[xiph-cvs] r6730 - trunk/theora/doc/spec
tterribe at xiph.org
tterribe at xiph.org
Wed May 19 20:31:00 PDT 2004
Author: tterribe
Date: 2004-05-19 23:30:56 -0400 (Wed, 19 May 2004)
New Revision: 6730
Modified:
trunk/theora/doc/spec/spec.tex
Log:
Clarified some wording and finished the MB modes section.
<p>Modified: trunk/theora/doc/spec/spec.tex
===================================================================
--- trunk/theora/doc/spec/spec.tex 2004-05-20 02:33:38 UTC (rev 6729)
+++ trunk/theora/doc/spec/spec.tex 2004-05-20 03:30:56 UTC (rev 6730)
@@ -1,3788 +1,3796 @@
-\documentclass[11pt,letterpaper]{book}
-
-\usepackage{latexsym}
-\usepackage{amssymb}
-\usepackage{amsmath}
-\usepackage{bm}
-\usepackage{textcomp}
-\usepackage{graphicx}
-\usepackage{booktabs}
-\usepackage{tabularx}
-\usepackage{longtable}
-\usepackage{ltablex}
-\usepackage{wrapfig}
-\usepackage[pdfpagemode=None,pdfstartview=FitH,pdfview=FitH,colorlinks=true]%
- {hyperref}
-
-\newtheorem{theorem}{Theorem}[section]
-\newcommand{\idx}[1]{{\ensuremath{\mathit{#1}}}}
-\newcommand{\qti}{\idx{qti}}
-\newcommand{\qtj}{\idx{qtj}}
-\newcommand{\pli}{\idx{pli}}
-\newcommand{\plj}{\idx{plj}}
-\newcommand{\qi}{\idx{qi}}
-\newcommand{\ci}{\idx{ci}}
-\newcommand{\bmi}{\idx{bmi}}
-\newcommand{\bmj}{\idx{bmj}}
-\newcommand{\qri}{\idx{qri}}
-\newcommand{\qrj}{\idx{qrj}}
-\newcommand{\hti}{\idx{hti}}
-\newcommand{\sbi}{\idx{sbi}}
-\newcommand{\bi}{\idx{bi}}
-\newcommand{\mbi}{\idx{mbi}}
-\newcommand{\mi}{\idx{mi}}
-\newcommand{\ti}{\idx{ti}}
-%This somewhat odd construct ensures that \bitvar{\qi}, etc., will set the
-% qi in bold face, even though it is in a \mathit font, yet \bitvar{VAR} will
-% set VAR in a bold, roman font.
-\newcommand{\bitvar}[1]{\ensuremath{\mathbf{\bm #1}}}
-\newcommand{\locvar}[1]{\ensuremath{\mathrm{#1}}}
-\newcommand{\term}[1]{{\em #1}}
-\newcommand{\bin}[1]{\ensuremath{\mathtt{b#1}}}
-\newcommand{\hex}[1]{\ensuremath{\mathtt{0x#1}}}
-\newcommand{\ilog}{\ensuremath{\mathop{\mathrm{ilog}}\nolimits}}
-
-%Section-based table, figure, and equation numbering.
-\numberwithin{equation}{chapter}
-\numberwithin{figure}{chapter}
-\numberwithin{table}{chapter}
-
-\keepXColumns
-
-\pagestyle{headings}
-\bibliographystyle{alpha}
-
-\title{Theora I Specification}
-\author{Xiph.org Foundation}
-\date{\today}
-
-
-\begin{document}
-
-\frontmatter
-
-\begin{titlepage}
-\maketitle
-\end{titlepage}
-\thispagestyle{empty}
-\cleardoublepage
-
-\pagenumbering{roman}
-
-\thispagestyle{plain}
-\tableofcontents
-\cleardoublepage
-
-\thispagestyle{plain}
-\listoffigures
-\cleardoublepage
-
-\thispagestyle{plain}
-\listoftables
-\cleardoublepage
-
-\thispagestyle{plain}
-\markboth{{\sc Notation and Conventions}}{{\sc Notation and Conventions}}
-\chapter*{Notation and Conventions}
-
-All parameters either passed in or out of a decoding procedure are given in
- \bitvar{bold\ face}.
-
-The prefix \bin{} indicates that the following value is to be interpreted as a
- binary number (base 2).
-\begin{verse}
-{\bf Example:} The value \bin{1110100} is equal to the decimal value 116.
-\end{verse}
-
-The prefix \hex{} indicates the the following value is to be interpreted as a
- hexadecimal number (base 16).
-\begin{verse}
-{\bf Example:} The value \hex{74} is equal to the decimal value 116.
-\end{verse}
-
-The following operators are defined:
-
-\begin{description}
-\item[$|a|$]
-The absolute value of a number $a$.
-\begin{align*}
-|a| & = \left\{\begin{array}{ll}
--a, & a < 0 \\
-a, & a \ge 0
-\end{array}\right.
-\end{align*}
-
-\item[$a*b$]
-Multiplication of a number $a$ by a number $b$.
-\item[$\frac{a}{b}$]
-Exact division of a number $a$ by a number $b$, producing a potentially
- non-integer result.
-
-\item[$\left\lfloor a\right\rfloor$]
-The largest integer less than or equal to a real number $a$.
-
-\item[$\left\lceil a\right\rceil$]
-The smallest integer greater than or equal to a real number $a$.
-
-\item[$a//b$]
-Integer division of $a$ by $b$.
-\begin{align*}
-a//b & = \left\{\begin{array}{ll}
-\left\lceil\frac{a}{b}\right\rceil, & a < 0 \\
-\left\lfloor\frac{a}{b}\right\rfloor, & a \ge 0
-\end{array}\right.
-\end{align*}
-
-\item[$a\%b$]
-The remainder from the integer division of $a$ by $b$.
-\begin{align*}
-a\%b & = |a|-|b|*|a//b|
-\end{align*}
-Note that with this definition, the result is always non-negative and less than
- $|b|$.
-
-\item[$a<<b$]
-The value obtained by left-shifting the two's complement integer $a$ by $b$
- bits.
-For purposes of this specification, overflow is ignored, and so this is
- equivalent to integer multiplication of $a$ by $2^b$.
-
-\item[$a>>b$]
-The value obtained by right-shifting the two's complement integer $a$ by $b$
- bits, filling in the leftmost bits of the new value with $0$ if $a$ is
- non-negative and $1$ if $a$ is negative.
-This is {\em not} equivalent to integer division of $a$ by $2^b$.
-Instead,
-\begin{align*}
-a>>b & = \left\lfloor\frac{a}{2^b}\right\rfloor.
-\end{align*}
-
-\item[$\ilog(a)$]
-The minimum number of bits required to store a positive integer $a$ in
- two's complement notation, or $0$ for a non-positive integer $a$.
-\begin{align*}
-\ilog(a) = \left\{\begin{array}{ll}
-0, & a \le 0 \\
-\left\lceil\log_2{a}\right\rceil, & a > 0
-\end{array}\right.
-\end{align*}
-
-\begin{verse}
-{\bf Examples:}
-\begin{itemize}
-\item $\ilog(-1)=0$
-\item $\ilog(0)=0$
-\item $\ilog(1)=1$
-\item $\ilog(2)=2$
-\item $\ilog(3)=2$
-\item $\ilog(4)=3$
-\item $\ilog(7)=3$
-\end{itemize}
-\end{verse}
-
-\item[$\min(a,b)$]
-The minimum of two numbers $a$ and $b$.
-
-\item[$\max(a,b)$]
-The maximum of two numbers $a$ and $b$.
-
-\end{description}
-\cleardoublepage
-
-
-\thispagestyle{plain}
-\markboth{{\sc Key words}}{{\sc Key words}}
-\chapter*{Key words}
-
-%We can't rewrite this, because this is text required by RFC 2119, so we use
-% some emergency stretching to get it typeset properly.
-\setlength{\emergencystretch}{2em}
-The key words ``MUST'', ``MUST NOT'', ``REQUIRED'', ``SHALL'', ``SHALL NOT'',
- ``SHOULD'', ``SHOULD NOT'', ``RECOMMENDED'', ``MAY'', and ``OPTIONAL'' in this
- document are to be intrepreted as described in RFC 2119 \cite{rfc2119}.\par
-\setlength{\emergencystretch}{0em}
-
-Where such assertions are placed on the contents of a Theora bitstream itself,
- implementations should be prepared to encounter bitstreams that do not follow
- these requirements.
-An application's behavior in the presecence of such non-conforming bitstreams
- is not defined by this specification, but any reasonable method of handling
- them MAY be used.
-By way of example, applications MAY discard the current frame, retain the
- current output thus far, or attempt to continue on by assuming some default
- values for the erroneous bits.
-When such an error occurs in the bitstream headers, an application MAY refuse
- to decode the entire stream.
-An application SHOULD NOT allow such non-conformant bitstreams to overflow
- buffers and potentially execute arbitrary code, as this represents a serious
- security risk.
-
-An application MUST, however, ensure any reserved bits have the value zero, and
- refuse to decode the stream if they are not.
-These are used as place holders for future bitstream features with which the
- current bitstream is forward-compatible.
-%RG: shouldn't this be 'MAY not increment...the version number'?
-Such features will not increment the bitstream version number, and can only be
- recognized by checking the value of these reserved bits.
-
-\cleardoublepage
-
-
-
-\mainmatter
-
-\pagenumbering{arabic}
-\setcounter{page}{1}
-
-\chapter{Introduction}
-
-%[silvia: COMMENTED OUT, should move somewhere else]
-%This section provides a high level description of the Theora codec's
-% construction.
-%A bit-by-bit specification appears beginning in Section~\ref{sec:bitpacking}.
-%The later sections assume a high-level understanding of the Theora decode
-% process, which is provided below.
-%
-%\section{Overview}
-
-Theora is a general purpose, lossy video codec.
-It is based on the VP3 video codec produced by On2 Technologies
- (\url{http://www.on2.com/}).
-On2 donated the VP3.1 source code to the Xiph.org Foundation and released it
- under a BSD-like license.
-On2 also made an irrevocable, royalty-free license grant for any patent claims
- it might have over the software and any derivatives.
-No formal specification exists for the VP3 format beyond this source code,
- however Mike Melanson maintains a detailed description \cite{Mel04}.
-Portions of this specification were adopted from that text with permission.
-
-\section{VP3 and Theora}
-
-Theora contains a superset of the features that were available in the original
- VP3 codec.
-Content encoded with VP3.1 can be losslessly transcoded into the Theora format.
-%TODO: what about VP3.1 etc? source tables all say 'VP31'
-Theora content cannot, in general, be losslessly transcoded into the VP3
- format.
-If a feature is not available in the original VP3 format, this is mentioned
- when that feature is defined.
-A complete list of these features appears in Appendix~REF.
-%TODO: VP3 - theora comparison in appendix
-
-
-\section{Video Formats}
-
-Theora I currently supports progressive video data of arbitrary dimensions at a
- constant frame rate in one of several $Y'C_bC_r$ color spaces.
-The precise definition the supported color spaces appears in
- Section~\ref{sec:colorspaces}.
-Three different chroma subsampling formats are supported: 4:2:0, 4:2:2,
- and 4:4:4.
-The precise details of each of these formats and their sampling locations are
- described in Section~\ref{sec:pixfmts}.
-
-The Theora I format does not support interlaced material, variable frame rates,
- bit-depths larger than 8 bits per component, nor alternate color spaces such
- as RGB or arbitrary multi-channel spaces.
-Black and white content can be efficiently encoded, however, because the
- uniform chroma planes compress well.
-Support for interlaced material is planned for a future version.
-\begin{verse}
-{\bf Note:} Infrequently changing frame rates---as when film and video sequences
- are cut together---can be supported in the Ogg container format by chaining
- several Theora streams together.
-\end{verse}
-Support for increased bit depths or additional color spaces is not planned.
-
-\section{Classification}
-
-Theora I is a block-based lossy transform codec that utilizes an
- $8\times 8$ Type-II Discrete Cosine Transform and block-based motion
- compensation.
-This places it in the same class of codecs as MPEG-1, -2, -4, and H.263.
-The details of how individual blocks are organized and how DCT coefficients are
- organized in the bitstream differ substantially from these codecs, however.
-Theora supports only intra frames (I frames in MPEG) and inter frames (P frames
- in MPEG).
-There is no equivalent to the bi-predictive frames (B frames) found in MPEG
- codecs.
-
-\section{Assumptions}
-
-The Theora codec design assumes a complex, psychovisually-aware encoder and a
- simple, low-complexity decoder.
-%TODO: Talk more about implementation complexity.
-
-Theora provides none of its own framing, synchronization, or protection against
- transmission errors.
-An encoder is solely a method of accepting input video frames and
- compressing these frames into raw, unformatted `packets'.
-The decoder then accepts these raw packets in sequence, decodes them, and
- synthesizes a fascimile of the original video frames.
-Theora is a free-form variable bit rate (VBR) codec, and packets have no
- minimum size, maximum size, or fixed/expected size.
-
-Theora packets are thus intended to be used with a transport mechanism that
- provides free-form framing, synchronization, positioning, and error correction
- in accordance with these design assumptions, such as Ogg (for file transport)
- or RTP (for network multicast).
-For the purposes of a few examples in this document, we will assume that Theora
- is embedded in an Ogg stream specifically, although this is by no means a
- requirement or fundamental assumption in the Theora design.
-
-The specification for embedding Theora into an Ogg transport stream is given in
- Appendix~\ref{app:oggencapsulation}.
-
-\section{Codec Setup and Probability Model}
-
-Theora's heritage is the proprietary commerical codec VP3, and it retains a
- fair amount of inflexibility when compared to Vorbis \cite{vorbis}, the first
- Xiph.org codec, which began as a research codec.
-However, to provide additional scope for encoder improvement, Theora adopts
- some of the configurable aspects of decoder setup that are present in Vorbis.
-This configuration data is not available in VP3, which uses hardcoded values
- instead.
-
-Theora makes the same controversial design decision that Vorbis made to include
- the entire probability model for the DCT coefficients and all the quantization
- parameters in the bitstream headers.
-This is often several hundred fields.
-It is therefore impossible to decode any frame in the stream without
- having previously fetched the codec info and codec setup headers.
-
-\begin{verse}
-{\bf Note:} Theora {\em can} initiate decode at an arbitrary intra-frame packet
- within a bitstream so long as the codec has been initialized with the setup
- headers.
-\end{verse}
-
-Thus, Theora headers are both required for decode to begin and relatively large
- as bitstream headers go.
-The header size is unbounded, although as a rule-of-thumb less than 16kB is
- recommended, and Xiph.org's reference encoder follows this suggestion.
-%TODO: Is 8kB enough? My setup header is 7.4kB, that doesn't leave much room
-% for comments.
-%RG: the lesson from vorbis is that as small as possible is really
-% important in some applications. Practically, what's acceptable
-% depends a great deal on the target bitrate. I'd leave 16 kB in the
-% spec for now. fwiw more than 1k of comments is quite unusual.
-
-Our own design work indicates that 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
- points out limitations in some existing software/interface designs.
-However, we find that it does not fundamentally limit Theora's suitable
- application space.
-
-%silvia: renamed
-%\subsection{Format Specification}
-\section{Format Conformance}
-
-The Theora format is well-defined by its decode specification; any encoder that
- produces packets that are correctly decoded by an implementation following
- this specification may be considered a proper Theora encoder.
-A decoder must faithfully and completely implement the specification defined
- herein %, except where noted,
- to be considered a conformant Theora decoder.
-A decoder need not be implemented strictly as described, but the
- actual decoder process MUST be {\em entirely mathematically equivalent}
- to the described process.
-Where appropriate, a non-normative description of encoder processes is
- included.
-These sections will be marked as such, and a proper Theora encoder is not
- bound to follow them.
-
-%TODO: \subsection{Hardware Profile}
-
-
-\chapter{Coded Video Structure}
-
-Theora's encoding and decoding process is based on $8\times 8$ blocks of pixels.
-This sections describes how a video frame is laid out, divided into such
-blocks, and how those blocks are organized.
-
-\section{Frame Layout}
-
-A video frame in Theora is a two-dimensional array of pixels.
-Theora, like VP3, uses a right-handed coordinate system, with the origin in the
- lower-left corner of the frame.
-This is contrary to many video formats which use a left-handed coordinate
- system with the origin in the upper-left corner of the frame.
-%INT: This means that for interlaced material, the definition of `even fields'
-%INT: and `odd fields' may be reversed between Theora and other video codecs.
-%INT: This document will always refer to them as `top fields' and `bottom
-%INT: fields'.
-
-Theora divides the pixel array up into three separate \term{color planes}, one
- for each of the $Y'$, $C_b$, and $C_r$ components of the pixel.
-The $Y'$ plane is also called the \term{luma plane}, and the $C_b$ and $C_r$
- planes are also called the \term{chroma planes}.
-Each plane is assigned a numerical value, as shown in
- Table~\ref{tab:color-planes}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cl}\toprule
-Index & Color Plane \\\midrule
-$0$ & $Y'$ \\
-$1$ & $C_b$ \\
-$2$ & $C_r$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Color Plane Indices}
-\label{tab:color-planes}
-\end{table}
-
-In some pixel formats, the chroma planes are subsampled by a factor of two
- in one or both directions.
-This means that the width or height of the chroma planes may be half that of
- the total frame width and height.
-The luma plane is never subsampled.
-
-\section{Picture Region}
-
-An encoded video frame in Theora is required to have a width and height that
- are multiples of sixteen, making an integral number of blocks even when the
- chroma planes are subsampled.
-However, inside a frame a smaller \term{picture region} may be defined
- to present material whose dimensions are not a multiple of sixteen pixels, as
- shown in Figure~\ref{fig:pic-frame}.
-The picture region can be offset from the lower-left corner of the frame by up
- to 255 pixels in each direction, and may have an arbitrary width and height,
- provided that it is contained entirely within the coded frame.
-It is this picture region that contains the actual video data.
-The portions of the frame which lie outside the picture region may contain
- arbitrary image data, so the frame must be cropped to the picture region
- before display.
-The picture region plays no other role in the decode process, which operates on
- the entire video frame.
-
-\begin{figure}[htb]
-\begin{center}
-\include{pic-frame}
-\end{center}
-\caption{Location of frame and picture regions}
-\label{fig:pic-frame}
-\end{figure}
-
-\section{Blocks and Super Blocks}
-\label{sec:blocks-and-sbs}
-
-Each color plane is subdivided into \term{blocks} of $8\times 8$ pixels.
-Blocks are grouped into $4\times 4$ arrays called \term{super blocks} as
-shown in Figure~\ref{fig:superblock}.
-Each color plane has its own set of blocks and super blocks.
-The boundaries of blocks and super blocks in the luma plane do not necessarily
- coincide with those of the chroma planes, if the chroma planes have been
- subsampled.
-
-\begin{figure}[htb]
- \begin{center}
- \include{superblock}
- \end{center}
- \caption{Subdivision of a frame into blocks and super blocks}
- \label{fig:superblock}
-\end{figure}
-
-Blocks are accessed in two different orders in the various decoder processes.
-The first is \term{raster order}, illustrated in Figure~\ref{fig:raster-block}.
-This indexes each block in row-major order, starting in the lower left and
- proceeding along the bottom row, followed by the next row up starting on the
- left, etc.
-
-\begin{figure}[htb]
-\begin{center}
-\include{raster-block}
-\end{center}
-\caption{Raster ordering of nxm blocks}
-\label{fig:raster-block}
-\end{figure}
-
-The second is \term{coded order}.
-In coded order, blocks are accessed by super block.
-Within each frame, super blocks are traversed in raster order,
- similar to raster order for blocks.
-Within each super block, however, blocks are accessed in a Hilbert curve
- pattern, illustrated in Figure~\ref{fig:hilbert-block}.
-If a color plane does not contain a complete super block on the top or right
- sides, the same ordering is still used, simply with any blocks outside the
- frame boundary ommitted.
-
-\begin{figure}[htb]
-\begin{center}
-\include{hilbert-block}
-\end{center}
-\caption{Hilbert curve ordering of blocks within a super block}
-\label{fig:hilbert-block}
-\end{figure}
-
-To illustrate these two orderings, consider a frame that is 240 pixels wide and
- 48 pixels high.
-Each row of the luma plane has 30 blocks and 8 super blocks, and there are 6
- rows of blocks and two rows of super blocks.
-
-When accessed in raster order, each block in the luma plane is assigned the
- following indices:
-
-\vspace{\baselineskip}
-\begin{center}
-\begin{tabular}{|cccc|c|cc|}\hline
-150 & 151 & 152 & 153 & $\ldots$ & 178 & 179 \\
-120 & 121 & 122 & 123 & $\ldots$ & 148 & 149 \\\hline
- 90 & 91 & 92 & 93 & $\ldots$ & 118 & 119 \\
- 60 & 61 & 62 & 63 & $\ldots$ & 88 & 89 \\
- 30 & 31 & 32 & 33 & $\ldots$ & 58 & 59 \\
- 0 & 1 & 2 & 3 & $\ldots$ & 28 & 29 \\\hline
-\end{tabular}
-\end{center}
-\vspace{\baselineskip}
-
-Here the index values specify the order in which the blocks would be accessed.
-
-When accessed in coded order, each block in the luma plane is assigned the
- following indices, illustrating the different order of access:
-
-\vspace{\baselineskip}
-\begin{center}
-\begin{tabular}{|cccc|c|cc|}\hline
-123 & 122 & 125 & 124 & $\ldots$ & 179 & 178 \\
-120 & 121 & 126 & 127 & $\ldots$ & 176 & 177 \\\hline
- 5 & 6 & 9 & 10 & $\ldots$ & 117 & 118 \\
- 4 & 7 & 8 & 11 & $\ldots$ & 116 & 119 \\
- 3 & 2 & 13 & 12 & $\ldots$ & 115 & 114 \\
- 0 & 1 & 14 & 15 & $\ldots$ & 112 & 113 \\\hline
-\end{tabular}
-\end{center}
-\vspace{\baselineskip}
-
-The indices of the blocks are numbered continuously from one color plane to the
- next.
-They do not reset to zero at the start of each plane.
-The implication is that the blocks from all planes are treated as a unit during
- the various processing steps.
-
-\section{Macro Blocks}
-\label{sec:mbs}
-
-A macro block contains a $2\times 2$ array of blocks in the luma plane
- {\em and} the co-located blocks in the chroma planes, as shown in Figure~\ref{fig:macroblock}.
-Thus macro blocks can represent anywhere from six to twelve blocks, depending
- on how the chroma planes are subsampled.
-This is in contrast to super blocks, which only contain macro blocks from a
- single color plane.
-% the whole super vs. macro blocks thing is a little confusing, and it can be
-% hard to remember which is what initially. A figure would/will help here,
-% but I tried to add some text emphasizing the difference in terms of
-% functionality.
-%TBT: At this point we haven't described any functionality yet.
-%TBT: As far as the reader knows, the only purpose of the blocks, macro blocks
-%TBT: and super blocks is for data organization---and for blocks and super
-%TBT: blocks, this is essentially true.
-%TBT: So lets restrict the differences we emphasize to those of data
-%TBT: organization, which the sentence I just added above does.
-Macro bocks contain information about coding mode and motion vectors for the
- corresponding blocks in all color planes.
-
-\begin{figure}[htb]
- \begin{center}
- \include{macroblock}
- \end{center}
- \caption{Subdivision of a frame into macro blocks}
- \label{fig:macroblock}
-\end{figure}
-
-Macro blocks are also accessed in a \term{coded order}.
-This coded order proceeds by examining each super block in the luma plane in
- raster order, and traversing the four macro blocks inside using a smaller
- Hilbert curve, as shown in Figure~\ref{fig:hilbert-mb}.
-%r: I rearranged the wording to make a more formal idiom here
-If the luma plane does not contain a complete super block on the top or right
- sides, the same ordering is still used, with any macro blocks outside
- the frame boundary simply omitted.
-Because the frame size is constrained to be a multiple of 16, there are never
- any partial macro blocks.
-Unlike blocks, macro blocks need never be accessed in a pure raster order.
-
-\begin{figure}[htb]
-\begin{center}
-\include{hilbert-mb}
-\end{center}
-\caption{Hilbert curve ordering of macro blocks within a super block}
-\label{fig:hilbert-mb}
-\end{figure}
-
-Using the same frame size as the example above, there are 15 macro blocks in
- each row and 3 rows of macro blocks.
-They are assigned the following indices:
-
-\vspace{\baselineskip}
-\begin{center}
-\begin{tabular}{|cc|cc|c|cc|c|}\hline
-30 & 31 & 32 & 33 & $\cdots$ & 42 & 43 & 44 \\\hline
- 1 & 2 & 5 & 6 & $\cdots$ & 25 & 26 & 29 \\
- 0 & 3 & 4 & 7 & $\cdots$ & 24 & 27 & 28 \\\hline
-\end{tabular}
-\end{center}
-\vspace{\baselineskip}
-
-\section{Coding Modes and Prediction}
-
-Each block is coded using one of a small, fixed set of \term{coding modes} that
- define how the block is predicted from previous frames.
-A block is predicted using one of two \term{reference frames}, selected
- according to the coding mode.
-A reference frame is the fully decoded version of a previous frame in the
- stream.
-The first available reference frame is the previous intra frame, called the
- \term{golden frame}.
-The second available reference frame is the previous frame, whether it was an
- intra frame or an inter frame.
-If the previous frame was an intra frame, then both reference frames are the
- same.
-
-Two coding modes in particular are worth mentioning here.
-The INTRA mode is used for blocks that are not predicted from either reference
- frame.
-This is the only coding mode allowed in intra frames.
-The INTER\_NOMV coding mode uses the co-located contents of the block in the
- previous frame as the predictor.
-This is the default coding mode.
-
-\section{DCT Coefficients}
-
-To each block's predictor, a \term{residual} is added to form the final
- contents of the block.
-%r: I reworded this next sentence to try and make it more decoder-oriented
-%TBT: Same content with 2/3 the words... sounds good to me.
-The residual is stored as a set of quantized coefficients from an integer
- approximation of a two-dimensional Type II Discrete Cosine Transform.
-The DCT takes an $8\times 8$ array of pixel values as input and returns an
- $8\times 8$ array of coefficient values.
-The \term{natural ordering} of these coefficients is defined to be row-major
- order, from lowest to highest frequency.
-They are also often indexed in \term{zig-zag order}, as shown in
- Table~\ref{tab:zig-zag}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}[c]{r|c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c}
-\multicolumn{1}{r}{} &0&&1&&2&&3&&4&&5&&6&&7 \\\cline{2-16}
-0 & 0 &$\rightarrow$& 1 && 5 &$\rightarrow$& 6 && 14 &$\rightarrow$& 15 && 27 &$\rightarrow$& 28 \\[-0.5\defaultaddspace]
- & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
-1 & 2 & & 4 && 7 & & 13 && 16 & & 26 && 29 & & 42 \\[-0.5\defaultaddspace]
- &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
-2 & 3 & & 8 && 12 & & 17 && 25 & & 30 && 41 & & 43 \\[-0.5\defaultaddspace]
- & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
-3 & 9 & & 11 && 18 & & 24 && 31 & & 40 && 44 & & 53 \\[-0.5\defaultaddspace]
- &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
-4 & 10 & & 19 && 23 & & 32 && 39 & & 45 && 52 & & 54 \\[-0.5\defaultaddspace]
- & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
-5 & 20 & & 22 && 33 & & 38 && 46 & & 51 && 55 & & 60 \\[-0.5\defaultaddspace]
- &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
-6 & 21 & & 34 && 37 & & 47 && 50 & & 56 && 59 & & 61 \\[-0.5\defaultaddspace]
- & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
-7 & 35 &$\rightarrow$& 36 && 48 &$\rightarrow$& 49 && 57 &$\rightarrow$& 58 && 62 &$\rightarrow$& 63
-\end{tabular}
-\end{center}
-\caption{Zig-zag order}
-\label{tab:zig-zag}
-\end{table}
-
-Note that the row and column indices refer to {\em frequency number} and not
- pixel locations.
-The frequency numbers are defined independently of the memory organization of
- the pixels.
-They have been written from top to bottom here to follow conventional notation,
- despite the right-handed coordinate system Theora uses for pixel locations.
-%RG: I'd rather we were internally consistent and put dc at the lower left.
-Many implementations of the DCT operate `in-place'.
-That is, they return DCT coefficients in the same memory buffer that the
- initial pixel values were stored in.
-Due to the right-handed coordinate system used for pixel locations in Theora,
- one must note carefully how both pixel values and DCT coefficients are
- organized in memory in such a system.
-
-DCT coefficient $(0,0)$ is called the \term{DC coefficient}.
-All the other coefficients are called \term{AC coefficients}.
-
-
-\chapter{Decoding}
-
-\section{Decoder Configuration}
-
-Decoder setup consists of configuration of the quantization matrices and the
- Huffman codebooks for the DCT coefficients, and a table of limit values for
- the deblocking filter.
-The remainder of the decoding pipeline is not configurable.
-
-\subsection{Global Configuration}
-
-The global codec configuration consists of a few video related fields, such as
- frame rate, frame size, picture size and offset, aspect ratio, color space,
- pixel format, and a version number.
-The version number is divided into a major version, a minor version, amd a
- minor revision number.
-%r: afaik the released vp3 codec called itself 3.1 and is compatible w/ theora
-%r: even though we received the in-progress 3.2 codebase
-For the format defined in this specification, these are `3', `2', and
- `0', respectively, in reference to Theora's origin as a successor to the VP3.1
- format.
-
-\subsection{Quantization Matrices}
-
-Theora allows up to 384 different quantization matrices to be defined, one for
- each \term{quantization type}, \term{color plane} ($Y'$, $C_b$, or $C_r$), and
- \term{quantization index}, \qi, which ranges from zero to 63, inclusive.
-There are currently two quantization types defined, which depend on the coding
- mode of the block being dequantized, as shown in Table~\ref{tab:quant-types}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cl}\toprule
-Quantization Type & Usage \\\midrule
-$0$ & INTRA-mode blocks \\
-$1$ & Blocks in any other mode. \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Quantization Type Indices}
-\label{tab:quant-types}
-\end{table}
-
-%r: I think 'nominally' is more specific than 'generally' here
-The quantization index, on the other hand, nominally represents a progressive
- range of quality levels, from low quality near zero to high quality near 63.
-However, the interpretation is arbitrary, and it is possible, for example, to
- partition the scale into two completely separate ranges with 32 levels each
- that are meant to represent different classes of source material, or any
- other arrangement that suits the encoder's requirements.
-
-Each quantization matrix is an $8\times 8$ matrix of 16-bit values, which is
- used to quantize the output of the $8\times 8$ DCT\@.
-Quantization matrices are specified using three components: a
- \term{base matrix} and two \term{scale values}.
-The first scale value is the \term{DC scale}, which is applied to the DC
- component of the base matrix.
-The second scale value is the \term{AC scale}, which is applied to all the
- other components of the base matrix.
-There are 64 DC scale values and 64 AC scale values, one for each \qi\ value.
-
-There are 64 elements in each base matrix, one for each DCT coefficient.
-They are stored in natural order.
-There is a separate set of base matrices for each quantization type and each
- color plane, with up to 64 possible base matrices in each set, one for each
- \qi\ value.
-%r: we will mention that the given matricies must bound the \qi range
-%r: in the detailed section. it's not important at this level.
-Typically the bitstream contains matrices for only a sparse subset of the
- possible \qi\ values.
-The base matrices for the remainder of the \qi\ values are computed using
- linear interpolation.
-This configuration allows the encoder to adjust the quantization matrices to
- approximate the complex, non-linear response of the human visual system to
- different quantization errors.
-
-Finally, because the in-loop deblocking filter strength depends on the strength
- of the quantization matrices defined in this header, a table of 64 \term{loop
- filter limit values} is defined, one for each \qi\ value.
-
-The precise specification of how all of this information is decoded appears in
- Section~REF.
-
-\subsection{Huffman Codebooks}
-
-Theora uses 80 configurable binary Huffman codes to represent the 32 tokens
- used to encode DCT coefficients.
-Each of the 32 token values has a different semantic meaning and is used to
- represent single coefficient values, zero runs, combinations of the two, and
- \term{End-Of-Block markers}.
-
-The 80 codes are divided up into five groups of 16, with each group
- corresponding to a set of DCT coefficient indices.
-The first group corresponds to the DC coefficient, while the remaining four
- groups correspond to different subsets of the AC coefficients.
-Within each frame, two pairs of 4-bit codebook indices are stored.
-The first pair selects which codebooks to use from the DC coefficient group for
- the $Y'$ coefficients and the $C_b$ and $C_r$ coefficients.
-The second pair selects which codebooks to use from {\em all four} of the AC
- coefficient groups for the $Y'$ coefficients and the $C_b$ and $C_r$
- coefficients.
-
-The precise specification of how the codebooks are decoded appears in
- Section~REF.
-
-\section{High-Level Decode Process}
-
-\subsection{Decoder Setup}
-
-Before decoding can begin, a decoder MUST be initialized using the bitstream
- headers corresponding to the stream to be decoded.
-Theora uses three header packets; all are required, in order, by this
- specification.
-Once set up, decode may begin at any intra-frame packet---or even inter-frame
- packets, provided the appropriate decoded reference frames have already been
- decoded and cached---belonging to the Theora stream.
-In Theora I, all packets after the three initial headers are intra-frame or
- inter-frame packets.
-
-The header packets are, in order, the identification header, the comment
- header, and the setup header.
-
-\paragraph{Identification Header}
-
-The identification header identifies the stream as Theora, provides a version
- number, and defines the characteristics of the video stream such as frame
- size.
-A complete description of the identification header appears in
- Section~\ref{sec:idheader}.
-
-\paragraph{Comment Header}
-
-The comment header includes user text comments (`tags') and a vendor string
- for the application/library that produced the stream.
-The format of the comment header is the same as that used in the Vorbis I and
- Speex codecs, with slight modifications due to the use of a different bit
- packing mechanism.
-A complete description of how the comment header is coded appears in
- Section~\ref{sec:commentheader}, along with a suggested set of tags.
-
-\paragraph{Setup Header}
-
-The setup header includes extensive codec setup information, including the
- complete set of quantization matrices and Huffman codebooks needed to decode
- the DCT coefficients.
-A complete description of the setup header appears in
- Section~\ref{sec:setupheader}.
-
-\subsection{Decode Procedure}
-
-The decoding and synthesis procedure for all video packets is fundamentally the
- same, with some steps omitted for intra frames.
-\begin{itemize}
-\item
-Decode packet type flag.
-\item
-Decode frame header.
-\item
-Decode coded block information (inter frames only).
-\item
-Decode macro block mode information (inter frames only).
-\item
-Decode motion vectors (inter frames only).
-\item
-Decode block-level \qi\ information.
-\item
-Decode DC coefficient for each coded block.
-\item
-Decode 1st AC coefficient for each coded block.
-\item
-Decode 2nd AC coefficient for each coded block.
-\item
-$\ldots$
-\item
-Decode 63rd AC coefficient for each coded block.
-\item Perform DC coefficient prediction.
-\item Reconstruct coded blocks.
-\item Copy uncoded bocks.
-\item Perform loop filtering.
-\end{itemize}
-
-Note that clever rearrangement of the steps in this process is possible.
-As an example, in a memory-constrained environment, one can make multiple
- passes through the DCT coefficients to avoid buffering them all in memory.
-On the first pass, the starting location of each coefficient is identified, and
- then 64 separate get pointers are used to read in the 64 DCT coefficients
- required to reconstruct each coded block in sequence.
-This operation produces entirely equivalent output and is naturally perfectly
- legal.
-It may even be a benefit in non-memory-constrained environments due to a
- reduced cache footprint.
-
-Theora makes equivalence easy to check by defining all decoding operations in
- terms of exact integer operations.
-No floating-point math is required, and in particular, the implementation of
- the iDCT transform MUST be followed precisely.
-This prevents the decoder mismatch problem commonly associated with codecs that
- provide a less rigorous transform specification.
-Such a mismatch problem would be devastating to Theora, since a single rounding
- error in one frame could propagate throughout the entire succeeding frame due
- to DC prediction.
-
-\paragraph{Packet Type Decode}
-
-Theora I uses four packet types.
-The first three packet types mark each of the three Theora headers described
- above.
-The fourth packet type marks a video packet.
-All other packet types are reserved; packets marked with a reserved type should
- be ignored.
-
-\paragraph{Frame Header Decode}
-
-The frame header contains some global information about the current frame.
-The first is the frame type field, which specifies if this is an intra frame or
- an inter frame.
-Inter frames predict their contents from previously decoded reference frames.
-Intra frames can be independently decoded with no established reference frames.
-
-The next piece of information in the frame header is the list of \qi\ values
- allowed in the frame.
-Theora allows from one to three different \qi\ values to be used in a single
- frame, each of which selects a set of six quantization matrices, one for each
- quantization type (inter or intra), and one for each color plane.
-The first \qi\ value is {\em always} used when dequantizing DC coefficients.
-The \qi\ value used when dequantizing AC coefficients, however, can vary from
- block to block.
-VP3, in contrast, only allows a single \qi\ value per frame for both the DC and
- AC coefficients.
-
-\paragraph{Coded Block Information}
-
-This stage determines which blocks in the frame are coded and which are
- uncoded.
-A \term{coded block list} is constructed which lists all the coded blocks in
- coded order.
-For intra frames, every block is coded, and so no data needs to be read from
- the packet.
-
-\paragraph{Macro Block Mode Information}
-
-For intra frames, every block is coded in INTRA mode, and this stage is
- skipped.
-In inter frames a \term{coded macro block list} is constructed from the coded
- block list.
-Any macro block which has at least one of its luma blocks coded is considered
- coded; all other macro blocks are uncoded, even if they contain coded chroma
- blocks.
-A coding mode is decoded for each coded macro block, and assigned to all its
- constituent coded blocks.
-All coded chroma blocks in uncoded macro blocks are assigned the INTER\_NOMV
- coding mode.
-
-\paragraph{Motion Vectors}
-
-Intra frames are coded entirely in INTRA mode, and so this stage is skipped.
-Some inter coding modes, however, require one or more motion vectors to be
- specified for each macro block.
-These are decoded in this stage, and an appropriate motion vector is assigned
- to each coded block in the macro block.
-
-\paragraph{Block-Level \qi\ Information}
-
-If a frame allows multiple \qi\ values, the \qi\ value assigned to each block
- is decoded here.
-Frames that use only a single \qi\ value have nothing to decode.
-
-\paragraph{DCT Coefficients}
-
-Finally, the quantized DCT coefficients are decoded.
-A list of DCT coefficients in zig-zag order for a single block is represented
- by a list of tokens.
-A token can take on one of 32 different values, each with a different semantic
- meaning.
-A single token can represent a single DCT coefficient, a run of zero
- coefficients within a single block, a combination of a run of zero
- coefficients followed by a single non-zero coefficient, an
- \term{End-Of-Block marker}, or a run of EOB markers.
-EOB markers signify that the remainder of the block is one long zero run.
-Unlike JPEG and MPEG, there is no requirement for each block to end with
- a special marker.
-If non-EOB tokens yield values for all 64 of the coefficients in a block, then
- no EOB marker occurs.
-
-Each token is associated with a specific \term{token index} in a block.
-For single-coefficient tokens, this index is the zig-zag index of the token in
- the block.
-For zero-run tokens, this index is the zig-zag index of the {\em first}
- coefficient in the run.
-For combination tokens, the index is again the zig-zag index of the first
- coefficient in the zero run.
-For EOB markers, which signify that the remainder of the block is one long zero
- run, the index is the zig-zag index of the first zero coefficient in that run.
-For EOB runs, the token index is that of the first EOB marker in the run.
-Due to zero runs and EOB markers, a block does not have to have a token for
- every zig-zag index.
-
-Tokens are grouped in the stream by token index, not by the block they
- originate from.
-This means that for each zig-zag index in turn, the tokens with that index from
- {\em all} the coded blocks are coded in coded block order.
-When decoding, a current token index is maintained for each coded block.
-This index is advanced by the number of coefficients that are added to the
- block as each token is decoded.
-After fully decoding all the tokens with token index \ti, the current token
- index of every coded block will be \ti\ or greater.
-
-If an EOB run of $n$ blocks is decoded at token index \ti, then it ends the
- next $n$ blocks in coded block order whose current token index is equal to
- \ti, but not greater.
-If there are fewer than $n$ blocks with a current token index of \ti, then the
- decoder goes through the coded block list again from the start, ending blocks
- with a current token index of $\ti+1$, and so on, until $n$ blocks have been
- ended.
-
-Tokens are read by parsing a Huffman code that depends on \ti\ and the color
- plane of the next coded block whose current token index is equal to \ti, but
- not greater.
-The Huffman codebooks are selected on a per-frame basis from the 80 codebooks
- defined in the setup header.
-Many tokens have a fixed number of \term{extra bits} associated with them.
-These bits are read from the packet immediately after the token is decoded.
-These are used to define things such as coefficient magnitude, sign, and the
- length of runs.
-
-\paragraph{DC Prediction}
-
-After the coefficients for each block are decoded, the quantized DC value of
- each block is adjusted based on the DC values of its neighbors.
-This adjustment is performed by scanning the blocks in raster order, not coded
- block order.
-
-\paragraph{Reconstruction}
-
-Finally, using the coding mode, motion vector (if applicable), quantized
- coefficient list, and \qi\ value defined for each block, all the coded blocks
- are reconstructed.
-The DCT coefficients are dequantized, an inverse DCT transform is applied, and
- the predictor is formed from the coding mode and motion vector and added to
- the result.
-
-\paragraph{Loop Filtering}
-
-To complete the reconstructed frame, an ``in-loop'' deblocking filter is applied to the edges of all coded blocks.
-
-
-\chapter{Video Formats}
-
-This section gives a precise description of the video formats that Theora is
- capable of storing.
-The Theora bitstream is capable of handling video at any arbitrary resolution
- up to $1048560\times 1048560$.
-Such video would require almost three terabytes of storage per frame for
- uncompressed data, so compliant decoders MAY refuse to decode images with
- sizes beyond their capabilities.
-%TODO: What MUST a "compliant" decoder accept?
-%TODO: What SHOULD a decoder use for an upper bound? (derive from total amount
-%TODO: of memory and memory bandwidth)
-%TODO: Any lower limits?
-%TODO: We really need hardware device profiles, but such things should be
-%TODO: developed with input from the hardware community.
-%TODO: And even then sometimes they're useless
-
-The remainder of this section talks about two specific aspects of the video
- format: the color space and the pixel format.
-The first describes how color is represented and how to transform that color
- representation into a device independent color space such as CIE $XYZ$ (1931).
-The second describes the various schemes for sampling the color values in time
- and space.
-
-\section{Color Space Conventions}
-
-There are a large number of different color standards used in digital video.
-Since Theora is a lossy codec, it restricts itself to only a few of them to
- simplify playback.
-Unlike the alternate method of describing all the parameters of the color
- model, this allows a few dedicated routines for color conversion to be written
- and heavily optimized in a decoder.
-More flexible conversion functions should instead be specified in an encoder,
- where additional computational complexity is more easily tolerated.
-The color spaces were selected to give a fair representation of color standards
- in use around the world today.
-Most of the standards that do not exactly match one of these can be converted
- to one fairly easily.
-
-All Theora color spaces are $Y'C_bC_r$ color spaces with one luma channel and
- two chroma channels.
-Each channel contains 8-bit discrete values in the range $0\ldots255$, which
- represent non-linear gamma pre-corrected signals.
-The Theora identification header contains an 8-bit value that describes the
- color space.
-This merely selects one of the color spaces available from an enumerated list.
-Currently, only two color spaces are defined, with a third possibility that
- indicates the color space is ``unknown".
-
-\section{Color Space Conversions and Parameters}
-\label{sec:color-xforms}
-
-The parameters which describe the conversions between each color space are
- listed below.
-These are the parameters needed to map colors from the encoded $Y'C_bC_r$
- representation to the device-independent color space CIE $XYZ$ (1931).
-These parameters define abstract mathematical conversion functions which are
- infinitely precise.
-The accuracy and precision with which the conversions are performed in a real
- system is determined by the quality of output desired and the available
- processing power.
-Exact decoder output is defined by this specification only in the original
- $Y'C_bC_r$ space.
-
-\begin{description}
-\item[$Y'C_bC_r$ to $Y'P_bP_r$:]
-\vspace{\baselineskip}\hfill
-
-This conversion takes 8-bit discrete values in the range $[0\ldots255]$ and
- maps them to real values in the range $[0\ldots1]$ for Y and
- $[-\frac{1}{2}\ldots\frac{1}{2}]$ for $P_b$ and $P_r$.
-Because some values may fall outside the offset and excursion defined for each
- channel in the $Y'C_bC_r$ space, the results may fall outside these ranges in
- $Y'P_bP_r$ space.
-No clamping should be done at this stage.
-
-\begin{align}
-Y'_\mathrm{out} & =
- \frac{Y'_\mathrm{in}-\mathrm{Offset}_Y}{\mathrm{Excursion}_Y} \\
-P_b & =
- \frac{C_b-\mathrm{Offset}_{C_b}}{\mathrm{Excursion}_{C_b}} \\
-P_r & =
- \frac{C_r-\mathrm{Offset}_{C_r}}{\mathrm{Excursion}_{C_r}}
-\end{align}
-
-Parameters: $\mathrm{Offset}_{Y,C_b,C_r}$, $\mathrm{Excursion}_{Y,C_b,C_r}$.
-
-\item[$Y'P_bP_r$ to $R'G'B'$:]
-\vspace{\baselineskip}\hfill
-
-This conversion takes the one luma and two chroma channel representation and
- maps it to the non-linear $R'G'B'$ space used to drive actual output devices.
-Values should be clamped into the range $[0\ldots1]$ after this stage.
-
-\begin{align}
-R' & = Y'+2(1-K_r)P_r \\
-G' & = Y'-2\frac{(1-K_b)K_b}{1-K_b-K_r}P_b-2\frac{(1-K_r)K_r}{1-K_b-K_r}P_r\\
-B' & = Y'+2(1-K_b)P_b
-\end{align}
-
-Parameters: $K_b,K_r$.
-
-\item[$R'G'B'$ to $RGB$ (Output device gamma correction):]
-\vspace{\baselineskip}\hfill
-
-This conversion takes the non-linear $R'G'B'$ voltage levels and maps them to
- linear light levels produced by the actual output device.
-Note that this conversion is only that of the output device, and its inverse is
- {\em not} that used by the input device.
-Because a dim viewing environment is assumed in most television standards, the
- overall gamma between the input and output devices is usually around $1.1$ to
- $1.2$, and not a strict $1.0$.
-
-For calibration with actual output devices, the model
-\begin{align}
-L & =(E'+\Delta)^\gamma
-\end{align}
- should be used, with $\Delta$ the free parameter and $\gamma$ held fixed to
- the value specified in this document.
-The conversion function presented here is an idealized version with $\Delta=0$.
-
-\begin{align}
-R & = R'^\gamma \\
-G & = G'^\gamma \\
-B & = B'^\gamma
-\end{align}
-
-Parameters: $\gamma$.
-
-\item[$RGB$ to $R'G'B'$ (Input device gamma correction):]
-\vspace{\baselineskip}\hfill
-
-%TODO: Tag section as non-normative
-
-This conversion takes linear light levels and maps them to the non-linear
- voltage levels produced in the actual input device.
-This information is merely informative.
-It is not required for building a decoder or for converting between the various
- formats and the actual output capabilities of a particular device.
-
-A linear segment is introduced on the low end to reduce noise in dark areas of
- the image.
-The rest of the scale is adjusted so that the power segment of the curve
- intersects the linear segment with the proper slope, and so that it still maps
- 0 to 0 and 1 to 1.
-
-\begin{align}
-R' & = \left\{
-\begin{array}{ll}
-\alpha R, & 0\le R<\delta \\
-(1+\epsilon)R^\beta-\epsilon, & \delta\le R\le1
-\end{array}\right. \\
-G' & = \left\{
-\begin{array}{ll}
-\alpha G, & 0\le G<\delta \\
-(1+\epsilon)G^\beta-\epsilon, & \delta\le G\le1
-\end{array}\right. \\
-B' & = \left\{
-\begin{array}{ll}
-\alpha B, & 0\le B<\delta \\
-(1+\epsilon)B^\beta-\epsilon, & \delta\le B\le1
-\end{array}\right.
-\end{align}
-
-Parameters: $\beta$, $\alpha$, $\delta$, $\epsilon$.
-
-\item[$RGB$ to CIE $XYZ$ (1931):]
-\vspace{\baselineskip}\hfill
-
-This conversion maps a device-dependent linear RGB space to the
- device-independent linear CIE $XYZ$ space.
-The parameters are the CIE chromaticity coordinates of the three
- primaries---red, green, and blue---as well as the chromaticity coordinates
- of the white point of the device.
-This is how hardware manufacturers and standards typically describe a
- particular $RGB$ space.
-The math required to convert these parameters into a useful transformation
- matrix is reproduced below.
-
-\begin{align}
-F & =
-\left[\begin{array}{ccc}
-\frac{x_r}{y_r} & \frac{x_g}{y_g} & \frac{x_b}{y_b} \\
-1 & 1 & 1 \\
-\frac{1-x_r-y_r}{y_r} & \frac{1-x_g-y_g}{y_g} & \frac{1-x_b-y_b}{y_b}
-\end{array}\right] \\
-\left[\begin{array}{c}
-s_r \\
-s_g \\
-s_b
-\end{array}\right] & =
-F^{-1}\left[\begin{array}{c}
-\frac{x_w}{y_w} \\
-1 \\
-\frac{1-x_w-y_w}{y_w}
-\end{array}\right] \\
-\left[\begin{array}{c}
-X \\
-Y \\
-Z
-\end{array}\right] & =
-F\left[\begin{array}{c}
-s_rR \\
-s_gG \\
-s_bB
-\end{array}\right]
-\end{align}
-Parameters: $x_r,x_g,x_b,x_w, y_r,y_g,y_b,y_w$.
-
-\end{description}
-
-\section{Available Color Spaces}
-\label{sec:colorspaces}
-
-These are the color spaces currently defined for use by Theora video.
-Each one has a short name, with which it is referred to in this document, and
- a more detailed specification of the standards from which its parameters are
- derived.
-Some standards do not specify all the parameters necessary.
-For these unspecified parameters, this document serves as the definition of
- what should be used when encoding or decoding Theora video.
-
-\subsection{Rec.~470M (Rec.~ITU-R~BT.470-6 System M/NTSC with
- Rec.~ITU-R~BT.601-5)}
-\label{sec:470m}
-
-This color space is used by broadcast television and DVDs in much of the
- Americas, Japan, Korea, and the Union of Myanmar \cite{rec470}.
-This color space may also be used for System M/PAL (Brazil), with an
- appropriate conversion supplied by the encoder to compensate for the
- different gamma value.
-See Section~\ref{sec:470bg} for an appropriate gamma value to assume for M/PAL
- input.
-
-In the US, studio monitors are adjusted to a D65 white point
- ($x_w,y_w=0.313,0.329$).
-In Japan, studio monitors are adjusted to a D white of 9300K
- ($x_w,y_w=0.285,0.293$).
-
-Rec.~470 does not specify a digital encoding of the color signals.
-For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
- $R'G'B'$ signals specified by Rec.~470.
-
-Rec.~470 does not specify an input gamma function.
-For Theora, the Rec.~709 \cite{rec709} input function is assumed.
-This is the same as that specified by SMPTE 170M \cite{smpte170m}, which claims
- to reflect modern practice in the creation of NTSC signals circa 1994.
-
-The parameters for all the color transformations defined in
- Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470m}.
-
-\begin{table}[htb]
-\begin{align*}
-\mathrm{Offset}_{Y,C_b,C_r} & = (16, 128, 128) \\
-\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
-K_r & = 0.299 \\
-K_b & = 0.114 \\
-\gamma & = 2.2 \\
-\beta & = 0.45 \\
-\alpha & = 4.5 \\
-\delta & = 0.018 \\
-\epsilon & = 0.099 \\
-x_r,y_r & = 0.67, 0.33 \\
-x_g,y_g & = 0.21, 0.71 \\
-x_b,y_b & = 0.14, 0.08 \\
-\text{(Illuminant C) } x_w,y_w & = 0.310, 0.316 \\
-\end{align*}
-\caption{Rec.~470M Parameters}
-\label{tab:470m}
-\end{table}
-
-\subsection{Rec.~470BG (Rec.~ITU-R~BT.470-6 Systems B and G with
- Rec.~ITU-R~BT.601-5)}
-\label{sec:470bg}
-
-This color space is used by the PAL and SECAM systems in much of the rest of
- the world \cite{rec470}
-This can be used directly by systems (B, B1, D, D1, G, H, I, K, N)/PAL and (B,
- D, G, H, K, K1, L)/SECAM\@.
-
-Note that the Rec.~470BG chromaticity values are different from those
- specified in Rec.~470M\@.
-When PAL and SECAM systems were first designed, they were based upon the same
- primaries as NTSC\@.
-However, as methods of making color picture tubes have changed, the primaries
- used have changed as well.
-The U.S. recommends using correction circuitry to approximate the existing,
- standard NTSC primaries.
-Current PAL and SECAM systems have standardized on primaries in accord with
- more recent technology.
-
-Rec.~470 provisionally permits the use of the NTSC chromaticity values (given
- in Section~\ref{sec:470m}) with legacy PAL and SECAM equipment.
-In Theora, material must be decoded assuming the new PAL and SECAM primaries.
-Material intended for display on old legacy devices should be converted by the
- decoder.
-
-The official Rec.~470BG specifies a gamma value of $\gamma=2.8$.
-However, in practice this value is unrealistically high \cite{Poyn97}.
-Rec.~470BG states that the overall system gamma should be approximately
- $\gamma\beta=1.2$.
-Since most cameras pre-correct with a gamma value of $\beta=0.45$,
- this suggests an output device gamma of approximately $\gamma=2.67$.
-This is the value recommended for use with PAL systems in Theora.
-
-Rec.~470 does not specify a digital encoding of the color signals.
-For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
- $R'G'B'$ signals specified by Rec.~470.
-
-Rec.~470 does not specify an input gamma function.
-For Theora, the Rec 709 \cite{rec709} input function is assumed.
-
-The parameters for all the color transformations defined in
- Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470bg}.
-
-\begin{table}[htb]
-\begin{align*}
-\mathrm{Offset}_{Y,C_b,C_r} & = (16, 128, 128) \\
-\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
-K_r & = 0.299 \\
-K_b & = 0.114 \\
-\gamma & = 2.67 \\
-\beta & = 0.45 \\
-\alpha & = 4.5 \\
-\delta & = 0.018 \\
-\epsilon & = 0.099 \\
-x_r,y_r & = 0.64, 0.33 \\
-x_g,y_g & = 0.29, 0.60 \\
-x_b,y_b & = 0.15, 0.06 \\
-\text{(D65) } x_w,y_w & = 0.313, 0.329 \\
-\end{align*}
-\caption{Rec.~470BG Parameters}
-\label{tab:470bg}
-\end{table}
-
-\section{Pixel Formats}
-\label{sec:pixfmts}
-
-Theora supports several different pixel formats, each of which uses different
- subsampling for the chroma planes relative to the luma plane.
-
-\subsection{4:4:4 Subsampling}
-\label{sec:444}
-
-All three color planes are stored at full resolution.
-The samples in the different planes are all at co-located sites.
-
-%TODO: Figure.
-%YRB YRB
-%
-%
-%
-%YRB YRB
-%
-%
-%
-
-
-\subsection{4:2:2 Subsampling}
-\label{sec:422}
-
-The $C_b$ and $C_r$ planes are stored with half the horizontal resolution of
- the $Y'$ plane.
-Thus, each of these planes has half the number of horizontal blocks as the luma
- plane.
-Similarly, they have half the number of horizontal super blocks, rounded up.
-Macro blocks are defined across color planes, and so their number does not
- change, but each macro block contains half as many chroma blocks.
-
-The chroma samples are vertically aligned with the luma samples, but
- horizontally centered between two luma samples.
-Thus, each luma sample has a unique closest chroma sample.
-A horizontal phase shift may be required to produce signals which use different
- horizontal chroma sampling locations for compatibility with different systems.
-
-%TODO: Figure.
-%Y RB Y Y RB Y
-%
-%
-%
-%Y RB Y Y RB Y
-%
-%
-%
-
-\subsection{4:2:0 Subsampling}
-\label{sec:420}
-
-The $C_b$ and $C_r$ planes are stored with half the horizontal and half the
- vertical resolution of the $Y'$ plane.
-Thus, each of these planes has half the number of horizontal blocks and half
- the number of vertical blocks as the luma plane, for a total of one quarter
- the number of blocks.
-Similarly, they have half the number of horizontal super blocks and half the
- number of vertical super blocks, rounded up.
-Macro blocks are defined across color planes, and so their number does not
- change, but each macro block contains within it one quarter as many
- chroma blocks.
-
-The chroma samples are vertically and horizontally centered between four luma
- samples.
-Thus, each luma sample has a unique closest chroma sample.
-This is the same sub-sampling pattern used with JPEG, MJPEG, and MPEG-1, and
- was inherited from VP3.
-A horizontal or vertical phase shift may be required to produce signals which
- use different chroma sampling locations for compatibility with different
- systems.
-
-%TODO: Figure.
-%Y Y Y Y
-%
-% RB RB
-%
-%Y Y Y Y
-%
-%
-%
-%Y Y Y Y
-%
-% RB RB
-%
-%Y Y Y Y
-%
-%
-%
-
-\subsection{Subsampling and the Picture Region}
-
-Although the frame size must be an integral number of macro blocks, and thus
- both the number of pixels and the number of blocks in each direction must be
- even, no such requirement is made of the picture region.
-Thus, when using subsampled pixel formats, careful attention must be paid to
- which chroma samples correspond to which luma samples.
-
-As mentioned above, for each pixel format, there is a unique chroma sample that
- is the closest to each luma sample.
-When cropping the chroma planes to the picture region, all the chroma samples
- corresponding to a luma sample in the cropped picture region must be included.
-Thus, when dividing the width or height of the picture region by two to obtain
- the size of the subsampled chroma planes, they must be rounded up.
-
-Furthermore, the sampling locations are defined relative to the frame,
- {\em not} the picture region.
-When the width of the picture region is odd in the 4:2:2 and 4:2:0 formats,
- then the locations of chroma samples relative to the luma samples depends on
- whether or not the X offset of the picture region is odd.
-If the offset is even, each column of chroma samples corresponds to two columns
- of luma samples, except the last column which corresponds to one.
-If the offset is odd, then it is the first column of chroma samples which
- corresponds to only one column of luma samples, while the remaining columns
- each correspond to two.
-
-A similar process is followed with the rows of a picture region of odd height
- encoded in the 4:2:0 format.
-If the Y offset is even, each row of chroma samples corresponds to two rows of
- luma samples, except the last row which corresponds to one.
-If the offset is odd, then it is the first row of chroma samples which
- corresponds to only one row of luma samples, while the remaining rows each
- correspond to two.
-
-%TODO: Figures!
-
-%TODO: informational section for encoders:
-% When the chroma planes are subsampled, encoders SHOULD chose picture
-% offsets and dimensions that are even so that the subsampling
-% positions are reproduced cleanly.
-
-\chapter{Bitpacking Convention}
-\label{sec:bitpacking}
-
-\section{Overview}
-
-The Theora codec uses relatively unstructured raw packets containing
- binary integer fields of arbitrary width.
-Logically, each packet is a bitstream in which bits are written one-by-one by
- the encoder and then read one-by-one in the same order by the decoder.
-Most current binary storage arrangements group bits into a native storage unit
- of eight bits (octets), sixteen bits, thirty-two bits, or less commonly other
- fixed sizes.
-The Theora bitpacking convention specifies the correct mapping of the logical
- packet bitstream into an actual representation in fixed-width units.
-
-\subsection{Octets and Bytes}
-
-In most contemporary architectures, a `byte' is synonymous with an `octect',
- that is, eight bits.
-For purposes of the bitpacking convention, a byte implies the smallest native
- integer storage representation offered by a platform.
-Modern file systems invariably offer bytes as the fundamental atom of storage.
-
-The most ubiquitous architectures today consider a `byte' to be an octet.
-Note, however, that the Theora bitpacking convention is still well defined for
- any native byte size; an implementation can use the native bit-width of a
- given storage system.
-This document assumes that a byte is one octet for purposes of example only.
-
-\subsection{Words and Byte Order}
-
-A `word' is an integer size that is a grouped multiple of the byte size.
-Most architectures consider a word to be a group of two, four, or eight bytes.
-Each byte in the word can be ranked by order of `significance', e.g.\ the
- significance of the bits in each byte when storing a binary integer in the
- word.
-Several byte orderings are possible in a word.
-The common ones are
-\begin{itemize}
-\item{Big-endian:}
-in which the most significant byte comes first, e.g.\ 3-2-1-0,
-\item{Little-endian:}
-in which the least significant byte comes first, e.g.\ 0-1-2-3, and
-\item{Mixed-endian:}
-one of the less-common orderings that cannot be put into the above two
- categories, e.g.\ 3-1-2-0 or 0-2-1-3.
-\end{itemize}
-
-The Theora 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
- code that operates on a word of storage at a time rather than a byte.
-Logically, bytes are always encoded and decoded in order from byte zero through
- byte $n$.
-
-\subsection{Bit Order}
-
-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.
-Bits in a byte are numbered from zero at the LSb to $n$ for the MSb, where
- $n=7$ in an octet.
-
-\section{Coding Bits into Bytes}
-
-The Theora codec needs to encode 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 read at the bit position immediately
- after the end of the previous field.
-
-The decoder logically unpacks integers by first reading the MSb of a binary
- integer from the logical bitstream, followed by the next most significant
- bit, etc., until the required number of bits have been read.
-When unpacking the bytes into bits, the decoder begins by reading the MSb of
- the integer to be read from the most significant unread bit position of the
- source byte, followed by the next-most significant bit position of the
- destination integer, and so on up to the requested number of bits.
-Note that this differs from the Vorbis I codec, which
- begins decoding with the LSb of the source integer, reading it from the
- LSb of the source byte.
-When all the bits of the current source byte are read, decoding continues with
- the MSb of the next byte.
-Any unfilled bits in the last byte of the packet MUST be cleared to zero by the
- encoder.
-
-\subsection{Signedness}
-
-The binary integers decoded by the above process may be either signed or
- unsigned.
-This varies from integer to integer, and this specification
- indicates how each value should be interpreted as it is read.
-That is, depending on context, the three bit binary pattern \bin{111} can be
- taken to represent either `$7$' as an unsigned integer or `$-1$' as a signed,
- two's complement integer.
-
-\subsection{Encoding Example}
-
-The following example shows the state of an (8-bit) byte stream after several
- binary integers are encoded, including the location of the put pointer for the
- next bit to write to and the total length of the stream in bytes.
-
-Encode the 4 bit unsigned integer value `12' (\bin{1100}) into an empty byte
- stream.
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{}& &&&&$\downarrow$&&&& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
- 0 & 0 & 0 & 0 & $\leftarrow$ \\
-byte 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
-byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 1 byte
-\end{tabular}
-\vspace{\baselineskip}
-
-Continue by encoding the 3 bit signed integer value `-1' (\bin{111}).
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{} &&&&&&&&$\downarrow$& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
- \textbf{1} & \textbf{1} & \textbf{1} & 0 & $\leftarrow$ \\
-byte 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
-byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 1 byte
-\end{tabular}
-\vspace{\baselineskip}
-
-Continue by encoding the 7 bit integer value `17' (\bin{0010001}).
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{} &&&&&&&$\downarrow$&& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
- \textbf{1} & \textbf{1} & \textbf{1} & \textbf{0} & \\
-byte 1 & \textbf{0} & \textbf{1} & \textbf{0} & \textbf{0} &
- \textbf{0} & \textbf{1} & 0 & 0 & $\leftarrow$ \\
-byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
-\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
-byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 2 bytes
-\end{tabular}
-\vspace{\baselineskip}
-
-Continue by encoding the 13 bit integer value `6969' (\bin{11011\ 00111001}).
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{} &&&&$\downarrow$&&&&& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
- \textbf{1} & \textbf{1} & \textbf{1} & \textbf{0} & \\
-byte 1 & \textbf{0} & \textbf{1} & \textbf{0} & \textbf{0} &
- \textbf{0} & \textbf{1} & \textbf{1} & \textbf{1} & \\
-byte 2 & \textbf{0} & \textbf{1} & \textbf{1} & \textbf{0} &
- \textbf{0} & \textbf{1} & \textbf{1} & \textbf{1} & \\
-byte 3 & \textbf{0} & \textbf{0} & \textbf{1} &
- 0 & 0 & 0 & 0 & 0 & $\leftarrow$ \\
-\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
-byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 4 bytes
-\end{tabular}
-\vspace{\baselineskip}
-
-\subsection{Decoding Example}
-
-The following example shows the state of the (8-bit) byte stream encoded in the
- previous example after several binary integers are decoded, including the
- location of the get pointer for the next bit to read.
-
-Read a two bit unsigned integer from the example encoded above.
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{} &&&$\downarrow$&&&&&& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & 0 & 0 & 1 & 1 & 1 & 0 & $\leftarrow$ \\
-byte 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & \\
-byte 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & \\
-byte 3 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 4 bytes
-\end{tabular}
-\vspace{\baselineskip}
-
-Value read: 3 (\bin{11}).
-
-Read another two bit unsigned integer from the example encoded above.
-
-\begin{tabular}{r|ccccccccl}
-\multicolumn{1}{r}{} &&&&&$\downarrow$&&&& \\
- & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
-byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
- 1 & 1 & 1 & 0 & $\leftarrow$ \\
-byte 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & \\
-byte 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & \\
-byte 3 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 &
-byte stream length: 4 bytes
-\end{tabular}
-\vspace{\baselineskip}
-
-Value read: 0 (\bin{00}).
-
-Two things are worth noting here.
-\begin{itemize}
-\item
-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.
-No artificial alignment boundaries are maintained in the bitstream.
-\item
-The first value is the integer `$3$' only because the context stated we were
- reading an unsigned integer.
-Had the context stated we were reading a signed integer, the returned value
- would have been the integer `$-1$'.
-\end{itemize}
-
-\subsection{End-of-Packet Alignment}
-
-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 bitstream encoded as a byte stream MUST begin and end on a
- byte boundary.
-Often, the encoded packet bitstream is not an integer number of bytes, and so
- there is unused space in the last byte of a packet.
-
-%r: I think the generality here is necessary to be consistent with our assertions
-%r: elsewhere about being independent of transport and byte width
-When a Theora encoder produces packets for embedding in a byte-aligned
- container, unused space in the last byte of a packet is always zeroed during
- the encoding process.
-Thus, should this unused space be read, it will return binary zeroes.
-There is no marker pattern or stuffing bits that will allow the decoder to
- obtain the exact size, in bits, of the original bitstream.
-This knowledge is not required for decoding.
-
-Attempting to read past the end of an encoded packet results in an
- `end-of-packet' condition.
-Any further read operations after an `end-of-packet' condition shall also
- return `end-of-packet'.
-Unlike Vorbis, Theora does not use truncated packets as a normal mode of
- operation.
-Therefore if a decoder encounters the `end-of-packet' condition during normal
- decoding, it may attempt to use the bits that were read to recover as much of
- encoded data as possible, signal a warning or error, or both.
-
-\subsection{Reading Zero Bit Integers}
-
-Reading a zero bit integer returns the value `$0$' and does not increment
- the stream pointer.
-Reading to the end of the packet, but not past the end, so that an
- `end-of-packet' condition is 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 integer after a previous read sets the `end-of-packet'
- condition shall fail, also returning `end-of-packet'.
-
-\chapter{Bitstream Headers}
-\label{sec:headers}
-
-A Theora bitstream begins with three header packets.
-The header packets are, in order, the identification header, the comment
- header, and the setup header.
-All are required for decode compliance.
-An end-of-packet condition encountered while decoding the identification or
- setup header packets renders the stream undecodable.
-An end-of-packet condition encountered while decode the comment header is a
- non-fatal error condition, and MAY be ignored by a decoder.
-
-\paragraph{VP3 Compatibility}
-
-VP3 relies on the headers provided by its container, usually either AVI or
- Quicktime.
-As such, several parameters available in these headers are not available to VP3
- streams.
-These are indicated as they appear in the sections below.
-
-\section{Common Header Decode}
-\label{sub:common-header}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{HEADERTYPE} & Integer & 8 & No & The type of the header being
- decoded. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:} None.
-\medskip
-
-Each header packet begins with the same header fields, which are decoded as
- follows:
-
-\begin{enumerate}
-\item
-Read an 8-bit unsigned integer as \bitvar{HEADERTYPE}.
-If the most significant bit of this integer is not set, then stop.
-This is not a header packet.
-\item
-Read 6 8-bit unsigned integers.
-If these do not have the values \hex{74}, \hex{68}, \hex{65}, \hex{6F},
- \hex{72}, and \hex{61}, respectively, then stop.
-This stream is not decodable by this specification.
-These values correspond to the ASCII values of the characters `t', `h', `e',
- `o', `r', and `a'.
-\end{enumerate}
-
-Decode continues according to \bitvar{HEADERTYPE}.
-The identification header is type \hex{80}, the comment header is type
- \hex{81}, and the setup header is type \hex{82}.
-These packets must occur in the order: identification, comment, setup.
-%r: I clarified the initial-bit scheme here
-%TBT: Dashes let the reader know they'll have to pick up the rest of the
-%TBT: sentence after the explanatory phrase.
-%TBT: Otherwise it just sounds like the bit must exist.
-All header packets have the most significant bit of the type
- field---which is the initial bit in the packet---set.
-This distinguishes them from video data packets in which the first bit
- is unset.
-% extra header packets are a feature Dan argued for way back when for
-% backward-compatible extensions (and icc colourspace for example)
-% I think it's reasonable
-%TBT: You can always just stick more stuff in the setup header.
-Packets with other header types (\hex{83}--\hex{FF}) are reserved and MUST be
- ignored.
-
-\section{Identification Header Decode}
-\label{sec:idheader}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{VMAJ} & Integer & 8 & No & The major version number. \\
-\bitvar{VMIN} & Integer & 8 & No & The minor version number. \\
-\bitvar{VREV} & Integer & 8 & No & The version revision number. \\
-\bitvar{FMBW} & Integer & 16 & No & The width of the frame in macro
- blocks. \\
-\bitvar{FMBH} & Integer & 16 & No & The height of the frame in macro
- blocks. \\
-\bitvar{NSBS} & Integer & 32 & No & The total number of super blocks in a
- frame. \\
-\bitvar{NBS} & Integer & 32 & No & The total number of blocks in a
- frame. \\
-\bitvar{NMBS} & Integer & 32 & No & The total number of macro blocks in a
- frame. \\
-\bitvar{PICW} & Integer & 20 & No & The width of the picture region in
- pixels. \\
-\bitvar{PICH} & Integer & 20 & No & The height of the picture region in
- pixels. \\
-\bitvar{PICX} & Integer & 8 & No & The X offset of the picture region in
- pixels. \\
-\bitvar{PICY} & Integer & 8 & No & The Y offset of the picture region in
- pixels. \\
-\bitvar{FRN} & Integer & 32 & No & The frame-rate numerator. \\
-\bitvar{FRD} & Integer & 32 & No & The frame-rate denominator. \\
-\bitvar{PARN} & Integer & 24 & No & The pixel aspect-ratio numerator. \\
-\bitvar{PARD} & Integer & 24 & No & The pixel aspect-ratio denominator. \\
-\bitvar{CS} & Integer & 8 & No & The color space. \\
-\bitvar{PF} & Integer & 8 & No & The pixel format. \\
-\bitvar{NOMBR} & Integer & 24 & No & The nominal bitrate of the stream, in
- bits per second. \\
-\bitvar{QUAL} & Integer & 6 & No & The quality hint. \\
-\bitvar{KFGSHIFT} & Integer & 5 & No & The amount to shift the key frame
- number by in the granule position. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:} None.
-\medskip
-
-The identification header is a short header with only a few fields used to
- declare the stream definitively as Theora and provide detailed information
- about the format of the fully decoded video data.
-The identification header is decoded as follows:
-
-\begin{enumerate}
-\item
-Decode the common header fields according to the procedure described in
- Section~\ref{sub:common-header}.
-If \bitvar{HEADERTYPE} returned by this procedure is not \hex{80}, then stop.
-This packet is not the identification header.
-\item
-Read an 8-bit unsigned integer as \bitvar{VMAJ}.
-If \bitvar{VMAJ} is not $3$, then stop.
-This stream is not decodable according to this specification.
-\item
-Read an 8-bit unsigned integer as \bitvar{VMIN}.
-If \bitvar{VMIN} is not $2$, then stop.
-This stream is not decodable according to this specification.
-\item
-Read an 8-bit unsigned integer as \bitvar{VREV}.
-If \bitvar{VREV} is not $0$, then stop.
-This stream is not decodable according to this specification.
-\item
-Read a 16-bit unsigned integer as \bitvar{FMBW}.
-This MUST be greater than zero.
-This specifies the width of the coded frame in macro blocks.
-The actual width of the frame in pixels is $\bitvar{FMBW}*16$.
-\item
-Read a 16-bit unsigned integer as \bitvar{FMBH}.
-This MUST be greater than zero.
-This specifies the height of the coded frame in macro blocks.
-The actual height of the frame in pixels is $\bitvar{FMBH}*16$.
-\item
-Read a 24-bit unsigned integer as \bitvar{PICW}.
-This MUST be no greater than $(\bitvar{FMBW}*16)$.
-Note that 24 bits are read, even though only 20 bits are sufficient to specify
- any value of the picture width.
-This is done to preserve octet alignment in this header, to allow for a
- simplified parser implementation.
-\item
-Read a 24-bit unsigned integer as \bitvar{PICH}.
-This MUST be no greater than $(\bitvar{FMBH}*16)$.
-Together with \bitvar{PICW}, this specifies the size of the displayable picture
- region within the coded frame.
-See Figure~\ref{fig:pic-frame}.
-Again, 24 bits are read instead of 20.
-\item
-Read an 8-bit unsigned integer as \bitvar{PICX}.
-This MUST be no greater than $(\bitvar{FMBW}*16-\bitvar{PICX})$.
-\item
-Read an 8-bit unsigned integer as \bitvar{PICY}.
-This MUST be no greater than $(\bitvar{FMBH}*16-\bitvar{PICY})$.
-Together with \bitvar{PICX}, this specifies the location of the lower-left
- corner of the displayable picture region.
-See Figure~\ref{fig:pic-frame}.
-\item
-Read a 32-bit unsigned integer as \bitvar{FRN}.
-This MUST be greater than zero.
-\item
-Read a 32-bit unsigned integer as \bitvar{FRD}.
-This MUST be greater than zero.
-Theora is a fixed-frame rate video codec.
-Frames are sampled at the constant rate of $\frac{\bitvar{FRN}}{\bitvar{FRD}}$
- frames per second.
-The presentation time of the first frame is at zero seconds.
-No mechanism is provided to specify a non-zero offset for the initial
- frame.
-\item
-Read a 24-bit unsigned integer as \bitvar{PARN}.
-\item
-Read a 24-bit unsigned integer as \bitvar{PRAD}.
-Together with \bitvar{PARN}, these specify the aspect ratio of the pixels
- within a frame, defined as the ratio of the physical width of a pixel to its
- physical height.
-This is given by the ratio $\bitvar{PARN}:\bitvar{PARD}$.
-Either of these fields MAY be zero, in which case the pixel aspect ratio
- defaults to $1:1$.
-\item
-Read an 8-bit unsigned integer as \bitvar{CS}.
-This is a value from an enumerated list of the available color spaces, given in
- Table~\ref{tab:colorspaces}.
-The `Undefined' value indicates that color space information was not available
- to the encoder.
-It MAY be specified by the application via an external means.
-If a reserved value is given, a decoder MAY refuse to decode the stream.
-\begin{table}[htb]
-\begin{center}
-\begin{tabular*}{215pt}{cl@{\extracolsep{\fill}}c}\toprule
-Value & Color Space \\\midrule
-$0$ & Undefined. \\
-$1$ & Rec.~470M (see Section~\ref{sec:470m}). \\
-$2$ & Rec.~470BG (see Section~\ref{sec:470bg}). \\
-$3$ & Reserved. \\
-$\vdots$ & \\
-$255$ & \\
-\bottomrule\end{tabular*}
-\end{center}
-\caption{Enumerated List of Color Spaces}
-\label{tab:colorspaces}
-\end{table}
-\item
-Read a 24-bit unsigned integer as \bitvar{NOMBR}.
-The \bitvar{NOMBR} field is used only as a hint.
-For pure VBR streams, this value may be considerably off.
-The field MAY be set to zero to indicate that the encoder did not care to
- speculate.
-\item
-Read a 6-bit unsigned integer as \bitvar{QUAL}.
-This value is used to provide a hint as to the relative quality of the stream
- when compared to others produced by the same encoder.
-Larger values indicate higher quality.
-This can be used, for example, to select among several streams containing the
- same material encoded with different settings.
-\item
-Read a 5-bit unsigned integer as \bitvar{KFGSHIFT}.
-The \bitvar{KFGSHIFT} is used to partition the granule position associated with
- each packet into two different parts.
-The frame number of the last key frame, starting from zero, is stored in the
- upper $64-\bitvar{KFGSHIFT}$ bits, while the lower \bitvar{KFGSHIFT} bits
- contain the number of frames since the last keyframe.
-Complete details on the granule position mapping are specified in Section~REF.
-\item
-Read a 2-bit unsigned integer as \bitvar{PF}.
-The \bitvar{PF} field contains a value from an enumerated list of the available
- pixel formats, given in Table~\ref{tab:pixel-formats}.
-If the reserved value $1$ is given, stop.
-This stream is not decodable according to this specification.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular*}{215pt}{cl@{\extracolsep{\fill}}c}\toprule
-Value & Pixel Format \\\midrule
-$0$ & 4:2:0 (see Section~\ref{sec:420}). \\
-$1$ & Reserved. \\
-$2$ & 4:2:2 (see Section~\ref{sec:422}). \\
-$3$ & 4:4:4 (see Section~\ref{sec:444}). \\
-\bottomrule\end{tabular*}
-\end{center}
-\caption{Enumerated List of Pixel Formats}
-\label{tab:pixel-formats}
-\end{table}
-
-\item
-Read a 3-bit unsigned integer.
-These bits are reserved.
-If this value is not zero, then stop.
-This stream is not decodable according to this specification.
-\item
-Assign \bitvar{NSBS} a value according to \bitvar{PF}, as given by
- Table~\ref{tab:nsbs-for-pf}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cc}\toprule
-\bitvar{PF} & \bitvar{NSBS} \\\midrule
-$0$ & $\begin{aligned}
-&((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)\\
-& +2*((\bitvar{FMBW}+3)//4)*((\bitvar{FMBH}+3)//4)
-\end{aligned}$ \\\midrule
-$2$ & $\begin{aligned}
-&((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)\\
-& +2*((\bitvar{FMBW}+3)//4)*((\bitvar{FMBH}+1)//2)
-\end{aligned}$ \\\midrule
-$3$ & $3*((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Number of Super Blocks for each Pixel Format}
-\label{tab:nsbs-for-pf}
-\end{table}
-
-\item
-Assign \bitvar{NBS} a value according to \bitvar{PF}, as given by
- Table~\ref{tab:nbs-for-pf}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cc}\toprule
-\bitvar{PF} & \bitvar{NBS} \\\midrule
-$0$ & $6*\bitvar{FMBW}*\bitvar{FMBH}$ \\\midrule
-$2$ & $8*\bitvar{FMBW}*\bitvar{FMBH}$ \\\midrule
-$3$ & $12*\bitvar{FMBW}*\bitvar{FMBH}$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Number of Super Blocks for each Pixel Format}
-\label{tab:nbs-for-pf}
-\end{table}
-
-\item
-Assign \bitvar{NMBS} the value $(\bitvar{FMBW}*\bitvar{FMBH})$.
-
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-VP3 does not correctly handle frame sizes that are not a multiple of 16.
-Thus, \bitvar{PICW} and \bitvar{PICH} should be set to the frame width and
- height in pixels, respectively, and \bitvar{PICX} and \bitvar{PICY} should be
- set to zero.
-VP3 headers do not specify a color space.
-VP3 only supports the 4:2:0 pixel format.
-
-\section{Comment Header}
-\label{sec:commentheader}
-
-The Theora comment header is the second of three header packets that begin a
- Theora stream.
-It is meant for short text comments, not aribtrary metadata; arbitrary metadata
- belongs in a separate logical stream that provides greater structure and
- machine parseability.
-
-%r: I tried to morph this a little more in the direction of our application space
-The comment field is meant to be used much like someone jotting a quick note on
- the label of a video.
-It should be a little information to remember the disc or tape by and explain it to
- others; a short, to-the-point text note that can be more than 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, e.g.:
-
-%TODO: Example
-
-The comment header is stored as a logical list of eight-bit clean vectors; the
- number of vectors is bounded at $2^{32}-1$ and the length of each vector is
- limited to $2^{32}-1$ 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 a vendor name,
- also eight-bit clean with a length encoded in 32 bits.
-%TODO: The 1.0 release of libtheora sets the vendor string to ...
-
-\subsection{Comment Length Decode}
-\label{sub:comment-len}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{LEN} & Integer & 32 & No & A single 32-bit length value. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{LEN0} & Integer & 8 & No & The first octet of the string length. \\
-\locvar{LEN1} & Integer & 8 & No & The second octet of the string length. \\
-\locvar{LEN2} & Integer & 8 & No & The third octet of the string length. \\
-\locvar{LEN3} & Integer & 8 & No & The fourth octet of the string
- length. \\
-\bottomrule\end{tabularx}
-\medskip
-
-A single comment vector is decoded as follows:
-
-\begin{enumerate}
-\item
-Read an 8-bit unsigned integer as \locvar{LEN0}.
-\item
-Read an 8-bit unsigned integer as \locvar{LEN1}.
-\item
-Read an 8-bit unsigned integer as \locvar{LEN2}.
-\item
-Read an 8-bit unsigned integer as \locvar{LEN3}.
-\item
-Assign \bitvar{LEN} the value $(\locvar{LEN0}+(\locvar{LEN1}<<8)+
- (\locvar{LEN2}<<16)+(\locvar{LEN3}<<24))$.
-This construction is used so that on platforms with 8-bit bytes, the memory
- organization of the comment header is identical with that of Vorbis I,
- allowing for common parsing code despite the different bit packing
- conventions.
-\end{enumerate}
-
-\subsection{Comment Header Decode}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{VENDOR} & \multicolumn{3}{l}{String} & The vendor string. \\
-\bitvar{NCOMMENTS} & Integer & 32 & No & The number of user
- comments. \\
-\bitvar{COMMENTS} & \multicolumn{3}{l}{String Array} & A list of
- \bitvar{NCOMMENTS} user comment values. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{\ci} & Integer & 32 & No & The index of the current user
- comment. \\
-\bottomrule\end{tabularx}
-\medskip
-
-The complete comment header is decoded as follows:
-
-\begin{enumerate}
-\item
-Decode the common header fields according to the procedure described in
- Section~\ref{sub:common-header}.
-If \bitvar{HEADERTYPE} returned by this procedure is not \hex{81}, then stop.
-This packet is not the comment header.
-\item
-Decode the length of the vendor string using the procedure given in
- Section~\ref{sub:comment-len} into \bitvar{LEN}.
-\item
-Read \bitvar{LEN} 8-bit unsigned integers.
-\item
-Set the string \bitvar{VENDOR} to the contents of these octets.
-\item
-Decode the number of user comments using the procedure given in
- Section~\ref{sub:comment-len} into \bitvar{LEN}.
-\item
-Assign \bitvar{NCOMMENTS} the value stored in \bitvar{LEN}.
-\item
-For each consecutive value of \locvar{\ci} from $0$ to
- $(\bitvar{NCOMMENTS}-1)$, inclusive:
-\begin{enumerate}
-\item
-Decode the length of the current user comment using the procedure given in
- Section~\ref{sub:comment-len} into \bitvar{LEN}.
-\item
-Read \bitvar{LEN} 8-bit unsigned integers.
-\item
-Set the string $\bitvar{COMMENTS}[\locvar{\ci}]$ to the contents of these
- octets.
-\end{enumerate}
-\end{enumerate}
-
-The comment header comprises the entirety of the second header packet.
-Unlike the first header packet, it is not generally the only packet on the
- second page and may span multiple pages.
-The length of the comment header packet is (practically) unbounded.
-The comment header packet is not optional; it must be present in the stream
- even if it is logically empty.
-
-%TODO: \paragraph{VP3 Compatibility}
-
-\subsection{User Comment Format}
-
-The user 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:
-\begin{center}
-\begin{tabular}{rcl}
-$\bitvar{COMMENTS}[0]$ & = & ``TITLE=the look of Theora" \\
-$\bitvar{COMMENTS}[1]$ & = & ``DIRECTOR=me"
-\end{tabular}
-\end{center}
-
-The field name is case-insensitive and MUST consist of ASCII characters
- \hex{20} through \hex{7D}, \hex{3D} (`=') excluded.
-ASCII \hex{41} through \hex{5A} inclusive (characters `A'--`Z') are to be
- considered equivalent to ASCII \hex{61} through \hex{7A} inclusive
- (characters `a'--`z').
-An entirely empty field name---one that is zero characters long---is not
- disallowed.
-
-The field name is immediately followed by ASCII \hex{3D} (`='); this equals
- sign is used to terminate the field name.
-
-The data immediately after \hex{3D} until the end of the vector is the eight-bit
- clean value of the field contents encoded as a UTF-8 string.
-%TODO: Cite UTF-8 standard.
-
-Field names MUST NOT be `internationalized'; this is a concession to
- simplicity, not an attempt to exclude the majority of the world that doesn't
- speak English.
-Applications MAY wish to present internationalized versions of the standard
- field names listed below to the user, but they are not to be stored in the
- bitstream.
-Field {\em contents}, however, use the UTF-8 character encoding to allow easy
- representation of any language.
-
-Individual `vendors' MAY use non-standard field names within reason.
-The proper use of comment fields as human-readable notes has already been
- explained.
-Abuse will be discouraged.
-
-There is no vendor-specific prefix to `non-standard' field names.
-Vendors SHOULD make some effort to avoid arbitrarily polluting the common
- namespace.
-%"and other bodies"?
-%If you're going to be that vague, you might as well not say anything at all.
-Xiph.org and other bodies will generally collect and rationalize the more
- useful tags to help with standardization.
-
-Field names are not restricted to occur only once within a comment header.
-%TODO: Example
-
-\paragraph{Field Names}
-
-Below is a proposed, minimal list of standard field names with a description of
- their intended use.
-No field names are mandatory; a comment header may contain one or more, all, or
- none of the names in this list.
-
-\begin{description}
-\item{TITLE:} Video name.
-%TODO: Complete list
-\end{description}
-
-\section{Setup Header}
-\label{sec:setupheader}
-
-The Theora setup header contains the limit values used to drive the loop
- filter, the base matrices and scale values used to build the dequantization
- tables, and the Huffman tables used to unpack the DCT tokens.
-Because the contents of this header are specific to Theora, no concessions have
- been made to keep the fields octet-aligned for easy parsing.
-
-\subsection{Loop Filter Limit Table Decode}
-\label{sub:loop-filter-limits}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{LFLIMS} & \multicolumn{1}{p{40pt}}{Integer array} &
- 7 & No & A 64-element array of loop filter limit
- values. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{\qi} & Integer & 6 & No & The quantization index. \\
-\locvar{NBITS} & Integer & 3 & No & The size of values being read in the
- current table. \\
-\bottomrule\end{tabularx}
-\medskip
-
-This procedure decodes the table of loop filter limit values used to drive the
- loop filter, which is described in Section~REF.
-It is decoded as follows:
-
-\begin{enumerate}
-\item
-Read a 3-bit unsigned integer as \locvar{NBITS}.
-\item
-For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
-\begin{enumerate}
-\item
-Read an \locvar{NBITS}-bit unsigned integer as $\bitvar{LFLIMS}[\locvar{\qi}]$.
-\end{enumerate}
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-The loop filter limit values are hardcoded in VP3.
-The values used are given in Appendix~REF.
-
-\subsection{Quantization Parameters Decode}
-\label{sub:quant-params}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- AC coefficients for each \qi\ value. \\
-\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- the DC coefficient for each \qi\ value. \\
-\bitvar{NBMS} & Integer & 10 & No & The number of base matrices. \\
-\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 8 & No & A $\bitvar{NBMS}\times 64$ array
- containing the base matrices. \\
-\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 6 & No & A $2\times 3$ array containing the
- number of quant ranges for a given \qti\ and \pli, respectively.
-This is at most $63$. \\
-\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 6 & No & A $2\times 3\times 63$ array of the
- sizes of each quant range for a given \qti\ and \pli, respectively.
-Only the first $\bitvar{NQRS}[\qti][\pli]$ values are used. \\
-\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 9 & No & A $2\times 3\times 64$ array of the
- \bmi's used for each quant range for a given \qti\ and \pli, respectively.
-Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values are used. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{\qti} & Integer & 1 & No & A quantization type index.
-See Table~\ref{tab:quant-types}.\\
-\locvar{\qtj} & Integer & 1 & No & A quantization type index. \\
-\locvar{\pli} & Integer & 2 & No & A color plane index.
-See Table~\ref{tab:color-planes}.\\
-\locvar{\plj} & Integer & 2 & No & A color plane index. \\
-\locvar{\qi} & Integer & 6 & No & The quantization index. \\
-\locvar{\ci} & Integer & 6 & No & The DCT coefficient index. \\
-\locvar{\bmi} & Integer & 9 & No & The base matrix index. \\
-\locvar{\qri} & Integer & 6 & No & The quant range index. \\
-\locvar{NBITS} & Integer & 5 & No & The size of fields to read. \\
-\locvar{NEWQR} & Integer & 1 & No & Flag that indicates a new set of quant
- ranges will be defined. \\
-\locvar{RPQR} & Integer & 1 & No & Flag that indicates the quant ranges to
- copy will come from the same color plane. \\
-\bottomrule\end{tabularx}
-\medskip
-
-The AC scale and DC scale values are defined in two simple tables with 64
- values each, one for each \qi\ value.
-The same scale values are used for every quantization type and color plane.
-
-The base matrices for all quantization types and color planes are stored in a
- single table.
-These are then referenced by index in several sets of \term{quant ranges}.
-The purpose of the quant ranges is to specify which base matrices are used for
- which \qi\ values.
-
-A set of quant ranges is defined for each quantization type and color plane.
-To save space in the header, bit flags allow a set of quant ranges to be copied
- from a previously defined set instead of being specified explicitly.
-Every set except the first one can be copied from the immediately preceding
- set.
-Similarly, if the quantization type is not $0$, the set can be copied from the
- set defined for the same color plane for the preceding quantization type.
-This formulation allows compact representation of, for example, the same
- set of quant ranges to be used for both chroma channels, as was done in
- the original VP3, or the same set of quant ranges to be used for INTRA
- and INTER modes.
-
-Each quant range is defined by a size and two base matrix indices, one for each
- end of the range.
-The base matrix for the end of one range is used as the start of the next
- range, so that for $n$ ranges, $n+1$ base matrices are specified.
-The base matrices for the \qi\ values between the two endpoints of the range
- are generated by linear interpolation.
-
-%TODO: figure
-
-The location of the endpoints of each range is encoded by their size.
-The \qi\ value for the left end-point is the sum of the sizes of all preceding
- ranges, and the \qi\ value for the right end-point adds the size of the
- current range.
-Thus the sum of the sizes of all the ranges MUST be 63, so that the last range
- falls on the last possible \qi\ value.
-
-The complete set of quantization parameters are decoded as follows:
-
-\begin{enumerate}
-\item
-Read a 4-bit unsigned integer.
-Assign \locvar{NBITS} the value read, plus one.
-\item
-For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
-\begin{enumerate}
-\item
-Read an \locvar{NBITS}-bit unsigned integer as
- $\bitvar{ACSCALE}[\locvar{\qi}]$.
-\end{enumerate}
-\item
-Read a 4-bit unsigned integer.
-Assign \locvar{NBITS} the value read, plus one.
-\item
-For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
-\begin{enumerate}
-\item
-Read an \locvar{NBITS}-bit unsigned integer as
- $\bitvar{DCSCALE}[\locvar{\qi}]$.
-\end{enumerate}
-\item
-Read a 9-bit unsigned integer.
-Assign \bitvar{NBMS} the value decoded, plus one.
-\bitvar{NBMS} MUST be no greater than 384.
-\item
-For each consecutive value of \locvar{\bmi} from $0$ to $(\bitvar{NBMS}-1)$,
- inclusive:
-\begin{enumerate}
-\item
-For each consecutive value of \locvar{\ci} from $0$ to $63$, inclusive:
-\begin{enumerate}
-\item
-Read an 8-bit unsigned integer as $\bitvar{BMS}[\locvar{\bmi}][\locvar{\ci}]$.
-\end{enumerate}
-\end{enumerate}
-\item
-For each consecutive value of \locvar{\qti} from $0$ to $1$, inclusive:
-\begin{enumerate}
-\item
-For each consecutive value of \locvar{\pli} from $0$ to $2$, inclusive:
-\begin{enumerate}
-\item
-If $\locvar{\qti}>0$ or $\locvar{\pli}>0$, read a 1-bit unsigned integer as
- \locvar{NEWQR}.
-\item
-Else, assign \locvar{NEWQR} the value one.
-\item
-If \locvar{NEWQR} is zero, then we are copying a previously defined set of
- quant ranges.
-In that case:
-\begin{enumerate}
-\item
-If $\locvar{\qti}>0$, read a 1-bit unsigned integer as \locvar{RPQR}.
-\item
-Else, assign \locvar{RPQR} the value zero.
-\item
-If \locvar{RPQR} is one, assign \locvar{\qtj} the value $(\locvar{\qti}-1)$
- and assign \locvar{\plj} the value \locvar{\pli}.
-This selects the set of quant ranges defined for the same color plane as this
- one, but for the previous quantization type.
-\item
-Else assign \locvar{\qtj} the value $(3*\locvar{\qti}+\locvar{\pli}-1)//3$ and
- assign \locvar{\plj} the value $(\locvar{\pli}+2)\%3$.
-This selects the most recent set of quant ranges defined.
-\item
-Assign $\bitvar{NQRS}[\locvar{\qti}][\locvar{\pli}]$ the value
- $\bitvar{NQRS}[\locvar{\qtj}][\locvar{\plj}]$.
-\item
-Assign $\bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}]$ the values in
- $\bitvar{QRSIZES}[\locvar{\qtj}][\locvar{\plj}]$.
-\item
-Assign $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}]$ the values in
- $\bitvar{QRBMIS}[\locvar{\qtj}][\locvar{\plj}]$.
-\end{enumerate}
-\item
-Else, \locvar{NEWQR} is one, which indicates that we are defining a new set of
- quant ranges.
-In that case:
-\begin{enumerate}
-\item
-Assign $\locvar{\qri}$ the value zero.
-\item
-Assign $\locvar{\qi}$ the value zero.
-\item
-Read an $\ilog(\bitvar{NBMS}-1)$-bit unsigned integer as\\
- $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
-If this is greater than or equal to \bitvar{NBMS}, stop.
-The stream is undecodable.
-\item
-\label{step:qr-loop}
-Read an $\ilog(63-\locvar{\qi})$-bit unsigned integer.
-Assign\\ $\bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$ the value
- read, plus one.
-\item
-Assign \locvar{\qi} the value $\locvar{\qi}+
- \bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
-\item
-Assign \locvar{\qri} the value $\locvar{\qri}+1$.
-\item
-Read an $\ilog(\bitvar{NBMS}-1)$-bit unsigned integer as\\
- $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
-\item
-If \locvar{\qi} is less than 63, go back to step~\ref{step:qr-loop}.
-\item
-If \locvar{\qi} is greater than 63, stop.
-The stream is undecodable.
-\item
-Assign $\bitvar{NQRS}[\locvar{\qti}][\locvar{\pli}]$ the value \locvar{\qri}.
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-The quantization parameters are hardcoded in VP3.
-The values used are given in Appendix~REF.
-
-\subsection{Computing a Quantization Matrix}
-\label{sub:quant-mat}
-
-\paragraph{Input parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- AC coefficients for each \qi\ value. \\
-\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- the DC coefficient for each \qi\ value. \\
-\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 8 & No & A $\bitvar{NBMS}\times 64$ array
- containing the base matrices. \\
-\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 6 & No & A $2\times 3$ array containing the
- number of quant ranges for a given \qti\ and \pli, respectively.
-This is at most $63$. \\
-\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 6 & No & A $2\times 3\times 63$ array of the
- sizes of each quant range for a given \qti\ and \pli, respectively.
-Only the first $\bitvar{NQRS}[\qti][\pli]$ values are used. \\
-\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 9 & No & A $2\times 3\times 64$ array of the
- \bmi's used for each quant range for a given \qti\ and \pli, respectively.
-Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values are used. \\
-\bitvar{\qti} & Integer & 1 & No & A quantization type index.
-See Table~\ref{tab:quant-types}.\\
-\bitvar{\pli} & Integer & 2 & No & A color plane index.
-See Table~\ref{tab:color-planes}.\\
-\bitvar{\qi} & Integer & 6 & No & The quantization index. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{QMAT} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of quantization
- values for each DCT coefficient. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{\ci} & Integer & 6 & No & The DCT coefficient index. \\
-\locvar{\bmi} & Integer & 9 & No & The base matrix index. \\
-\locvar{\bmj} & Integer & 9 & No & The base matrix index. \\
-\locvar{\qri} & Integer & 6 & No & The quant range index. \\
-\locvar{QISTART} & Integer & 6 & No & The left end-point of the \qi\ range. \\
-\locvar{QIEND } & Integer & 6 & No & The right end-point of the \qi\ range. \\
-\locvar{BM} & \multicolumn{1}{p{40pt}}{Integer array} &
- 8 & No & A 64-element array containing the
- interpolated base matrix. \\
-\locvar{QMIN} & Integer & 16 & No & The minimum quantization value allowed
- for the current coefficient. \\
-\locvar{QSCALE} & Integer & 16 & No & The current scale value. \\
-\bottomrule\end{tabularx}
-\medskip
-
-The following procedure can be used to generate a single quantization matrix
- for a given quantization type, color plane, and \qi\ value, given the
- quantization parameters decoded in Section~\ref{sub:quant-params}.
-
-Note that the product of the scale value and the base matrix value is in units
- of $100$ths of a pixel value, and thus is divided by $100$ to return it to
- units of a single pixel value.
-This value is then scaled by four, to match the scaling of the DCT output,
- which is also a factor of four larger than the orthonormal version of the
- transform.
-
-\begin{enumerate}
-\item
-Assign \locvar{\qri} the index of a quant range such that
-\begin{displaymath}
-\sum_{\qrj=0}^{\locvar{\qri}-1}
- \bitvar{\qi} \ge \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj],
-\end{displaymath}
- and
-\begin{displaymath}
-\sum_{\qrj=0}^{\locvar{\qri}}
- \bitvar{\qi} \le \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj],
-\end{displaymath}
- where summation from $0$ to $-1$ is zero.
-If there is more than one such value of $\locvar{\qri}$, i.e., if \bitvar{\qi}
- lies on the end point of a quant range, then which one is used is immaterial.
-\item
-Assign \locvar{QISTART} the value
-\begin{displaymath}
-\sum_{\qrj=0}^{\qri-1} \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj].
-\end{displaymath}
-\item
-Assign \locvar{QIEND} the value
-\begin{displaymath}
-\sum_{\qrj=0}^{\qri} \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj].
-\end{displaymath}
-\item
-Assign \locvar{\bmi} the value
- $\bitvar{QRBMIS}[\bitvar{\qti}][\bitvar{\pli}][\qri]$.
-\item
-Assign \locvar{\bmj} the value
- $\bitvar{QRBMIS}[\bitvar{\qti}][\bitvar{\pli}][\qri+1]$.
-\item
-For each consecutive value of \locvar{\ci} from $0$ to $63$, inclusive:
-\begin{enumerate}
-\item
-Assign $\locvar{BM}[\locvar{\ci}]$ the value
-\begin{displaymath}
-\begin{split}
-(&2*(\locvar{QIEND}-\bitvar{\qi})*\bitvar{BMS}[\locvar{\bmi}][\locvar{\ci}]\\
- &+2*(\bitvar{\qi}-
- \locvar{QISTART})*\bitvar{BMS}[\locvar{\bmj}][\locvar{\ci}]\\
- &+\bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\locvar{\qri}])//
- (2*\bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\locvar{\qri}])
-\end{split}
-\end{displaymath}
-\item
-Assign \locvar{QMIN} the value given by Table~\ref{tab:qmin} according to
- \bitvar{\qti} and \locvar{\ci}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{ccr}\toprule
-Coefficient & \bitvar{\qti} & \locvar{QMIN} \\\midrule
-$\locvar{\ci}=0$ & $0$ & $16$ \\
-$\locvar{\ci}>0$ & $0$ & $8$ \\
-$\locvar{\ci}=0$ & $1$ & $32$ \\
-$\locvar{\ci}>0$ & $1$ & $16$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Minimum Quantization Values}
-\label{tab:qmin}
-\end{table}
-
-\item
-If \locvar{\ci} equals zero, assign $\locvar{QSCALE}$ the value
- $\bitvar{DCSCALE}[\bitvar{\qi}]$.
-\item
-Else, assign $\locvar{QSCALE}$ the value
- $\bitvar{ACSCALE}[\bitvar{\qi}]$.
-\item
-Assign $\bitvar{QMAT}[\locvar{\ci}]$ the value
-\begin{displaymath}
-\max(\locvar{QMIN},
- \min((\locvar{QSCALE}*\locvar{BM}[\locvar{\ci}]//100)*4,4096)).
-\end{displaymath}
-\end{enumerate}
-\end{enumerate}
-
-\subsection{DCT Token Huffman Tables}
-\label{sub:huffman-tables}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{HTS} & \multicolumn{3}{l}{Huffman table array}
- & An 80-element array of Huffman tables
- with up to 32 entries each. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{HBITS} & Bit string & 32 & No & A string of up to 32 bits. \\
-\locvar{TOKEN} & Integer & 5 & No & A single DCT token value. \\
-\locvar{ISLEAF} & Integer & 1 & No & Flag that indicates if the current
- node of the tree being decoded is a leaf node. \\
-\bottomrule\end{tabularx}
-\medskip
-
-The Huffman tables used to decode DCT tokens are stored in the setup header in
- the form of a binary tree.
-This enforces the requirements that the code be full---so that any sequence of
- bits will produce a valid sequence of tokens---and that the code be
- prefix-free so that there is no ambiguity when decoding.
-
-One more restriction is placed on the tables that is not explicitly enforced by
- the bitstream syntax, but nevertheless must be obeyed by compliant encoders.
-There must be no more than 32 entries in a single table.
-Note that this restriction along with the fullness requirement limit the
- maximum size of a single Huffman code to 32 bits.
-It is probably a good idea to enforce this latter consequence explicitly when
- implementing the decoding procedure as a recursive algorithm, so as to prevent
- a possible stack overflow given an invalid bitstream.
-
-Although there are 32 different DCT tokens, and thus a normal table will have
- exactly 32 entries, this is not explicitly required.
-It is allowable to use a Huffman code that omits some---but not all---of the
- possible token values.
-It is also allowable, if not particularly useful, to specify multiple codes for
- the same token value in a single table.
-
-The tree is decoded as follows:
-
-\begin{enumerate}
-\item
-For each consecutive value of \locvar{\hti} from $0$ to $80$, inclusive:
-\begin{enumerate}
-\item
-Set \locvar{HBITS} to the empty string.
-\item
-\label{step:huff-tree-loop}
-If \locvar{HBITS} is longer than 32 bits in length, stop.
-The stream is undecodable.
-\item
-Read a 1-bit unsigned integer as \locvar{ISLEAF}.
-\item
-If \locvar{ISLEAF} is one:
-\begin{enumerate}
-\item
-If the number of entries in table $\bitvar{HTS}[\locvar{\hti}]$ is already 32,
- stop.
-The stream is undecodable.
-\item
-Read a 5-bit unsigned integer as \locvar{TOKEN}.
-\item
-Add the pair $(\locvar{HBITS},\locvar{TOKEN})$ to Huffman table
- $\bitvar{HTS}[\locvar{\hti}]$.
-\end{enumerate}
-\item
-Otherwise:
-\begin{enumerate}
-\item
-Add a `0' to the end of \locvar{HBITS}.
-\item
-Decode the `0' sub-tree using this procedure, starting from
- step~\ref{step:huff-tree-loop}.
-\item
-Remove the `0' from the end of \locvar{HBITS} and add a `1' to the end of
- \locvar{HBITS}.
-\item
-Decode the `1' sub-tree using this procedure, starting from
- step~\ref{step:huff-tree-loop}.
-\item
-Remove the `1' from the end of \locvar{HBITS}.
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-The DCT token Huffman tables are hardcoded in VP3.
-The values used are given in Appendix~REF.
-
-\subsection{Setup Header Decode}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{LFLIMS} & \multicolumn{1}{p{40pt}}{Integer array} &
- 7 & No & A 64-element array of loop filter limit
- values. \\
-\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- AC coefficients for each \qi\ value. \\
-\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
- 16 & No & A 64-element array of scale values for
- the DC coefficient for each \qi\ value. \\
-\bitvar{NBMS} & Integer & 10 & No & The number of base matrices. \\
-\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 8 & No & A $\bitvar{NBMS}\times 64$ array
- containing the base matrices. \\
-\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
- 6 & No & A $2\times 3$ array containing the
- number of quant ranges for a given \qti\ and \pli, respectively.
-This is at most $63$. \\
-\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 6 & No & A $2\times 3\times 63$ array of the
- sizes of each quant range for a given \qti\ and \pli, respectively.
-Only the first $\bitvar{NQRS}[\qti][\pli]$ values will be used. \\
-\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
- 9 & No & A $2\times 3\times 64$ array of the
- \bmi's used for each quant range for a given \qti\ and \pli, respectively.
-Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values will be used. \\
-\bitvar{HTS} & \multicolumn{3}{l}{Huffman table array}
- & An 80-element array of Huffman tables
- with up to 32 entries each. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:} None.
-\medskip
-
-The complete setup header is decoded as follows:
-
-\begin{enumerate}
-\item
-Decode the common header fields according to the procedure described in
- Section~\ref{sub:common-header}.
-If \bitvar{HEADERTYPE} returned by this procedure is not \hex{82}, then stop.
-This packet is not the setup header.
-\item
-Decode the loop filter limit value table using the procedure given in
- Section~\ref{sub:loop-filter-limits} into \bitvar{LFLIMS}.
-\item
-Decode the quantization parameters using the procedure given in
- Section~\ref{sub:quant-params}.
-The results are stored in \bitvar{ACSCALE}, \bitvar{DCSCALE}, \bitvar{NBMS},
- \bitvar{BMS}, \bitvar{NQRS}, \bitvar{QRSIZES}, and \bitvar{QRBMIS}.
-\item
-Decode the DCT token Huffman tables using the procedure given in
- Section~\ref{sub:huffman-tables} into \bitvar{HTS}.
-\end{enumerate}
-
-\chapter{Frame Decode}
-
-This section describes the complete procedure necessary to decode a single
- frame.
-This begins with the frame header, followed by coded block flags, macro block
- modes, motion vectors, block-level \qi\ values, and finally the DCT residual
- tokens, which are used to reconstruct the frame.
-
-\section{Frame Header Decode}
-\label{sub:frame-header}
-
-\paragraph{Input parameters:} None.
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
-\bitvar{NQIS} & Integer & 2 & No & The number of \qi\ values. \\
-\bitvar{QIS} & \multicolumn{1}{p{40pt}}{Integer array} &
- 6 & No & An \bitvar{NQIS}-element array of
- \qi\ values. \\
-\bitvar{MOREQIS} & Integer & 1 & No & A flag indicating there are more
- \qi\ values to be decoded. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{MOREQIS} & Integer & 1 & No & A flag indicating there are more
- \qi\ values to be decoded. \\
-\bottomrule\end{tabularx}
-\medskip
-
-The frame header selects which type of frame is being decoded, intra or inter,
- and contains the list of \qi\ values that will be used in this frame.
-The first \qi\ value will be used for {\em all} DC coefficients in all blocks.
-This is done to ensure that DC prediction, which is done in the quantized
- domain, works as expected.
-The AC coefficients, however, can be dequantized using any \qi\ value on the
- list, selected on a block-by-block basis.
-
-\begin{enumerate}
-\item
-Read a 1-bit unsigned integer.
-If the value read is not zero, stop.
-This is not a data packet.
-\item
-Read a 1-bit unsigned integer as \bitvar{FTYPE}.
-This is the type of frame being decoded, as given in
- Table~\ref{tab:frame-type}.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cl}\toprule
-\bitvar{FTYPE} & Frame Type \\\midrule
-$0$ & Intra frame \\
-$1$ & Inter frame \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Frame Type Values}
-\label{tab:frame-type}
-\end{table}
-
-\item
-Read in a 6-bit unsigned integer as $\bitvar{QIS}[0]$.
-\item
-Read a 1-bit unsigned integer as \locvar{MOREQIS}.
-\item
-If \locvar{MOREQIS} is zero, set \bitvar{NQIS} to 1.
-\item
-Otherwise:
-\begin{enumerate}
-\item
-Read in a 6-bit unsigned integer as $\bitvar{QIS}[1]$.
-\item
-Read a 1-bit unsigned integer as \locvar{MOREQIS}.
-\item
-If \locvar{MOREQIS} is zero, set \bitvar{NQIS} to 2.
-\item
-Otherwise:
-\begin{enumerate}
-\item
-Read in a 6-bit unsigned integer as $\bitvar{QIS}[2]$.
-\item
-Set \bitvar{NQIS} to 3.
-\end{enumerate}
-\end{enumerate}
-\item
-If \bitvar{FTYPE} is 0, read a 3-bit unsigned integer.
-If this value is not zero, stop.
-This frame is not decodable according to this specification.
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-The precise format of the frame header is substantially different in Theora
- than in VP3.
-The original VP3 format includes a larger number of unused, reserved bits that
- are required to be zero.
-The original VP3 frame header also can contain only a single \qi\ value,
- because VP3 does not support block-level \qi\ values and uses the same
- \qi\ value for all the coefficients in a frame.
-
-\section{Run-Length Encoded Bit Strings}
-
-Two variations of run-length encoding are used to store sequences of bits for
- the block coded flags and the block-level \qi\ values.
-The procedures to decode these bit sequences are specified in the following two
- sections.
-
-\subsection{Long-Run Bit String Decode}
-\label{sub:long-run}
-
-\paragraph{Input parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{NBITS} & Integer & 36 & No & The number of bits to decode. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{BITS} & Bit string & & & The decoded bits. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{LEN} & Integer & 36 & No & The number of bits decoded so far. \\
-\locvar{BIT} & Integer & 1 & No & The value associated with the current
- run. \\
-\locvar{RLEN} & Integer & 13 & No & The length of the current run. \\
-\locvar{RBITS} & Integer & 4 & No & The number of extra bits needed to
- decode the run length. \\
-\locvar{RSTART} & Integer & 6 & No & The start of the possible run-length
- values for a given Huffman code. \\
-\locvar{ROFFS} & Integer & 12 & No & The offset from \locvar{RSTART} of the
- run-length. \\
-\bottomrule\end{tabularx}
-\medskip
-
-There is no practical limit to the number of consecutive 0's and 1's that can
- be decoded with this procedure.
-In reality, the run length is limited by the number of blocks in a single
- frame, because more will never be requested.
-A separate procedure described in Section~\ref{sub:short-run} is used when
- there is a known limit on the maximum size of the runs.
-
-For the first run, a single bit value is read, and then a Huffman-coded
- representation of a run length is decoded, and that many copies of the bit
- value are appended to the bit string.
-For each consecutive run, the value of the bit is toggled instead of being read
- from the bitstream.
-
-The only exception is if the length of the previous run was 4129, the maximum
- possible length encodable by the Huffman-coded representation.
-In this case another bit value is read from the stream, to allow for
- consecutive runs of 0's or 1's longer than this maximum.
-
-Note that in both cases---for the first run and after a run of length 4129---if
- no more bits are needed, then no bit value is read.
-
-The complete decoding procedure is as follows:
-
-\begin{enumerate}
-\item
-Assign \locvar{LEN} the value 0.
-\item
-Assign \bitvar{BITS} the empty string.
-\item
-If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
- \bitvar{BITS}.
-\item
-Read a 1-bit unsigned integer as \locvar{BIT}.
-\item
-\label{step:long-run-loop}
-Read a bit at a time until one of the Huffman codes given in
- Table~\ref{tab:long-run} is recognized.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{lrrl}\toprule
-Huffman Code & \locvar{RSTART} & \locvar{RBITS} & Run Lengths \\\midrule
-\bin{0} & $1$ & $0$ & $1$ \\
-\bin{10} & $2$ & $1$ & $2\ldots 3$ \\
-\bin{110} & $4$ & $1$ & $4\ldots 5$ \\
-\bin{1110} & $6$ & $2$ & $6\ldots 9$ \\
-\bin{11110} & $10$ & $3$ & $10\ldots 17$ \\
-\bin{111110} & $18$ & $4$ & $18\ldots 33$ \\
-\bin{111111} & $34$ & $12$ & $34\ldots 4129$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Huffman Codes for Long Run Lengths}
-\label{tab:long-run}
-\end{table}
-
-\item
-Assign \locvar{RSTART} and \locvar{RBITS} the values given in
- Table~\ref{tab:long-run} according to the Huffman code read.
-\item
-Read an \locvar{RBITS}-bit unsigned integer as \locvar{ROFFS}.
-\item
-Assign \locvar{RLEN} the value $(\locvar{RSTART}+\locvar{ROFFS})$.
-\item
-Append \locvar{RLEN} copies of \locvar{BIT} to \bitvar{BITS}.
-\item
-Add \locvar{RLEN} to the value \locvar{LEN}.
-\locvar{LEN} MUST be less than or equal to \bitvar{NBITS}.
-\item
-If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
- \bitvar{BITS}.
-\item
-If \locvar{RLEN} equals 4129, read a 1-bit unsigned integer as \locvar{BIT}.
-\item
-Otherwise, assign \locvar{BIT} the value $(1-\locvar{BIT})$.
-\item
-Continue decoding runs from step~\ref{step:long-run-loop}.
-\end{enumerate}
-
-\paragraph{VP3 Compatibility}
-
-VP3 does not read a new bit value after decoding a run length of 4129.
-This limits the maximum number of consecutive 0's or 1's to 4129 in
- VP3-compatible streams.
-For reasonable video sizes of $1920\times 1080$ or less in 4:2:0 format---the
- only format VP3 supports---this does not pose any problems because runs this
- long are not needed.
-
-\subsection{Short-Run Bit String Decode}
-\label{sub:short-run}
-
-\paragraph{Input parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{NBITS} & Integer & 36 & No & The number of bits to decode. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{BITS} & Bit string & & & The decoded bits. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{LEN} & Integer & 36 & No & The number of bits decoded so far. \\
-\locvar{BIT} & Integer & 1 & No & The value associated with the current
- run. \\
-\locvar{RLEN} & Integer & 13 & No & The length of the current run. \\
-\locvar{RBITS} & Integer & 4 & No & The number of extra bits needed to
- decode the run length. \\
-\locvar{RSTART} & Integer & 6 & No & The start of the possible run-length
- values for a given Huffman code. \\
-\locvar{ROFFS} & Integer & 12 & No & The offset from \locvar{RSTART} of the
- run-length. \\
-\bottomrule\end{tabularx}
-\medskip
-
-This procedure is similar to the procedure outlined in
- Section~\ref{sub:long-run}, except that the maximum number of consecutive 0's
- or 1's is limited to 30.
-This is the maximum run length needed when encoding a bit for each of the 16
- blocks in a super block when it is known that not all the bits in a super
- block are the same.
-
-The complete decoding procedure is as follows:
-
-\begin{enumerate}
-\item
-Assign \locvar{LEN} the value 0.
-\item
-Assign \bitvar{BITS} the empty string.
-\item
-If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
- \bitvar{BITS}.
-\item
-Read a 1-bit unsigned integer as \locvar{BIT}.
-\item
-\label{step:short-run-loop}
-Read a bit at a time until one of the Huffman codes given in
- Table~\ref{tab:short-run} is recognized.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{lrrl}\toprule
-Huffman Code & \locvar{RSTART} & \locvar{RBITS} & Run Lengths \\\midrule
-\bin{0} & $1$ & $1$ & $1\ldots 2$ \\
-\bin{10} & $3$ & $1$ & $3\ldots 4$ \\
-\bin{110} & $5$ & $1$ & $5\ldots 6$ \\
-\bin{1110} & $7$ & $2$ & $7\ldots 10$ \\
-\bin{11110} & $11$ & $2$ & $11\ldots 14$ \\
-\bin{11111} & $15$ & $4$ & $15\ldots 30$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Huffman Codes for Short Run Lengths}
-\label{tab:short-run}
-\end{table}
-
-\item
-Assign \locvar{RSTART} and \locvar{RBITS} the values given in
- Table~\ref{tab:short-run} according to the Huffman code read.
-\item
-Read an \locvar{RBITS}-bit unsigned integer as \locvar{ROFFS}.
-\item
-Assign \locvar{RLEN} the value $(\locvar{RSTART}+\locvar{ROFFS})$.
-\item
-Append \locvar{RLEN} copies of \locvar{BIT} to \bitvar{BITS}.
-\item
-Add \locvar{RLEN} to the value \locvar{LEN}.
-\locvar{LEN} MUST be less than or equal to \bitvar{NBITS}.
-\item
-If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
- \bitvar{BITS}.
-\item
-Assign \locvar{BIT} the value $(1-\locvar{BIT})$.
-\item
-Continue decoding runs from step~\ref{step:short-run-loop}.
-\end{enumerate}
-
-\section{Coded Block Flags Decode}
-\label{sub:coded-blocks}
-
-\paragraph{Input parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
-\bitvar{NSBS} & Integer & 32 & No & The total number of super blocks in a
- frame. \\
-\bitvar{NBS} & Integer & 36 & No & The total number of blocks in a
- frame. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{BCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 1 & No & An \bitvar{NBS}-element array of flags
- indicating which blocks are coded. \\
-\bitvar{NBCODED} & Integer & 36 & No & The number of coded blocks. \\
-\bitvar{NLBCODED} & Integer & 36 & No & The number of coded blocks in the luma
- plane. \\
-\bitvar{CODEDBS} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 36 & No & An \bitvar{NBCODED}-element list of the
- indices of all the coded blocks. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{NBITS} & Integer & 36 & No & The length of a bit string to decode. \\
-\locvar{BITS} & Bit string & & & A decoded set of flags. \\
-\locvar{SBPCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 1 & No & An \bitvar{NSBS}-element array of flags
- indicating whether or not each super block is partially coded. \\
-\locvar{SBFCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 1 & No & An \bitvar{NSBS}-element array of flags
- indicating whether or not each non-partially coded super block is fully
- coded. \\
-\locvar{\sbi} & Integer & 32 & No & The index of the current super
- block. \\
-\locvar{\bi} & Integer & 32 & No & The index of the current block in coded
- order. \\
-\bottomrule\end{tabularx}
-\medskip
-
-This procedure determines which blocks are coded in a given frame.
-In an intra frame, it marks blocks are coded.
-In an inter frame, however, any or all of the blocks may remain uncoded.
-
-It is important to note that flags are still decoded for any blocks which lie
- entirely outside the picture region, even though they are not displayed.
-These blocks must be faithfully reconstructed, however, because their contents
- can be used as predictors in future frames.
-
-This procedure outputs two redundant representations of the coded blocks, for
- ease of reference elsewhere in the decoding process: a list of bit flags, one
- for each block, marking it coded or not coded, and a list of the indices of
- the coded blocks, in coded order.
-These are decoded as follows:
-
-\begin{enumerate}
-\item
-Assign \bitvar{NBCODED} the value zero.
-\item
-Assign \bitvar{NLBCODED} the value zero.
-\item
-If \bitvar{FTYPE} is zero (intra frame):
-\begin{enumerate}
-\item
-For each consecutive block in coded order (see
- Section~\ref{sec:blocks-and-sbs})---indexed by \locvar{\bi}:
-\begin{enumerate}
-\item
-Assign $\bitvar{BCODED}[\locvar{\bi}]$ the value one.
-\item
-Assign $\bitvar{CODEDBS}[\bitvar{NBCODED}]$ the value \locvar{\bi}.
-\item
-Assign \bitvar{NBCODED} the value $(\bitvar{NBCODED}+1)$.
-\item
-If \locvar{\bi} is in the luma plane, assign \bitvar{NLBCODED} the value
- $(\bitvar{NLBCODED}+1)$.
-\end{enumerate}
-\end{enumerate}
-\item
-Otherwise (inter frame):
-\begin{enumerate}
-\item
-Assign \locvar{NBITS} the value \bitvar{NSBS}.
-\item
-Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
- described in Section~\ref{sub:long-run}.
-This represents the list of partially coded super blocks.
-\item
-For each consecutive super block in raster order---indexed by
- \locvar{\sbi}---remove the bit at the head of the string \locvar{BITS} and
- assign it to $\locvar{SBPCODED}[\locvar{\sbi}]$.
-\item
-Assign \locvar{NBITS} the total number of super blocks such that \\
- $\locvar{SBPCODED}[\locvar{\sbi}]$ equals zero.
-\item
-Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
- described in Section~\ref{sub:long-run}.
-This represents the list of fully coded super blocks.
-\item
-For each consecutive super block in raster order---indexed by
- \locvar{\sbi}---such that $\locvar{SBPCODED}[\locvar{\sbi}]$ equals zero,
- remove the bit at the head of the string \locvar{BITS} and assign it to
- $\locvar{SBFCODED}[\locvar{\sbi}]$.
-\item
-Assign \locvar{NBITS} the number of blocks contained in super blocks where
- $\locvar{SBPCODED}[\locvar{\sbi}]$ equals one.
-Note that this might {\em not} be equal to 16 times the number of partially
- coded super blocks, since super blocks which overlap the edge of the frame
- will have fewer than 16 blocks in them.
-\item
-Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
- described in Section~\ref{sub:short-run}.
-\item
-For each block in coded order---indexed by \locvar{\bi}:
-\begin{enumerate}
-\item
-Assign \locvar{\sbi} the index of the super block containing block
- \locvar{\bi}.
-\item
-If $\locvar{SBPCODED}[\locvar{\sbi}]$ is zero, assign
- $\bitvar{BCODED}[\locvar{\bi}]$ the value $\locvar{SBFCODED}[\locvar{\sbi}]$.
-\item
-Otherwise, remove the bit at the head of the string \locvar{BITS} and assign it
- to $\bitvar{BCODED}[\locvar{\bi}]$.
-\item
-If $\bitvar{BCODED}[\locvar{\bi}]$ is one:
-\begin{enumerate}
-\item
-Assign $\bitvar{CODEDBS}[\bitvar{NBCODED}]$ the value $\locvar{\bi}$.
-\item
-Assign \bitvar{NBCODED} the value $(\bitvar{NBCODED}+1)$.
-\item
-If \locvar{\bi} is in the luma plane, assign \bitvar{NLBCODED} the value
- $(\bitvar{NLBCODED}+1)$.
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-
-\section{Macro Block Coding Modes}
-
-\paragraph{Input parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
-\bitvar{NMBS} & Integer & 32 & No & The total number of macro blocks in a
- frame. \\
-\bitvar{BCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 1 & No & An \bitvar{NBS}-element array of flags
- indicating which blocks are coded. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Output parameters:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\bitvar{MBMODES} & \multicolumn{1}{p{40pt}}{Integer Array} &
- 3 & No & An \bitvar{NMBS}-element array of coding
- modes for each macro block. \\
-\bottomrule\end{tabularx}
-
-\paragraph{Variables used:}\hfill\\*
-\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
-\multicolumn{1}{c}{Name} &
-\multicolumn{1}{c}{Type} &
-\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
-\multicolumn{1}{c}{Signed?} &
-\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
-\locvar{\mbi} & Integer & 32 & No & The index of the current macro
- block. \\
-\locvar{\bi} & Integer & 32 & No & The index of the current block in coded
- order. \\
-\bottomrule\end{tabularx}
-\medskip
-
-In an intra frame, every macro block marked as coded in INTRA mode.
-In an inter frame, however, a macro block can be coded in one of eight coding
- modes, given in Table~\ref{tab:coding-modes}.
-All of the blocks in all color planes contained in a macro block will be
- assigned the coding mode of that macro block.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{cl}\toprule
-Index & Coding Mode \\\midrule
-$0$ & INTER\_NOMV \\
-$1$ & INTRA \\
-$2$ & INTER\_MV \\
-$3$ & INTER\_MV\_LAST \\
-$4$ & INTER\_MV\_LAST2 \\
-$5$ & INTER\_GOLDEN\_NOMV \\
-$6$ & INTER\_GOLDEN\_MV \\
-$7$ & INTER\_MV\_FOUR \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Coding Modes}
-\label{tab:coding-modes}
-\end{table}
-
-An important thing to note is that a coding mode is only stored in the
- bitstream if it has at least {\em luma} block coded.
-A macro block with no coded blocks in the luma plane defaults to being coded in
- INTER\_NOMV mode, even if it contains coded blocks in the chroma planes.
-
-Coding modes are encoded using one of eight different schemes.
-Schemes 0 through 6 use the same simple Huffman code to represent the mode
- numbers, as given in Table~\ref{tab:mode-codes}.
-The difference in the schemes is the mode number assigned to each code.
-Scheme 0 uses an assignment specified in the bitstream, while schemes 1--6 use
- a fixed assignment, also given in Table~\ref{tab:mode-codes}.
-Scheme 7 simply codes each mode directly in the bitstream using three bits.
-
-\begin{table}[htb]
-\begin{center}
-\begin{tabular}{lcccccc}\toprule
-Scheme & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ \\\cmidrule{2-7}
-Huffman Code & \multicolumn{6}{c}{Coding Mode} \\\midrule
-\bin{0} & $3$ & $3$ & $3$ & $3$ & $0$ & $0$ \\
-\bin{10} & $4$ & $4$ & $2$ & $2$ & $3$ & $5$ \\
-\bin{110} & $2$ & $0$ & $4$ & $0$ & $4$ & $3$ \\
-\bin{1110} & $0$ & $2$ & $0$ & $4$ & $2$ & $4$ \\
-\bin{11110} & $1$ & $1$ & $1$ & $1$ & $1$ & $2$ \\
-\bin{111110} & $5$ & $5$ & $5$ & $5$ & $5$ & $1$ \\
-\bin{1111110} & $6$ & $6$ & $6$ & $6$ & $6$ & $6$ \\
-\bin{1111111} & $7$ & $7$ & $7$ & $7$ & $7$ & $7$ \\
-\bottomrule\end{tabular}
-\end{center}
-\caption{Coding Modes}
-\label{tab:mode-codes}
-\end{table}
-
-\begin{enumerate}
-\item
-If \bitvar{FTYPE} is 0 (intra frame):
-\begin{enumerate}
-\item
-For each consecutive value of \locvar{\mbi} from 0 to $(\bitvar{NMBS}-1)$,
- inclusive, assign $\bitvar{MBMODES}[\mbi]$ the value 0 (INTRA).
-\end{enumerate}
-\item
-Otherwise (inter frame):
-\begin{enumerate}
-\item
-Read a 3-bit unsigned integer as \locvar{MSCHEME}.
-\item
-If \locvar{MSCHEME} is 0:
-\begin{enumerate}
-\item
-For each consecutive value of \locvar{MODE} from 0 to 7, inclusive:
-\begin{enumerate}
-\item
-Read a 3-bit unsigned integer as \locvar{\mi}.
-\item
-Assign $\locvar{MALPHABET}[\mi]$ the value \locvar{MODE}.
-\end{enumerate}
-\end{enumerate}
-\item
-Otherwise, if \locvar{MSCHEME} is not 7, assign the entries of
- \locvar{MALPHABET} the values in the corresponding column of
- Table~\ref{tab:mode-codes}.
-\item
-For each consecutive macro block in coded order (see
- Section~\ref{sec:mbs})---indexed by \locvar{\mbi}:
-\begin{enumerate}
-\item
-If a block \locvar{\bi} in the luma plane of macro block \locvar{\mbi} exists
- such that $\bitvar{BCODED}[\locvar{\bi}]$ is 1:
-\begin{enumerate}
-\item
-If \locvar{MSCHEME} is not 7, read one bit at a time until one of the Huffman
- codes in Table~\ref{tab:mode-codes} is recognized, and assign
- $\bitvar{MBMODE}[\locvar{\mbi}]$ the value $\locvar{MALPHABET}[\locvar{\mi}]$,
- where \locvar{\mi} is the index of the Huffman code decoded.
-\item
-Otherwise, if no luma-plane blocks in the macro block are coded, read a 3-bit
- unsigned integer as $\bitvar{MBMODE}[\locvar{\mbi}]$.
-\end{enumerate}
-\item
-Otherwise, assign $\bitvar{MBMODE}[\locvar{\mbi}]$ the value 0 (INTER\_NOMV).
-\end{enumerate}
-\end{enumerate}
-\end{enumerate}
-
-\clearpage
-
-%\backmatter
-\appendix
-
-\chapter{Ogg Bitstream Encapsulation}
-\label{app:oggencapsulation}
-
-\section{Overview}
-
-This document specifies the embedding or encapsulation of Theora packets
- in an Ogg transport stream.
-
-Ogg is a stream oriented wrapper for coded, linear time-based data.
-It provides syncronization, multiplexing, framing, error detection and
- seeking landmarks for the decoder and complements the raw packet format
- used by the Theora codec.
-
-This document assumes familiarity with the details of the Ogg standard.
-The Xiph.org documentation provides an overview of the Ogg transport stream
- format at \url{http://www.xiph.org/ogg/doc/oggstream.html} and a detailed
- description at \url{http://www.xiph.org/ogg/doc/framing.html}.
-The format is also defined in RFC~3533 \cite{rfc3533}.
-While Theora packets can be embedded in a wide variety of media
- containers and streaming mechanisms, the Xiph.org Foundation
- recommends Ogg as the native format for Theora video in file-oriented
- storage and transmission contexts.
-
-\subsection{MIME type}
-
-The correct MIME type of any Ogg file is {\tt application/ogg}.
-Outside of an encapsulation, the mime type {\tt video/x-theora} may
- be used to refer specifically to the Theora compressed video stream.
-
-\section{Embedding in a logical bitstream}
-
-Ogg separates a {\em logical bitstream} consisting of the framing of
- a particular sequence of packets and complete within itself from
- the {\em physical bitstream} which may consist either of a single
- logical bitstream or a number of logical bitstreams multiplexed
- together.
-This section specifies the embedding of Theora packets in a logical Ogg
- bitstream.
-The mapping of Ogg Theora logical bitstreams into a multiplexed physical Ogg
- stream is described in the next section.
-
-\subsection{Headers}
-
-The initial info header packet appears by itself in a single Ogg page.
-This page defines the start of the logical stream and MUST have
- the `beginning of stream' flag set.
-
-The second and third header packets (metadata comments and decoder
- setup data) can together span one or more Ogg pages.
-If there are additional non-normative header packets, they MUST be
- included in this sequence of pages as well.
-The comment header packet MUST begin the second Ogg page in the logical
- bitstream, and there MUST be a page break between the last header
- packet and the first frame data packet.
-
-These two page break requirements facilitate stream identification and
- simplify header acquisition for seeking and live streaming applications.
-
-All header pages MUST have their granule position field set to zero.
-%TODO: or -1?
-%TBT: What are we doing now?
-
-\subsection{Frame data}
-
-The first frame data packet in a logical bitstream MUST begin a fresh page.
-All other data packets are placed one at a time into Ogg pages
- until the end of the stream.
-Packets can span pages and multiple packets can be placed within any
- one page.
-The last page in the logical bitstream MUST have its `end of stream'
- flag set.
-
-Frame data pages MUST be marked with a granule index corresponding to
- the display time of the last frame/packet that finishes in that page.
-
-{\bf Note:}
-This scheme is still under discussion.
-It has also been proposed that pages be labeled with a granule corresponding to
- the first frame that begins on that page.
-This simplifies seeking and mux, but is different from the published
- definition of the Ogg granule field.
-This document will be updated when the issue is settled.
-
-%TODO: \subsection{Granule position}
-
-\section{Multiplexed stream mapping}
-
-Applications supporting Ogg Theora I must support Theora bitstreams
- multiplexed with compressed audio data in the Vorbis I and Speex
- formats, and should support Ogg-encapsulated MNG graphics for overlays.
-% and the Writ format for text-based titling.
-%TBT: That's great... do these things have specifications?
-
-Multiple audio and video bitstreams may be multiplexed together.
-How playback of multiple/alternate streams is handled is up to the
- application.
-Some conventions based on included metadata aide interoperability
- in this respect.
-%TODO: describe multiple vs. alternate streams, language mapping
-% and reference metadata descriptions.
-
-\subsection{Chained streams}
-
-Ogg Theora decoders and playback applications MUST support both grouped
- streams (multiplexed concurrent logical streams) and chained streams
- (sequential concatenation of independent physical bitstreams).
-
-The number and codec data types of multiplexed streams and the decoder
- parameters for those stream types that re-occur can all change at a
- chaining boundary.
-A playback application MUST be prepared to handle such changes and
- SHOULD do so smoothly with the minimum possible visible disruption.
-The specification of grouped streams below applies independently to each
- segment of a chained bitstream.
-
-\subsection{Grouped streams}
-
-At the beginning of a multiplexed stream, the `beginning of stream'
- pages for each logical bitstream will be grouped together.
-Within these, the first page to occur MUST be the Theora page.
-This facilitates identification of Ogg Theora files among other
- Ogg-encapsulated content.
-A playback application must nevertheless handle streams where this
- arrangement is not correct.
-%TBT: Then what's the point of requiring it in the spec?
-
-If there is more than one Theora logical stream, the first page should
- be from the primary stream.
-That is, the best choice for the stream a generic player should begin
- displaying without special user direction.
-If there is more than one audio stream, or of any other stream
- type, the identification page of the primary stream of that type
- should be placed before the others.
-%TBT: That's all pretty vague.
-
-After the `beginning of stream' pages, the header pages of each of
- the logical streams should be grouped together before any data pages
- occur.
-%TBT: should or must?
-
-After all the header pages have been placed,
- the data pages are multiplexed together.
-They should be placed in the stream in increasing order by the playback
- time equivalents of their granule fields.
-This facilitates seeking while limiting the buffering requirements of the
- playback demultiplexer.
-%TODO: A lot of this language is encoder-oriented.
-%TODO: We define a decoder-oriented specification.
-%TODO: The language should be changed to match.
-
-\clearpage
-\chapter{Colophon}
-
-Ogg is a \href{http://www.xiph.org}{Xiph.org Foundation} 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 \href{http://www.xiph.org/about.html}{About the Xiph.org Foundation} for
- details.
-
-Ogg Theora is the first Ogg video codec.
-Anyone may freely use and distribute the Ogg and Theora specifications, whether
- in private, public, or corporate capacity.
-However, the Xiph.org Foundation and the Ogg project reserve the right to set
- the Ogg Theora specification and certify specification compliance.
-
-Xiph.org's Theora software codec implementation is distributed under a BSD-like
- license.
-This does not restrict third parties from distributing independent
- implementations of Theora software under other licenses.
-
-\begin{wrapfigure}{l}{0pt}
-\includegraphics{xifish}
-\end{wrapfigure}
-
-These pages are copyright \textcopyright{} 2004 Xiph.org Foundation.
-All rights reserved.
-Ogg, Theora, Vorbis, Xiph.org Foundation and their logos are trademarks
- (\texttrademark) of the \href{http://www.xiph.org}{Xiph.org Foundation}.
-
-This document is set in \LaTeX.
-
-
-
-\clearpage
-\bibliography{spec}
-
-\end{document}
+\documentclass[11pt,letterpaper]{book}
+
+\usepackage{latexsym}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{bm}
+\usepackage{textcomp}
+\usepackage{graphicx}
+\usepackage{booktabs}
+\usepackage{tabularx}
+\usepackage{longtable}
+\usepackage{ltablex}
+\usepackage{wrapfig}
+\usepackage[pdfpagemode=None,pdfstartview=FitH,pdfview=FitH,colorlinks=true]%
+ {hyperref}
+
+\newtheorem{theorem}{Theorem}[section]
+\newcommand{\idx}[1]{{\ensuremath{\mathit{#1}}}}
+\newcommand{\qti}{\idx{qti}}
+\newcommand{\qtj}{\idx{qtj}}
+\newcommand{\pli}{\idx{pli}}
+\newcommand{\plj}{\idx{plj}}
+\newcommand{\qi}{\idx{qi}}
+\newcommand{\ci}{\idx{ci}}
+\newcommand{\bmi}{\idx{bmi}}
+\newcommand{\bmj}{\idx{bmj}}
+\newcommand{\qri}{\idx{qri}}
+\newcommand{\qrj}{\idx{qrj}}
+\newcommand{\hti}{\idx{hti}}
+\newcommand{\sbi}{\idx{sbi}}
+\newcommand{\bi}{\idx{bi}}
+\newcommand{\mbi}{\idx{mbi}}
+\newcommand{\mi}{\idx{mi}}
+\newcommand{\ti}{\idx{ti}}
+%This somewhat odd construct ensures that \bitvar{\qi}, etc., will set the
+% qi in bold face, even though it is in a \mathit font, yet \bitvar{VAR} will
+% set VAR in a bold, roman font.
+\newcommand{\bitvar}[1]{\ensuremath{\mathbf{\bm #1}}}
+\newcommand{\locvar}[1]{\ensuremath{\mathrm{#1}}}
+\newcommand{\term}[1]{{\em #1}}
+\newcommand{\bin}[1]{\ensuremath{\mathtt{b#1}}}
+\newcommand{\hex}[1]{\ensuremath{\mathtt{0x#1}}}
+\newcommand{\ilog}{\ensuremath{\mathop{\mathrm{ilog}}\nolimits}}
+
+%Section-based table, figure, and equation numbering.
+\numberwithin{equation}{chapter}
+\numberwithin{figure}{chapter}
+\numberwithin{table}{chapter}
+
+\keepXColumns
+
+\pagestyle{headings}
+\bibliographystyle{alpha}
+
+\title{Theora I Specification}
+\author{Xiph.org Foundation}
+\date{\today}
+
+
+\begin{document}
+
+\frontmatter
+
+\begin{titlepage}
+\maketitle
+\end{titlepage}
+\thispagestyle{empty}
+\cleardoublepage
+
+\pagenumbering{roman}
+
+\thispagestyle{plain}
+\tableofcontents
+\cleardoublepage
+
+\thispagestyle{plain}
+\listoffigures
+\cleardoublepage
+
+\thispagestyle{plain}
+\listoftables
+\cleardoublepage
+
+\thispagestyle{plain}
+\markboth{{\sc Notation and Conventions}}{{\sc Notation and Conventions}}
+\chapter*{Notation and Conventions}
+
+All parameters either passed in or out of a decoding procedure are given in
+ \bitvar{bold\ face}.
+
+The prefix \bin{} indicates that the following value is to be interpreted as a
+ binary number (base 2).
+\begin{verse}
+{\bf Example:} The value \bin{1110100} is equal to the decimal value 116.
+\end{verse}
+
+The prefix \hex{} indicates the the following value is to be interpreted as a
+ hexadecimal number (base 16).
+\begin{verse}
+{\bf Example:} The value \hex{74} is equal to the decimal value 116.
+\end{verse}
+
+The following operators are defined:
+
+\begin{description}
+\item[$|a|$]
+The absolute value of a number $a$.
+\begin{align*}
+|a| & = \left\{\begin{array}{ll}
+-a, & a < 0 \\
+a, & a \ge 0
+\end{array}\right.
+\end{align*}
+
+\item[$a*b$]
+Multiplication of a number $a$ by a number $b$.
+\item[$\frac{a}{b}$]
+Exact division of a number $a$ by a number $b$, producing a potentially
+ non-integer result.
+
+\item[$\left\lfloor a\right\rfloor$]
+The largest integer less than or equal to a real number $a$.
+
+\item[$\left\lceil a\right\rceil$]
+The smallest integer greater than or equal to a real number $a$.
+
+\item[$a//b$]
+Integer division of $a$ by $b$.
+\begin{align*}
+a//b & = \left\{\begin{array}{ll}
+\left\lceil\frac{a}{b}\right\rceil, & a < 0 \\
+\left\lfloor\frac{a}{b}\right\rfloor, & a \ge 0
+\end{array}\right.
+\end{align*}
+
+\item[$a\%b$]
+The remainder from the integer division of $a$ by $b$.
+\begin{align*}
+a\%b & = |a|-|b|*|a//b|
+\end{align*}
+Note that with this definition, the result is always non-negative and less than
+ $|b|$.
+
+\item[$a<<b$]
+The value obtained by left-shifting the two's complement integer $a$ by $b$
+ bits.
+For purposes of this specification, overflow is ignored, and so this is
+ equivalent to integer multiplication of $a$ by $2^b$.
+
+\item[$a>>b$]
+The value obtained by right-shifting the two's complement integer $a$ by $b$
+ bits, filling in the leftmost bits of the new value with $0$ if $a$ is
+ non-negative and $1$ if $a$ is negative.
+This is {\em not} equivalent to integer division of $a$ by $2^b$.
+Instead,
+\begin{align*}
+a>>b & = \left\lfloor\frac{a}{2^b}\right\rfloor.
+\end{align*}
+
+\item[$\ilog(a)$]
+The minimum number of bits required to store a positive integer $a$ in
+ two's complement notation, or $0$ for a non-positive integer $a$.
+\begin{align*}
+\ilog(a) = \left\{\begin{array}{ll}
+0, & a \le 0 \\
+\left\lceil\log_2{a}\right\rceil, & a > 0
+\end{array}\right.
+\end{align*}
+
+\begin{verse}
+{\bf Examples:}
+\begin{itemize}
+\item $\ilog(-1)=0$
+\item $\ilog(0)=0$
+\item $\ilog(1)=1$
+\item $\ilog(2)=2$
+\item $\ilog(3)=2$
+\item $\ilog(4)=3$
+\item $\ilog(7)=3$
+\end{itemize}
+\end{verse}
+
+\item[$\min(a,b)$]
+The minimum of two numbers $a$ and $b$.
+
+\item[$\max(a,b)$]
+The maximum of two numbers $a$ and $b$.
+
+\end{description}
+\cleardoublepage
+
+
+\thispagestyle{plain}
+\markboth{{\sc Key words}}{{\sc Key words}}
+\chapter*{Key words}
+
+%We can't rewrite this, because this is text required by RFC 2119, so we use
+% some emergency stretching to get it typeset properly.
+\setlength{\emergencystretch}{2em}
+The key words ``MUST'', ``MUST NOT'', ``REQUIRED'', ``SHALL'', ``SHALL NOT'',
+ ``SHOULD'', ``SHOULD NOT'', ``RECOMMENDED'', ``MAY'', and ``OPTIONAL'' in this
+ document are to be intrepreted as described in RFC 2119 \cite{rfc2119}.\par
+\setlength{\emergencystretch}{0em}
+
+Where such assertions are placed on the contents of a Theora bitstream itself,
+ implementations should be prepared to encounter bitstreams that do not follow
+ these requirements.
+An application's behavior in the presecence of such non-conforming bitstreams
+ is not defined by this specification, but any reasonable method of handling
+ them MAY be used.
+By way of example, applications MAY discard the current frame, retain the
+ current output thus far, or attempt to continue on by assuming some default
+ values for the erroneous bits.
+When such an error occurs in the bitstream headers, an application MAY refuse
+ to decode the entire stream.
+An application SHOULD NOT allow such non-conformant bitstreams to overflow
+ buffers and potentially execute arbitrary code, as this represents a serious
+ security risk.
+
+An application MUST, however, ensure any reserved bits have the value zero, and
+ refuse to decode the stream if they are not.
+These are used as place holders for future bitstream features with which the
+ current bitstream is forward-compatible.
+%RG: shouldn't this be 'MAY not increment...the version number'?
+Such features will not increment the bitstream version number, and can only be
+ recognized by checking the value of these reserved bits.
+
+\cleardoublepage
+
+
+
+\mainmatter
+
+\pagenumbering{arabic}
+\setcounter{page}{1}
+
+\chapter{Introduction}
+
+Theora is a general purpose, lossy video codec.
+It is based on the VP3 video codec produced by On2 Technologies
+ (\url{http://www.on2.com/}).
+On2 donated the VP3.1 source code to the Xiph.org Foundation and released it
+ under a BSD-like license.
+On2 also made an irrevocable, royalty-free license grant for any patent claims
+ it might have over the software and any derivatives.
+No formal specification exists for the VP3 format beyond this source code,
+ however Mike Melanson maintains a detailed description \cite{Mel04}.
+Portions of this specification were adopted from that text with permission.
+
+\section{VP3 and Theora}
+
+Theora contains a superset of the features that were available in the original
+ VP3 codec.
+Content encoded with VP3.1 can be losslessly transcoded into the Theora format.
+%TODO: what about VP3.1 etc? source tables all say 'VP31'
+Theora content cannot, in general, be losslessly transcoded into the VP3
+ format.
+If a feature is not available in the original VP3 format, this is mentioned
+ when that feature is defined.
+A complete list of these features appears in Appendix~REF.
+%TODO: VP3 - theora comparison in appendix
+
+
+\section{Video Formats}
+
+Theora I currently supports progressive video data of arbitrary dimensions at a
+ constant frame rate in one of several $Y'C_bC_r$ color spaces.
+The precise definition the supported color spaces appears in
+ Section~\ref{sec:colorspaces}.
+Three different chroma subsampling formats are supported: 4:2:0, 4:2:2,
+ and 4:4:4.
+The precise details of each of these formats and their sampling locations are
+ described in Section~\ref{sec:pixfmts}.
+
+The Theora I format does not support interlaced material, variable frame rates,
+ bit-depths larger than 8 bits per component, nor alternate color spaces such
+ as RGB or arbitrary multi-channel spaces.
+Black and white content can be efficiently encoded, however, because the
+ uniform chroma planes compress well.
+Support for interlaced material is planned for a future version.
+\begin{verse}
+{\bf Note:} Infrequently changing frame rates---as when film and video
+ sequences are cut together---can be supported in the Ogg container format by
+ chaining several Theora streams together.
+\end{verse}
+Support for increased bit depths or additional color spaces is not planned.
+
+\section{Classification}
+
+Theora I is a block-based lossy transform codec that utilizes an
+ $8\times 8$ Type-II Discrete Cosine Transform and block-based motion
+ compensation.
+This places it in the same class of codecs as MPEG-1, -2, -4, and H.263.
+The details of how individual blocks are organized and how DCT coefficients are
+ organized in the bitstream differ substantially from these codecs, however.
+Theora supports only intra frames (I frames in MPEG) and inter frames (P frames
+ in MPEG).
+There is no equivalent to the bi-predictive frames (B frames) found in MPEG
+ codecs.
+
+\section{Assumptions}
+
+The Theora codec design assumes a complex, psychovisually-aware encoder and a
+ simple, low-complexity decoder.
+%TODO: Talk more about implementation complexity.
+
+Theora provides none of its own framing, synchronization, or protection against
+ transmission errors.
+An encoder is solely a method of accepting input video frames and
+ compressing these frames into raw, unformatted `packets'.
+The decoder then accepts these raw packets in sequence, decodes them, and
+ synthesizes a fascimile of the original video frames.
+Theora is a free-form variable bit rate (VBR) codec, and packets have no
+ minimum size, maximum size, or fixed/expected size.
+
+Theora packets are thus intended to be used with a transport mechanism that
+ provides free-form framing, synchronization, positioning, and error correction
+ in accordance with these design assumptions, such as Ogg (for file transport)
+ or RTP (for network multicast).
+For the purposes of a few examples in this document, we will assume that Theora
+ is embedded in an Ogg stream specifically, although this is by no means a
+ requirement or fundamental assumption in the Theora design.
+
+The specification for embedding Theora into an Ogg transport stream is given in
+ Appendix~\ref{app:oggencapsulation}.
+
+\section{Codec Setup and Probability Model}
+
+Theora's heritage is the proprietary commerical codec VP3, and it retains a
+ fair amount of inflexibility when compared to Vorbis \cite{vorbis}, the first
+ Xiph.org codec, which began as a research codec.
+However, to provide additional scope for encoder improvement, Theora adopts
+ some of the configurable aspects of decoder setup that are present in Vorbis.
+This configuration data is not available in VP3, which uses hardcoded values
+ instead.
+
+Theora makes the same controversial design decision that Vorbis made to include
+ the entire probability model for the DCT coefficients and all the quantization
+ parameters in the bitstream headers.
+This is often several hundred fields.
+It is therefore impossible to decode any frame in the stream without
+ having previously fetched the codec info and codec setup headers.
+
+\begin{verse}
+{\bf Note:} Theora {\em can} initiate decode at an arbitrary intra-frame packet
+ within a bitstream so long as the codec has been initialized with the setup
+ headers.
+\end{verse}
+
+Thus, Theora headers are both required for decode to begin and relatively large
+ as bitstream headers go.
+The header size is unbounded, although as a rule-of-thumb less than 16kB is
+ recommended, and Xiph.org's reference encoder follows this suggestion.
+%TODO: Is 8kB enough? My setup header is 7.4kB, that doesn't leave much room
+% for comments.
+%RG: the lesson from vorbis is that as small as possible is really
+% important in some applications. Practically, what's acceptable
+% depends a great deal on the target bitrate. I'd leave 16 kB in the
+% spec for now. fwiw more than 1k of comments is quite unusual.
+
+Our own design work indicates that 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
+ points out limitations in some existing software/interface designs.
+However, we find that it does not fundamentally limit Theora's suitable
+ application space.
+
+%silvia: renamed
+%\subsection{Format Specification}
+\section{Format Conformance}
+
+The Theora format is well-defined by its decode specification; any encoder that
+ produces packets that are correctly decoded by an implementation following
+ this specification may be considered a proper Theora encoder.
+A decoder must faithfully and completely implement the specification defined
+ herein %, except where noted,
+ to be considered a conformant Theora decoder.
+A decoder need not be implemented strictly as described, but the
+ actual decoder process MUST be {\em entirely mathematically equivalent}
+ to the described process.
+Where appropriate, a non-normative description of encoder processes is
+ included.
+These sections will be marked as such, and a proper Theora encoder is not
+ bound to follow them.
+
+%TODO: \subsection{Hardware Profile}
+
+
+\chapter{Coded Video Structure}
+
+Theora's encoding and decoding process is based on $8\times 8$ blocks of
+ pixels.
+This sections describes how a video frame is laid out, divided into
+ blocks, and how those blocks are organized.
+
+\section{Frame Layout}
+
+A video frame in Theora is a two-dimensional array of pixels.
+Theora, like VP3, uses a right-handed coordinate system, with the origin in the
+ lower-left corner of the frame.
+This is contrary to many video formats which use a left-handed coordinate
+ system with the origin in the upper-left corner of the frame.
+%INT: This means that for interlaced material, the definition of `even fields'
+%INT: and `odd fields' may be reversed between Theora and other video codecs.
+%INT: This document will always refer to them as `top fields' and `bottom
+%INT: fields'.
+
+Theora divides the pixel array up into three separate \term{color planes}, one
+ for each of the $Y'$, $C_b$, and $C_r$ components of the pixel.
+The $Y'$ plane is also called the \term{luma plane}, and the $C_b$ and $C_r$
+ planes are also called the \term{chroma planes}.
+Each plane is assigned a numerical value, as shown in
+ Table~\ref{tab:color-planes}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cl}\toprule
+Index & Color Plane \\\midrule
+$0$ & $Y'$ \\
+$1$ & $C_b$ \\
+$2$ & $C_r$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Color Plane Indices}
+\label{tab:color-planes}
+\end{table}
+
+In some pixel formats, the chroma planes are subsampled by a factor of two
+ in one or both directions.
+This means that the width or height of the chroma planes may be half that of
+ the total frame width and height.
+The luma plane is never subsampled.
+
+\section{Picture Region}
+
+An encoded video frame in Theora is required to have a width and height that
+ are multiples of sixteen, making an integral number of blocks even when the
+ chroma planes are subsampled.
+However, inside a frame a smaller \term{picture region} may be defined
+ to present material whose dimensions are not a multiple of sixteen pixels, as
+ shown in Figure~\ref{fig:pic-frame}.
+The picture region can be offset from the lower-left corner of the frame by up
+ to 255 pixels in each direction, and may have an arbitrary width and height,
+ provided that it is contained entirely within the coded frame.
+It is this picture region that contains the actual video data.
+The portions of the frame which lie outside the picture region may contain
+ arbitrary image data, so the frame must be cropped to the picture region
+ before display.
+The picture region plays no other role in the decode process, which operates on
+ the entire video frame.
+
+\begin{figure}[htb]
+\begin{center}
+\include{pic-frame}
+\end{center}
+\caption{Location of frame and picture regions}
+\label{fig:pic-frame}
+\end{figure}
+
+\section{Blocks and Super Blocks}
+\label{sec:blocks-and-sbs}
+
+Each color plane is subdivided into \term{blocks} of $8\times 8$ pixels.
+Blocks are grouped into $4\times 4$ arrays called \term{super blocks} as
+ shown in Figure~\ref{fig:superblock}.
+Each color plane has its own set of blocks and super blocks.
+If the chroma planes are subsampled, they are still divided into $8\times 8$
+ blocks of pixels; there are just fewer blocks than in the luma plane.
+The boundaries of blocks and super blocks in the luma plane do not necessarily
+ coincide with those of the chroma planes, if the chroma planes have been
+ subsampled.
+
+\begin{figure}[htb]
+\begin{center}
+\include{superblock}
+\end{center}
+\caption{Subdivision of a frame into blocks and super blocks}
+\label{fig:superblock}
+\end{figure}
+
+Blocks are accessed in two different orders in the various decoder processes.
+The first is \term{raster order}, illustrated in Figure~\ref{fig:raster-block}.
+This indexes each block in row-major order, starting in the lower left of the
+ frame and continuing along the bottom row of the entire frame, followed by the
+ next row up, starting on the left edge of the frame, etc.
+
+\begin{figure}[htb]
+\begin{center}
+\include{raster-block}
+\end{center}
+\caption{Raster ordering of $n\times m$ blocks}
+\label{fig:raster-block}
+\end{figure}
+
+The second is \term{coded order}.
+In coded order, blocks are accessed by super block.
+Within each frame, super blocks are traversed in raster order,
+ similar to raster order for blocks.
+Within each super block, however, blocks are accessed in a Hilbert curve
+ pattern, illustrated in Figure~\ref{fig:hilbert-block}.
+If a color plane does not contain a complete super block on the top or right
+ sides, the same ordering is still used, simply with any blocks outside the
+ frame boundary ommitted.
+
+\begin{figure}[htb]
+\begin{center}
+\include{hilbert-block}
+\end{center}
+\caption{Hilbert curve ordering of blocks within a super block}
+\label{fig:hilbert-block}
+\end{figure}
+
+To illustrate these two orderings, consider a frame that is 240 pixels wide and
+ 48 pixels high.
+Each row of the luma plane has 30 blocks and 8 super blocks, and there are 6
+ rows of blocks and two rows of super blocks.
+
+When accessed in raster order, each block in the luma plane is assigned the
+ following indices:
+
+\vspace{\baselineskip}
+\begin{center}
+\begin{tabular}{|ccccccc|}\hline
+150 & 151 & 152 & 153 & $\ldots$ & 178 & 179 \\
+120 & 121 & 122 & 123 & $\ldots$ & 148 & 149 \\\hline
+ 90 & 91 & 92 & 93 & $\ldots$ & 118 & 119 \\
+ 60 & 61 & 62 & 63 & $\ldots$ & 88 & 89 \\
+ 30 & 31 & 32 & 33 & $\ldots$ & 58 & 59 \\
+ 0 & 1 & 2 & 3 & $\ldots$ & 28 & 29 \\\hline
+\end{tabular}
+\end{center}
+\vspace{\baselineskip}
+
+Here the index values specify the order in which the blocks would be accessed.
+
+When accessed in coded order, each block in the luma plane is assigned the
+ following indices, illustrating the different order of access:
+
+\vspace{\baselineskip}
+\begin{center}
+\begin{tabular}{|cccc|c|cc|}\hline
+123 & 122 & 125 & 124 & $\ldots$ & 179 & 178 \\
+120 & 121 & 126 & 127 & $\ldots$ & 176 & 177 \\\hline
+ 5 & 6 & 9 & 10 & $\ldots$ & 117 & 118 \\
+ 4 & 7 & 8 & 11 & $\ldots$ & 116 & 119 \\
+ 3 & 2 & 13 & 12 & $\ldots$ & 115 & 114 \\
+ 0 & 1 & 14 & 15 & $\ldots$ & 112 & 113 \\\hline
+\end{tabular}
+\end{center}
+\vspace{\baselineskip}
+
+The indices of the blocks are numbered continuously from one color plane to the
+ next.
+They do not reset to zero at the start of each plane.
+The implication is that the blocks from all planes are treated as a unit during
+ the various processing steps.
+
+\section{Macro Blocks}
+\label{sec:mbs}
+
+A macro block contains a $2\times 2$ array of blocks in the luma plane
+ {\em and} the co-located blocks in the chroma planes, as shown in
+ Figure~\ref{fig:macroblock}.
+Thus macro blocks can represent anywhere from six to twelve blocks, depending
+ on how the chroma planes are subsampled.
+This is in contrast to super blocks, which only contain blocks from a single
+ color plane.
+% the whole super vs. macro blocks thing is a little confusing, and it can be
+% hard to remember which is what initially. A figure would/will help here,
+% but I tried to add some text emphasizing the difference in terms of
+% functionality.
+%TBT: At this point we haven't described any functionality yet.
+%TBT: As far as the reader knows, the only purpose of the blocks, macro blocks
+%TBT: and super blocks is for data organization---and for blocks and super
+%TBT: blocks, this is essentially true.
+%TBT: So lets restrict the differences we emphasize to those of data
+%TBT: organization, which the sentence I just added above does.
+Macro bocks contain information about coding mode and motion vectors for the
+ corresponding blocks in all color planes.
+
+\begin{figure}[htb]
+ \begin{center}
+ \include{macroblock}
+ \end{center}
+ \caption{Subdivision of a frame into macro blocks}
+ \label{fig:macroblock}
+\end{figure}
+
+Macro blocks are also accessed in a \term{coded order}.
+This coded order proceeds by examining each super block in the luma plane in
+ raster order, and traversing the four macro blocks inside using a smaller
+ Hilbert curve, as shown in Figure~\ref{fig:hilbert-mb}.
+%r: I rearranged the wording to make a more formal idiom here
+If the luma plane does not contain a complete super block on the top or right
+ sides, the same ordering is still used, with any macro blocks outside
+ the frame boundary simply omitted.
+Because the frame size is constrained to be a multiple of 16, there are never
+ any partial macro blocks.
+Unlike blocks, macro blocks need never be accessed in a pure raster order.
+
+\begin{figure}[htb]
+\begin{center}
+\include{hilbert-mb}
+\end{center}
+\caption{Hilbert curve ordering of macro blocks within a super block}
+\label{fig:hilbert-mb}
+\end{figure}
+
+Using the same frame size as the example above, there are 15 macro blocks in
+ each row and 3 rows of macro blocks.
+The macro blocks are assigned the following indices:
+
+\vspace{\baselineskip}
+\begin{center}
+\begin{tabular}{|cc|cc|c|cc|c|}\hline
+30 & 31 & 32 & 33 & $\cdots$ & 42 & 43 & 44 \\\hline
+ 1 & 2 & 5 & 6 & $\cdots$ & 25 & 26 & 29 \\
+ 0 & 3 & 4 & 7 & $\cdots$ & 24 & 27 & 28 \\\hline
+\end{tabular}
+\end{center}
+\vspace{\baselineskip}
+
+\section{Coding Modes and Prediction}
+
+Each block is coded using one of a small, fixed set of \term{coding modes} that
+ define how the block is predicted from previous frames.
+A block is predicted using one of two \term{reference frames}, selected
+ according to the coding mode.
+A reference frame is the fully decoded version of a previous frame in the
+ stream.
+The first available reference frame is the previous intra frame, called the
+ \term{golden frame}.
+The second available reference frame is the previous frame, whether it was an
+ intra frame or an inter frame.
+If the previous frame was an intra frame, then both reference frames are the
+ same.
+
+Two coding modes in particular are worth mentioning here.
+The INTRA mode is used for blocks that are not predicted from either reference
+ frame.
+This is the only coding mode allowed in intra frames.
+The INTER\_NOMV coding mode uses the co-located contents of the block in the
+ previous frame as the predictor.
+This is the default coding mode.
+
+\section{DCT Coefficients}
+
+To each block's predictor, a \term{residual} is added to form the final
+ contents of the block.
+%r: I reworded this next sentence to try and make it more decoder-oriented
+%TBT: Same content with 2/3 the words... sounds good to me.
+The residual is stored as a set of quantized coefficients from an integer
+ approximation of a two-dimensional Type II Discrete Cosine Transform.
+The DCT takes an $8\times 8$ array of pixel values as input and returns an
+ $8\times 8$ array of coefficient values.
+The \term{natural ordering} of these coefficients is defined to be row-major
+ order, from lowest to highest frequency.
+They are also often indexed in \term{zig-zag order}, as shown in
+ Table~\ref{tab:zig-zag}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}[c]{r|c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c}
+\multicolumn{1}{r}{} &0&&1&&2&&3&&4&&5&&6&&7 \\\cline{2-16}
+0 & 0 &$\rightarrow$& 1 && 5 &$\rightarrow$& 6 && 14 &$\rightarrow$& 15 && 27 &$\rightarrow$& 28 \\[-0.5\defaultaddspace]
+ & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
+1 & 2 & & 4 && 7 & & 13 && 16 & & 26 && 29 & & 42 \\[-0.5\defaultaddspace]
+ &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
+2 & 3 & & 8 && 12 & & 17 && 25 & & 30 && 41 & & 43 \\[-0.5\defaultaddspace]
+ & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
+3 & 9 & & 11 && 18 & & 24 && 31 & & 40 && 44 & & 53 \\[-0.5\defaultaddspace]
+ &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
+4 & 10 & & 19 && 23 & & 32 && 39 & & 45 && 52 & & 54 \\[-0.5\defaultaddspace]
+ & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
+5 & 20 & & 22 && 33 & & 38 && 46 & & 51 && 55 & & 60 \\[-0.5\defaultaddspace]
+ &$\downarrow$&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&&$\swarrow$&&$\nearrow$&$\downarrow$ \\
+6 & 21 & & 34 && 37 & & 47 && 50 & & 56 && 59 & & 61 \\[-0.5\defaultaddspace]
+ & &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$&&$\nearrow$& &$\swarrow$& \\
+7 & 35 &$\rightarrow$& 36 && 48 &$\rightarrow$& 49 && 57 &$\rightarrow$& 58 && 62 &$\rightarrow$& 63
+\end{tabular}
+\end{center}
+\caption{Zig-zag order}
+\label{tab:zig-zag}
+\end{table}
+
+Note that the row and column indices refer to {\em frequency number} and not
+ pixel locations.
+The frequency numbers are defined independently of the memory organization of
+ the pixels.
+They have been written from top to bottom here to follow conventional notation,
+ despite the right-handed coordinate system Theora uses for pixel locations.
+%RG: I'd rather we were internally consistent and put dc at the lower left.
+Many implementations of the DCT operate `in-place'.
+That is, they return DCT coefficients in the same memory buffer that the
+ initial pixel values were stored in.
+Due to the right-handed coordinate system used for pixel locations in Theora,
+ one must note carefully how both pixel values and DCT coefficients are
+ organized in memory in such a system.
+
+DCT coefficient $(0,0)$ is called the \term{DC coefficient}.
+All the other coefficients are called \term{AC coefficients}.
+
+
+\chapter{Decoding Overview}
+
+This section provides a high level description of the Theora codec's
+ construction.
+A bit-by-bit specification appears beginning in Section~\ref{sec:bitpacking}.
+The later sections assume a high-level understanding of the Theora decode
+ process, which is provided below.
+
+\section{Decoder Configuration}
+
+Decoder setup consists of configuration of the quantization matrices and the
+ Huffman codebooks for the DCT coefficients, and a table of limit values for
+ the deblocking filter.
+The remainder of the decoding pipeline is not configurable.
+
+\subsection{Global Configuration}
+
+The global codec configuration consists of a few video related fields, such as
+ frame rate, frame size, picture size and offset, aspect ratio, color space,
+ pixel format, and a version number.
+The version number is divided into a major version, a minor version, amd a
+ minor revision number.
+%r: afaik the released vp3 codec called itself 3.1 and is compatible w/ theora
+%r: even though we received the in-progress 3.2 codebase
+For the format defined in this specification, these are `3', `2', and
+ `0', respectively, in reference to Theora's origin as a successor to the VP3.1
+ format.
+
+\subsection{Quantization Matrices}
+
+Theora allows up to 384 different quantization matrices to be defined, one for
+ each \term{quantization type}, \term{color plane} ($Y'$, $C_b$, or $C_r$), and
+ \term{quantization index}, \qi, which ranges from zero to 63, inclusive.
+There are currently two quantization types defined, which depend on the coding
+ mode of the block being dequantized, as shown in Table~\ref{tab:quant-types}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cl}\toprule
+Quantization Type & Usage \\\midrule
+$0$ & INTRA-mode blocks \\
+$1$ & Blocks in any other mode. \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Quantization Type Indices}
+\label{tab:quant-types}
+\end{table}
+
+%r: I think 'nominally' is more specific than 'generally' here
+The quantization index, on the other hand, nominally represents a progressive
+ range of quality levels, from low quality near zero to high quality near 63.
+However, the interpretation is arbitrary, and it is possible, for example, to
+ partition the scale into two completely separate ranges with 32 levels each
+ that are meant to represent different classes of source material, or any
+ other arrangement that suits the encoder's requirements.
+
+Each quantization matrix is an $8\times 8$ matrix of 16-bit values, which is
+ used to quantize the output of the $8\times 8$ DCT\@.
+Quantization matrices are specified using three components: a
+ \term{base matrix} and two \term{scale values}.
+The first scale value is the \term{DC scale}, which is applied to the DC
+ component of the base matrix.
+The second scale value is the \term{AC scale}, which is applied to all the
+ other components of the base matrix.
+There are 64 DC scale values and 64 AC scale values, one for each \qi\ value.
+
+There are 64 elements in each base matrix, one for each DCT coefficient.
+They are stored in natural order.
+There is a separate set of base matrices for each quantization type and each
+ color plane, with up to 64 possible base matrices in each set, one for each
+ \qi\ value.
+%r: we will mention that the given matricies must bound the \qi range
+%r: in the detailed section. it's not important at this level.
+Typically the bitstream contains matrices for only a sparse subset of the
+ possible \qi\ values.
+The base matrices for the remainder of the \qi\ values are computed using
+ linear interpolation.
+This configuration allows the encoder to adjust the quantization matrices to
+ approximate the complex, non-linear response of the human visual system to
+ different quantization errors.
+
+Finally, because the in-loop deblocking filter strength depends on the strength
+ of the quantization matrices defined in this header, a table of 64 \term{loop
+ filter limit values} is defined, one for each \qi\ value.
+
+The precise specification of how all of this information is decoded appears in
+ Section~REF.
+
+\subsection{Huffman Codebooks}
+
+Theora uses 80 configurable binary Huffman codes to represent the 32 tokens
+ used to encode DCT coefficients.
+Each of the 32 token values has a different semantic meaning and is used to
+ represent single coefficient values, zero runs, combinations of the two, and
+ \term{End-Of-Block markers}.
+
+The 80 codes are divided up into five groups of 16, with each group
+ corresponding to a set of DCT coefficient indices.
+The first group corresponds to the DC coefficient, while the remaining four
+ groups correspond to different subsets of the AC coefficients.
+Within each frame, two pairs of 4-bit codebook indices are stored.
+The first pair selects which codebooks to use from the DC coefficient group for
+ the $Y'$ coefficients and the $C_b$ and $C_r$ coefficients.
+The second pair selects which codebooks to use from {\em all four} of the AC
+ coefficient groups for the $Y'$ coefficients and the $C_b$ and $C_r$
+ coefficients.
+
+The precise specification of how the codebooks are decoded appears in
+ Section~REF.
+
+\section{High-Level Decode Process}
+
+\subsection{Decoder Setup}
+
+Before decoding can begin, a decoder MUST be initialized using the bitstream
+ headers corresponding to the stream to be decoded.
+Theora uses three header packets; all are required, in order, by this
+ specification.
+Once set up, decode may begin at any intra-frame packet---or even inter-frame
+ packets, provided the appropriate decoded reference frames have already been
+ decoded and cached---belonging to the Theora stream.
+In Theora I, all packets after the three initial headers are intra-frame or
+ inter-frame packets.
+
+The header packets are, in order, the identification header, the comment
+ header, and the setup header.
+
+\paragraph{Identification Header}
+
+The identification header identifies the stream as Theora, provides a version
+ number, and defines the characteristics of the video stream such as frame
+ size.
+A complete description of the identification header appears in
+ Section~\ref{sec:idheader}.
+
+\paragraph{Comment Header}
+
+The comment header includes user text comments (`tags') and a vendor string
+ for the application/library that produced the stream.
+The format of the comment header is the same as that used in the Vorbis I and
+ Speex codecs, with slight modifications due to the use of a different bit
+ packing mechanism.
+A complete description of how the comment header is coded appears in
+ Section~\ref{sec:commentheader}, along with a suggested set of tags.
+
+\paragraph{Setup Header}
+
+The setup header includes extensive codec setup information, including the
+ complete set of quantization matrices and Huffman codebooks needed to decode
+ the DCT coefficients.
+A complete description of the setup header appears in
+ Section~\ref{sec:setupheader}.
+
+\subsection{Decode Procedure}
+
+The decoding and synthesis procedure for all video packets is fundamentally the
+ same, with some steps omitted for intra frames.
+\begin{itemize}
+\item
+Decode packet type flag.
+\item
+Decode frame header.
+\item
+Decode coded block information (inter frames only).
+\item
+Decode macro block mode information (inter frames only).
+\item
+Decode motion vectors (inter frames only).
+\item
+Decode block-level \qi\ information.
+\item
+Decode DC coefficient for each coded block.
+\item
+Decode 1st AC coefficient for each coded block.
+\item
+Decode 2nd AC coefficient for each coded block.
+\item
+$\ldots$
+\item
+Decode 63rd AC coefficient for each coded block.
+\item Perform DC coefficient prediction.
+\item Reconstruct coded blocks.
+\item Copy uncoded bocks.
+\item Perform loop filtering.
+\end{itemize}
+
+Note that clever rearrangement of the steps in this process is possible.
+As an example, in a memory-constrained environment, one can make multiple
+ passes through the DCT coefficients to avoid buffering them all in memory.
+On the first pass, the starting location of each coefficient is identified, and
+ then 64 separate get pointers are used to read in the 64 DCT coefficients
+ required to reconstruct each coded block in sequence.
+This operation produces entirely equivalent output and is naturally perfectly
+ legal.
+It may even be a benefit in non-memory-constrained environments due to a
+ reduced cache footprint.
+
+Theora makes equivalence easy to check by defining all decoding operations in
+ terms of exact integer operations.
+No floating-point math is required, and in particular, the implementation of
+ the iDCT transform MUST be followed precisely.
+This prevents the decoder mismatch problem commonly associated with codecs that
+ provide a less rigorous transform specification.
+Such a mismatch problem would be devastating to Theora, since a single rounding
+ error in one frame could propagate throughout the entire succeeding frame due
+ to DC prediction.
+
+\paragraph{Packet Type Decode}
+
+Theora I uses four packet types.
+The first three packet types mark each of the three Theora headers described
+ above.
+The fourth packet type marks a video packet.
+All other packet types are reserved; packets marked with a reserved type should
+ be ignored.
+
+\paragraph{Frame Header Decode}
+
+The frame header contains some global information about the current frame.
+The first is the frame type field, which specifies if this is an intra frame or
+ an inter frame.
+Inter frames predict their contents from previously decoded reference frames.
+Intra frames can be independently decoded with no established reference frames.
+
+The next piece of information in the frame header is the list of \qi\ values
+ allowed in the frame.
+Theora allows from one to three different \qi\ values to be used in a single
+ frame, each of which selects a set of six quantization matrices, one for each
+ quantization type (inter or intra), and one for each color plane.
+The first \qi\ value is {\em always} used when dequantizing DC coefficients.
+The \qi\ value used when dequantizing AC coefficients, however, can vary from
+ block to block.
+VP3, in contrast, only allows a single \qi\ value per frame for both the DC and
+ AC coefficients.
+
+\paragraph{Coded Block Information}
+
+This stage determines which blocks in the frame are coded and which are
+ uncoded.
+A \term{coded block list} is constructed which lists all the coded blocks in
+ coded order.
+For intra frames, every block is coded, and so no data needs to be read from
+ the packet.
+
+\paragraph{Macro Block Mode Information}
+
+For intra frames, every block is coded in INTRA mode, and this stage is
+ skipped.
+In inter frames a \term{coded macro block list} is constructed from the coded
+ block list.
+Any macro block which has at least one of its luma blocks coded is considered
+ coded; all other macro blocks are uncoded, even if they contain coded chroma
+ blocks.
+A coding mode is decoded for each coded macro block, and assigned to all its
+ constituent coded blocks.
+All coded chroma blocks in uncoded macro blocks are assigned the INTER\_NOMV
+ coding mode.
+
+\paragraph{Motion Vectors}
+
+Intra frames are coded entirely in INTRA mode, and so this stage is skipped.
+Some inter coding modes, however, require one or more motion vectors to be
+ specified for each macro block.
+These are decoded in this stage, and an appropriate motion vector is assigned
+ to each coded block in the macro block.
+
+\paragraph{Block-Level \qi\ Information}
+
+If a frame allows multiple \qi\ values, the \qi\ value assigned to each block
+ is decoded here.
+Frames that use only a single \qi\ value have nothing to decode.
+
+\paragraph{DCT Coefficients}
+
+Finally, the quantized DCT coefficients are decoded.
+A list of DCT coefficients in zig-zag order for a single block is represented
+ by a list of tokens.
+A token can take on one of 32 different values, each with a different semantic
+ meaning.
+A single token can represent a single DCT coefficient, a run of zero
+ coefficients within a single block, a combination of a run of zero
+ coefficients followed by a single non-zero coefficient, an
+ \term{End-Of-Block marker}, or a run of EOB markers.
+EOB markers signify that the remainder of the block is one long zero run.
+Unlike JPEG and MPEG, there is no requirement for each block to end with
+ a special marker.
+If non-EOB tokens yield values for all 64 of the coefficients in a block, then
+ no EOB marker occurs.
+
+Each token is associated with a specific \term{token index} in a block.
+For single-coefficient tokens, this index is the zig-zag index of the token in
+ the block.
+For zero-run tokens, this index is the zig-zag index of the {\em first}
+ coefficient in the run.
+For combination tokens, the index is again the zig-zag index of the first
+ coefficient in the zero run.
+For EOB markers, which signify that the remainder of the block is one long zero
+ run, the index is the zig-zag index of the first zero coefficient in that run.
+For EOB runs, the token index is that of the first EOB marker in the run.
+Due to zero runs and EOB markers, a block does not have to have a token for
+ every zig-zag index.
+
+Tokens are grouped in the stream by token index, not by the block they
+ originate from.
+This means that for each zig-zag index in turn, the tokens with that index from
+ {\em all} the coded blocks are coded in coded block order.
+When decoding, a current token index is maintained for each coded block.
+This index is advanced by the number of coefficients that are added to the
+ block as each token is decoded.
+After fully decoding all the tokens with token index \ti, the current token
+ index of every coded block will be \ti\ or greater.
+
+If an EOB run of $n$ blocks is decoded at token index \ti, then it ends the
+ next $n$ blocks in coded block order whose current token index is equal to
+ \ti, but not greater.
+If there are fewer than $n$ blocks with a current token index of \ti, then the
+ decoder goes through the coded block list again from the start, ending blocks
+ with a current token index of $\ti+1$, and so on, until $n$ blocks have been
+ ended.
+
+Tokens are read by parsing a Huffman code that depends on \ti\ and the color
+ plane of the next coded block whose current token index is equal to \ti, but
+ not greater.
+The Huffman codebooks are selected on a per-frame basis from the 80 codebooks
+ defined in the setup header.
+Many tokens have a fixed number of \term{extra bits} associated with them.
+These bits are read from the packet immediately after the token is decoded.
+These are used to define things such as coefficient magnitude, sign, and the
+ length of runs.
+
+\paragraph{DC Prediction}
+
+After the coefficients for each block are decoded, the quantized DC value of
+ each block is adjusted based on the DC values of its neighbors.
+This adjustment is performed by scanning the blocks in raster order, not coded
+ block order.
+
+\paragraph{Reconstruction}
+
+Finally, using the coding mode, motion vector (if applicable), quantized
+ coefficient list, and \qi\ value defined for each block, all the coded blocks
+ are reconstructed.
+The DCT coefficients are dequantized, an inverse DCT transform is applied, and
+ the predictor is formed from the coding mode and motion vector and added to
+ the result.
+
+\paragraph{Loop Filtering}
+
+To complete the reconstructed frame, an ``in-loop'' deblocking filter is
+ applied to the edges of all coded blocks.
+
+
+\chapter{Video Formats}
+
+This section gives a precise description of the video formats that Theora is
+ capable of storing.
+The Theora bitstream is capable of handling video at any arbitrary resolution
+ up to $1048560\times 1048560$.
+Such video would require almost three terabytes of storage per frame for
+ uncompressed data, so compliant decoders MAY refuse to decode images with
+ sizes beyond their capabilities.
+%TODO: What MUST a "compliant" decoder accept?
+%TODO: What SHOULD a decoder use for an upper bound? (derive from total amount
+%TODO: of memory and memory bandwidth)
+%TODO: Any lower limits?
+%TODO: We really need hardware device profiles, but such things should be
+%TODO: developed with input from the hardware community.
+%TODO: And even then sometimes they're useless
+
+The remainder of this section talks about two specific aspects of the video
+ format: the color space and the pixel format.
+The first describes how color is represented and how to transform that color
+ representation into a device independent color space such as CIE $XYZ$ (1931).
+The second describes the various schemes for sampling the color values in time
+ and space.
+
+\section{Color Space Conventions}
+
+There are a large number of different color standards used in digital video.
+Since Theora is a lossy codec, it restricts itself to only a few of them to
+ simplify playback.
+Unlike the alternate method of describing all the parameters of the color
+ model, this allows a few dedicated routines for color conversion to be written
+ and heavily optimized in a decoder.
+More flexible conversion functions should instead be specified in an encoder,
+ where additional computational complexity is more easily tolerated.
+The color spaces were selected to give a fair representation of color standards
+ in use around the world today.
+Most of the standards that do not exactly match one of these can be converted
+ to one fairly easily.
+
+All Theora color spaces are $Y'C_bC_r$ color spaces with one luma channel and
+ two chroma channels.
+Each channel contains 8-bit discrete values in the range $0\ldots255$, which
+ represent non-linear gamma pre-corrected signals.
+The Theora identification header contains an 8-bit value that describes the
+ color space.
+This merely selects one of the color spaces available from an enumerated list.
+Currently, only two color spaces are defined, with a third possibility that
+ indicates the color space is ``unknown".
+
+\section{Color Space Conversions and Parameters}
+\label{sec:color-xforms}
+
+The parameters which describe the conversions between each color space are
+ listed below.
+These are the parameters needed to map colors from the encoded $Y'C_bC_r$
+ representation to the device-independent color space CIE $XYZ$ (1931).
+These parameters define abstract mathematical conversion functions which are
+ infinitely precise.
+The accuracy and precision with which the conversions are performed in a real
+ system is determined by the quality of output desired and the available
+ processing power.
+Exact decoder output is defined by this specification only in the original
+ $Y'C_bC_r$ space.
+
+\begin{description}
+\item[$Y'C_bC_r$ to $Y'P_bP_r$:]
+\vspace{\baselineskip}\hfill
+
+This conversion takes 8-bit discrete values in the range $[0\ldots255]$ and
+ maps them to real values in the range $[0\ldots1]$ for Y and
+ $[-\frac{1}{2}\ldots\frac{1}{2}]$ for $P_b$ and $P_r$.
+Because some values may fall outside the offset and excursion defined for each
+ channel in the $Y'C_bC_r$ space, the results may fall outside these ranges in
+ $Y'P_bP_r$ space.
+No clamping should be done at this stage.
+
+\begin{align}
+Y'_\mathrm{out} & =
+ \frac{Y'_\mathrm{in}-\mathrm{Offset}_Y}{\mathrm{Excursion}_Y} \\
+P_b & =
+ \frac{C_b-\mathrm{Offset}_{C_b}}{\mathrm{Excursion}_{C_b}} \\
+P_r & =
+ \frac{C_r-\mathrm{Offset}_{C_r}}{\mathrm{Excursion}_{C_r}}
+\end{align}
+
+Parameters: $\mathrm{Offset}_{Y,C_b,C_r}$, $\mathrm{Excursion}_{Y,C_b,C_r}$.
+
+\item[$Y'P_bP_r$ to $R'G'B'$:]
+\vspace{\baselineskip}\hfill
+
+This conversion takes the one luma and two chroma channel representation and
+ maps it to the non-linear $R'G'B'$ space used to drive actual output devices.
+Values should be clamped into the range $[0\ldots1]$ after this stage.
+
+\begin{align}
+R' & = Y'+2(1-K_r)P_r \\
+G' & = Y'-2\frac{(1-K_b)K_b}{1-K_b-K_r}P_b-2\frac{(1-K_r)K_r}{1-K_b-K_r}P_r\\
+B' & = Y'+2(1-K_b)P_b
+\end{align}
+
+Parameters: $K_b,K_r$.
+
+\item[$R'G'B'$ to $RGB$ (Output device gamma correction):]
+\vspace{\baselineskip}\hfill
+
+This conversion takes the non-linear $R'G'B'$ voltage levels and maps them to
+ linear light levels produced by the actual output device.
+Note that this conversion is only that of the output device, and its inverse is
+ {\em not} that used by the input device.
+Because a dim viewing environment is assumed in most television standards, the
+ overall gamma between the input and output devices is usually around $1.1$ to
+ $1.2$, and not a strict $1.0$.
+
+For calibration with actual output devices, the model
+\begin{align}
+L & =(E'+\Delta)^\gamma
+\end{align}
+ should be used, with $\Delta$ the free parameter and $\gamma$ held fixed to
+ the value specified in this document.
+The conversion function presented here is an idealized version with $\Delta=0$.
+
+\begin{align}
+R & = R'^\gamma \\
+G & = G'^\gamma \\
+B & = B'^\gamma
+\end{align}
+
+Parameters: $\gamma$.
+
+\item[$RGB$ to $R'G'B'$ (Input device gamma correction):]
+\vspace{\baselineskip}\hfill
+
+%TODO: Tag section as non-normative
+
+This conversion takes linear light levels and maps them to the non-linear
+ voltage levels produced in the actual input device.
+This information is merely informative.
+It is not required for building a decoder or for converting between the various
+ formats and the actual output capabilities of a particular device.
+
+A linear segment is introduced on the low end to reduce noise in dark areas of
+ the image.
+The rest of the scale is adjusted so that the power segment of the curve
+ intersects the linear segment with the proper slope, and so that it still maps
+ 0 to 0 and 1 to 1.
+
+\begin{align}
+R' & = \left\{
+\begin{array}{ll}
+\alpha R, & 0\le R<\delta \\
+(1+\epsilon)R^\beta-\epsilon, & \delta\le R\le1
+\end{array}\right. \\
+G' & = \left\{
+\begin{array}{ll}
+\alpha G, & 0\le G<\delta \\
+(1+\epsilon)G^\beta-\epsilon, & \delta\le G\le1
+\end{array}\right. \\
+B' & = \left\{
+\begin{array}{ll}
+\alpha B, & 0\le B<\delta \\
+(1+\epsilon)B^\beta-\epsilon, & \delta\le B\le1
+\end{array}\right.
+\end{align}
+
+Parameters: $\beta$, $\alpha$, $\delta$, $\epsilon$.
+
+\item[$RGB$ to CIE $XYZ$ (1931):]
+\vspace{\baselineskip}\hfill
+
+This conversion maps a device-dependent linear RGB space to the
+ device-independent linear CIE $XYZ$ space.
+The parameters are the CIE chromaticity coordinates of the three
+ primaries---red, green, and blue---as well as the chromaticity coordinates
+ of the white point of the device.
+This is how hardware manufacturers and standards typically describe a
+ particular $RGB$ space.
+The math required to convert these parameters into a useful transformation
+ matrix is reproduced below.
+
+\begin{align}
+F & =
+\left[\begin{array}{ccc}
+\frac{x_r}{y_r} & \frac{x_g}{y_g} & \frac{x_b}{y_b} \\
+1 & 1 & 1 \\
+\frac{1-x_r-y_r}{y_r} & \frac{1-x_g-y_g}{y_g} & \frac{1-x_b-y_b}{y_b}
+\end{array}\right] \\
+\left[\begin{array}{c}
+s_r \\
+s_g \\
+s_b
+\end{array}\right] & =
+F^{-1}\left[\begin{array}{c}
+\frac{x_w}{y_w} \\
+1 \\
+\frac{1-x_w-y_w}{y_w}
+\end{array}\right] \\
+\left[\begin{array}{c}
+X \\
+Y \\
+Z
+\end{array}\right] & =
+F\left[\begin{array}{c}
+s_rR \\
+s_gG \\
+s_bB
+\end{array}\right]
+\end{align}
+Parameters: $x_r,x_g,x_b,x_w, y_r,y_g,y_b,y_w$.
+
+\end{description}
+
+\section{Available Color Spaces}
+\label{sec:colorspaces}
+
+These are the color spaces currently defined for use by Theora video.
+Each one has a short name, with which it is referred to in this document, and
+ a more detailed specification of the standards from which its parameters are
+ derived.
+Some standards do not specify all the parameters necessary.
+For these unspecified parameters, this document serves as the definition of
+ what should be used when encoding or decoding Theora video.
+
+\subsection{Rec.~470M (Rec.~ITU-R~BT.470-6 System M/NTSC with
+ Rec.~ITU-R~BT.601-5)}
+\label{sec:470m}
+
+This color space is used by broadcast television and DVDs in much of the
+ Americas, Japan, Korea, and the Union of Myanmar \cite{rec470}.
+This color space may also be used for System M/PAL (Brazil), with an
+ appropriate conversion supplied by the encoder to compensate for the
+ different gamma value.
+See Section~\ref{sec:470bg} for an appropriate gamma value to assume for M/PAL
+ input.
+
+In the US, studio monitors are adjusted to a D65 white point
+ ($x_w,y_w=0.313,0.329$).
+In Japan, studio monitors are adjusted to a D white of 9300K
+ ($x_w,y_w=0.285,0.293$).
+
+Rec.~470 does not specify a digital encoding of the color signals.
+For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
+ $R'G'B'$ signals specified by Rec.~470.
+
+Rec.~470 does not specify an input gamma function.
+For Theora, the Rec.~709 \cite{rec709} input function is assumed.
+This is the same as that specified by SMPTE 170M \cite{smpte170m}, which claims
+ to reflect modern practice in the creation of NTSC signals circa 1994.
+
+The parameters for all the color transformations defined in
+ Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470m}.
+
+\begin{table}[htb]
+\begin{align*}
+\mathrm{Offset}_{Y,C_b,C_r} & = (16, 128, 128) \\
+\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
+K_r & = 0.299 \\
+K_b & = 0.114 \\
+\gamma & = 2.2 \\
+\beta & = 0.45 \\
+\alpha & = 4.5 \\
+\delta & = 0.018 \\
+\epsilon & = 0.099 \\
+x_r,y_r & = 0.67, 0.33 \\
+x_g,y_g & = 0.21, 0.71 \\
+x_b,y_b & = 0.14, 0.08 \\
+\text{(Illuminant C) } x_w,y_w & = 0.310, 0.316 \\
+\end{align*}
+\caption{Rec.~470M Parameters}
+\label{tab:470m}
+\end{table}
+
+\subsection{Rec.~470BG (Rec.~ITU-R~BT.470-6 Systems B and G with
+ Rec.~ITU-R~BT.601-5)}
+\label{sec:470bg}
+
+This color space is used by the PAL and SECAM systems in much of the rest of
+ the world \cite{rec470}
+This can be used directly by systems (B, B1, D, D1, G, H, I, K, N)/PAL and (B,
+ D, G, H, K, K1, L)/SECAM\@.
+
+Note that the Rec.~470BG chromaticity values are different from those
+ specified in Rec.~470M\@.
+When PAL and SECAM systems were first designed, they were based upon the same
+ primaries as NTSC\@.
+However, as methods of making color picture tubes have changed, the primaries
+ used have changed as well.
+The U.S. recommends using correction circuitry to approximate the existing,
+ standard NTSC primaries.
+Current PAL and SECAM systems have standardized on primaries in accord with
+ more recent technology.
+
+Rec.~470 provisionally permits the use of the NTSC chromaticity values (given
+ in Section~\ref{sec:470m}) with legacy PAL and SECAM equipment.
+In Theora, material must be decoded assuming the new PAL and SECAM primaries.
+Material intended for display on old legacy devices should be converted by the
+ decoder.
+
+The official Rec.~470BG specifies a gamma value of $\gamma=2.8$.
+However, in practice this value is unrealistically high \cite{Poyn97}.
+Rec.~470BG states that the overall system gamma should be approximately
+ $\gamma\beta=1.2$.
+Since most cameras pre-correct with a gamma value of $\beta=0.45$,
+ this suggests an output device gamma of approximately $\gamma=2.67$.
+This is the value recommended for use with PAL systems in Theora.
+
+Rec.~470 does not specify a digital encoding of the color signals.
+For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
+ $R'G'B'$ signals specified by Rec.~470.
+
+Rec.~470 does not specify an input gamma function.
+For Theora, the Rec 709 \cite{rec709} input function is assumed.
+
+The parameters for all the color transformations defined in
+ Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470bg}.
+
+\begin{table}[htb]
+\begin{align*}
+\mathrm{Offset}_{Y,C_b,C_r} & = (16, 128, 128) \\
+\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
+K_r & = 0.299 \\
+K_b & = 0.114 \\
+\gamma & = 2.67 \\
+\beta & = 0.45 \\
+\alpha & = 4.5 \\
+\delta & = 0.018 \\
+\epsilon & = 0.099 \\
+x_r,y_r & = 0.64, 0.33 \\
+x_g,y_g & = 0.29, 0.60 \\
+x_b,y_b & = 0.15, 0.06 \\
+\text{(D65) } x_w,y_w & = 0.313, 0.329 \\
+\end{align*}
+\caption{Rec.~470BG Parameters}
+\label{tab:470bg}
+\end{table}
+
+\section{Pixel Formats}
+\label{sec:pixfmts}
+
+Theora supports several different pixel formats, each of which uses different
+ subsampling for the chroma planes relative to the luma plane.
+
+\subsection{4:4:4 Subsampling}
+\label{sec:444}
+
+All three color planes are stored at full resolution.
+The samples in the different planes are all at co-located sites.
+
+%TODO: Figure.
+%YRB YRB
+%
+%
+%
+%YRB YRB
+%
+%
+%
+
+
+\subsection{4:2:2 Subsampling}
+\label{sec:422}
+
+The $C_b$ and $C_r$ planes are stored with half the horizontal resolution of
+ the $Y'$ plane.
+Thus, each of these planes has half the number of horizontal blocks as the luma
+ plane.
+Similarly, they have half the number of horizontal super blocks, rounded up.
+Macro blocks are defined across color planes, and so their number does not
+ change, but each macro block contains half as many chroma blocks.
+
+The chroma samples are vertically aligned with the luma samples, but
+ horizontally centered between two luma samples.
+Thus, each luma sample has a unique closest chroma sample.
+A horizontal phase shift may be required to produce signals which use different
+ horizontal chroma sampling locations for compatibility with different systems.
+
+%TODO: Figure.
+%Y RB Y Y RB Y
+%
+%
+%
+%Y RB Y Y RB Y
+%
+%
+%
+
+\subsection{4:2:0 Subsampling}
+\label{sec:420}
+
+The $C_b$ and $C_r$ planes are stored with half the horizontal and half the
+ vertical resolution of the $Y'$ plane.
+Thus, each of these planes has half the number of horizontal blocks and half
+ the number of vertical blocks as the luma plane, for a total of one quarter
+ the number of blocks.
+Similarly, they have half the number of horizontal super blocks and half the
+ number of vertical super blocks, rounded up.
+Macro blocks are defined across color planes, and so their number does not
+ change, but each macro block contains within it one quarter as many
+ chroma blocks.
+
+The chroma samples are vertically and horizontally centered between four luma
+ samples.
+Thus, each luma sample has a unique closest chroma sample.
+This is the same sub-sampling pattern used with JPEG, MJPEG, and MPEG-1, and
+ was inherited from VP3.
+A horizontal or vertical phase shift may be required to produce signals which
+ use different chroma sampling locations for compatibility with different
+ systems.
+
+%TODO: Figure.
+%Y Y Y Y
+%
+% RB RB
+%
+%Y Y Y Y
+%
+%
+%
+%Y Y Y Y
+%
+% RB RB
+%
+%Y Y Y Y
+%
+%
+%
+
+\subsection{Subsampling and the Picture Region}
+
+Although the frame size must be an integral number of macro blocks, and thus
+ both the number of pixels and the number of blocks in each direction must be
+ even, no such requirement is made of the picture region.
+Thus, when using subsampled pixel formats, careful attention must be paid to
+ which chroma samples correspond to which luma samples.
+
+As mentioned above, for each pixel format, there is a unique chroma sample that
+ is the closest to each luma sample.
+When cropping the chroma planes to the picture region, all the chroma samples
+ corresponding to a luma sample in the cropped picture region must be included.
+Thus, when dividing the width or height of the picture region by two to obtain
+ the size of the subsampled chroma planes, they must be rounded up.
+
+Furthermore, the sampling locations are defined relative to the frame,
+ {\em not} the picture region.
+When the width of the picture region is odd in the 4:2:2 and 4:2:0 formats,
+ then the locations of chroma samples relative to the luma samples depends on
+ whether or not the X offset of the picture region is odd.
+If the offset is even, each column of chroma samples corresponds to two columns
+ of luma samples, except the last column which corresponds to one.
+If the offset is odd, then it is the first column of chroma samples which
+ corresponds to only one column of luma samples, while the remaining columns
+ each correspond to two.
+
+A similar process is followed with the rows of a picture region of odd height
+ encoded in the 4:2:0 format.
+If the Y offset is even, each row of chroma samples corresponds to two rows of
+ luma samples, except the last row which corresponds to one.
+If the offset is odd, then it is the first row of chroma samples which
+ corresponds to only one row of luma samples, while the remaining rows each
+ correspond to two.
+
+%TODO: Figures!
+
+%TODO: informational section for encoders:
+% When the chroma planes are subsampled, encoders SHOULD chose picture
+% offsets and dimensions that are even so that the subsampling
+% positions are reproduced cleanly.
+
+\chapter{Bitpacking Convention}
+\label{sec:bitpacking}
+
+\section{Overview}
+
+The Theora codec uses relatively unstructured raw packets containing
+ binary integer fields of arbitrary width.
+Logically, each packet is a bitstream in which bits are written one-by-one by
+ the encoder and then read one-by-one in the same order by the decoder.
+Most current binary storage arrangements group bits into a native storage unit
+ of eight bits (octets), sixteen bits, thirty-two bits, or less commonly other
+ fixed sizes.
+The Theora bitpacking convention specifies the correct mapping of the logical
+ packet bitstream into an actual representation in fixed-width units.
+
+\subsection{Octets and Bytes}
+
+In most contemporary architectures, a `byte' is synonymous with an `octect',
+ that is, eight bits.
+For purposes of the bitpacking convention, a byte implies the smallest native
+ integer storage representation offered by a platform.
+Modern file systems invariably offer bytes as the fundamental atom of storage.
+
+The most ubiquitous architectures today consider a `byte' to be an octet.
+Note, however, that the Theora bitpacking convention is still well defined for
+ any native byte size; an implementation can use the native bit-width of a
+ given storage system.
+This document assumes that a byte is one octet for purposes of example only.
+
+\subsection{Words and Byte Order}
+
+A `word' is an integer size that is a grouped multiple of the byte size.
+Most architectures consider a word to be a group of two, four, or eight bytes.
+Each byte in the word can be ranked by order of `significance', e.g.\ the
+ significance of the bits in each byte when storing a binary integer in the
+ word.
+Several byte orderings are possible in a word.
+The common ones are
+\begin{itemize}
+\item{Big-endian:}
+in which the most significant byte comes first, e.g.\ 3-2-1-0,
+\item{Little-endian:}
+in which the least significant byte comes first, e.g.\ 0-1-2-3, and
+\item{Mixed-endian:}
+one of the less-common orderings that cannot be put into the above two
+ categories, e.g.\ 3-1-2-0 or 0-2-1-3.
+\end{itemize}
+
+The Theora 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
+ code that operates on a word of storage at a time rather than a byte.
+Logically, bytes are always encoded and decoded in order from byte zero through
+ byte $n$.
+
+\subsection{Bit Order}
+
+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.
+Bits in a byte are numbered from zero at the LSb to $n$ for the MSb, where
+ $n=7$ in an octet.
+
+\section{Coding Bits into Bytes}
+
+The Theora codec needs to encode 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 read at the bit position immediately
+ after the end of the previous field.
+
+The decoder logically unpacks integers by first reading the MSb of a binary
+ integer from the logical bitstream, followed by the next most significant
+ bit, etc., until the required number of bits have been read.
+When unpacking the bytes into bits, the decoder begins by reading the MSb of
+ the integer to be read from the most significant unread bit position of the
+ source byte, followed by the next-most significant bit position of the
+ destination integer, and so on up to the requested number of bits.
+Note that this differs from the Vorbis I codec, which
+ begins decoding with the LSb of the source integer, reading it from the
+ LSb of the source byte.
+When all the bits of the current source byte are read, decoding continues with
+ the MSb of the next byte.
+Any unfilled bits in the last byte of the packet MUST be cleared to zero by the
+ encoder.
+
+\subsection{Signedness}
+
+The binary integers decoded by the above process may be either signed or
+ unsigned.
+This varies from integer to integer, and this specification
+ indicates how each value should be interpreted as it is read.
+That is, depending on context, the three bit binary pattern \bin{111} can be
+ taken to represent either `$7$' as an unsigned integer or `$-1$' as a signed,
+ two's complement integer.
+
+\subsection{Encoding Example}
+
+The following example shows the state of an (8-bit) byte stream after several
+ binary integers are encoded, including the location of the put pointer for the
+ next bit to write to and the total length of the stream in bytes.
+
+Encode the 4 bit unsigned integer value `12' (\bin{1100}) into an empty byte
+ stream.
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{}& &&&&$\downarrow$&&&& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
+ 0 & 0 & 0 & 0 & $\leftarrow$ \\
+byte 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
+byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 1 byte
+\end{tabular}
+\vspace{\baselineskip}
+
+Continue by encoding the 3 bit signed integer value `-1' (\bin{111}).
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{} &&&&&&&&$\downarrow$& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
+ \textbf{1} & \textbf{1} & \textbf{1} & 0 & $\leftarrow$ \\
+byte 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
+byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 1 byte
+\end{tabular}
+\vspace{\baselineskip}
+
+Continue by encoding the 7 bit integer value `17' (\bin{0010001}).
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{} &&&&&&&$\downarrow$&& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
+ \textbf{1} & \textbf{1} & \textbf{1} & \textbf{0} & \\
+byte 1 & \textbf{0} & \textbf{1} & \textbf{0} & \textbf{0} &
+ \textbf{0} & \textbf{1} & 0 & 0 & $\leftarrow$ \\
+byte 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+byte 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\
+\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
+byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 2 bytes
+\end{tabular}
+\vspace{\baselineskip}
+
+Continue by encoding the 13 bit integer value `6969' (\bin{11011\ 00111001}).
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{} &&&&$\downarrow$&&&&& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
+ \textbf{1} & \textbf{1} & \textbf{1} & \textbf{0} & \\
+byte 1 & \textbf{0} & \textbf{1} & \textbf{0} & \textbf{0} &
+ \textbf{0} & \textbf{1} & \textbf{1} & \textbf{1} & \\
+byte 2 & \textbf{0} & \textbf{1} & \textbf{1} & \textbf{0} &
+ \textbf{0} & \textbf{1} & \textbf{1} & \textbf{1} & \\
+byte 3 & \textbf{0} & \textbf{0} & \textbf{1} &
+ 0 & 0 & 0 & 0 & 0 & $\leftarrow$ \\
+\multicolumn{1}{c|}{$\vdots$}&\multicolumn{8}{c}{$\vdots$}& \\
+byte $n$ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 4 bytes
+\end{tabular}
+\vspace{\baselineskip}
+
+\subsection{Decoding Example}
+
+The following example shows the state of the (8-bit) byte stream encoded in the
+ previous example after several binary integers are decoded, including the
+ location of the get pointer for the next bit to read.
+
+Read a two bit unsigned integer from the example encoded above.
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{} &&&$\downarrow$&&&&&& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & 0 & 0 & 1 & 1 & 1 & 0 & $\leftarrow$ \\
+byte 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & \\
+byte 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & \\
+byte 3 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 4 bytes
+\end{tabular}
+\vspace{\baselineskip}
+
+Value read: 3 (\bin{11}).
+
+Read another two bit unsigned integer from the example encoded above.
+
+\begin{tabular}{r|ccccccccl}
+\multicolumn{1}{r}{} &&&&&$\downarrow$&&&& \\
+ & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & \\\cline{1-9}
+byte 0 & \textbf{1} & \textbf{1} & \textbf{0} & \textbf{0} &
+ 1 & 1 & 1 & 0 & $\leftarrow$ \\
+byte 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & \\
+byte 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & \\
+byte 3 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 &
+byte stream length: 4 bytes
+\end{tabular}
+\vspace{\baselineskip}
+
+Value read: 0 (\bin{00}).
+
+Two things are worth noting here.
+\begin{itemize}
+\item
+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.
+No artificial alignment boundaries are maintained in the bitstream.
+\item
+The first value is the integer `$3$' only because the context stated we were
+ reading an unsigned integer.
+Had the context stated we were reading a signed integer, the returned value
+ would have been the integer `$-1$'.
+\end{itemize}
+
+\subsection{End-of-Packet Alignment}
+
+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 bitstream encoded as a byte stream MUST begin and end on a
+ byte boundary.
+Often, the encoded packet bitstream is not an integer number of bytes, and so
+ there is unused space in the last byte of a packet.
+
+%r: I think the generality here is necessary to be consistent with our assertions
+%r: elsewhere about being independent of transport and byte width
+When a Theora encoder produces packets for embedding in a byte-aligned
+ container, unused space in the last byte of a packet is always zeroed during
+ the encoding process.
+Thus, should this unused space be read, it will return binary zeroes.
+There is no marker pattern or stuffing bits that will allow the decoder to
+ obtain the exact size, in bits, of the original bitstream.
+This knowledge is not required for decoding.
+
+Attempting to read past the end of an encoded packet results in an
+ `end-of-packet' condition.
+Any further read operations after an `end-of-packet' condition shall also
+ return `end-of-packet'.
+Unlike Vorbis, Theora does not use truncated packets as a normal mode of
+ operation.
+Therefore if a decoder encounters the `end-of-packet' condition during normal
+ decoding, it may attempt to use the bits that were read to recover as much of
+ encoded data as possible, signal a warning or error, or both.
+
+\subsection{Reading Zero Bit Integers}
+
+Reading a zero bit integer returns the value `$0$' and does not increment
+ the stream pointer.
+Reading to the end of the packet, but not past the end, so that an
+ `end-of-packet' condition is 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 integer after a previous read sets the `end-of-packet'
+ condition shall fail, also returning `end-of-packet'.
+
+\chapter{Bitstream Headers}
+\label{sec:headers}
+
+A Theora bitstream begins with three header packets.
+The header packets are, in order, the identification header, the comment
+ header, and the setup header.
+All are required for decode compliance.
+An end-of-packet condition encountered while decoding the identification or
+ setup header packets renders the stream undecodable.
+An end-of-packet condition encountered while decode the comment header is a
+ non-fatal error condition, and MAY be ignored by a decoder.
+
+\paragraph{VP3 Compatibility}
+
+VP3 relies on the headers provided by its container, usually either AVI or
+ Quicktime.
+As such, several parameters available in these headers are not available to VP3
+ streams.
+These are indicated as they appear in the sections below.
+
+\section{Common Header Decode}
+\label{sub:common-header}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{HEADERTYPE} & Integer & 8 & No & The type of the header being
+ decoded. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:} None.
+\medskip
+
+Each header packet begins with the same header fields, which are decoded as
+ follows:
+
+\begin{enumerate}
+\item
+Read an 8-bit unsigned integer as \bitvar{HEADERTYPE}.
+If the most significant bit of this integer is not set, then stop.
+This is not a header packet.
+\item
+Read 6 8-bit unsigned integers.
+If these do not have the values \hex{74}, \hex{68}, \hex{65}, \hex{6F},
+ \hex{72}, and \hex{61}, respectively, then stop.
+This stream is not decodable by this specification.
+These values correspond to the ASCII values of the characters `t', `h', `e',
+ `o', `r', and `a'.
+\end{enumerate}
+
+Decode continues according to \bitvar{HEADERTYPE}.
+The identification header is type \hex{80}, the comment header is type
+ \hex{81}, and the setup header is type \hex{82}.
+These packets must occur in the order: identification, comment, setup.
+%r: I clarified the initial-bit scheme here
+%TBT: Dashes let the reader know they'll have to pick up the rest of the
+%TBT: sentence after the explanatory phrase.
+%TBT: Otherwise it just sounds like the bit must exist.
+All header packets have the most significant bit of the type
+ field---which is the initial bit in the packet---set.
+This distinguishes them from video data packets in which the first bit
+ is unset.
+% extra header packets are a feature Dan argued for way back when for
+% backward-compatible extensions (and icc colourspace for example)
+% I think it's reasonable
+%TBT: You can always just stick more stuff in the setup header.
+Packets with other header types (\hex{83}--\hex{FF}) are reserved and MUST be
+ ignored.
+
+\section{Identification Header Decode}
+\label{sec:idheader}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{VMAJ} & Integer & 8 & No & The major version number. \\
+\bitvar{VMIN} & Integer & 8 & No & The minor version number. \\
+\bitvar{VREV} & Integer & 8 & No & The version revision number. \\
+\bitvar{FMBW} & Integer & 16 & No & The width of the frame in macro
+ blocks. \\
+\bitvar{FMBH} & Integer & 16 & No & The height of the frame in macro
+ blocks. \\
+\bitvar{NSBS} & Integer & 32 & No & The total number of super blocks in a
+ frame. \\
+\bitvar{NBS} & Integer & 32 & No & The total number of blocks in a
+ frame. \\
+\bitvar{NMBS} & Integer & 32 & No & The total number of macro blocks in a
+ frame. \\
+\bitvar{PICW} & Integer & 20 & No & The width of the picture region in
+ pixels. \\
+\bitvar{PICH} & Integer & 20 & No & The height of the picture region in
+ pixels. \\
+\bitvar{PICX} & Integer & 8 & No & The X offset of the picture region in
+ pixels. \\
+\bitvar{PICY} & Integer & 8 & No & The Y offset of the picture region in
+ pixels. \\
+\bitvar{FRN} & Integer & 32 & No & The frame-rate numerator. \\
+\bitvar{FRD} & Integer & 32 & No & The frame-rate denominator. \\
+\bitvar{PARN} & Integer & 24 & No & The pixel aspect-ratio numerator. \\
+\bitvar{PARD} & Integer & 24 & No & The pixel aspect-ratio denominator. \\
+\bitvar{CS} & Integer & 8 & No & The color space. \\
+\bitvar{PF} & Integer & 8 & No & The pixel format. \\
+\bitvar{NOMBR} & Integer & 24 & No & The nominal bitrate of the stream, in
+ bits per second. \\
+\bitvar{QUAL} & Integer & 6 & No & The quality hint. \\
+\bitvar{KFGSHIFT} & Integer & 5 & No & The amount to shift the key frame
+ number by in the granule position. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:} None.
+\medskip
+
+The identification header is a short header with only a few fields used to
+ declare the stream definitively as Theora and provide detailed information
+ about the format of the fully decoded video data.
+The identification header is decoded as follows:
+
+\begin{enumerate}
+\item
+Decode the common header fields according to the procedure described in
+ Section~\ref{sub:common-header}.
+If \bitvar{HEADERTYPE} returned by this procedure is not \hex{80}, then stop.
+This packet is not the identification header.
+\item
+Read an 8-bit unsigned integer as \bitvar{VMAJ}.
+If \bitvar{VMAJ} is not $3$, then stop.
+This stream is not decodable according to this specification.
+\item
+Read an 8-bit unsigned integer as \bitvar{VMIN}.
+If \bitvar{VMIN} is not $2$, then stop.
+This stream is not decodable according to this specification.
+\item
+Read an 8-bit unsigned integer as \bitvar{VREV}.
+If \bitvar{VREV} is not $0$, then stop.
+This stream is not decodable according to this specification.
+\item
+Read a 16-bit unsigned integer as \bitvar{FMBW}.
+This MUST be greater than zero.
+This specifies the width of the coded frame in macro blocks.
+The actual width of the frame in pixels is $\bitvar{FMBW}*16$.
+\item
+Read a 16-bit unsigned integer as \bitvar{FMBH}.
+This MUST be greater than zero.
+This specifies the height of the coded frame in macro blocks.
+The actual height of the frame in pixels is $\bitvar{FMBH}*16$.
+\item
+Read a 24-bit unsigned integer as \bitvar{PICW}.
+This MUST be no greater than $(\bitvar{FMBW}*16)$.
+Note that 24 bits are read, even though only 20 bits are sufficient to specify
+ any value of the picture width.
+This is done to preserve octet alignment in this header, to allow for a
+ simplified parser implementation.
+\item
+Read a 24-bit unsigned integer as \bitvar{PICH}.
+This MUST be no greater than $(\bitvar{FMBH}*16)$.
+Together with \bitvar{PICW}, this specifies the size of the displayable picture
+ region within the coded frame.
+See Figure~\ref{fig:pic-frame}.
+Again, 24 bits are read instead of 20.
+\item
+Read an 8-bit unsigned integer as \bitvar{PICX}.
+This MUST be no greater than $(\bitvar{FMBW}*16-\bitvar{PICX})$.
+\item
+Read an 8-bit unsigned integer as \bitvar{PICY}.
+This MUST be no greater than $(\bitvar{FMBH}*16-\bitvar{PICY})$.
+Together with \bitvar{PICX}, this specifies the location of the lower-left
+ corner of the displayable picture region.
+See Figure~\ref{fig:pic-frame}.
+\item
+Read a 32-bit unsigned integer as \bitvar{FRN}.
+This MUST be greater than zero.
+\item
+Read a 32-bit unsigned integer as \bitvar{FRD}.
+This MUST be greater than zero.
+Theora is a fixed-frame rate video codec.
+Frames are sampled at the constant rate of $\frac{\bitvar{FRN}}{\bitvar{FRD}}$
+ frames per second.
+The presentation time of the first frame is at zero seconds.
+No mechanism is provided to specify a non-zero offset for the initial
+ frame.
+\item
+Read a 24-bit unsigned integer as \bitvar{PARN}.
+\item
+Read a 24-bit unsigned integer as \bitvar{PRAD}.
+Together with \bitvar{PARN}, these specify the aspect ratio of the pixels
+ within a frame, defined as the ratio of the physical width of a pixel to its
+ physical height.
+This is given by the ratio $\bitvar{PARN}:\bitvar{PARD}$.
+Either of these fields MAY be zero, in which case the pixel aspect ratio
+ defaults to $1:1$.
+\item
+Read an 8-bit unsigned integer as \bitvar{CS}.
+This is a value from an enumerated list of the available color spaces, given in
+ Table~\ref{tab:colorspaces}.
+The `Undefined' value indicates that color space information was not available
+ to the encoder.
+It MAY be specified by the application via an external means.
+If a reserved value is given, a decoder MAY refuse to decode the stream.
+\begin{table}[htb]
+\begin{center}
+\begin{tabular*}{215pt}{cl@{\extracolsep{\fill}}c}\toprule
+Value & Color Space \\\midrule
+$0$ & Undefined. \\
+$1$ & Rec.~470M (see Section~\ref{sec:470m}). \\
+$2$ & Rec.~470BG (see Section~\ref{sec:470bg}). \\
+$3$ & Reserved. \\
+$\vdots$ & \\
+$255$ & \\
+\bottomrule\end{tabular*}
+\end{center}
+\caption{Enumerated List of Color Spaces}
+\label{tab:colorspaces}
+\end{table}
+\item
+Read a 24-bit unsigned integer as \bitvar{NOMBR}.
+The \bitvar{NOMBR} field is used only as a hint.
+For pure VBR streams, this value may be considerably off.
+The field MAY be set to zero to indicate that the encoder did not care to
+ speculate.
+\item
+Read a 6-bit unsigned integer as \bitvar{QUAL}.
+This value is used to provide a hint as to the relative quality of the stream
+ when compared to others produced by the same encoder.
+Larger values indicate higher quality.
+This can be used, for example, to select among several streams containing the
+ same material encoded with different settings.
+\item
+Read a 5-bit unsigned integer as \bitvar{KFGSHIFT}.
+The \bitvar{KFGSHIFT} is used to partition the granule position associated with
+ each packet into two different parts.
+The frame number of the last key frame, starting from zero, is stored in the
+ upper $64-\bitvar{KFGSHIFT}$ bits, while the lower \bitvar{KFGSHIFT} bits
+ contain the number of frames since the last keyframe.
+Complete details on the granule position mapping are specified in Section~REF.
+\item
+Read a 2-bit unsigned integer as \bitvar{PF}.
+The \bitvar{PF} field contains a value from an enumerated list of the available
+ pixel formats, given in Table~\ref{tab:pixel-formats}.
+If the reserved value $1$ is given, stop.
+This stream is not decodable according to this specification.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular*}{215pt}{cl@{\extracolsep{\fill}}c}\toprule
+Value & Pixel Format \\\midrule
+$0$ & 4:2:0 (see Section~\ref{sec:420}). \\
+$1$ & Reserved. \\
+$2$ & 4:2:2 (see Section~\ref{sec:422}). \\
+$3$ & 4:4:4 (see Section~\ref{sec:444}). \\
+\bottomrule\end{tabular*}
+\end{center}
+\caption{Enumerated List of Pixel Formats}
+\label{tab:pixel-formats}
+\end{table}
+
+\item
+Read a 3-bit unsigned integer.
+These bits are reserved.
+If this value is not zero, then stop.
+This stream is not decodable according to this specification.
+\item
+Assign \bitvar{NSBS} a value according to \bitvar{PF}, as given by
+ Table~\ref{tab:nsbs-for-pf}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cc}\toprule
+\bitvar{PF} & \bitvar{NSBS} \\\midrule
+$0$ & $\begin{aligned}
+&((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)\\
+& +2*((\bitvar{FMBW}+3)//4)*((\bitvar{FMBH}+3)//4)
+\end{aligned}$ \\\midrule
+$2$ & $\begin{aligned}
+&((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)\\
+& +2*((\bitvar{FMBW}+3)//4)*((\bitvar{FMBH}+1)//2)
+\end{aligned}$ \\\midrule
+$3$ & $3*((\bitvar{FMBW}+1)//2)*((\bitvar{FMBH}+1)//2)$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Number of Super Blocks for each Pixel Format}
+\label{tab:nsbs-for-pf}
+\end{table}
+
+\item
+Assign \bitvar{NBS} a value according to \bitvar{PF}, as given by
+ Table~\ref{tab:nbs-for-pf}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cc}\toprule
+\bitvar{PF} & \bitvar{NBS} \\\midrule
+$0$ & $6*\bitvar{FMBW}*\bitvar{FMBH}$ \\\midrule
+$2$ & $8*\bitvar{FMBW}*\bitvar{FMBH}$ \\\midrule
+$3$ & $12*\bitvar{FMBW}*\bitvar{FMBH}$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Number of Super Blocks for each Pixel Format}
+\label{tab:nbs-for-pf}
+\end{table}
+
+\item
+Assign \bitvar{NMBS} the value $(\bitvar{FMBW}*\bitvar{FMBH})$.
+
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+VP3 does not correctly handle frame sizes that are not a multiple of 16.
+Thus, \bitvar{PICW} and \bitvar{PICH} should be set to the frame width and
+ height in pixels, respectively, and \bitvar{PICX} and \bitvar{PICY} should be
+ set to zero.
+VP3 headers do not specify a color space.
+VP3 only supports the 4:2:0 pixel format.
+
+\section{Comment Header}
+\label{sec:commentheader}
+
+The Theora comment header is the second of three header packets that begin a
+ Theora stream.
+It is meant for short text comments, not aribtrary metadata; arbitrary metadata
+ belongs in a separate logical stream that provides greater structure and
+ machine parseability.
+
+%r: I tried to morph this a little more in the direction of our application space
+The comment field is meant to be used much like someone jotting a quick note on
+ the label of a video.
+It should be a little information to remember the disc or tape by and explain it to
+ others; a short, to-the-point text note that can be more than 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, e.g.:
+
+%TODO: Example
+
+The comment header is stored as a logical list of eight-bit clean vectors; the
+ number of vectors is bounded at $2^{32}-1$ and the length of each vector is
+ limited to $2^{32}-1$ 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 a vendor name,
+ also eight-bit clean with a length encoded in 32 bits.
+%TODO: The 1.0 release of libtheora sets the vendor string to ...
+
+\subsection{Comment Length Decode}
+\label{sub:comment-len}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{LEN} & Integer & 32 & No & A single 32-bit length value. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{LEN0} & Integer & 8 & No & The first octet of the string length. \\
+\locvar{LEN1} & Integer & 8 & No & The second octet of the string length. \\
+\locvar{LEN2} & Integer & 8 & No & The third octet of the string length. \\
+\locvar{LEN3} & Integer & 8 & No & The fourth octet of the string
+ length. \\
+\bottomrule\end{tabularx}
+\medskip
+
+A single comment vector is decoded as follows:
+
+\begin{enumerate}
+\item
+Read an 8-bit unsigned integer as \locvar{LEN0}.
+\item
+Read an 8-bit unsigned integer as \locvar{LEN1}.
+\item
+Read an 8-bit unsigned integer as \locvar{LEN2}.
+\item
+Read an 8-bit unsigned integer as \locvar{LEN3}.
+\item
+Assign \bitvar{LEN} the value $(\locvar{LEN0}+(\locvar{LEN1}<<8)+
+ (\locvar{LEN2}<<16)+(\locvar{LEN3}<<24))$.
+This construction is used so that on platforms with 8-bit bytes, the memory
+ organization of the comment header is identical with that of Vorbis I,
+ allowing for common parsing code despite the different bit packing
+ conventions.
+\end{enumerate}
+
+\subsection{Comment Header Decode}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{VENDOR} & \multicolumn{3}{l}{String} & The vendor string. \\
+\bitvar{NCOMMENTS} & Integer & 32 & No & The number of user
+ comments. \\
+\bitvar{COMMENTS} & \multicolumn{3}{l}{String Array} & A list of
+ \bitvar{NCOMMENTS} user comment values. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{\ci} & Integer & 32 & No & The index of the current user
+ comment. \\
+\bottomrule\end{tabularx}
+\medskip
+
+The complete comment header is decoded as follows:
+
+\begin{enumerate}
+\item
+Decode the common header fields according to the procedure described in
+ Section~\ref{sub:common-header}.
+If \bitvar{HEADERTYPE} returned by this procedure is not \hex{81}, then stop.
+This packet is not the comment header.
+\item
+Decode the length of the vendor string using the procedure given in
+ Section~\ref{sub:comment-len} into \bitvar{LEN}.
+\item
+Read \bitvar{LEN} 8-bit unsigned integers.
+\item
+Set the string \bitvar{VENDOR} to the contents of these octets.
+\item
+Decode the number of user comments using the procedure given in
+ Section~\ref{sub:comment-len} into \bitvar{LEN}.
+\item
+Assign \bitvar{NCOMMENTS} the value stored in \bitvar{LEN}.
+\item
+For each consecutive value of \locvar{\ci} from $0$ to
+ $(\bitvar{NCOMMENTS}-1)$, inclusive:
+\begin{enumerate}
+\item
+Decode the length of the current user comment using the procedure given in
+ Section~\ref{sub:comment-len} into \bitvar{LEN}.
+\item
+Read \bitvar{LEN} 8-bit unsigned integers.
+\item
+Set the string $\bitvar{COMMENTS}[\locvar{\ci}]$ to the contents of these
+ octets.
+\end{enumerate}
+\end{enumerate}
+
+The comment header comprises the entirety of the second header packet.
+Unlike the first header packet, it is not generally the only packet on the
+ second page and may span multiple pages.
+The length of the comment header packet is (practically) unbounded.
+The comment header packet is not optional; it must be present in the stream
+ even if it is logically empty.
+
+%TODO: \paragraph{VP3 Compatibility}
+
+\subsection{User Comment Format}
+
+The user 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:
+\begin{center}
+\begin{tabular}{rcl}
+$\bitvar{COMMENTS}[0]$ & = & ``TITLE=the look of Theora" \\
+$\bitvar{COMMENTS}[1]$ & = & ``DIRECTOR=me"
+\end{tabular}
+\end{center}
+
+The field name is case-insensitive and MUST consist of ASCII characters
+ \hex{20} through \hex{7D}, \hex{3D} (`=') excluded.
+ASCII \hex{41} through \hex{5A} inclusive (characters `A'--`Z') are to be
+ considered equivalent to ASCII \hex{61} through \hex{7A} inclusive
+ (characters `a'--`z').
+An entirely empty field name---one that is zero characters long---is not
+ disallowed.
+
+The field name is immediately followed by ASCII \hex{3D} (`='); this equals
+ sign is used to terminate the field name.
+
+The data immediately after \hex{3D} until the end of the vector is the eight-bit
+ clean value of the field contents encoded as a UTF-8 string.
+%TODO: Cite UTF-8 standard.
+
+Field names MUST NOT be `internationalized'; this is a concession to
+ simplicity, not an attempt to exclude the majority of the world that doesn't
+ speak English.
+Applications MAY wish to present internationalized versions of the standard
+ field names listed below to the user, but they are not to be stored in the
+ bitstream.
+Field {\em contents}, however, use the UTF-8 character encoding to allow easy
+ representation of any language.
+
+Individual `vendors' MAY use non-standard field names within reason.
+The proper use of comment fields as human-readable notes has already been
+ explained.
+Abuse will be discouraged.
+
+There is no vendor-specific prefix to `non-standard' field names.
+Vendors SHOULD make some effort to avoid arbitrarily polluting the common
+ namespace.
+%"and other bodies"?
+%If you're going to be that vague, you might as well not say anything at all.
+Xiph.org and other bodies will generally collect and rationalize the more
+ useful tags to help with standardization.
+
+Field names are not restricted to occur only once within a comment header.
+%TODO: Example
+
+\paragraph{Field Names}
+
+Below is a proposed, minimal list of standard field names with a description of
+ their intended use.
+No field names are mandatory; a comment header may contain one or more, all, or
+ none of the names in this list.
+
+\begin{description}
+\item{TITLE:} Video name.
+%TODO: Complete list
+\end{description}
+
+\section{Setup Header}
+\label{sec:setupheader}
+
+The Theora setup header contains the limit values used to drive the loop
+ filter, the base matrices and scale values used to build the dequantization
+ tables, and the Huffman tables used to unpack the DCT tokens.
+Because the contents of this header are specific to Theora, no concessions have
+ been made to keep the fields octet-aligned for easy parsing.
+
+\subsection{Loop Filter Limit Table Decode}
+\label{sub:loop-filter-limits}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{LFLIMS} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 7 & No & A 64-element array of loop filter limit
+ values. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{\qi} & Integer & 6 & No & The quantization index. \\
+\locvar{NBITS} & Integer & 3 & No & The size of values being read in the
+ current table. \\
+\bottomrule\end{tabularx}
+\medskip
+
+This procedure decodes the table of loop filter limit values used to drive the
+ loop filter, which is described in Section~REF.
+It is decoded as follows:
+
+\begin{enumerate}
+\item
+Read a 3-bit unsigned integer as \locvar{NBITS}.
+\item
+For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
+\begin{enumerate}
+\item
+Read an \locvar{NBITS}-bit unsigned integer as $\bitvar{LFLIMS}[\locvar{\qi}]$.
+\end{enumerate}
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+The loop filter limit values are hardcoded in VP3.
+The values used are given in Appendix~REF.
+
+\subsection{Quantization Parameters Decode}
+\label{sub:quant-params}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ AC coefficients for each \qi\ value. \\
+\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ the DC coefficient for each \qi\ value. \\
+\bitvar{NBMS} & Integer & 10 & No & The number of base matrices. \\
+\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 8 & No & A $\bitvar{NBMS}\times 64$ array
+ containing the base matrices. \\
+\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 6 & No & A $2\times 3$ array containing the
+ number of quant ranges for a given \qti\ and \pli, respectively.
+This is at most $63$. \\
+\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 6 & No & A $2\times 3\times 63$ array of the
+ sizes of each quant range for a given \qti\ and \pli, respectively.
+Only the first $\bitvar{NQRS}[\qti][\pli]$ values are used. \\
+\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 9 & No & A $2\times 3\times 64$ array of the
+ \bmi's used for each quant range for a given \qti\ and \pli, respectively.
+Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values are used. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{\qti} & Integer & 1 & No & A quantization type index.
+See Table~\ref{tab:quant-types}.\\
+\locvar{\qtj} & Integer & 1 & No & A quantization type index. \\
+\locvar{\pli} & Integer & 2 & No & A color plane index.
+See Table~\ref{tab:color-planes}.\\
+\locvar{\plj} & Integer & 2 & No & A color plane index. \\
+\locvar{\qi} & Integer & 6 & No & The quantization index. \\
+\locvar{\ci} & Integer & 6 & No & The DCT coefficient index. \\
+\locvar{\bmi} & Integer & 9 & No & The base matrix index. \\
+\locvar{\qri} & Integer & 6 & No & The quant range index. \\
+\locvar{NBITS} & Integer & 5 & No & The size of fields to read. \\
+\locvar{NEWQR} & Integer & 1 & No & Flag that indicates a new set of quant
+ ranges will be defined. \\
+\locvar{RPQR} & Integer & 1 & No & Flag that indicates the quant ranges to
+ copy will come from the same color plane. \\
+\bottomrule\end{tabularx}
+\medskip
+
+The AC scale and DC scale values are defined in two simple tables with 64
+ values each, one for each \qi\ value.
+The same scale values are used for every quantization type and color plane.
+
+The base matrices for all quantization types and color planes are stored in a
+ single table.
+These are then referenced by index in several sets of \term{quant ranges}.
+The purpose of the quant ranges is to specify which base matrices are used for
+ which \qi\ values.
+
+A set of quant ranges is defined for each quantization type and color plane.
+To save space in the header, bit flags allow a set of quant ranges to be copied
+ from a previously defined set instead of being specified explicitly.
+Every set except the first one can be copied from the immediately preceding
+ set.
+Similarly, if the quantization type is not $0$, the set can be copied from the
+ set defined for the same color plane for the preceding quantization type.
+This formulation allows compact representation of, for example, the same
+ set of quant ranges in both chroma channels, as is done in the original VP3,
+ or the same set of quant ranges in INTRA and INTER modes.
+
+Each quant range is defined by a size and two base matrix indices, one for each
+ end of the range.
+The base matrix for the end of one range is used as the start of the next
+ range, so that for $n$ ranges, $n+1$ base matrices are specified.
+The base matrices for the \qi\ values between the two endpoints of the range
+ are generated by linear interpolation.
+
+%TODO: figure
+
+The location of the endpoints of each range is encoded by their size.
+The \qi\ value for the left end-point is the sum of the sizes of all preceding
+ ranges, and the \qi\ value for the right end-point adds the size of the
+ current range.
+Thus the sum of the sizes of all the ranges MUST be 63, so that the last range
+ falls on the last possible \qi\ value.
+
+The complete set of quantization parameters are decoded as follows:
+
+\begin{enumerate}
+\item
+Read a 4-bit unsigned integer.
+Assign \locvar{NBITS} the value read, plus one.
+\item
+For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
+\begin{enumerate}
+\item
+Read an \locvar{NBITS}-bit unsigned integer as
+ $\bitvar{ACSCALE}[\locvar{\qi}]$.
+\end{enumerate}
+\item
+Read a 4-bit unsigned integer.
+Assign \locvar{NBITS} the value read, plus one.
+\item
+For each consecutive value of \locvar{\qi} from $0$ to $63$, inclusive:
+\begin{enumerate}
+\item
+Read an \locvar{NBITS}-bit unsigned integer as
+ $\bitvar{DCSCALE}[\locvar{\qi}]$.
+\end{enumerate}
+\item
+Read a 9-bit unsigned integer.
+Assign \bitvar{NBMS} the value decoded, plus one.
+\bitvar{NBMS} MUST be no greater than 384.
+\item
+For each consecutive value of \locvar{\bmi} from $0$ to $(\bitvar{NBMS}-1)$,
+ inclusive:
+\begin{enumerate}
+\item
+For each consecutive value of \locvar{\ci} from $0$ to $63$, inclusive:
+\begin{enumerate}
+\item
+Read an 8-bit unsigned integer as $\bitvar{BMS}[\locvar{\bmi}][\locvar{\ci}]$.
+\end{enumerate}
+\end{enumerate}
+\item
+For each consecutive value of \locvar{\qti} from $0$ to $1$, inclusive:
+\begin{enumerate}
+\item
+For each consecutive value of \locvar{\pli} from $0$ to $2$, inclusive:
+\begin{enumerate}
+\item
+If $\locvar{\qti}>0$ or $\locvar{\pli}>0$, read a 1-bit unsigned integer as
+ \locvar{NEWQR}.
+\item
+Else, assign \locvar{NEWQR} the value one.
+\item
+If \locvar{NEWQR} is zero, then we are copying a previously defined set of
+ quant ranges.
+In that case:
+\begin{enumerate}
+\item
+If $\locvar{\qti}>0$, read a 1-bit unsigned integer as \locvar{RPQR}.
+\item
+Else, assign \locvar{RPQR} the value zero.
+\item
+If \locvar{RPQR} is one, assign \locvar{\qtj} the value $(\locvar{\qti}-1)$
+ and assign \locvar{\plj} the value \locvar{\pli}.
+This selects the set of quant ranges defined for the same color plane as this
+ one, but for the previous quantization type.
+\item
+Else assign \locvar{\qtj} the value $(3*\locvar{\qti}+\locvar{\pli}-1)//3$ and
+ assign \locvar{\plj} the value $(\locvar{\pli}+2)\%3$.
+This selects the most recent set of quant ranges defined.
+\item
+Assign $\bitvar{NQRS}[\locvar{\qti}][\locvar{\pli}]$ the value
+ $\bitvar{NQRS}[\locvar{\qtj}][\locvar{\plj}]$.
+\item
+Assign $\bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}]$ the values in
+ $\bitvar{QRSIZES}[\locvar{\qtj}][\locvar{\plj}]$.
+\item
+Assign $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}]$ the values in
+ $\bitvar{QRBMIS}[\locvar{\qtj}][\locvar{\plj}]$.
+\end{enumerate}
+\item
+Else, \locvar{NEWQR} is one, which indicates that we are defining a new set of
+ quant ranges.
+In that case:
+\begin{enumerate}
+\item
+Assign $\locvar{\qri}$ the value zero.
+\item
+Assign $\locvar{\qi}$ the value zero.
+\item
+Read an $\ilog(\bitvar{NBMS}-1)$-bit unsigned integer as\\
+ $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
+If this is greater than or equal to \bitvar{NBMS}, stop.
+The stream is undecodable.
+\item
+\label{step:qr-loop}
+Read an $\ilog(63-\locvar{\qi})$-bit unsigned integer.
+Assign\\ $\bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$ the value
+ read, plus one.
+\item
+Assign \locvar{\qi} the value $\locvar{\qi}+
+ \bitvar{QRSIZES}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
+\item
+Assign \locvar{\qri} the value $\locvar{\qri}+1$.
+\item
+Read an $\ilog(\bitvar{NBMS}-1)$-bit unsigned integer as\\
+ $\bitvar{QRBMIS}[\locvar{\qti}][\locvar{\pli}][\locvar{\qri}]$.
+\item
+If \locvar{\qi} is less than 63, go back to step~\ref{step:qr-loop}.
+\item
+If \locvar{\qi} is greater than 63, stop.
+The stream is undecodable.
+\item
+Assign $\bitvar{NQRS}[\locvar{\qti}][\locvar{\pli}]$ the value \locvar{\qri}.
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+The quantization parameters are hardcoded in VP3.
+The values used are given in Appendix~REF.
+
+\subsection{Computing a Quantization Matrix}
+\label{sub:quant-mat}
+
+\paragraph{Input parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ AC coefficients for each \qi\ value. \\
+\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ the DC coefficient for each \qi\ value. \\
+\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 8 & No & A $\bitvar{NBMS}\times 64$ array
+ containing the base matrices. \\
+\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 6 & No & A $2\times 3$ array containing the
+ number of quant ranges for a given \qti\ and \pli, respectively.
+This is at most $63$. \\
+\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 6 & No & A $2\times 3\times 63$ array of the
+ sizes of each quant range for a given \qti\ and \pli, respectively.
+Only the first $\bitvar{NQRS}[\qti][\pli]$ values are used. \\
+\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 9 & No & A $2\times 3\times 64$ array of the
+ \bmi's used for each quant range for a given \qti\ and \pli, respectively.
+Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values are used. \\
+\bitvar{\qti} & Integer & 1 & No & A quantization type index.
+See Table~\ref{tab:quant-types}.\\
+\bitvar{\pli} & Integer & 2 & No & A color plane index.
+See Table~\ref{tab:color-planes}.\\
+\bitvar{\qi} & Integer & 6 & No & The quantization index. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{QMAT} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of quantization
+ values for each DCT coefficient. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{\ci} & Integer & 6 & No & The DCT coefficient index. \\
+\locvar{\bmi} & Integer & 9 & No & The base matrix index. \\
+\locvar{\bmj} & Integer & 9 & No & The base matrix index. \\
+\locvar{\qri} & Integer & 6 & No & The quant range index. \\
+\locvar{QISTART} & Integer & 6 & No & The left end-point of the \qi\ range. \\
+\locvar{QIEND } & Integer & 6 & No & The right end-point of the \qi\ range. \\
+\locvar{BM} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 8 & No & A 64-element array containing the
+ interpolated base matrix. \\
+\locvar{QMIN} & Integer & 16 & No & The minimum quantization value allowed
+ for the current coefficient. \\
+\locvar{QSCALE} & Integer & 16 & No & The current scale value. \\
+\bottomrule\end{tabularx}
+\medskip
+
+The following procedure can be used to generate a single quantization matrix
+ for a given quantization type, color plane, and \qi\ value, given the
+ quantization parameters decoded in Section~\ref{sub:quant-params}.
+
+Note that the product of the scale value and the base matrix value is in units
+ of $100$ths of a pixel value, and thus is divided by $100$ to return it to
+ units of a single pixel value.
+This value is then scaled by four, to match the scaling of the DCT output,
+ which is also a factor of four larger than the orthonormal version of the
+ transform.
+
+\begin{enumerate}
+\item
+Assign \locvar{\qri} the index of a quant range such that
+\begin{displaymath}
+\sum_{\qrj=0}^{\locvar{\qri}-1}
+ \bitvar{\qi} \ge \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj],
+\end{displaymath}
+ and
+\begin{displaymath}
+\sum_{\qrj=0}^{\locvar{\qri}}
+ \bitvar{\qi} \le \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj],
+\end{displaymath}
+ where summation from $0$ to $-1$ is zero.
+If there is more than one such value of $\locvar{\qri}$, i.e., if \bitvar{\qi}
+ lies on the end point of a quant range, then which one is used is immaterial.
+\item
+Assign \locvar{QISTART} the value
+\begin{displaymath}
+\sum_{\qrj=0}^{\qri-1} \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj].
+\end{displaymath}
+\item
+Assign \locvar{QIEND} the value
+\begin{displaymath}
+\sum_{\qrj=0}^{\qri} \bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\qrj].
+\end{displaymath}
+\item
+Assign \locvar{\bmi} the value
+ $\bitvar{QRBMIS}[\bitvar{\qti}][\bitvar{\pli}][\qri]$.
+\item
+Assign \locvar{\bmj} the value
+ $\bitvar{QRBMIS}[\bitvar{\qti}][\bitvar{\pli}][\qri+1]$.
+\item
+For each consecutive value of \locvar{\ci} from $0$ to $63$, inclusive:
+\begin{enumerate}
+\item
+Assign $\locvar{BM}[\locvar{\ci}]$ the value
+\begin{displaymath}
+\begin{split}
+(&2*(\locvar{QIEND}-\bitvar{\qi})*\bitvar{BMS}[\locvar{\bmi}][\locvar{\ci}]\\
+ &+2*(\bitvar{\qi}-
+ \locvar{QISTART})*\bitvar{BMS}[\locvar{\bmj}][\locvar{\ci}]\\
+ &+\bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\locvar{\qri}])//
+ (2*\bitvar{QRSIZES}[\bitvar{\qti}][\bitvar{\pli}][\locvar{\qri}])
+\end{split}
+\end{displaymath}
+\item
+Assign \locvar{QMIN} the value given by Table~\ref{tab:qmin} according to
+ \bitvar{\qti} and \locvar{\ci}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{ccr}\toprule
+Coefficient & \bitvar{\qti} & \locvar{QMIN} \\\midrule
+$\locvar{\ci}=0$ & $0$ & $16$ \\
+$\locvar{\ci}>0$ & $0$ & $8$ \\
+$\locvar{\ci}=0$ & $1$ & $32$ \\
+$\locvar{\ci}>0$ & $1$ & $16$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Minimum Quantization Values}
+\label{tab:qmin}
+\end{table}
+
+\item
+If \locvar{\ci} equals zero, assign $\locvar{QSCALE}$ the value
+ $\bitvar{DCSCALE}[\bitvar{\qi}]$.
+\item
+Else, assign $\locvar{QSCALE}$ the value
+ $\bitvar{ACSCALE}[\bitvar{\qi}]$.
+\item
+Assign $\bitvar{QMAT}[\locvar{\ci}]$ the value
+\begin{displaymath}
+\max(\locvar{QMIN},
+ \min((\locvar{QSCALE}*\locvar{BM}[\locvar{\ci}]//100)*4,4096)).
+\end{displaymath}
+\end{enumerate}
+\end{enumerate}
+
+\subsection{DCT Token Huffman Tables}
+\label{sub:huffman-tables}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{HTS} & \multicolumn{3}{l}{Huffman table array}
+ & An 80-element array of Huffman tables
+ with up to 32 entries each. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{HBITS} & Bit string & 32 & No & A string of up to 32 bits. \\
+\locvar{TOKEN} & Integer & 5 & No & A single DCT token value. \\
+\locvar{ISLEAF} & Integer & 1 & No & Flag that indicates if the current
+ node of the tree being decoded is a leaf node. \\
+\bottomrule\end{tabularx}
+\medskip
+
+The Huffman tables used to decode DCT tokens are stored in the setup header in
+ the form of a binary tree.
+This enforces the requirements that the code be full---so that any sequence of
+ bits will produce a valid sequence of tokens---and that the code be
+ prefix-free so that there is no ambiguity when decoding.
+
+One more restriction is placed on the tables that is not explicitly enforced by
+ the bitstream syntax, but nevertheless must be obeyed by compliant encoders.
+There must be no more than 32 entries in a single table.
+Note that this restriction along with the fullness requirement limit the
+ maximum size of a single Huffman code to 32 bits.
+It is probably a good idea to enforce this latter consequence explicitly when
+ implementing the decoding procedure as a recursive algorithm, so as to prevent
+ a possible stack overflow given an invalid bitstream.
+
+Although there are 32 different DCT tokens, and thus a normal table will have
+ exactly 32 entries, this is not explicitly required.
+It is allowable to use a Huffman code that omits some---but not all---of the
+ possible token values.
+It is also allowable, if not particularly useful, to specify multiple codes for
+ the same token value in a single table.
+
+The tree is decoded as follows:
+
+\begin{enumerate}
+\item
+For each consecutive value of \locvar{\hti} from $0$ to $80$, inclusive:
+\begin{enumerate}
+\item
+Set \locvar{HBITS} to the empty string.
+\item
+\label{step:huff-tree-loop}
+If \locvar{HBITS} is longer than 32 bits in length, stop.
+The stream is undecodable.
+\item
+Read a 1-bit unsigned integer as \locvar{ISLEAF}.
+\item
+If \locvar{ISLEAF} is one:
+\begin{enumerate}
+\item
+If the number of entries in table $\bitvar{HTS}[\locvar{\hti}]$ is already 32,
+ stop.
+The stream is undecodable.
+\item
+Read a 5-bit unsigned integer as \locvar{TOKEN}.
+\item
+Add the pair $(\locvar{HBITS},\locvar{TOKEN})$ to Huffman table
+ $\bitvar{HTS}[\locvar{\hti}]$.
+\end{enumerate}
+\item
+Otherwise:
+\begin{enumerate}
+\item
+Add a `0' to the end of \locvar{HBITS}.
+\item
+Decode the `0' sub-tree using this procedure, starting from
+ step~\ref{step:huff-tree-loop}.
+\item
+Remove the `0' from the end of \locvar{HBITS} and add a `1' to the end of
+ \locvar{HBITS}.
+\item
+Decode the `1' sub-tree using this procedure, starting from
+ step~\ref{step:huff-tree-loop}.
+\item
+Remove the `1' from the end of \locvar{HBITS}.
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+The DCT token Huffman tables are hardcoded in VP3.
+The values used are given in Appendix~REF.
+
+\subsection{Setup Header Decode}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{LFLIMS} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 7 & No & A 64-element array of loop filter limit
+ values. \\
+\bitvar{ACSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ AC coefficients for each \qi\ value. \\
+\bitvar{DCSCALE} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 16 & No & A 64-element array of scale values for
+ the DC coefficient for each \qi\ value. \\
+\bitvar{NBMS} & Integer & 10 & No & The number of base matrices. \\
+\bitvar{BMS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 8 & No & A $\bitvar{NBMS}\times 64$ array
+ containing the base matrices. \\
+\bitvar{NQRS} & \multicolumn{1}{p{50pt}}{2D Integer array} &
+ 6 & No & A $2\times 3$ array containing the
+ number of quant ranges for a given \qti\ and \pli, respectively.
+This is at most $63$. \\
+\bitvar{QRSIZES} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 6 & No & A $2\times 3\times 63$ array of the
+ sizes of each quant range for a given \qti\ and \pli, respectively.
+Only the first $\bitvar{NQRS}[\qti][\pli]$ values will be used. \\
+\bitvar{QRBMIS} & \multicolumn{1}{p{50pt}}{3D Integer array} &
+ 9 & No & A $2\times 3\times 64$ array of the
+ \bmi's used for each quant range for a given \qti\ and \pli, respectively.
+Only the first $(\bitvar{NQRS}[\qti][\pli]+1)$ values will be used. \\
+\bitvar{HTS} & \multicolumn{3}{l}{Huffman table array}
+ & An 80-element array of Huffman tables
+ with up to 32 entries each. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:} None.
+\medskip
+
+The complete setup header is decoded as follows:
+
+\begin{enumerate}
+\item
+Decode the common header fields according to the procedure described in
+ Section~\ref{sub:common-header}.
+If \bitvar{HEADERTYPE} returned by this procedure is not \hex{82}, then stop.
+This packet is not the setup header.
+\item
+Decode the loop filter limit value table using the procedure given in
+ Section~\ref{sub:loop-filter-limits} into \bitvar{LFLIMS}.
+\item
+Decode the quantization parameters using the procedure given in
+ Section~\ref{sub:quant-params}.
+The results are stored in \bitvar{ACSCALE}, \bitvar{DCSCALE}, \bitvar{NBMS},
+ \bitvar{BMS}, \bitvar{NQRS}, \bitvar{QRSIZES}, and \bitvar{QRBMIS}.
+\item
+Decode the DCT token Huffman tables using the procedure given in
+ Section~\ref{sub:huffman-tables} into \bitvar{HTS}.
+\end{enumerate}
+
+\chapter{Frame Decode}
+
+This section describes the complete procedure necessary to decode a single
+ frame.
+This begins with the frame header, followed by coded block flags, macro block
+ modes, motion vectors, block-level \qi\ values, and finally the DCT residual
+ tokens, which are used to reconstruct the frame.
+
+\section{Frame Header Decode}
+\label{sub:frame-header}
+
+\paragraph{Input parameters:} None.
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
+\bitvar{NQIS} & Integer & 2 & No & The number of \qi\ values. \\
+\bitvar{QIS} & \multicolumn{1}{p{40pt}}{Integer array} &
+ 6 & No & An \bitvar{NQIS}-element array of
+ \qi\ values. \\
+\bitvar{MOREQIS} & Integer & 1 & No & A flag indicating there are more
+ \qi\ values to be decoded. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{MOREQIS} & Integer & 1 & No & A flag indicating there are more
+ \qi\ values to be decoded. \\
+\bottomrule\end{tabularx}
+\medskip
+
+The frame header selects which type of frame is being decoded, intra or inter,
+ and contains the list of \qi\ values that will be used in this frame.
+The first \qi\ value will be used for {\em all} DC coefficients in all blocks.
+This is done to ensure that DC prediction, which is done in the quantized
+ domain, works as expected.
+The AC coefficients, however, can be dequantized using any \qi\ value on the
+ list, selected on a block-by-block basis.
+
+\begin{enumerate}
+\item
+Read a 1-bit unsigned integer.
+If the value read is not zero, stop.
+This is not a data packet.
+\item
+Read a 1-bit unsigned integer as \bitvar{FTYPE}.
+This is the type of frame being decoded, as given in
+ Table~\ref{tab:frame-type}.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cl}\toprule
+\bitvar{FTYPE} & Frame Type \\\midrule
+$0$ & Intra frame \\
+$1$ & Inter frame \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Frame Type Values}
+\label{tab:frame-type}
+\end{table}
+
+\item
+Read in a 6-bit unsigned integer as $\bitvar{QIS}[0]$.
+\item
+Read a 1-bit unsigned integer as \locvar{MOREQIS}.
+\item
+If \locvar{MOREQIS} is zero, set \bitvar{NQIS} to 1.
+\item
+Otherwise:
+\begin{enumerate}
+\item
+Read in a 6-bit unsigned integer as $\bitvar{QIS}[1]$.
+\item
+Read a 1-bit unsigned integer as \locvar{MOREQIS}.
+\item
+If \locvar{MOREQIS} is zero, set \bitvar{NQIS} to 2.
+\item
+Otherwise:
+\begin{enumerate}
+\item
+Read in a 6-bit unsigned integer as $\bitvar{QIS}[2]$.
+\item
+Set \bitvar{NQIS} to 3.
+\end{enumerate}
+\end{enumerate}
+\item
+If \bitvar{FTYPE} is 0, read a 3-bit unsigned integer.
+If this value is not zero, stop.
+This frame is not decodable according to this specification.
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+The precise format of the frame header is substantially different in Theora
+ than in VP3.
+The original VP3 format includes a larger number of unused, reserved bits that
+ are required to be zero.
+The original VP3 frame header also can contain only a single \qi\ value,
+ because VP3 does not support block-level \qi\ values and uses the same
+ \qi\ value for all the coefficients in a frame.
+
+\section{Run-Length Encoded Bit Strings}
+
+Two variations of run-length encoding are used to store sequences of bits for
+ the block coded flags and the block-level \qi\ values.
+The procedures to decode these bit sequences are specified in the following two
+ sections.
+
+\subsection{Long-Run Bit String Decode}
+\label{sub:long-run}
+
+\paragraph{Input parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{NBITS} & Integer & 36 & No & The number of bits to decode. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{BITS} & Bit string & & & The decoded bits. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{LEN} & Integer & 36 & No & The number of bits decoded so far. \\
+\locvar{BIT} & Integer & 1 & No & The value associated with the current
+ run. \\
+\locvar{RLEN} & Integer & 13 & No & The length of the current run. \\
+\locvar{RBITS} & Integer & 4 & No & The number of extra bits needed to
+ decode the run length. \\
+\locvar{RSTART} & Integer & 6 & No & The start of the possible run-length
+ values for a given Huffman code. \\
+\locvar{ROFFS} & Integer & 12 & No & The offset from \locvar{RSTART} of the
+ run-length. \\
+\bottomrule\end{tabularx}
+\medskip
+
+There is no practical limit to the number of consecutive 0's and 1's that can
+ be decoded with this procedure.
+In reality, the run length is limited by the number of blocks in a single
+ frame, because more will never be requested.
+A separate procedure described in Section~\ref{sub:short-run} is used when
+ there is a known limit on the maximum size of the runs.
+
+For the first run, a single bit value is read, and then a Huffman-coded
+ representation of a run length is decoded, and that many copies of the bit
+ value are appended to the bit string.
+For each consecutive run, the value of the bit is toggled instead of being read
+ from the bitstream.
+
+The only exception is if the length of the previous run was 4129, the maximum
+ possible length encodable by the Huffman-coded representation.
+In this case another bit value is read from the stream, to allow for
+ consecutive runs of 0's or 1's longer than this maximum.
+
+Note that in both cases---for the first run and after a run of length 4129---if
+ no more bits are needed, then no bit value is read.
+
+The complete decoding procedure is as follows:
+
+\begin{enumerate}
+\item
+Assign \locvar{LEN} the value 0.
+\item
+Assign \bitvar{BITS} the empty string.
+\item
+If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
+ \bitvar{BITS}.
+\item
+Read a 1-bit unsigned integer as \locvar{BIT}.
+\item
+\label{step:long-run-loop}
+Read a bit at a time until one of the Huffman codes given in
+ Table~\ref{tab:long-run} is recognized.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{lrrl}\toprule
+Huffman Code & \locvar{RSTART} & \locvar{RBITS} & Run Lengths \\\midrule
+\bin{0} & $1$ & $0$ & $1$ \\
+\bin{10} & $2$ & $1$ & $2\ldots 3$ \\
+\bin{110} & $4$ & $1$ & $4\ldots 5$ \\
+\bin{1110} & $6$ & $2$ & $6\ldots 9$ \\
+\bin{11110} & $10$ & $3$ & $10\ldots 17$ \\
+\bin{111110} & $18$ & $4$ & $18\ldots 33$ \\
+\bin{111111} & $34$ & $12$ & $34\ldots 4129$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Huffman Codes for Long Run Lengths}
+\label{tab:long-run}
+\end{table}
+
+\item
+Assign \locvar{RSTART} and \locvar{RBITS} the values given in
+ Table~\ref{tab:long-run} according to the Huffman code read.
+\item
+Read an \locvar{RBITS}-bit unsigned integer as \locvar{ROFFS}.
+\item
+Assign \locvar{RLEN} the value $(\locvar{RSTART}+\locvar{ROFFS})$.
+\item
+Append \locvar{RLEN} copies of \locvar{BIT} to \bitvar{BITS}.
+\item
+Add \locvar{RLEN} to the value \locvar{LEN}.
+\locvar{LEN} MUST be less than or equal to \bitvar{NBITS}.
+\item
+If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
+ \bitvar{BITS}.
+\item
+If \locvar{RLEN} equals 4129, read a 1-bit unsigned integer as \locvar{BIT}.
+\item
+Otherwise, assign \locvar{BIT} the value $(1-\locvar{BIT})$.
+\item
+Continue decoding runs from step~\ref{step:long-run-loop}.
+\end{enumerate}
+
+\paragraph{VP3 Compatibility}
+
+VP3 does not read a new bit value after decoding a run length of 4129.
+This limits the maximum number of consecutive 0's or 1's to 4129 in
+ VP3-compatible streams.
+For reasonable video sizes of $1920\times 1080$ or less in 4:2:0 format---the
+ only format VP3 supports---this does not pose any problems because runs this
+ long are not needed.
+
+\subsection{Short-Run Bit String Decode}
+\label{sub:short-run}
+
+\paragraph{Input parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{NBITS} & Integer & 36 & No & The number of bits to decode. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{BITS} & Bit string & & & The decoded bits. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{LEN} & Integer & 36 & No & The number of bits decoded so far. \\
+\locvar{BIT} & Integer & 1 & No & The value associated with the current
+ run. \\
+\locvar{RLEN} & Integer & 13 & No & The length of the current run. \\
+\locvar{RBITS} & Integer & 4 & No & The number of extra bits needed to
+ decode the run length. \\
+\locvar{RSTART} & Integer & 6 & No & The start of the possible run-length
+ values for a given Huffman code. \\
+\locvar{ROFFS} & Integer & 12 & No & The offset from \locvar{RSTART} of the
+ run-length. \\
+\bottomrule\end{tabularx}
+\medskip
+
+This procedure is similar to the procedure outlined in
+ Section~\ref{sub:long-run}, except that the maximum number of consecutive 0's
+ or 1's is limited to 30.
+This is the maximum run length needed when encoding a bit for each of the 16
+ blocks in a super block when it is known that not all the bits in a super
+ block are the same.
+
+The complete decoding procedure is as follows:
+
+\begin{enumerate}
+\item
+Assign \locvar{LEN} the value 0.
+\item
+Assign \bitvar{BITS} the empty string.
+\item
+If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
+ \bitvar{BITS}.
+\item
+Read a 1-bit unsigned integer as \locvar{BIT}.
+\item
+\label{step:short-run-loop}
+Read a bit at a time until one of the Huffman codes given in
+ Table~\ref{tab:short-run} is recognized.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{lrrl}\toprule
+Huffman Code & \locvar{RSTART} & \locvar{RBITS} & Run Lengths \\\midrule
+\bin{0} & $1$ & $1$ & $1\ldots 2$ \\
+\bin{10} & $3$ & $1$ & $3\ldots 4$ \\
+\bin{110} & $5$ & $1$ & $5\ldots 6$ \\
+\bin{1110} & $7$ & $2$ & $7\ldots 10$ \\
+\bin{11110} & $11$ & $2$ & $11\ldots 14$ \\
+\bin{11111} & $15$ & $4$ & $15\ldots 30$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Huffman Codes for Short Run Lengths}
+\label{tab:short-run}
+\end{table}
+
+\item
+Assign \locvar{RSTART} and \locvar{RBITS} the values given in
+ Table~\ref{tab:short-run} according to the Huffman code read.
+\item
+Read an \locvar{RBITS}-bit unsigned integer as \locvar{ROFFS}.
+\item
+Assign \locvar{RLEN} the value $(\locvar{RSTART}+\locvar{ROFFS})$.
+\item
+Append \locvar{RLEN} copies of \locvar{BIT} to \bitvar{BITS}.
+\item
+Add \locvar{RLEN} to the value \locvar{LEN}.
+\locvar{LEN} MUST be less than or equal to \bitvar{NBITS}.
+\item
+If \locvar{LEN} equals \bitvar{NBITS}, return the completely decoded string
+ \bitvar{BITS}.
+\item
+Assign \locvar{BIT} the value $(1-\locvar{BIT})$.
+\item
+Continue decoding runs from step~\ref{step:short-run-loop}.
+\end{enumerate}
+
+\section{Coded Block Flags Decode}
+\label{sub:coded-blocks}
+
+\paragraph{Input parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
+\bitvar{NSBS} & Integer & 32 & No & The total number of super blocks in a
+ frame. \\
+\bitvar{NBS} & Integer & 36 & No & The total number of blocks in a
+ frame. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{BCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 1 & No & An \bitvar{NBS}-element array of flags
+ indicating which blocks are coded. \\
+\bitvar{NBCODED} & Integer & 36 & No & The number of coded blocks. \\
+\bitvar{NLBCODED} & Integer & 36 & No & The number of coded blocks in the luma
+ plane. \\
+\bitvar{CODEDBS} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 36 & No & An \bitvar{NBCODED}-element list of the
+ indices of all the coded blocks. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{NBITS} & Integer & 36 & No & The length of a bit string to decode. \\
+\locvar{BITS} & Bit string & & & A decoded set of flags. \\
+\locvar{SBPCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 1 & No & An \bitvar{NSBS}-element array of flags
+ indicating whether or not each super block is partially coded. \\
+\locvar{SBFCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 1 & No & An \bitvar{NSBS}-element array of flags
+ indicating whether or not each non-partially coded super block is fully
+ coded. \\
+\locvar{\sbi} & Integer & 32 & No & The index of the current super
+ block. \\
+\locvar{\bi} & Integer & 32 & No & The index of the current block in coded
+ order. \\
+\bottomrule\end{tabularx}
+\medskip
+
+This procedure determines which blocks are coded in a given frame.
+In an intra frame, it marks blocks are coded.
+In an inter frame, however, any or all of the blocks may remain uncoded.
+
+It is important to note that flags are still decoded for any blocks which lie
+ entirely outside the picture region, even though they are not displayed.
+These blocks must be faithfully reconstructed, however, because their contents
+ can be used as predictors in future frames.
+
+This procedure outputs two redundant representations of the coded blocks, for
+ ease of reference elsewhere in the decoding process: a list of bit flags, one
+ for each block, marking it coded or not coded, and a list of the indices of
+ the coded blocks, in coded order.
+These are decoded as follows:
+
+\begin{enumerate}
+\item
+Assign \bitvar{NBCODED} the value zero.
+\item
+Assign \bitvar{NLBCODED} the value zero.
+\item
+If \bitvar{FTYPE} is zero (intra frame):
+\begin{enumerate}
+\item
+For each consecutive block in coded order (see
+ Section~\ref{sec:blocks-and-sbs})---indexed by \locvar{\bi}:
+\begin{enumerate}
+\item
+Assign $\bitvar{BCODED}[\locvar{\bi}]$ the value one.
+\item
+Assign $\bitvar{CODEDBS}[\bitvar{NBCODED}]$ the value \locvar{\bi}.
+\item
+Assign \bitvar{NBCODED} the value $(\bitvar{NBCODED}+1)$.
+\item
+If \locvar{\bi} is in the luma plane, assign \bitvar{NLBCODED} the value
+ $(\bitvar{NLBCODED}+1)$.
+\end{enumerate}
+\end{enumerate}
+\item
+Otherwise (inter frame):
+\begin{enumerate}
+\item
+Assign \locvar{NBITS} the value \bitvar{NSBS}.
+\item
+Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
+ described in Section~\ref{sub:long-run}.
+This represents the list of partially coded super blocks.
+\item
+For each consecutive super block in raster order---indexed by
+ \locvar{\sbi}---remove the bit at the head of the string \locvar{BITS} and
+ assign it to $\locvar{SBPCODED}[\locvar{\sbi}]$.
+\item
+Assign \locvar{NBITS} the total number of super blocks such that \\
+ $\locvar{SBPCODED}[\locvar{\sbi}]$ equals zero.
+\item
+Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
+ described in Section~\ref{sub:long-run}.
+This represents the list of fully coded super blocks.
+\item
+For each consecutive super block in raster order---indexed by
+ \locvar{\sbi}---such that $\locvar{SBPCODED}[\locvar{\sbi}]$ equals zero,
+ remove the bit at the head of the string \locvar{BITS} and assign it to
+ $\locvar{SBFCODED}[\locvar{\sbi}]$.
+\item
+Assign \locvar{NBITS} the number of blocks contained in super blocks where
+ $\locvar{SBPCODED}[\locvar{\sbi}]$ equals one.
+Note that this might {\em not} be equal to 16 times the number of partially
+ coded super blocks, since super blocks which overlap the edge of the frame
+ will have fewer than 16 blocks in them.
+\item
+Read an \locvar{NBITS}-bit bit string into \locvar{BITS}, using the procedure
+ described in Section~\ref{sub:short-run}.
+\item
+For each block in coded order---indexed by \locvar{\bi}:
+\begin{enumerate}
+\item
+Assign \locvar{\sbi} the index of the super block containing block
+ \locvar{\bi}.
+\item
+If $\locvar{SBPCODED}[\locvar{\sbi}]$ is zero, assign
+ $\bitvar{BCODED}[\locvar{\bi}]$ the value $\locvar{SBFCODED}[\locvar{\sbi}]$.
+\item
+Otherwise, remove the bit at the head of the string \locvar{BITS} and assign it
+ to $\bitvar{BCODED}[\locvar{\bi}]$.
+\item
+If $\bitvar{BCODED}[\locvar{\bi}]$ is one:
+\begin{enumerate}
+\item
+Assign $\bitvar{CODEDBS}[\bitvar{NBCODED}]$ the value $\locvar{\bi}$.
+\item
+Assign \bitvar{NBCODED} the value $(\bitvar{NBCODED}+1)$.
+\item
+If \locvar{\bi} is in the luma plane, assign \bitvar{NLBCODED} the value
+ $(\bitvar{NLBCODED}+1)$.
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+
+\section{Macro Block Coding Modes}
+
+\paragraph{Input parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{FTYPE} & Integer & 1 & No & The frame type. \\
+\bitvar{NMBS} & Integer & 32 & No & The total number of macro blocks in a
+ frame. \\
+\bitvar{BCODED} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 1 & No & An \bitvar{NBS}-element array of flags
+ indicating which blocks are coded. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Output parameters:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\bitvar{MBMODES} & \multicolumn{1}{p{40pt}}{Integer Array} &
+ 3 & No & An \bitvar{NMBS}-element array of coding
+ modes for each macro block. \\
+\bottomrule\end{tabularx}
+
+\paragraph{Variables used:}\hfill\\*
+\begin{tabularx}{\textwidth}{@{}llrcX@{}}\toprule
+\multicolumn{1}{c}{Name} &
+\multicolumn{1}{c}{Type} &
+\multicolumn{1}{p{30pt}}{\centering Size (bits)} &
+\multicolumn{1}{c}{Signed?} &
+\multicolumn{1}{c}{Description and restrictions} \\\midrule\endhead
+\locvar{MSCHEME} & Integer & 3 & No & The mode coding scheme. \\
+\locvar{MALPHABET} & \multicolumn{1}{p{40pt}}{Integer array}
+ & 3 & No & The list of modes corresponding to each
+ Huffman code. \\
+\locvar{\mbi} & Integer & 32 & No & The index of the current macro
+ block. \\
+\locvar{\bi} & Integer & 32 & No & The index of the current block in coded
+ order. \\
+\locvar{\mi} & Integer & 32 & No & The index of a Huffman code from
+ Table~\ref{tab:mode-codes}, starting from $0$. \\
+\bottomrule\end{tabularx}
+\medskip
+
+In an intra frame, every macro block marked as coded in INTRA mode.
+In an inter frame, however, a macro block can be coded in one of eight coding
+ modes, given in Table~\ref{tab:coding-modes}.
+All of the blocks in all color planes contained in a macro block will be
+ assigned the coding mode of that macro block.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{cl}\toprule
+Index & Coding Mode \\\midrule
+$0$ & INTER\_NOMV \\
+$1$ & INTRA \\
+$2$ & INTER\_MV \\
+$3$ & INTER\_MV\_LAST \\
+$4$ & INTER\_MV\_LAST2 \\
+$5$ & INTER\_GOLDEN\_NOMV \\
+$6$ & INTER\_GOLDEN\_MV \\
+$7$ & INTER\_MV\_FOUR \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Coding Modes}
+\label{tab:coding-modes}
+\end{table}
+
+An important thing to note is that a coding mode is only stored in the
+ bitstream if it has at least {\em luma} block coded.
+A macro block with no coded blocks in the luma plane defaults to being coded in
+ INTER\_NOMV mode, even if it contains coded blocks in the chroma planes.
+
+Coding modes are encoded using one of eight different schemes.
+Schemes 0 through 6 use the same simple Huffman code to represent the mode
+ numbers, as given in Table~\ref{tab:mode-codes}.
+The difference in the schemes is the mode number assigned to each code.
+Scheme 0 uses an assignment specified in the bitstream, while schemes 1--6 use
+ a fixed assignment, also given in Table~\ref{tab:mode-codes}.
+Scheme 7 simply codes each mode directly in the bitstream using three bits.
+
+\begin{table}[htb]
+\begin{center}
+\begin{tabular}{lcccccc}\toprule
+Scheme & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ \\\cmidrule{2-7}
+Huffman Code & \multicolumn{6}{c}{Coding Mode} \\\midrule
+\bin{0} & $3$ & $3$ & $3$ & $3$ & $0$ & $0$ \\
+\bin{10} & $4$ & $4$ & $2$ & $2$ & $3$ & $5$ \\
+\bin{110} & $2$ & $0$ & $4$ & $0$ & $4$ & $3$ \\
+\bin{1110} & $0$ & $2$ & $0$ & $4$ & $2$ & $4$ \\
+\bin{11110} & $1$ & $1$ & $1$ & $1$ & $1$ & $2$ \\
+\bin{111110} & $5$ & $5$ & $5$ & $5$ & $5$ & $1$ \\
+\bin{1111110} & $6$ & $6$ & $6$ & $6$ & $6$ & $6$ \\
+\bin{1111111} & $7$ & $7$ & $7$ & $7$ & $7$ & $7$ \\
+\bottomrule\end{tabular}
+\end{center}
+\caption{Coding Modes}
+\label{tab:mode-codes}
+\end{table}
+
+\begin{enumerate}
+\item
+If \bitvar{FTYPE} is 0 (intra frame):
+\begin{enumerate}
+\item
+For each consecutive value of \locvar{\mbi} from 0 to $(\bitvar{NMBS}-1)$,
+ inclusive, assign $\bitvar{MBMODES}[\mbi]$ the value 0 (INTRA).
+\end{enumerate}
+\item
+Otherwise (inter frame):
+\begin{enumerate}
+\item
+Read a 3-bit unsigned integer as \locvar{MSCHEME}.
+\item
+If \locvar{MSCHEME} is 0:
+\begin{enumerate}
+\item
+For each consecutive value of \locvar{MODE} from 0 to 7, inclusive:
+\begin{enumerate}
+\item
+Read a 3-bit unsigned integer as \locvar{\mi}.
+\item
+Assign $\locvar{MALPHABET}[\mi]$ the value \locvar{MODE}.
+\end{enumerate}
+\end{enumerate}
+\item
+Otherwise, if \locvar{MSCHEME} is not 7, assign the entries of
+ \locvar{MALPHABET} the values in the corresponding column of
+ Table~\ref{tab:mode-codes}.
+\item
+For each consecutive macro block in coded order (see
+ Section~\ref{sec:mbs})---indexed by \locvar{\mbi}:
+\begin{enumerate}
+\item
+If a block \locvar{\bi} in the luma plane of macro block \locvar{\mbi} exists
+ such that $\bitvar{BCODED}[\locvar{\bi}]$ is 1:
+\begin{enumerate}
+\item
+If \locvar{MSCHEME} is not 7, read one bit at a time until one of the Huffman
+ codes in Table~\ref{tab:mode-codes} is recognized, and assign
+ $\bitvar{MBMODES}[\locvar{\mbi}]$ the value
+ $\locvar{MALPHABET}[\locvar{\mi}]$, where \locvar{\mi} is the index of the
+ Huffman code decoded.
+\item
+Otherwise, if no luma-plane blocks in the macro block are coded, read a 3-bit
+ unsigned integer as $\bitvar{MBMODES}[\locvar{\mbi}]$.
+\end{enumerate}
+\item
+Otherwise, assign $\bitvar{MBMODE}[\locvar{\mbi}]$ the value 0 (INTER\_NOMV).
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+
+\clearpage
+
+%\backmatter
+\appendix
+
+\chapter{Ogg Bitstream Encapsulation}
+\label{app:oggencapsulation}
+
+\section{Overview}
+
+This document specifies the embedding or encapsulation of Theora packets
+ in an Ogg transport stream.
+
+Ogg is a stream oriented wrapper for coded, linear time-based data.
+It provides syncronization, multiplexing, framing, error detection and
+ seeking landmarks for the decoder and complements the raw packet format
+ used by the Theora codec.
+
+This document assumes familiarity with the details of the Ogg standard.
+The Xiph.org documentation provides an overview of the Ogg transport stream
+ format at \url{http://www.xiph.org/ogg/doc/oggstream.html} and a detailed
+ description at \url{http://www.xiph.org/ogg/doc/framing.html}.
+The format is also defined in RFC~3533 \cite{rfc3533}.
+While Theora packets can be embedded in a wide variety of media
+ containers and streaming mechanisms, the Xiph.org Foundation
+ recommends Ogg as the native format for Theora video in file-oriented
+ storage and transmission contexts.
+
+\subsection{MIME type}
+
+The correct MIME type of any Ogg file is {\tt application/ogg}.
+Outside of an encapsulation, the mime type {\tt video/x-theora} may
+ be used to refer specifically to the Theora compressed video stream.
+
+\section{Embedding in a logical bitstream}
+
+Ogg separates a {\em logical bitstream} consisting of the framing of
+ a particular sequence of packets and complete within itself from
+ the {\em physical bitstream} which may consist either of a single
+ logical bitstream or a number of logical bitstreams multiplexed
+ together.
+This section specifies the embedding of Theora packets in a logical Ogg
+ bitstream.
+The mapping of Ogg Theora logical bitstreams into a multiplexed physical Ogg
+ stream is described in the next section.
+
+\subsection{Headers}
+
+The initial info header packet appears by itself in a single Ogg page.
+This page defines the start of the logical stream and MUST have
+ the `beginning of stream' flag set.
+
+The second and third header packets (metadata comments and decoder
+ setup data) can together span one or more Ogg pages.
+If there are additional non-normative header packets, they MUST be
+ included in this sequence of pages as well.
+The comment header packet MUST begin the second Ogg page in the logical
+ bitstream, and there MUST be a page break between the last header
+ packet and the first frame data packet.
+
+These two page break requirements facilitate stream identification and
+ simplify header acquisition for seeking and live streaming applications.
+
+All header pages MUST have their granule position field set to zero.
+%TODO: or -1?
+%TBT: What are we doing now?
+
+\subsection{Frame data}
+
+The first frame data packet in a logical bitstream MUST begin a fresh page.
+All other data packets are placed one at a time into Ogg pages
+ until the end of the stream.
+Packets can span pages and multiple packets can be placed within any
+ one page.
+The last page in the logical bitstream MUST have its `end of stream'
+ flag set.
+
+Frame data pages MUST be marked with a granule index corresponding to
+ the display time of the last frame/packet that finishes in that page.
+
+{\bf Note:}
+This scheme is still under discussion.
+It has also been proposed that pages be labeled with a granule corresponding to
+ the first frame that begins on that page.
+This simplifies seeking and mux, but is different from the published
+ definition of the Ogg granule field.
+This document will be updated when the issue is settled.
+
+%TODO: \subsection{Granule position}
+
+\section{Multiplexed stream mapping}
+
+Applications supporting Ogg Theora I must support Theora bitstreams
+ multiplexed with compressed audio data in the Vorbis I and Speex
+ formats, and should support Ogg-encapsulated MNG graphics for overlays.
+% and the Writ format for text-based titling.
+%TBT: That's great... do these things have specifications?
+
+Multiple audio and video bitstreams may be multiplexed together.
+How playback of multiple/alternate streams is handled is up to the
+ application.
+Some conventions based on included metadata aide interoperability
+ in this respect.
+%TODO: describe multiple vs. alternate streams, language mapping
+% and reference metadata descriptions.
+
+\subsection{Chained streams}
+
+Ogg Theora decoders and playback applications MUST support both grouped
+ streams (multiplexed concurrent logical streams) and chained streams
+ (sequential concatenation of independent physical bitstreams).
+
+The number and codec data types of multiplexed streams and the decoder
+ parameters for those stream types that re-occur can all change at a
+ chaining boundary.
+A playback application MUST be prepared to handle such changes and
+ SHOULD do so smoothly with the minimum possible visible disruption.
+The specification of grouped streams below applies independently to each
+ segment of a chained bitstream.
+
+\subsection{Grouped streams}
+
+At the beginning of a multiplexed stream, the `beginning of stream'
+ pages for each logical bitstream will be grouped together.
+Within these, the first page to occur MUST be the Theora page.
+This facilitates identification of Ogg Theora files among other
+ Ogg-encapsulated content.
+A playback application must nevertheless handle streams where this
+ arrangement is not correct.
+%TBT: Then what's the point of requiring it in the spec?
+
+If there is more than one Theora logical stream, the first page should
+ be from the primary stream.
+That is, the best choice for the stream a generic player should begin
+ displaying without special user direction.
+If there is more than one audio stream, or of any other stream
+ type, the identification page of the primary stream of that type
+ should be placed before the others.
+%TBT: That's all pretty vague.
+
+After the `beginning of stream' pages, the header pages of each of
+ the logical streams should be grouped together before any data pages
+ occur.
+%TBT: should or must?
+
+After all the header pages have been placed,
+ the data pages are multiplexed together.
+They should be placed in the stream in increasing order by the playback
+ time equivalents of their granule fields.
+This facilitates seeking while limiting the buffering requirements of the
+ playback demultiplexer.
+%TODO: A lot of this language is encoder-oriented.
+%TODO: We define a decoder-oriented specification.
+%TODO: The language should be changed to match.
+
+\clearpage
+\chapter{Colophon}
+
+Ogg is a \href{http://www.xiph.org}{Xiph.org Foundation} 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 \href{http://www.xiph.org/about.html}{About the Xiph.org Foundation} for
+ details.
+
+Ogg Theora is the first Ogg video codec.
+Anyone may freely use and distribute the Ogg and Theora specifications, whether
+ in private, public, or corporate capacity.
+However, the Xiph.org Foundation and the Ogg project reserve the right to set
+ the Ogg Theora specification and certify specification compliance.
+
+Xiph.org's Theora software codec implementation is distributed under a BSD-like
+ license.
+This does not restrict third parties from distributing independent
+ implementations of Theora software under other licenses.
+
+\begin{wrapfigure}{l}{0pt}
+\includegraphics{xifish}
+\end{wrapfigure}
+
+These pages are copyright \textcopyright{} 2004 Xiph.org Foundation.
+All rights reserved.
+Ogg, Theora, Vorbis, Xiph.org Foundation and their logos are trademarks
+ (\texttrademark) of the \href{http://www.xiph.org}{Xiph.org Foundation}.
+
+This document is set in \LaTeX.
+
+
+
+\clearpage
+\bibliography{spec}
+
+\end{document}
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