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diff --git a/doc/02-bitpacking.tex b/doc/02-bitpacking.tex new file mode 100644 index 0000000..905dcaf --- /dev/null +++ b/doc/02-bitpacking.tex @@ -0,0 +1,246 @@ +% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- +%!TEX root = Vorbis_I_spec.tex +\section{Bitpacking Convention} \label{vorbis:spec:bitpacking} + +\subsection{Overview} + +The Vorbis codec uses relatively unstructured raw packets containing +arbitrary-width binary integer fields. Logically, these packets are a +bitstream in which bits are coded one-by-one by the encoder and then +read one-by-one in the same monotonically increasing order by the +decoder. Most current binary storage arrangements group bits into a +native word size of eight bits (octets), sixteen bits, thirty-two bits +or, less commonly other fixed word sizes. The Vorbis bitpacking +convention specifies the correct mapping of the logical packet +bitstream into an actual representation in fixed-width words. + + +\subsubsection{octets, bytes and words} + +In most contemporary architectures, a 'byte' is synonymous with an +'octet', that is, eight bits. This has not always been the case; +seven, ten, eleven and sixteen bit 'bytes' have been used. For +purposes of the bitpacking convention, a byte implies the native, +smallest integer storage representation offered by a platform. On +modern platforms, this is generally assumed to be eight bits (not +necessarily because of the processor but because of the +filesystem/memory architecture. Modern filesystems invariably offer +bytes as the fundamental atom of storage). A 'word' is an integer +size that is a grouped multiple of this smallest size. + +The most ubiquitous architectures today consider a 'byte' to be an +octet (eight bits) and a word to be a group of two, four or eight +bytes (16, 32 or 64 bits). Note however that the Vorbis bitpacking +convention is still well defined for any native byte size; Vorbis uses +the native bit-width of a given storage system. This document assumes +that a byte is one octet for purposes of example. + +\subsubsection{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 of the byte. Bits in a byte are numbered from zero at the LSb to +$n$ ($n=7$ in an octet) for the +MSb. + + + +\subsubsection{byte order} + +Words are native groupings of multiple bytes. Several byte orderings +are possible in a word; the common ones are 3-2-1-0 ('big endian' or +'most significant byte first' in which the highest-valued byte comes +first), 0-1-2-3 ('little endian' or 'least significant byte first' in +which the lowest value byte comes first) and less commonly 3-1-2-0 and +0-2-1-3 ('mixed endian'). + +The Vorbis bitpacking convention specifies storage and bitstream +manipulation at the byte, not word, level, thus host word ordering is +of a concern only during optimization when writing high performance +code that operates on a word of storage at a time rather than by byte. +Logically, bytes are always coded and decoded in order from byte zero +through byte $n$. + + + +\subsubsection{coding bits into byte sequences} + +The Vorbis codec has need to code arbitrary bit-width integers, from +zero to 32 bits wide, into packets. These integer fields are not +aligned to the boundaries of the byte representation; the next field +is written at the bit position at which the previous field ends. + +The encoder logically packs integers by writing the LSb of a binary +integer to the logical bitstream first, followed by next least +significant bit, etc, until the requested number of bits have been +coded. When packing the bits into bytes, the encoder begins by +placing the LSb of the integer to be written into the least +significant unused bit position of the destination byte, followed by +the next-least significant bit of the source integer and so on up to +the requested number of bits. When all bits of the destination byte +have been filled, encoding continues by zeroing all bits of the next +byte and writing the next bit into the bit position 0 of that byte. +Decoding follows the same process as encoding, but by reading bits +from the byte stream and reassembling them into integers. + + + +\subsubsection{signedness} + +The signedness of a specific number resulting from decode is to be +interpreted by the decoder given decode context. That is, the three +bit binary pattern 'b111' can be taken to represent either 'seven' as +an unsigned integer, or '-1' as a signed, two's complement integer. +The encoder and decoder are responsible for knowing if fields are to +be treated as signed or unsigned. + + + +\subsubsection{coding example} + +Code the 4 bit integer value '12' [b1100] into an empty bytestream. +Bytestream result: + +\begin{Verbatim}[commandchars=\\\{\}] + | + V + + 7 6 5 4 3 2 1 0 +byte 0 [0 0 0 0 1 1 0 0] <- +byte 1 [ ] +byte 2 [ ] +byte 3 [ ] + ... +byte n [ ] bytestream length == 1 byte + +\end{Verbatim} + + +Continue by coding the 3 bit integer value '-1' [b111]: + +\begin{Verbatim}[commandchars=\\\{\}] + | + V + + 7 6 5 4 3 2 1 0 +byte 0 [0 1 1 1 1 1 0 0] <- +byte 1 [ ] +byte 2 [ ] +byte 3 [ ] + ... +byte n [ ] bytestream length == 1 byte +\end{Verbatim} + + +Continue by coding the 7 bit integer value '17' [b0010001]: + +\begin{Verbatim}[commandchars=\\\{\}] + | + V + + 7 6 5 4 3 2 1 0 +byte 0 [1 1 1 1 1 1 0 0] +byte 1 [0 0 0 0 1 0 0 0] <- +byte 2 [ ] +byte 3 [ ] + ... +byte n [ ] bytestream length == 2 bytes + bit cursor == 6 +\end{Verbatim} + + +Continue by coding the 13 bit integer value '6969' [b110 11001110 01]: + +\begin{Verbatim}[commandchars=\\\{\}] + | + V + + 7 6 5 4 3 2 1 0 +byte 0 [1 1 1 1 1 1 0 0] +byte 1 [0 1 0 0 1 0 0 0] +byte 2 [1 1 0 0 1 1 1 0] +byte 3 [0 0 0 0 0 1 1 0] <- + ... +byte n [ ] bytestream length == 4 bytes + +\end{Verbatim} + + + + +\subsubsection{decoding example} + +Reading from the beginning of the bytestream encoded in the above example: + +\begin{Verbatim}[commandchars=\\\{\}] + | + V + + 7 6 5 4 3 2 1 0 +byte 0 [1 1 1 1 1 1 0 0] <- +byte 1 [0 1 0 0 1 0 0 0] +byte 2 [1 1 0 0 1 1 1 0] +byte 3 [0 0 0 0 0 1 1 0] bytestream length == 4 bytes + +\end{Verbatim} + + +We read two, two-bit integer fields, resulting in the returned numbers +'b00' and 'b11'. 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. There are no artificial alignment +boundaries maintained in the bitstream. + +\item The second value is the +two-bit-wide integer 'b11'. This value may be interpreted either as +the unsigned value '3', or the signed value '-1'. Signedness is +dependent on decode context. +\end{itemize} + + + + +\subsubsection{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 bytestream (encoded bitstream) must begin and end on a byte +boundary. Often, the encoded bitstream is not an integer number of +bytes, and so there is unused (uncoded) space in the last byte of a +packet. + +Unused space in the last byte of a bytestream is always zeroed during +the coding process. Thus, should this unused space be read, it will +return binary zeroes. + +Attempting to read past the end of an encoded packet results in an +'end-of-packet' condition. End-of-packet is not to be considered an +error; it is merely a state indicating that there is insufficient +remaining data to fulfill the desired read size. Vorbis uses truncated +packets as a normal mode of operation, and as such, decoders must +handle reading past the end of a packet as a typical mode of +operation. Any further read operations after an 'end-of-packet' +condition shall also return 'end-of-packet'. + + + +\subsubsection{reading zero bits} + +Reading a zero-bit-wide integer returns the value '0' and does not +increment the stream cursor. Reading to the end of the packet (but +not past, such that an 'end-of-packet' condition has not triggered) +and then reading a zero bit integer shall succeed, returning 0, and +not trigger an end-of-packet condition. Reading a zero-bit-wide +integer after a previous read sets 'end-of-packet' shall also fail +with 'end-of-packet'. + + + + + + |