Zstandard Compression Format

Notices

Copyright (c) 2016-present Yann Collet, Facebook, Inc.

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

0.3.1 (25/10/18)

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 text of the specification assumes a basic background in programming at the level of bits and other primitive data representations.

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.

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.

This specification is intended for use by implementers of software to compress data into Zstandard format and/or decompress data from Zstandard format. The Zstandard format is supported by an open source reference implementation, written in portable C, and available at : https://github.com/facebook/zstd .

Overall conventions

In this document:

  • square brackets i.e. [ and ] are used to indicate optional fields or parameters.
  • the naming convention for identifiers is Mixed_Case_With_Underscores

Definitions

Content compressed by Zstandard is transformed into a Zstandard frame. Multiple frames can be appended into a single file or stream. A frame is completely 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 contains arbitrary content, which is described by its header, 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.

Overview

Frames

Zstandard compressed data is made of one or more frames. Each frame is independent and can be decompressed independently of other frames. The decompressed content of multiple concatenated frames is the concatenation of each frame decompressed content.

There are two frame formats defined by Zstandard: Zstandard frames and Skippable frames. Zstandard frames contain compressed data, while skippable frames contain custom user metadata.

Zstandard frames

The structure of a single Zstandard frame is following:

Magic_NumberFrame_HeaderData_Block[More data blocks][Content_Checksum]
4 bytes2-14 bytesn bytes0-4 bytes

Magic_Number

4 Bytes, little-endian format. Value : 0xFD2FB528 Note: This value was selected to be less probable to find at the beginning of some random file. It avoids trivial patterns (0x00, 0xFF, repeated bytes, increasing bytes, etc.), contains byte values outside of ASCII range, and doesn't map into UTF8 space. It reduces the chances that a text file represent this value by accident.

Frame_Header

2 to 14 Bytes, detailed in Frame_Header.

Data_Block

Detailed in Blocks. That’s where compressed data is stored.

Content_Checksum

An optional 32-bit checksum, only present if Content_Checksum_flag is set. The content checksum is the result of xxh64() hash function digesting the original (decoded) data as input, and a seed of zero. The low 4 bytes of the checksum are stored in little-endian format.

Frame_Header

The Frame_Header has a variable size, with a minimum of 2 bytes, and up to 14 bytes depending on optional parameters. The structure of Frame_Header is following:

Frame_Header_Descriptor[Window_Descriptor][Dictionary_ID][Frame_Content_Size]
1 byte0-1 byte0-4 bytes0-8 bytes

Frame_Header_Descriptor

The first header's byte is called the Frame_Header_Descriptor. It describes which other fields are present. Decoding this byte is enough to tell the size of Frame_Header.

Bit numberField name
7-6Frame_Content_Size_flag
5Single_Segment_flag
4Unused_bit
3Reserved_bit
2Content_Checksum_flag
1-0Dictionary_ID_flag

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

Frame_Content_Size_flag

This is a 2-bits flag (= Frame_Header_Descriptor >> 6), specifying if Frame_Content_Size (the decompressed data size) is provided within the header. Flag_Value provides FCS_Field_Size, which is the number of bytes used by Frame_Content_Size according to the following table:

Flag_Value0123
FCS_Field_Size0 or 1248

When Flag_Value is 0, FCS_Field_Size depends on Single_Segment_flag : if Single_Segment_flag is set, FCS_Field_Size is 1. Otherwise, FCS_Field_Size is 0 : Frame_Content_Size is not provided.

Single_Segment_flag

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

In this case, Window_Descriptor byte is skipped, but Frame_Content_Size is necessarily present. As a consequence, the decoder must allocate a memory segment of size equal or larger than Frame_Content_Size.

In order to preserve the decoder from unreasonable memory requirements, a decoder is allowed to 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 only a recommendation, each decoder is free to support higher or lower limits, depending on local limitations.

Unused_bit

A decoder compliant with this specification version shall not interpret this bit. It might be used in any future version, to signal a property which is transparent to properly decode the frame. An encoder compliant with this specification version must set this bit to zero.

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 to decode the frame correctly.

Content_Checksum_flag

If this flag is set, a 32-bits Content_Checksum will be present at frame's end. See Content_Checksum paragraph.

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 as DID_Field_Size.

Flag_Value0123
DID_Field_Size0124

Window_Descriptor

Provides guarantees on minimum memory buffer required to decompress a frame. This information is important for decoders to allocate enough memory.

The Window_Descriptor byte is optional. When Single_Segment_flag is set, Window_Descriptor is not present. In this case, Window_Size is Frame_Content_Size, which can be any value from 0 to 2^64-1 bytes (16 ExaBytes).

Bit numbers7-32-0
Field nameExponentMantissa

The minimum memory buffer size is called Window_Size. It is described by the following formulas :

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

The minimum Window_Size is 1 KB. The maximum Window_Size is (1<<41) + 7*(1<<38) bytes, which is 3.75 TB.

In general, larger Window_Size tend to improve compression ratio, but at the cost of memory usage.

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

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

For improved interoperability, it‘s recommended for decoders to support Window_Size of up to 8 MB, and it’s recommended for encoders to not generate frame requiring Window_Size larger 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. Dictionary_ID field is optional. When it‘s not present, it’s up to the decoder to know which dictionary to use.

Dictionary_ID field size is provided by DID_Field_Size. DID_Field_Size is directly derived from value of 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. Format is little-endian.

It's allowed to represent a small ID (for example 13) with a large 4-bytes dictionary ID, even if it is less efficient.

Reserved ranges : Within private environments, any Dictionary_ID can be used.

However, for frames and dictionaries distributed in public space, Dictionary_ID must be attributed carefully. Rules for public environment are not yet decided, but the following ranges are reserved for some future registrar :

  • low range : <= 32767
  • high range : >= (1 << 31)

Outside of these ranges, any value of Dictionary_ID which is both >= 32768 and < (1<<31) can be used freely, even in public environment.

Frame_Content_Size

This is the original (uncompressed) size. This information is optional. Frame_Content_Size uses a variable number of bytes, provided by FCS_Field_Size. FCS_Field_Size is provided by the value of Frame_Content_Size_flag. FCS_Field_Size can be equal to 0 (not present), 1, 2, 4 or 8 bytes.

FCS_Field_SizeRange
0unknown
10 - 255
2256 - 65791
40 - 2^32-1
80 - 2^64-1

Frame_Content_Size format is little-endian. When FCS_Field_Size is 1, 4 or 8 bytes, the value is read directly. When FCS_Field_Size is 2, the offset of 256 is added. It's allowed to represent a small size (for example 18) using any compatible variant.

Blocks

After Magic_Number and Frame_Header, there are some number of blocks. Each frame must have at least one block, but there is no upper limit on the number of blocks per frame.

The structure of a block is as follows:

Block_HeaderBlock_Content
3 bytesn bytes

Block_Header uses 3 bytes, written using little-endian convention. It contains 3 fields :

Last_BlockBlock_TypeBlock_Size
bit 0bits 1-2bits 3-23

Last_Block

The lowest bit signals if this block is the last one. The frame will end after this last block. It may be followed by an optional Content_Checksum (see Zstandard Frames).

Block_Type

The next 2 bits represent the Block_Type. There are 4 block types :

Value0123
Block_TypeRaw_BlockRLE_BlockCompressed_BlockReserved

  • Raw_Block - this is an uncompressed block. Block_Content contains Block_Size bytes.

  • RLE_Block - this is a single byte, repeated Block_Size times. Block_Content consists of a single byte. On the decompression side, this byte must be repeated Block_Size times.

  • Compressed_Block - this is a Zstandard compressed block, explained later on. Block_Size is the length of Block_Content, the compressed data. The decompressed size is not known, but its maximum possible value is guaranteed (see below)

  • Reserved - this is not a block. This value cannot be used with current version of this specification. If such a value is present, it is considered corrupted data.

Block_Size

The upper 21 bits of Block_Header represent the Block_Size. Block_Size is the size of the block excluding the header. A block can contain any number of bytes (even zero), up to Block_Maximum_Decompressed_Size, which is the smallest of:

  • Window_Size
  • 128 KB

A Compressed_Block has the extra restriction that Block_Size is always strictly less than the decompressed size. If this condition cannot be respected, the block must be sent uncompressed instead (Raw_Block).

Compressed Blocks

To decompress a compressed block, the compressed size must be provided from Block_Size field within Block_Header.

A compressed block consists of 2 sections :

The results of the two sections are then combined to produce the decompressed data in Sequence Execution

Prerequisites

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

  • Previous decoded data, up to a distance of Window_Size, or beginning of the Frame, whichever is smaller.
  • List of “recent offsets” from previous Compressed_Block.
  • The previous Huffman tree, required by Treeless_Literals_Block type
  • Previous FSE decoding tables, required by Repeat_Mode for each symbol type (literals lengths, match lengths, offsets)

Note that decoding tables aren't always from the previous Compressed_Block.

  • Every decoding table can come from a dictionary.
  • The Huffman tree comes from the previous Compressed_Literals_Block.

Literals Section

All literals are regrouped in the first part of the block. They can be decoded first, and then copied during [Sequence Execution], or they can be decoded on the flow during [Sequence Execution].

Literals can be stored uncompressed or compressed using Huffman prefix codes. When compressed, an optional tree description can be present, followed by 1 or 4 streams.

Literals_Section_Header[Huffman_Tree_Description][jumpTable]Stream1[Stream2][Stream3][Stream4]

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.

Literals_Block_TypeSize_FormatRegenerated_Size[Compressed_Size]
2 bits1 - 2 bits5 - 20 bits0 - 18 bits

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

Literals_Block_Type

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

Literals_Block_TypeValue
Raw_Literals_Block0
RLE_Literals_Block1
Compressed_Literals_Block2
Treeless_Literals_Block3
  • Raw_Literals_Block - Literals are stored uncompressed.
  • RLE_Literals_Block - Literals consist of a single byte value repeated Regenerated_Size times.
  • Compressed_Literals_Block - This is a standard Huffman-compressed block, starting with a Huffman tree description. See details below.
  • Treeless_Literals_Block - This is a Huffman-compressed block, using Huffman tree from previous Huffman-compressed literals block. Huffman_Tree_Description will be skipped. Note: If this mode is triggered without any previous Huffman-table in the frame (or dictionary), this should be treated as data corruption.

Size_Format

Size_Format is divided into 2 families :

  • For Raw_Literals_Block and RLE_Literals_Block, it's only necessary to decode Regenerated_Size. There is no Compressed_Size field.
  • For Compressed_Block and Treeless_Literals_Block, it‘s required to decode both Compressed_Size and Regenerated_Size (the decompressed size). It’s also necessary to decode the number of streams (1 or 4).

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

Size_Format for Raw_Literals_Block and RLE_Literals_Block :

Size_Format uses 1 or 2 bits. Its value is : Size_Format = (Literals_Section_Header[0]>>2) & 3

  • Size_Format == 00 or 10 : Size_Format uses 1 bit. Regenerated_Size uses 5 bits (0-31). Literals_Section_Header uses 1 byte. Regenerated_Size = Literals_Section_Header[0]>>3
  • Size_Format == 01 : Size_Format uses 2 bits. Regenerated_Size uses 12 bits (0-4095). Literals_Section_Header uses 2 bytes. Regenerated_Size = (Literals_Section_Header[0]>>4) + (Literals_Section_Header[1]<<4)
  • Size_Format == 11 : Size_Format uses 2 bits. Regenerated_Size uses 20 bits (0-1048575). Literals_Section_Header uses 3 bytes. Regenerated_Size = (Literals_Section_Header[0]>>4) + (Literals_Section_Header[1]<<4) + (Literals_Section_Header[2]<<12)

Only Stream1 is present for these cases. Note : it‘s allowed to represent a short value (for example 13) using a long format, even if it’s less efficient.

Size_Format for Compressed_Literals_Block and Treeless_Literals_Block :

Size_Format always uses 2 bits.

  • Size_Format == 00 : A single stream. Both Regenerated_Size and Compressed_Size use 10 bits (0-1023). Literals_Section_Header uses 3 bytes.
  • Size_Format == 01 : 4 streams. Both Regenerated_Size and Compressed_Size use 10 bits (0-1023). Literals_Section_Header uses 3 bytes.
  • Size_Format == 10 : 4 streams. Both Regenerated_Size and Compressed_Size use 14 bits (0-16383). Literals_Section_Header uses 4 bytes.
  • Size_Format == 11 : 4 streams. Both Regenerated_Size and Compressed_Size use 18 bits (0-262143). Literals_Section_Header uses 5 bytes.

Both Compressed_Size and Regenerated_Size fields follow little-endian convention. Note: Compressed_Size includes the size of the Huffman Tree description when it is present.

Raw Literals Block

The data in Stream1 is Regenerated_Size bytes long, it contains the raw literals data to be used during [Sequence Execution].

RLE Literals Block

Stream1 consists of a single byte which should be repeated Regenerated_Size times to generate the decoded literals.

Compressed Literals Block and Treeless Literals Block

Both of these modes contain Huffman encoded data.

For Treeless_Literals_Block, the Huffman table comes from previously compressed literals block, or from a dictionary.

Huffman_Tree_Description

This section is only present when Literals_Block_Type type is Compressed_Literals_Block (2). The format of the Huffman tree description can be found at Huffman Tree description. The size of Huffman_Tree_Description is determined during decoding process, it must be used to determine where streams begin. Total_Streams_Size = Compressed_Size - Huffman_Tree_Description_Size.

Jump Table

The Jump Table is only present when there are 4 Huffman-coded streams.

Reminder : Huffman compressed data consists of either 1 or 4 Huffman-coded streams.

If only one stream is present, it is a single bitstream occupying the entire remaining portion of the literals block, encoded as described within Huffman-Coded Streams.

If there are four streams, Literals_Section_Header only provided enough information to know the decompressed and compressed sizes of all four streams combined. The decompressed size of each stream is equal to (Regenerated_Size+3)/4, except for the last stream which may be up to 3 bytes smaller, to reach a total decompressed size as specified in Regenerated_Size.

The compressed size of each stream is provided explicitly in the Jump Table. Jump Table is 6 bytes long, and consist of three 2-byte little-endian fields, describing the compressed sizes of the first three streams. Stream4_Size is computed from total Total_Streams_Size minus sizes of other streams.

Stream4_Size = Total_Streams_Size - 6 - Stream1_Size - Stream2_Size - Stream3_Size.

Note: if Stream1_Size + Stream2_Size + Stream3_Size > Total_Streams_Size, data is considered corrupted.

Each of these 4 bitstreams is then decoded independently as a Huffman-Coded stream, as described at Huffman-Coded Streams

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 Literals Section. A match copy command specifies an offset and a length.

When all sequences are decoded, if there are literals left in the literals section, these bytes are added at the end of the block.

This is described in more detail in Sequence Execution.

The Sequences_Section regroup all symbols required to decode commands. There are 3 symbol types : literals lengths, offsets and match lengths. They are encoded together, interleaved, in a single bitstream.

The Sequences_Section starts by a header, followed by optional probability tables for each symbol type, followed by the bitstream.

Sequences_Section_Header[Literals_Length_Table][Offset_Table][Match_Length_Table]bitStream

To decode the Sequences_Section, it's required to know its size. Its size is deduced from the size of Literals_Section: Sequences_Section_Size = Block_Size - Literals_Section_Size.

Sequences_Section_Header

Consists of 2 items:

  • Number_of_Sequences
  • Symbol compression modes

Number_of_Sequences

This is a variable size field 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. Decompressed content is defined entirely as Literals Section content. The FSE tables used in Repeat_Mode aren't updated.
  • if (byte0 < 128) : Number_of_Sequences = byte0 . Uses 1 byte.
  • if (byte0 < 255) : Number_of_Sequences = ((byte0-128) << 8) + byte1 . Uses 2 bytes.
  • if (byte0 == 255): Number_of_Sequences = byte1 + (byte2<<8) + 0x7F00 . Uses 3 bytes.

Symbol compression modes

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

Bit number7-65-43-21-0
Field nameLiterals_Lengths_ModeOffsets_ModeMatch_Lengths_ModeReserved

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

Literals_Lengths_Mode, Offsets_Mode and Match_Lengths_Mode define the Compression_Mode of literals lengths, offsets, and match lengths symbols respectively.

They follow the same enumeration :

Value0123
Compression_ModePredefined_ModeRLE_ModeFSE_Compressed_ModeRepeat_Mode
  • Predefined_Mode : A predefined FSE distribution table is used, defined in default distributions. No distribution table will be present.
  • RLE_Mode : The table description consists of a single byte, which contains the symbol's value. This symbol will be used for all sequences.
  • FSE_Compressed_Mode : standard FSE compression. A distribution table will be present. The format of this distribution table is described in FSE Table Description. Note that the maximum allowed accuracy log for literals length and match length tables is 9, and the maximum accuracy log for the offsets table is 8. FSE_Compressed_Mode must not be used when only one symbol is present, RLE_Mode should be used instead (although any other mode will work).
  • Repeat_Mode : The table used in the previous Compressed_Block with Number_of_Sequences > 0 will be used again, or if this is the first block, table in the dictionary will be used. Note that this includes RLE_mode, so if Repeat_Mode follows RLE_Mode, the same symbol will be repeated. It also includes Predefined_Mode, in which case Repeat_Mode will have same outcome as Predefined_Mode. No distribution table will be present. If this mode is used without any previous sequence table in the frame (nor dictionary) to repeat, this should be treated as corruption.

The codes for literals lengths, match lengths, and offsets.

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

Literals length codes

Literals length codes are values ranging from 0 to 35 included. They define lengths from 0 to 131071 bytes. The literals length is equal to the decoded Baseline plus the result of reading Number_of_Bits bits from the bitstream, as a little-endian value.

Literals_Length_Code0-15
lengthLiterals_Length_Code
Number_of_Bits0
Literals_Length_Code1617181920212223
Baseline1618202224283240
Number_of_Bits11112233
Literals_Length_Code2425262728293031
Baseline4864128256512102420484096
Number_of_Bits46789101112
Literals_Length_Code32333435
Baseline8192163843276865536
Number_of_Bits13141516
Match length codes

Match length codes are values ranging from 0 to 52 included. They define lengths from 3 to 131074 bytes. The match length is equal to the decoded Baseline plus the result of reading Number_of_Bits bits from the bitstream, as a little-endian value.

Match_Length_Code0-31
valueMatch_Length_Code + 3
Number_of_Bits0
Match_Length_Code3233343536373839
Baseline3537394143475159
Number_of_Bits11112233
Match_Length_Code4041424344454647
Baseline67839913125951510272051
Number_of_Bits4457891011
Match_Length_Code4849505152
Baseline40998195163873277165539
Number_of_Bits1213141516
Offset codes

Offset codes are values ranging from 0 to N.

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 31.

An offset code is also the number of additional bits to read in little-endian fashion, and can be translated into an Offset_Value using the following formulas :

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

It means that maximum Offset_Value is (2^(N+1))-1 supporting back-reference distances up to (2^(N+1))-4, but is limited by maximum back-reference distance.

Offset_Value from 1 to 3 are special : they define “repeat codes”. This is described in more detail in Repeat Offsets.

Decoding Sequences

FSE bitstreams are read in reverse direction than written. In zstd, the compressor writes bits forward into a block and the decompressor must read the bitstream backwards.

To find the start of the bitstream it is therefore necessary to know the offset of the last byte of the block which can be found by counting Block_Size bytes after the block header.

After writing the last bit containing information, the compressor writes a single 1-bit and then fills the byte with 0-7 0 bits of padding. The last byte of the compressed bitstream cannot be 0 for that reason.

When decompressing, the last byte containing the padding is the first byte to read. The decompressor needs to skip 0-7 initial 0-bits and the first 1-bit it occurs. Afterwards, the useful part of the bitstream begins.

FSE decoding requires a ‘state’ to be carried from symbol to symbol. For more explanation on FSE decoding, see the FSE section.

For sequence decoding, a separate state keeps track of each literal lengths, offsets, and match lengths symbols. Some FSE primitives are also used. For more details on the operation of these primitives, see the FSE section.

Starting states

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

It starts by Literals_Length_State, followed by Offset_State, and finally Match_Length_State.

Reminder : always keep in mind that all values are read backward, so the ‘start’ of the bitstream is at the highest position in memory, immediately before the last 1-bit for padding.

After decoding the starting states, a single sequence is decoded Number_Of_Sequences times. These sequences are decoded in order from first to last. Since the compressor writes the bitstream in the forward direction, this means the compressor must encode the sequences starting with the last one and ending with the first.

Decoding a sequence

For each of the symbol types, the FSE state can be used to determine the appropriate code. The code then defines the Baseline and Number_of_Bits to read for each type. See the description of the codes for how to determine these values.

Decoding starts by reading the Number_of_Bits required to decode Offset. It then does the same for Match_Length, and then for Literals_Length. This sequence is then used for sequence execution.

If it is not the last sequence in the block, the next operation is to update states. Using the rules pre-calculated in the decoding tables, Literals_Length_State is updated, followed by Match_Length_State, and then Offset_State. See the FSE section for details on how to update states from the bitstream.

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

Default Distributions

If Predefined_Mode is selected for a symbol type, its FSE decoding table is generated from a predefined distribution table defined here. For details on how to convert this distribution into a decoding table, see the FSE section.

Literals Length

The decoding table uses an accuracy log of 6 bits (64 states).

short literalsLength_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 Length

The decoding table uses an accuracy log 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

The decoding table uses an accuracy log of 5 bits (32 states), and supports a maximum N value of 28, allowing offset values up to 536,870,908 .

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

short offsetCodes_defaultDistribution[29] =
        { 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 };

Sequence Execution

Once literals and sequences have been decoded, they are combined to produce the decoded content of a block.

Each sequence consists of a tuple of (literals_length, offset_value, match_length), decoded as described in the Sequences Section. To execute a sequence, first copy literals_length bytes from the decoded literals to the output.

Then match_length bytes are copied from previous decoded data. The offset to copy from is determined by offset_value: if offset_value > 3, then the offset is offset_value - 3. If offset_value is from 1-3, the offset is a special repeat offset value. See the repeat offset section for how the offset is determined in this case.

The offset is defined as from the current position, so an offset of 6 and a match length of 3 means that 3 bytes should be copied from 6 bytes back. Note that all offsets leading to previously decoded data must be smaller than Window_Size defined in Frame_Header_Descriptor.

Repeat offsets

As seen in Sequence Execution, the first 3 values define a repeated offset and we will call them Repeated_Offset1, Repeated_Offset2, and Repeated_Offset3. They are sorted in recency order, with Repeated_Offset1 meaning “most recent one”.

If offset_value == 1, then the offset used is Repeated_Offset1, etc.

There is an exception though, when current sequence's literals_length = 0. In this case, repeated offsets are shifted by one, so an offset_value of 1 means Repeated_Offset2, an offset_value of 2 means Repeated_Offset3, and an offset_value of 3 means Repeated_Offset1 - 1_byte.

For the first block, the starting offset history is populated with following values : Repeated_Offset1=1, Repeated_Offset2=4, Repeated_Offset3=8, unless a dictionary is used, in which case they come from the dictionary.

Then each block gets its starting offset history from the ending values of the most recent Compressed_Block. Note that blocks which are not Compressed_Block are skipped, they do not contribute to offset history.

Offset updates rules

The newest offset takes the lead in offset history, shifting others back by one rank, up to the previous rank of the new offset if it was present in history.

Examples :

In the common case, when new offset is not part of history : Repeated_Offset3 = Repeated_Offset2 Repeated_Offset2 = Repeated_Offset1 Repeated_Offset1 = NewOffset

When the new offset is part of history, there may be specific adjustments.

When NewOffset == Repeated_Offset1, offset history remains actually unmodified.

When NewOffset == Repeated_Offset2, Repeated_Offset1 and Repeated_Offset2 ranks are swapped. Repeated_Offset3 is unmodified.

When NewOffset == Repeated_Offset3, there is actually no difference with the common case : all offsets are shifted by one rank, NewOffset (== Repeated_Offset3) becomes the new Repeated_Offset1.

Also worth mentioning, the specific corner case when offset_value == 3, and the literal length of the current sequence is zero. In which case , NewOffset = Repeated_Offset1 - 1_byte. Here also, from an offset history update perspective, it's just a common case : Repeated_Offset3 = Repeated_Offset2 Repeated_Offset2 = Repeated_Offset1 Repeated_Offset1 = NewOffset ( == Repeated_Offset1 - 1_byte )

Skippable Frames

Magic_NumberFrame_SizeUser_Data
4 bytes4 bytesn bytes

Skippable frames allow the insertion of user-defined metadata into a flow of concatenated frames.

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

From a compliant decoder perspective, skippable frames need just be skipped, and their content ignored, resuming decoding after the skippable frame.

It can be noted that a skippable frame can be used to watermark a stream of concatenated frames embedding any kind of tracking information (even just an UUID). Users wary of such possibility should scan the stream of concatenated frames in an attempt to detect such frame for analysis or removal.

Magic_Number

4 Bytes, little-endian format. Value : 0x184D2A5?, which means any value from 0x184D2A50 to 0x184D2A5F. All 16 values are valid to identify a skippable frame. This specification doesn't detail any specific tagging for skippable frames.

Frame_Size

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

User_Data

The User_Data can be anything. Data will just be skipped by the decoder.

Entropy Encoding

Two types of entropy encoding are used by the Zstandard format: FSE, and Huffman coding. Huffman is used to compress literals, while FSE is used for all other symbols (Literals_Length_Code, Match_Length_Code, offset codes) and to compress Huffman headers.

FSE

FSE, short for Finite State Entropy, is an entropy codec based on ANS. FSE encoding/decoding involves a state that is carried over between symbols, so decoding must be done in the opposite direction as encoding. Therefore, all FSE bitstreams are read from end to beginning. Note that the order of the bits in the stream is not reversed, we just read the elements in the reverse order they are written.

For additional details on FSE, see Finite State Entropy.

FSE decoding involves a decoding table which has a power of 2 size, and contain three elements: Symbol, Num_Bits, and Baseline. The log2 of the table size is its Accuracy_Log. An FSE state value represents an index in this table.

To obtain the initial state value, consume Accuracy_Log bits from the stream as a little-endian value. The next symbol in the stream is the Symbol indicated in the table for that state. To obtain the next state value, the decoder should consume Num_Bits bits from the stream as a little-endian value and add it to Baseline.

FSE Table Description

To decode FSE streams, it is necessary to construct the decoding table. The Zstandard format encodes FSE table descriptions as follows:

An FSE distribution table describes the probabilities of all symbols from 0 to the last present one (included) on a normalized scale of 1 << Accuracy_Log . Note that there must be two or more symbols with nonzero probability.

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

The bitstream starts by reporting on which scale it operates. Let's low4Bits designate the lowest 4 bits of the first byte : Accuracy_Log = low4bits + 5.

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

  • Remaining probabilities + 1 : example : Presuming an Accuracy_Log of 8, and presuming 100 probabilities points have already been distributed, the decoder may read any value from 0 to 256 - 100 + 1 == 157 (inclusive). Therefore, it must read log2sup(157) == 8 bits.

  • Value decoded : small values use 1 less bit : example : Presuming values from 0 to 157 (inclusive) are possible, 255-157 = 98 values are remaining in an 8-bits field. They are used this way : first 98 values (hence from 0 to 97) use only 7 bits, values from 98 to 157 use 8 bits. This is achieved through this scheme :

    Value readValue decodedNumber of bits used
    0 - 970 - 977
    98 - 12798 - 1278
    128 - 2250 - 977
    226 - 255128 - 1578

Symbols probabilities are read one by one, in order.

Probability is obtained from Value decoded by following formula : 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 the next section. For the purpose of calculating total allocated probability points, 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 << Accuracy_Log, decoding is complete. If the last symbol makes cumulated total go above 1 << Accuracy_Log, distribution is considered corrupted.

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.

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 Table_Size = 1 << Accuracy_Log. 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 and retreating. These symbols define a full state reset, reading Accuracy_Log bits.

All remaining symbols are allocated in their natural order. Starting from symbol 0 and table position 0, each symbol gets allocated 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 by a “less than 1” probability symbol. position does not reset between symbols, it simply iterates through each position in the table, switching to the next symbol when enough states have been allocated to the current one.

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. The process is repeated for each symbol.

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 Accuracy_Log 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”, doubling the number of shares (32 in width), requiring one more bit in the process.

Baseline is assigned starting from the higher states using fewer bits, and proceeding naturally, then resuming at the first state, each takes its allocated width from Baseline.

state order01234
width3232321616
Number_of_Bits55544
range number24601
Baseline326496016
range32-6364-9596-1270-1516-31

The next state is determined from current state by reading the required Number_of_Bits, and adding the specified Baseline.

See Appendix A for the results of this process applied to the default distributions.

Huffman Coding

Zstandard Huffman-coded streams are read backwards, similar to the FSE bitstreams. Therefore, to find the start of the bitstream, it is therefore to know the offset of the last byte of the Huffman-coded stream.

After writing the last bit containing information, the compressor writes a single 1-bit and then fills the byte with 0-7 0 bits of padding. The last byte of the compressed bitstream cannot be 0 for that reason.

When decompressing, the last byte containing the padding is the first byte to read. The decompressor needs to skip 0-7 initial 0-bits and the first 1-bit it occurs. Afterwards, the useful part of the bitstream begins.

The bitstream contains Huffman-coded symbols in little-endian order, with the codes defined by the method below.

Huffman Tree Description

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 with values from 0 to Max_Number_of_Bits. Transformation from Weight to Number_of_Bits follows this formula :

Number_of_Bits = Weight ? (Max_Number_of_Bits + 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 Max_Number_of_Bits, the depth of the current tree. Max_Number_of_Bits must be <= 11, otherwise the representation is considered corrupted.

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

literal value012345
Number_of_Bits123044

The tree depth is 4, since its longest elements uses 4 bits (longest elements are the one with smallest frequency). Value 5 will not be listed, as it can be determined from values for 0-4, nor will values above 5 as they are all 0. Values from 0 to 4 will be listed using Weight instead of Number_of_Bits. Weight formula is :

Weight = Number_of_Bits ? (Max_Number_of_Bits + 1 - Number_of_Bits) : 0

It gives the following series of weights :

literal value01234
Weight43201

The decoder will do the inverse operation : having collected weights of literal symbols from 0 to 4, it knows the last literal, 5, is present with a non-zero Weight. The Weight of 5 can be determined by advancing to the next power of 2. The sum of 2^(Weight-1) (excluding 0's) is : 8 + 4 + 2 + 0 + 1 = 15. Nearest larger power of 2 value is 16. Therefore, Max_Number_of_Bits = 4 and Weight[5] = 16-15 = 1.

Huffman Tree header

This is a single byte value (0-255), which describes how the series of weights is encoded.

  • if headerByte < 128 : the series of weights is compressed using FSE (see below). The length of the FSE-compressed series is equal to headerByte (0-127).

  • if headerByte >= 128 :

    • the series of weights uses a direct representation, where each Weight is encoded directly as a 4 bits field (0-15).
    • They are encoded forward, 2 weights to a byte, first weight taking the top four bits and second one taking the bottom four.
      • e.g. the following operations could be used to read the weights: Weight[0] = (Byte[0] >> 4), Weight[1] = (Byte[0] & 0xf), etc.
    • The full representation occupies Ceiling(Number_of_Weights/2) bytes, meaning it uses only full bytes even if Number_of_Weights is odd.
    • Number_of_Weights = headerByte - 127.
      • Note that maximum Number_of_Weights is 255-127 = 128, therefore, only up to 128 Weight can be encoded using direct representation.
      • Since the last non-zero Weight is not encoded, this scheme is compatible with alphabet sizes of up to 129 symbols, hence including literal symbol 128.
      • If any literal symbol > 128 has a non-zero Weight, direct representation is not possible. In such case, it's necessary to use FSE compression.

Finite State Entropy (FSE) compression of Huffman weights

In this case, the series of Huffman 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 possible decompressed size, which is 255, since literal values span from 0 to 255, and last symbol’s Weight is not represented.

An FSE bitstream starts by a header, describing probabilities distribution. It will create a Decoding Table. For a list of Huffman weights, the maximum accuracy log is 6 bits. For more description see the FSE header description

The Huffman header compression uses 2 states, which share the same FSE distribution table. The first state (State1) encodes the even indexed symbols, and the second (State2) encodes the odd indexed symbols. State1 is initialized first, and then State2, and they take turns decoding a single symbol and updating their state. For more details on these FSE operations, see the FSE section.

The number of symbols to decode is determined by tracking bitStream overflow condition: If updating state after decoding a symbol would require more bits than remain in the stream, it is assumed that extra bits are 0. Then, symbols for each of the final states are decoded and the process is complete.

Conversion from weights to Huffman prefix codes

All present symbols shall now have a Weight value. It is possible to transform weights into Number_of_Bits, using this formula:

Number_of_Bits = (Weight>0) ? Max_Number_of_Bits + 1 - Weight : 0

Symbols are sorted by Weight. Within same Weight, symbols keep natural sequential order. Symbols with a Weight of zero are removed. Then, starting from lowest Weight, prefix codes are distributed in sequential order.

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

Literal012345
Weight432011

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

Literal345210
Weight011234
Number_of_Bits044321
prefix codesN/A00000001001011

Huffman-coded Streams

Given a Huffman decoding table, it's possible to decode a Huffman-coded stream.

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 last one. 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 contains 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. Since the bitstream is encoded in reverse order, starting from the end read symbols in forward order.

For example, if the literal sequence “0145” was encoded using above prefix code, it would be encoded (in reverse order) as:

Symbol5410Padding
Encoding0000000101100001

Resulting in following 2-bytes bitstream :

00010000 00001101

Here is an alternative representation with the symbol codes separated by underscore:

0001_0000 00001_1_01

Reading highest Max_Number_of_Bits bits, it's 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.

Dictionary Format

Zstandard is compatible with “raw content” dictionaries, free of any format restriction, except that they must be at least 8 bytes. These dictionaries function as if they were just the Content part of a formatted dictionary.

But dictionaries created by zstd --train follow a format, described here.

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

Magic_NumberDictionary_IDEntropy_TablesContent

Magic_Number : 4 bytes ID, value 0xEC30A437, little-endian format

Dictionary_ID : 4 bytes, stored in little-endian format. Dictionary_ID can be any value, except 0 (which means no Dictionary_ID). 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, the following ranges are reserved and shall not be used :

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

Entropy_Tables : follow the same format as tables in compressed blocks. See the relevant FSE and Huffman sections for how to decode these tables. They are stored in following order : Huffman tables for literals, FSE table for offsets, FSE table for match lengths, and FSE table for literals lengths. These tables populate the Repeat Stats literals mode and Repeat distribution mode for sequence decoding. It's finally followed by 3 offset values, populating recent offsets (instead of using {1,4,8}), stored in order, 4-bytes little-endian each, for a total of 12 bytes. Each recent offset must have a value < dictionary size.

Content : The rest of the dictionary is its content. The content act as a “past” in front of data to compress or decompress, so it can be referenced in sequence commands. As long as the amount of data decoded from this frame is less than or equal to Window_Size, sequence commands may specify offsets longer than the total length of decoded output so far to reference back to the dictionary, even parts of the dictionary with offsets larger than Window_Size.
After the total output has surpassed Window_Size however, this is no longer allowed and the dictionary is no longer accessible.

If a dictionary is provided by an external source, it should be loaded with great care, its content considered untrusted.

Appendix A - Decoding tables for predefined codes

This appendix contains FSE decoding tables for the predefined literal length, match length, and offset codes. The tables have been constructed using the algorithm as given above in chapter “from normalized distribution to decoding tables”. The tables here can be used as examples to crosscheck that an implementation build its decoding tables correctly.

Literal Length Code:

StateSymbolNumber_Of_BitsBase
0040
10416
21532
3350
4450
5650
6750
7950
81050
91250
101460
111650
121850
131950
142150
152250
162450
1725532
182650
192760
202960
213160
220432
23140
24250
254532
26550
277532
28850
2910532
301150
311360
3216532
331750
3419532
352050
3622532
372350
382540
3925416
4026532
412860
423060
430448
441416
452532
463532
475532
486532
498532
509532
5111532
5212532
531560
5417532
5518532
5620532
5721532
5823532
5924532
603560
613460
623360
633260

Match Length Code:

StateSymbolNumber_Of_BitsBase
0060
1140
22532
3350
4550
5650
6850
71060
81360
91660
101960
112260
122560
132860
143160
153360
163560
173760
183960
194160
204360
214560
221416
23240
243532
25450
266532
27750
28960
291260
301560
311860
322160
332460
342760
353060
363260
373460
383660
393860
404060
414260
424460
431432
441448
452416
464532
475532
487532
498532
501160
511460
521760
532060
542360
552660
562960
575260
585160
595060
604960
614860
624760
634660

Offset Code:

StateSymbolNumber_Of_BitsBase
0050
1640
2950
31550
42150
5350
6740
71250
81850
92350
10550
11840
121450
132050
14250
157416
161150
171750
182250
19450
208416
211350
221950
23150
246416
251050
261650
272850
282750
292650
302550
312450

Appendix B - Resources for implementers

An open source reference implementation is available on : https://github.com/facebook/zstd

The project contains a frame generator, called decodeCorpus, which can be used by any 3rd-party implementation to verify that a tested decoder is compliant with the specification.

decodeCorpus generates random valid frames. A compliant decoder should be able to decode them all, or at least provide a meaningful error code explaining for which reason it cannot (memory limit restrictions for example).

Version changes

  • 0.3.1 : minor clarification regarding offset history update rules
  • 0.3.0 : minor edits to match RFC8478
  • 0.2.9 : clarifications for huffman weights direct representation, by Ulrich Kunitz
  • 0.2.8 : clarifications for IETF RFC discuss
  • 0.2.7 : clarifications from IETF RFC review, by Vijay Gurbani and Nick Terrell
  • 0.2.6 : fixed an error in huffman example, by Ulrich Kunitz
  • 0.2.5 : minor typos and clarifications
  • 0.2.4 : section restructuring, by Sean Purcell
  • 0.2.3 : clarified several details, by Sean Purcell
  • 0.2.2 : added predefined codes, by Johannes Rudolph
  • 0.2.1 : clarify field names, by Przemyslaw Skibinski
  • 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