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diff --git a/src/zstd/doc/zstd_compression_format.md b/src/zstd/doc/zstd_compression_format.md new file mode 100644 index 000000000..fc61726fc --- /dev/null +++ b/src/zstd/doc/zstd_compression_format.md @@ -0,0 +1,1694 @@ +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 + +0.3.5 (13/11/19) + + +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](http://www.zstandard.org). +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](http://www.xxhash.org), +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](#frames) + - [Zstandard frames](#zstandard-frames) + - [Blocks](#blocks) + - [Literals Section](#literals-section) + - [Sequences Section](#sequences-section) + - [Sequence Execution](#sequence-execution) + - [Skippable frames](#skippable-frames) +- [Entropy Encoding](#entropy-encoding) + - [FSE](#fse) + - [Huffman Coding](#huffman-coding) +- [Dictionary Format](#dictionary-format) + +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_Number` | `Frame_Header` |`Data_Block`| [More data blocks] | [`Content_Checksum`] | +|:--------------:|:--------------:|:----------:| ------------------ |:--------------------:| +| 4 bytes | 2-14 bytes | n bytes | | 0-4 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`](#frame_header). + +__`Data_Block`__ + +Detailed in [`Blocks`](#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](http://www.xxhash.org) +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 byte | 0-1 byte | 0-4 bytes | 0-8 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 number | Field name | +| ---------- | ---------- | +| 7-6 | `Frame_Content_Size_flag` | +| 5 | `Single_Segment_flag` | +| 4 | `Unused_bit` | +| 3 | `Reserved_bit` | +| 2 | `Content_Checksum_flag` | +| 1-0 | `Dictionary_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_Value` | 0 | 1 | 2 | 3 | +| -------------- | ------ | --- | --- | --- | +|`FCS_Field_Size`| 0 or 1 | 2 | 4 | 8 | + +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_Value` | 0 | 1 | 2 | 3 | +| -------------- | --- | --- | --- | --- | +|`DID_Field_Size`| 0 | 1 | 2 | 4 | + +#### `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 numbers | 7-3 | 2-0 | +| ----------- | ---------- | ---------- | +| Field name | `Exponent` | `Mantissa` | + +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_Size` | Range | +| ---------------- | ---------- | +| 0 | unknown | +| 1 | 0 - 255 | +| 2 | 256 - 65791| +| 4 | 0 - 2^32-1 | +| 8 | 0 - 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_Header` | `Block_Content` | +|:--------------:|:---------------:| +| 3 bytes | n bytes | + +__`Block_Header`__ + +`Block_Header` uses 3 bytes, written using __little-endian__ convention. +It contains 3 fields : + +| `Last_Block` | `Block_Type` | `Block_Size` | +|:------------:|:------------:|:------------:| +| bit 0 | bits 1-2 | bits 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](#zstandard-frames)). + +__`Block_Type`__ + +The next 2 bits represent the `Block_Type`. +`Block_Type` influences the meaning of `Block_Size`. +There are 4 block types : + +| Value | 0 | 1 | 2 | 3 | +| ------------ | ----------- | ----------- | ------------------ | --------- | +| `Block_Type` | `Raw_Block` | `RLE_Block` | `Compressed_Block` | `Reserved`| + +- `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](#compressed-blocks), + 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`. + +When `Block_Type` is `Compressed_Block` or `Raw_Block`, +`Block_Size` is the size of `Block_Content` (hence excluding `Block_Header`). + +When `Block_Type` is `RLE_Block`, since `Block_Content`’s size is always 1, +`Block_Size` represents the number of times this byte must be repeated. + +`Block_Size` is limited by `Block_Maximum_Size` (see below). + +__`Block_Content`__ and __`Block_Maximum_Size`__ + +The size of `Block_Content` is limited by `Block_Maximum_Size`, +which is the smallest of: +- `Window_Size` +- 128 KB + +`Block_Maximum_Size` is constant for a given frame. +This maximum is applicable to both the decompressed size +and the compressed size of any block in the frame. + +The reasoning for this limit is that a decoder can read this information +at the beginning of a frame and use it to allocate buffers. +The guarantees on the size of blocks ensure that +the buffers will be large enough for any following block of the valid frame. + + +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 : +- [Literals Section](#literals-section) +- [Sequences Section](#sequences-section) + +The results of the two sections are then combined to produce the decompressed +data in [Sequence Execution](#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_Type` | `Size_Format` | `Regenerated_Size` | [`Compressed_Size`] | +| --------------------- | ------------- | ------------------ | ------------------- | +| 2 bits | 1 - 2 bits | 5 - 20 bits | 0 - 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_Type` | Value | +| --------------------------- | ----- | +| `Raw_Literals_Block` | 0 | +| `RLE_Literals_Block` | 1 | +| `Compressed_Literals_Block` | 2 | +| `Treeless_Literals_Block` | 3 | + +- `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](#dictionary-format)), 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](#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](#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](#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](#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 number| 7-6 | 5-4 | 3-2 | 1-0 | +| -------- | ----------------------- | -------------- | -------------------- | ---------- | +|Field name| `Literals_Lengths_Mode` | `Offsets_Mode` | `Match_Lengths_Mode` | `Reserved` | + +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 : + +| Value | 0 | 1 | 2 | 3 | +| ------------------ | ----------------- | ---------- | --------------------- | ------------- | +| `Compression_Mode` | `Predefined_Mode` | `RLE_Mode` | `FSE_Compressed_Mode` | `Repeat_Mode` | + +- `Predefined_Mode` : A predefined FSE distribution table is used, defined in + [default distributions](#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](#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](#dictionary-format)) 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_Code` | 0-15 | +| ---------------------- | ---------------------- | +| length | `Literals_Length_Code` | +| `Number_of_Bits` | 0 | + +| `Literals_Length_Code` | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | +| ---------------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | +| `Baseline` | 16 | 18 | 20 | 22 | 24 | 28 | 32 | 40 | +| `Number_of_Bits` | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 3 | + +| `Literals_Length_Code` | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | +| ---------------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | +| `Baseline` | 48 | 64 | 128 | 256 | 512 | 1024 | 2048 | 4096 | +| `Number_of_Bits` | 4 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | + +| `Literals_Length_Code` | 32 | 33 | 34 | 35 | +| ---------------------- | ---- | ---- | ---- | ---- | +| `Baseline` | 8192 |16384 |32768 |65536 | +| `Number_of_Bits` | 13 | 14 | 15 | 16 | + + +##### 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_Code` | 0-31 | +| ------------------- | ----------------------- | +| value | `Match_Length_Code` + 3 | +| `Number_of_Bits` | 0 | + +| `Match_Length_Code` | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | +| ------------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | +| `Baseline` | 35 | 37 | 39 | 41 | 43 | 47 | 51 | 59 | +| `Number_of_Bits` | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 3 | + +| `Match_Length_Code` | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | +| ------------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | +| `Baseline` | 67 | 83 | 99 | 131 | 259 | 515 | 1027 | 2051 | +| `Number_of_Bits` | 4 | 4 | 5 | 7 | 8 | 9 | 10 | 11 | + +| `Match_Length_Code` | 48 | 49 | 50 | 51 | 52 | +| ------------------- | ---- | ---- | ---- | ---- | ---- | +| `Baseline` | 4099 | 8195 |16387 |32771 |65539 | +| `Number_of_Bits` | 12 | 13 | 14 | 15 | 16 | + +##### 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](#window_descriptor). + +`Offset_Value` from 1 to 3 are special : they define "repeat codes". +This is described in more detail in [Repeat Offsets](#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](#fse). + +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](#fse). + +##### 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. + +[description of the codes]: #the-codes-for-literals-lengths-match-lengths-and-offsets + +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](#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](#fse) 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]. + +[FSE section]: #from-normalized-distribution-to-decoding-tables + +##### 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](#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](#repeat-offsets) 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](#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 Codes]: #offset-codes + +###### 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_Number` | `Frame_Size` | `User_Data` | +|:--------------:|:------------:|:-----------:| +| 4 bytes | 4 bytes | n 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. + +[LZ4]:http://www.lz4.org + +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]. + +[Finite State Entropy]:https://github.com/Cyan4973/FiniteStateEntropy/ + +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`. + +[ANS]: https://en.wikipedia.org/wiki/Asymmetric_Numeral_Systems + +### 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 read | Value decoded | Number of bits used | + | ---------- | ------------- | ------------------- | + | 0 - 97 | 0 - 97 | 7 | + | 98 - 127 | 98 - 127 | 8 | + | 128 - 225 | 0 - 97 | 7 | + | 226 - 255 | 128 - 157 | 8 | + +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. + +[next section]:#from-normalized-distribution-to-decoding-tables + +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 (`Number_of_Bits` and `Baseline`). + +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. + +Then, all remaining symbols, sorted in natural order, are allocated cells. +Starting from symbol `0` (if it exists), and table position `0`, +each symbol gets allocated as many cells as its probability. +Cell allocation is spreaded, not linear : +each successor position follows 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 process guarantees that the table is entirely filled. +Each cell corresponds to a state value, which contains the symbol being decoded. + +To add the `Number_of_Bits` and `Baseline` required to retrieve next state, +it's first necessary to sort all occurrences of each symbol in state order. +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 cells, corresponding to 5 state values. +These state values are then sorted in natural order. + +Next power of 2 after 5 is 8. +Space of probabilities must be divided into 8 equal parts. +Presuming the `Accuracy_Log` is 7, it defines a space of 128 states. +Divided by 8, each share is 16 large. + +In order to reach 8 shares, 8-5=3 lowest states will count "double", +doubling their shares (32 in width), hence requiring one more bit. + +Baseline is assigned starting from the higher states using fewer bits, +increasing at each state, then resuming at the first state, +each state takes its allocated width from Baseline. + +| state value | 1 | 39 | 77 | 84 | 122 | +| state order | 0 | 1 | 2 | 3 | 4 | +| ---------------- | ----- | ----- | ------ | ---- | ------ | +| width | 32 | 32 | 32 | 16 | 16 | +| `Number_of_Bits` | 5 | 5 | 5 | 4 | 4 | +| range number | 2 | 4 | 6 | 0 | 1 | +| `Baseline` | 32 | 64 | 96 | 0 | 16 | +| range | 32-63 | 64-95 | 96-127 | 0-15 | 16-31 | + +During decoding, the next state value is determined from current state value, +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. + +[Appendix A]: #appendix-a---decoding-tables-for-predefined-codes + + +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 value | 0 | 1 | 2 | 3 | 4 | 5 | +| ---------------- | --- | --- | --- | --- | --- | --- | +| `Number_of_Bits` | 1 | 2 | 3 | 0 | 4 | 4 | + +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 value | 0 | 1 | 2 | 3 | 4 | +| ------------- | --- | --- | --- | --- | --- | +| `Weight` | 4 | 3 | 2 | 0 | 1 | + +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](#fse-table-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](#fse). + +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 : + +| Literal | 0 | 1 | 2 | 3 | 4 | 5 | +| -------- | --- | --- | --- | --- | --- | --- | +| `Weight` | 4 | 3 | 2 | 0 | 1 | 1 | + +Sorted by weight and then natural sequential order, +it gives the following distribution : + +| Literal | 3 | 4 | 5 | 2 | 1 | 0 | +| ---------------- | --- | --- | --- | --- | --- | ---- | +| `Weight` | 0 | 1 | 1 | 2 | 3 | 4 | +| `Number_of_Bits` | 0 | 4 | 4 | 3 | 2 | 1 | +| prefix codes | N/A | 0000| 0001| 001 | 01 | 1 | + +### 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: + +|Symbol | 5 | 4 | 1 | 0 | Padding | +|--------|------|------|----|---|---------| +|Encoding|`0000`|`0001`|`01`|`1`| `00001` | + +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_Number` | `Dictionary_ID` | `Entropy_Tables` | `Content` | +| -------------- | --------------- | ---------------- | --------- | + +__`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](#fse-table-description) + and [Huffman](#huffman-tree-description) 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. + +[compressed blocks]: #the-format-of-compressed_block + +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: + +| State | Symbol | Number_Of_Bits | Base | +| ----- | ------ | -------------- | ---- | +| 0 | 0 | 4 | 0 | +| 1 | 0 | 4 | 16 | +| 2 | 1 | 5 | 32 | +| 3 | 3 | 5 | 0 | +| 4 | 4 | 5 | 0 | +| 5 | 6 | 5 | 0 | +| 6 | 7 | 5 | 0 | +| 7 | 9 | 5 | 0 | +| 8 | 10 | 5 | 0 | +| 9 | 12 | 5 | 0 | +| 10 | 14 | 6 | 0 | +| 11 | 16 | 5 | 0 | +| 12 | 18 | 5 | 0 | +| 13 | 19 | 5 | 0 | +| 14 | 21 | 5 | 0 | +| 15 | 22 | 5 | 0 | +| 16 | 24 | 5 | 0 | +| 17 | 25 | 5 | 32 | +| 18 | 26 | 5 | 0 | +| 19 | 27 | 6 | 0 | +| 20 | 29 | 6 | 0 | +| 21 | 31 | 6 | 0 | +| 22 | 0 | 4 | 32 | +| 23 | 1 | 4 | 0 | +| 24 | 2 | 5 | 0 | +| 25 | 4 | 5 | 32 | +| 26 | 5 | 5 | 0 | +| 27 | 7 | 5 | 32 | +| 28 | 8 | 5 | 0 | +| 29 | 10 | 5 | 32 | +| 30 | 11 | 5 | 0 | +| 31 | 13 | 6 | 0 | +| 32 | 16 | 5 | 32 | +| 33 | 17 | 5 | 0 | +| 34 | 19 | 5 | 32 | +| 35 | 20 | 5 | 0 | +| 36 | 22 | 5 | 32 | +| 37 | 23 | 5 | 0 | +| 38 | 25 | 4 | 0 | +| 39 | 25 | 4 | 16 | +| 40 | 26 | 5 | 32 | +| 41 | 28 | 6 | 0 | +| 42 | 30 | 6 | 0 | +| 43 | 0 | 4 | 48 | +| 44 | 1 | 4 | 16 | +| 45 | 2 | 5 | 32 | +| 46 | 3 | 5 | 32 | +| 47 | 5 | 5 | 32 | +| 48 | 6 | 5 | 32 | +| 49 | 8 | 5 | 32 | +| 50 | 9 | 5 | 32 | +| 51 | 11 | 5 | 32 | +| 52 | 12 | 5 | 32 | +| 53 | 15 | 6 | 0 | +| 54 | 17 | 5 | 32 | +| 55 | 18 | 5 | 32 | +| 56 | 20 | 5 | 32 | +| 57 | 21 | 5 | 32 | +| 58 | 23 | 5 | 32 | +| 59 | 24 | 5 | 32 | +| 60 | 35 | 6 | 0 | +| 61 | 34 | 6 | 0 | +| 62 | 33 | 6 | 0 | +| 63 | 32 | 6 | 0 | + +#### Match Length Code: + +| State | Symbol | Number_Of_Bits | Base | +| ----- | ------ | -------------- | ---- | +| 0 | 0 | 6 | 0 | +| 1 | 1 | 4 | 0 | +| 2 | 2 | 5 | 32 | +| 3 | 3 | 5 | 0 | +| 4 | 5 | 5 | 0 | +| 5 | 6 | 5 | 0 | +| 6 | 8 | 5 | 0 | +| 7 | 10 | 6 | 0 | +| 8 | 13 | 6 | 0 | +| 9 | 16 | 6 | 0 | +| 10 | 19 | 6 | 0 | +| 11 | 22 | 6 | 0 | +| 12 | 25 | 6 | 0 | +| 13 | 28 | 6 | 0 | +| 14 | 31 | 6 | 0 | +| 15 | 33 | 6 | 0 | +| 16 | 35 | 6 | 0 | +| 17 | 37 | 6 | 0 | +| 18 | 39 | 6 | 0 | +| 19 | 41 | 6 | 0 | +| 20 | 43 | 6 | 0 | +| 21 | 45 | 6 | 0 | +| 22 | 1 | 4 | 16 | +| 23 | 2 | 4 | 0 | +| 24 | 3 | 5 | 32 | +| 25 | 4 | 5 | 0 | +| 26 | 6 | 5 | 32 | +| 27 | 7 | 5 | 0 | +| 28 | 9 | 6 | 0 | +| 29 | 12 | 6 | 0 | +| 30 | 15 | 6 | 0 | +| 31 | 18 | 6 | 0 | +| 32 | 21 | 6 | 0 | +| 33 | 24 | 6 | 0 | +| 34 | 27 | 6 | 0 | +| 35 | 30 | 6 | 0 | +| 36 | 32 | 6 | 0 | +| 37 | 34 | 6 | 0 | +| 38 | 36 | 6 | 0 | +| 39 | 38 | 6 | 0 | +| 40 | 40 | 6 | 0 | +| 41 | 42 | 6 | 0 | +| 42 | 44 | 6 | 0 | +| 43 | 1 | 4 | 32 | +| 44 | 1 | 4 | 48 | +| 45 | 2 | 4 | 16 | +| 46 | 4 | 5 | 32 | +| 47 | 5 | 5 | 32 | +| 48 | 7 | 5 | 32 | +| 49 | 8 | 5 | 32 | +| 50 | 11 | 6 | 0 | +| 51 | 14 | 6 | 0 | +| 52 | 17 | 6 | 0 | +| 53 | 20 | 6 | 0 | +| 54 | 23 | 6 | 0 | +| 55 | 26 | 6 | 0 | +| 56 | 29 | 6 | 0 | +| 57 | 52 | 6 | 0 | +| 58 | 51 | 6 | 0 | +| 59 | 50 | 6 | 0 | +| 60 | 49 | 6 | 0 | +| 61 | 48 | 6 | 0 | +| 62 | 47 | 6 | 0 | +| 63 | 46 | 6 | 0 | + +#### Offset Code: + +| State | Symbol | Number_Of_Bits | Base | +| ----- | ------ | -------------- | ---- | +| 0 | 0 | 5 | 0 | +| 1 | 6 | 4 | 0 | +| 2 | 9 | 5 | 0 | +| 3 | 15 | 5 | 0 | +| 4 | 21 | 5 | 0 | +| 5 | 3 | 5 | 0 | +| 6 | 7 | 4 | 0 | +| 7 | 12 | 5 | 0 | +| 8 | 18 | 5 | 0 | +| 9 | 23 | 5 | 0 | +| 10 | 5 | 5 | 0 | +| 11 | 8 | 4 | 0 | +| 12 | 14 | 5 | 0 | +| 13 | 20 | 5 | 0 | +| 14 | 2 | 5 | 0 | +| 15 | 7 | 4 | 16 | +| 16 | 11 | 5 | 0 | +| 17 | 17 | 5 | 0 | +| 18 | 22 | 5 | 0 | +| 19 | 4 | 5 | 0 | +| 20 | 8 | 4 | 16 | +| 21 | 13 | 5 | 0 | +| 22 | 19 | 5 | 0 | +| 23 | 1 | 5 | 0 | +| 24 | 6 | 4 | 16 | +| 25 | 10 | 5 | 0 | +| 26 | 16 | 5 | 0 | +| 27 | 28 | 5 | 0 | +| 28 | 27 | 5 | 0 | +| 29 | 26 | 5 | 0 | +| 30 | 25 | 5 | 0 | +| 31 | 24 | 5 | 0 | + + + +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]: https://github.com/facebook/zstd/tree/v1.3.4/tests#decodecorpus---tool-to-generate-zstandard-frames-for-decoder-testing + +`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 +--------------- +- 0.3.5 : clarifications for Block_Maximum_Size +- 0.3.4 : clarifications for FSE decoding table +- 0.3.3 : clarifications for field Block_Size +- 0.3.2 : remove additional block size restriction on compressed blocks +- 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 |