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