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- <head><title>Vorbis I specification</title>
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- <div class="maketitle">
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- <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 3, 2012</span></div>
- </div>
- <h3 class="likesectionHead"><a
- id="x1-1000"></a>Contents</h3>
- <div class="tableofcontents">
-  <span class="sectionToc" >1 <a
- href="#x1-20001" id="QQ2-1-2">Introduction and Description</a></span>
- <br />  <span class="subsectionToc" >1.1 <a
- href="#x1-30001.1" id="QQ2-1-3">Overview</a></span>
- <br />   <span class="subsubsectionToc" >1.1.1 <a
- href="#x1-40001.1.1" id="QQ2-1-4">Application</a></span>
- <br />   <span class="subsubsectionToc" >1.1.2 <a
- href="#x1-50001.1.2" id="QQ2-1-5">Classification</a></span>
- <br />   <span class="subsubsectionToc" >1.1.3 <a
- href="#x1-60001.1.3" id="QQ2-1-6">Assumptions</a></span>
- <br />   <span class="subsubsectionToc" >1.1.4 <a
- href="#x1-70001.1.4" id="QQ2-1-7">Codec Setup and Probability Model</a></span>
- <br />   <span class="subsubsectionToc" >1.1.5 <a
- href="#x1-90001.1.5" id="QQ2-1-9">Format Specification</a></span>
- <br />   <span class="subsubsectionToc" >1.1.6 <a
- href="#x1-100001.1.6" id="QQ2-1-10">Hardware Profile</a></span>
- <br />  <span class="subsectionToc" >1.2 <a
- href="#x1-110001.2" id="QQ2-1-11">Decoder Configuration</a></span>
- <br />   <span class="subsubsectionToc" >1.2.1 <a
- href="#x1-120001.2.1" id="QQ2-1-13">Global Config</a></span>
- <br />   <span class="subsubsectionToc" >1.2.2 <a
- href="#x1-130001.2.2" id="QQ2-1-14">Mode</a></span>
- <br />   <span class="subsubsectionToc" >1.2.3 <a
- href="#x1-140001.2.3" id="QQ2-1-15">Mapping</a></span>
-
-
- <br />   <span class="subsubsectionToc" >1.2.4 <a
- href="#x1-150001.2.4" id="QQ2-1-16">Floor</a></span>
- <br />   <span class="subsubsectionToc" >1.2.5 <a
- href="#x1-160001.2.5" id="QQ2-1-17">Residue</a></span>
- <br />   <span class="subsubsectionToc" >1.2.6 <a
- href="#x1-170001.2.6" id="QQ2-1-18">Codebooks</a></span>
- <br />  <span class="subsectionToc" >1.3 <a
- href="#x1-180001.3" id="QQ2-1-19">High-level Decode Process</a></span>
- <br />   <span class="subsubsectionToc" >1.3.1 <a
- href="#x1-190001.3.1" id="QQ2-1-20">Decode Setup</a></span>
- <br />   <span class="subsubsectionToc" >1.3.2 <a
- href="#x1-230001.3.2" id="QQ2-1-24">Decode Procedure</a></span>
- <br /> <span class="sectionToc" >2 <a
- href="#x1-360002" id="QQ2-1-39">Bitpacking Convention</a></span>
- <br />  <span class="subsectionToc" >2.1 <a
- href="#x1-370002.1" id="QQ2-1-40">Overview</a></span>
- <br />   <span class="subsubsectionToc" >2.1.1 <a
- href="#x1-380002.1.1" id="QQ2-1-41">octets, bytes and words</a></span>
- <br />   <span class="subsubsectionToc" >2.1.2 <a
- href="#x1-390002.1.2" id="QQ2-1-42">bit order</a></span>
- <br />   <span class="subsubsectionToc" >2.1.3 <a
- href="#x1-400002.1.3" id="QQ2-1-43">byte order</a></span>
- <br />   <span class="subsubsectionToc" >2.1.4 <a
- href="#x1-410002.1.4" id="QQ2-1-44">coding bits into byte sequences</a></span>
- <br />   <span class="subsubsectionToc" >2.1.5 <a
- href="#x1-420002.1.5" id="QQ2-1-45">signedness</a></span>
- <br />   <span class="subsubsectionToc" >2.1.6 <a
- href="#x1-430002.1.6" id="QQ2-1-46">coding example</a></span>
- <br />   <span class="subsubsectionToc" >2.1.7 <a
- href="#x1-440002.1.7" id="QQ2-1-47">decoding example</a></span>
- <br />   <span class="subsubsectionToc" >2.1.8 <a
- href="#x1-450002.1.8" id="QQ2-1-48">end-of-packet alignment</a></span>
- <br />   <span class="subsubsectionToc" >2.1.9 <a
- href="#x1-460002.1.9" id="QQ2-1-49">reading zero bits</a></span>
- <br /> <span class="sectionToc" >3 <a
- href="#x1-470003" id="QQ2-1-50">Probability Model and Codebooks</a></span>
- <br />  <span class="subsectionToc" >3.1 <a
- href="#x1-480003.1" id="QQ2-1-51">Overview</a></span>
- <br />   <span class="subsubsectionToc" >3.1.1 <a
- href="#x1-490003.1.1" id="QQ2-1-52">Bitwise operation</a></span>
- <br />  <span class="subsectionToc" >3.2 <a
- href="#x1-500003.2" id="QQ2-1-53">Packed codebook format</a></span>
- <br />   <span class="subsubsectionToc" >3.2.1 <a
- href="#x1-510003.2.1" id="QQ2-1-54">codebook decode</a></span>
- <br />  <span class="subsectionToc" >3.3 <a
- href="#x1-570003.3" id="QQ2-1-62">Use of the codebook abstraction</a></span>
- <br /> <span class="sectionToc" >4 <a
- href="#x1-580004" id="QQ2-1-63">Codec Setup and Packet Decode</a></span>
- <br />  <span class="subsectionToc" >4.1 <a
- href="#x1-590004.1" id="QQ2-1-64">Overview</a></span>
- <br />  <span class="subsectionToc" >4.2 <a
- href="#x1-600004.2" id="QQ2-1-65">Header decode and decode setup</a></span>
- <br />   <span class="subsubsectionToc" >4.2.1 <a
- href="#x1-610004.2.1" id="QQ2-1-66">Common header decode</a></span>
- <br />   <span class="subsubsectionToc" >4.2.2 <a
- href="#x1-620004.2.2" id="QQ2-1-67">Identification header</a></span>
- <br />   <span class="subsubsectionToc" >4.2.3 <a
- href="#x1-630004.2.3" id="QQ2-1-68">Comment header</a></span>
-
-
- <br />   <span class="subsubsectionToc" >4.2.4 <a
- href="#x1-640004.2.4" id="QQ2-1-69">Setup header</a></span>
- <br />  <span class="subsectionToc" >4.3 <a
- href="#x1-710004.3" id="QQ2-1-77">Audio packet decode and synthesis</a></span>
- <br />   <span class="subsubsectionToc" >4.3.1 <a
- href="#x1-720004.3.1" id="QQ2-1-78">packet type, mode and window decode</a></span>
- <br />   <span class="subsubsectionToc" >4.3.2 <a
- href="#x1-730004.3.2" id="QQ2-1-79">floor curve decode</a></span>
- <br />   <span class="subsubsectionToc" >4.3.3 <a
- href="#x1-740004.3.3" id="QQ2-1-80">nonzero vector propagate</a></span>
- <br />   <span class="subsubsectionToc" >4.3.4 <a
- href="#x1-750004.3.4" id="QQ2-1-81">residue decode</a></span>
- <br />   <span class="subsubsectionToc" >4.3.5 <a
- href="#x1-760004.3.5" id="QQ2-1-82">inverse coupling</a></span>
- <br />   <span class="subsubsectionToc" >4.3.6 <a
- href="#x1-770004.3.6" id="QQ2-1-83">dot product</a></span>
- <br />   <span class="subsubsectionToc" >4.3.7 <a
- href="#x1-780004.3.7" id="QQ2-1-84">inverse MDCT</a></span>
- <br />   <span class="subsubsectionToc" >4.3.8 <a
- href="#x1-790004.3.8" id="QQ2-1-85">overlap_add</a></span>
- <br />   <span class="subsubsectionToc" >4.3.9 <a
- href="#x1-800004.3.9" id="QQ2-1-86">output channel order</a></span>
- <br /> <span class="sectionToc" >5 <a
- href="#x1-810005" id="QQ2-1-87">comment field and header specification</a></span>
- <br />  <span class="subsectionToc" >5.1 <a
- href="#x1-820005.1" id="QQ2-1-88">Overview</a></span>
- <br />  <span class="subsectionToc" >5.2 <a
- href="#x1-830005.2" id="QQ2-1-89">Comment encoding</a></span>
- <br />   <span class="subsubsectionToc" >5.2.1 <a
- href="#x1-840005.2.1" id="QQ2-1-90">Structure</a></span>
- <br />   <span class="subsubsectionToc" >5.2.2 <a
- href="#x1-850005.2.2" id="QQ2-1-91">Content vector format</a></span>
- <br />   <span class="subsubsectionToc" >5.2.3 <a
- href="#x1-880005.2.3" id="QQ2-1-94">Encoding</a></span>
- <br /> <span class="sectionToc" >6 <a
- href="#x1-890006" id="QQ2-1-95">Floor type 0 setup and decode</a></span>
- <br />  <span class="subsectionToc" >6.1 <a
- href="#x1-900006.1" id="QQ2-1-96">Overview</a></span>
- <br />  <span class="subsectionToc" >6.2 <a
- href="#x1-910006.2" id="QQ2-1-97">Floor 0 format</a></span>
- <br />   <span class="subsubsectionToc" >6.2.1 <a
- href="#x1-920006.2.1" id="QQ2-1-98">header decode</a></span>
- <br />   <span class="subsubsectionToc" >6.2.2 <a
- href="#x1-930006.2.2" id="QQ2-1-99">packet decode</a></span>
- <br />   <span class="subsubsectionToc" >6.2.3 <a
- href="#x1-940006.2.3" id="QQ2-1-100">curve computation</a></span>
- <br /> <span class="sectionToc" >7 <a
- href="#x1-950007" id="QQ2-1-101">Floor type 1 setup and decode</a></span>
- <br />  <span class="subsectionToc" >7.1 <a
- href="#x1-960007.1" id="QQ2-1-102">Overview</a></span>
- <br />  <span class="subsectionToc" >7.2 <a
- href="#x1-970007.2" id="QQ2-1-103">Floor 1 format</a></span>
- <br />   <span class="subsubsectionToc" >7.2.1 <a
- href="#x1-980007.2.1" id="QQ2-1-104">model</a></span>
- <br />   <span class="subsubsectionToc" >7.2.2 <a
- href="#x1-990007.2.2" id="QQ2-1-109">header decode</a></span>
- <br />   <span class="subsubsectionToc" >7.2.3 <a
- href="#x1-1000007.2.3" id="QQ2-1-110">packet decode</a></span>
-
-
- <br />   <span class="subsubsectionToc" >7.2.4 <a
- href="#x1-1010007.2.4" id="QQ2-1-111">curve computation</a></span>
- <br /> <span class="sectionToc" >8 <a
- href="#x1-1020008" id="QQ2-1-112">Residue setup and decode</a></span>
- <br />  <span class="subsectionToc" >8.1 <a
- href="#x1-1030008.1" id="QQ2-1-113">Overview</a></span>
- <br />  <span class="subsectionToc" >8.2 <a
- href="#x1-1040008.2" id="QQ2-1-114">Residue format</a></span>
- <br />  <span class="subsectionToc" >8.3 <a
- href="#x1-1050008.3" id="QQ2-1-116">residue 0</a></span>
- <br />  <span class="subsectionToc" >8.4 <a
- href="#x1-1060008.4" id="QQ2-1-117">residue 1</a></span>
- <br />  <span class="subsectionToc" >8.5 <a
- href="#x1-1070008.5" id="QQ2-1-118">residue 2</a></span>
- <br />  <span class="subsectionToc" >8.6 <a
- href="#x1-1080008.6" id="QQ2-1-120">Residue decode</a></span>
- <br />   <span class="subsubsectionToc" >8.6.1 <a
- href="#x1-1090008.6.1" id="QQ2-1-121">header decode</a></span>
- <br />   <span class="subsubsectionToc" >8.6.2 <a
- href="#x1-1100008.6.2" id="QQ2-1-122">packet decode</a></span>
- <br />   <span class="subsubsectionToc" >8.6.3 <a
- href="#x1-1110008.6.3" id="QQ2-1-123">format 0 specifics</a></span>
- <br />   <span class="subsubsectionToc" >8.6.4 <a
- href="#x1-1120008.6.4" id="QQ2-1-124">format 1 specifics</a></span>
- <br />   <span class="subsubsectionToc" >8.6.5 <a
- href="#x1-1130008.6.5" id="QQ2-1-125">format 2 specifics</a></span>
- <br /> <span class="sectionToc" >9 <a
- href="#x1-1140009" id="QQ2-1-126">Helper equations</a></span>
- <br />  <span class="subsectionToc" >9.1 <a
- href="#x1-1150009.1" id="QQ2-1-127">Overview</a></span>
- <br />  <span class="subsectionToc" >9.2 <a
- href="#x1-1160009.2" id="QQ2-1-128">Functions</a></span>
- <br />   <span class="subsubsectionToc" >9.2.1 <a
- href="#x1-1170009.2.1" id="QQ2-1-129">ilog</a></span>
- <br />   <span class="subsubsectionToc" >9.2.2 <a
- href="#x1-1180009.2.2" id="QQ2-1-130">float32_unpack</a></span>
- <br />   <span class="subsubsectionToc" >9.2.3 <a
- href="#x1-1190009.2.3" id="QQ2-1-131">lookup1_values</a></span>
- <br />   <span class="subsubsectionToc" >9.2.4 <a
- href="#x1-1200009.2.4" id="QQ2-1-132">low_neighbor</a></span>
- <br />   <span class="subsubsectionToc" >9.2.5 <a
- href="#x1-1210009.2.5" id="QQ2-1-133">high_neighbor</a></span>
- <br />   <span class="subsubsectionToc" >9.2.6 <a
- href="#x1-1220009.2.6" id="QQ2-1-134">render_point</a></span>
- <br />   <span class="subsubsectionToc" >9.2.7 <a
- href="#x1-1230009.2.7" id="QQ2-1-135">render_line</a></span>
- <br /> <span class="sectionToc" >10 <a
- href="#x1-12400010" id="QQ2-1-136">Tables</a></span>
- <br />  <span class="subsectionToc" >10.1 <a
- href="#x1-12500010.1" id="QQ2-1-137">floor1_inverse_dB_table</a></span>
- <br /> <span class="sectionToc" >A <a
- href="#x1-126000A" id="QQ2-1-138">Embedding Vorbis into an Ogg stream</a></span>
- <br />  <span class="subsectionToc" >A.1 <a
- href="#x1-127000A.1" id="QQ2-1-139">Overview</a></span>
- <br />   <span class="subsubsectionToc" >A.1.1 <a
- href="#x1-128000A.1.1" id="QQ2-1-140">Restrictions</a></span>
- <br />   <span class="subsubsectionToc" >A.1.2 <a
- href="#x1-129000A.1.2" id="QQ2-1-141">MIME type</a></span>
-
-
- <br />  <span class="subsectionToc" >A.2 <a
- href="#x1-130000A.2" id="QQ2-1-142">Encapsulation</a></span>
- <br /> <span class="sectionToc" >B <a
- href="#x1-132000B" id="QQ2-1-144">Vorbis encapsulation in RTP</a></span>
- </div>
-
-
- <h3 class="sectionHead"><span class="titlemark">1. </span> <a
- id="x1-20001"></a>Introduction and Description</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">1.1. </span> <a
- id="x1-30001.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >This document provides a high level description of the Vorbis codec’s construction. A bit-by-bit
- specification appears beginning in <a
- href="#x1-580004">Section 4</a>, “<a
- href="#x1-580004">Codec Setup and Packet Decode<!--tex4ht:ref: vorbis:spec:codec --></a>”. The later
- sections assume a high-level understanding of the Vorbis decode process, which is provided
- here.
- <!--l. 15--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.1. </span> <a
- id="x1-40001.1.1"></a>Application</h5>
- <!--l. 16--><p class="noindent" >Vorbis is a general purpose perceptual audio CODEC intended to allow maximum encoder
- flexibility, thus allowing it to scale competitively over an exceptionally wide range of bitrates. At
- the high quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits) it is in the same
- league as MPEG-2 and MPC. Similarly, the 1.0 encoder can encode high-quality CD and DAT
- rate stereo at below 48kbps without resampling to a lower rate. Vorbis is also intended for lower
- and higher sample rates (from 8kHz telephony to 192kHz digital masters) and a range of channel
- representations (monaural, polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
- discrete channels).
- <!--l. 29--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.2. </span> <a
- id="x1-50001.1.2"></a>Classification</h5>
- <!--l. 30--><p class="noindent" >Vorbis I is a forward-adaptive monolithic transform CODEC based on the Modified Discrete
- Cosine Transform. The codec is structured to allow addition of a hybrid wavelet filterbank in
- Vorbis II to offer better transient response and reproduction using a transform better suited to
- localized time events.
-
-
- <!--l. 37--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.3. </span> <a
- id="x1-60001.1.3"></a>Assumptions</h5>
- <!--l. 39--><p class="noindent" >The Vorbis CODEC design assumes a complex, psychoacoustically-aware encoder and simple,
- low-complexity decoder. Vorbis decode is computationally simpler than mp3, although it does
- require more working memory as Vorbis has no static probability model; the vector codebooks
- used in the first stage of decoding from the bitstream are packed in their entirety into the Vorbis
- bitstream headers. In packed form, these codebooks occupy only a few kilobytes; the extent to
- which they are pre-decoded into a cache is the dominant factor in decoder memory
- usage.
- <!--l. 50--><p class="noindent" >Vorbis provides none of its own framing, synchronization or protection against errors; it
- is solely a method of accepting input audio, dividing it into individual frames and
- compressing these frames into raw, unformatted ’packets’. The decoder then accepts
- these raw packets in sequence, decodes them, synthesizes audio frames from them, and
- reassembles the frames into a facsimile of the original audio stream. Vorbis is a free-form
- variable bit rate (VBR) codec and packets have no minimum size, maximum size, or
- fixed/expected size. Packets are designed that they may be truncated (or padded)
- and remain decodable; this is not to be considered an error condition and is used
- extensively in bitrate management in peeling. Both the transport mechanism and
- decoder must allow that a packet may be any size, or end before or after packet decode
- expects.
- <!--l. 64--><p class="noindent" >Vorbis packets are thus intended to be used with a transport mechanism that provides free-form
- framing, sync, positioning and error correction in accordance with these design assumptions, such
- as Ogg (for file transport) or RTP (for network multicast). For purposes of a few examples in this
- document, we will assume that Vorbis is to be embedded in an Ogg stream specifically,
- although this is by no means a requirement or fundamental assumption in the Vorbis
- design.
- <!--l. 72--><p class="noindent" >The specification for embedding Vorbis into an Ogg transport stream is in <a
- href="#x1-126000A">Section A</a>,
- “<a
- href="#x1-126000A">Embedding Vorbis into an Ogg stream<!--tex4ht:ref: vorbis:over:ogg --></a>”.
- <!--l. 77--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.4. </span> <a
- id="x1-70001.1.4"></a>Codec Setup and Probability Model</h5>
- <!--l. 79--><p class="noindent" >Vorbis’ heritage is as a research CODEC and its current design reflects a desire to allow multiple
- decades of continuous encoder improvement before running out of room within the codec
- specification. For these reasons, configurable aspects of codec setup intentionally lean toward the
- extreme of forward adaptive.
-
-
- <!--l. 85--><p class="noindent" >The single most controversial design decision in Vorbis (and the most unusual for a Vorbis
- developer to keep in mind) is that the entire probability model of the codec, the Huffman and
- VQ codebooks, is packed into the bitstream header along with extensive CODEC setup
- parameters (often several hundred fields). This makes it impossible, as it would be with
- MPEG audio layers, to embed a simple frame type flag in each audio packet, or begin
- decode at any frame in the stream without having previously fetched the codec setup
- header.
- <!--l. 95--><p class="noindent" ><span class="likesubparagraphHead"><a
- id="x1-80001.1.4"></a><span
- class="cmbx-12">Note:</span></span> Vorbis <span
- class="cmti-12">can </span>initiate decode at any arbitrary packet within a bitstream so long as the codec
- has been initialized/setup with the setup headers.
- <!--l. 101--><p class="noindent" >Thus, Vorbis headers are both required for decode to begin and relatively large as bitstream
- headers go. The header size is unbounded, although for streaming a rule-of-thumb of 4kB or less
- is recommended (and Xiph.Org’s Vorbis encoder follows this suggestion).
- <!--l. 106--><p class="noindent" >Our own design work indicates the primary liability of the required header is in mindshare; it is
- an unusual design and thus causes some amount of complaint among engineers as this runs
- against current design trends (and also points out limitations in some existing software/interface
- designs, such as Windows’ ACM codec framework). However, we find that it does not
- fundamentally limit Vorbis’ suitable application space.
- <!--l. 115--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.5. </span> <a
- id="x1-90001.1.5"></a>Format Specification</h5>
- <!--l. 116--><p class="noindent" >The Vorbis format is well-defined by its decode specification; any encoder that produces packets
- that are correctly decoded by the reference Vorbis decoder described below may be considered
- a proper Vorbis encoder. A decoder must faithfully and completely implement the
- specification defined below (except where noted) to be considered a proper Vorbis
- decoder.
- <!--l. 123--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.1.6. </span> <a
- id="x1-100001.1.6"></a>Hardware Profile</h5>
-
-
- <!--l. 124--><p class="noindent" >Although Vorbis decode is computationally simple, it may still run into specific limitations of an
- embedded design. For this reason, embedded designs are allowed to deviate in limited ways from
- the ‘full’ decode specification yet still be certified compliant. These optional omissions are
- labelled in the spec where relevant.
- <!--l. 131--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">1.2. </span> <a
- id="x1-110001.2"></a>Decoder Configuration</h4>
- <!--l. 133--><p class="noindent" >Decoder setup consists of configuration of multiple, self-contained component abstractions that
- perform specific functions in the decode pipeline. Each different component instance of a specific
- type is semantically interchangeable; decoder configuration consists both of internal component
- configuration, as well as arrangement of specific instances into a decode pipeline. Componentry
- arrangement is roughly as follows:
- <div class="center"
- >
- <!--l. 141--><p class="noindent" >
- <!--l. 142--><p class="noindent" ><img
- src="components.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 1: </span><span
- class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-110011 -->
- </div>
- <!--l. 146--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.1. </span> <a
- id="x1-120001.2.1"></a>Global Config</h5>
- <!--l. 147--><p class="noindent" >Global codec configuration consists of a few audio related fields (sample rate, channels), Vorbis
- version (always ’0’ in Vorbis I), bitrate hints, and the lists of component instances. All other
- configuration is in the context of specific components.
- <!--l. 152--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.2. </span> <a
- id="x1-130001.2.2"></a>Mode</h5>
-
-
- <!--l. 154--><p class="noindent" >Each Vorbis frame is coded according to a master ’mode’. A bitstream may use one or many
- modes.
- <!--l. 157--><p class="noindent" >The mode mechanism is used to encode a frame according to one of multiple possible
- methods with the intention of choosing a method best suited to that frame. Different
- modes are, e.g. how frame size is changed from frame to frame. The mode number of a
- frame serves as a top level configuration switch for all other specific aspects of frame
- decode.
- <!--l. 164--><p class="noindent" >A ’mode’ configuration consists of a frame size setting, window type (always 0, the Vorbis
- window, in Vorbis I), transform type (always type 0, the MDCT, in Vorbis I) and a mapping
- number. The mapping number specifies which mapping configuration instance to use for low-level
- packet decode and synthesis.
- <!--l. 171--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.3. </span> <a
- id="x1-140001.2.3"></a>Mapping</h5>
- <!--l. 173--><p class="noindent" >A mapping contains a channel coupling description and a list of ’submaps’ that bundle sets
- of channel vectors together for grouped encoding and decoding. These submaps are
- not references to external components; the submap list is internal and specific to a
- mapping.
- <!--l. 178--><p class="noindent" >A ’submap’ is a configuration/grouping that applies to a subset of floor and residue vectors
- within a mapping. The submap functions as a last layer of indirection such that specific special
- floor or residue settings can be applied not only to all the vectors in a given mode, but also
- specific vectors in a specific mode. Each submap specifies the proper floor and residue
- instance number to use for decoding that submap’s spectral floor and spectral residue
- vectors.
- <!--l. 186--><p class="noindent" >As an example:
- <!--l. 188--><p class="noindent" >Assume a Vorbis stream that contains six channels in the standard 5.1 format. The sixth
- channel, as is normal in 5.1, is bass only. Therefore it would be wasteful to encode a
- full-spectrum version of it as with the other channels. The submapping mechanism can be used
- to apply a full range floor and residue encoding to channels 0 through 4, and a bass-only
- representation to the bass channel, thus saving space. In this example, channels 0-4 belong to
- submap 0 (which indicates use of a full-range floor) and channel 5 belongs to submap 1, which
- uses a bass-only representation.
-
-
- <!--l. 199--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.4. </span> <a
- id="x1-150001.2.4"></a>Floor</h5>
- <!--l. 201--><p class="noindent" >Vorbis encodes a spectral ’floor’ vector for each PCM channel. This vector is a low-resolution
- representation of the audio spectrum for the given channel in the current frame, generally used
- akin to a whitening filter. It is named a ’floor’ because the Xiph.Org reference encoder has
- historically used it as a unit-baseline for spectral resolution.
- <!--l. 208--><p class="noindent" >A floor encoding may be of two types. Floor 0 uses a packed LSP representation on a dB
- amplitude scale and Bark frequency scale. Floor 1 represents the curve as a piecewise linear
- interpolated representation on a dB amplitude scale and linear frequency scale. The two floors
- are semantically interchangeable in encoding/decoding. However, floor type 1 provides more
- stable inter-frame behavior, and so is the preferred choice in all coupled-stereo and
- high bitrate modes. Floor 1 is also considerably less expensive to decode than floor
- 0.
- <!--l. 218--><p class="noindent" >Floor 0 is not to be considered deprecated, but it is of limited modern use. No known Vorbis
- encoder past Xiph.Org’s own beta 4 makes use of floor 0.
- <!--l. 222--><p class="noindent" >The values coded/decoded by a floor are both compactly formatted and make use of entropy
- coding to save space. For this reason, a floor configuration generally refers to multiple
- codebooks in the codebook component list. Entropy coding is thus provided as an
- abstraction, and each floor instance may choose from any and all available codebooks when
- coding/decoding.
- <!--l. 230--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.5. </span> <a
- id="x1-160001.2.5"></a>Residue</h5>
- <!--l. 231--><p class="noindent" >The spectral residue is the fine structure of the audio spectrum once the floor curve has been
- subtracted out. In simplest terms, it is coded in the bitstream using cascaded (multi-pass) vector
- quantization according to one of three specific packing/coding algorithms numbered
- 0 through 2. The packing algorithm details are configured by residue instance. As
- with the floor components, the final VQ/entropy encoding is provided by external
- codebook instances and each residue instance may choose from any and all available
- codebooks.
- <!--l. 241--><p class="noindent" >
-
-
- <h5 class="subsubsectionHead"><span class="titlemark">1.2.6. </span> <a
- id="x1-170001.2.6"></a>Codebooks</h5>
- <!--l. 243--><p class="noindent" >Codebooks are a self-contained abstraction that perform entropy decoding and, optionally, use
- the entropy-decoded integer value as an offset into an index of output value vectors, returning
- the indicated vector of values.
- <!--l. 248--><p class="noindent" >The entropy coding in a Vorbis I codebook is provided by a standard Huffman binary tree
- representation. This tree is tightly packed using one of several methods, depending on whether
- codeword lengths are ordered or unordered, or the tree is sparse.
- <!--l. 253--><p class="noindent" >The codebook vector index is similarly packed according to index characteristic. Most commonly,
- the vector index is encoded as a single list of values of possible values that are then permuted
- into a list of n-dimensional rows (lattice VQ).
- <!--l. 260--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">1.3. </span> <a
- id="x1-180001.3"></a>High-level Decode Process</h4>
- <!--l. 262--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.3.1. </span> <a
- id="x1-190001.3.1"></a>Decode Setup</h5>
- <!--l. 264--><p class="noindent" >Before decoding can begin, a decoder must initialize using the bitstream headers matching the
- stream to be decoded. Vorbis uses three header packets; all are required, in-order, by
- this specification. Once set up, decode may begin at any audio packet belonging to
- the Vorbis stream. In Vorbis I, all packets after the three initial headers are audio
- packets.
- <!--l. 271--><p class="noindent" >The header packets are, in order, the identification header, the comments header, and the setup
- header.
- <!--l. 274--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-200001.3.1"></a><span
- class="cmbx-12">Identification Header</span></span>
- The identification header identifies the bitstream as Vorbis, Vorbis version, and the simple audio
- characteristics of the stream such as sample rate and number of channels.
-
-
- <!--l. 279--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-210001.3.1"></a><span
- class="cmbx-12">Comment Header</span></span>
- The comment header includes user text comments (“tags”) and a vendor string for the
- application/library that produced the bitstream. The encoding and proper use of the comment
- header is described in <a
- href="#x1-810005">Section 5</a>, “<a
- href="#x1-810005">comment field and header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
- <!--l. 284--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-220001.3.1"></a><span
- class="cmbx-12">Setup Header</span></span>
- The setup header includes extensive CODEC setup information as well as the complete VQ and
- Huffman codebooks needed for decode.
- <!--l. 289--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">1.3.2. </span> <a
- id="x1-230001.3.2"></a>Decode Procedure</h5>
- <!--l. 291--><p class="noindent" >The decoding and synthesis procedure for all audio packets is fundamentally the same.
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem">decode packet type flag
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">decode mode number
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">decode window shape (long windows only)
- </dd><dt class="enumerate-enumitem">
- 4. </dt><dd
- class="enumerate-enumitem">decode floor
- </dd><dt class="enumerate-enumitem">
- 5. </dt><dd
- class="enumerate-enumitem">decode residue into residue vectors
- </dd><dt class="enumerate-enumitem">
- 6. </dt><dd
- class="enumerate-enumitem">inverse channel coupling of residue vectors
- </dd><dt class="enumerate-enumitem">
- 7. </dt><dd
- class="enumerate-enumitem">generate floor curve from decoded floor data
- </dd><dt class="enumerate-enumitem">
- 8. </dt><dd
- class="enumerate-enumitem">compute dot product of floor and residue, producing audio spectrum vector
- </dd><dt class="enumerate-enumitem">
- 9. </dt><dd
- class="enumerate-enumitem">inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis
- I
-
-
- </dd><dt class="enumerate-enumitem">
- 10. </dt><dd
- class="enumerate-enumitem">overlap/add left-hand output of transform with right-hand output of previous frame
- </dd><dt class="enumerate-enumitem">
- 11. </dt><dd
- class="enumerate-enumitem">store right hand-data from transform of current frame for future lapping
- </dd><dt class="enumerate-enumitem">
- 12. </dt><dd
- class="enumerate-enumitem">if not first frame, return results of overlap/add as audio result of current frame</dd></dl>
- <!--l. 308--><p class="noindent" >Note that clever rearrangement of the synthesis arithmetic is possible; as an example, one can
- take advantage of symmetries in the MDCT to store the right-hand transform data of a partial
- MDCT for a 50% inter-frame buffer space savings, and then complete the transform later before
- overlap/add with the next frame. This optimization produces entirely equivalent output and is
- naturally perfectly legal. The decoder must be <span
- class="cmti-12">entirely mathematically equivalent </span>to the
- specification, it need not be a literal semantic implementation.
- <!--l. 317--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-240001.3.2"></a><span
- class="cmbx-12">Packet type decode</span></span>
- Vorbis I uses four packet types. The first three packet types mark each of the three Vorbis
- headers described above. The fourth packet type marks an audio packet. All other packet types
- are reserved; packets marked with a reserved type should be ignored.
- <!--l. 324--><p class="noindent" >Following the three header packets, all packets in a Vorbis I stream are audio. The first step of
- audio packet decode is to read and verify the packet type; <span
- class="cmti-12">a non-audio packet when audio is</span>
- <span
- class="cmti-12">expected indicates stream corruption or a non-compliant stream. The decoder must ignore the</span>
- <span
- class="cmti-12">packet and not attempt decoding it to audio</span>.
- <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-250001.3.2"></a><span
- class="cmbx-12">Mode decode</span></span>
- Vorbis allows an encoder to set up multiple, numbered packet ’modes’, as described earlier, all of
- which may be used in a given Vorbis stream. The mode is encoded as an integer used as a direct
- offset into the mode instance index.
- <!--l. 341--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-260001.3.2"></a><span
- class="cmbx-12">Window shape decode (long windows only)</span></span>
- Vorbis frames may be one of two PCM sample sizes specified during codec setup. In Vorbis I,
- legal frame sizes are powers of two from 64 to 8192 samples. Aside from coupling, Vorbis
- handles channels as independent vectors and these frame sizes are in samples per
- channel.
-
-
- <!--l. 348--><p class="noindent" >Vorbis uses an overlapping transform, namely the MDCT, to blend one frame into the next,
- avoiding most inter-frame block boundary artifacts. The MDCT output of one frame is windowed
- according to MDCT requirements, overlapped 50% with the output of the previous frame and
- added. The window shape assures seamless reconstruction.
- <!--l. 354--><p class="noindent" >This is easy to visualize in the case of equal sized-windows:
- <div class="center"
- >
- <!--l. 356--><p class="noindent" >
- <!--l. 357--><p class="noindent" ><img
- src="window1.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 2: </span><span
- class="content">overlap of two equal-sized windows</span></div><!--tex4ht:label?: x1-260012 -->
- </div>
- <!--l. 361--><p class="noindent" >And slightly more complex in the case of overlapping unequal sized windows:
- <div class="center"
- >
- <!--l. 364--><p class="noindent" >
- <!--l. 365--><p class="noindent" ><img
- src="window2.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 3: </span><span
- class="content">overlap of a long and a short window</span></div><!--tex4ht:label?: x1-260023 -->
- </div>
- <!--l. 369--><p class="noindent" >In the unequal-sized window case, the window shape of the long window must be modified for
- seamless lapping as above. It is possible to correctly infer window shape to be applied to the
- current window from knowing the sizes of the current, previous and next window. It is legal for a
- decoder to use this method. However, in the case of a long window (short windows require no
- modification), Vorbis also codes two flag bits to specify pre- and post- window shape. Although
- not strictly necessary for function, this minor redundancy allows a packet to be fully decoded to
- the point of lapping entirely independently of any other packet, allowing easier abstraction of
- decode layers as well as allowing a greater level of easy parallelism in encode and
- decode.
- <!--l. 382--><p class="noindent" >A description of valid window functions for use with an inverse MDCT can be found in <span class="cite">[<a
- href="#XSporer/Brandenburg/Edler">1</a>]</span>.
- Vorbis windows all use the slope function
- <center class="math-display" >
- <img
- src="Vorbis_I_spec0x.png" alt="y = sin (.5 ∗ π sin2((x + .5)∕n ∗ π)).
-
-
- " class="math-display" ></center>
- <!--l. 385--><p class="nopar" >
- <!--l. 389--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-270001.3.2"></a><span
- class="cmbx-12">floor decode</span></span>
- Each floor is encoded/decoded in channel order, however each floor belongs to a ’submap’ that
- specifies which floor configuration to use. All floors are decoded before residue decode
- begins.
- <!--l. 395--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-280001.3.2"></a><span
- class="cmbx-12">residue decode</span></span>
- Although the number of residue vectors equals the number of channels, channel coupling may
- mean that the raw residue vectors extracted during decode do not map directly to specific
- channels. When channel coupling is in use, some vectors will correspond to coupled magnitude or
- angle. The coupling relationships are described in the codec setup and may differ from frame to
- frame, due to different mode numbers.
- <!--l. 404--><p class="noindent" >Vorbis codes residue vectors in groups by submap; the coding is done in submap order from
- submap 0 through n-1. This differs from floors which are coded using a configuration provided by
- submap number, but are coded individually in channel order.
- <!--l. 411--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-290001.3.2"></a><span
- class="cmbx-12">inverse channel coupling</span></span>
- A detailed discussion of stereo in the Vorbis codec can be found in the document
- <a
- href="stereo.html" >Stereo Channel Coupling in the Vorbis CODEC</a>. Vorbis is not limited to only stereo
- coupling, but the stereo document also gives a good overview of the generic coupling
- mechanism.
- <!--l. 419--><p class="noindent" >Vorbis coupling applies to pairs of residue vectors at a time; decoupling is done in-place a
- pair at a time in the order and using the vectors specified in the current mapping
- configuration. The decoupling operation is the same for all pairs, converting square polar
- representation (where one vector is magnitude and the second angle) back to Cartesian
- representation.
- <!--l. 426--><p class="noindent" >After decoupling, in order, each pair of vectors on the coupling list, the resulting residue vectors
- represent the fine spectral detail of each output channel.
-
-
- <!--l. 432--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-300001.3.2"></a><span
- class="cmbx-12">generate floor curve</span></span>
- The decoder may choose to generate the floor curve at any appropriate time. It is reasonable to
- generate the output curve when the floor data is decoded from the raw packet, or it
- can be generated after inverse coupling and applied to the spectral residue directly,
- combining generation and the dot product into one step and eliminating some working
- space.
- <!--l. 441--><p class="noindent" >Both floor 0 and floor 1 generate a linear-range, linear-domain output vector to be multiplied
- (dot product) by the linear-range, linear-domain spectral residue.
- <!--l. 447--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-310001.3.2"></a><span
- class="cmbx-12">compute floor/residue dot product</span></span>
- This step is straightforward; for each output channel, the decoder multiplies the floor curve and
- residue vectors element by element, producing the finished audio spectrum of each
- channel.
- <!--l. 455--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
- implementation might be to assume that a 32 bit fixed-point representation for floor and
- residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
- in all cases because it happens to mostly work with the current Xiph.Org reference
- encoder.
- <!--l. 462--><p class="noindent" >However, floor vector values can span <span
- class="cmsy-10x-x-120">∼</span>140dB (<span
- class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
- vector should represent a minimum of 120dB (<span
- class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
- bit PCM device. For the residue vector to represent full scale if the floor is nailed
- to <span
- class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
- full scale if the floor is nailed at 0dB, it must be able to represent <span
- class="cmsy-10x-x-120">−</span>140dB to +0dB.
- Thus, in order to handle full range dynamics, a residue vector may span <span
- class="cmsy-10x-x-120">−</span>140dB to
- +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
- residue vector must be able to represent a 48 bit range and the dot product must
- be able to handle an effective 48 bit times 24 bit multiplication. This range may be
- achieved using large (64 bit or larger) integers, or implementing a movable binary point
- representation.
- <!--l. 479--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-320001.3.2"></a><span
- class="cmbx-12">inverse monolithic transform (MDCT)</span></span>
- The audio spectrum is converted back into time domain PCM audio via an inverse Modified
- Discrete Cosine Transform (MDCT). A detailed description of the MDCT is available in
- <span class="cite">[<a
- href="#XSporer/Brandenburg/Edler">1</a>]</span>.
- <!--l. 485--><p class="noindent" >Note that the PCM produced directly from the MDCT is not yet finished audio; it must be
-
-
- lapped with surrounding frames using an appropriate window (such as the Vorbis window) before
- the MDCT can be considered orthogonal.
- <!--l. 492--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-330001.3.2"></a><span
- class="cmbx-12">overlap/add data</span></span>
- Windowed MDCT output is overlapped and added with the right hand data of the previous
- window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
- current window (as illustrated in the window overlap diagram). At this point, the audio data
- between the center of the previous frame and the center of the current frame is now finished and
- ready to be returned.
- <!--l. 501--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-340001.3.2"></a><span
- class="cmbx-12">cache right hand data</span></span>
- The decoder must cache the right hand portion of the current frame to be lapped with the left
- hand portion of the next frame.
- <!--l. 507--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-350001.3.2"></a><span
- class="cmbx-12">return finished audio data</span></span>
- The overlapped portion produced from overlapping the previous and current frame data
- is finished data to be returned by the decoder. This data spans from the center of
- the previous window to the center of the current window. In the case of same-sized
- windows, the amount of data to return is one-half block consisting of and only of the
- overlapped portions. When overlapping a short and long window, much of the returned
- range is not actually overlap. This does not damage transform orthogonality. Pay
- attention however to returning the correct data range; the amount of data to be returned
- is:
- <!--l. 519--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb1">
- <a
- id="x1-35002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> window_blocksize(previous_window)/4+window_blocksize(current_window)/4</span>
- </div>
- <!--l. 523--><p class="noindent" >from the center of the previous window to the center of the current window.
- <!--l. 526--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
- encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
- PCM output offset is ’0’ (as no data has been returned yet).
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">2. </span> <a
- id="x1-360002"></a>Bitpacking Convention</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">2.1. </span> <a
- id="x1-370002.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >The Vorbis codec uses relatively unstructured raw packets containing arbitrary-width binary
- integer fields. Logically, these packets are a bitstream in which bits are coded one-by-one by the
- encoder and then read one-by-one in the same monotonically increasing order by the decoder.
- Most current binary storage arrangements group bits into a native word size of eight bits
- (octets), sixteen bits, thirty-two bits or, less commonly other fixed word sizes. The Vorbis
- bitpacking convention specifies the correct mapping of the logical packet bitstream into an actual
- representation in fixed-width words.
- <!--l. 19--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.1. </span> <a
- id="x1-380002.1.1"></a>octets, bytes and words</h5>
- <!--l. 21--><p class="noindent" >In most contemporary architectures, a ’byte’ is synonymous with an ’octet’, that is, eight bits.
- This has not always been the case; seven, ten, eleven and sixteen bit ’bytes’ have been used.
- For purposes of the bitpacking convention, a byte implies the native, smallest integer
- storage representation offered by a platform. On modern platforms, this is generally
- assumed to be eight bits (not necessarily because of the processor but because of the
- filesystem/memory architecture. Modern filesystems invariably offer bytes as the fundamental
- atom of storage). A ’word’ is an integer size that is a grouped multiple of this smallest
- size.
- <!--l. 32--><p class="noindent" >The most ubiquitous architectures today consider a ’byte’ to be an octet (eight bits) and a word
- to be a group of two, four or eight bytes (16, 32 or 64 bits). Note however that the Vorbis
- bitpacking convention is still well defined for any native byte size; Vorbis uses the native
- bit-width of a given storage system. This document assumes that a byte is one octet for purposes
- of example.
- <!--l. 39--><p class="noindent" >
-
-
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.2. </span> <a
- id="x1-390002.1.2"></a>bit order</h5>
- <!--l. 41--><p class="noindent" >A byte has a well-defined ’least significant’ bit (LSb), which is the only bit set when the byte is
- storing the two’s complement integer value +1. A byte’s ’most significant’ bit (MSb) is at the
- opposite end of the byte. Bits in a byte are numbered from zero at the LSb to <span
- class="cmmi-12">n </span>(<span
- class="cmmi-12">n </span>= 7 in an
- octet) for the MSb.
- <!--l. 50--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.3. </span> <a
- id="x1-400002.1.3"></a>byte order</h5>
- <!--l. 52--><p class="noindent" >Words are native groupings of multiple bytes. Several byte orderings are possible in a word; the
- common ones are 3-2-1-0 (’big endian’ or ’most significant byte first’ in which the
- highest-valued byte comes first), 0-1-2-3 (’little endian’ or ’least significant byte first’ in
- which the lowest value byte comes first) and less commonly 3-1-2-0 and 0-2-1-3 (’mixed
- endian’).
- <!--l. 59--><p class="noindent" >The Vorbis bitpacking convention specifies storage and bitstream manipulation at the byte, not
- word, level, thus host word ordering is of a concern only during optimization when writing high
- performance code that operates on a word of storage at a time rather than by byte.
- Logically, bytes are always coded and decoded in order from byte zero through byte
- <span
- class="cmmi-12">n</span>.
- <!--l. 68--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.4. </span> <a
- id="x1-410002.1.4"></a>coding bits into byte sequences</h5>
- <!--l. 70--><p class="noindent" >The Vorbis codec has need to code arbitrary bit-width integers, from zero to 32 bits
- wide, into packets. These integer fields are not aligned to the boundaries of the byte
- representation; the next field is written at the bit position at which the previous field
- ends.
- <!--l. 75--><p class="noindent" >The encoder logically packs integers by writing the LSb of a binary integer to the logical
- bitstream first, followed by next least significant bit, etc, until the requested number of bits
- have been coded. When packing the bits into bytes, the encoder begins by placing
- the LSb of the integer to be written into the least significant unused bit position of
- the destination byte, followed by the next-least significant bit of the source integer
- and so on up to the requested number of bits. When all bits of the destination byte
- have been filled, encoding continues by zeroing all bits of the next byte and writing
- the next bit into the bit position 0 of that byte. Decoding follows the same process
-
-
- as encoding, but by reading bits from the byte stream and reassembling them into
- integers.
- <!--l. 90--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.5. </span> <a
- id="x1-420002.1.5"></a>signedness</h5>
- <!--l. 92--><p class="noindent" >The signedness of a specific number resulting from decode is to be interpreted by the decoder
- given decode context. That is, the three bit binary pattern ’b111’ can be taken to represent
- either ’seven’ as an unsigned integer, or ’-1’ as a signed, two’s complement integer. The
- encoder and decoder are responsible for knowing if fields are to be treated as signed or
- unsigned.
- <!--l. 101--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.6. </span> <a
- id="x1-430002.1.6"></a>coding example</h5>
- <!--l. 103--><p class="noindent" >Code the 4 bit integer value ’12’ [b1100] into an empty bytestream. Bytestream result:
- <!--l. 106--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb2">
- <a
- id="x1-43002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> |</span>
- <br class="fancyvrb" /><a
- id="x1-43004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> V</span>
- <br class="fancyvrb" /><a
- id="x1-43006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-43008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-43010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> <-</span>
- <br class="fancyvrb" /><a
- id="x1-43012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ...</span>
- <br class="fancyvrb" /><a
- id="x1-43020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> n</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bytestream</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> byte</span>
- <br class="fancyvrb" /><a
- id="x1-43022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 121--><p class="noindent" >Continue by coding the 3 bit integer value ’-1’ [b111]:
- <!--l. 123--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb3">
- <a
- id="x1-43024r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> |</span>
- <br class="fancyvrb" /><a
- id="x1-43026r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> V</span>
- <br class="fancyvrb" /><a
- id="x1-43028r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-43030r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-43032r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> <-</span>
- <br class="fancyvrb" /><a
- id="x1-43034r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-43036r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43038r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43040r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ...</span>
- <br class="fancyvrb" /><a
- id="x1-43042r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> n</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bytestream</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> byte</span>
- </div>
- <!--l. 137--><p class="noindent" >Continue by coding the 7 bit integer value ’17’ [b0010001]:
- <!--l. 139--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb4">
- <a
- id="x1-43044r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> |</span>
- <br class="fancyvrb" /><a
- id="x1-43046r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> V</span>
- <br class="fancyvrb" /><a
- id="x1-43048r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-43050r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-43052r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> [1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-43054r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> <-</span>
- <br class="fancyvrb" /><a
- id="x1-43056r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43058r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-43060r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ...</span>
- <br class="fancyvrb" /><a
- id="x1-43062r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> n</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bytestream</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> bytes</span>
- <br class="fancyvrb" /><a
- id="x1-43064r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> cursor</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 6</span>
- </div>
- <!--l. 154--><p class="noindent" >Continue by coding the 13 bit integer value ’6969’ [b110 11001110 01]:
- <!--l. 156--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb5">
- <a
- id="x1-43066r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> |</span>
- <br class="fancyvrb" /><a
- id="x1-43068r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> V</span>
- <br class="fancyvrb" /><a
- id="x1-43070r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-43072r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-43074r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> [1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-43076r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-43078r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> [1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-43080r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> <-</span>
- <br class="fancyvrb" /><a
- id="x1-43082r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ...</span>
- <br class="fancyvrb" /><a
- id="x1-43084r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> n</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bytestream</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bytes</span>
- <br class="fancyvrb" /><a
- id="x1-43086r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 173--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.7. </span> <a
- id="x1-440002.1.7"></a>decoding example</h5>
- <!--l. 175--><p class="noindent" >Reading from the beginning of the bytestream encoded in the above example:
- <!--l. 177--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb6">
-
-
- <a
- id="x1-44002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> |</span>
- <br class="fancyvrb" /><a
- id="x1-44004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> V</span>
- <br class="fancyvrb" /><a
- id="x1-44006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-44008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-44010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> [1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> <-</span>
- <br class="fancyvrb" /><a
- id="x1-44012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-44014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> [1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0]</span>
- <br class="fancyvrb" /><a
- id="x1-44016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> [0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> bytestream</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> ==</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bytes</span>
- <br class="fancyvrb" /><a
- id="x1-44018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 190--><p class="noindent" >We read two, two-bit integer fields, resulting in the returned numbers ’b00’ and ’b11’. Two things
- are worth noting here:
- <ul class="itemize1">
- <li class="itemize">Although these four bits were originally written as a single four-bit integer, reading
- some other combination of bit-widths from the bitstream is well defined. There are
- no artificial alignment boundaries maintained in the bitstream.
- </li>
- <li class="itemize">The second value is the two-bit-wide integer ’b11’. This value may be interpreted
- either as the unsigned value ’3’, or the signed value ’-1’. Signedness is dependent on
- decode context.</li></ul>
- <!--l. 208--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.8. </span> <a
- id="x1-450002.1.8"></a>end-of-packet alignment</h5>
- <!--l. 210--><p class="noindent" >The typical use of bitpacking is to produce many independent byte-aligned packets which are
- embedded into a larger byte-aligned container structure, such as an Ogg transport bitstream.
- Externally, each bytestream (encoded bitstream) must begin and end on a byte boundary. Often,
- the encoded bitstream is not an integer number of bytes, and so there is unused (uncoded) space
- in the last byte of a packet.
- <!--l. 218--><p class="noindent" >Unused space in the last byte of a bytestream is always zeroed during the coding process. Thus,
- should this unused space be read, it will return binary zeroes.
- <!--l. 222--><p class="noindent" >Attempting to read past the end of an encoded packet results in an ’end-of-packet’ condition.
- End-of-packet is not to be considered an error; it is merely a state indicating that there is
- insufficient remaining data to fulfill the desired read size. Vorbis uses truncated packets as a
- normal mode of operation, and as such, decoders must handle reading past the end of a packet as
- a typical mode of operation. Any further read operations after an ’end-of-packet’ condition shall
- also return ’end-of-packet’.
-
-
- <!--l. 233--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">2.1.9. </span> <a
- id="x1-460002.1.9"></a>reading zero bits</h5>
- <!--l. 235--><p class="noindent" >Reading a zero-bit-wide integer returns the value ’0’ and does not increment the stream cursor.
- Reading to the end of the packet (but not past, such that an ’end-of-packet’ condition has not
- triggered) and then reading a zero bit integer shall succeed, returning 0, and not trigger an
- end-of-packet condition. Reading a zero-bit-wide integer after a previous read sets ’end-of-packet’
- shall also fail with ’end-of-packet’.
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">3. </span> <a
- id="x1-470003"></a>Probability Model and Codebooks</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">3.1. </span> <a
- id="x1-480003.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >Unlike practically every other mainstream audio codec, Vorbis has no statically configured
- probability model, instead packing all entropy decoding configuration, VQ and Huffman, into the
- bitstream itself in the third header, the codec setup header. This packed configuration consists of
- multiple ’codebooks’, each containing a specific Huffman-equivalent representation for decoding
- compressed codewords as well as an optional lookup table of output vector values to which a
- decoded Huffman value is applied as an offset, generating the final decoded output corresponding
- to a given compressed codeword.
- <!--l. 18--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">3.1.1. </span> <a
- id="x1-490003.1.1"></a>Bitwise operation</h5>
- <!--l. 19--><p class="noindent" >The codebook mechanism is built on top of the vorbis bitpacker. Both the codebooks themselves
- and the codewords they decode are unrolled from a packet as a series of arbitrary-width values
- read from the stream according to <a
- href="#x1-360002">Section 2</a>, “<a
- href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>”.
- <!--l. 27--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">3.2. </span> <a
- id="x1-500003.2"></a>Packed codebook format</h4>
- <!--l. 29--><p class="noindent" >For purposes of the examples below, we assume that the storage system’s native byte width is
- eight bits. This is not universally true; see <a
- href="#x1-360002">Section 2</a>, “<a
- href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” for discussion
- relating to non-eight-bit bytes.
-
-
- <!--l. 34--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">3.2.1. </span> <a
- id="x1-510003.2.1"></a>codebook decode</h5>
- <!--l. 36--><p class="noindent" >A codebook begins with a 24 bit sync pattern, 0x564342:
- <!--l. 38--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb7">
- <a
- id="x1-51002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 0:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> (0x42)</span>
- <br class="fancyvrb" /><a
- id="x1-51004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 1:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> (0x43)</span>
- <br class="fancyvrb" /><a
- id="x1-51006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 2:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> (0x56)</span>
- </div>
- <!--l. 44--><p class="noindent" >16 bit <span
- class="cmtt-12">[codebook_dimensions] </span>and 24 bit <span
- class="cmtt-12">[codebook_entries] </span>fields:
- <!--l. 46--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb8">
- <a
- id="x1-51008r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51010r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 3:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-51012r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 4:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> [codebook_dimensions]</span><span
- class="cmtt-8"> (16</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> unsigned)</span>
- <br class="fancyvrb" /><a
- id="x1-51014r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51016r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 5:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-51018r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 6:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-51020r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 7:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> [codebook_entries]</span><span
- class="cmtt-8"> (24</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> unsigned)</span>
- <br class="fancyvrb" /><a
- id="x1-51022r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 57--><p class="noindent" >Next is the <span
- class="cmtt-12">[ordered] </span>bit flag:
- <!--l. 59--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb9">
- <a
- id="x1-51024r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51026r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 8:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> [ordered]</span><span
- class="cmtt-8"> (1</span><span
- class="cmtt-8"> bit)</span>
- <br class="fancyvrb" /><a
- id="x1-51028r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 65--><p class="noindent" >Each entry, numbering a total of <span
- class="cmtt-12">[codebook_entries]</span>, is assigned a codeword length.
- We now read the list of codeword lengths and store these lengths in the array
- <span
- class="cmtt-12">[codebook_codeword_lengths]</span>. Decode of lengths is according to whether the <span
- class="cmtt-12">[ordered] </span>flag
- is set or unset.
- <ul class="itemize1">
- <li class="itemize">If the <span
- class="cmtt-12">[ordered] </span>flag is unset, the codeword list is not length ordered and the decoder
- needs to read each codeword length one-by-one.
- <!--l. 77--><p class="noindent" >The decoder first reads one additional bit flag, the <span
- class="cmtt-12">[sparse] </span>flag. This flag determines
- whether or not the codebook contains unused entries that are not to be included in
-
-
- the codeword decode tree:
- <!--l. 82--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb10">
- <a
- id="x1-51030r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> byte</span><span
- class="cmtt-8"> 8:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> X</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ]</span><span
- class="cmtt-8"> [sparse]</span><span
- class="cmtt-8"> flag</span><span
- class="cmtt-8"> (1</span><span
- class="cmtt-8"> bit)</span>
- </div>
- <!--l. 86--><p class="noindent" >The decoder now performs for each of the <span
- class="cmtt-12">[codebook_entries] </span>codebook entries:
- <!--l. 89--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb11">
- <a
- id="x1-51032r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51034r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> if([sparse]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set)</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51036r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51038r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [flag]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> one</span><span
- class="cmtt-8"> bit;</span>
- <br class="fancyvrb" /><a
- id="x1-51040r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> if([flag]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set)</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51042r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51044r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> five</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer;</span>
- <br class="fancyvrb" /><a
- id="x1-51046r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> for</span><span
- class="cmtt-8"> this</span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> [length]+1;</span>
- <br class="fancyvrb" /><a
- id="x1-51048r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51050r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51052r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51054r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> this</span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> unused.</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> mark</span><span
- class="cmtt-8"> it</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> such.</span>
- <br class="fancyvrb" /><a
- id="x1-51056r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51058r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-51060r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51062r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> sparse</span><span
- class="cmtt-8"> flag</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51064r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51066r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> five</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer;</span>
- <br class="fancyvrb" /><a
- id="x1-51068r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> for</span><span
- class="cmtt-8"> this</span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> [length]+1;</span>
- <br class="fancyvrb" /><a
- id="x1-51070r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51072r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-51074r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- </li>
- <li class="itemize">If the <span
- class="cmtt-12">[ordered] </span>flag is set, the codeword list for this codebook is encoded in
- ascending length order. Rather than reading a length for every codeword, the
- encoder reads the number of codewords per length. That is, beginning at entry
- zero:
- <!--l. 120--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb12">
- <a
- id="x1-51076r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [current_entry]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0;</span>
- <br class="fancyvrb" /><a
- id="x1-51078r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [current_length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> five</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> 1;</span>
- <br class="fancyvrb" /><a
- id="x1-51080r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [number]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> </span><a
- href="#x1-1170009.2.1"><span
- class="cmtt-8">ilog</span></a><span
- class="cmtt-8">([codebook_entries]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [current_entry])</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-51082r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> entries</span><span
- class="cmtt-8"> [current_entry]</span><span
- class="cmtt-8"> through</span><span
- class="cmtt-8"> [current_entry]+[number]-1,</span><span
- class="cmtt-8"> inclusive,</span>
- <br class="fancyvrb" /><a
- id="x1-51084r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> [codebook_codeword_lengths]</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> [current_length]</span>
- <br class="fancyvrb" /><a
- id="x1-51086r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> [current_entry]</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> [number]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [current_entry]</span>
- <br class="fancyvrb" /><a
- id="x1-51088r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [current_length]</span><span
- class="cmtt-8"> by</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-51090r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> [current_entry]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [codebook_entries]</span><span
- class="cmtt-8"> ERROR</span><span
- class="cmtt-8"> CONDITION;</span>
- <br class="fancyvrb" /><a
- id="x1-51092r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> decoder</span><span
- class="cmtt-8"> will</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> be</span><span
- class="cmtt-8"> able</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> this</span><span
- class="cmtt-8"> stream.</span>
- <br class="fancyvrb" /><a
- id="x1-51094r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> [current_entry]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [codebook_entries],</span><span
- class="cmtt-8"> repeat</span><span
- class="cmtt-8"> process</span><span
- class="cmtt-8"> starting</span><span
- class="cmtt-8"> at</span><span
- class="cmtt-8"> 3)</span>
- <br class="fancyvrb" /><a
- id="x1-51096r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> done.</span>
-
-
- </div>
- </li></ul>
- <!--l. 136--><p class="noindent" >After all codeword lengths have been decoded, the decoder reads the vector lookup table. Vorbis
- I supports three lookup types:
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem">No lookup
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">Implicitly populated value mapping (lattice VQ)
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">Explicitly populated value mapping (tessellated or ’foam’ VQ)</dd></dl>
- <!--l. 149--><p class="noindent" >The lookup table type is read as a four bit unsigned integer:
- <div class="fancyvrb" id="fancyvrb13">
- <a
- id="x1-51101r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [codebook_lookup_type]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> four</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- </div>
- <!--l. 154--><p class="noindent" >Codebook decode precedes according to <span
- class="cmtt-12">[codebook_lookup_type]</span>:
- <ul class="itemize1">
- <li class="itemize">Lookup type zero indicates no lookup to be read. Proceed past lookup decode.
- </li>
- <li class="itemize">Lookup types one and two are similar, differing only in the number of lookup values to
- be read. Lookup type one reads a list of values that are permuted in a set pattern to
- build a list of vectors, each vector of order <span
- class="cmtt-12">[codebook_dimensions] </span>scalars. Lookup
- type two builds the same vector list, but reads each scalar for each vector explicitly,
- rather than building vectors from a smaller list of possible scalar values. Lookup
- decode proceeds as follows:
- <!--l. 168--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb14">
- <a
- id="x1-51103r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [codebook_minimum_value]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1180009.2.2"><span
- class="cmtt-8">float32_unpack</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer)</span>
- <br class="fancyvrb" /><a
- id="x1-51105r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [codebook_delta_value]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1180009.2.2"><span
- class="cmtt-8">float32_unpack</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer)</span>
- <br class="fancyvrb" /><a
- id="x1-51107r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [codebook_value_bits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-51109r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [codebook_sequence_p]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> boolean</span><span
- class="cmtt-8"> flag</span>
- <br class="fancyvrb" /><a
- id="x1-51111r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51113r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [codebook_lookup_type]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51115r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51117r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [codebook_lookup_values]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1190009.2.3"><span
- class="cmtt-8">lookup1_values</span></a><span
- class="cmtt-8">([codebook_entries],</span><span
- class="cmtt-8"> [codebook_dimensions]</span><span
- class="cmtt-8"> )</span>
- <br class="fancyvrb" /><a
- id="x1-51119r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51121r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-51123r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51125r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [codebook_lookup_values]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [codebook_entries]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [codebook_dimensions]</span>
- <br class="fancyvrb" /><a
- id="x1-51127r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51129r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-51131r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-51133r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> total</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [codebook_lookup_values]</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integers</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [codebook_value_bits]</span><span
- class="cmtt-8"> each;</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-51135r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> store</span><span
- class="cmtt-8"> these</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> order</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [codebook_multiplicands]</span>
- </div>
- </li>
- <li class="itemize">A <span
- class="cmtt-12">[codebook_lookup_type] </span>of greater than two is reserved and indicates a stream that is
- not decodable by the specification in this document.
- </li></ul>
- <!--l. 195--><p class="noindent" >An ’end of packet’ during any read operation in the above steps is considered an error condition
- rendering the stream undecodable.
- <!--l. 198--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-520003.2.1"></a><span
- class="cmbx-12">Huffman decision tree representation</span></span>
- The <span
- class="cmtt-12">[codebook_codeword_lengths] </span>array and <span
- class="cmtt-12">[codebook_entries] </span>value uniquely define the
- Huffman decision tree used for entropy decoding.
- <!--l. 204--><p class="noindent" >Briefly, each used codebook entry (recall that length-unordered codebooks support unused
- codeword entries) is assigned, in order, the lowest valued unused binary Huffman codeword
- possible. Assume the following codeword length list:
- <!--l. 209--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb15">
- <a
- id="x1-52002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 0:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-52004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 1:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span>
- <br class="fancyvrb" /><a
- id="x1-52006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 2:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span>
- <br class="fancyvrb" /><a
- id="x1-52008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 3:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span>
- <br class="fancyvrb" /><a
- id="x1-52010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 4:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span>
- <br class="fancyvrb" /><a
- id="x1-52012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 5:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-52014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 6:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 3</span>
- <br class="fancyvrb" /><a
- id="x1-52016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 7:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 3</span>
- </div>
- <!--l. 220--><p class="noindent" >Assigning codewords in order (lowest possible value of the appropriate length to highest) results
- in the following codeword list:
- <!--l. 223--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb16">
- <a
- id="x1-52018r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 0:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 00</span>
- <br class="fancyvrb" /><a
- id="x1-52020r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 1:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 0100</span>
- <br class="fancyvrb" /><a
- id="x1-52022r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 2:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 0101</span>
- <br class="fancyvrb" /><a
- id="x1-52024r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 3:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 0110</span>
- <br class="fancyvrb" /><a
- id="x1-52026r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 4:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 0111</span>
- <br class="fancyvrb" /><a
- id="x1-52028r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 5:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 10</span>
- <br class="fancyvrb" /><a
- id="x1-52030r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 6:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 110</span>
- <br class="fancyvrb" /><a
- id="x1-52032r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> entry</span><span
- class="cmtt-8"> 7:</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> codeword</span><span
- class="cmtt-8"> 111</span>
- </div>
-
-
- <!--l. 235--><p class="noindent" ><span class="likesubparagraphHead"><a
- id="x1-530003.2.1"></a><span
- class="cmbx-12">Note:</span></span> Unlike most binary numerical values in this document, we intend the above codewords to
- be read and used bit by bit from left to right, thus the codeword ’001’ is the bit string ’zero, zero,
- one’. When determining ’lowest possible value’ in the assignment definition above, the leftmost
- bit is the MSb.
- <!--l. 243--><p class="noindent" >It is clear that the codeword length list represents a Huffman decision tree with the entry
- numbers equivalent to the leaves numbered left-to-right:
- <div class="center"
- >
- <!--l. 247--><p class="noindent" >
- <!--l. 248--><p class="noindent" ><img
- src="hufftree.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 4: </span><span
- class="content">huffman tree illustration</span></div><!--tex4ht:label?: x1-530014 -->
- </div>
- <!--l. 253--><p class="noindent" >As we assign codewords in order, we see that each choice constructs a new leaf in the leftmost
- possible position.
- <!--l. 256--><p class="noindent" >Note that it’s possible to underspecify or overspecify a Huffman tree via the length list.
- In the above example, if codeword seven were eliminated, it’s clear that the tree is
- unfinished:
- <div class="center"
- >
- <!--l. 260--><p class="noindent" >
- <!--l. 261--><p class="noindent" ><img
- src="hufftree-under.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 5: </span><span
- class="content">underspecified huffman tree illustration</span></div><!--tex4ht:label?: x1-530025 -->
- </div>
- <!--l. 266--><p class="noindent" >Similarly, in the original codebook, it’s clear that the tree is fully populated and a ninth
- codeword is impossible. Both underspecified and overspecified trees are an error condition
- rendering the stream undecodable. 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.
- <!--l. 274--><p class="noindent" >Codebook entries marked ’unused’ are simply skipped in the assigning process. They have no
- codeword and do not appear in the decision tree, thus it’s impossible for any bit pattern read
- from the stream to decode to that entry number.
-
-
- <!--l. 281--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-540003.2.1"></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="x1-54002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> [codebook\_multiplicands]</span><span
- class="cmtt-8"> array</span>
- <br class="fancyvrb" /><a
- id="x1-54004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_minimum\_value]</span>
- <br class="fancyvrb" /><a
- id="x1-54006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_delta\_value]</span>
- <br class="fancyvrb" /><a
- id="x1-54008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_sequence\_p]</span>
- <br class="fancyvrb" /><a
- id="x1-54010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_lookup\_type]</span>
- <br class="fancyvrb" /><a
- id="x1-54012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_entries]</span>
- <br class="fancyvrb" /><a
- id="x1-54014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_dimensions]</span>
- <br class="fancyvrb" /><a
- id="x1-54016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook\_lookup\_values]</span>
- </div>
- <!--l. 297--><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. 302--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-550003.2.1"></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. 311--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb18">
- <a
- id="x1-55002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0;</span>
- <br class="fancyvrb" /><a
- id="x1-55004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [index_divisor]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 1;</span>
- <br class="fancyvrb" /><a
- id="x1-55006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [codebook_dimensions]-1</span><span
- class="cmtt-8"> (once</span><span
- class="cmtt-8"> for</span><span
- class="cmtt-8"> each</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> vector)</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-55008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [multiplicand_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [lookup_offset]</span><span
- class="cmtt-8"> divided</span><span
- class="cmtt-8"> by</span><span
- class="cmtt-8"> [index_divisor]</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-55012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> division</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> modulo</span><span
- class="cmtt-8"> [codebook_lookup_values]</span>
- <br class="fancyvrb" /><a
- id="x1-55014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [value_vector]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-55018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [codebook_multiplicands]</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [multiplicand_offset]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> *</span>
- <br class="fancyvrb" /><a
- id="x1-55020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook_delta_value]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [codebook_minimum_value]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [last];</span>
- <br class="fancyvrb" /><a
- id="x1-55022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [codebook_sequence_p]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [value_vector]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-55026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [index_divisor]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [index_divisor]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [codebook_lookup_values]</span>
- <br class="fancyvrb" /><a
- id="x1-55030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-55034r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-55036r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> calculation</span><span
- class="cmtt-8"> completed.</span>
- </div>
-
-
- <!--l. 334--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-560003.2.1"></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. 344--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb19">
- <a
- id="x1-56002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0;</span>
- <br class="fancyvrb" /><a
- id="x1-56004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [multiplicand_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [lookup_offset]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [codebook_dimensions]</span>
- <br class="fancyvrb" /><a
- id="x1-56006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [codebook_dimensions]-1</span><span
- class="cmtt-8"> (once</span><span
- class="cmtt-8"> for</span><span
- class="cmtt-8"> each</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> vector)</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-56008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-56010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [value_vector]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-56012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [codebook_multiplicands]</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [multiplicand_offset]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> *</span>
- <br class="fancyvrb" /><a
- id="x1-56014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [codebook_delta_value]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [codebook_minimum_value]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [last];</span>
- <br class="fancyvrb" /><a
- id="x1-56016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-56018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [codebook_sequence_p]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [value_vector]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-56020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-56022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [multiplicand_offset]</span>
- <br class="fancyvrb" /><a
- id="x1-56024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-56026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-56028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-56030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> calculation</span><span
- class="cmtt-8"> completed.</span>
- </div>
- <!--l. 370--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">3.3. </span> <a
- id="x1-570003.3"></a>Use of the codebook abstraction</h4>
- <!--l. 372--><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. 382--><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. 389--><p class="noindent" >Using a codebook to read from the packet bitstream consists first of reading and decoding the
- next codeword in the bitstream. The decoder reads bits until the accumulated bits match a
- codeword in the codebook. This process can be though of as logically walking the
- Huffman decode tree by reading one bit at a time from the bitstream, and using the
- bit as a decision boolean to take the 0 branch (left in the above examples) or the 1
- branch (right in the above examples). Walking the tree finishes when the decode process
- hits a leaf in the decision tree; the result is the entry number corresponding to that
- leaf. Reading past the end of a packet propagates the ’end-of-stream’ condition to the
- decoder.
- <!--l. 401--><p class="noindent" >When used in a scalar context, the resulting codeword entry is the desired return
- value.
- <!--l. 404--><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="x1-580004"></a>Codec Setup and Packet Decode</h3>
- <!--l. 7--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">4.1. </span> <a
- id="x1-590004.1"></a>Overview</h4>
- <!--l. 9--><p class="noindent" >This document serves as the top-level reference document for the bit-by-bit decode specification
- of Vorbis I. This document assumes a high-level understanding of the Vorbis decode
- process, which is provided in <a
- href="#x1-20001">Section 1</a>, “<a
- href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>”. <a
- href="#x1-360002">Section 2</a>,
- “<a
- href="#x1-360002">Bitpacking Convention<!--tex4ht:ref: vorbis:spec:bitpacking --></a>” covers reading and writing bit fields from and to bitstream
- packets.
- <!--l. 17--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">4.2. </span> <a
- id="x1-600004.2"></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="x1-610004.2.1"></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="x1-61002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [packet_type]</span><span
- class="cmtt-8"> :</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> value</span>
- <br class="fancyvrb" /><a
- id="x1-61004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> 0x76,</span><span
- class="cmtt-8"> 0x6f,</span><span
- class="cmtt-8"> 0x72,</span><span
- class="cmtt-8"> 0x62,</span><span
- class="cmtt-8"> 0x69,</span><span
- class="cmtt-8"> 0x73:</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> characters</span><span
- class="cmtt-8"> ’v’,’o’,’r’,’b’,’i’,’s’</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> six</span><span
- class="cmtt-8"> octets</span>
- </div>
-
-
- <!--l. 36--><p class="noindent" >Decode continues according to packet type; the identification header is type 1, the comment
- header type 3 and the setup header type 5 (these types are all odd as a packet with a leading
- single bit of ’0’ is an audio packet). The packets must occur in the order of identification,
- comment, setup.
- <!--l. 44--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.2.2. </span> <a
- id="x1-620004.2.2"></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="x1-62002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [vorbis_version]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-62004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [audio_channels]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span>
- <br class="fancyvrb" /><a
- id="x1-62006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [audio_sample_rate]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-62008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [bitrate_maximum]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> signed</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-62010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [bitrate_nominal]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> signed</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-62012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [bitrate_minimum]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> signed</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-62014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [blocksize_0]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> exponent</span><span
- class="cmtt-8"> (read</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer)</span>
- <br class="fancyvrb" /><a
- id="x1-62016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> [blocksize_1]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> exponent</span><span
- class="cmtt-8"> (read</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer)</span>
- <br class="fancyvrb" /><a
- id="x1-62018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [framing_flag]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> one</span><span
- class="cmtt-8"> bit</span>
- </div>
- <!--l. 63--><p class="noindent" ><span
- class="cmtt-12">[vorbis_version] </span>is to read ’0’ in order to be compatible with this document. Both
- <span
- class="cmtt-12">[audio_channels] </span>and <span
- class="cmtt-12">[audio_sample_rate] </span>must read greater than zero. Allowed final
- blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in Vorbis I. <span
- class="cmtt-12">[blocksize_0]</span>
- must be less than or equal to <span
- class="cmtt-12">[blocksize_1]</span>. The framing bit must be nonzero. Failure to meet
- any of these conditions renders a stream undecodable.
- <!--l. 71--><p class="noindent" >The bitrate fields above are used only as hints. The nominal bitrate field especially may be
- considerably off in purely VBR streams. The fields are meaningful only when greater than
- zero.
- <ul class="itemize1">
- <li class="itemize">All three fields set to the same value implies a fixed rate, or tightly bounded, nearly
- fixed-rate bitstream
- </li>
- <li class="itemize">Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
-
-
- </li>
- <li class="itemize">Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
- </li>
- <li class="itemize">None set indicates the encoder does not care to speculate.</li></ul>
- <!--l. 85--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.2.3. </span> <a
- id="x1-630004.2.3"></a>Comment header</h5>
- <!--l. 86--><p class="noindent" >Comment header decode and data specification is covered in <a
- href="#x1-810005">Section 5</a>, “<a
- href="#x1-810005">comment field and
- header specification<!--tex4ht:ref: vorbis:spec:comment --></a>”.
- <!--l. 90--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.2.4. </span> <a
- id="x1-640004.2.4"></a>Setup header</h5>
- <!--l. 92--><p class="noindent" >Vorbis codec setup is configurable to an extreme degree:
- <div class="center"
- >
- <!--l. 94--><p class="noindent" >
- <!--l. 95--><p class="noindent" ><img
- src="components.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 6: </span><span
- class="content">decoder pipeline configuration</span></div><!--tex4ht:label?: x1-640016 -->
- </div>
- <!--l. 100--><p class="noindent" >The setup header contains the bulk of the codec setup information needed for decode. The setup
- header contains, in order, the lists of codebook configurations, time-domain transform
- configurations (placeholders in Vorbis I), floor configurations, residue configurations, channel
- mapping configurations and mode configurations. It finishes with a framing bit of ’1’. Header
- decode proceeds in the following order:
- <!--l. 108--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-650004.2.4"></a><span
- class="cmbx-12">Codebooks</span></span>
-
-
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[vorbis_codebook_count] </span>= read eight bits as unsigned integer and add one
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">Decode <span
- class="cmtt-12">[vorbis_codebook_count] </span>codebooks in order as defined in <a
- href="#x1-470003">Section 3</a>,
- “<a
- href="#x1-470003">Probability Model and Codebooks<!--tex4ht:ref: vorbis:spec:codebook --></a>”. Save each configuration, in order, in an array
- of codebook configurations <span
- class="cmtt-12">[vorbis_codebook_configurations]</span>.</dd></dl>
- <!--l. 120--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-660004.2.4"></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="x1-670004.2.4"></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="#x1-890006">Section 6</a>,
- “<a
- href="#x1-890006">Floor type 0 setup and decode<!--tex4ht:ref: vorbis:spec:floor0 --></a>”; save this configuration in slot <span
- class="cmtt-12">[i] </span>of the floor
- configuration array <span
- class="cmtt-12">[vorbis_floor_configurations]</span>.
-
-
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem">If the floor type is one, decode the floor configuration as defined in <a
- href="#x1-950007">Section 7</a>,
- “<a
- href="#x1-950007">Floor type 1 setup and decode<!--tex4ht:ref: vorbis:spec:floor1 --></a>”; save this configuration in slot <span
- class="cmtt-12">[i] </span>of the floor
- configuration array <span
- class="cmtt-12">[vorbis_floor_configurations]</span>.
- </dd><dt class="enumerate-enumitem">
- d) </dt><dd
- class="enumerate-enumitem">If the the floor type is greater than one, this stream is undecodable; ERROR
- CONDITION</dd></dl>
- </dd></dl>
- <!--l. 157--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-680004.2.4"></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="#x1-1020008">Section 8</a>, “<a
- href="#x1-1020008">Residue setup and decode<!--tex4ht:ref: vorbis:spec:residue --></a>”; save this configuration in slot <span
- class="cmtt-12">[i] </span>of
- the residue configuration array <span
- class="cmtt-12">[vorbis_residue_configurations]</span>.
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem">If the the residue type is greater than two, this stream is undecodable; ERROR
- CONDITION</dd></dl>
- </dd></dl>
- <!--l. 177--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-690004.2.4"></a><span
- class="cmbx-12">Mappings</span></span>
- Mappings are used to set up specific pipelines for encoding multichannel audio with varying
- channel mapping applications. Vorbis I uses a single mapping type (0), with implicit PCM
- channel mappings.
-
-
- <!--l. 188--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[vorbis_mapping_count] </span>= read 6 bits as unsigned integer and add one
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">For each <span
- class="cmtt-12">[i] </span>of <span
- class="cmtt-12">[vorbis_mapping_count] </span>mapping numbers:
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem">read the mapping type: 16 bits as unsigned integer. There’s no reason to save
- the mapping type in Vorbis I.
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem">If the mapping type is nonzero, the stream is undecodable
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem">If the mapping type is zero:
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- i. </dt><dd
- class="enumerate-enumitem">read 1 bit as a boolean flag
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- A. </dt><dd
- class="enumerate-enumitem">if set, <span
- class="cmtt-12">[vorbis_mapping_submaps] </span>= read 4 bits as unsigned integer
- and add one
- </dd><dt class="enumerate-enumitem">
- B. </dt><dd
- class="enumerate-enumitem">if unset, <span
- class="cmtt-12">[vorbis_mapping_submaps] </span>= 1</dd></dl>
- </dd><dt class="enumerate-enumitem">
- ii. </dt><dd
- class="enumerate-enumitem">read 1 bit as a boolean flag
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- A. </dt><dd
- class="enumerate-enumitem">if set, square polar channel mapping is in use:
- <ul class="itemize1">
- <li class="itemize"><span
- class="cmtt-12">[vorbis_mapping_coupling_steps] </span>= read 8 bits as unsigned
- integer and add one
- </li>
- <li class="itemize">for <span
- class="cmtt-12">[j] </span>each of <span
- class="cmtt-12">[vorbis_mapping_coupling_steps] </span>steps:
- <ul class="itemize2">
- <li class="itemize">vector <span
- class="cmtt-12">[vorbis_mapping_magnitude] </span>element <span
- class="cmtt-12">[j]</span>= read
- <a
- href="#x1-1170009.2.1">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="#x1-1170009.2.1">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="x1-700004.2.4"></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="x1-710004.3"></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="x1-720004.3.1"></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="#x1-1170009.2.1">ilog</a>([vorbis_mode_count]-1) bits <span
- class="cmtt-12">[mode_number]</span>
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">decode blocksize <span
- class="cmtt-12">[n] </span>is equal to <span
- class="cmtt-12">[blocksize_0] </span>if <span
- class="cmtt-12">[vorbis_mode_blockflag] </span>is 0,
- else <span
- class="cmtt-12">[n] </span>is equal to <span
- class="cmtt-12">[blocksize_1]</span>.
- </dd><dt class="enumerate-enumitem">
- 4. </dt><dd
- class="enumerate-enumitem">perform window selection and setup; this window is used later by the inverse
- MDCT:
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem">if this is a long window (the <span
- class="cmtt-12">[vorbis_mode_blockflag] </span>flag of this mode is
- set):
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- i. </dt><dd
- class="enumerate-enumitem">read 1 bit for <span
- class="cmtt-12">[previous_window_flag]</span>
- </dd><dt class="enumerate-enumitem">
- ii. </dt><dd
- class="enumerate-enumitem">read 1 bit for <span
- class="cmtt-12">[next_window_flag]</span>
-
-
- </dd><dt class="enumerate-enumitem">
- iii. </dt><dd
- class="enumerate-enumitem">if <span
- class="cmtt-12">[previous_window_flag] </span>is not set, the left half of the window will
- be a hybrid window for lapping with a short block. See <a
- href="#paragraph.1" >paragraph <a
- href="#x1-260001.3.2">1.3.2</a></a>,
- “<a
- href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
- overlapping dissimilar windows. Else, the left half window will have normal
- long shape.
- </dd><dt class="enumerate-enumitem">
- iv. </dt><dd
- class="enumerate-enumitem">if <span
- class="cmtt-12">[next_window_flag] </span>is not set, the right half of the window will be
- a hybrid window for lapping with a short block. See <a
- href="#x1-260001.3.2">paragraph 1.3.2</a>,
- “<a
- href="#x1-260001.3.2">Window shape decode (long windows only)<!--tex4ht:ref: vorbis:spec:window --></a>” for an illustration of
- overlapping dissimilar windows. Else, the left right window will have normal
- long shape.</dd></dl>
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem">if this is a short window, the window is always the same short-window
- shape.</dd></dl>
- </dd></dl>
- <!--l. 321--><p class="noindent" >Vorbis windows all use the slope function <span
- class="cmmi-12">y </span>= sin(<img
- src="Vorbis_I_spec1x.png" alt="π2" class="frac" align="middle"> <span
- class="cmsy-10x-x-120">∗</span> sin <sup><span
- class="cmr-8">2</span></sup>((<span
- class="cmmi-12">x </span>+ 0<span
- class="cmmi-12">.</span>5)<span
- class="cmmi-12">∕n </span><span
- class="cmsy-10x-x-120">∗ </span><span
- class="cmmi-12">π</span>)), where <span
- class="cmmi-12">n </span>is window
- size and <span
- class="cmmi-12">x </span>ranges 0<span
- class="cmmi-12">…</span><span
- class="cmmi-12">n</span><span
- class="cmsy-10x-x-120">− </span>1, but dissimilar lapping requirements can affect overall shape. Window
- generation proceeds as follows:
- <!--l. 327--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[window_center] </span>= <span
- class="cmtt-12">[n] </span>/ 2
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">if (<span
- class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
- class="cmtt-12">[previous_window_flag] </span>is not set)
- then
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_window_start] </span>= <span
- class="cmtt-12">[n]</span>/4 - <span
- class="cmtt-12">[blocksize_0]</span>/4
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_window_end] </span>= <span
- class="cmtt-12">[n]</span>/4 + <span
- class="cmtt-12">[blocksize_0]</span>/4
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_n] </span>= <span
- class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
- <!--l. 336--><p class="noindent" >else
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_window_start] </span>= 0
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_window_end] </span>= <span
- class="cmtt-12">[window_center]</span>
-
-
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[left_n] </span>= <span
- class="cmtt-12">[n]</span>/2</dd></dl>
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">if (<span
- class="cmtt-12">[vorbis_mode_blockflag] </span>is set and <span
- class="cmtt-12">[next_window_flag] </span>is not set) then
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_window_start] </span>= <span
- class="cmtt-12">[n]*3</span>/4 - <span
- class="cmtt-12">[blocksize_0]</span>/4
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_window_end] </span>= <span
- class="cmtt-12">[n]*3</span>/4 + <span
- class="cmtt-12">[blocksize_0]</span>/4
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_n] </span>= <span
- class="cmtt-12">[blocksize_0]</span>/2</dd></dl>
- <!--l. 352--><p class="noindent" >else
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_window_start] </span>= <span
- class="cmtt-12">[window_center]</span>
- </dd><dt class="enumerate-enumitem">
- b) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_window_end] </span>= <span
- class="cmtt-12">[n]</span>
- </dd><dt class="enumerate-enumitem">
- c) </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[right_n] </span>= <span
- class="cmtt-12">[n]</span>/2</dd></dl>
- </dd><dt class="enumerate-enumitem">
- 4. </dt><dd
- class="enumerate-enumitem">window from range 0 ... <span
- class="cmtt-12">[left_window_start]</span>-1 inclusive is zero
- </dd><dt class="enumerate-enumitem">
- 5. </dt><dd
- class="enumerate-enumitem">for <span
- class="cmtt-12">[i] </span>in range <span
- class="cmtt-12">[left_window_start] </span>... <span
- class="cmtt-12">[left_window_end]</span>-1, window(<span
- class="cmtt-12">[i]</span>) =
- sin(<img
- src="Vorbis_I_spec2x.png" alt="π
- 2" class="frac" align="middle"> <span
- class="cmsy-10x-x-120">∗</span> sin <sup><span
- class="cmr-8">2</span></sup>( (<span
- class="cmtt-12">[i]</span>-<span
- class="cmtt-12">[left_window_start]</span>+0.5) / <span
- class="cmtt-12">[left_n] </span><span
- class="cmsy-10x-x-120">∗</span><img
- src="Vorbis_I_spec3x.png" alt="π
- 2" class="frac" align="middle">) )
- </dd><dt class="enumerate-enumitem">
- 6. </dt><dd
- class="enumerate-enumitem">window from range <span
- class="cmtt-12">[left_window_end] </span>... <span
- class="cmtt-12">[right_window_start]</span>-1 inclusive is
- one
- </dd><dt class="enumerate-enumitem">
- 7. </dt><dd
- class="enumerate-enumitem">for <span
- class="cmtt-12">[i] </span>in range <span
- class="cmtt-12">[right_window_start] </span>... <span
- class="cmtt-12">[right_window_end]</span>-1, window(<span
- class="cmtt-12">[i]</span>) =
- sin(<img
- src="Vorbis_I_spec4x.png" alt="π
- 2" class="frac" align="middle"> <span
- class="cmsy-10x-x-120">∗</span> sin <sup><span
- class="cmr-8">2</span></sup>( (<span
- class="cmtt-12">[i]</span>-<span
- class="cmtt-12">[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="π
- 2" class="frac" align="middle"> + <img
- src="Vorbis_I_spec6x.png" alt="π
- 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="x1-730004.3.2"></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="#x1-930006.2.2">subsubsection 6.2.2</a>, “<a
- href="#x1-930006.2.2">packet decode<!--tex4ht:ref: vorbis:spec:floor0-decode --></a>”
- </dd><dt class="enumerate-enumitem">
- 4. </dt><dd
- class="enumerate-enumitem">if the type of this floor is one then decode the floor for channel <span
- class="cmtt-12">[i] </span>according to the
- <a
- href="#x1-1000007.2.3">subsubsection 7.2.3</a>, “<a
- href="#x1-1000007.2.3">packet decode<!--tex4ht:ref: vorbis:spec:floor1-decode --></a>”
- </dd><dt class="enumerate-enumitem">
- 5. </dt><dd
- class="enumerate-enumitem">save the needed decoded floor information for channel for later synthesis
- </dd><dt class="enumerate-enumitem">
- 6. </dt><dd
- class="enumerate-enumitem">if the decoded floor returned ’unused’, set vector <span
- class="cmtt-12">[no_residue] </span>element <span
- class="cmtt-12">[i] </span>to true,
- else set vector <span
- class="cmtt-12">[no_residue] </span>element <span
- class="cmtt-12">[i] </span>to false</dd></dl>
- <!--l. 406--><p class="noindent" >An end-of-packet condition during floor decode shall result in packet decode zeroing all channel
- output vectors and skipping to the add/overlap output stage.
- <!--l. 412--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.3.3. </span> <a
- id="x1-740004.3.3"></a>nonzero vector propagate</h5>
- <!--l. 414--><p class="noindent" >A possible result of floor decode is that a specific vector is marked ’unused’ which indicates that
- that final output vector is all-zero values (and the floor is zero). The residue for that vector is not
- coded in the stream, save for one complication. If some vectors are used and some are not,
-
-
- channel coupling could result in mixing a zeroed and nonzeroed vector to produce two nonzeroed
- vectors.
- <!--l. 421--><p class="noindent" >for each <span
- class="cmtt-12">[i] </span>from 0 ... <span
- class="cmtt-12">[vorbis_mapping_coupling_steps]</span>-1
- <!--l. 424--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem">if either <span
- class="cmtt-12">[no_residue] </span>entry for channel (<span
- class="cmtt-12">[vorbis_mapping_magnitude] </span>element
- <span
- class="cmtt-12">[i]</span>) or channel (<span
- class="cmtt-12">[vorbis_mapping_angle] </span>element <span
- class="cmtt-12">[i]</span>) are set to false, then both
- must be set to false. Note that an ’unused’ floor has no decoded floor information; it
- is important that this is remembered at floor curve synthesis time.</dd></dl>
- <!--l. 436--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.3.4. </span> <a
- id="x1-750004.3.4"></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="x1-760004.3.5"></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="x1-770004.3.6"></a>dot product</h5>
- <!--l. 531--><p class="noindent" >For each channel, synthesize the floor curve from the decoded floor information, according to
- packet type. Note that the vector synthesis length for floor computation is <span
- class="cmtt-12">[n]</span>/2.
- <!--l. 535--><p class="noindent" >For each channel, multiply each element of the floor curve by each element of that
- channel’s residue vector. The result is the dot product of the floor and residue vectors for
- each channel; the produced vectors are the length <span
- class="cmtt-12">[n]</span>/2 audio spectrum for each
- channel.
- <!--l. 543--><p class="noindent" >One point is worth mentioning about this dot product; a common mistake in a fixed point
- implementation might be to assume that a 32 bit fixed-point representation for floor and
- residue and direct multiplication of the vectors is sufficient for acceptable spectral depth
- in all cases because it happens to mostly work with the current Xiph.Org reference
- encoder.
- <!--l. 550--><p class="noindent" >However, floor vector values can span <span
- class="cmsy-10x-x-120">∼</span>140dB (<span
- class="cmsy-10x-x-120">∼</span>24 bits unsigned), and the audio spectrum
- vector should represent a minimum of 120dB (<span
- class="cmsy-10x-x-120">∼</span>21 bits with sign), even when output is to a 16
- bit PCM device. For the residue vector to represent full scale if the floor is nailed
- to <span
- class="cmsy-10x-x-120">−</span>140dB, it must be able to span 0 to +140dB. For the residue vector to reach
- full scale if the floor is nailed at 0dB, it must be able to represent <span
- class="cmsy-10x-x-120">−</span>140dB to +0dB.
- Thus, in order to handle full range dynamics, a residue vector may span <span
- class="cmsy-10x-x-120">−</span>140dB to
- +140dB entirely within spec. A 280dB range is approximately 48 bits with sign; thus the
- residue vector must be able to represent a 48 bit range and the dot product must
- be able to handle an effective 48 bit times 24 bit multiplication. This range may be
- achieved using large (64 bit or larger) integers, or implementing a movable binary point
- representation.
- <!--l. 567--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.3.7. </span> <a
- id="x1-780004.3.7"></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="x1-790004.3.8"></a>overlap_add</h5>
- <!--l. 578--><p class="noindent" >Windowed MDCT output is overlapped and added with the right hand data of the previous
- window such that the 3/4 point of the previous window is aligned with the 1/4 point of the
- current window (as illustrated in <a
- href="#x1-260001.3.2">paragraph 1.3.2</a>, “<a
- href="#x1-260001.3.2">Window shape decode (long windows
- only)<!--tex4ht:ref: vorbis:spec:window --></a>”). The overlapped portion produced from overlapping the previous and current frame data
- is finished data to be returned by the decoder. This data spans from the center of
- the previous window to the center of the current window. In the case of same-sized
- windows, the amount of data to return is one-half block consisting of and only of the
- overlapped portions. When overlapping a short and long window, much of the returned
- range does not actually overlap. This does not damage transform orthogonality. Pay
- attention however to returning the correct data range; the amount of data to be returned
- is:
- <!--l. 592--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb22">
- <a
- id="x1-79002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> window\_blocksize(previous\_window)/4+window\_blocksize(current\_window)/4</span>
- </div>
- <!--l. 596--><p class="noindent" >from the center (element windowsize/2) of the previous window to the center (element
- windowsize/2-1, inclusive) of the current window.
- <!--l. 599--><p class="noindent" >Data is not returned from the first frame; it must be used to ’prime’ the decode engine. The
- encoder accounts for this priming when calculating PCM offsets; after the first frame, the proper
- PCM output offset is ’0’ (as no data has been returned yet).
- <!--l. 606--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">4.3.9. </span> <a
- id="x1-800004.3.9"></a>output channel order</h5>
- <!--l. 608--><p class="noindent" >Vorbis I specifies only a channel mapping type 0. In mapping type 0, channel mapping is
- implicitly defined as follows for standard audio applications. As of revision 16781 (20100113), the
- specification adds defined channel locations for 6.1 and 7.1 surround. Ordering/location for
-
-
- greater-than-eight channels remains ’left to the implementation’.
- <!--l. 614--><p class="noindent" >These channel orderings refer to order within the encoded stream. It is naturally possible for a
- decoder to produce output with channels in any order. Any such decoder should explicitly
- document channel reordering behavior.
- <!--l. 620--><p class="noindent" >
- <dl class="description"><dt class="description">
- <span
- class="cmssbx-10x-x-120">one channel</span> </dt><dd
- class="description">the stream is monophonic
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">two channels</span> </dt><dd
- class="description">the stream is stereo. channel order: left, right
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">three channels</span> </dt><dd
- class="description">the stream is a 1d-surround encoding. channel order: left, center, right
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">four channels</span> </dt><dd
- class="description">the stream is quadraphonic surround. channel order: front left, front right,
- rear left, rear right
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">five channels</span> </dt><dd
- class="description">the stream is five-channel surround. channel order: front left, center, front
- right, rear left, rear right
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">six channels</span> </dt><dd
- class="description">the stream is 5.1 surround. channel order: front left, center, front right, rear
- left, rear right, LFE
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">seven channels</span> </dt><dd
- class="description">the stream is 6.1 surround. channel order: front left, center, front right,
- side left, side right, rear center, LFE
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">eight channels</span> </dt><dd
- class="description">the stream is 7.1 surround. channel order: front left, center, front right,
- side left, side right, rear left, rear right, LFE
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">greater than eight channels</span> </dt><dd
- class="description">channel use and order is defined by the application
- </dd></dl>
- <!--l. 656--><p class="noindent" >Applications using Vorbis for dedicated purposes may define channel mapping as seen fit. Future
- channel mappings (such as three and four channel <a
- href="http://www.ambisonic.net/" >Ambisonics</a>) will make use of channel
- mappings other than mapping 0.
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">5. </span> <a
- id="x1-810005"></a>comment field and header specification</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">5.1. </span> <a
- id="x1-820005.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >The Vorbis text comment header is the second (of three) header packets that begin a Vorbis
- bitstream. It is meant for short text comments, not arbitrary metadata; arbitrary metadata
- belongs in a separate logical bitstream (usually an XML stream type) that provides greater
- structure and machine parseability.
- <!--l. 14--><p class="noindent" >The comment field is meant to be used much like someone jotting a quick note on the bottom of
- a CDR. It should be a little information to remember the disc by and explain it to others; a
- short, to-the-point text note that need not only be a couple words, but isn’t going to be more
- than a short paragraph. The essentials, in other words, whatever they turn out to be,
- eg:
- <!--l. 21--><p class="noindent" >
- <div class="quote">
- <!--l. 22--><p class="noindent" >Honest Bob and the Factory-to-Dealer-Incentives, <span
- class="cmti-12">“I’m Still Around”</span>, opening
- for Moxy Früvous, 1997.</div>
- <!--l. 29--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">5.2. </span> <a
- id="x1-830005.2"></a>Comment encoding</h4>
- <!--l. 31--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">5.2.1. </span> <a
- id="x1-840005.2.1"></a>Structure</h5>
- <!--l. 33--><p class="noindent" >The comment header is logically a list of eight-bit-clean vectors; the number of vectors is
- bounded to 2<sup><span
- class="cmr-8">32</span></sup> <span
- class="cmsy-10x-x-120">− </span>1 and the length of each vector is limited to 2<sup><span
- class="cmr-8">32</span></sup> <span
- class="cmsy-10x-x-120">− </span>1 bytes. The vector length is
-
-
- encoded; the vector contents themselves are not null terminated. In addition to the vector list,
- there is a single vector for vendor name (also 8 bit clean, length encoded in 32 bits). For
- example, the 1.0 release of libvorbis set the vendor string to “Xiph.Org libVorbis I
- 20020717”.
- <!--l. 41--><p class="noindent" >The vector lengths and number of vectors are stored lsb first, according to the bit
- packing conventions of the vorbis codec. However, since data in the comment header
- is octet-aligned, they can simply be read as unaligned 32 bit little endian unsigned
- integers.
- <!--l. 46--><p class="noindent" >The comment header is decoded as follows:
- <!--l. 48--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb23">
- <a
- id="x1-84002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [vendor\_length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-84004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [vendor\_string]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> UTF-8</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> [vendor\_length]</span><span
- class="cmtt-8"> octets</span>
- <br class="fancyvrb" /><a
- id="x1-84006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [user\_comment\_list\_length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-84008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [user\_comment\_list\_length]</span><span
- class="cmtt-8"> times</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-84010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [length]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 32</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-84012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> this</span><span
- class="cmtt-8"> iteration’s</span><span
- class="cmtt-8"> user</span><span
- class="cmtt-8"> comment</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> UTF-8</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> [length]</span><span
- class="cmtt-8"> octets</span>
- <br class="fancyvrb" /><a
- id="x1-84014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-84016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [framing\_bit]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> single</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> boolean</span>
- <br class="fancyvrb" /><a
- id="x1-84018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [framing\_bit]</span><span
- class="cmtt-8"> unset</span><span
- class="cmtt-8"> or</span><span
- class="cmtt-8"> end-of-packet</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> ERROR</span>
- <br class="fancyvrb" /><a
- id="x1-84020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> done.</span>
- </div>
- <!--l. 64--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">5.2.2. </span> <a
- id="x1-850005.2.2"></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="x1-85002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> comment[0]="ARTIST=me";</span>
- <br class="fancyvrb" /><a
- id="x1-85004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> comment[1]="TITLE=the</span><span
- class="cmtt-8"> sound</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> Vorbis";</span>
- </div>
- </div>
-
-
- <!--l. 77--><p class="noindent" >The field name is case-insensitive and may consist of ASCII 0x20 through 0x7D, 0x3D (’=’)
- excluded. ASCII 0x41 through 0x5A inclusive (characters A-Z) is to be considered equivalent to
- ASCII 0x61 through 0x7A inclusive (characters a-z).
- <!--l. 83--><p class="noindent" >The field name is immediately followed by ASCII 0x3D (’=’); this equals sign is used to
- terminate the field name.
- <!--l. 87--><p class="noindent" >0x3D is followed by 8 bit clean UTF-8 encoded value of the field contents to the end of the
- field.
- <!--l. 91--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-860005.2.2"></a><span
- class="cmbx-12">Field names</span></span>
- Below is a proposed, minimal list of standard field names with a description of intended use. No
- single or group of field names is mandatory; a comment header may contain one, all or none of
- the names in this list.
- <!--l. 99--><p class="noindent" >
- <dl class="description"><dt class="description">
- <span
- class="cmssbx-10x-x-120">TITLE</span> </dt><dd
- class="description">Track/Work name
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">VERSION</span> </dt><dd
- class="description">The version field may be used to differentiate multiple versions of the same
- track title in a single collection. (e.g. remix info)
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">ALBUM</span> </dt><dd
- class="description">The collection name to which this track belongs
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">TRACKNUMBER</span> </dt><dd
- class="description">The track number of this piece if part of a specific larger collection or
- album
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">ARTIST</span> </dt><dd
- class="description">The artist generally considered responsible for the work. In popular music this is
- usually the performing band or singer. For classical music it would be the composer.
- For an audio book it would be the author of the original text.
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">PERFORMER</span> </dt><dd
- class="description">The artist(s) who performed the work. In classical music this would be the
- conductor, orchestra, soloists. In an audio book it would be the actor who did the
- reading. In popular music this is typically the same as the ARTIST and is omitted.
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">COPYRIGHT</span> </dt><dd
- class="description">Copyright attribution, e.g., ’2001 Nobody’s Band’ or ’1999 Jack Moffitt’
- </dd><dt class="description">
-
-
- <span
- class="cmssbx-10x-x-120">LICENSE</span> </dt><dd
- class="description">License information, eg, ’All Rights Reserved’, ’Any Use Permitted’, a URL to
- a license such as a Creative
- Commons license (”www.creativecommons.org/blahblah/license.html”) or the EFF
- Open Audio License (’distributed under the terms of the Open Audio License. see
- http://www.eff.org/IP/Open_licenses/eff_oal.html for details’), etc.
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">ORGANIZATION</span> </dt><dd
- class="description">Name of the organization producing the track (i.e. the ’record label’)
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">DESCRIPTION</span> </dt><dd
- class="description">A short text description of the contents
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">GENRE</span> </dt><dd
- class="description">A short text indication of music genre
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">DATE</span> </dt><dd
- class="description">Date the track was recorded
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">LOCATION</span> </dt><dd
- class="description">Location where track was recorded
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">CONTACT</span> </dt><dd
- class="description">Contact information for the creators or distributors of the track. This could
- be a URL, an email address, the physical address of the producing label.
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">ISRC</span> </dt><dd
- class="description">International Standard Recording Code for the track; see <a
- href="http://www.ifpi.org/isrc/" >the ISRC intro page</a> for
- more information on ISRC numbers.
- </dd></dl>
- <!--l. 158--><p class="noindent" ><span class="paragraphHead"><a
- id="x1-870005.2.2"></a><span
- class="cmbx-12">Implications</span></span>
- Field names should not be ’internationalized’; this is a concession to simplicity not
- an attempt to exclude the majority of the world that doesn’t speak English. Field
- <span
- class="cmti-12">contents</span>, however, use the UTF-8 character encoding to allow easy representation of any
- language.
- <!--l. 166--><p class="noindent" >We have the length of the entirety of the field and restrictions on the field name so that
- the field name is bounded in a known way. Thus we also have the length of the field
- contents.
- <!--l. 170--><p class="noindent" >Individual ’vendors’ may use non-standard field names within reason. The proper
- use of comment fields should be clear through context at this point. Abuse will be
- discouraged.
-
-
- <!--l. 174--><p class="noindent" >There is no vendor-specific prefix to ’nonstandard’ field names. Vendors should make some effort
- to avoid arbitrarily polluting the common namespace. We will generally collect the more useful
- tags here to help with standardization.
- <!--l. 179--><p class="noindent" >Field names are not required to be unique (occur once) within a comment header. As an
- example, assume a track was recorded by three well know artists; the following is permissible,
- and encouraged:
- <!--l. 183--><p class="noindent" >
- <div class="quote">
- <!--l. 184--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb25">
- <a
- id="x1-87002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ARTIST=Dizzy</span><span
- class="cmtt-8"> Gillespie</span>
- <br class="fancyvrb" /><a
- id="x1-87004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ARTIST=Sonny</span><span
- class="cmtt-8"> Rollins</span>
- <br class="fancyvrb" /><a
- id="x1-87006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> ARTIST=Sonny</span><span
- class="cmtt-8"> Stitt</span>
- </div>
- </div>
- <!--l. 197--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">5.2.3. </span> <a
- id="x1-880005.2.3"></a>Encoding</h5>
- <!--l. 199--><p class="noindent" >The comment header comprises the entirety of the second bitstream header packet. Unlike the
- first bitstream header packet, it is not generally the only packet on the second page and may not
- be restricted to within the second bitstream page. The length of the comment header packet is
- (practically) unbounded. The comment header packet is not optional; it must be present in the
- bitstream even if it is effectively empty.
- <!--l. 207--><p class="noindent" >The comment header is encoded as follows (as per Ogg’s standard bitstream mapping which
- renders least-significant-bit of the word to be coded into the least significant available bit of the
- current bitstream octet first):
- <!--l. 213--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem">Vendor string length (32 bit unsigned quantity specifying number of octets)
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">Vendor string ([vendor string length] octets coded from beginning of string to end of
- string, not null terminated)
-
-
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">Number of comment fields (32 bit unsigned quantity specifying number of fields)
- </dd><dt class="enumerate-enumitem">
- 4. </dt><dd
- class="enumerate-enumitem">Comment field 0 length (if [Number of comment fields] <span
- class="cmmi-12">> </span>0; 32 bit unsigned quantity
- specifying number of octets)
- </dd><dt class="enumerate-enumitem">
- 5. </dt><dd
- class="enumerate-enumitem">Comment field 0 ([Comment field 0 length] octets coded from beginning of string to
- end of string, not null terminated)
- </dd><dt class="enumerate-enumitem">
- 6. </dt><dd
- class="enumerate-enumitem">Comment field 1 length (if [Number of comment fields] <span
- class="cmmi-12">> </span>1...)...
- </dd></dl>
- <!--l. 234--><p class="noindent" >This is actually somewhat easier to describe in code; implementation of the above can be found
- in <span
- class="cmtt-12">vorbis/lib/info.c</span>, <span
- class="cmtt-12">_vorbis_pack_comment() </span>and <span
- class="cmtt-12">_vorbis_unpack_comment()</span>.
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">6. </span> <a
- id="x1-890006"></a>Floor type 0 setup and decode</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">6.1. </span> <a
- id="x1-900006.1"></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="x1-910006.2"></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="x1-920006.2.1"></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="x1-92002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [floor0_order]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-92004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [floor0_rate]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 16</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-92006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [floor0_bark_map_size]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> 16</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-92008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [floor0_amplitude_bits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> six</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-92010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [floor0_amplitude_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> eight</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-92012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [floor0_number_of_books]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> four</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-92014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [floor0_book_list]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> list</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [floor0_number_of_books]</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integers</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> eight</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> each;</span>
- </div>
-
-
- <!--l. 40--><p class="noindent" >An end-of-packet condition during any of these bitstream reads renders this stream undecodable.
- In addition, any element of the array <span
- class="cmtt-12">[floor0_book_list] </span>that is greater than the maximum
- codebook number for this bitstream is an error condition that also renders the stream
- undecodable.
- <!--l. 48--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">6.2.2. </span> <a
- id="x1-930006.2.2"></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="x1-93002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [amplitude]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [floor0_amplitude_bits]</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-93004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [amplitude]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-93006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [coefficients]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> empty,</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> length</span><span
- class="cmtt-8"> vector</span>
- <br class="fancyvrb" /><a
- id="x1-93008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [booknumber]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> </span><a
- href="#x1-1170009.2.1"><span
- class="cmtt-8">ilog</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> [floor0_number_of_books]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-93010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [booknumber]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> highest</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> decode</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> undecodable</span>
- <br class="fancyvrb" /><a
- id="x1-93012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> zero;</span>
- <br class="fancyvrb" /><a
- id="x1-93014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [temp_vector]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> bitstream</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [floor0_book_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [booknumber]</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> VQ</span><span
- class="cmtt-8"> context.</span>
- <br class="fancyvrb" /><a
- id="x1-93016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> each</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [temp_vector]</span>
- <br class="fancyvrb" /><a
- id="x1-93018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [last]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> last</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [temp_vector]</span>
- <br class="fancyvrb" /><a
- id="x1-93020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> concatenate</span><span
- class="cmtt-8"> [temp_vector]</span><span
- class="cmtt-8"> onto</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> end</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> [coefficients]</span><span
- class="cmtt-8"> vector</span>
- <br class="fancyvrb" /><a
- id="x1-93022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (length</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [coefficients]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [floor0_order],</span><span
- class="cmtt-8"> continue</span><span
- class="cmtt-8"> at</span><span
- class="cmtt-8"> step</span><span
- class="cmtt-8"> 6</span>
- <br class="fancyvrb" /><a
- id="x1-93024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-93026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-93028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-93030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> done.</span>
- <br class="fancyvrb" /><a
- id="x1-93032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 76--><p class="noindent" >Take note of the following properties of decode:
- <ul class="itemize1">
- <li class="itemize">An <span
- class="cmtt-12">[amplitude] </span>value of zero must result in a return code that indicates this channel
- is unused in this frame (the output of the channel will be all-zeroes in synthesis).
- Several later stages of decode don’t occur for an unused channel.
- </li>
- <li class="itemize">An end-of-packet condition during decode should be considered a nominal occruence;
- if end-of-packet is reached during any read operation above, floor decode is to return
- ’unused’ status as if the <span
- class="cmtt-12">[amplitude] </span>value had read zero at the beginning of decode.
- </li>
- <li class="itemize">The book number used for decode can, in fact, be stored in the bitstream in <a
- href="#x1-1170009.2.1">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="x1-940006.2.3"></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=" {
- min (floor0_bark_map_size − 1,foobar ) for i ∈ [0,n − 1 ]
- mapi = − 1 for i = n
- " class="par-math-display" ></center>
- <!--l. 128--><p class="nopar" >
- <!--l. 130--><p class="noindent" >where
- <center class="par-math-display" >
- <img
- src="Vorbis_I_spec8x.png" alt=" ⌊ ⌋
- (floor0_rate ⋅ i) floor0_bark_map_size
- foobar = bark -------2n------- ⋅-bark(.5 ⋅ floor0_rate-)
- " class="par-math-display" ></center>
-
-
- <!--l. 137--><p class="nopar" >
- <!--l. 139--><p class="noindent" >and
- <center class="par-math-display" >
- <img
- src="Vorbis_I_spec9x.png" alt=" 2
- bark(x) = 13.1arctan (.00074x ) + 2.24 arctan(.0000000185x + .0001x )
- " class="par-math-display" ></center>
- <!--l. 143--><p class="nopar" >
- <!--l. 145--><p class="noindent" >The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the
- result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output
- LSP curve <span
- class="cmtt-12">[output] </span>on a log (dB) amplitude scale, mapping it to linear amplitude in the last
- step:
- <!--l. 151--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[i] </span>= 0
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem"><span
- class="cmtt-12">[</span><span
- class="cmmi-12">ω</span><span
- class="cmtt-12">] </span>= <span
- class="cmmi-12">π </span>* map element <span
- class="cmtt-12">[i] </span>/ <span
- class="cmtt-12">[floor0_bark_map_size]</span>
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">if ( <span
- class="cmtt-12">[floor0_order] </span>is odd )
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- a) </dt><dd
- class="enumerate-enumitem">calculate <span
- class="cmtt-12">[p] </span>and <span
- class="cmtt-12">[q] </span>according to: <div class="eqnarray">
- <center class="math-display" >
- <img
- src="Vorbis_I_spec10x.png" alt=" floor0_order−3
- 2 ∏2 2
- p = (1 − cos ω) 4(cos([coefficients ]2j+1) − cosω )
- floor0_order−1 j=0
- 1 ----∏2----
- q = -- 4(cos([coefficients ]2j) − cosω )2
- 4 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">
- b) </dt><dd
- class="enumerate-enumitem">calculate <span
- class="cmtt-12">[p] </span>and <span
- class="cmtt-12">[q] </span>according to: <div class="eqnarray">
- <center class="math-display" >
- <img
- src="Vorbis_I_spec11x.png" alt=" floor0_order−2
- (1-−-cosω-) ∏2 2
- p = 2 4(cos([coefficients ]2j+1) − cosω)
- j=0
- floor0_∏o2rder−-2
- q = (1-+-cosω-) 4(cos([coefficients ]2j) − cos ω)2
- 2 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=" ( ( ))
- exp .11512925 amplitude---⋅ floor0_amplitute_√offset---− floor0_amplitude_offset
- (2floor0_amplitude_bits − 1) p + q
- " 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>
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">7. </span> <a
- id="x1-950007"></a>Floor type 1 setup and decode</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">7.1. </span> <a
- id="x1-960007.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >Vorbis floor type one uses a piecewise straight-line representation to encode a spectral envelope
- curve. The representation plots this curve mechanically on a linear frequency axis and a
- logarithmic (dB) amplitude axis. The integer plotting algorithm used is similar to Bresenham’s
- algorithm.
- <!--l. 16--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">7.2. </span> <a
- id="x1-970007.2"></a>Floor 1 format</h4>
- <!--l. 18--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">7.2.1. </span> <a
- id="x1-980007.2.1"></a>model</h5>
- <!--l. 20--><p class="noindent" >Floor type one represents a spectral curve as a series of line segments. Synthesis constructs a
- floor curve using iterative prediction in a process roughly equivalent to the following simplified
- description:
- <ul class="itemize1">
- <li class="itemize">the first line segment (base case) is a logical line spanning from x˙0,y˙0 to x˙1,y˙1
- where in the base case x˙0=0 and x˙1=[n], the full range of the spectral floor to be
- computed.
- </li>
- <li class="itemize">the induction step chooses a point x˙new within an existing logical line segment and
- produces a y˙new value at that point computed from the existing line’s y value at
- x˙new (as plotted by the line) and a difference value decoded from the bitstream
- packet.
-
-
- </li>
- <li class="itemize">floor computation produces two new line segments, one running from x˙0,y˙0 to
- x˙new,y˙new and from x˙new,y˙new to x˙1,y˙1. This step is performed logically even if
- y˙new represents no change to the amplitude value at x˙new so that later refinement
- is additionally bounded at x˙new.
- </li>
- <li class="itemize">the induction step repeats, using a list of x values specified in the codec setup header
- at floor 1 initialization time. Computation is completed at the end of the x value list.
- </li></ul>
- <!--l. 48--><p class="noindent" >Consider the following example, with values chosen for ease of understanding rather than
- representing typical configuration:
- <!--l. 51--><p class="noindent" >For the below example, we assume a floor setup with an [n] of 128. The list of selected X values
- in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0,
- 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an
- example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following
- way, beginning with the first line:
- <div class="center"
- >
- <!--l. 59--><p class="noindent" >
- <!--l. 60--><p class="noindent" ><img
- src="floor1-1.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 7: </span><span
- class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980017 -->
- </div>
- <!--l. 64--><p class="noindent" >We now draw new logical lines to reflect the correction to new˙Y, and iterate for X positions 32
- and 96:
- <div class="center"
- >
- <!--l. 67--><p class="noindent" >
- <!--l. 68--><p class="noindent" ><img
- src="floor1-2.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 8: </span><span
- class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980028 -->
- </div>
- <!--l. 72--><p class="noindent" >Although the new Y value at X position 96 is unchanged, it is still used later as an endpoint for
- further refinement. From here on, the pattern should be clear; we complete the floor computation
- as follows:
-
-
- <div class="center"
- >
- <!--l. 76--><p class="noindent" >
- <!--l. 77--><p class="noindent" ><img
- src="floor1-3.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 9: </span><span
- class="content">graph of example floor</span></div><!--tex4ht:label?: x1-980039 -->
- </div>
- <div class="center"
- >
- <!--l. 81--><p class="noindent" >
- <!--l. 82--><p class="noindent" ><img
- src="floor1-4.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 10: </span><span
- class="content">graph of example floor</span></div><!--tex4ht:label?: x1-9800410 -->
- </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="x1-990007.2.2"></a>header decode</h5>
- <!--l. 96--><p class="noindent" >A list of floor X values is stored in the packet header in interleaved format (used in list order
- during packet decode and synthesis). This list is split into partitions, and each partition is
- assigned to a partition class. X positions 0 and [n] are implicit and do not belong to an explicit
- partition or partition class.
- <!--l. 102--><p class="noindent" >A partition class consists of a representation vector width (the number of Y values which
- the partition class encodes at once), a ’subclass’ value representing the number of
- alternate entropy books the partition class may use in representing Y values, the list of
- [subclass] books and a master book used to encode which alternate books were chosen
- for representation in a given packet. The master/subclass mechanism is meant to be
- used as a flexible representation cascade while still using codebooks only in a scalar
- context.
-
-
- <!--l. 112--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb28">
- <a
- id="x1-99002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [floor1_partitions]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [maximum_class]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> -1</span>
- <br class="fancyvrb" /><a
- id="x1-99008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [floor1_partitions]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_partition_class_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [maximum_class]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> largest</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_partition_class_list]</span>
- <br class="fancyvrb" /><a
- id="x1-99022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [maximum_class]</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_dimensions]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-99028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  8)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_subclasses]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_subclasses]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> nonzero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99034r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_masterbooks]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99036r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99038r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99040r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99042r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> (2</span><span
- class="cmtt-8"> exponent</span><span
- class="cmtt-8"> [floor1_class_subclasses]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i])</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99044r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99046r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [floor1_subclass_books]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i],[j]</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-99048r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> subtract</span><span
- class="cmtt-8"> one</span>
- <br class="fancyvrb" /><a
- id="x1-99050r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99052r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99054r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99056r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> [floor1_multiplier]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> one</span>
- <br class="fancyvrb" /><a
- id="x1-99058r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> [rangebits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99060r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-99062r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [1]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> exponent</span><span
- class="cmtt-8"> [rangebits];</span>
- <br class="fancyvrb" /><a
- id="x1-99064r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 17)</span><span
- class="cmtt-8"> [floor1_values]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-99066r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 18)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [floor1_partitions]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99068r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99070r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 19)</span><span
- class="cmtt-8"> [current_class_number]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_partition_class_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-99072r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 20)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> ([floor1_class_dimensions]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [current_class_number])-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-99074r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 21)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([floor1_values])</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-99076r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> [rangebits]</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-99078r39"></a><span
- class="cmr-6">39</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 22)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [floor1_values]</span><span
- class="cmtt-8"> by</span><span
- class="cmtt-8"> one</span>
- <br class="fancyvrb" /><a
- id="x1-99080r40"></a><span
- class="cmr-6">40</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99082r41"></a><span
- class="cmr-6">41</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-99084r42"></a><span
- class="cmr-6">42</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-99086r43"></a><span
- class="cmr-6">43</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 23)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 158--><p class="noindent" >An end-of-packet condition while reading any aspect of a floor 1 configuration during
- setup renders a stream undecodable. In addition, a <span
- class="cmtt-12">[floor1_class_masterbooks] </span>or
- <span
- class="cmtt-12">[floor1_subclass_books] </span>scalar element greater than the highest numbered codebook
- configured in this stream is an error condition that renders the stream undecodable. Vector
- [floor1_x_list] is limited to a maximum length of 65 elements; a setup indicating more than 65
- total elements (including elements 0 and 1 set prior to the read loop) renders the stream
- undecodable. All vector [floor1_x_list] element values must be unique within the vector; a
- non-unique value renders the stream undecodable.
-
-
- <!--l. 170--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">7.2.3. </span> <a
- id="x1-1000007.2.3"></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="x1-100002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [nonzero]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> boolean</span>
- </div>
- <!--l. 178--><p class="noindent" >If <span
- class="cmtt-12">[nonzero] </span>is unset, that indicates this channel contained no audio energy in this frame.
- Decode immediately returns a status indicating this floor curve (and thus this channel) is unused
- this frame. (A return status of ’unused’ is different from decoding a floor that has all
- points set to minimum representation amplitude, which happens to be approximately
- -140dB).
- <!--l. 186--><p class="noindent" >Assuming <span
- class="cmtt-12">[nonzero] </span>is set, decode proceeds as follows:
- <!--l. 188--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb30">
- <a
- id="x1-100004r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [range]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span><span
- class="cmtt-8"> 256,</span><span
- class="cmtt-8"> 128,</span><span
- class="cmtt-8"> 86,</span><span
- class="cmtt-8"> 64</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([floor1_multiplier]-1)</span>
- <br class="fancyvrb" /><a
- id="x1-100006r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> </span><a
- href="#x1-1170009.2.1"><span
- class="cmtt-8">ilog</span></a><span
- class="cmtt-8">([range]-1)</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-100008r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [1]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> </span><a
- href="#x1-1170009.2.1"><span
- class="cmtt-8">ilog</span></a><span
- class="cmtt-8">([range]-1)</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-100010r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2;</span>
- <br class="fancyvrb" /><a
- id="x1-100012r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [floor1_partitions]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-100014r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100016r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [class]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_partition_class]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-100018r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [cdim]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_dimensions]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [class]</span>
- <br class="fancyvrb" /><a
- id="x1-100020r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> [cbits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_class_subclasses]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [class]</span>
- <br class="fancyvrb" /><a
- id="x1-100022r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [csub]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> (2</span><span
- class="cmtt-8"> exponent</span><span
- class="cmtt-8"> [cbits])-1</span>
- <br class="fancyvrb" /><a
- id="x1-100024r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> [cval]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-100026r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [cbits]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-100028r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100030r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> [cval]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> number</span>
- <br class="fancyvrb" /><a
- id="x1-100032r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> (vector</span><span
- class="cmtt-8"> [floor1_class_masterbooks]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [class])</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-100034r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-100036r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100038r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [cdim]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-100040r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100042r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> [book]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [floor1_subclass_books]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [class],([cval]</span><span
- class="cmtt-8"> bitwise</span><span
- class="cmtt-8"> AND</span><span
- class="cmtt-8"> [csub])</span>
- <br class="fancyvrb" /><a
- id="x1-100044r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> [cval]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [cval]</span><span
- class="cmtt-8"> right</span><span
- class="cmtt-8"> shifted</span><span
- class="cmtt-8"> [cbits]</span><span
- class="cmtt-8"> bits</span>
- <br class="fancyvrb" /><a
- id="x1-100046r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [book]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-100048r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100050r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 17)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([j]+[offset])</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> codebook</span>
- <br class="fancyvrb" /><a
- id="x1-100052r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [book]</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-100054r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100056r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [book]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-100058r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100060r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 18)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([j]+[offset])</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-100062r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100064r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-100066r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-100068r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100070r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 19)</span><span
- class="cmtt-8"> [offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [offset]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [cdim]</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-100072r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100074r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-100076r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-100078r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 20)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 229--><p class="noindent" >An end-of-packet condition during curve decode should be considered a nominal occurrence; if
- end-of-packet is reached during any read operation above, floor decode is to return ’unused’
- status as if the <span
- class="cmtt-12">[nonzero] </span>flag had been unset at the beginning of decode.
- <!--l. 235--><p class="noindent" >Vector <span
- class="cmtt-12">[floor1_Y] </span>contains the values from packet decode needed for floor 1 synthesis.
- <!--l. 240--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">7.2.4. </span> <a
- id="x1-1010007.2.4"></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="x1-101002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [range]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span><span
- class="cmtt-8"> 256,</span><span
- class="cmtt-8"> 128,</span><span
- class="cmtt-8"> 86,</span><span
- class="cmtt-8"> 64</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([floor1_multiplier]-1)</span>
- <br class="fancyvrb" /><a
- id="x1-101004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> set</span>
- <br class="fancyvrb" /><a
- id="x1-101006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [1]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> set</span>
- <br class="fancyvrb" /><a
- id="x1-101008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span>
- <br class="fancyvrb" /><a
- id="x1-101010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [1]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [1]</span>
- <br class="fancyvrb" /><a
- id="x1-101012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [floor1_values]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [low_neighbor_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1200009.2.4"><span
- class="cmtt-8">low_neighbor</span></a><span
- class="cmtt-8">([floor1_X_list],[i])</span>
- <br class="fancyvrb" /><a
- id="x1-101018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> [high_neighbor_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1210009.2.5"><span
- class="cmtt-8">high_neighbor</span></a><span
- class="cmtt-8">([floor1_X_list],[i])</span>
- <br class="fancyvrb" /><a
- id="x1-101020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [predicted]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> </span><a
- href="#x1-1220009.2.6"><span
- class="cmtt-8">render_point</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [low_neighbor_offset],</span>
- <br class="fancyvrb" /><a
- id="x1-101024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [low_neighbor_offset],</span>
- <br class="fancyvrb" /><a
- id="x1-101026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [high_neighbor_offset],</span>
- <br class="fancyvrb" /><a
- id="x1-101028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [high_neighbor_offset],</span>
- <br class="fancyvrb" /><a
- id="x1-101030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_X_list]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> )</span>
- <br class="fancyvrb" /><a
- id="x1-101032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101034r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-101036r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [range]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [predicted]</span>
- <br class="fancyvrb" /><a
- id="x1-101038r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [predicted]</span>
- <br class="fancyvrb" /><a
- id="x1-101040r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101042r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101044r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> [room]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-101046r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101048r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101050r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101052r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> [room]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-101054r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101056r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101058r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101060r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> nonzero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101062r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101064r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 17)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [low_neighbor_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> set</span>
- <br class="fancyvrb" /><a
- id="x1-101066r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 18)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [high_neighbor_offset]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> set</span>
- <br class="fancyvrb" /><a
- id="x1-101068r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 19)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> set</span>
- <br class="fancyvrb" /><a
- id="x1-101070r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 20)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> or</span><span
- class="cmtt-8"> equal</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> [room]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101072r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101074r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 21)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101076r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101078r39"></a><span
- class="cmr-6">39</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 22)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [predicted]</span>
- <br class="fancyvrb" /><a
- id="x1-101080r40"></a><span
- class="cmr-6">40</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101082r41"></a><span
- class="cmr-6">41</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [lowroom]</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101084r42"></a><span
- class="cmr-6">42</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101086r43"></a><span
- class="cmr-6">43</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 23)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [predicted]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [highroom]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-101088r44"></a><span
- class="cmr-6">44</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101090r45"></a><span
- class="cmr-6">45</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101092r46"></a><span
- class="cmr-6">46</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101094r47"></a><span
- class="cmr-6">47</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [room]</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101096r48"></a><span
- class="cmr-6">48</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101098r49"></a><span
- class="cmr-6">49</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 24)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> ([val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> odd)</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101100r50"></a><span
- class="cmr-6">50</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101102r51"></a><span
- class="cmr-6">51</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 25)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-101104r52"></a><span
- class="cmr-6">52</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [predicted]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> (([val]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> divided</span><span
- class="cmtt-8"> by</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> division)</span>
- <br class="fancyvrb" /><a
- id="x1-101106r53"></a><span
- class="cmr-6">53</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101108r54"></a><span
- class="cmr-6">54</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> even</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101110r55"></a><span
- class="cmr-6">55</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101112r56"></a><span
- class="cmr-6">56</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 26)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-101114r57"></a><span
- class="cmr-6">57</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [predicted]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> ([val]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> division)</span>
- <br class="fancyvrb" /><a
- id="x1-101116r58"></a><span
- class="cmr-6">58</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101118r59"></a><span
- class="cmr-6">59</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101120r60"></a><span
- class="cmr-6">60</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101122r61"></a><span
- class="cmr-6">61</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101124r62"></a><span
- class="cmr-6">62</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101126r63"></a><span
- class="cmr-6">63</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> [val]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101128r64"></a><span
- class="cmr-6">64</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101130r65"></a><span
- class="cmr-6">65</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 27)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_step2_flag]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> unset</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-101132r66"></a><span
- class="cmr-6">66</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 28)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [predicted]</span>
- <br class="fancyvrb" /><a
- id="x1-101134r67"></a><span
- class="cmr-6">67</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101136r68"></a><span
- class="cmr-6">68</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101138r69"></a><span
- class="cmr-6">69</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101140r70"></a><span
- class="cmr-6">70</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101142r71"></a><span
- class="cmr-6">71</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101144r72"></a><span
- class="cmr-6">72</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 29)</span><span
- class="cmtt-8"> done</span>
- <br class="fancyvrb" /><a
- id="x1-101146r73"></a><span
- class="cmr-6">73</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- </dd><dt class="description">
- <span
- class="cmssbx-10x-x-120">step 2: curve synthesis</span> </dt><dd
- class="description">
- <!--l. 351--><p class="noindent" >Curve synthesis generates a return vector <span
- class="cmtt-12">[floor] </span>of length <span
- class="cmtt-12">[n] </span>(where <span
- class="cmtt-12">[n] </span>is provided by
- the decode process calling to floor decode). Floor 1 curve synthesis makes use of the
- <span
- class="cmtt-12">[floor1_X_list]</span>, <span
- class="cmtt-12">[floor1_final_Y] </span>and <span
- class="cmtt-12">[floor1_step2_flag] </span>vectors, as well as
- [floor1_multiplier] and [floor1_values] values.
- <!--l. 358--><p class="noindent" >Decode begins by sorting the scalars from vectors <span
- class="cmtt-12">[floor1_X_list]</span>, <span
- class="cmtt-12">[floor1_final_Y] </span>and
- <span
- class="cmtt-12">[floor1_step2_flag] </span>together into new vectors <span
- class="cmtt-12">[floor1_X_list]’</span>, <span
- class="cmtt-12">[floor1_final_Y]’</span>
- and <span
- class="cmtt-12">[floor1_step2_flag]’ </span>according to ascending sort order of the values in
- <span
- class="cmtt-12">[floor1_X_list]</span>. That is, sort the values of <span
- class="cmtt-12">[floor1_X_list] </span>and then apply the same
- permutation to elements of the other two vectors so that the X, Y and step2_flag values
- still match.
- <!--l. 368--><p class="noindent" >Then compute the final curve in one pass:
- <!--l. 370--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb32">
- <a
- id="x1-101148r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [hx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-101150r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [lx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-101152r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [ly]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor1_final_Y]’</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [0]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [floor1_multiplier]</span>
- <br class="fancyvrb" /><a
- id="x1-101154r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [floor1_values]-1</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101156r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101158r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [floor1_step2_flag]’</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101160r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101162r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> [hy]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [floor1_final_Y]’</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [floor1_multiplier]</span>
- <br class="fancyvrb" /><a
- id="x1-101164r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [hx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [floor1_X_list]’</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-101166r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> </span><a
- href="#x1-1230009.2.7"><span
- class="cmtt-8">render_line</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> [lx],</span><span
- class="cmtt-8"> [ly],</span><span
- class="cmtt-8"> [hx],</span><span
- class="cmtt-8"> [hy],</span><span
- class="cmtt-8"> [floor]</span><span
- class="cmtt-8"> )</span>
- <br class="fancyvrb" /><a
- id="x1-101168r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [lx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [hx]</span>
- <br class="fancyvrb" /><a
- id="x1-101170r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> [ly]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [hy]</span>
- <br class="fancyvrb" /><a
- id="x1-101172r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101174r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101176r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101178r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [hx]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [n]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101180r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101182r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> </span><a
- href="#x1-1230009.2.7"><span
- class="cmtt-8">render_line</span></a><span
- class="cmtt-8">(</span><span
- class="cmtt-8"> [hx],</span><span
- class="cmtt-8"> [hy],</span><span
- class="cmtt-8"> [n],</span><span
- class="cmtt-8"> [hy],</span><span
- class="cmtt-8"> [floor]</span><span
- class="cmtt-8"> )</span>
- <br class="fancyvrb" /><a
- id="x1-101184r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101186r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101188r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101190r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [hx]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [n]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">{</span>
- <br class="fancyvrb" /><a
- id="x1-101192r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101194r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> truncate</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor]</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> [n]</span><span
- class="cmtt-8"> elements</span>
- <br class="fancyvrb" /><a
- id="x1-101196r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101198r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmsy-8">}</span>
- <br class="fancyvrb" /><a
- id="x1-101200r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
-
-
- <br class="fancyvrb" /><a
- id="x1-101202r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> for</span><span
- class="cmtt-8"> each</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [floor],</span><span
- class="cmtt-8"> perform</span><span
- class="cmtt-8"> a</span><span
- class="cmtt-8"> lookup</span><span
- class="cmtt-8"> substitution</span><span
- class="cmtt-8"> using</span>
- <br class="fancyvrb" /><a
- id="x1-101204r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> [floor]</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> an</span><span
- class="cmtt-8"> offset</span><span
- class="cmtt-8"> into</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> </span><a
- href="#x1-12500010.1"><span
- class="cmtt-8">[floor1_inverse_dB_static_table]</span></a>
- <br class="fancyvrb" /><a
- id="x1-101206r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-101208r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> done</span>
- <br class="fancyvrb" /><a
- id="x1-101210r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- </dd></dl>
-
-
- <h3 class="sectionHead"><span class="titlemark">8. </span> <a
- id="x1-1020008"></a>Residue setup and decode</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">8.1. </span> <a
- id="x1-1030008.1"></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="x1-1040008.2"></a>Residue format</h4>
- <!--l. 25--><p class="noindent" >Residue format partitions each vector in the vector bundle into chunks, classifies each
- chunk, encodes the chunk classifications and finally encodes the chunks themselves
- using the the specific VQ arrangement defined for each selected classification. The
- exact interleaving and partitioning vary by residue encoding number, however the
- high-level process used to classify and encode the residue vector is the same in all three
- variants.
- <!--l. 33--><p class="noindent" >A set of coded residue vectors are all of the same length. High level coding structure, ignoring for
- the moment exactly how a partition is encoded and simply trusting that it is, is as
- follows:
- <ul class="itemize1">
- <li class="itemize">Each vector is partitioned into multiple equal sized chunks according to configuration
- specified. If we have a vector size of <span
- class="cmti-12">n</span>, a partition size <span
- class="cmti-12">residue</span><span
- class="cmti-12">_partition</span><span
- class="cmti-12">_size</span>,
- and a total of <span
- class="cmti-12">ch </span>residue vectors, the total number of partitioned chunks coded
-
-
- is <span
- class="cmti-12">n</span>/<span
- class="cmti-12">residue</span><span
- class="cmti-12">_partition</span><span
- class="cmti-12">_size</span>*<span
- class="cmti-12">ch</span>. It is important to note that the integer division
- truncates. In the below example, we assume an example <span
- class="cmti-12">residue</span><span
- class="cmti-12">_partition</span><span
- class="cmti-12">_size </span>of 8.
- </li>
- <li class="itemize">Each partition in each vector has a classification number that specifies which of
- multiple configured VQ codebook setups are used to decode that partition. The
- classification numbers of each partition can be thought of as forming a vector in
- their own right, as in the illustration below. Just as the residue vectors are coded
- in grouped partitions to increase encoding efficiency, the classification vector is also
- partitioned into chunks. The integer elements of each scalar in a classification chunk
- are built into a single scalar that represents the classification numbers in that chunk.
- In the below example, the classification codeword encodes two classification numbers.
- </li>
- <li class="itemize">The values in a residue vector may be encoded monolithically in a single pass through
- the residue vector, but more often efficient codebook design dictates that each vector
- is encoded as the additive sum of several passes through the residue vector using
- more than one VQ codebook. Thus, each residue value potentially accumulates values
- from multiple decode passes. The classification value associated with a partition is
- the same in each pass, thus the classification codeword is coded only in the first pass.
- </li></ul>
- <div class="center"
- >
- <!--l. 70--><p class="noindent" >
- <!--l. 71--><p class="noindent" ><img
- src="residue-pack.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 11: </span><span
- class="content">illustration of residue vector format</span></div><!--tex4ht:label?: x1-10400111 -->
- </div>
- <!--l. 77--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">8.3. </span> <a
- id="x1-1050008.3"></a>residue 0</h4>
- <!--l. 79--><p class="noindent" >Residue 0 and 1 differ only in the way the values within a residue partition are interleaved during
- partition encoding (visually treated as a black box–or cyan box or brown box–in the above
- figure).
- <!--l. 83--><p class="noindent" >Residue encoding 0 interleaves VQ encoding according to the dimension of the codebook used to
-
-
- encode a partition in a specific pass. The dimension of the codebook need not be the same in
- multiple passes, however the partition size must be an even multiple of the codebook
- dimension.
- <!--l. 89--><p class="noindent" >As an example, assume a partition vector of size eight, to be encoded by residue 0 using
- codebook sizes of 8, 4, 2 and 1:
- <!--l. 92--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb33">
- <a
- id="x1-105002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-105004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> original</span><span
- class="cmtt-8"> residue</span><span
- class="cmtt-8"> vector:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-105006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-105008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-105010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-105012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-105014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-105016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-105018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-105020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-105022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 106--><p class="noindent" >It is worth mentioning at this point that no configurable value in the residue coding setup is
- restricted to a power of two.
- <!--l. 111--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">8.4. </span> <a
- id="x1-1060008.4"></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="x1-106002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-106004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> original</span><span
- class="cmtt-8"> residue</span><span
- class="cmtt-8"> vector:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-106006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-106008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-106010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-106012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-106014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-106016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-106018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-106020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> dimensions</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> encoded</span><span
- class="cmtt-8"> as:</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 1</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 4</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 5</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> ],</span><span
- class="cmtt-8"> [</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> ]</span>
- <br class="fancyvrb" /><a
- id="x1-106022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
-
-
- </div>
- <!--l. 137--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">8.5. </span> <a
- id="x1-1070008.5"></a>residue 2</h4>
- <!--l. 139--><p class="noindent" >Residue type two can be thought of as a variant of residue type 1. Rather than encoding multiple
- passed-in vectors as in residue type 1, the <span
- class="cmti-12">ch </span>passed in vectors of length <span
- class="cmti-12">n </span>are first interleaved
- and flattened into a single vector of length <span
- class="cmti-12">ch</span>*<span
- class="cmti-12">n</span>. Encoding then proceeds as in type 1. Decoding
- is as in type 1 with decode interleave reversed. If operating on a single vector to begin with,
- residue type 1 and type 2 are equivalent.
- <div class="center"
- >
- <!--l. 147--><p class="noindent" >
- <!--l. 148--><p class="noindent" ><img
- src="residue2.png" alt="PIC"
- >
- <br /> <div class="caption"
- ><span class="id">Figure 12: </span><span
- class="content">illustration of residue type 2</span></div><!--tex4ht:label?: x1-10700112 -->
- </div>
- <!--l. 153--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">8.6. </span> <a
- id="x1-1080008.6"></a>Residue decode</h4>
- <!--l. 155--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">8.6.1. </span> <a
- id="x1-1090008.6.1"></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="x1-109002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [residue\_begin]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 24</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-109004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [residue\_end]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 24</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-109006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [residue\_partition\_size]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 24</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> one</span>
- <br class="fancyvrb" /><a
- id="x1-109008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [residue\_classifications]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 6</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> add</span><span
- class="cmtt-8"> one</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-109010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [residue\_classbook]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- </div>
- <!--l. 166--><p class="noindent" ><span
- class="cmtt-12">[residue_begin] </span>and <span
- class="cmtt-12">[residue_end] </span>select the specific sub-portion of each vector that is
- actually coded; it implements akin to a bandpass where, for coding purposes, the vector
- effectively begins at element <span
- class="cmtt-12">[residue_begin] </span>and ends at <span
- class="cmtt-12">[residue_end]</span>. Preceding and
- following values in the unpacked vectors are zeroed. Note that for residue type 2, these
- values as well as <span
- class="cmtt-12">[residue_partition_size]</span>apply to the interleaved vector, not the
- individual vectors before interleave. <span
- class="cmtt-12">[residue_partition_size] </span>is as explained above,
- <span
- class="cmtt-12">[residue_classifications] </span>is the number of possible classification to which a partition can
- belong and <span
- class="cmtt-12">[residue_classbook] </span>is the codebook number used to code classification
- codewords. The number of dimensions in book <span
- class="cmtt-12">[residue_classbook] </span>determines how
- many classification values are grouped into a single classification codeword. Note that
- the number of entries and dimensions in book <span
- class="cmtt-12">[residue_classbook]</span>, along with
- <span
- class="cmtt-12">[residue_classifications]</span>, overdetermines to possible number of classification
- codewords. If <span
- class="cmtt-12">[residue_classifications]</span>ˆ<span
- class="cmtt-12">[residue_classbook]</span>.dimensions exceeds
- <span
- class="cmtt-12">[residue_classbook]</span>.entries, the bitstream should be regarded to be undecodable.
- <!--l. 190--><p class="noindent" >Next we read a bitmap pattern that specifies which partition classes code values in which
- passes.
- <!--l. 193--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb36">
- <a
- id="x1-109012r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [residue\_classifications]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-109014r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109016r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [high\_bits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-109018r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [low\_bits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 3</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-109020r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [bitflag]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> one</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> boolean</span>
- <br class="fancyvrb" /><a
- id="x1-109022r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [bitflag]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> [high\_bits]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> five</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-109024r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [residue\_cascade]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [high\_bits]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [low\_bits]</span>
- <br class="fancyvrb" /><a
- id="x1-109026r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-109028r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 205--><p class="noindent" >Finally, we read in a list of book numbers, each corresponding to specific bit set in the cascade
- bitmap. We loop over the possible codebook classifications and the maximum possible number of
- encoding stages (8 in Vorbis I, as constrained by the elements of the cascade bitmap being eight
- bits):
- <!--l. 211--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb37">
- <a
- id="x1-109030r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [residue\_classifications]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-109032r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109034r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-109036r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109038r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [residue\_cascade]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> set</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-109040r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109042r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [residue\_books]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i][j]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> 8</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> as</span><span
- class="cmtt-8"> unsigned</span><span
- class="cmtt-8"> integer</span>
- <br class="fancyvrb" /><a
- id="x1-109044r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109046r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> {</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-109048r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109050r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [residue\_books]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i][j]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> unused</span>
- <br class="fancyvrb" /><a
- id="x1-109052r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109054r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-109056r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-109058r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-109060r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-109062r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 231--><p class="noindent" >An end-of-packet condition at any point in header decode renders the stream undecodable.
- In addition, any codebook number greater than the maximum numbered codebook
- set up in this stream also renders the stream undecodable. All codebooks in array
- [residue_books] are required to have a value mapping. The presence of codebook in array
- [residue_books] without a value mapping (maptype equals zero) renders the stream
- undecodable.
- <!--l. 241--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">8.6.2. </span> <a
- id="x1-1100008.6.2"></a>packet decode</h5>
- <!--l. 243--><p class="noindent" >Format 0 and 1 packet decode is identical except for specific partition interleave. Format 2 packet
- decode can be built out of the format 1 decode process. Thus we describe first the decode
- infrastructure identical to all three formats.
- <!--l. 248--><p class="noindent" >In addition to configuration information, the residue decode process is passed the number of
- vectors in the submap bundle and a vector of flags indicating if any of the vectors are not to be
- decoded. If the passed in number of vectors is 3 and vector number 1 is marked ’do not decode’,
- decode skips vector 1 during the decode loop. However, even ’do not decode’ vectors are
- allocated and zeroed.
- <!--l. 255--><p class="noindent" >Depending on the values of <span
- class="cmtt-12">[residue_begin] </span>and <span
- class="cmtt-12">[residue_end]</span>, it is obvious that the
- encoded portion of a residue vector may be the entire possible residue vector or some other strict
- subset of the actual residue vector size with zero padding at either uncoded end. However, it is
- also possible to set <span
- class="cmtt-12">[residue_begin] </span>and <span
- class="cmtt-12">[residue_end] </span>to specify a range partially or wholly
- beyond the maximum vector size. Before beginning residue decode, limit <span
- class="cmtt-12">[residue_begin]</span>
- and <span
- class="cmtt-12">[residue_end] </span>to the maximum possible vector size as follows. We assume that
- the number of vectors being encoded, <span
- class="cmtt-12">[ch] </span>is provided by the higher level decoding
- process.
- <!--l. 269--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb38">
- <a
- id="x1-110002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [actual\_size]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> current</span><span
- class="cmtt-8"> blocksize/2;</span>
- <br class="fancyvrb" /><a
- id="x1-110004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> residue</span><span
- class="cmtt-8"> encoding</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> format</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-110006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [actual\_size]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [actual\_size]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [ch];</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-110008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [limit\_residue\_begin]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> maximum</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> ([residue\_begin],[actual\_size]);</span>
- <br class="fancyvrb" /><a
- id="x1-110010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [limit\_residue\_end]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> maximum</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> ([residue\_end],[actual\_size]);</span>
- </div>
- <!--l. 277--><p class="noindent" >The following convenience values are conceptually useful to clarifying the decode process:
- <!--l. 280--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb39">
- <a
- id="x1-110012r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [classwords\_per\_codeword]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [codebook\_dimensions]</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> [residue\_classbook]</span>
- <br class="fancyvrb" /><a
- id="x1-110014r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [n\_to\_read]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [limit\_residue\_end]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [limit\_residue\_begin]</span>
- <br class="fancyvrb" /><a
- id="x1-110016r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [partitions\_to\_read]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [n\_to\_read]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> [residue\_partition\_size]</span>
- </div>
- <!--l. 286--><p class="noindent" >Packet decode proceeds as follows, matching the description offered earlier in the document.
- <div class="fancyvrb" id="fancyvrb40">
- <a
- id="x1-110018r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> allocate</span><span
- class="cmtt-8"> and</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> all</span><span
- class="cmtt-8"> vectors</span><span
- class="cmtt-8"> that</span><span
- class="cmtt-8"> will</span><span
- class="cmtt-8"> be</span><span
- class="cmtt-8"> returned.</span>
- <br class="fancyvrb" /><a
- id="x1-110020r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> ([n\_to\_read]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> zero),</span><span
- class="cmtt-8"> stop;</span><span
- class="cmtt-8"> there</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> no</span><span
- class="cmtt-8"> residue</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> decode.</span>
- <br class="fancyvrb" /><a
- id="x1-110022r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [pass]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> 7</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110024r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110026r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [partition\_count]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-110028r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110030r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> while</span><span
- class="cmtt-8"> [partition\_count]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [partitions\_to\_read]</span>
- <br class="fancyvrb" /><a
- id="x1-110032r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110034r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> ([pass]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> zero)</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110036r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110038r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ..</span><span
- class="cmtt-8"> [ch]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110040r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110042r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> marked</span><span
- class="cmtt-8"> ’do</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> decode’</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110044r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110046r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [temp]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> [residue\_classbook]</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> scalar</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-110048r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> descending</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> [classwords\_per\_codeword]-1</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110050r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110052r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [classifications]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [j],([i]+[partition\_count])</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-110054r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [temp]</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> modulo</span><span
- class="cmtt-8"> [residue\_classifications]</span>
- <br class="fancyvrb" /><a
- id="x1-110056r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> [temp]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [temp]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> [residue\_classifications]</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> division</span>
- <br class="fancyvrb" /><a
- id="x1-110058r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110060r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110062r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110064r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110066r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110068r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110070r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110072r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110074r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110076r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ..</span><span
- class="cmtt-8"> ([classwords\_per\_codeword]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> while</span><span
- class="cmtt-8"> [partition\_count]</span>
- <br class="fancyvrb" /><a
- id="x1-110078r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> also</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [partitions\_to\_read]</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110080r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110082r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ..</span><span
- class="cmtt-8"> [ch]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110084r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110086r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> marked</span><span
- class="cmtt-8"> ’do</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> decode’</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110088r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110090r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> [vqclass]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [classifications]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [j],[partition\_count]</span>
- <br class="fancyvrb" /><a
- id="x1-110092r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 17)</span><span
- class="cmtt-8"> [vqbook]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> array</span><span
- class="cmtt-8"> [residue\_books]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [vqclass],[pass]</span>
- <br class="fancyvrb" /><a
- id="x1-110094r39"></a><span
- class="cmr-6">39</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 18)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> ([vqbook]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> not</span><span
- class="cmtt-8"> ’unused’)</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-110096r40"></a><span
- class="cmr-6">40</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110098r41"></a><span
- class="cmr-6">41</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 19)</span><span
- class="cmtt-8"> decode</span><span
- class="cmtt-8"> partition</span><span
- class="cmtt-8"> into</span><span
- class="cmtt-8"> output</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [j],</span><span
- class="cmtt-8"> starting</span><span
- class="cmtt-8"> at</span><span
- class="cmtt-8"> scalar</span>
- <br class="fancyvrb" /><a
- id="x1-110100r42"></a><span
- class="cmr-6">42</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> offset</span><span
- class="cmtt-8"> [limit\_residue\_begin]+[partition\_count]*[residue\_partition\_size]</span><span
- class="cmtt-8"> using</span>
- <br class="fancyvrb" /><a
- id="x1-110102r43"></a><span
- class="cmr-6">43</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [vqbook]</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> VQ</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-110104r44"></a><span
- class="cmr-6">44</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-110106r45"></a><span
- class="cmr-6">45</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110108r46"></a><span
- class="cmr-6">46</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110110r47"></a><span
- class="cmr-6">47</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 20)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [partition\_count]</span><span
- class="cmtt-8"> by</span><span
- class="cmtt-8"> one</span>
- <br class="fancyvrb" /><a
- id="x1-110112r48"></a><span
- class="cmr-6">48</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110114r49"></a><span
- class="cmr-6">49</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110116r50"></a><span
- class="cmr-6">50</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110118r51"></a><span
- class="cmr-6">51</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-110120r52"></a><span
- class="cmr-6">52</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-110122r53"></a><span
- class="cmr-6">53</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 21)</span><span
- class="cmtt-8"> done</span>
- <br class="fancyvrb" /><a
- id="x1-110124r54"></a><span
- class="cmr-6">54</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- </div>
- <!--l. 344--><p class="noindent" >An end-of-packet condition during packet decode is to be considered a nominal occurrence.
- Decode returns the result of vector decode up to that point.
- <!--l. 350--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">8.6.3. </span> <a
- id="x1-1110008.6.3"></a>format 0 specifics</h5>
- <!--l. 352--><p class="noindent" >Format zero decodes partitions exactly as described earlier in the ’Residue Format: residue 0’
- section. The following pseudocode presents the same algorithm. Assume:
- <ul class="itemize1">
- <li class="itemize"><span
- class="cmtt-12">[n] </span>is the value in <span
- class="cmtt-12">[residue_partition_size]</span>
- </li>
- <li class="itemize"><span
- class="cmtt-12">[v] </span>is the residue vector
- </li>
- <li class="itemize"><span
- class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
- <!--l. 363--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb41">
- <a
- id="x1-111002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [step]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [n]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> [codebook\_dimensions]</span>
- <br class="fancyvrb" /><a
- id="x1-111004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [step]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-111006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-111008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [entry\_temp]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> current</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> VQ</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-111010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [codebook\_dimensions]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-111012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-111014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-111016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([offset]+[i]+[j]*[step])</span><span
- class="cmtt-8"> +</span>
- <br class="fancyvrb" /><a
- id="x1-111018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [entry\_temp]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [j]</span>
- <br class="fancyvrb" /><a
- id="x1-111020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-111022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-111024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-111026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-111028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-111030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> done</span>
- <br class="fancyvrb" /><a
- id="x1-111032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
-
-
- </div>
- <!--l. 384--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">8.6.4. </span> <a
- id="x1-1120008.6.4"></a>format 1 specifics</h5>
- <!--l. 386--><p class="noindent" >Format 1 decodes partitions exactly as described earlier in the ’Residue Format: residue 1’
- section. The following pseudocode presents the same algorithm. Assume:
- <ul class="itemize1">
- <li class="itemize"><span
- class="cmtt-12">[n] </span>is the value in <span
- class="cmtt-12">[residue_partition_size]</span>
- </li>
- <li class="itemize"><span
- class="cmtt-12">[v] </span>is the residue vector
- </li>
- <li class="itemize"><span
- class="cmtt-12">[offset] </span>is the beginning read offset in [v]</li></ul>
- <!--l. 398--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb42">
- <a
- id="x1-112002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-112004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [entry\_temp]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> read</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> from</span><span
- class="cmtt-8"> packet</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> current</span><span
- class="cmtt-8"> codebook</span><span
- class="cmtt-8"> in</span><span
- class="cmtt-8"> VQ</span><span
- class="cmtt-8"> context</span>
- <br class="fancyvrb" /><a
- id="x1-112006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [codebook\_dimensions]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-112008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-112010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([offset]+[i])</span><span
- class="cmtt-8"> =</span>
- <br class="fancyvrb" /><a
- id="x1-112012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8">  </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([offset]+[i])</span><span
- class="cmtt-8"> +</span>
- <br class="fancyvrb" /><a
- id="x1-112014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [entry\_temp]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [j]</span>
- <br class="fancyvrb" /><a
- id="x1-112016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [i]</span>
- <br class="fancyvrb" /><a
- id="x1-112018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-112020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-112022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-112024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> [n]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> continue</span><span
- class="cmtt-8"> at</span><span
- class="cmtt-8"> step</span><span
- class="cmtt-8"> 2</span>
- <br class="fancyvrb" /><a
- id="x1-112026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 416--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">8.6.5. </span> <a
- id="x1-1130008.6.5"></a>format 2 specifics</h5>
- <!--l. 418--><p class="noindent" >Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an
- additional post-decode step after a normal format 1 decode.
-
-
- <!--l. 421--><p class="noindent" >Format 2 handles ’do not decode’ vectors differently than residue 0 or 1; if all vectors are marked
- ’do not decode’, no decode occurrs. However, if at least one vector is to be decoded, all
- the vectors are decoded. We then request normal format 1 to decode a single vector
- representing all output channels, rather than a vector for each channel. After decode,
- deinterleave the vector into independent vectors, one for each output channel. That
- is:
- <!--l. 429--><p class="noindent" >
- <dl class="enumerate-enumitem"><dt class="enumerate-enumitem">
- 1. </dt><dd
- class="enumerate-enumitem">If all vectors 0 through <span
- class="cmti-12">ch</span>-1 are marked ’do not decode’, allocate and clear a single
- vector <span
- class="cmtt-12">[v]</span>of length <span
- class="cmti-12">ch*n </span>and skip step 2 below; proceed directly to the post-decode
- step.
- </dd><dt class="enumerate-enumitem">
- 2. </dt><dd
- class="enumerate-enumitem">Rather than performing format 1 decode to produce <span
- class="cmti-12">ch </span>vectors of length <span
- class="cmti-12">n </span>each, call
- format 1 decode to produce a single vector <span
- class="cmtt-12">[v] </span>of length <span
- class="cmti-12">ch*n</span>.
- </dd><dt class="enumerate-enumitem">
- 3. </dt><dd
- class="enumerate-enumitem">Post decode: Deinterleave the single vector <span
- class="cmtt-12">[v] </span>returned by format 1 decode as
- described above into <span
- class="cmti-12">ch </span>independent vectors, one for each outputchannel, according
- to:
- <div class="fancyvrb" id="fancyvrb43">
- <a
- id="x1-113005r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [n]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-113007r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-113009r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [ch]-1</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-113011r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-113013r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> output</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> number</span><span
- class="cmtt-8"> [j]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [i]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> ([i]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [ch]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [j])</span>
- <br class="fancyvrb" /><a
- id="x1-113015r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-113017r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-113019r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-113021r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-113023r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> done</span>
- </div>
- </dd></dl>
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">9. </span> <a
- id="x1-1140009"></a>Helper equations</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">9.1. </span> <a
- id="x1-1150009.1"></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="x1-1160009.2"></a>Functions</h4>
- <!--l. 15--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.1. </span> <a
- id="x1-1170009.2.1"></a>ilog</h5>
- <!--l. 17--><p class="noindent" >The ”ilog(x)” function returns the position number (1 through n) of the highest set bit in the
- two’s complement integer value <span
- class="cmtt-12">[x]</span>. Values of <span
- class="cmtt-12">[x] </span>less than zero are defined to return
- zero.
- <!--l. 20--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb44">
- <a
- id="x1-117002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [return\_value]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0;</span>
- <br class="fancyvrb" /><a
- id="x1-117004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> greater</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-117006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-117008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> increment</span><span
- class="cmtt-8"> [return\_value];</span>
- <br class="fancyvrb" /><a
- id="x1-117010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> logical</span><span
- class="cmtt-8"> shift</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> one</span><span
- class="cmtt-8"> bit</span><span
- class="cmtt-8"> to</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> right,</span><span
- class="cmtt-8"> padding</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> MSb</span><span
- class="cmtt-8"> with</span><span
- class="cmtt-8"> zero</span>
- <br class="fancyvrb" /><a
- id="x1-117012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> repeat</span><span
- class="cmtt-8"> at</span><span
- class="cmtt-8"> step</span><span
- class="cmtt-8"> 2)</span>
- <br class="fancyvrb" /><a
- id="x1-117014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-117016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-117018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-117020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> done</span>
- </div>
-
-
- <!--l. 33--><p class="noindent" >Examples:
- <ul class="itemize1">
- <li class="itemize">ilog(0) = 0;
- </li>
- <li class="itemize">ilog(1) = 1;
- </li>
- <li class="itemize">ilog(2) = 2;
- </li>
- <li class="itemize">ilog(3) = 2;
- </li>
- <li class="itemize">ilog(4) = 3;
- </li>
- <li class="itemize">ilog(7) = 3;
- </li>
- <li class="itemize">ilog(negative number) = 0;</li></ul>
- <!--l. 48--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.2. </span> <a
- id="x1-1180009.2.2"></a>float32_unpack</h5>
- <!--l. 50--><p class="noindent" >”float32_unpack(x)” is intended to translate the packed binary representation of a Vorbis
- codebook float value into the representation used by the decoder for floating point numbers. For
- purposes of this example, we will unpack a Vorbis float32 into a host-native floating point
- number.
- <!--l. 56--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb45">
- <a
- id="x1-118002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> [mantissa]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> bitwise</span><span
- class="cmtt-8"> AND</span><span
- class="cmtt-8"> 0x1fffff</span><span
- class="cmtt-8"> (unsigned</span><span
- class="cmtt-8"> result)</span>
- <br class="fancyvrb" /><a
- id="x1-118004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [sign]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> bitwise</span><span
- class="cmtt-8"> AND</span><span
- class="cmtt-8"> 0x80000000</span><span
- class="cmtt-8"> (unsigned</span><span
- class="cmtt-8"> result)</span>
- <br class="fancyvrb" /><a
- id="x1-118006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [exponent]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> bitwise</span><span
- class="cmtt-8"> AND</span><span
- class="cmtt-8"> 0x7fe00000)</span><span
- class="cmtt-8"> shifted</span><span
- class="cmtt-8"> right</span><span
- class="cmtt-8"> 21</span><span
- class="cmtt-8"> bits</span><span
- class="cmtt-8"> (unsigned</span><span
- class="cmtt-8"> result)</span>
- <br class="fancyvrb" /><a
- id="x1-118008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [sign]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> nonzero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> then</span><span
- class="cmtt-8"> negate</span><span
- class="cmtt-8"> [mantissa]</span>
- <br class="fancyvrb" /><a
- id="x1-118010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> return</span><span
- class="cmtt-8"> [mantissa]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> 2</span><span
- class="cmtt-8"> ^</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [exponent]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> 788</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> )</span>
- </div>
-
-
- <!--l. 66--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.3. </span> <a
- id="x1-1190009.2.3"></a>lookup1_values</h5>
- <!--l. 68--><p class="noindent" >”lookup1_values(codebook_entries,codebook_dimensions)” is used to compute the
- correct length of the value index for a codebook VQ lookup table of lookup type 1.
- The values on this list are permuted to construct the VQ vector lookup table of size
- <span
- class="cmtt-12">[codebook_entries]</span>.
- <!--l. 74--><p class="noindent" >The return value for this function is defined to be ’the greatest integer value for which
- <span
- class="cmtt-12">[return_value] </span>to the power of <span
- class="cmtt-12">[codebook_dimensions] </span>is less than or equal to
- <span
- class="cmtt-12">[codebook_entries]</span>’.
- <!--l. 81--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.4. </span> <a
- id="x1-1200009.2.4"></a>low_neighbor</h5>
- <!--l. 83--><p class="noindent" >”low_neighbor(v,x)” finds the position <span
- class="cmtt-12">n </span>in vector <span
- class="cmtt-12">[v] </span>of the greatest value scalar element for
- which <span
- class="cmtt-12">n </span>is less than <span
- class="cmtt-12">[x] </span>and vector <span
- class="cmtt-12">[v] </span>element <span
- class="cmtt-12">n </span>is less than vector <span
- class="cmtt-12">[v] </span>element
- <span
- class="cmtt-12">[x]</span>.
- <!--l. 88--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.5. </span> <a
- id="x1-1210009.2.5"></a>high_neighbor</h5>
- <!--l. 90--><p class="noindent" >”high_neighbor(v,x)” finds the position <span
- class="cmtt-12">n </span>in vector [v] of the lowest value scalar element for
- which <span
- class="cmtt-12">n </span>is less than <span
- class="cmtt-12">[x] </span>and vector <span
- class="cmtt-12">[v] </span>element <span
- class="cmtt-12">n </span>is greater than vector <span
- class="cmtt-12">[v] </span>element
- <span
- class="cmtt-12">[x]</span>.
- <!--l. 97--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.6. </span> <a
- id="x1-1220009.2.6"></a>render_point</h5>
- <!--l. 99--><p class="noindent" >”render_point(x0,y0,x1,y1,X)” is used to find the Y value at point X along the line specified by
- x0, x1, y0 and y1. This function uses an integer algorithm to solve for the point directly without
- calculating intervening values along the line.
-
-
- <!--l. 104--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb46">
- <a
- id="x1-122002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [dy]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y1]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [y0]</span>
- <br class="fancyvrb" /><a
- id="x1-122004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> [adx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [x1]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [x0]</span>
- <br class="fancyvrb" /><a
- id="x1-122006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> [ady]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> absolute</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [dy]</span>
- <br class="fancyvrb" /><a
- id="x1-122008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [ady]</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> ([X]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [x0])</span>
- <br class="fancyvrb" /><a
- id="x1-122010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> [off]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> [adx]</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> division</span>
- <br class="fancyvrb" /><a
- id="x1-122012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [dy]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> zero</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-122014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-122016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> [Y]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y0]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [off]</span>
- <br class="fancyvrb" /><a
- id="x1-122018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-122020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-122022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-122024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> [Y]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y0]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [off]</span>
- <br class="fancyvrb" /><a
- id="x1-122026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-122028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-122030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-122032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> done</span>
- </div>
- <!--l. 125--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">9.2.7. </span> <a
- id="x1-1230009.2.7"></a>render_line</h5>
- <!--l. 127--><p class="noindent" >Floor decode type one uses the integer line drawing algorithm of ”render_line(x0, y0, x1, y1, v)”
- to construct an integer floor curve for contiguous piecewise line segments. Note that it has not
- been relevant elsewhere, but here we must define integer division as rounding division of both
- positive and negative numbers toward zero.
- <!--l. 134--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb47">
- <a
- id="x1-123002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [dy]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y1]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [y0]</span>
- <br class="fancyvrb" /><a
- id="x1-123004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [adx]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [x1]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [x0]</span>
- <br class="fancyvrb" /><a
- id="x1-123006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [ady]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> absolute</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [dy]</span>
- <br class="fancyvrb" /><a
- id="x1-123008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4)</span><span
- class="cmtt-8"> [base]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [dy]</span><span
- class="cmtt-8"> /</span><span
- class="cmtt-8"> [adx]</span><span
- class="cmtt-8"> using</span><span
- class="cmtt-8"> integer</span><span
- class="cmtt-8"> division</span>
- <br class="fancyvrb" /><a
- id="x1-123010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [x0]</span>
- <br class="fancyvrb" /><a
- id="x1-123012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [y]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y0]</span>
- <br class="fancyvrb" /><a
- id="x1-123014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> 0</span>
- <br class="fancyvrb" /><a
- id="x1-123016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 8)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [dy]</span><span
- class="cmtt-8"> is</span><span
- class="cmtt-8"> less</span><span
- class="cmtt-8"> than</span><span
- class="cmtt-8"> 0</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-123020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9)</span><span
- class="cmtt-8"> [sy]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [base]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-123024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-123028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 10)</span><span
- class="cmtt-8"> [sy]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [base]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> 1</span>
- <br class="fancyvrb" /><a
- id="x1-123032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123034r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-123036r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123038r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 11)</span><span
- class="cmtt-8"> [ady]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [ady]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> (absolute</span><span
- class="cmtt-8"> value</span><span
- class="cmtt-8"> of</span><span
- class="cmtt-8"> [base])</span><span
- class="cmtt-8"> *</span><span
- class="cmtt-8"> [adx]</span>
- <br class="fancyvrb" /><a
- id="x1-123040r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 12)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y]</span>
- <br class="fancyvrb" /><a
- id="x1-123042r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123044r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 13)</span><span
- class="cmtt-8"> iterate</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> over</span><span
- class="cmtt-8"> the</span><span
- class="cmtt-8"> range</span><span
- class="cmtt-8"> [x0]+1</span><span
- class="cmtt-8"> ...</span><span
- class="cmtt-8"> [x1]-1</span><span
- class="cmtt-8"> {</span>
-
-
- <br class="fancyvrb" /><a
- id="x1-123046r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123048r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 14)</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [ady];</span>
- <br class="fancyvrb" /><a
- id="x1-123050r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 15)</span><span
- class="cmtt-8"> if</span><span
- class="cmtt-8"> (</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> >=</span><span
- class="cmtt-8"> [adx]</span><span
- class="cmtt-8"> )</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-123052r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123054r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 16)</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [err]</span><span
- class="cmtt-8"> -</span><span
- class="cmtt-8"> [adx]</span>
- <br class="fancyvrb" /><a
- id="x1-123056r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 17)</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> [y]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [sy]</span>
- <br class="fancyvrb" /><a
- id="x1-123058r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123060r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span><span
- class="cmtt-8"> else</span><span
- class="cmtt-8"> {</span>
- <br class="fancyvrb" /><a
- id="x1-123062r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123064r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 18)</span><span
- class="cmtt-8"> [y]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y]</span><span
- class="cmtt-8"> +</span><span
- class="cmtt-8"> [base]</span>
- <br class="fancyvrb" /><a
- id="x1-123066r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123068r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- <br class="fancyvrb" /><a
- id="x1-123070r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123072r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 19)</span><span
- class="cmtt-8"> vector</span><span
- class="cmtt-8"> [v]</span><span
- class="cmtt-8"> element</span><span
- class="cmtt-8"> [x]</span><span
- class="cmtt-8"> =</span><span
- class="cmtt-8"> [y]</span>
- <br class="fancyvrb" /><a
- id="x1-123074r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span>
- <br class="fancyvrb" /><a
- id="x1-123076r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> }</span>
- </div>
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">10. </span> <a
- id="x1-12400010"></a>Tables</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">10.1. </span> <a
- id="x1-12500010.1"></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 consiting of the
- following values (read left to right then top to bottom):
- <!--l. 12--><p class="noindent" >
- <div class="fancyvrb" id="fancyvrb48">
- <a
- id="x1-125002r1"></a><span
- class="cmr-6">1</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.0649863e-07,</span><span
- class="cmtt-8"> 1.1341951e-07,</span><span
- class="cmtt-8"> 1.2079015e-07,</span><span
- class="cmtt-8"> 1.2863978e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125004r2"></a><span
- class="cmr-6">2</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.3699951e-07,</span><span
- class="cmtt-8"> 1.4590251e-07,</span><span
- class="cmtt-8"> 1.5538408e-07,</span><span
- class="cmtt-8"> 1.6548181e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125006r3"></a><span
- class="cmr-6">3</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.7623575e-07,</span><span
- class="cmtt-8"> 1.8768855e-07,</span><span
- class="cmtt-8"> 1.9988561e-07,</span><span
- class="cmtt-8"> 2.1287530e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125008r4"></a><span
- class="cmr-6">4</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.2670913e-07,</span><span
- class="cmtt-8"> 2.4144197e-07,</span><span
- class="cmtt-8"> 2.5713223e-07,</span><span
- class="cmtt-8"> 2.7384213e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125010r5"></a><span
- class="cmr-6">5</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.9163793e-07,</span><span
- class="cmtt-8"> 3.1059021e-07,</span><span
- class="cmtt-8"> 3.3077411e-07,</span><span
- class="cmtt-8"> 3.5226968e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125012r6"></a><span
- class="cmr-6">6</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3.7516214e-07,</span><span
- class="cmtt-8"> 3.9954229e-07,</span><span
- class="cmtt-8"> 4.2550680e-07,</span><span
- class="cmtt-8"> 4.5315863e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125014r7"></a><span
- class="cmr-6">7</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4.8260743e-07,</span><span
- class="cmtt-8"> 5.1396998e-07,</span><span
- class="cmtt-8"> 5.4737065e-07,</span><span
- class="cmtt-8"> 5.8294187e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125016r8"></a><span
- class="cmr-6">8</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 6.2082472e-07,</span><span
- class="cmtt-8"> 6.6116941e-07,</span><span
- class="cmtt-8"> 7.0413592e-07,</span><span
- class="cmtt-8"> 7.4989464e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125018r9"></a><span
- class="cmr-6">9</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7.9862701e-07,</span><span
- class="cmtt-8"> 8.5052630e-07,</span><span
- class="cmtt-8"> 9.0579828e-07,</span><span
- class="cmtt-8"> 9.6466216e-07,</span>
- <br class="fancyvrb" /><a
- id="x1-125020r10"></a><span
- class="cmr-6">10</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.0273513e-06,</span><span
- class="cmtt-8"> 1.0941144e-06,</span><span
- class="cmtt-8"> 1.1652161e-06,</span><span
- class="cmtt-8"> 1.2409384e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125022r11"></a><span
- class="cmr-6">11</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.3215816e-06,</span><span
- class="cmtt-8"> 1.4074654e-06,</span><span
- class="cmtt-8"> 1.4989305e-06,</span><span
- class="cmtt-8"> 1.5963394e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125024r12"></a><span
- class="cmr-6">12</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.7000785e-06,</span><span
- class="cmtt-8"> 1.8105592e-06,</span><span
- class="cmtt-8"> 1.9282195e-06,</span><span
- class="cmtt-8"> 2.0535261e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125026r13"></a><span
- class="cmr-6">13</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.1869758e-06,</span><span
- class="cmtt-8"> 2.3290978e-06,</span><span
- class="cmtt-8"> 2.4804557e-06,</span><span
- class="cmtt-8"> 2.6416497e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125028r14"></a><span
- class="cmr-6">14</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.8133190e-06,</span><span
- class="cmtt-8"> 2.9961443e-06,</span><span
- class="cmtt-8"> 3.1908506e-06,</span><span
- class="cmtt-8"> 3.3982101e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125030r15"></a><span
- class="cmr-6">15</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3.6190449e-06,</span><span
- class="cmtt-8"> 3.8542308e-06,</span><span
- class="cmtt-8"> 4.1047004e-06,</span><span
- class="cmtt-8"> 4.3714470e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125032r16"></a><span
- class="cmr-6">16</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4.6555282e-06,</span><span
- class="cmtt-8"> 4.9580707e-06,</span><span
- class="cmtt-8"> 5.2802740e-06,</span><span
- class="cmtt-8"> 5.6234160e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125034r17"></a><span
- class="cmr-6">17</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5.9888572e-06,</span><span
- class="cmtt-8"> 6.3780469e-06,</span><span
- class="cmtt-8"> 6.7925283e-06,</span><span
- class="cmtt-8"> 7.2339451e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125036r18"></a><span
- class="cmr-6">18</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7.7040476e-06,</span><span
- class="cmtt-8"> 8.2047000e-06,</span><span
- class="cmtt-8"> 8.7378876e-06,</span><span
- class="cmtt-8"> 9.3057248e-06,</span>
- <br class="fancyvrb" /><a
- id="x1-125038r19"></a><span
- class="cmr-6">19</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9.9104632e-06,</span><span
- class="cmtt-8"> 1.0554501e-05,</span><span
- class="cmtt-8"> 1.1240392e-05,</span><span
- class="cmtt-8"> 1.1970856e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125040r20"></a><span
- class="cmr-6">20</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.2748789e-05,</span><span
- class="cmtt-8"> 1.3577278e-05,</span><span
- class="cmtt-8"> 1.4459606e-05,</span><span
- class="cmtt-8"> 1.5399272e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125042r21"></a><span
- class="cmr-6">21</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.6400004e-05,</span><span
- class="cmtt-8"> 1.7465768e-05,</span><span
- class="cmtt-8"> 1.8600792e-05,</span><span
- class="cmtt-8"> 1.9809576e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125044r22"></a><span
- class="cmr-6">22</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.1096914e-05,</span><span
- class="cmtt-8"> 2.2467911e-05,</span><span
- class="cmtt-8"> 2.3928002e-05,</span><span
- class="cmtt-8"> 2.5482978e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125046r23"></a><span
- class="cmr-6">23</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 2.7139006e-05,</span><span
- class="cmtt-8"> 2.8902651e-05,</span><span
- class="cmtt-8"> 3.0780908e-05,</span><span
- class="cmtt-8"> 3.2781225e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125048r24"></a><span
- class="cmr-6">24</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 3.4911534e-05,</span><span
- class="cmtt-8"> 3.7180282e-05,</span><span
- class="cmtt-8"> 3.9596466e-05,</span><span
- class="cmtt-8"> 4.2169667e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125050r25"></a><span
- class="cmr-6">25</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 4.4910090e-05,</span><span
- class="cmtt-8"> 4.7828601e-05,</span><span
- class="cmtt-8"> 5.0936773e-05,</span><span
- class="cmtt-8"> 5.4246931e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125052r26"></a><span
- class="cmr-6">26</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 5.7772202e-05,</span><span
- class="cmtt-8"> 6.1526565e-05,</span><span
- class="cmtt-8"> 6.5524908e-05,</span><span
- class="cmtt-8"> 6.9783085e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125054r27"></a><span
- class="cmr-6">27</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 7.4317983e-05,</span><span
- class="cmtt-8"> 7.9147585e-05,</span><span
- class="cmtt-8"> 8.4291040e-05,</span><span
- class="cmtt-8"> 8.9768747e-05,</span>
- <br class="fancyvrb" /><a
- id="x1-125056r28"></a><span
- class="cmr-6">28</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 9.5602426e-05,</span><span
- class="cmtt-8"> 0.00010181521,</span><span
- class="cmtt-8"> 0.00010843174,</span><span
- class="cmtt-8"> 0.00011547824,</span>
- <br class="fancyvrb" /><a
- id="x1-125058r29"></a><span
- class="cmr-6">29</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00012298267,</span><span
- class="cmtt-8"> 0.00013097477,</span><span
- class="cmtt-8"> 0.00013948625,</span><span
- class="cmtt-8"> 0.00014855085,</span>
- <br class="fancyvrb" /><a
- id="x1-125060r30"></a><span
- class="cmr-6">30</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00015820453,</span><span
- class="cmtt-8"> 0.00016848555,</span><span
- class="cmtt-8"> 0.00017943469,</span><span
- class="cmtt-8"> 0.00019109536,</span>
- <br class="fancyvrb" /><a
- id="x1-125062r31"></a><span
- class="cmr-6">31</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00020351382,</span><span
- class="cmtt-8"> 0.00021673929,</span><span
- class="cmtt-8"> 0.00023082423,</span><span
- class="cmtt-8"> 0.00024582449,</span>
- <br class="fancyvrb" /><a
- id="x1-125064r32"></a><span
- class="cmr-6">32</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00026179955,</span><span
- class="cmtt-8"> 0.00027881276,</span><span
- class="cmtt-8"> 0.00029693158,</span><span
- class="cmtt-8"> 0.00031622787,</span>
- <br class="fancyvrb" /><a
- id="x1-125066r33"></a><span
- class="cmr-6">33</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00033677814,</span><span
- class="cmtt-8"> 0.00035866388,</span><span
- class="cmtt-8"> 0.00038197188,</span><span
- class="cmtt-8"> 0.00040679456,</span>
- <br class="fancyvrb" /><a
- id="x1-125068r34"></a><span
- class="cmr-6">34</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00043323036,</span><span
- class="cmtt-8"> 0.00046138411,</span><span
- class="cmtt-8"> 0.00049136745,</span><span
- class="cmtt-8"> 0.00052329927,</span>
- <br class="fancyvrb" /><a
- id="x1-125070r35"></a><span
- class="cmr-6">35</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00055730621,</span><span
- class="cmtt-8"> 0.00059352311,</span><span
- class="cmtt-8"> 0.00063209358,</span><span
- class="cmtt-8"> 0.00067317058,</span>
- <br class="fancyvrb" /><a
- id="x1-125072r36"></a><span
- class="cmr-6">36</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00071691700,</span><span
- class="cmtt-8"> 0.00076350630,</span><span
- class="cmtt-8"> 0.00081312324,</span><span
- class="cmtt-8"> 0.00086596457,</span>
- <br class="fancyvrb" /><a
- id="x1-125074r37"></a><span
- class="cmr-6">37</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.00092223983,</span><span
- class="cmtt-8"> 0.00098217216,</span><span
- class="cmtt-8"> 0.0010459992,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0011139742,</span>
- <br class="fancyvrb" /><a
- id="x1-125076r38"></a><span
- class="cmr-6">38</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0011863665,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0012634633,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0013455702,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0014330129,</span>
- <br class="fancyvrb" /><a
- id="x1-125078r39"></a><span
- class="cmr-6">39</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0015261382,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0016253153,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0017309374,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0018434235,</span>
- <br class="fancyvrb" /><a
- id="x1-125080r40"></a><span
- class="cmr-6">40</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0019632195,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.0020908006,</span><span
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- class="cmtt-8"> 0.0022266726,</span><span
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- class="cmtt-8"> </span><span
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- class="cmtt-8"> </span><span
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- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.34289114,</span><span
- class="cmtt-8"> </span><span
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- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.44109412,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.46975890,</span>
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- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.50028648,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.53279791,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.56742212,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.60429640,</span>
- <br class="fancyvrb" /><a
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- class="cmtt-8"> </span><span
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- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.68538959,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.72993007,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.77736504,</span>
- <br class="fancyvrb" /><a
- id="x1-125128r64"></a><span
- class="cmr-6">64</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.82788260,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.88168307,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 0.9389798,</span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> </span><span
- class="cmtt-8"> 1.</span>
- </div>
-
-
-
-
- <h3 class="sectionHead"><span class="titlemark">A. </span> <a
- id="x1-126000A"></a>Embedding Vorbis into an Ogg stream</h3>
- <!--l. 6--><p class="noindent" >
- <h4 class="subsectionHead"><span class="titlemark">A.1. </span> <a
- id="x1-127000A.1"></a>Overview</h4>
- <!--l. 8--><p class="noindent" >This document describes using Ogg logical and physical transport streams to encapsulate Vorbis
- compressed audio packet data into file form.
- <!--l. 12--><p class="noindent" >The <a
- href="#x1-20001">Section 1</a>, “<a
- href="#x1-20001">Introduction and Description<!--tex4ht:ref: vorbis:spec:intro --></a>” provides an overview of the construction of
- Vorbis audio packets.
- <!--l. 15--><p class="noindent" >The <a
- href="oggstream.html" >Ogg bitstream overview</a> and <a
- href="framing.html" >Ogg logical bitstream and framing spec</a> provide detailed
- descriptions of Ogg transport streams. This specification document assumes a working
- knowledge of the concepts covered in these named backround documents. Please read them
- first.
- <!--l. 22--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">A.1.1. </span> <a
- id="x1-128000A.1.1"></a>Restrictions</h5>
- <!--l. 24--><p class="noindent" >The Ogg/Vorbis I specification currently dictates that Ogg/Vorbis streams use Ogg transport
- streams in degenerate, unmultiplexed form only. That is:
- <ul class="itemize1">
- <li class="itemize">A meta-headerless Ogg file encapsulates the Vorbis I packets
- </li>
- <li class="itemize">The Ogg stream may be chained, i.e., contain multiple, contigous logical streams
- (links).
- </li>
- <li class="itemize">The Ogg stream must be unmultiplexed (only one stream, a Vorbis audio stream,
- per link)
- </li></ul>
-
-
- <!--l. 41--><p class="noindent" >This is not to say that it is not currently possible to multiplex Vorbis with other media
- types into a multi-stream Ogg file. At the time this document was written, Ogg was
- becoming a popular container for low-bitrate movies consisting of DivX video and Vorbis
- audio. However, a ’Vorbis I audio file’ is taken to imply Vorbis audio existing alone
- within a degenerate Ogg stream. A compliant ’Vorbis audio player’ is not required to
- implement Ogg support beyond the specific support of Vorbis within a degenrate Ogg
- stream (naturally, application authors are encouraged to support full multiplexed Ogg
- handling).
- <!--l. 55--><p class="noindent" >
- <h5 class="subsubsectionHead"><span class="titlemark">A.1.2. </span> <a
- id="x1-129000A.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="x1-130000A.2"></a>Encapsulation</h4>
- <!--l. 67--><p class="noindent" >Ogg encapsulation of a Vorbis packet stream is straightforward.
- <ul class="itemize1">
- <li class="itemize">The first Vorbis packet (the identification header), which uniquely identifies a stream
- as Vorbis audio, is placed alone in the first page of the logical Ogg stream. This
- results in a first Ogg page of exactly 58 bytes at the very beginning of the logical
- stream.
- </li>
- <li class="itemize">This first page is marked ’beginning of stream’ in the page flags.
- </li>
- <li class="itemize">The second and third vorbis packets (comment and setup headers) may span one or
- more pages beginning on the second page of the logical stream. However many pages
- they span, the third header packet finishes the page on which it ends. The next (first
- audio) packet must begin on a fresh page.
-
-
- </li>
- <li class="itemize">The granule position of these first pages containing only headers is zero.
- </li>
- <li class="itemize">The first audio packet of the logical stream begins a fresh Ogg page.
- </li>
- <li class="itemize">Packets are placed into ogg pages in order until the end of stream.
- </li>
- <li class="itemize">The last page is marked ’end of stream’ in the page flags.
- </li>
- <li class="itemize">Vorbis packets may span page boundaries.
- </li>
- <li class="itemize">The granule position of pages containing Vorbis audio is in units of PCM audio
- samples (per channel; a stereo stream’s granule position does not increment at twice
- the speed of a mono stream).
- </li>
- <li class="itemize">The granule position of a page represents the end PCM sample position of the last
- packet <span
- class="cmti-12">completed </span>on that page. The ’last PCM sample’ is the last complete sample
- returned by decode, not an internal sample awaiting lapping with a subsequent block.
- A page that is entirely spanned by a single packet (that completes on a subsequent
- page) has no granule position, and the granule position is set to ’-1’.
- <!--l. 126--><p class="noindent" >Note that the last decoded (fully lapped) PCM sample from a packet is not
- necessarily the middle sample from that block. If, eg, the current Vorbis packet
- encodes a ”long block” and the next Vorbis packet encodes a ”short block”, the last
- decodable sample from the current packet be at position (3*long_block_length/4) -
- (short_block_length/4).
- </li>
- <li class="itemize">The granule (PCM) position of the first page need not indicate that the stream
- started at position zero. Although the granule position belongs to the last completed
- packet on the page and a valid granule position must be positive, by inference it may
- indicate that the PCM position of the beginning of audio is positive or negative.
- <ul class="itemize2">
- <li class="itemize">A positive starting value simply indicates that this stream begins at some
- positive time offset, potentially within a larger program. This is a common case
- when connecting to the middle of broadcast stream.
- </li>
- <li class="itemize">A negative value indicates that output samples preceeding time zero should be
-
-
- discarded during decoding; this technique is used to allow sample-granularity
- editing of the stream start time of already-encoded Vorbis streams. The number
- of samples to be discarded must not exceed the overlap-add span of the first two
- audio packets.
- </li></ul>
- <!--l. 161--><p class="noindent" >In both of these cases in which the initial audio PCM starting offset is nonzero, the
- second finished audio packet must flush the page on which it appears and the
- third packet begin a fresh page. This allows the decoder to always be able to
- perform PCM position adjustments before needing to return any PCM data from
- synthesis, resulting in correct positioning information without any aditional seeking
- logic.
- <!--l. 170--><p class="noindent" ><span class="likesubparagraphHead"><a
- id="x1-131000A.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="x1-132000B"></a>Vorbis encapsulation in RTP</h3>
- <!--l. 8--><p class="noindent" >Please consult RFC 5215 <span
- class="cmti-12">“RTP Payload Format for Vorbis Encoded Audio” </span>for description of
- how to embed Vorbis audio in an RTP stream.
-
-
-
-
- <h3 class="likesectionHead"><a
- id="x1-133000B"></a>Colophon</h3>
- <!--l. 6--><p class="noindent" ><img
- src="Vorbis_I_spec13x.png" alt="PIC" class="graphics"><!--tex4ht:graphics
- name="Vorbis_I_spec13x.png" src="xifish.pdf"
- -->
- <!--l. 10--><p class="noindent" >Ogg is a <a
- href="http://www.xiph.org/" >Xiph.Org Foundation</a> effort to protect essential tenets of Internet multimedia from
- corporate hostage-taking; Open Source is the net’s greatest tool to keep everyone honest. See
- <a
- href="http://www.xiph.org/about.html" >About the Xiph.Org Foundation</a> for details.
- <!--l. 17--><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. 23--><p class="noindent" >Xiph.Org’s Vorbis software CODEC implementation is distributed under a BSD-like license. This
- does not restrict third parties from distributing independent implementations of Vorbis software
- under other licenses.
- <!--l. 28--><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) 1994-2007 Xiph.Org Foundation. All rights
- reserved.
- <!--l. 33--><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="x1-134000B"></a>References</h3>
- <!--l. 125--><p class="noindent" >
- <div class="thebibliography">
- <p class="bibitem" ><span class="biblabel">
- [1]<span class="bibsp">   </span></span><a
- id="XSporer/Brandenburg/Edler"></a>T. Sporer, K. Brandenburg and
- B. Edler, The use of multirate filter banks for coding of high quality digital audio,
- <a
- href="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps" class="url" ><span
- class="cmtt-12">http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps</span></a>.
- </p>
- </div>
-
- </body></html>
-
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