release/src/router/libvorbis/doc/02-bitpacking.tex

   1 % -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
   2 %!TEX root = Vorbis_I_spec.tex
   3 % $Id$
   4 \section{Bitpacking Convention} \label{vorbis:spec:bitpacking}
   5
   6 \subsection{Overview}
   7
   8 The Vorbis codec uses relatively unstructured raw packets containing
   9 arbitrary-width binary integer fields.  Logically, these packets are a
  10 bitstream in which bits are coded one-by-one by the encoder and then
  11 read one-by-one in the same monotonically increasing order by the
  12 decoder.  Most current binary storage arrangements group bits into a
  13 native word size of eight bits (octets), sixteen bits, thirty-two bits
  14 or, less commonly other fixed word sizes.  The Vorbis bitpacking
  15 convention specifies the correct mapping of the logical packet
  16 bitstream into an actual representation in fixed-width words.
  17
  18
  19 \subsubsection{octets, bytes and words}
  20
  21 In most contemporary architectures, a 'byte' is synonymous with an
  22 'octet', that is, eight bits.  This has not always been the case;
  23 seven, ten, eleven and sixteen bit 'bytes' have been used.  For
  24 purposes of the bitpacking convention, a byte implies the native,
  25 smallest integer storage representation offered by a platform.  On
  26 modern platforms, this is generally assumed to be eight bits (not
  27 necessarily because of the processor but because of the
  28 filesystem/memory architecture.  Modern filesystems invariably offer
  29 bytes as the fundamental atom of storage).  A 'word' is an integer
  30 size that is a grouped multiple of this smallest size.
  31
  32 The most ubiquitous architectures today consider a 'byte' to be an
  33 octet (eight bits) and a word to be a group of two, four or eight
  34 bytes (16, 32 or 64 bits).  Note however that the Vorbis bitpacking
  35 convention is still well defined for any native byte size; Vorbis uses
  36 the native bit-width of a given storage system. This document assumes
  37 that a byte is one octet for purposes of example.
  38
  39 \subsubsection{bit order}
  40
  41 A byte has a well-defined 'least significant' bit (LSb), which is the
  42 only bit set when the byte is storing the two's complement integer
  43 value +1.  A byte's 'most significant' bit (MSb) is at the opposite
  44 end of the byte. Bits in a byte are numbered from zero at the LSb to
  45 $n$ ($n=7$ in an octet) for the
  46 MSb.
  47
  48
  49
  50 \subsubsection{byte order}
  51
  52 Words are native groupings of multiple bytes.  Several byte orderings
  53 are possible in a word; the common ones are 3-2-1-0 ('big endian' or
  54 'most significant byte first' in which the highest-valued byte comes
  55 first), 0-1-2-3 ('little endian' or 'least significant byte first' in
  56 which the lowest value byte comes first) and less commonly 3-1-2-0 and
  57 0-2-1-3 ('mixed endian').
  58
  59 The Vorbis bitpacking convention specifies storage and bitstream
  60 manipulation at the byte, not word, level, thus host word ordering is
  61 of a concern only during optimization when writing high performance
  62 code that operates on a word of storage at a time rather than by byte.
  63 Logically, bytes are always coded and decoded in order from byte zero
  64 through byte $n$.
  65
  66
  67
  68 \subsubsection{coding bits into byte sequences}
  69
  70 The Vorbis codec has need to code arbitrary bit-width integers, from
  71 zero to 32 bits wide, into packets.  These integer fields are not
  72 aligned to the boundaries of the byte representation; the next field
  73 is written at the bit position at which the previous field ends.
  74
  75 The encoder logically packs integers by writing the LSb of a binary
  76 integer to the logical bitstream first, followed by next least
  77 significant bit, etc, until the requested number of bits have been
  78 coded.  When packing the bits into bytes, the encoder begins by
  79 placing the LSb of the integer to be written into the least
  80 significant unused bit position of the destination byte, followed by
  81 the next-least significant bit of the source integer and so on up to
  82 the requested number of bits.  When all bits of the destination byte
  83 have been filled, encoding continues by zeroing all bits of the next
  84 byte and writing the next bit into the bit position 0 of that byte.
  85 Decoding follows the same process as encoding, but by reading bits
  86 from the byte stream and reassembling them into integers.
  87
  88
  89
  90 \subsubsection{signedness}
  91
  92 The signedness of a specific number resulting from decode is to be
  93 interpreted by the decoder given decode context.  That is, the three
  94 bit binary pattern 'b111' can be taken to represent either 'seven' as
  95 an unsigned integer, or '-1' as a signed, two's complement integer.
  96 The encoder and decoder are responsible for knowing if fields are to
  97 be treated as signed or unsigned.
  98
  99
 100
 101 \subsubsection{coding example}
 102
 103 Code the 4 bit integer value '12' [b1100] into an empty bytestream.
 104 Bytestream result:
 105
 106 \begin{Verbatim}[commandchars=\\\{\}]
 107               |
 108               V
 109
 110         7 6 5 4 3 2 1 0
 111 byte 0 [0 0 0 0 1 1 0 0]  <-
 112 byte 1 [               ]
 113 byte 2 [               ]
 114 byte 3 [               ]
 115              ...
 116 byte n [               ]  bytestream length == 1 byte
 117
 118 \end{Verbatim}
 119
 120
 121 Continue by coding the 3 bit integer value '-1' [b111]:
 122
 123 \begin{Verbatim}[commandchars=\\\{\}]
 124         |
 125         V
 126
 127         7 6 5 4 3 2 1 0
 128 byte 0 [0 1 1 1 1 1 0 0]  <-
 129 byte 1 [               ]
 130 byte 2 [               ]
 131 byte 3 [               ]
 132              ...
 133 byte n [               ]  bytestream length == 1 byte
 134 \end{Verbatim}
 135
 136
 137 Continue by coding the 7 bit integer value '17' [b0010001]:
 138
 139 \begin{Verbatim}[commandchars=\\\{\}]
 140           |
 141           V
 142
 143         7 6 5 4 3 2 1 0
 144 byte 0 [1 1 1 1 1 1 0 0]
 145 byte 1 [0 0 0 0 1 0 0 0]  <-
 146 byte 2 [               ]
 147 byte 3 [               ]
 148              ...
 149 byte n [               ]  bytestream length == 2 bytes
 150                           bit cursor == 6
 151 \end{Verbatim}
 152
 153
 154 Continue by coding the 13 bit integer value '6969' [b110 11001110 01]:
 155
 156 \begin{Verbatim}[commandchars=\\\{\}]
 157                 |
 158                 V
 159
 160         7 6 5 4 3 2 1 0
 161 byte 0 [1 1 1 1 1 1 0 0]
 162 byte 1 [0 1 0 0 1 0 0 0]
 163 byte 2 [1 1 0 0 1 1 1 0]
 164 byte 3 [0 0 0 0 0 1 1 0]  <-
 165              ...
 166 byte n [               ]  bytestream length == 4 bytes
 167
 168 \end{Verbatim}
 169
 170
 171
 172
 173 \subsubsection{decoding example}
 174
 175 Reading from the beginning of the bytestream encoded in the above example:
 176
 177 \begin{Verbatim}[commandchars=\\\{\}]
 178                       |
 179                       V
 180
 181         7 6 5 4 3 2 1 0
 182 byte 0 [1 1 1 1 1 1 0 0]  <-
 183 byte 1 [0 1 0 0 1 0 0 0]
 184 byte 2 [1 1 0 0 1 1 1 0]
 185 byte 3 [0 0 0 0 0 1 1 0]  bytestream length == 4 bytes
 186
 187 \end{Verbatim}
 188
 189
 190 We read two, two-bit integer fields, resulting in the returned numbers
 191 'b00' and 'b11'.  Two things are worth noting here:
 192
 193 \begin{itemize}
 194 \item Although these four bits were originally written as a single
 195 four-bit integer, reading some other combination of bit-widths from the
 196 bitstream is well defined.  There are no artificial alignment
 197 boundaries maintained in the bitstream.
 198
 199 \item The second value is the
 200 two-bit-wide integer 'b11'.  This value may be interpreted either as
 201 the unsigned value '3', or the signed value '-1'.  Signedness is
 202 dependent on decode context.
 203 \end{itemize}
 204
 205
 206
 207
 208 \subsubsection{end-of-packet alignment}
 209
 210 The typical use of bitpacking is to produce many independent
 211 byte-aligned packets which are embedded into a larger byte-aligned
 212 container structure, such as an Ogg transport bitstream.  Externally,
 213 each bytestream (encoded bitstream) must begin and end on a byte
 214 boundary.  Often, the encoded bitstream is not an integer number of
 215 bytes, and so there is unused (uncoded) space in the last byte of a
 216 packet.
 217
 218 Unused space in the last byte of a bytestream is always zeroed during
 219 the coding process.  Thus, should this unused space be read, it will
 220 return binary zeroes.
 221
 222 Attempting to read past the end of an encoded packet results in an
 223 'end-of-packet' condition.  End-of-packet is not to be considered an
 224 error; it is merely a state indicating that there is insufficient
 225 remaining data to fulfill the desired read size.  Vorbis uses truncated
 226 packets as a normal mode of operation, and as such, decoders must
 227 handle reading past the end of a packet as a typical mode of
 228 operation. Any further read operations after an 'end-of-packet'
 229 condition shall also return 'end-of-packet'.
 230
 231
 232
 233 \subsubsection{reading zero bits}
 234
 235 Reading a zero-bit-wide integer returns the value '0' and does not
 236 increment the stream cursor.  Reading to the end of the packet (but
 237 not past, such that an 'end-of-packet' condition has not triggered)
 238 and then reading a zero bit integer shall succeed, returning 0, and
 239 not trigger an end-of-packet condition.  Reading a zero-bit-wide
 240 integer after a previous read sets 'end-of-packet' shall also fail
 241 with 'end-of-packet'.
 242
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