zstd/zstd_compression_format.md

Zstandard Compression Format

Notices

Copyright (c) 2016 Yann Collet

Permission is granted to copy and distribute this document for any purpose and without charge, including translations into other languages and incorporation into compilations, provided that the copyright notice and this notice are preserved, and that any substantive changes or deletions from the original are clearly marked. Distribution of this document is unlimited.

Version

0.2.0 (22/07/16)

Introduction

The purpose of this document is to define a lossless compressed data format, that is independent of CPU type, operating system, file system and character set, suitable for file compression, pipe and streaming compression, using the Zstandard algorithm.

The data can be produced or consumed, even for an arbitrarily long sequentially presented input data stream, using only an a priori bounded amount of intermediate storage, and hence can be used in data communications. The format uses the Zstandard compression method, and optional xxHash-64 checksum method, for detection of data corruption.

The data format defined by this specification does not attempt to allow random access to compressed data.

This specification is intended for use by implementers of software to compress data into Zstandard format and/or decompress data from Zstandard format. The text of the specification assumes a basic background in programming at the level of bits and other primitive data representations.

Unless otherwise indicated below, a compliant compressor must produce data sets that conform to the specifications presented here. It doesn’t need to support all options though.

A compliant decompressor must be able to decompress at least one working set of parameters that conforms to the specifications presented here. It may also ignore informative fields, such as checksum. Whenever it does not support a parameter defined in the compressed stream, it must produce a non-ambiguous error code and associated error message explaining which parameter is unsupported.

Definitions

A content compressed by Zstandard is transformed into a Zstandard frame. Multiple frames can be appended into a single file or stream. A frame is totally independent, has a defined beginning and end, and a set of parameters which tells the decoder how to decompress it.

A frame encapsulates one or multiple blocks. Each block can be compressed or not, and has a guaranteed maximum content size, which depends on frame parameters. Unlike frames, each block depends on previous blocks for proper decoding. However, each block can be decompressed without waiting for its successor, allowing streaming operations.

General Structure of Zstandard Frame format

MagicNb	Frame Header	Block	[More blocks]	EndMark
4 bytes	2-14 bytes			3 bytes

Magic Number

4 Bytes, Little endian format. Value : 0xFD2FB527

Frame Header

2 to 14 Bytes, detailed in next part.

Data Blocks

Detailed in next chapter. That’s where compressed data is stored.

EndMark

The flow of blocks ends when the last block header brings an end signal . This last block header may optionally host a Content Checksum .

Content Checksum

Content Checksum verify that frame content has been regenerated correctly. The content checksum is the result of xxh64() hash function digesting the original (decoded) data as input, and a seed of zero. Bits from 11 to 32 (included) are extracted to form a 22 bits checksum stored into the endmark body.

mask22bits = (1<<22)-1;
contentChecksum = (XXH64(content, size, 0) >> 11) & mask22bits;

Content checksum is only present when its associated flag is set in the frame descriptor. Its usage is optional.

Frame Concatenation

In some circumstances, it may be required to append multiple frames, for example in order to add new data to an existing compressed file without re-framing it.

In such case, each frame brings its own set of descriptor flags. Each frame is considered independent. The only relation between frames is their sequential order.

The ability to decode multiple concatenated frames within a single stream or file is left outside of this specification. As an example, the reference zstd command line utility is able to decode all concatenated frames in their sequential order, delivering the final decompressed result as if it was a single content.

Frame Header

FHD	[WD]	[dictID]	[Content Size]
1 byte	0-1 byte	0-4 bytes	0 - 8 bytes

Frame header has a variable size, which uses a minimum of 2 bytes, and up to 14 bytes depending on optional parameters.

FHD byte (Frame Header Descriptor)

The first Header's byte is called the Frame Header Descriptor. It tells which other fields are present. Decoding this byte is enough to tell the size of Frame Header.

BitNb	7-6	5	4	3	2	1-0
FieldName	FCSize	Segment	Unused	Reserved	Checksum	dictID

In this table, bit 7 is highest bit, while bit 0 is lowest.

Frame Content Size flag

This is a 2-bits flag (= FHD >> 6), specifying if decompressed data size is provided within the header.

Value	0	1	2	3
FieldSize	0-1	2	4	8

Value 0 meaning depends on single segment mode : it either means 0 (size not provided) if the WD byte is present, or 1 (frame content size <= 255 bytes) otherwise.

Single Segment

If this flag is set, data shall be regenerated within a single continuous memory segment.

In which case, WD byte is not present, but Frame Content Size field necessarily is. As a consequence, the decoder must allocate a memory segment of size >= Frame Content Size.

In order to preserve the decoder from unreasonable memory requirement, a decoder can reject a compressed frame which requests a memory size beyond decoder's authorized range.

For broader compatibility, decoders are recommended to support memory sizes of at least 8 MB. This is just a recommendation, each decoder is free to support higher or lower limits, depending on local limitations.

Unused bit

The value of this bit should be set to zero. A decoder compliant with this specification version should not interpret it. It might be used in a future version, to signal a property which is not mandatory to properly decode the frame.

Reserved bit

This bit is reserved for some future feature. Its value must be zero. A decoder compliant with this specification version must ensure it is not set. This bit may be used in a future revision, to signal a feature that must be interpreted in order to decode the frame.

Content checksum flag

If this flag is set, a content checksum will be present into the EndMark. The checksum is a 22 bits value extracted from the XXH64() of data, and stored into endMark. See Content Checksum .

Dictionary ID flag

This is a 2-bits flag (= FHD & 3), telling if a dictionary ID is provided within the header. It also specifies the size of this field.

Value	0	1	2	3
FieldSize	0	1	2	4

WD byte (Window Descriptor)

Provides guarantees on maximum back-reference distance that will be present within compressed data. This information is useful for decoders to allocate enough memory.

WD byte is optional. It's not present in single segment mode. In which case, the maximum back-reference distance is the content size itself, which can be any value from 1 to 2^64-1 bytes (16 EB).

BitNb	7-3	0-2
FieldName	Exponent	Mantissa

Maximum distance is given by the following formulae :

windowLog = 10 + Exponent;
windowBase = 1 << windowLog;
windowAdd = (windowBase / 8) * Mantissa;
windowSize = windowBase + windowAdd;

The minimum window size is 1 KB. The maximum size is 15*(1<<38) bytes, which is 1.875 TB.

To properly decode compressed data, a decoder will need to allocate a buffer of at least windowSize bytes.

In order to preserve decoder from unreasonable memory requirements, a decoder can refuse a compressed frame which requests a memory size beyond decoder's authorized range.

For improved interoperability, decoders are recommended to be compatible with window sizes of 8 MB. Encoders are recommended to not request more than 8 MB. It's merely a recommendation though, decoders are free to support larger or lower limits, depending on local limitations.

Dictionary ID

This is a variable size field, which contains the ID of the dictionary required to properly decode the frame. Note that this field is optional. When it's not present, it's up to the caller to make sure it uses the correct dictionary.

Field size depends on Dictionary ID flag. 1 byte can represent an ID 0-255. 2 bytes can represent an ID 0-65535. 4 bytes can represent an ID 0-4294967295.

It's allowed to represent a small ID (for example 13) with a large 4-bytes dictionary ID, losing some compacity in the process.

Reserved ranges : If the frame is going to be distributed in a private environment, any dictionary ID can be used. However, for public distribution of compressed frames using a dictionary, some ranges are reserved for future use :

• low : 1 - 32767 : reserved
• high : >= (2^31) : reserved

Frame Content Size

This is the original (uncompressed) size. This information is optional, and only present if associated flag is set. Content size is provided using 1, 2, 4 or 8 Bytes. Format is Little endian.

Field Size	Range
0	0
1	0 - 255
2	256 - 65791
4	0 - 2^32-1
8	0 - 2^64-1

When field size is 1, 4 or 8 bytes, the value is read directly. When field size is 2, an offset of 256 is added. It's allowed to represent a small size (ex: 18) using any compatible variant. A size of 0 means content size is unknown. In which case, the WD byte will necessarily be present, and becomes the only hint to guide memory allocation.

In order to preserve decoder from unreasonable memory requirement, a decoder can refuse a compressed frame which requests a memory size beyond decoder's authorized range.

Data Blocks

B. Header	data
3 bytes

Block Header

This field uses 3-bytes, format is little-endian.

The 2 lowest bits represent the block type, while the remaining 22 bits represent the (compressed) block size.

There are 4 block types :

Value	0	1	2	3
Block Type	Raw	RLE	Compressed	EndMark

• Compressed : this is a Zstandard compressed block, detailed in another section of this specification. "block size" is the compressed size. Decompressed size is unknown, but its maximum possible value is guaranteed (see below)
• Raw : this is an uncompressed block. "block size" is the number of bytes to read and copy.
• RLE : this is a single byte, repeated N times. In which case, "block size" is the size to regenerate, while the "compressed" block is just 1 byte (the byte to repeat).
• EndMark : this is not a block. Signal the end of the frame. The rest of the field may be optionally filled by a checksum (see Content Checksum).

Block sizes must respect a few rules :

• In compressed mode, compressed size if always strictly < decompressed size.
• Block decompressed size is always <= maximum back-reference distance .
• Block decompressed size is always <= 128 KB

Data

Where the actual data to decode stands. It might be compressed or not, depending on previous field indications. A data block is not necessarily "full" : since an arbitrary “flush” may happen anytime, block decompressed content can be any size, up to Block Maximum Decompressed Size, which is the smallest of :

• Maximum back-reference distance
• 128 KB

Skippable Frames

Magic Number	Frame Size	User Data
4 bytes	4 bytes

Skippable frames allow the insertion of user-defined data into a flow of concatenated frames. Its design is pretty straightforward, with the sole objective to allow the decoder to quickly skip over user-defined data and continue decoding.

Skippable frames defined in this specification are compatible with LZ4 ones.

Magic Number :

4 Bytes, Little endian format. Value : 0x184D2A5X, which means any value from 0x184D2A50 to 0x184D2A5F. All 16 values are valid to identify a skippable frame.

Frame Size :

This is the size, in bytes, of the following User Data (without including the magic number nor the size field itself). 4 Bytes, Little endian format, unsigned 32-bits. This means User Data can’t be bigger than (2^32-1) Bytes.

User Data :

User Data can be anything. Data will just be skipped by the decoder.

Compressed block format

This specification details the content of a compressed block. A compressed block has a size, which must be known. It also has a guaranteed maximum regenerated size, in order to properly allocate destination buffer. See Data Blocks for more details.

A compressed block consists of 2 sections :

• Literals section
• Sequences section

Prerequisites

To decode a compressed block, the following elements are necessary :

• Previous decoded blocks, up to a distance of windowSize, or all previous blocks in "single segment" mode.
• List of "recent offsets" from previous compressed block.
• Decoding tables of previous compressed block for each symbol type (literals, litLength, matchLength, offset).

Literals section

Literals are compressed using Huffman prefix codes. During sequence phase, literals will be entangled with match copy operations. All literals are regrouped in the first part of the block. They can be decoded first, and then copied during sequence operations, or they can be decoded on the flow, as needed by sequence commands.

Header	[Tree Description]	Stream1	[Stream2]	[Stream3]	[Stream4]

Literals can be compressed, or uncompressed. When compressed, an optional tree description can be present, followed by 1 or 4 streams.

Literals section header

Header is in charge of describing how literals are packed. It's a byte-aligned variable-size bitfield, ranging from 1 to 5 bytes, using little-endian convention.

EncodingType	sizes format	regenerated size	[compressed size]
2 bits	1 - 2 bits	5 - 20 bits	0 - 18 bits

In this representation, bits on the left are smallest bits.

Encoding Type :

This field uses 2 lowest bits of first byte, describing 4 different block types :

Value	0	1	2	3
Block Type	Raw	RLE	Compressed	RepeatStats

• Compressed : This is a standard huffman-compressed block, starting with a huffman tree description. See details below.
• Repeat Stats : This is a huffman-compressed block, using huffman tree from previous huffman-compressed literals block. Huffman tree description will be skipped.
• Raw : Literals are stored uncompressed.
• RLE : Literals consist of a single byte value repeated N times.

Sizes format :

Sizes format are divided into 2 families :

• For compressed block, it requires to decode both the compressed size and the decompressed size. It will also decode the number of streams.
• For Raw or RLE blocks, it's enough to decode the size to regenerate.

For values spanning several bytes, convention is Little-endian.

Sizes format for Raw and RLE literals block :

• Value : x0 : Regenerated size uses 5 bits (0-31). Total literal header size is 1 byte. size = h[0]>>3;
• Value : 01 : Regenerated size uses 12 bits (0-4095). Total literal header size is 2 bytes. size = (h[0]>>4) + (h[1]<<4);
• Value : 11 : Regenerated size uses 20 bits (0-1048575). Total literal header size is 3 bytes. size = (h[0]>>4) + (h[1]<<4) + (h[2]<<12);

Note : it's allowed to represent a short value (ex : 13) using a long format, accepting the reduced compacity.

Sizes format for Compressed literals block :

Note : also applicable to "repeat-stats" blocks.

• Value : 00 : Single stream. Compressed and regenerated sizes use 10 bits (0-1023). Total literal header size is 3 bytes.
• Value : 01 : 4 streams. Compressed and regenerated sizes use 10 bits (0-1023). Total literal header size is 3 bytes.
• Value : 10 : 4 streams. Compressed and regenerated sizes use 14 bits (0-16383). Total literal header size is 4 bytes.
• Value : 11 : 4 streams. Compressed and regenerated sizes use 18 bits (0-262143). Total literal header size is 5 bytes.

Compressed and regenerated size fields follow little endian convention.

Huffman Tree description

This section is only present when literals block type is Compressed (0).

Prefix coding represents symbols from an a priori known alphabet by bit sequences (codewords), one codeword for each symbol, in a manner such that different symbols may be represented by bit sequences of different lengths, but a parser can always parse an encoded string unambiguously symbol-by-symbol.

Given an alphabet with known symbol frequencies, the Huffman algorithm allows the construction of an optimal prefix code using the fewest bits of any possible prefix codes for that alphabet.

Prefix code must not exceed a maximum code length. More bits improve accuracy but cost more header size, and require more memory or more complex decoding operations. This specification limits maximum code length to 11 bits.

Representation

All literal values from zero (included) to last present one (excluded) are represented by weight values, from 0 to maxBits. Transformation from weight to nbBits follows this formulae : nbBits = weight ? maxBits + 1 - weight : 0; . The last symbol's weight is deduced from previously decoded ones, by completing to the nearest power of 2. This power of 2 gives maxBits, the depth of the current tree.

Example : Let's presume the following huffman tree must be described :

literal	0	1	2	3	4	5
nbBits	1	2	3	0	4	4

The tree depth is 4, since its smallest element uses 4 bits. Value 5 will not be listed, nor will values above 5. Values from 0 to 4 will be listed using weight instead of nbBits. Weight formula is : weight = nbBits ? maxBits + 1 - nbBits : 0; It gives the following serie of weights :

weights	4	3	2	0	1
literal	0	1	2	3	4

The decoder will do the inverse operation : having collected weights of literals from 0 to 4, it knows the last literal, 5, is present with a non-zero weight. The weight of 5 can be deducted by joining to the nearest power of 2. Sum of 2^(weight-1) (excluding 0) is : 8 + 4 + 2 + 0 + 1 = 15 Nearest power of 2 is 16. Therefore, maxBits = 4 and weight[5] = 1.

Huffman Tree header

This is a single byte value (0-255), which tells how to decode the list of weights.

• if headerByte >= 242 : this is one of 14 pre-defined weight distributions :

value	242	243	244	245	246	247	248	249	250	251	252	253	254	255
Nb of 1s	1	2	3	4	7	8	15	16	31	32	63	64	127	128
Complement	1	2	1	4	1	8	1	16	1	32	1	64	1	128

Note : complement is found by using "join to nearest power of 2" rule.

• if headerByte >= 128 : this is a direct representation, where each weight is written directly as a 4 bits field (0-15). The full representation occupies ((nbSymbols+1)/2) bytes, meaning it uses a last full byte even if nbSymbols is odd. nbSymbols = headerByte - 127;. Note that maximum nbSymbols is 241-127 = 114. A larger serie must necessarily use FSE compression.

• if headerByte < 128 : the serie of weights is compressed by FSE. The length of the FSE-compressed serie is headerByte (0-127).

FSE (Finite State Entropy) compression of huffman weights

The serie of weights is compressed using FSE compression. It's a single bitstream with 2 interleaved states, sharing a single distribution table.

To decode an FSE bitstream, it is necessary to know its compressed size. Compressed size is provided by headerByte. It's also necessary to know its maximum decompressed size, which is 255, since literal values span from 0 to 255, and last symbol value is not represented.

An FSE bitstream starts by a header, describing probabilities distribution. It will create a Decoding Table. Table must be pre-allocated, which requires to support a maximum accuracy. For a list of huffman weights, recommended maximum is 7 bits.

FSE header is described in relevant chapter, and so is FSE bitstream. The main difference is that Huffman header compression uses 2 states, which share the same FSE distribution table. Bitstream contains only FSE symbols, there are no interleaved "raw bitfields". The number of symbols to decode is discovered by tracking bitStream overflow condition. When both states have overflowed the bitstream, end is reached.

Conversion from weights to huffman prefix codes

All present symbols shall now have a weight value. Symbols are sorted by weight. Symbols with a weight of zero are removed. Within same weight, symbols keep natural order. Starting from lowest weight, symbols are being allocated to a range. A weight directly represents a range, following the formulae : range = weight ? 1 << (weight-1) : 0 ; Similarly, it is possible to transform weights into nbBits : nbBits = nbBits ? maxBits + 1 - weight : 0; .

Example : Let's presume the following list of weights has been decoded :

Literal	0	1	2	3	4	5
weight	4	3	2	0	1	1

Sorted by weight and then natural order, it gives the following distribution :

Literal	3	4	5	2	1	0
weight	0	1	1	2	3	4
range	0	1	1	2	4	8
table entries	N/A	0	1	2-3	4-7	8-15
nb bits	0	4	4	3	2	1
prefix codes	N/A	0000	0001	001	01	1

Literals bitstreams

Bitstreams sizes

As seen in a previous paragraph, there are 2 flavors of huffman-compressed literals : single stream, and 4-streams.

4-streams is useful for CPU with multiple execution units and OoO operations. Since each stream can be decoded independently, it's possible to decode them up to 4x faster than a single stream, presuming the CPU has enough parallelism available.

For single stream, header provides both the compressed and regenerated size. For 4-streams though, header only provides compressed and regenerated size of all 4 streams combined. In order to properly decode the 4 streams, it's necessary to know the compressed and regenerated size of each stream.

Regenerated size is easiest : each stream has a size of (totalSize+3)/4, except the last one, which is up to 3 bytes smaller, to reach totalSize.

Compressed size must be provided explicitly : in the 4-streams variant, bitstreams are preceded by 3 unsigned Little Endian 16-bits values. Each value represents the compressed size of one stream, in order. The last stream size is deducted from total compressed size and from already known stream sizes : stream4CSize = totalCSize - 6 - stream1CSize - stream2CSize - stream3CSize;

Bitstreams read and decode

Each bitstream must be read backward, that is starting from the end down to the beginning. Therefore it's necessary to know the size of each bitstream.

It's also necessary to know exactly which bit is the latest. This is detected by a final bit flag : the highest bit of latest byte is a final-bit-flag. Consequently, a last byte of 0 is not possible. And the final-bit-flag itself is not part of the useful bitstream. Hence, the last byte contain between 0 and 7 useful bits.

Starting from the end, it's possible to read the bitstream in a little-endian fashion, keeping track of already used bits.

Reading the last maxBits bits, it's then possible to compare extracted value to decoding table, determining the symbol to decode and number of bits to discard.

The process continues up to reading the required number of symbols per stream. If a bitstream is not entirely and exactly consumed, hence reaching exactly its beginning position with all bits consumed, the decoding process is considered faulty.

Sequences section

A compressed block is a succession of sequences . A sequence is a literal copy command, followed by a match copy command. A literal copy command specifies a length. It is the number of bytes to be copied (or extracted) from the literal section. A match copy command specifies an offset and a length. The offset gives the position to copy from, which can be within a previous block.

There are 3 symbol types, literalLength, matchLength and offset, which are encoded together, interleaved in a single bitstream.

Each symbol is a code in its own context, which specifies a baseline and a number of bits to add. Codes are FSE compressed, and interleaved with raw additional bits in the same bitstream.

The Sequences section starts by a header, followed by optional Probability tables for each symbol type, followed by the bitstream.

Header	[LitLengthTable]	[OffsetTable]	[MatchLengthTable]	bitStream

To decode the Sequence section, it's required to know its size. This size is deducted from blockSize - literalSectionSize.

Sequences section header

Consists in 2 items :

• Nb of Sequences
• Flags providing Symbol compression types

Nb of Sequences

This is a variable size field, nbSeqs, using between 1 and 3 bytes. Let's call its first byte byte0.

• if (byte0 == 0) : there are no sequences. The sequence section stops there. Regenerated content is defined entirely by literals section.
• if (byte0 < 128) : nbSeqs = byte0; . Uses 1 byte.
• if (byte0 < 255) : nbSeqs = ((byte0-128) << 8) + byte1; . Uses 2 bytes.
• if (byte0 == 255): nbSeqs = byte1 + (byte2<<8) + 0x7F00; . Uses 3 bytes.

Symbol compression modes

This is a single byte, defining the compression mode of each symbol type.

BitNb	7-6	5-4	3-2	1-0
FieldName	LLtype	OFType	MLType	Reserved

The last field, Reserved, must be all-zeroes.

LLtype, OFType and MLType define the compression mode of Literal Lengths, Offsets and Match Lengths respectively.

They follow the same enumeration :

Value	0	1	2	3
Compression Mode	predef	RLE	Compressed	Repeat

• "predef" : uses a pre-defined distribution table.
• "RLE" : it's a single code, repeated nbSeqs times.
• "Repeat" : re-use distribution table from previous compressed block.
• "Compressed" : standard FSE compression. A distribution table will be present. It will be described in next part.

Symbols decoding

Literal Lengths codes

Literal lengths codes are values ranging from 0 to 35 included. They define lengths from 0 to 131071 bytes.

Code	0-15
length	Code
nbBits	0

Code	16	17	18	19	20	21	22	23
Baseline	16	18	20	22	24	28	32	40
nb Bits	1	1	1	1	2	2	3	3

Code	24	25	26	27	28	29	30	31
Baseline	48	64	128	256	512	1024	2048	4096
nb Bits	4	6	7	8	9	10	11	12

Code	32	33	34	35
Baseline	8192	16384	32768	65536
nb Bits	13	14	15	16

Default distribution

When "compression mode" is "predef"", a pre-defined distribution is used for FSE compression.

Below is its definition. It uses an accuracy of 6 bits (64 states).

short literalLengths_defaultDistribution[36] =
        { 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
          2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1, 1, 1,
         -1,-1,-1,-1 };

Match Lengths codes

Match lengths codes are values ranging from 0 to 52 included. They define lengths from 3 to 131074 bytes.

Code	0-31
value	Code + 3
nbBits	0

Code	32	33	34	35	36	37	38	39
Baseline	35	37	39	41	43	47	51	59
nb Bits	1	1	1	1	2	2	3	3

Code	40	41	42	43	44	45	46	47
Baseline	67	83	99	131	258	514	1026	2050
nb Bits	4	4	5	7	8	9	10	11

Code	48	49	50	51	52
Baseline	4098	8194	16486	32770	65538
nb Bits	12	13	14	15	16

Default distribution

When "compression mode" is defined as "predef", a pre-defined distribution is used for FSE compression.

Here is its definition. It uses an accuracy of 6 bits (64 states).

short matchLengths_defaultDistribution[53] =
        { 1, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,-1,-1,
         -1,-1,-1,-1,-1 };

Offset codes

Offset codes are values ranging from 0 to N, with N being limited by maximum backreference distance.

A decoder is free to limit its maximum N supported. Recommendation is to support at least up to 22. For information, at the time of this writing. the reference decoder supports a maximum N value of 28 in 64-bits mode.

An offset code is also the nb of additional bits to read, and can be translated into an OFValue using the following formulae :

OFValue = (1 << offsetCode) + readNBits(offsetCode);
if (OFValue > 3) offset = OFValue - 3;

OFValue from 1 to 3 are special : they define "repeat codes", which means one of the previous offsets will be repeated. They are sorted in recency order, with 1 meaning the most recent one. See Repeat offsets paragraph.

Default distribution

When "compression mode" is defined as "predef", a pre-defined distribution is used for FSE compression.

Here is its definition. It uses an accuracy of 5 bits (32 states), and supports a maximum N of 28, allowing offset values up to 536,870,908 .

If any sequence in the compressed block requires an offset larger than this, it's not possible to use the default distribution to represent it.

short offsetCodes_defaultDistribution[53] =
        { 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1,-1,-1,-1,-1,-1 };

Distribution tables

Following the header, up to 3 distribution tables can be described. They are, in order :

• Literal lengthes
• Offsets
• Match Lengthes

The content to decode depends on their respective compression mode :

• Repeat mode : no content. Re-use distribution from previous compressed block.
• Predef : no content. Use pre-defined distribution table.
• RLE : 1 byte. This is the only code to use across the whole compressed block.
• FSE : A distribution table is present.

FSE distribution table : condensed format

An FSE distribution table describes the probabilities of all symbols from 0 to the last present one (included) on a normalized scale of 1 << AccuracyLog .

It's a bitstream which is read forward, in little-endian fashion. It's not necessary to know its exact size, since it will be discovered and reported by the decoding process.

The bitstream starts by reporting on which scale it operates. AccuracyLog = low4bits + 5; Note that maximum AccuracyLog for literal and match lengthes is 9, and for offsets it is 8. Higher values are considered errors.

Then follow each symbol value, from 0 to last present one. The nb of bits used by each field is variable. It depends on :

• Remaining probabilities + 1 : example : Presuming an AccuracyLog of 8, and presuming 100 probabilities points have already been distributed, the decoder may read any value from 0 to 255 - 100 + 1 == 156 (included). Therefore, it must read log2sup(156) == 8 bits.

• Value decoded : small values use 1 less bit : example : Presuming values from 0 to 156 (included) are possible, 255-156 = 99 values are remaining in an 8-bits field. They are used this way : first 99 values (hence from 0 to 98) use only 7 bits, values from 99 to 156 use 8 bits. This is achieved through this scheme :

  Value read	Value decoded	nb Bits used
  0 - 98	0 - 98	7
  99 - 127	99 - 127	8
  128 - 226	0 - 98	7
  227 - 255	128 - 156	8

Symbols probabilities are read one by one, in order.

Probability is obtained from Value decoded by following formulae : Proba = value - 1;

It means value 0 becomes negative probability -1. -1 is a special probability, which means less than 1. Its effect on distribution table is described in next paragraph. For the purpose of calculating cumulated distribution, it counts as one.

When a symbol has a probability of zero, it is followed by a 2-bits repeat flag. This repeat flag tells how many probabilities of zeroes follow the current one. It provides a number ranging from 0 to 3. If it is a 3, another 2-bits repeat flag follows, and so on.

When last symbol reaches cumulated total of 1 << AccuracyLog, decoding is complete. Then the decoder can tell how many bytes were used in this process, and how many symbols are present.

The bitstream consumes a round number of bytes. Any remaining bit within the last byte is just unused.

If the last symbol makes cumulated total go above 1 << AccuracyLog, distribution is considered corrupted.

FSE decoding : from normalized distribution to decoding tables

The distribution of normalized probabilities is enough to create a unique decoding table.

It follows the following build rule :

The table has a size of tableSize = 1 << AccuracyLog;. Each cell describes the symbol decoded, and instructions to get the next state.

Symbols are scanned in their natural order for less than 1 probabilities. Symbols with this probability are being attributed a single cell, starting from the end of the table. These symbols define a full state reset, reading AccuracyLog bits.

All remaining symbols are sorted in their natural order. Starting from symbol 0 and table position 0, each symbol gets attributed as many cells as its probability. Cell allocation is spreaded, not linear : each successor position follow this rule :

position += (tableSize>>1) + (tableSize>>3) + 3;
position &= tableSize-1;

A position is skipped if already occupied, typically by a "less than 1" probability symbol.

The result is a list of state values. Each state will decode the current symbol.

To get the Number of bits and baseline required for next state, it's first necessary to sort all states in their natural order. The lower states will need 1 more bit than higher ones.

Example : Presuming a symbol has a probability of 5. It receives 5 state values. States are sorted in natural order.

Next power of 2 is 8. Space of probabilities is divided into 8 equal parts. Presuming the AccuracyLog is 7, it defines 128 states. Divided by 8, each share is 16 large.

In order to reach 8, 8-5=3 lowest states will count "double", taking shares twice larger, requiring one more bit in the process.

Numbering starts from higher states using less bits.

state order	0	1	2	3	4
width	32	32	32	16	16
nb Bits	5	5	5	4	4
range nb	2	4	6	0	1
baseline	32	64	96	0	16
range	32-63	64-95	96-127	0-15	16-31

Next state is determined from current state by reading the required number of bits, and adding the specified baseline.

Bitstream

All sequences are stored in a single bitstream, read backward. It is therefore necessary to know the bitstream size, which is deducted from compressed block size.

The last useful bit of the stream is followed by an end-bit-flag. Highest bit of last byte is this flag. It does not belong to the useful part of the bitstream. Therefore, last byte has 0-7 useful bits. Note that it also means that last byte cannot be 0.

Starting states

The bitstream starts with initial state values, each using the required number of bits in their respective accuracy, decoded previously from their normalized distribution.

It starts by Literal Length State, followed by Offset State, and finally Match Length State.

Reminder : always keep in mind that all values are read backward.

Decoding a sequence

A state gives a code. A code provides a baseline and number of bits to add. See Symbol Decoding section for details on each symbol.

Decoding starts by reading the nb of bits required to decode offset. It then does the same for match length, and then for literal length.

Offset / matchLength / litLength define a sequence. It starts by inserting the number of literals defined by litLength, then continue by copying matchLength bytes from currentPos - offset.

The next operation is to update states. Using rules pre-calculated in the decoding tables, Literal Length State is updated, followed by Match Length State, and then Offset State.

This operation will be repeated NbSeqs times. At the end, the bitstream shall be entirely consumed, otherwise bitstream is considered corrupted.

Repeat offsets

As seen in Offset Codes, the first 3 values define a repeated offset. They are sorted in recency order, with 1 meaning "most recent one".

There is an exception though, when current sequence's literal length is 0. In which case, 1 would just make previous match longer. Therefore, in such case, 1 means in fact 2, and 2 is impossible. Meaning of 3 is unmodified.

Repeat offsets start with the following values : 1, 4 and 8 (in order).

Then each block receives its start value from previous compressed block. Note that non-compressed blocks are skipped, they do not contribute to offset history.

Offset updates rules

When the new offset is a normal one, offset history is simply translated by one position, with the new offset taking first spot.

• When repeat offset 1 (most recent) is used, history is unmodified.
• When repeat offset 2 is used, it's swapped with offset 1.
• When repeat offset 3 is used, it takes first spot, pushing the other ones by one position.

Dictionary format

zstd is compatible with "pure content" dictionaries, free of any format restriction. But dictionaries created by zstd --train follow a format, described here.

Pre-requisites : a dictionary has a known length, defined either by a buffer limit, or a file size.

Header	DictID	Stats	Content

Header : 4 bytes ID, value 0xEC30A437, Little Endian format

Dict_ID : 4 bytes, stored in Little Endian format. DictID can be any value, except 0 (which means no DictID). It's used by decoders to check if they use the correct dictionary. Reserved ranges : If the frame is going to be distributed in a private environment, any dictionary ID can be used. However, for public distribution of compressed frames, some ranges are reserved for future use :

          - low range : 1 - 32767 : reserved
          - high range : >= (2^31) : reserved

Stats : Entropy tables, following the same format as a compressed blocks. They are stored in following order : Huffman tables for literals, FSE table for offset, FSE table for matchLenth, and FSE table for litLength. It's finally followed by 3 offset values, populating recent offsets, stored in order, 4-bytes little endian each, for a total of 12 bytes.

Content : Where the actual dictionary content is. Content size depends on Dictionary size.

Version changes

• 0.2.0 : numerous format adjustments for zstd v0.8
• 0.1.2 : limit huffman tree depth to 11 bits
• 0.1.1 : reserved dictID ranges
• 0.1.0 : initial release