l. 33--><p class="noindent" >Examples: + <ul class="itemize1"> + <li class="itemize">ilog(0) = 0; + </li> + <li class="itemize">ilog(1) = 1; + + + + </li> + <li class="itemize">ilog(2) = 2; + </li> + <li class="itemize">ilog(3) = 2; + </li> + <li class="itemize">ilog(4) = 3; + </li> + <li class="itemize">ilog(7) = 3; + </li> + <li class="itemize">ilog(negative number) = 0;</li></ul> +<!--l. 48--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a + id="x1-1200009.2.2"></a>float32_unpack</h5> +<!--l. 50--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis +codebook float value into the representation used by the decoder for floating point numbers. For +purposes of this example, we will unpack a Vorbis float32 into a host-native floating point +number. +<!--l. 56--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb45"><a + id="x1-120002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> [mantissa]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> bitwise</span><span +class="cmtt-8"> AND</span><span +class="cmtt-8"> 0x1fffff</span><span +class="cmtt-8"> (unsigned</span><span +class="cmtt-8"> result)</span><br class="fancyvrb" /><a + id="x1-120004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [sign]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> bitwise</span><span +class="cmtt-8"> AND</span><span +class="cmtt-8"> 0x80000000</span><span +class="cmtt-8"> (unsigned</span><span +class="cmtt-8"> result)</span> +<br class="fancyvrb" /><a + id="x1-120006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [exponent]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> bitwise</span><span +class="cmtt-8"> AND</span><span +class="cmtt-8"> 0x7fe00000)</span><span +class="cmtt-8"> shifted</span><span +class="cmtt-8"> right</span><span +class="cmtt-8"> 21</span><span +class="cmtt-8"> bits</span><span +class="cmtt-8"> (unsigned</span><span +class="cmtt-8"> result)</span> +<br class="fancyvrb" /><a + id="x1-120008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [sign]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> nonzero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> then</span><span +class="cmtt-8"> negate</span><span +class="cmtt-8"> [mantissa]</span><br class="fancyvrb" /><a + id="x1-120010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> return</span><span +class="cmtt-8"> [mantissa]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> 2</span><span +class="cmtt-8"> ^</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [exponent]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> 788</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> )</span></div> +<!--l. 66--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a + id="x1-1210009.2.3"></a>lookup1_values</h5> +<!--l. 68--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the +correct length of the value index for a codebook VQ lookup table of lookup type 1. +The values on this list are permuted to construct the VQ vector lookup table of size +<span +class="cmtt-12">[codebook_entries]</span>. +<!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which +<span +class="cmtt-12">[return_value] </span>to the power of <span +class="cmtt-12">[codebook_dimensions] </span>is less than or equal to +<span +class="cmtt-12">[codebook_entries]</span>’. + + + +<!--l. 81--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a + id="x1-1220009.2.4"></a>low_neighbor</h5> +<!--l. 83--><p class="noindent" >”low_neighbor(v,x)” finds the position <span +class="cmtt-12">n </span>in vector <span +class="cmtt-12">[v] </span>of the greatest value scalar element for +which <span +class="cmtt-12">n </span>is less than <span +class="cmtt-12">[x] </span>and vector <span +class="cmtt-12">[v] </span>element <span +class="cmtt-12">n </span>is less than vector <span +class="cmtt-12">[v] </span>element +<span +class="cmtt-12">[x]</span>. +<!--l. 88--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a + id="x1-1230009.2.5"></a>high_neighbor</h5> +<!--l. 90--><p class="noindent" >”high_neighbor(v,x)” finds the position <span +class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for +which <span +class="cmtt-12">n </span>is less than <span +class="cmtt-12">[x] </span>and vector <span +class="cmtt-12">[v] </span>element <span +class="cmtt-12">n </span>is greater than vector <span +class="cmtt-12">[v] </span>element +<span +class="cmtt-12">[x]</span>. +<!--l. 97--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a + id="x1-1240009.2.6"></a>render_point</h5> +<!--l. 99--><p class="noindent" >”render_point(x0,y0,x1,y1,X)” is used to find the Y value at point X along the line specified by +x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without +calculating intervening values along the line. +<!--l. 104--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb46"><a + id="x1-124002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [dy]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y1]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a + id="x1-124004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> [adx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [x1]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a + id="x1-124006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> [ady]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> absolute</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a + id="x1-124008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [ady]</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> ([X]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [x0])</span> +<br class="fancyvrb" /><a + id="x1-124010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> [off]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> [adx]</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> division</span><br class="fancyvrb" /><a + id="x1-124012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [dy]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> zero</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-124014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-124016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> [Y]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y0]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [off]</span> +<br class="fancyvrb" /><a + id="x1-124018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-124020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-124022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-124024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> [Y]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y0]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [off]</span><br class="fancyvrb" /><a + id="x1-124026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-124028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-124030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-124032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> done</span></div> +<!--l. 125--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a + id="x1-1250009.2.7"></a>render_line</h5> + + + +<!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)” +to construct an integer floor curve for contiguous piecewise line segments. Note that it has not +been relevant elsewhere, but here we must define integer division as rounding division of both +positive and negative numbers toward zero. +<!--l. 134--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb47"><a + id="x1-125002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [dy]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y1]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a + id="x1-125004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [adx]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [x1]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a + id="x1-125006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [ady]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> absolute</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [dy]</span><br class="fancyvrb" /><a + id="x1-125008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4)</span><span +class="cmtt-8"> [base]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [dy]</span><span +class="cmtt-8"> /</span><span +class="cmtt-8"> [adx]</span><span +class="cmtt-8"> using</span><span +class="cmtt-8"> integer</span><span +class="cmtt-8"> division</span> +<br class="fancyvrb" /><a + id="x1-125010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [x0]</span><br class="fancyvrb" /><a + id="x1-125012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [y]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y0]</span><br class="fancyvrb" /><a + id="x1-125014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> 0</span><br class="fancyvrb" /><a + id="x1-125016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 8)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [dy]</span><span +class="cmtt-8"> is</span><span +class="cmtt-8"> less</span><span +class="cmtt-8"> than</span><span +class="cmtt-8"> 0</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-125020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9)</span><span +class="cmtt-8"> [sy]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [base]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> 1</span> +<br class="fancyvrb" /><a + id="x1-125024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-125028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 10)</span><span +class="cmtt-8"> [sy]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [base]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> 1</span><br class="fancyvrb" /><a + id="x1-125032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125034r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-125036r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125038r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 11)</span><span +class="cmtt-8"> [ady]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [ady]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> (absolute</span><span +class="cmtt-8"> value</span><span +class="cmtt-8"> of</span><span +class="cmtt-8"> [base])</span><span +class="cmtt-8"> *</span><span +class="cmtt-8"> [adx]</span> +<br class="fancyvrb" /><a + id="x1-125040r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 12)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y]</span><br class="fancyvrb" /><a + id="x1-125042r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125044r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 13)</span><span +class="cmtt-8"> iterate</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> over</span><span +class="cmtt-8"> the</span><span +class="cmtt-8"> range</span><span +class="cmtt-8"> [x0]+1</span><span +class="cmtt-8"> ...</span><span +class="cmtt-8"> [x1]-1</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-125046r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125048r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 14)</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [ady];</span> +<br class="fancyvrb" /><a + id="x1-125050r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 15)</span><span +class="cmtt-8"> if</span><span +class="cmtt-8"> (</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> >=</span><span +class="cmtt-8"> [adx]</span><span +class="cmtt-8"> )</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-125052r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125054r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 16)</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [err]</span><span +class="cmtt-8"> -</span><span +class="cmtt-8"> [adx]</span><br class="fancyvrb" /><a + id="x1-125056r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 17)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [y]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [sy]</span><br class="fancyvrb" /><a + id="x1-125058r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span> +<br class="fancyvrb" /><a + id="x1-125060r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><span +class="cmtt-8"> else</span><span +class="cmtt-8"> {</span><br class="fancyvrb" /><a + id="x1-125062r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125064r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 18)</span><span +class="cmtt-8"> [y]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y]</span><span +class="cmtt-8"> +</span><span +class="cmtt-8"> [base]</span><br class="fancyvrb" /><a + id="x1-125066r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125068r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span><br class="fancyvrb" /><a + id="x1-125070r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125072r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 19)</span><span +class="cmtt-8"> vector</span><span +class="cmtt-8"> [v]</span><span +class="cmtt-8"> element</span><span +class="cmtt-8"> [x]</span><span +class="cmtt-8"> =</span><span +class="cmtt-8"> [y]</span><br class="fancyvrb" /><a + id="x1-125074r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><br class="fancyvrb" /><a + id="x1-125076r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> }</span></div> + + + + + + +<h3 class="sectionHead"><span class="titlemark">10. </span> <a + id="x1-12600010"></a>Tables</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a + id="x1-12700010.1"></a>floor1_inverse_dB_table</h4> +<!--l. 8--><p class="noindent" >The vector <span +class="cmtt-12">[floor1_inverse_dB_table] </span>is a 256 element static lookup table consisting of the +following values (read left to right then top to bottom): +<!--l. 12--><p class="noindent" > +<div class="fancyvrb" id="fancyvrb48"><a + id="x1-127002r1"></a><span +class="cmr-6">1</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.0649863e-07,</span><span +class="cmtt-8"> 1.1341951e-07,</span><span +class="cmtt-8"> 1.2079015e-07,</span><span +class="cmtt-8"> 1.2863978e-07,</span><br class="fancyvrb" /><a + id="x1-127004r2"></a><span +class="cmr-6">2</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.3699951e-07,</span><span +class="cmtt-8"> 1.4590251e-07,</span><span +class="cmtt-8"> 1.5538408e-07,</span><span +class="cmtt-8"> 1.6548181e-07,</span> +<br class="fancyvrb" /><a + id="x1-127006r3"></a><span +class="cmr-6">3</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.7623575e-07,</span><span +class="cmtt-8"> 1.8768855e-07,</span><span +class="cmtt-8"> 1.9988561e-07,</span><span +class="cmtt-8"> 2.1287530e-07,</span><br class="fancyvrb" /><a + id="x1-127008r4"></a><span +class="cmr-6">4</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.2670913e-07,</span><span +class="cmtt-8"> 2.4144197e-07,</span><span +class="cmtt-8"> 2.5713223e-07,</span><span +class="cmtt-8"> 2.7384213e-07,</span> +<br class="fancyvrb" /><a + id="x1-127010r5"></a><span +class="cmr-6">5</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.9163793e-07,</span><span +class="cmtt-8"> 3.1059021e-07,</span><span +class="cmtt-8"> 3.3077411e-07,</span><span +class="cmtt-8"> 3.5226968e-07,</span><br class="fancyvrb" /><a + id="x1-127012r6"></a><span +class="cmr-6">6</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3.7516214e-07,</span><span +class="cmtt-8"> 3.9954229e-07,</span><span +class="cmtt-8"> 4.2550680e-07,</span><span +class="cmtt-8"> 4.5315863e-07,</span> +<br class="fancyvrb" /><a + id="x1-127014r7"></a><span +class="cmr-6">7</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4.8260743e-07,</span><span +class="cmtt-8"> 5.1396998e-07,</span><span +class="cmtt-8"> 5.4737065e-07,</span><span +class="cmtt-8"> 5.8294187e-07,</span><br class="fancyvrb" /><a + id="x1-127016r8"></a><span +class="cmr-6">8</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 6.2082472e-07,</span><span +class="cmtt-8"> 6.6116941e-07,</span><span +class="cmtt-8"> 7.0413592e-07,</span><span +class="cmtt-8"> 7.4989464e-07,</span> +<br class="fancyvrb" /><a + id="x1-127018r9"></a><span +class="cmr-6">9</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7.9862701e-07,</span><span +class="cmtt-8"> 8.5052630e-07,</span><span +class="cmtt-8"> 9.0579828e-07,</span><span +class="cmtt-8"> 9.6466216e-07,</span><br class="fancyvrb" /><a + id="x1-127020r10"></a><span +class="cmr-6">10</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.0273513e-06,</span><span +class="cmtt-8"> 1.0941144e-06,</span><span +class="cmtt-8"> 1.1652161e-06,</span><span +class="cmtt-8"> 1.2409384e-06,</span> +<br class="fancyvrb" /><a + id="x1-127022r11"></a><span +class="cmr-6">11</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.3215816e-06,</span><span +class="cmtt-8"> 1.4074654e-06,</span><span +class="cmtt-8"> 1.4989305e-06,</span><span +class="cmtt-8"> 1.5963394e-06,</span><br class="fancyvrb" /><a + id="x1-127024r12"></a><span +class="cmr-6">12</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.7000785e-06,</span><span +class="cmtt-8"> 1.8105592e-06,</span><span +class="cmtt-8"> 1.9282195e-06,</span><span +class="cmtt-8"> 2.0535261e-06,</span> +<br class="fancyvrb" /><a + id="x1-127026r13"></a><span +class="cmr-6">13</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.1869758e-06,</span><span +class="cmtt-8"> 2.3290978e-06,</span><span +class="cmtt-8"> 2.4804557e-06,</span><span +class="cmtt-8"> 2.6416497e-06,</span><br class="fancyvrb" /><a + id="x1-127028r14"></a><span +class="cmr-6">14</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.8133190e-06,</span><span +class="cmtt-8"> 2.9961443e-06,</span><span +class="cmtt-8"> 3.1908506e-06,</span><span +class="cmtt-8"> 3.3982101e-06,</span> +<br class="fancyvrb" /><a + id="x1-127030r15"></a><span +class="cmr-6">15</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3.6190449e-06,</span><span +class="cmtt-8"> 3.8542308e-06,</span><span +class="cmtt-8"> 4.1047004e-06,</span><span +class="cmtt-8"> 4.3714470e-06,</span><br class="fancyvrb" /><a + id="x1-127032r16"></a><span +class="cmr-6">16</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4.6555282e-06,</span><span +class="cmtt-8"> 4.9580707e-06,</span><span +class="cmtt-8"> 5.2802740e-06,</span><span +class="cmtt-8"> 5.6234160e-06,</span> +<br class="fancyvrb" /><a + id="x1-127034r17"></a><span +class="cmr-6">17</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5.9888572e-06,</span><span +class="cmtt-8"> 6.3780469e-06,</span><span +class="cmtt-8"> 6.7925283e-06,</span><span +class="cmtt-8"> 7.2339451e-06,</span><br class="fancyvrb" /><a + id="x1-127036r18"></a><span +class="cmr-6">18</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7.7040476e-06,</span><span +class="cmtt-8"> 8.2047000e-06,</span><span +class="cmtt-8"> 8.7378876e-06,</span><span +class="cmtt-8"> 9.3057248e-06,</span> +<br class="fancyvrb" /><a + id="x1-127038r19"></a><span +class="cmr-6">19</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9.9104632e-06,</span><span +class="cmtt-8"> 1.0554501e-05,</span><span +class="cmtt-8"> 1.1240392e-05,</span><span +class="cmtt-8"> 1.1970856e-05,</span><br class="fancyvrb" /><a + id="x1-127040r20"></a><span +class="cmr-6">20</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.2748789e-05,</span><span +class="cmtt-8"> 1.3577278e-05,</span><span +class="cmtt-8"> 1.4459606e-05,</span><span +class="cmtt-8"> 1.5399272e-05,</span> +<br class="fancyvrb" /><a + id="x1-127042r21"></a><span +class="cmr-6">21</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.6400004e-05,</span><span +class="cmtt-8"> 1.7465768e-05,</span><span +class="cmtt-8"> 1.8600792e-05,</span><span +class="cmtt-8"> 1.9809576e-05,</span><br class="fancyvrb" /><a + id="x1-127044r22"></a><span +class="cmr-6">22</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.1096914e-05,</span><span +class="cmtt-8"> 2.2467911e-05,</span><span +class="cmtt-8"> 2.3928002e-05,</span><span +class="cmtt-8"> 2.5482978e-05,</span> +<br class="fancyvrb" /><a + id="x1-127046r23"></a><span +class="cmr-6">23</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 2.7139006e-05,</span><span +class="cmtt-8"> 2.8902651e-05,</span><span +class="cmtt-8"> 3.0780908e-05,</span><span +class="cmtt-8"> 3.2781225e-05,</span><br class="fancyvrb" /><a + id="x1-127048r24"></a><span +class="cmr-6">24</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 3.4911534e-05,</span><span +class="cmtt-8"> 3.7180282e-05,</span><span +class="cmtt-8"> 3.9596466e-05,</span><span +class="cmtt-8"> 4.2169667e-05,</span> +<br class="fancyvrb" /><a + id="x1-127050r25"></a><span +class="cmr-6">25</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 4.4910090e-05,</span><span +class="cmtt-8"> 4.7828601e-05,</span><span +class="cmtt-8"> 5.0936773e-05,</span><span +class="cmtt-8"> 5.4246931e-05,</span><br class="fancyvrb" /><a + id="x1-127052r26"></a><span +class="cmr-6">26</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 5.7772202e-05,</span><span +class="cmtt-8"> 6.1526565e-05,</span><span +class="cmtt-8"> 6.5524908e-05,</span><span +class="cmtt-8"> 6.9783085e-05,</span> +<br class="fancyvrb" /><a + id="x1-127054r27"></a><span +class="cmr-6">27</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 7.4317983e-05,</span><span +class="cmtt-8"> 7.9147585e-05,</span><span +class="cmtt-8"> 8.4291040e-05,</span><span +class="cmtt-8"> 8.9768747e-05,</span><br class="fancyvrb" /><a + id="x1-127056r28"></a><span +class="cmr-6">28</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 9.5602426e-05,</span><span +class="cmtt-8"> 0.00010181521,</span><span +class="cmtt-8"> 0.00010843174,</span><span +class="cmtt-8"> 0.00011547824,</span> +<br class="fancyvrb" /><a + id="x1-127058r29"></a><span +class="cmr-6">29</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00012298267,</span><span +class="cmtt-8"> 0.00013097477,</span><span +class="cmtt-8"> 0.00013948625,</span><span +class="cmtt-8"> 0.00014855085,</span><br class="fancyvrb" /><a + id="x1-127060r30"></a><span +class="cmr-6">30</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00015820453,</span><span +class="cmtt-8"> 0.00016848555,</span><span +class="cmtt-8"> 0.00017943469,</span><span +class="cmtt-8"> 0.00019109536,</span> +<br class="fancyvrb" /><a + id="x1-127062r31"></a><span +class="cmr-6">31</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00020351382,</span><span +class="cmtt-8"> 0.00021673929,</span><span +class="cmtt-8"> 0.00023082423,</span><span +class="cmtt-8"> 0.00024582449,</span><br class="fancyvrb" /><a + id="x1-127064r32"></a><span +class="cmr-6">32</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00026179955,</span><span +class="cmtt-8"> 0.00027881276,</span><span +class="cmtt-8"> 0.00029693158,</span><span +class="cmtt-8"> 0.00031622787,</span> +<br class="fancyvrb" /><a + id="x1-127066r33"></a><span +class="cmr-6">33</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00033677814,</span><span +class="cmtt-8"> 0.00035866388,</span><span +class="cmtt-8"> 0.00038197188,</span><span +class="cmtt-8"> 0.00040679456,</span><br class="fancyvrb" /><a + id="x1-127068r34"></a><span +class="cmr-6">34</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00043323036,</span><span +class="cmtt-8"> 0.00046138411,</span><span +class="cmtt-8"> 0.00049136745,</span><span +class="cmtt-8"> 0.00052329927,</span> +<br class="fancyvrb" /><a + id="x1-127070r35"></a><span +class="cmr-6">35</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00055730621,</span><span +class="cmtt-8"> 0.00059352311,</span><span +class="cmtt-8"> 0.00063209358,</span><span +class="cmtt-8"> 0.00067317058,</span><br class="fancyvrb" /><a + id="x1-127072r36"></a><span +class="cmr-6">36</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00071691700,</span><span +class="cmtt-8"> 0.00076350630,</span><span +class="cmtt-8"> 0.00081312324,</span><span +class="cmtt-8"> 0.00086596457,</span> +<br class="fancyvrb" /><a + id="x1-127074r37"></a><span +class="cmr-6">37</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.00092223983,</span><span +class="cmtt-8"> 0.00098217216,</span><span +class="cmtt-8"> 0.0010459992,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0011139742,</span><br class="fancyvrb" /><a + id="x1-127076r38"></a><span +class="cmr-6">38</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0011863665,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0012634633,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0013455702,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0014330129,</span> +<br class="fancyvrb" /><a + id="x1-127078r39"></a><span +class="cmr-6">39</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0015261382,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0016253153,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0017309374,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0018434235,</span><br class="fancyvrb" /><a + id="x1-127080r40"></a><span +class="cmr-6">40</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0019632195,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0020908006,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0022266726,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0023713743,</span> +<br class="fancyvrb" /><a + id="x1-127082r41"></a><span +class="cmr-6">41</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0025254795,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0026895994,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0028643847,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0030505286,</span><br class="fancyvrb" /><a + id="x1-127084r42"></a><span +class="cmr-6">42</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0032487691,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0034598925,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0036847358,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0039241906,</span> +<br class="fancyvrb" /><a + id="x1-127086r43"></a><span +class="cmr-6">43</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0041792066,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0044507950,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.0047400328,</span><span 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+class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.77736504,</span><br class="fancyvrb" /><a + id="x1-127128r64"></a><span +class="cmr-6">64</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.82788260,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.88168307,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 0.9389798,</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> 1.</span></div> + + + + + + +<h3 class="sectionHead"><span class="titlemark">A. </span> <a + id="x1-128000A"></a>Embedding Vorbis into an Ogg stream</h3> +<!--l. 6--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a + id="x1-129000A.1"></a>Overview</h4> +<!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis +compressed audio packet data into file form. +<!--l. 12--><p class="noindent" >The <a +href="#x1-20001">section 1</a>, “<a +href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of Vorbis +audio packets. +<!--l. 15--><p class="noindent" >The <a +href="oggstream.html" >Ogg bitstream overview</a> and <a +href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed +descriptions of Ogg transport streams. This specification document assumes a working +knowledge of the concepts covered in these named backround documents. Please read them +first. +<!--l. 22--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a + id="x1-130000A.1.1"></a>Restrictions</h5> +<!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport +streams in degenerate, unmultiplexed form only. That is: + <ul class="itemize1"> + <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets + </li> + <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams + (links). + </li> + <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream, + per link) + </li></ul> + + + +<!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media +types into a multi-stream Ogg file. At the time this document was written, Ogg was +becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis +audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone +within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to +implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg +stream (naturally, application authors are encouraged to support full multiplexed Ogg +handling). +<!--l. 55--><p class="noindent" > +<h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a + id="x1-131000A.1.2"></a>MIME type</h5> +<!--l. 57--><p class="noindent" >The MIME type of Ogg files depend on the context. Specifically, complex multimedia and +applications should use <span +class="cmtt-12">application/ogg</span>, while visual media should use <span +class="cmtt-12">video/ogg</span>, and audio +<span +class="cmtt-12">audio/ogg</span>. Vorbis data encapsulated in Ogg may appear in any of those types. RTP +encapsulated Vorbis should use <span +class="cmtt-12">audio/vorbis </span>+ <span +class="cmtt-12">audio/vorbis-config</span>. +<!--l. 65--><p class="noindent" > +<h4 class="subsectionHead"><span class="titlemark">A.2. </span> <a + id="x1-132000A.2"></a>Encapsulation</h4> +<!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward. + <ul class="itemize1"> + <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream + as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This + results in a first Ogg page of exactly 58 bytes at the very beginning of the logical + stream. + </li> + <li class="itemize">This first page is marked ’beginning of stream’ in the page flags. + </li> + <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or + more pages beginning on the second page of the logical stream. However many pages + they span, the third header packet finishes the page on which it ends. The next (first + audio) packet must begin on a fresh page. + + + + </li> + <li class="itemize">The granule position of these first pages containing only headers is zero. + </li> + <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page. + </li> + <li class="itemize">Packets are placed into ogg pages in order until the end of stream. + </li> + <li class="itemize">The last page is marked ’end of stream’ in the page flags. + </li> + <li class="itemize">Vorbis packets may span page boundaries. + </li> + <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio + samples (per channel; a stereo stream’s granule position does not increment at twice + the speed of a mono stream). + </li> + <li class="itemize">The granule position of a page represents the end PCM sample position of the last + packet <span +class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample + returned by decode, not an internal sample awaiting lapping with a subsequent block. + A page that is entirely spanned by a single packet (that completes on a subsequent + page) has no granule position, and the granule position is set to ’-1’. + <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not + necessarily the middle sample from that block. If, eg, the current Vorbis packet + encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last + decodable sample from the current packet be at position (3*long_block_length/4) - + (short_block_length/4). + </li> + <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream + started at position zero. Although the granule position belongs to the last completed + packet on the page and a valid granule position must be positive, by inference it may + indicate that the PCM position of the beginning of audio is positive or negative. + <ul class="itemize2"> + <li class="itemize">A positive starting value simply indicates that this stream begins at some + positive time offset, potentially within a larger program. This is a common case + when connecting to the middle of broadcast stream. + </li> + <li class="itemize">A negative value indicates that output samples preceeding time zero should be + + + + discarded during decoding; this technique is used to allow sample-granularity + editing of the stream start time of already-encoded Vorbis streams. The number + of samples to be discarded must not exceed the overlap-add span of the first two + audio packets. + </li></ul> + <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the + second finished audio packet must flush the page on which it appears and the + third packet begin a fresh page. This allows the decoder to always be able to + perform PCM position adjustments before needing to return any PCM data from + synthesis, resulting in correct positioning information without any aditional seeking + logic. + <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a + id="x1-133000A.2"></a><span +class="cmbx-12">Note:</span></span> Failure to do so should, at worst, cause a decoder implementation to return + incorrect positioning information for seeking operations at the very beginning of the + stream. + </li> + <li class="itemize">A granule position on the final page in a stream that indicates less audio data than the + final packet would normally return is used to end the stream on other than even frame + boundaries. The difference between the actual available data returned and the + declared amount indicates how many trailing samples to discard from the decoding + process. + </li></ul> + + + +<h3 class="sectionHead"><span class="titlemark">B. </span> <a + id="x1-134000B"></a>Vorbis encapsulation in RTP</h3> +<!--l. 8--><p class="noindent" >Please consult RFC 5215 <span +class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of +how to embed Vorbis audio in an RTP stream. + + + + + + +<h3 class="likesectionHead"><a + id="x1-135000B"></a>Colophon</h3> +<!--l. 6--><p class="noindent" ><img +src="fish_xiph_org.png" alt="PIC" +> +<!--l. 9--><p class="noindent" >Ogg is a <a +href="http://www.xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from +corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See +<a +href="http://www.xiph.org/about.html" >About the Xiph.Org Foundation</a> for details. +<!--l. 16--><p class="noindent" >Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and distribute the Ogg and +Vorbis specification, whether in a private, public or corporate capacity. However, the Xiph.Org +Foundation and the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis specification +and certify specification compliance. +<!--l. 22--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This +does not restrict third parties from distributing independent implementations of Vorbis software +under other licenses. +<!--l. 27--><p class="noindent" >Ogg, Vorbis, Xiph.Org Foundation and their logos are trademarks (tm) of the <a +href="http://www.xiph.org/" >Xiph.Org +Foundation</a>. These pages are copyright (C) 1994-2015 Xiph.Org Foundation. All rights +reserved. +<!--l. 32--><p class="noindent" >This document is set using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span +class="E">E</span>X</span></span>. + + + +<h3 class="likesectionHead"><a + id="x1-136000B"></a>References</h3> +<!--l. 133--><p class="noindent" > + <div class="thebibliography"> + <p class="bibitem" ><span class="biblabel"> + [1]<span class="bibsp">   </span></span><a + id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and + B. Edler, The use of multirate filter banks for coding of high quality digital audio, + <a +href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span +class="cmtt-12">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>. +</p> + </div> + +</body></html> + + + + |