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4.1.10.5.19.2 DIRECT2 Encoding Algorithm

The basic notion of the DIRECT2 encoding algorithm is that data appears unchanged in the compressed representation, and metadata is encoded in the same output stream, and in line with, the data.

The key to decoding the compressed data is recognizing what bytes are metadata and what bytes are data. The decoder MUST be able to identify the presence of metadata in the compressed and encoded data stream. Bitmasks are inserted periodically in the byte stream to provide this information to the decoder.

This section describes the bitmasks that enable the decoder to distinguish data from metadata. It also describes the process of encoding the metadata.

Bitmask

To distinguish data from metadata in the compressed byte stream, the data stream begins with a 4-byte bitmask that indicates to the decoder whether the next byte to be processed is data (a "0" value in the bit), or if the next byte (or series of bytes) is metadata (a "1" value in the bit). If a "0" bit is encountered, the next byte in the input stream is the next byte in the output stream. If a "1" bit is encountered, the next byte or series of bytes is metadata that MUST be interpreted further.

For example, a bitmask of 0x01000000 indicates that the first seven bytes are actual data, followed by encoded metadata that starts at the eighth byte. The metadata is followed by 24 additional bytes of data. A bitmask of 0x112000000 indicates that there will be metadata in the 4th, 8th, and 11th elements (note that the actual byte positions in the compressed data may be different because metadata elements will range from 2 to 6 bytes in length), with the remaining elements being data bytes.

When the bitmask has been consumed, the next four bytes in the input stream are another bitmask.

The bitmask must also contain a "1" in the bit following the last encoded element, to indicate the end of the compressed data. For example, given a hypothetical 8-bit bitmask, the string "ABCABCDEF" should be compressed as (0,0)A(0,0)B(0,0)C(3,3)D(0,0)E(0,0)F. Its bitmask would be b'00010001' (0x11). This would indicate three bytes of data, followed by metadata, followed by an additional 3 bytes, finally terminated with a "1" to indicate the end of the stream.

The final end bit is always necessary, even if an additional bitmask has to be allocated. If the string in the above example was "ABCABCDEFG", for example, it would require an additional bitmask. It would begin with the bitmask b'00010000', followed by the compressed data, and followed by another bitmask with a "1" as the next bit to indicate the end of the stream.

Encoding Metadata

In the output stream, actual data bytes are stored unchanged. Bitmasks are stored periodically to indicate whether the next byte or bytes are data or metadata. If the next bit in the bitmask is a "1", the next set of bytes in the input data stream is metadata (unless the last element of data was read, in which case the "1" bit would indicate the end of the stream as noted above). This metadata contains an offset back to the start of the data to be copied to the output stream, and the length of the data to be copied.

To represent the metadata as efficiently as possible, the encoding of that metadata is not fixed in length. The encoding algorithm supports the largest possible floating compression window to increase the probability of finding a large match; the larger the window, the greater the number of bytes that are needed for the offset. The encoding algorithm also supports the longest possible match; the longer the match length, the greater the number of bytes that are needed to encode the length.

Metadata Offset

The protocol assumes the metadata is two bytes in length. The three low-order bits are used to encode the length. The high-order 13 bits are a first complement of the offset, which is represented as a negative signed value in 2's complement. The offset is only encoded with those 13 bits. This value cannot be extended and defines the maximum size of the compression floating window. For example, the metadata 0x0018 is converted into the offset b'000000000011', and the length b'000'. The offset is '-4', computed by inverting the offset bits, treating the result as a 2's complement, and converting it to an integer.

Match Length

Unlike the metadata offset, the match length is extensible. If the length is less than 10 bytes, it is encoded in the three low-order bits of the 2-byte metadata. Although three bits seems to allow for a maximum length of six (the value b'111' is reserved), because the minimum match is three bytes, these three bits actually allow for the expression of lengths from three to nine. The match length goes from L = b'000' + 3 bytes, to L = b'110' + 3 bytes. Because smaller lengths are much more common than the larger lengths, the algorithm tries to optimize for smaller lengths. To encode a length between three and nine, we use the three bits that are "in-line" in the 2-byte metadata.

If the length of the match is greater than nine bytes, an initial bit pattern of b'111' is put in the three bits. This does not signify a length of 10 bytes, but instead a length that is greater than or equal to 10, which is included in the low-order nibble of the following byte.

Every other time that the length is greater than nine, an additional byte follows the initial 2-byte metadata. The first time that the additional byte is included, the low-order nibble is used as the additive length. The high-order nibble is "reserved" for the next metadata instance when the length is greater than nine. Therefore, the first time that the decoder encounters a length that is greater than nine, it reads the next byte from the data stream and the low-order nibble is extracted and used to compute the length for this metadata instance. The high-order nibble is remembered and used the next time that the decoder encounters a metadata length that is greater than nine. The third time that a length that is greater than nine is encountered, another extra byte is added after the 2-byte metadata, with the low-order nibble used for this length and the high-order nibble reserved for the fourth length that is greater than nine, and so on.

If the nibble from this "shared" byte is all "1s" (for example, b'1111'), another byte is added after the shared byte to hold more length. In this manner, a length of 24 is encoded as follows:

  • b'111' (in the three bits in the original two bytes of metadata), plus

  • b'1110' (in the nibble of the "shared' byte" of extended length)

  • b'111' means 10 bytes plus b'1110', which is 14, which results in a total of 24.

If the length is more than 24, the next byte is also used in the length calculation. In this manner, a length of 25 is encoded as follows:

  • b'111' (in the three bits in the original two bytes of metadata), plus

  • b'1111' (in the nibble of the "shared" byte of extended length), plus

  • b'00000000' (in the next byte).

This scheme is good for lengths of up to 278 (a length of 10 in the three bits in the original two bytes of metadata, plus a length of 15 in the nibble of the "shared" byte of extended length, plus a length of up to 254 in the extra byte).

A "full" (all b'1') bit pattern (b'111', b'1111', and b'11111111') means that there is more length in the following two bytes.

The final two bytes of length differ from the length information that comes earlier in the metadata. For lengths that are equal to 280 or greater, the length is calculated only from these last two bytes, and is not added to the previous length bits. The value in the last two bytes, a 16-bit integer, is three less than the metadata length. These last two bytes allow for a match length of up to 32,768 bytes + 3 bytes (the minimum match length).

The following table summarizes the length representation in metadata.

Note  Length is computed from the bits that are included in the metadata plus the minimum match length of three.

Length representation in metadata

Match length

Length bits in the metadata

24

b'111' (three bits in the original two bytes of metadata)

+

b'1110' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

25

b'111' (three bits in the original two bytes of metadata)

+

b'1111' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

+

b'00000000' (in the next byte)

26

b'111' (three bits in the original two bytes of metadata)

+

b'1111' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

+

b'00000001' (in the next byte)

279

b'111' (three bits in the original two bytes of metadata)

+

b'1111' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

+

b'11111110' (in the next byte)

280

b'111' (three bits in the original two bytes of metadata)

b'1111' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

b'11111111' (in the next byte)

0x0115 (in the next two bytes). These two bytes represent a length of 277 + 3 (minimum match length).

Note  All of the length is included in the final two bytes and is not additive, as were the previous length calculations for lengths that are smaller than 280 bytes.

281

b'111' (three bits in the original two bytes of metadata)

b'1111' (in the high-order or lower-order nibble, as appropriate, of the shared byte)

b'11111111' (in the next byte)

0x0116 (in the next two bytes). This is 278 + 3 (minimum match length).

Note  All of the length is included in the final two bytes and is not additive, as were the previous length calculations for lengths that are smaller than 280 bytes.

A "full" bit pattern in that last half word does not mean that more metadata is coming after the last bytes.

The LZ77 compression algorithm produces a well-compressed encoding for small valued lengths, but as the length increases, the encoding becomes less well compressed. A match length of greater than 278 bytes requires a relatively large number of bits: 3+4+8+16. This includes three bits in the original two bytes of metadata, four bits in the nibble in the "shared" byte, eight bits in the next byte, and 16 bits in the final two bytes of metadata.

 
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