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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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+<head><title>Vorbis I specification</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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+<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">
+&#x00A0;<span class="sectionToc" >1 <a
+href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >1.1 <a
+href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.1 <a
+href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.2 <a
+href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.3 <a
+href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.4 <a
+href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.5 <a
+href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.1.6 <a
+href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >1.2 <a
+href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.1 <a
+href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.2 <a
+href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.3 <a
+href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
+
+
+
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.4 <a
+href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.5 <a
+href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.2.6 <a
+href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >1.3 <a
+href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.3.1 <a
+href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >1.3.2 <a
+href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
+<br />&#x00A0;<span class="sectionToc" >2 <a
+href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >2.1 <a
+href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.1 <a
+href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.2 <a
+href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.3 <a
+href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.4 <a
+href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.5 <a
+href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.6 <a
+href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.7 <a
+href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.8 <a
+href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >2.1.9 <a
+href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
+<br />&#x00A0;<span class="sectionToc" >3 <a
+href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >3.1 <a
+href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >3.1.1 <a
+href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >3.2 <a
+href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >3.2.1 <a
+href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >3.3 <a
+href="#x1-580003.3" id="QQ2-1-63">Use of the codebook abstraction</a></span>
+<br />&#x00A0;<span class="sectionToc" >4 <a
+href="#x1-590004" id="QQ2-1-64">Codec Setup and Packet Decode</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >4.1 <a
+href="#x1-600004.1" id="QQ2-1-65">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >4.2 <a
+href="#x1-610004.2" id="QQ2-1-66">Header decode and decode setup</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.2.1 <a
+href="#x1-620004.2.1" id="QQ2-1-67">Common header decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.2.2 <a
+href="#x1-630004.2.2" id="QQ2-1-68">Identification header</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.2.3 <a
+href="#x1-640004.2.3" id="QQ2-1-69">Comment header</a></span>
+
+
+
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.2.4 <a
+href="#x1-650004.2.4" id="QQ2-1-70">Setup header</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >4.3 <a
+href="#x1-720004.3" id="QQ2-1-78">Audio packet decode and synthesis</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<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 />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.2 <a
+href="#x1-740004.3.2" id="QQ2-1-80">floor curve decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.3 <a
+href="#x1-750004.3.3" id="QQ2-1-81">nonzero vector propagate</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.4 <a
+href="#x1-760004.3.4" id="QQ2-1-82">residue decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.5 <a
+href="#x1-770004.3.5" id="QQ2-1-83">inverse coupling</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.6 <a
+href="#x1-780004.3.6" id="QQ2-1-84">dot product</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.7 <a
+href="#x1-790004.3.7" id="QQ2-1-85">inverse MDCT</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.8 <a
+href="#x1-800004.3.8" id="QQ2-1-86">overlap_add</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >4.3.9 <a
+href="#x1-810004.3.9" id="QQ2-1-87">output channel order</a></span>
+<br />&#x00A0;<span class="sectionToc" >5 <a
+href="#x1-820005" id="QQ2-1-88">comment field and header specification</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >5.1 <a
+href="#x1-830005.1" id="QQ2-1-89">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >5.2 <a
+href="#x1-840005.2" id="QQ2-1-90">Comment encoding</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >5.2.1 <a
+href="#x1-850005.2.1" id="QQ2-1-91">Structure</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >5.2.2 <a
+href="#x1-860005.2.2" id="QQ2-1-92">Content vector format</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >5.2.3 <a
+href="#x1-890005.2.3" id="QQ2-1-95">Encoding</a></span>
+<br />&#x00A0;<span class="sectionToc" >6 <a
+href="#x1-900006" id="QQ2-1-96">Floor type 0 setup and decode</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >6.1 <a
+href="#x1-910006.1" id="QQ2-1-97">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >6.2 <a
+href="#x1-920006.2" id="QQ2-1-98">Floor 0 format</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >6.2.1 <a
+href="#x1-930006.2.1" id="QQ2-1-99">header decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >6.2.2 <a
+href="#x1-940006.2.2" id="QQ2-1-100">packet decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >6.2.3 <a
+href="#x1-950006.2.3" id="QQ2-1-101">curve computation</a></span>
+<br />&#x00A0;<span class="sectionToc" >7 <a
+href="#x1-970007" id="QQ2-1-103">Floor type 1 setup and decode</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >7.1 <a
+href="#x1-980007.1" id="QQ2-1-104">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >7.2 <a
+href="#x1-990007.2" id="QQ2-1-105">Floor 1 format</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >7.2.1 <a
+href="#x1-1000007.2.1" id="QQ2-1-106">model</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >7.2.2 <a
+href="#x1-1010007.2.2" id="QQ2-1-111">header decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >7.2.3 <a
+href="#x1-1020007.2.3" id="QQ2-1-112">packet decode</a></span>
+
+
+
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >7.2.4 <a
+href="#x1-1030007.2.4" id="QQ2-1-113">curve computation</a></span>
+<br />&#x00A0;<span class="sectionToc" >8 <a
+href="#x1-1040008" id="QQ2-1-114">Residue setup and decode</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.1 <a
+href="#x1-1050008.1" id="QQ2-1-115">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.2 <a
+href="#x1-1060008.2" id="QQ2-1-116">Residue format</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.3 <a
+href="#x1-1070008.3" id="QQ2-1-118">residue 0</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.4 <a
+href="#x1-1080008.4" id="QQ2-1-119">residue 1</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.5 <a
+href="#x1-1090008.5" id="QQ2-1-120">residue 2</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >8.6 <a
+href="#x1-1100008.6" id="QQ2-1-122">Residue decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >8.6.1 <a
+href="#x1-1110008.6.1" id="QQ2-1-123">header decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >8.6.2 <a
+href="#x1-1120008.6.2" id="QQ2-1-124">packet decode</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >8.6.3 <a
+href="#x1-1130008.6.3" id="QQ2-1-125">format 0 specifics</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >8.6.4 <a
+href="#x1-1140008.6.4" id="QQ2-1-126">format 1 specifics</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >8.6.5 <a
+href="#x1-1150008.6.5" id="QQ2-1-127">format 2 specifics</a></span>
+<br />&#x00A0;<span class="sectionToc" >9 <a
+href="#x1-1160009" id="QQ2-1-128">Helper equations</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >9.1 <a
+href="#x1-1170009.1" id="QQ2-1-129">Overview</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >9.2 <a
+href="#x1-1180009.2" id="QQ2-1-130">Functions</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.1 <a
+href="#x1-1190009.2.1" id="QQ2-1-131">ilog</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.2 <a
+href="#x1-1200009.2.2" id="QQ2-1-132">float32_unpack</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.3 <a
+href="#x1-1210009.2.3" id="QQ2-1-133">lookup1_values</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.4 <a
+href="#x1-1220009.2.4" id="QQ2-1-134">low_neighbor</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.5 <a
+href="#x1-1230009.2.5" id="QQ2-1-135">high_neighbor</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.6 <a
+href="#x1-1240009.2.6" id="QQ2-1-136">render_point</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >9.2.7 <a
+href="#x1-1250009.2.7" id="QQ2-1-137">render_line</a></span>
+<br />&#x00A0;<span class="sectionToc" >10 <a
+href="#x1-12600010" id="QQ2-1-138">Tables</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >10.1 <a
+href="#x1-12700010.1" id="QQ2-1-139">floor1_inverse_dB_table</a></span>
+<br />&#x00A0;<span class="sectionToc" >A <a
+href="#x1-128000A" id="QQ2-1-140">Embedding Vorbis into an Ogg stream</a></span>
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >A.1 <a
+href="#x1-129000A.1" id="QQ2-1-141">Overview</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >A.1.1 <a
+href="#x1-130000A.1.1" id="QQ2-1-142">Restrictions</a></span>
+<br />&#x00A0;&#x00A0;&#x00A0;<span class="subsubsectionToc" >A.1.2 <a
+href="#x1-131000A.1.2" id="QQ2-1-143">MIME type</a></span>
+
+
+
+<br />&#x00A0;&#x00A0;<span class="subsectionToc" >A.2 <a
+href="#x1-132000A.2" id="QQ2-1-144">Encapsulation</a></span>
+<br />&#x00A0;<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&#8217;s construction. A bit-by-bit
+specification appears beginning in <a
+href="#x1-590004">section&#x00A0;4</a>, &#8220;<a
+href="#x1-590004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>&#8221;. 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 &#8217;packets&#8217;. 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&#x00A0;A</a>,
+&#8220;<a
+href="#x1-128000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>&#8221;.
+<!--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&#8217; 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&#8217;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&#8217; ACM codec framework). However, we find that it does not
+fundamentally limit Vorbis&#8217; 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 &#8216;full&#8217; 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&#x00A0;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 &#8217;0&#8217; 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 &#8217;mode&#8217;. 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 &#8217;mode&#8217; 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 &#8217;submaps&#8217; 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 &#8217;submap&#8217; 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&#8217;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 &#8217;floor&#8217; 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 &#8217;floor&#8217; 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&#8217;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 (&#8220;tags&#8221;) 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&#x00A0;5</a>, &#8220;<a
+href="#x1-820005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>&#8221;.
+<!--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 &#8217;modes&#8217;, 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&#x00A0;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&#x00A0;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 * &#x03C0; sin2((x + .5)&#x2215;n * &#x03C0;)).
+
+
+
+" 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 &#8217;submap&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;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 &#8217;prime&#8217; the decode engine. The
+encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
+PCM output offset is &#8217;0&#8217; (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 &#8217;byte&#8217; is synonymous with an &#8217;octet&#8217;, that is, eight bits.
+This has not always been the case; seven, ten, eleven and sixteen bit &#8217;bytes&#8217; 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 &#8217;word&#8217; 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 &#8217;byte&#8217; 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 &#8217;least significant&#8217; bit (LSb), which is the only bit set when the byte is
+storing the two&#8217;s complement integer value +1. A byte&#8217;s &#8217;most significant&#8217; 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 (&#8217;big endian&#8217; or &#8217;most significant byte first&#8217; in which the
+highest-valued byte comes first), 0-1-2-3 (&#8217;little endian&#8217; or &#8217;least significant byte first&#8217; in
+which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (&#8217;mixed
+endian&#8217;).
+<!--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 &#8217;b111&#8217; can be taken to represent
+either &#8217;seven&#8217; as an unsigned integer, or &#8217;-1&#8217; as a signed, two&#8217;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 &#8217;12&#8217; [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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;|</span><br class="fancyvrb" /><a
+ id="x1-43004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;V</span><br class="fancyvrb" /><a
+ id="x1-43006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-43008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-43010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;[0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;&#x003C;-</span><br class="fancyvrb" /><a
+ id="x1-43012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span>
+<br class="fancyvrb" /><a
+ id="x1-43014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-43016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-43018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;...</span><br class="fancyvrb" /><a
+ id="x1-43020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;n</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;bytestream</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;==</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;byte</span><br class="fancyvrb" /><a
+ id="x1-43022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span></div>
+<!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value &#8217;-1&#8217; [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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;|</span><br class="fancyvrb" /><a
+ id="x1-43026r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;V</span><br class="fancyvrb" /><a
+ id="x1-43028r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-43030r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-43032r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;[0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;&#x003C;-</span><br class="fancyvrb" /><a
+ id="x1-43034r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span>
+<br class="fancyvrb" /><a
+ id="x1-43036r7"></a><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;...</span><br class="fancyvrb" /><a
+ id="x1-43084r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;n</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;bytestream</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;==</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;bytes</span><br class="fancyvrb" /><a
+ id="x1-43086r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;|</span><br class="fancyvrb" /><a
+ id="x1-44004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;V</span><br class="fancyvrb" /><a
+ id="x1-44006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-44008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-44010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;[1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;&#x003C;-</span>
+<br class="fancyvrb" /><a
+ id="x1-44012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;[0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0]</span><br class="fancyvrb" /><a
+ id="x1-44014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;[1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0]</span><br class="fancyvrb" /><a
+ id="x1-44016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;[0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;bytestream</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;==</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;bytes</span><br class="fancyvrb" /><a
+ id="x1-44018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span></div>
+<!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers &#8217;b00&#8217; and &#8217;b11&#8217;. 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 &#8217;b11&#8217;. This value may be interpreted
+ either as the unsigned value &#8217;3&#8217;, or the signed value &#8217;-1&#8217;. 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 &#8217;end-of-packet&#8217; 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 &#8217;end-of-packet&#8217; condition shall
+also return &#8217;end-of-packet&#8217;.
+<!--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 &#8217;0&#8217; and does not increment the stream cursor.
+Reading to the end of the packet (but not past, such that an &#8217;end-of-packet&#8217; 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 &#8217;end-of-packet&#8217;
+shall also fail with &#8217;end-of-packet&#8217;.
+
+
+
+
+
+
+<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 &#8217;codebooks&#8217;, 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&#x00A0;2</a>, &#8220;<a
+href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>&#8221;.
+<!--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&#8217;s native byte width is
+eight bits. This is not universally true; see <a
+href="#x1-360002">section&#x00A0;2</a>, &#8220;<a
+href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>&#8221; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;0:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;(0x42)</span><br class="fancyvrb" /><a
+ id="x1-51004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;1:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;(0x43)</span><br class="fancyvrb" /><a
+ id="x1-51006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;2:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;(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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51010r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;3:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-51012r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;4:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;[codebook_dimensions]</span><span
+class="cmtt-8">&#x00A0;(16</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;unsigned)</span><br class="fancyvrb" /><a
+ id="x1-51014r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-51016r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;5:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-51018r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;6:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-51020r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;7:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;[codebook_entries]</span><span
+class="cmtt-8">&#x00A0;(24</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;unsigned)</span><br class="fancyvrb" /><a
+ id="x1-51022r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51026r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;8:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;[ordered]</span><span
+class="cmtt-8">&#x00A0;(1</span><span
+class="cmtt-8">&#x00A0;bit)</span><br class="fancyvrb" /><a
+ id="x1-51028r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;byte</span><span
+class="cmtt-8">&#x00A0;8:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;X</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;]</span><span
+class="cmtt-8">&#x00A0;[sparse]</span><span
+class="cmtt-8">&#x00A0;flag</span><span
+class="cmtt-8">&#x00A0;(1</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51034r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;if([sparse]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-51036r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51038r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[flag]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;one</span><span
+class="cmtt-8">&#x00A0;bit;</span><br class="fancyvrb" /><a
+ id="x1-51040r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;if([flag]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-51042r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-51044r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;five</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer;</span><br class="fancyvrb" /><a
+ id="x1-51046r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;for</span><span
+class="cmtt-8">&#x00A0;this</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;[length]+1;</span><br class="fancyvrb" /><a
+ id="x1-51048r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-51050r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><span
+class="cmtt-8">&#x00A0;else</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-51052r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51054r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;this</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;unused.</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;mark</span><span
+class="cmtt-8">&#x00A0;it</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;such.</span><br class="fancyvrb" /><a
+ id="x1-51056r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51058r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-51060r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51062r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><span
+class="cmtt-8">&#x00A0;else</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;sparse</span><span
+class="cmtt-8">&#x00A0;flag</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;not</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+ <br class="fancyvrb" /><a
+ id="x1-51064r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51066r18"></a><span
+class="cmr-6">18</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;five</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer;</span><br class="fancyvrb" /><a
+ id="x1-51068r19"></a><span
+class="cmr-6">19</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;for</span><span
+class="cmtt-8">&#x00A0;this</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;[length]+1;</span><br class="fancyvrb" /><a
+ id="x1-51070r20"></a><span
+class="cmr-6">20</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51072r21"></a><span
+class="cmr-6">21</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-51074r22"></a><span
+class="cmr-6">22</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0;</span><br class="fancyvrb" /><a
+ id="x1-51078r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[current_length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;five</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;1;</span>
+ <br class="fancyvrb" /><a
+ id="x1-51080r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[number]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;-</span><span
+class="cmtt-8">&#x00A0;[current_entry])</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+ <br class="fancyvrb" /><a
+ id="x1-51082r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;entries</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><span
+class="cmtt-8">&#x00A0;through</span><span
+class="cmtt-8">&#x00A0;[current_entry]+[number]-1,</span><span
+class="cmtt-8">&#x00A0;inclusive,</span>
+ <br class="fancyvrb" /><a
+ id="x1-51084r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;[codebook_codeword_lengths]</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;[current_length]</span>
+ <br class="fancyvrb" /><a
+ id="x1-51086r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;[number]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><br class="fancyvrb" /><a
+ id="x1-51088r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;increment</span><span
+class="cmtt-8">&#x00A0;[current_length]</span><span
+class="cmtt-8">&#x00A0;by</span><span
+class="cmtt-8">&#x00A0;1</span>
+ <br class="fancyvrb" /><a
+ id="x1-51090r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;greater</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[codebook_entries]</span><span
+class="cmtt-8">&#x00A0;ERROR</span><span
+class="cmtt-8">&#x00A0;CONDITION;</span><br class="fancyvrb" /><a
+ id="x1-51092r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;decoder</span><span
+class="cmtt-8">&#x00A0;will</span><span
+class="cmtt-8">&#x00A0;not</span><span
+class="cmtt-8">&#x00A0;be</span><span
+class="cmtt-8">&#x00A0;able</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;this</span><span
+class="cmtt-8">&#x00A0;stream.</span>
+ <br class="fancyvrb" /><a
+ id="x1-51094r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;[current_entry]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;less</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[codebook_entries],</span><span
+class="cmtt-8">&#x00A0;repeat</span><span
+class="cmtt-8">&#x00A0;process</span><span
+class="cmtt-8">&#x00A0;starting</span><span
+class="cmtt-8">&#x00A0;at</span><span
+class="cmtt-8">&#x00A0;3)</span><br class="fancyvrb" /><a
+ id="x1-51096r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;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 &#8217;foam&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_type]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;four</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[codebook_minimum_value]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1200009.2.2"><span
+class="cmtt-8">float32_unpack</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer)</span>
+ <br class="fancyvrb" /><a
+ id="x1-51105r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[codebook_delta_value]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1200009.2.2"><span
+class="cmtt-8">float32_unpack</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer)</span>
+ <br class="fancyvrb" /><a
+ id="x1-51107r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[codebook_value_bits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;1</span><br class="fancyvrb" /><a
+ id="x1-51109r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[codebook_sequence_p]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;boolean</span><span
+class="cmtt-8">&#x00A0;flag</span><br class="fancyvrb" /><a
+ id="x1-51111r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+
+
+
+ <br class="fancyvrb" /><a
+ id="x1-51113r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_type]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-51115r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51117r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_values]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;[codebook_dimensions]</span><span
+class="cmtt-8">&#x00A0;)</span>
+ <br class="fancyvrb" /><a
+ id="x1-51119r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51121r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><span
+class="cmtt-8">&#x00A0;else</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-51123r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51125r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_values]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[codebook_entries]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[codebook_dimensions]</span><br class="fancyvrb" /><a
+ id="x1-51127r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-51129r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-51131r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-51133r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;total</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_values]</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integers</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;[codebook_value_bits]</span><span
+class="cmtt-8">&#x00A0;each;</span>
+ <br class="fancyvrb" /><a
+ id="x1-51135r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;store</span><span
+class="cmtt-8">&#x00A0;these</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;order</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;[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 &#8217;end of packet&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;0:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;2</span><br class="fancyvrb" /><a
+ id="x1-52004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;1:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><br class="fancyvrb" /><a
+ id="x1-52006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;2:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><br class="fancyvrb" /><a
+ id="x1-52008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;3:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><br class="fancyvrb" /><a
+ id="x1-52010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;4:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><br class="fancyvrb" /><a
+ id="x1-52012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;5:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;2</span>
+<br class="fancyvrb" /><a
+ id="x1-52014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;6:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;3</span><br class="fancyvrb" /><a
+ id="x1-52016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;7:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;0:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;00</span><br class="fancyvrb" /><a
+ id="x1-52020r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;1:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;0100</span><br class="fancyvrb" /><a
+ id="x1-52022r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;2:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;0101</span><br class="fancyvrb" /><a
+ id="x1-52024r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;3:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;0110</span>
+<br class="fancyvrb" /><a
+ id="x1-52026r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;4:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;0111</span><br class="fancyvrb" /><a
+ id="x1-52028r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;5:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;10</span><br class="fancyvrb" /><a
+ id="x1-52030r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;6:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;110</span><br class="fancyvrb" /><a
+ id="x1-52032r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;entry</span><span
+class="cmtt-8">&#x00A0;7:</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;codeword</span><span
+class="cmtt-8">&#x00A0;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 &#8217;001&#8217; is the bit string &#8217;zero, zero,
+one&#8217;. When determining &#8217;lowest possible value&#8217; 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&#x00A0;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&#8217;s possible to underspecify or overspecify a Huffman tree via the length list.
+In the above example, if codeword seven were eliminated, it&#8217;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&#x00A0;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&#8217;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 &#8217;unused&#8217; are simply skipped in the assigning process. They have no
+codeword and do not appear in the decision tree, thus it&#8217;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 &#8217;single-entry codebook&#8217; 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 &#8217;in the wild&#8217; 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" >&#8220;<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>&#8221;
+<!--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 &#8217;write&#8217; 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. &#8217;Reading&#8217; 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 &#8217;1&#8217; instead of &#8217;0&#8217;; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;[codebook\_multiplicands]</span><span
+class="cmtt-8">&#x00A0;array</span><br class="fancyvrb" /><a
+ id="x1-55004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_minimum\_value]</span><br class="fancyvrb" /><a
+ id="x1-55006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_delta\_value]</span><br class="fancyvrb" /><a
+ id="x1-55008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_sequence\_p]</span>
+<br class="fancyvrb" /><a
+ id="x1-55010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_lookup\_type]</span><br class="fancyvrb" /><a
+ id="x1-55012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_entries]</span><br class="fancyvrb" /><a
+ id="x1-55014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook\_dimensions]</span><br class="fancyvrb" /><a
+ id="x1-55016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0;</span><br class="fancyvrb" /><a
+ id="x1-56004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[index_divisor]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;1;</span><br class="fancyvrb" /><a
+ id="x1-56006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[codebook_dimensions]-1</span><span
+class="cmtt-8">&#x00A0;(once</span><span
+class="cmtt-8">&#x00A0;for</span><span
+class="cmtt-8">&#x00A0;each</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;vector)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
+ id="x1-56008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-56010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[multiplicand_offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[lookup_offset]</span><span
+class="cmtt-8">&#x00A0;divided</span><span
+class="cmtt-8">&#x00A0;by</span><span
+class="cmtt-8">&#x00A0;[index_divisor]</span><span
+class="cmtt-8">&#x00A0;using</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-56012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;division</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;modulo</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_values]</span><br class="fancyvrb" /><a
+ id="x1-56014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-56016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[value_vector]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span>
+<br class="fancyvrb" /><a
+ id="x1-56018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[codebook_multiplicands]</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;number</span><span
+class="cmtt-8">&#x00A0;[multiplicand_offset]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;*</span>
+<br class="fancyvrb" /><a
+ id="x1-56020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook_delta_value]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[codebook_minimum_value]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[last];</span><br class="fancyvrb" /><a
+ id="x1-56022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-56024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[codebook_sequence_p]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[value_vector]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><br class="fancyvrb" /><a
+ id="x1-56026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-56028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[index_divisor]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[index_divisor]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[codebook_lookup_values]</span><br class="fancyvrb" /><a
+ id="x1-56030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-56032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-56034r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-56036r18"></a><span
+class="cmr-6">18</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;calculation</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0;</span><br class="fancyvrb" /><a
+ id="x1-57004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[multiplicand_offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[lookup_offset]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[codebook_dimensions]</span>
+<br class="fancyvrb" /><a
+ id="x1-57006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[codebook_dimensions]-1</span><span
+class="cmtt-8">&#x00A0;(once</span><span
+class="cmtt-8">&#x00A0;for</span><span
+class="cmtt-8">&#x00A0;each</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;vector)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-57008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-57010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[value_vector]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><br class="fancyvrb" /><a
+ id="x1-57012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[codebook_multiplicands]</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;number</span><span
+class="cmtt-8">&#x00A0;[multiplicand_offset]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;*</span>
+<br class="fancyvrb" /><a
+ id="x1-57014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;[codebook_delta_value]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[codebook_minimum_value]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[last];</span><br class="fancyvrb" /><a
+ id="x1-57016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-57018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[codebook_sequence_p]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[value_vector]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><br class="fancyvrb" /><a
+ id="x1-57020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-57022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;increment</span><span
+class="cmtt-8">&#x00A0;[multiplicand_offset]</span><br class="fancyvrb" /><a
+ id="x1-57024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-57026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-57028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-57030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;calculation</span><span
+class="cmtt-8">&#x00A0;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 &#8217;end-of-stream&#8217; 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&#x00A0;1</a>, &#8220;<a
+href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>&#8221;. <a
+href="#x1-360002">section&#x00A0;2</a>,
+&#8220;<a
+href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>&#8221; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[packet_type]</span><span
+class="cmtt-8">&#x00A0;:</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;value</span><br class="fancyvrb" /><a
+ id="x1-62004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;0x76,</span><span
+class="cmtt-8">&#x00A0;0x6f,</span><span
+class="cmtt-8">&#x00A0;0x72,</span><span
+class="cmtt-8">&#x00A0;0x62,</span><span
+class="cmtt-8">&#x00A0;0x69,</span><span
+class="cmtt-8">&#x00A0;0x73:</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;characters</span><span
+class="cmtt-8">&#x00A0;&#8217;v&#8217;,&#8217;o&#8217;,&#8217;r&#8217;,&#8217;b&#8217;,&#8217;i&#8217;,&#8217;s&#8217;</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;six</span><span
+class="cmtt-8">&#x00A0;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 &#8217;0&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[vorbis_version]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-63004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[audio_channels]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span>
+<br class="fancyvrb" /><a
+ id="x1-63006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[audio_sample_rate]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-63008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[bitrate_maximum]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;signed</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-63010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[bitrate_nominal]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;signed</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-63012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[bitrate_minimum]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;signed</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-63014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[blocksize_0]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;exponent</span><span
+class="cmtt-8">&#x00A0;(read</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer)</span><br class="fancyvrb" /><a
+ id="x1-63016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;[blocksize_1]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;exponent</span><span
+class="cmtt-8">&#x00A0;(read</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer)</span>
+<br class="fancyvrb" /><a
+ id="x1-63018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;[framing_flag]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;one</span><span
+class="cmtt-8">&#x00A0;bit</span></div>
+<!--l. 63--><p class="noindent" ><span
+class="cmtt-12">[vorbis_version] </span>is to read &#8217;0&#8217; 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&#x00A0;5</a>, &#8220;<a
+href="#x1-820005">comment field and
+header specification<!--tex4ht:ref: vorbis:spec:comment --></a>&#8221;.
+<!--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&#x00A0;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 &#8217;1&#8217;. 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&#x00A0;3</a>,
+ &#8220;<a
+href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>&#8221;. 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&#x00A0;6</a>,
+ &#8220;<a
+href="#x1-900006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>&#8221;; 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&#x00A0;7</a>,
+ &#8220;<a
+href="#x1-970007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>&#8221;; 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&#x00A0;8</a>, &#8220;<a
+href="#x1-1040008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>&#8221;; 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&#8217;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&#x00A0;<a
+href="#x1-260001.3.2">1.3.2</a></a>,
+ &#8220;<a
+href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>&#8221; 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&#x00A0;1.3.2</a>,
+
+
+
+ &#8220;<a
+href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>&#8221; 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="&#x03C0;
+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">&#x2215;n </span><span
+class="cmsy-10x-x-120">* </span><span
+class="cmmi-12">&#x03C0;</span>)), where <span
+class="cmmi-12">n </span>is window
+size and <span
+class="cmmi-12">x </span>ranges 0<span
+class="cmmi-12">&#x2026;</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="&#x03C0;
+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="&#x03C0;
+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="&#x03C0;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">[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="&#x03C0;2" class="frac" align="middle"> + <img
+src="Vorbis_I_spec6x.png" alt="&#x03C0;2" 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&#x00A0;6.2.2</a>, &#8220;<a
+href="#x1-940006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>&#8221;
+ </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&#x00A0;7.2.3</a>, &#8220;<a
+href="#x1-1020007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>&#8221;
+ </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 &#8217;unused&#8217;, 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 &#8217;unused&#8217; 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 &#8217;unused&#8217; 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&#8217;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&#x00A0;1.3.2</a>, &#8220;<a
+href="#x1-260001.3.2">Window shape decode (long windows
+only)<!--tex4ht:ref: vorbis:spec:window --></a>&#8221;). 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;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 &#8217;prime&#8217; the decode engine. The
+encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
+PCM output offset is &#8217;0&#8217; (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 &#8217;left to the implementation&#8217;.
+<!--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&#8217;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">&#8220;I&#8217;m Still Around&#8221;</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 &#8220;Xiph.Org libVorbis I
+20020717&#8221;.
+<!--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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[vendor\_length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-85004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[vendor\_string]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;UTF-8</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;[vendor\_length]</span><span
+class="cmtt-8">&#x00A0;octets</span>
+<br class="fancyvrb" /><a
+ id="x1-85006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[user\_comment\_list\_length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-85008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[user\_comment\_list\_length]</span><span
+class="cmtt-8">&#x00A0;times</span><span
+class="cmtt-8">&#x00A0;{</span>
+<br class="fancyvrb" /><a
+ id="x1-85010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[length]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;32</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-85012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;this</span><span
+class="cmtt-8">&#x00A0;iteration&#8217;s</span><span
+class="cmtt-8">&#x00A0;user</span><span
+class="cmtt-8">&#x00A0;comment</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;UTF-8</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;[length]</span><span
+class="cmtt-8">&#x00A0;octets</span>
+<br class="fancyvrb" /><a
+ id="x1-85014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-85016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[framing\_bit]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;single</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;boolean</span><br class="fancyvrb" /><a
+ id="x1-85018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[framing\_bit]</span><span
+class="cmtt-8">&#x00A0;unset</span><span
+class="cmtt-8">&#x00A0;or</span><span
+class="cmtt-8">&#x00A0;end-of-packet</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;ERROR</span><br class="fancyvrb" /><a
+ id="x1-85020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;comment[0]="ARTIST=me";</span><br class="fancyvrb" /><a
+ id="x1-86004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;comment[1]="TITLE=the</span><span
+class="cmtt-8">&#x00A0;sound</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;Vorbis";</span></div>
+ </div>
+<!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (&#8217;=&#8217;)
+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 (&#8217;=&#8217;); 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., &#8217;2001 Nobody&#8217;s Band&#8217; or &#8217;1999 Jack Moffitt&#8217;
+ </dd><dt class="description">
+<span
+class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
+class="description">License information, eg, &#8217;All Rights Reserved&#8217;, &#8217;Any Use Permitted&#8217;, a URL to
+ a license such as a Creative
+ Commons license (&#8221;www.creativecommons.org/blahblah/license.html&#8221;) or the EFF
+ Open Audio License (&#8217;distributed under the terms of the Open Audio License. see
+ http://www.eff.org/IP/Open_licenses/eff_oal.html for details&#8217;), 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 &#8217;record label&#8217;)
+ </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 &#8217;internationalized&#8217;; this is a concession to simplicity not
+an attempt to exclude the majority of the world that doesn&#8217;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 &#8217;vendors&#8217; 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 &#8217;nonstandard&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;ARTIST=Dizzy</span><span
+class="cmtt-8">&#x00A0;Gillespie</span><br class="fancyvrb" /><a
+ id="x1-88004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;ARTIST=Sonny</span><span
+class="cmtt-8">&#x00A0;Rollins</span><br class="fancyvrb" /><a
+ id="x1-88006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;ARTIST=Sonny</span><span
+class="cmtt-8">&#x00A0;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&#8217;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">&#x003E; </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">&#x003E; </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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[floor0_order]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-93004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[floor0_rate]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;16</span><span
+class="cmtt-8">&#x00A0;bits</span>
+<br class="fancyvrb" /><a
+ id="x1-93006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[floor0_bark_map_size]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;16</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-93008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[floor0_amplitude_bits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;six</span><span
+class="cmtt-8">&#x00A0;bits</span>
+<br class="fancyvrb" /><a
+ id="x1-93010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[floor0_amplitude_offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;eight</span><span
+class="cmtt-8">&#x00A0;bits</span>
+<br class="fancyvrb" /><a
+ id="x1-93012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[floor0_number_of_books]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;four</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;1</span>
+<br class="fancyvrb" /><a
+ id="x1-93014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;[floor0_book_list]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;list</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;[floor0_number_of_books]</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integers</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;eight</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[amplitude]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;[floor0_amplitude_bits]</span><span
+class="cmtt-8">&#x00A0;bits</span><br class="fancyvrb" /><a
+ id="x1-94004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[amplitude]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;greater</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;zero</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
+ id="x1-94006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[coefficients]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;empty,</span><span
+class="cmtt-8">&#x00A0;zero</span><span
+class="cmtt-8">&#x00A0;length</span><span
+class="cmtt-8">&#x00A0;vector</span><br class="fancyvrb" /><a
+ id="x1-94008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[booknumber]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1190009.2.1"><span
+class="cmtt-8">ilog</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;[floor0_number_of_books]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;bits</span>
+<br class="fancyvrb" /><a
+ id="x1-94010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[booknumber]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;greater</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;highest</span><span
+class="cmtt-8">&#x00A0;number</span><span
+class="cmtt-8">&#x00A0;decode</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;packet</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;undecodable</span><br class="fancyvrb" /><a
+ id="x1-94012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;zero;</span>
+<br class="fancyvrb" /><a
+ id="x1-94014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[temp_vector]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;from</span><span
+class="cmtt-8">&#x00A0;bitstream</span><span
+class="cmtt-8">&#x00A0;using</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;number</span><span
+class="cmtt-8">&#x00A0;[floor0_book_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[booknumber]</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;VQ</span><span
+class="cmtt-8">&#x00A0;context.</span>
+<br class="fancyvrb" /><a
+ id="x1-94016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;each</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[temp_vector]</span><br class="fancyvrb" /><a
+ id="x1-94018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;[last]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;last</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[temp_vector]</span>
+<br class="fancyvrb" /><a
+ id="x1-94020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;10)</span><span
+class="cmtt-8">&#x00A0;concatenate</span><span
+class="cmtt-8">&#x00A0;[temp_vector]</span><span
+class="cmtt-8">&#x00A0;onto</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;end</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;[coefficients]</span><span
+class="cmtt-8">&#x00A0;vector</span>
+<br class="fancyvrb" /><a
+ id="x1-94022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;11)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(length</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[coefficients]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;less</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[floor0_order],</span><span
+class="cmtt-8">&#x00A0;continue</span><span
+class="cmtt-8">&#x00A0;at</span><span
+class="cmtt-8">&#x00A0;step</span><span
+class="cmtt-8">&#x00A0;6</span><br class="fancyvrb" /><a
+ id="x1-94024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-94026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-94028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-94030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;12)</span><span
+class="cmtt-8">&#x00A0;done.</span><br class="fancyvrb" /><a
+ id="x1-94032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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&#8217;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
+ &#8217;unused&#8217; 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 &#x2208; [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=" &#x230A; &#x230B;
+ ( floor0_rate--&#x22C5; i) floor0_bark_map_size----
+f oobar = bark 2n &#x22C5; bark(.5 &#x22C5; 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">&#x03C9;</span><span
+class="cmtt-12">] </span>= <span
+class="cmmi-12">&#x03C0; </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&#x220F;_2order-3
+p = (1 - cos2&#x03C9;) 4(cos([coefficients ]2j+1) - cos&#x03C9; )2
+ j=0
+ floor0_order-1
+ 1 &#x220F;2 2
+q = 4- 4(cos([coefficients ]2j) - cos&#x03C9; )
+ 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 - cos&#x03C9; ) ---&#x220F;2-----
+p = ----------- 4(cos([coefficients ]2j+1) - cos&#x03C9;)2
+ 2 j=0
+ floor0_order--2
+ (1-+-cos&#x03C9;-) &#x220F;2 2
+q = 2 4(cos([coefficients ]2j) - cos &#x03C9;)
+ 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---&#x22C5; floor0_amplitute_offset---
+exp .11512925 (2floor0_amplitude_bits - 1)&#x221A;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&#8217;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&#x02D9;0,y&#x02D9;0 to x&#x02D9;1,y&#x02D9;1
+ where in the base case x&#x02D9;0=0 and x&#x02D9;1=[n], the full range of the spectral floor to be
+ computed.
+ </li>
+ <li class="itemize">the induction step chooses a point x&#x02D9;new within an existing logical line segment and
+ produces a y&#x02D9;new value at that point computed from the existing line&#8217;s y value at
+ x&#x02D9;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&#x02D9;0,y&#x02D9;0 to
+ x&#x02D9;new,y&#x02D9;new and from x&#x02D9;new,y&#x02D9;new to x&#x02D9;1,y&#x02D9;1. This step is performed logically even if
+ y&#x02D9;new represents no change to the amplitude value at x&#x02D9;new so that later refinement
+ is additionally bounded at x&#x02D9;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&#x00A0;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&#x02D9;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&#x00A0;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&#x00A0;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&#x00A0;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 &#8217;subclass&#8217; 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
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+class="cmtt-8">&#x00A0;[floor1_partitions]</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
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+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_partition_class_list]</span><span
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+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
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+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_partition_class_list]</span><br class="fancyvrb" /><a
+ id="x1-101022r11"></a><span
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+class="cmtt-8">&#x00A0;[maximum_class]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
+ id="x1-101024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-101026r13"></a><span
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+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_class_dimensions]</span><span
+class="cmtt-8">&#x00A0;element</span><span
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+<br class="fancyvrb" /><a
+ id="x1-101028r14"></a><span
+class="cmr-6">14</span><span
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+ id="x1-101032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-101034r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;10)</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;15)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-101062r31"></a><span
+class="cmr-6">31</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;16)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[1]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;exponent</span><span
+class="cmtt-8">&#x00A0;[rangebits];</span>
+<br class="fancyvrb" /><a
+ id="x1-101064r32"></a><span
+class="cmr-6">32</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;17)</span><span
+class="cmtt-8">&#x00A0;[floor1_values]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><br class="fancyvrb" /><a
+ id="x1-101066r33"></a><span
+class="cmr-6">33</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;18)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[floor1_partitions]-1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
+ id="x1-101068r34"></a><span
+class="cmr-6">34</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-101070r35"></a><span
+class="cmr-6">35</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;19)</span><span
+class="cmtt-8">&#x00A0;[current_class_number]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_partition_class_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span>
+<br class="fancyvrb" /><a
+ id="x1-101072r36"></a><span
+class="cmr-6">36</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;20)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;([floor1_class_dimensions]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[current_class_number])-1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span>
+<br class="fancyvrb" /><a
+ id="x1-101074r37"></a><span
+class="cmr-6">37</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;21)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([floor1_values])</span><span
+class="cmtt-8">&#x00A0;=</span><br class="fancyvrb" /><a
+ id="x1-101076r38"></a><span
+class="cmr-6">38</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;[rangebits]</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-101078r39"></a><span
+class="cmr-6">39</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;22)</span><span
+class="cmtt-8">&#x00A0;increment</span><span
+class="cmtt-8">&#x00A0;[floor1_values]</span><span
+class="cmtt-8">&#x00A0;by</span><span
+class="cmtt-8">&#x00A0;one</span><br class="fancyvrb" /><a
+ id="x1-101080r40"></a><span
+class="cmr-6">40</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-101082r41"></a><span
+class="cmr-6">41</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-101084r42"></a><span
+class="cmr-6">42</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-101086r43"></a><span
+class="cmr-6">43</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;23)</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[nonzero]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;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 &#8217;unused&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[range]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><span
+class="cmtt-8">&#x00A0;256,</span><span
+class="cmtt-8">&#x00A0;128,</span><span
+class="cmtt-8">&#x00A0;86,</span><span
+class="cmtt-8">&#x00A0;64</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([floor1_multiplier]-1)</span>
+
+
+
+<br class="fancyvrb" /><a
+ id="x1-102006r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-102008r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[1]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-102010r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2;</span><br class="fancyvrb" /><a
+ id="x1-102012r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[floor1_partitions]-1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-102014r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-102016r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[class]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_partition_class]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><br class="fancyvrb" /><a
+ id="x1-102018r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[cdim]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_class_dimensions]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[class]</span>
+<br class="fancyvrb" /><a
+ id="x1-102020r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;[cbits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_class_subclasses]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[class]</span><br class="fancyvrb" /><a
+ id="x1-102022r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;[csub]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;(2</span><span
+class="cmtt-8">&#x00A0;exponent</span><span
+class="cmtt-8">&#x00A0;[cbits])-1</span><br class="fancyvrb" /><a
+ id="x1-102024r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+ id="x1-102074r36"></a><span
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+ id="x1-102076r37"></a><span
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+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;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 &#8217;unused&#8217;
+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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[range]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><span
+class="cmtt-8">&#x00A0;256,</span><span
+class="cmtt-8">&#x00A0;128,</span><span
+class="cmtt-8">&#x00A0;86,</span><span
+class="cmtt-8">&#x00A0;64</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([floor1_multiplier]-1)</span><br class="fancyvrb" /><a
+ id="x1-103004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_step2_flag]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;set</span>
+ <br class="fancyvrb" /><a
+ id="x1-103006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_step2_flag]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[1]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;set</span><br class="fancyvrb" /><a
+ id="x1-103008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[1]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[1]</span><br class="fancyvrb" /><a
+ id="x1-103012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[floor1_values]-1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-103014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-103016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[low_neighbor_offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;[high_neighbor_offset]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;[predicted]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1240009.2.6"><span
+class="cmtt-8">render_point</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[low_neighbor_offset],</span>
+ <br class="fancyvrb" /><a
+ id="x1-103024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[low_neighbor_offset],</span>
+ <br class="fancyvrb" /><a
+ id="x1-103026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[high_neighbor_offset],</span>
+ <br class="fancyvrb" /><a
+ id="x1-103028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[high_neighbor_offset],</span>
+ <br class="fancyvrb" /><a
+ id="x1-103030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;)</span><br class="fancyvrb" /><a
+ id="x1-103032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103034r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;10)</span><span
+class="cmtt-8">&#x00A0;[val]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103036r18"></a><span
+class="cmr-6">18</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;11)</span><span
+class="cmtt-8">&#x00A0;[highroom]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[range]</span><span
+class="cmtt-8">&#x00A0;-</span><span
+class="cmtt-8">&#x00A0;[predicted]</span><br class="fancyvrb" /><a
+ id="x1-103038r19"></a><span
+class="cmr-6">19</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;12)</span><span
+class="cmtt-8">&#x00A0;[lowroom]</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[predicted]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103040r20"></a><span
+class="cmr-6">20</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;[lowroom]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
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+class="cmr-6">21</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103044r22"></a><span
+class="cmr-6">22</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+ <br class="fancyvrb" /><a
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+class="cmtt-8">&#x00A0;+</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
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+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103130r65"></a><span
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+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;27)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_step2_flag]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;unset</span>
+ <br class="fancyvrb" /><a
+ id="x1-103132r66"></a><span
+class="cmr-6">66</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;28)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[predicted]</span><br class="fancyvrb" /><a
+ id="x1-103134r67"></a><span
+class="cmr-6">67</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103136r68"></a><span
+class="cmr-6">68</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103138r69"></a><span
+class="cmr-6">69</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103140r70"></a><span
+class="cmr-6">70</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103142r71"></a><span
+class="cmr-6">71</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103144r72"></a><span
+class="cmr-6">72</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;29)</span><span
+class="cmtt-8">&#x00A0;done</span><br class="fancyvrb" /><a
+ id="x1-103146r73"></a><span
+class="cmr-6">73</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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]&#8217;</span>, <span
+class="cmtt-12">[floor1_final_Y]&#8217;</span>
+ and <span
+class="cmtt-12">[floor1_step2_flag]&#8217; </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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[hx]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-103150r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[lx]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-103152r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[ly]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]&#8217;</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[0]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[floor1_multiplier]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103154r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[floor1_values]-1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-103156r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103158r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[floor1_step2_flag]&#8217;</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-103160r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-103162r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;[hy]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[floor1_final_Y]&#8217;</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[floor1_multiplier]</span><br class="fancyvrb" /><a
+ id="x1-103164r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;[hx]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[floor1_X_list]&#8217;</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103166r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1250009.2.7"><span
+class="cmtt-8">render_line</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;[lx],</span><span
+class="cmtt-8">&#x00A0;[ly],</span><span
+class="cmtt-8">&#x00A0;[hx],</span><span
+class="cmtt-8">&#x00A0;[hy],</span><span
+class="cmtt-8">&#x00A0;[floor]</span><span
+class="cmtt-8">&#x00A0;)</span><br class="fancyvrb" /><a
+ id="x1-103168r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9)</span><span
+class="cmtt-8">&#x00A0;[lx]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[hx]</span><br class="fancyvrb" /><a
+ id="x1-103170r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;10)</span><span
+class="cmtt-8">&#x00A0;[ly]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[hy]</span>
+ <br class="fancyvrb" /><a
+ id="x1-103172r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103174r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103176r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103178r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;11)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[hx]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;less</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[n]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-103180r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103182r18"></a><span
+class="cmr-6">18</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;12)</span><span
+class="cmtt-8">&#x00A0;</span><a
+href="#x1-1250009.2.7"><span
+class="cmtt-8">render_line</span></a><span
+class="cmtt-8">(</span><span
+class="cmtt-8">&#x00A0;[hx],</span><span
+class="cmtt-8">&#x00A0;[hy],</span><span
+class="cmtt-8">&#x00A0;[n],</span><span
+class="cmtt-8">&#x00A0;[hy],</span><span
+class="cmtt-8">&#x00A0;[floor]</span><span
+class="cmtt-8">&#x00A0;)</span>
+ <br class="fancyvrb" /><a
+ id="x1-103184r19"></a><span
+class="cmr-6">19</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103186r20"></a><span
+class="cmr-6">20</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103188r21"></a><span
+class="cmr-6">21</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103190r22"></a><span
+class="cmr-6">22</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;13)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[hx]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;greater</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[n]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">{</span><br class="fancyvrb" /><a
+ id="x1-103192r23"></a><span
+class="cmr-6">23</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103194r24"></a><span
+class="cmr-6">24</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;14)</span><span
+class="cmtt-8">&#x00A0;truncate</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor]</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;[n]</span><span
+class="cmtt-8">&#x00A0;elements</span>
+ <br class="fancyvrb" /><a
+ id="x1-103196r25"></a><span
+class="cmr-6">25</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103198r26"></a><span
+class="cmr-6">26</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmsy-8">}</span><br class="fancyvrb" /><a
+ id="x1-103200r27"></a><span
+class="cmr-6">27</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103202r28"></a><span
+class="cmr-6">28</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;15)</span><span
+class="cmtt-8">&#x00A0;for</span><span
+class="cmtt-8">&#x00A0;each</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[floor],</span><span
+class="cmtt-8">&#x00A0;perform</span><span
+class="cmtt-8">&#x00A0;a</span><span
+class="cmtt-8">&#x00A0;lookup</span><span
+class="cmtt-8">&#x00A0;substitution</span><span
+class="cmtt-8">&#x00A0;using</span>
+
+
+
+ <br class="fancyvrb" /><a
+ id="x1-103204r29"></a><span
+class="cmr-6">29</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;scalar</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;from</span><span
+class="cmtt-8">&#x00A0;[floor]</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;an</span><span
+class="cmtt-8">&#x00A0;offset</span><span
+class="cmtt-8">&#x00A0;into</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-103208r31"></a><span
+class="cmr-6">31</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;16)</span><span
+class="cmtt-8">&#x00A0;done</span><br class="fancyvrb" /><a
+ id="x1-103210r32"></a><span
+class="cmr-6">32</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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&#x00A0;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&#8211;or cyan box or brown box&#8211;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-107004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;original</span><span
+class="cmtt-8">&#x00A0;residue</span><span
+class="cmtt-8">&#x00A0;vector:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-107006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-107008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-107010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-107012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-107014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-107016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span>
+<br class="fancyvrb" /><a
+ id="x1-107018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-107020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-107022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-108004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;original</span><span
+class="cmtt-8">&#x00A0;residue</span><span
+class="cmtt-8">&#x00A0;vector:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-108006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-108008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-108010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-108012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-108014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-108016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span>
+<br class="fancyvrb" /><a
+ id="x1-108018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-108020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;dimensions</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;encoded</span><span
+class="cmtt-8">&#x00A0;as:</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;1</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;4</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;5</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;],</span><span
+class="cmtt-8">&#x00A0;[</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;]</span><br class="fancyvrb" /><a
+ id="x1-108022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[residue\_begin]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;24</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-111004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[residue\_end]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;24</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-111006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[residue\_partition\_size]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;24</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;one</span>
+<br class="fancyvrb" /><a
+ id="x1-111008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[residue\_classifications]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;6</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;add</span><span
+class="cmtt-8">&#x00A0;one</span><br class="fancyvrb" /><a
+ id="x1-111010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[residue\_classbook]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;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>&#x02C6;<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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[residue\_classifications]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-111014r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111016r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[high\_bits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span>
+<br class="fancyvrb" /><a
+ id="x1-111018r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[low\_bits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;3</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-111020r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[bitflag]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;one</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;boolean</span>
+<br class="fancyvrb" /><a
+ id="x1-111022r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[bitflag]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;[high\_bits]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;five</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span>
+<br class="fancyvrb" /><a
+ id="x1-111024r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[residue\_cascade]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[high\_bits]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[low\_bits]</span><br class="fancyvrb" /><a
+ id="x1-111026r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-111028r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[residue\_classifications]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-111032r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111034r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;{</span>
+<br class="fancyvrb" /><a
+ id="x1-111036r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111038r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[residue\_cascade]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;set</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-111040r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-111042r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;[residue\_books]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i][j]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;8</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;as</span><span
+class="cmtt-8">&#x00A0;unsigned</span><span
+class="cmtt-8">&#x00A0;integer</span><br class="fancyvrb" /><a
+ id="x1-111044r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111046r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><span
+class="cmtt-8">&#x00A0;else</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-111048r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-111050r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;array</span><span
+class="cmtt-8">&#x00A0;[residue\_books]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i][j]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;unused</span><br class="fancyvrb" /><a
+ id="x1-111052r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111054r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-111056r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-111058r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-111060r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-111062r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;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 &#8217;do not decode&#8217;,
+decode skips vector 1 during the decode loop. However, even &#8217;do not decode&#8217; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[actual\_size]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;current</span><span
+class="cmtt-8">&#x00A0;blocksize/2;</span><br class="fancyvrb" /><a
+ id="x1-112004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;residue</span><span
+class="cmtt-8">&#x00A0;encoding</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;format</span><span
+class="cmtt-8">&#x00A0;2</span>
+<br class="fancyvrb" /><a
+ id="x1-112006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[actual\_size]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[actual\_size]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[ch];</span><br class="fancyvrb" /><a
+ id="x1-112008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[limit\_residue\_begin]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;minimum</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;([residue\_begin],[actual\_size]);</span>
+<br class="fancyvrb" /><a
+ id="x1-112010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;[limit\_residue\_end]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;minimum</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;([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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[classwords\_per\_codeword]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[codebook\_dimensions]</span><span
+class="cmtt-8">&#x00A0;value</span><span
+class="cmtt-8">&#x00A0;of</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;[residue\_classbook]</span>
+<br class="fancyvrb" /><a
+ id="x1-112014r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[n\_to\_read]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[limit\_residue\_end]</span><span
+class="cmtt-8">&#x00A0;-</span><span
+class="cmtt-8">&#x00A0;[limit\_residue\_begin]</span><br class="fancyvrb" /><a
+ id="x1-112016r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[partitions\_to\_read]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[n\_to\_read]</span><span
+class="cmtt-8">&#x00A0;/</span><span
+class="cmtt-8">&#x00A0;[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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;allocate</span><span
+class="cmtt-8">&#x00A0;and</span><span
+class="cmtt-8">&#x00A0;zero</span><span
+class="cmtt-8">&#x00A0;all</span><span
+class="cmtt-8">&#x00A0;vectors</span><span
+class="cmtt-8">&#x00A0;that</span><span
+class="cmtt-8">&#x00A0;will</span><span
+class="cmtt-8">&#x00A0;be</span><span
+class="cmtt-8">&#x00A0;returned.</span><br class="fancyvrb" /><a
+ id="x1-112020r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;([n\_to\_read]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;zero),</span><span
+class="cmtt-8">&#x00A0;stop;</span><span
+class="cmtt-8">&#x00A0;there</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;no</span><span
+class="cmtt-8">&#x00A0;residue</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;decode.</span>
+<br class="fancyvrb" /><a
+ id="x1-112022r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[pass]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;7</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-112024r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-112026r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;[partition\_count]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-112028r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-112030r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;while</span><span
+class="cmtt-8">&#x00A0;[partition\_count]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;less</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[partitions\_to\_read]</span><br class="fancyvrb" /><a
+ id="x1-112032r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-112034r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;([pass]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;zero)</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-112036r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-112038r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;..</span><span
+class="cmtt-8">&#x00A0;[ch]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-112040r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-112042r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;8)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;not</span><span
+class="cmtt-8">&#x00A0;marked</span><span
+class="cmtt-8">&#x00A0;&#8217;do</span><span
+class="cmtt-8">&#x00A0;not</span><span
+class="cmtt-8">&#x00A0;decode&#8217;</span><span
+class="cmtt-8">&#x00A0;{</span>
+<br class="fancyvrb" /><a
+ id="x1-112044r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-112046r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+ id="x1-112118r51"></a><span
+class="cmr-6">51</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-112120r52"></a><span
+class="cmr-6">52</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-112122r53"></a><span
+class="cmr-6">53</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;21)</span><span
+class="cmtt-8">&#x00A0;done</span><br class="fancyvrb" /><a
+ id="x1-112124r54"></a><span
+class="cmr-6">54</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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 &#8217;Residue Format: residue 0&#8217;
+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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[step]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[n]</span><span
+class="cmtt-8">&#x00A0;/</span><span
+class="cmtt-8">&#x00A0;[codebook\_dimensions]</span><br class="fancyvrb" /><a
+ id="x1-113004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[step]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-113006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-113008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[entry\_temp]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;from</span><span
+class="cmtt-8">&#x00A0;packet</span><span
+class="cmtt-8">&#x00A0;using</span><span
+class="cmtt-8">&#x00A0;current</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;VQ</span><span
+class="cmtt-8">&#x00A0;context</span>
+<br class="fancyvrb" /><a
+ id="x1-113010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[codebook\_dimensions]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-113012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-113014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([offset]+[i]+[j]*[step])</span><span
+class="cmtt-8">&#x00A0;=</span>
+<br class="fancyvrb" /><a
+ id="x1-113016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([offset]+[i]+[j]*[step])</span><span
+class="cmtt-8">&#x00A0;+</span><br class="fancyvrb" /><a
+ id="x1-113018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[entry\_temp]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[j]</span><br class="fancyvrb" /><a
+ id="x1-113020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-113022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-113024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-113026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-113028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-113030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;done</span><br class="fancyvrb" /><a
+ id="x1-113032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</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 &#8217;Residue Format: residue 1&#8217;
+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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0</span><br class="fancyvrb" /><a
+ id="x1-114004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[entry\_temp]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;read</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;from</span><span
+class="cmtt-8">&#x00A0;packet</span><span
+class="cmtt-8">&#x00A0;using</span><span
+class="cmtt-8">&#x00A0;current</span><span
+class="cmtt-8">&#x00A0;codebook</span><span
+class="cmtt-8">&#x00A0;in</span><span
+class="cmtt-8">&#x00A0;VQ</span><span
+class="cmtt-8">&#x00A0;context</span>
+<br class="fancyvrb" /><a
+ id="x1-114006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[codebook\_dimensions]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-114008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-114010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([offset]+[i])</span><span
+class="cmtt-8">&#x00A0;=</span>
+<br class="fancyvrb" /><a
+ id="x1-114012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0; </span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([offset]+[i])</span><span
+class="cmtt-8">&#x00A0;+</span><br class="fancyvrb" /><a
+ id="x1-114014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[entry\_temp]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[j]</span><br class="fancyvrb" /><a
+ id="x1-114016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;increment</span><span
+class="cmtt-8">&#x00A0;[i]</span><br class="fancyvrb" /><a
+ id="x1-114018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-114020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-114022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-114024r12"></a><span
+class="cmr-6">12</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;less</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;[n]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;continue</span><span
+class="cmtt-8">&#x00A0;at</span><span
+class="cmtt-8">&#x00A0;step</span><span
+class="cmtt-8">&#x00A0;2</span><br class="fancyvrb" /><a
+ id="x1-114026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7)</span><span
+class="cmtt-8">&#x00A0;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 &#8217;do not decode&#8217; vectors differently than residue 0 or 1; if all vectors are marked
+&#8217;do not decode&#8217;, 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 &#8217;do not decode&#8217;, 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[n]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-115007r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-115009r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;iterate</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;over</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;range</span><span
+class="cmtt-8">&#x00A0;0</span><span
+class="cmtt-8">&#x00A0;...</span><span
+class="cmtt-8">&#x00A0;[ch]-1</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-115011r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+ <br class="fancyvrb" /><a
+ id="x1-115013r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;output</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;number</span><span
+class="cmtt-8">&#x00A0;[j]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[i]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;([i]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;[ch]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[j])</span><br class="fancyvrb" /><a
+ id="x1-115015r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-115017r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-115019r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-115021r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-115023r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;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 &#8221;ilog(x)&#8221; function returns the position number (1 through n) of the highest set bit in the
+two&#8217;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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[return\_value]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;0;</span><br class="fancyvrb" /><a
+ id="x1-119004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;greater</span><span
+class="cmtt-8">&#x00A0;than</span><span
+class="cmtt-8">&#x00A0;zero</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-119006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-119008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;increment</span><span
+class="cmtt-8">&#x00A0;[return\_value];</span>
+<br class="fancyvrb" /><a
+ id="x1-119010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;logical</span><span
+class="cmtt-8">&#x00A0;shift</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;one</span><span
+class="cmtt-8">&#x00A0;bit</span><span
+class="cmtt-8">&#x00A0;to</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;right,</span><span
+class="cmtt-8">&#x00A0;padding</span><span
+class="cmtt-8">&#x00A0;the</span><span
+class="cmtt-8">&#x00A0;MSb</span><span
+class="cmtt-8">&#x00A0;with</span><span
+class="cmtt-8">&#x00A0;zero</span><br class="fancyvrb" /><a
+ id="x1-119012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;repeat</span><span
+class="cmtt-8">&#x00A0;at</span><span
+class="cmtt-8">&#x00A0;step</span><span
+class="cmtt-8">&#x00A0;2)</span><br class="fancyvrb" /><a
+ id="x1-119014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-119016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-119018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-119020r10"></a><span
+class="cmr-6">10</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6)</span><span
+class="cmtt-8">&#x00A0;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" >&#8221;float32_unpack(x)&#8221; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1)</span><span
+class="cmtt-8">&#x00A0;[mantissa]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;bitwise</span><span
+class="cmtt-8">&#x00A0;AND</span><span
+class="cmtt-8">&#x00A0;0x1fffff</span><span
+class="cmtt-8">&#x00A0;(unsigned</span><span
+class="cmtt-8">&#x00A0;result)</span><br class="fancyvrb" /><a
+ id="x1-120004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2)</span><span
+class="cmtt-8">&#x00A0;[sign]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;bitwise</span><span
+class="cmtt-8">&#x00A0;AND</span><span
+class="cmtt-8">&#x00A0;0x80000000</span><span
+class="cmtt-8">&#x00A0;(unsigned</span><span
+class="cmtt-8">&#x00A0;result)</span>
+<br class="fancyvrb" /><a
+ id="x1-120006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3)</span><span
+class="cmtt-8">&#x00A0;[exponent]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;bitwise</span><span
+class="cmtt-8">&#x00A0;AND</span><span
+class="cmtt-8">&#x00A0;0x7fe00000)</span><span
+class="cmtt-8">&#x00A0;shifted</span><span
+class="cmtt-8">&#x00A0;right</span><span
+class="cmtt-8">&#x00A0;21</span><span
+class="cmtt-8">&#x00A0;bits</span><span
+class="cmtt-8">&#x00A0;(unsigned</span><span
+class="cmtt-8">&#x00A0;result)</span>
+<br class="fancyvrb" /><a
+ id="x1-120008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4)</span><span
+class="cmtt-8">&#x00A0;if</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[sign]</span><span
+class="cmtt-8">&#x00A0;is</span><span
+class="cmtt-8">&#x00A0;nonzero</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;then</span><span
+class="cmtt-8">&#x00A0;negate</span><span
+class="cmtt-8">&#x00A0;[mantissa]</span><br class="fancyvrb" /><a
+ id="x1-120010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5)</span><span
+class="cmtt-8">&#x00A0;return</span><span
+class="cmtt-8">&#x00A0;[mantissa]</span><span
+class="cmtt-8">&#x00A0;*</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;2</span><span
+class="cmtt-8">&#x00A0;^</span><span
+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[exponent]</span><span
+class="cmtt-8">&#x00A0;-</span><span
+class="cmtt-8">&#x00A0;788</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;)</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" >&#8221;lookup1_values(codebook_entries,codebook_dimensions)&#8221; 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 &#8217;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>&#8217;.
+
+
+
+<!--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" >&#8221;low_neighbor(v,x)&#8221; 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" >&#8221;high_neighbor(v,x)&#8221; 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" >&#8221;render_point(x0,y0,x1,y1,X)&#8221; 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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+<!--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>
+
+
+
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+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" >
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+class="cmtt-8">&#x00A0;[err]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[err]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[ady];</span>
+<br class="fancyvrb" /><a
+ id="x1-125050r25"></a><span
+class="cmr-6">25</span><span
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+class="cmtt-8">&#x00A0;(</span><span
+class="cmtt-8">&#x00A0;[err]</span><span
+class="cmtt-8">&#x00A0;&#x003E;=</span><span
+class="cmtt-8">&#x00A0;[adx]</span><span
+class="cmtt-8">&#x00A0;)</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-125052r26"></a><span
+class="cmr-6">26</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;16)</span><span
+class="cmtt-8">&#x00A0;[err]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[err]</span><span
+class="cmtt-8">&#x00A0;-</span><span
+class="cmtt-8">&#x00A0;[adx]</span><br class="fancyvrb" /><a
+ id="x1-125056r28"></a><span
+class="cmr-6">28</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;17)</span><span
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+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[y]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[sy]</span><br class="fancyvrb" /><a
+ id="x1-125058r29"></a><span
+class="cmr-6">29</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span>
+<br class="fancyvrb" /><a
+ id="x1-125060r30"></a><span
+class="cmr-6">30</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><span
+class="cmtt-8">&#x00A0;else</span><span
+class="cmtt-8">&#x00A0;{</span><br class="fancyvrb" /><a
+ id="x1-125062r31"></a><span
+class="cmr-6">31</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-125064r32"></a><span
+class="cmr-6">32</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;18)</span><span
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+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[y]</span><span
+class="cmtt-8">&#x00A0;+</span><span
+class="cmtt-8">&#x00A0;[base]</span><br class="fancyvrb" /><a
+ id="x1-125066r33"></a><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</span><br class="fancyvrb" /><a
+ id="x1-125070r35"></a><span
+class="cmr-6">35</span><span
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+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-125072r36"></a><span
+class="cmr-6">36</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;19)</span><span
+class="cmtt-8">&#x00A0;vector</span><span
+class="cmtt-8">&#x00A0;[v]</span><span
+class="cmtt-8">&#x00A0;element</span><span
+class="cmtt-8">&#x00A0;[x]</span><span
+class="cmtt-8">&#x00A0;=</span><span
+class="cmtt-8">&#x00A0;[y]</span><br class="fancyvrb" /><a
+ id="x1-125074r37"></a><span
+class="cmr-6">37</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><br class="fancyvrb" /><a
+ id="x1-125076r38"></a><span
+class="cmr-6">38</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;}</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">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1.0649863e-07,</span><span
+class="cmtt-8">&#x00A0;1.1341951e-07,</span><span
+class="cmtt-8">&#x00A0;1.2079015e-07,</span><span
+class="cmtt-8">&#x00A0;1.2863978e-07,</span><br class="fancyvrb" /><a
+ id="x1-127004r2"></a><span
+class="cmr-6">2</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1.3699951e-07,</span><span
+class="cmtt-8">&#x00A0;1.4590251e-07,</span><span
+class="cmtt-8">&#x00A0;1.5538408e-07,</span><span
+class="cmtt-8">&#x00A0;1.6548181e-07,</span>
+<br class="fancyvrb" /><a
+ id="x1-127006r3"></a><span
+class="cmr-6">3</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1.7623575e-07,</span><span
+class="cmtt-8">&#x00A0;1.8768855e-07,</span><span
+class="cmtt-8">&#x00A0;1.9988561e-07,</span><span
+class="cmtt-8">&#x00A0;2.1287530e-07,</span><br class="fancyvrb" /><a
+ id="x1-127008r4"></a><span
+class="cmr-6">4</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2.2670913e-07,</span><span
+class="cmtt-8">&#x00A0;2.4144197e-07,</span><span
+class="cmtt-8">&#x00A0;2.5713223e-07,</span><span
+class="cmtt-8">&#x00A0;2.7384213e-07,</span>
+<br class="fancyvrb" /><a
+ id="x1-127010r5"></a><span
+class="cmr-6">5</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2.9163793e-07,</span><span
+class="cmtt-8">&#x00A0;3.1059021e-07,</span><span
+class="cmtt-8">&#x00A0;3.3077411e-07,</span><span
+class="cmtt-8">&#x00A0;3.5226968e-07,</span><br class="fancyvrb" /><a
+ id="x1-127012r6"></a><span
+class="cmr-6">6</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3.7516214e-07,</span><span
+class="cmtt-8">&#x00A0;3.9954229e-07,</span><span
+class="cmtt-8">&#x00A0;4.2550680e-07,</span><span
+class="cmtt-8">&#x00A0;4.5315863e-07,</span>
+<br class="fancyvrb" /><a
+ id="x1-127014r7"></a><span
+class="cmr-6">7</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4.8260743e-07,</span><span
+class="cmtt-8">&#x00A0;5.1396998e-07,</span><span
+class="cmtt-8">&#x00A0;5.4737065e-07,</span><span
+class="cmtt-8">&#x00A0;5.8294187e-07,</span><br class="fancyvrb" /><a
+ id="x1-127016r8"></a><span
+class="cmr-6">8</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;6.2082472e-07,</span><span
+class="cmtt-8">&#x00A0;6.6116941e-07,</span><span
+class="cmtt-8">&#x00A0;7.0413592e-07,</span><span
+class="cmtt-8">&#x00A0;7.4989464e-07,</span>
+<br class="fancyvrb" /><a
+ id="x1-127018r9"></a><span
+class="cmr-6">9</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7.9862701e-07,</span><span
+class="cmtt-8">&#x00A0;8.5052630e-07,</span><span
+class="cmtt-8">&#x00A0;9.0579828e-07,</span><span
+class="cmtt-8">&#x00A0;9.6466216e-07,</span><br class="fancyvrb" /><a
+ id="x1-127020r10"></a><span
+class="cmr-6">10</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1.0273513e-06,</span><span
+class="cmtt-8">&#x00A0;1.0941144e-06,</span><span
+class="cmtt-8">&#x00A0;1.1652161e-06,</span><span
+class="cmtt-8">&#x00A0;1.2409384e-06,</span>
+<br class="fancyvrb" /><a
+ id="x1-127022r11"></a><span
+class="cmr-6">11</span><span
+class="cmtt-8">&#x00A0;</span><span
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+ id="x1-127024r12"></a><span
+class="cmr-6">12</span><span
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+class="cmtt-8">&#x00A0;1.7000785e-06,</span><span
+class="cmtt-8">&#x00A0;1.8105592e-06,</span><span
+class="cmtt-8">&#x00A0;1.9282195e-06,</span><span
+class="cmtt-8">&#x00A0;2.0535261e-06,</span>
+<br class="fancyvrb" /><a
+ id="x1-127026r13"></a><span
+class="cmr-6">13</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2.1869758e-06,</span><span
+class="cmtt-8">&#x00A0;2.3290978e-06,</span><span
+class="cmtt-8">&#x00A0;2.4804557e-06,</span><span
+class="cmtt-8">&#x00A0;2.6416497e-06,</span><br class="fancyvrb" /><a
+ id="x1-127028r14"></a><span
+class="cmr-6">14</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;2.8133190e-06,</span><span
+class="cmtt-8">&#x00A0;2.9961443e-06,</span><span
+class="cmtt-8">&#x00A0;3.1908506e-06,</span><span
+class="cmtt-8">&#x00A0;3.3982101e-06,</span>
+<br class="fancyvrb" /><a
+ id="x1-127030r15"></a><span
+class="cmr-6">15</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;3.6190449e-06,</span><span
+class="cmtt-8">&#x00A0;3.8542308e-06,</span><span
+class="cmtt-8">&#x00A0;4.1047004e-06,</span><span
+class="cmtt-8">&#x00A0;4.3714470e-06,</span><br class="fancyvrb" /><a
+ id="x1-127032r16"></a><span
+class="cmr-6">16</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;4.6555282e-06,</span><span
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+class="cmtt-8">&#x00A0;5.2802740e-06,</span><span
+class="cmtt-8">&#x00A0;5.6234160e-06,</span>
+<br class="fancyvrb" /><a
+ id="x1-127034r17"></a><span
+class="cmr-6">17</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;5.9888572e-06,</span><span
+class="cmtt-8">&#x00A0;6.3780469e-06,</span><span
+class="cmtt-8">&#x00A0;6.7925283e-06,</span><span
+class="cmtt-8">&#x00A0;7.2339451e-06,</span><br class="fancyvrb" /><a
+ id="x1-127036r18"></a><span
+class="cmr-6">18</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;7.7040476e-06,</span><span
+class="cmtt-8">&#x00A0;8.2047000e-06,</span><span
+class="cmtt-8">&#x00A0;8.7378876e-06,</span><span
+class="cmtt-8">&#x00A0;9.3057248e-06,</span>
+<br class="fancyvrb" /><a
+ id="x1-127038r19"></a><span
+class="cmr-6">19</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;9.9104632e-06,</span><span
+class="cmtt-8">&#x00A0;1.0554501e-05,</span><span
+class="cmtt-8">&#x00A0;1.1240392e-05,</span><span
+class="cmtt-8">&#x00A0;1.1970856e-05,</span><br class="fancyvrb" /><a
+ id="x1-127040r20"></a><span
+class="cmr-6">20</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;1.2748789e-05,</span><span
+class="cmtt-8">&#x00A0;1.3577278e-05,</span><span
+class="cmtt-8">&#x00A0;1.4459606e-05,</span><span
+class="cmtt-8">&#x00A0;1.5399272e-05,</span>
+<br class="fancyvrb" /><a
+ id="x1-127042r21"></a><span
+class="cmr-6">21</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+ id="x1-127126r63"></a><span
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+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.64356699,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.68538959,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
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+class="cmtt-8">&#x00A0;0.72993007,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.77736504,</span><br class="fancyvrb" /><a
+ id="x1-127128r64"></a><span
+class="cmr-6">64</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.82788260,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.88168307,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;0.9389798,</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;</span><span
+class="cmtt-8">&#x00A0;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&#x00A0;1</a>, &#8220;<a
+href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>&#8221; 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 &#8217;Vorbis I audio file&#8217; is taken to imply Vorbis audio existing alone
+within a degenerate Ogg stream. A compliant &#8217;Vorbis audio player&#8217; 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 &#8217;beginning of stream&#8217; 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 &#8217;end of stream&#8217; 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&#8217;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 &#8217;last PCM sample&#8217; 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 &#8217;-1&#8217;.
+ <!--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 &#8221;long block&#8221; and the next Vorbis packet encodes a &#8221;short block&#8221;, 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">&#8220;RTP Payload Format for Vorbis Encoded Audio&#8221; </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&#8217;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&#8217;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">&#x00A0;&#x00A0;&#x00A0;</span></span><a
+ id="XSporer/Brandenburg/Edler"></a>T.&#x00A0;Sporer, K.&#x00A0;Brandenburg and
+ B.&#x00A0;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>
+
+
+
+