% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-

%!TEX root = Vorbis_I_spec.tex

% $Id$

\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'.