$Id: 02-bitpacking.xml 7186 2004-07-20 07:19:25Z xiphmont $

# Bitpacking Convention

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### coding example

Code the 4 bit integer value '12' [b1100] into an empty bytestream. Bytestream result:

                  |
                  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

Continue by coding the 3 bit integer value '-1' [b111]:

            |
            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

Continue by coding the 7 bit integer value '17' [b0010001]:

              |
              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

Continue by coding the 13 bit integer value '6969' [b110 11001110 01]:

                    |
                    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

### decoding example

Reading from the beginning of the bytestream encoded in the above example:

                          |
                          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

We read two, two-bit integer fields, resulting in the returned numbers 'b00' and 'b11'. Two things are worth noting here:

- 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.

- 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-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'.

### 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'.