<commit_before>Zstandard Compression Format
============================

### Notices

Copyright (c) 2016 <NAME>

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

### Version

0.2.0 (22/07/16)


Introduction
------------

The purpose of this document is to define a lossless compressed data format,
that is independent of CPU type, operating system,
file system and character set, suitable for
file compression, pipe and streaming compression,
using the [Zstandard algorithm](http://www.zstandard.org).

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.

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

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

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


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

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


General Structure of Zstandard Frame format
-------------------------------------------

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

__Magic Number__

4 Bytes, Little endian format.
Value : 0xFD2FB527

__Frame Header__

2 to 14 Bytes, detailed in [next part](#frame-header).

__Data Blocks__

Detailed in [next chapter](#data-blocks).
That’s where compressed data is stored.

__EndMark__

The flow of blocks ends when the last block header brings an _end signal_ .
This last block header may optionally host a __Content Checksum__ .

##### __Content Checksum__

Content Checksum verify that frame content has been regenerated correctly.
The content checksum is the result
of [xxh64() hash function](https://www.xxHash.com)
digesting the original (decoded) data as input, and a seed of zero.
Bits from 11 to 32 (included) are extracted to form a 22 bits checksum
stored into the endmark body.
```
mask22bits = (1<<22)-1;
contentChecksum = (XXH64(content, size, 0) >> 11) & mask22bits;
```
Content checksum is only present when its associated flag
is set in the frame descriptor.
Its usage is optional.

__Frame Concatenation__

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

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

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


Frame Header
-------------

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

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

__FHD byte__ (Frame Header Descriptor)

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

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

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

__Frame Content Size flag__

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

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

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

__Single Segment__

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

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

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

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

__Unused bit__

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

__Reserved bit__

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

__Content checksum flag__

If this flag is set, a content checksum will be present into the EndMark.
The checksum is a 22 bits value extracted from the XXH64() of data,
and stored into endMark. See [__Content Checksum__](#content-checksum) .

__Dictionary ID flag__

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

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

__WD byte__ (Window Descriptor)

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

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

|   BitNb   |    7-3   |    0-2   |
| --------- | -------- | -------- |
| FieldName | Exponent | Mantissa |

Maximum distance is given by the following formulae :
```
windowLog = 10 + Exponent;
windowBase = 1 << windowLog;
windowAdd = (windowBase / 8) * Mantissa;
windowSize = windowBase + windowAdd;
```
The minimum window size is 1 KB.
The maximum size is `15*(1<<38)` bytes, which is 1.875 TB.

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

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

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

__Dictionary ID__

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

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

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

_Reserved ranges :_
If the frame is going to be distributed in a private environment,
any dictionary ID can be used.
However, for public distribution of compressed frames using a dictionary,
some ranges are reserved for future use :
- low : 1 - 32767 : reserved
- high : >= (2^31) : reserved


__Frame Content Size__

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

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

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

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


Data Blocks
-----------

| B. Header |  data  |
|:---------:| ------ |
|  3 bytes  |        |


__Block Header__

This field uses 3-bytes, format is __little-endian__.

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

There are 4 block types :

|    Value   |      0     |  1  |  2  |    3    |
| ---------- | ---------- | --- | --- | ------- |
| Block Type | Compressed | Raw | RLE | EndMark |

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

Block sizes must respect a few rules :
- In compressed mode, compressed size if always strictly `< decompressed size`.
- Block decompressed size is always <= maximum back-reference distance .
- Block decompressed size is always <= 128 KB


__Data__

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


Skippable Frames
----------------

| Magic Number | Frame Size | User Data |
|:------------:|:----------:| --------- |
|   4 bytes    |  4 bytes   |           |

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

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

[LZ4]:http://www.lz4.org

__Magic Number__ :

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

__Frame Size__ :

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

__User Data__ :

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


Compressed block format
-----------------------
This specification details the content of a _compressed block_.
A compressed block has a size, which must be known.
It also has a guaranteed maximum regenerated size,
in order to properly allocate destination buffer.
See [Data Blocks](#data-blocks) for more details.

A compressed block consists of 2 sections :
- [Literals section](#literals-section)
- [Sequences section](#sequences-section)

### Prerequisites
To decode a compressed block, the following elements are necessary :
- Previous decoded blocks, up to a distance of `windowSize`,
  or all previous blocks in "single segment" mode.
- List of "recent offsets" from previous compressed block.
- Decoding tables of previous compressed block for each symbol type
  (literals, litLength, matchLength, offset).


### Literals section

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

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

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

#### Literals section header

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

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

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

__Block Type__ :

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

|    Value   |      0     |    1   |  2  |    3    |
| ---------- | ---------- | ------ | --- | ------- |
| Block Type | Compressed | Repeat | Raw |   RLE   |

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

__Sizes format__ :

Sizes format are divided into 2 families :

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

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

__Sizes format for Raw and RLE literals block__ :

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

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

__Sizes format for Compressed literals block__ :

Note : also applicable to "repeat-stats" blocks.
- Value : 00 : _Single stream_.
               Compressed and regenerated sizes use 10 bits (0-1023).
               Total literal header size is 3 bytes.
- Value : 01 : 4 streams.
               Compressed and regenerated sizes use 10 bits (0-1023).
               Total literal header size is 3 bytes.
- Value : 10 : 4 streams.
               Compressed and regenerated sizes use 14 bits (0-16383).
               Total literal header size is 4 bytes.
- Value : 11 : 4 streams.
               Compressed and regenerated sizes use 18 bits (0-262143).
               Total literal header size is 5 bytes.

Compressed and regenerated size fields follow little endian convention.

#### Huffman Tree description

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

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

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

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


##### Representation

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

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

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

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

| weights |  4  |  3  |  2  |  0  |  1  |
| ------- | --- | --- | --- | --- | --- |
| literal |  0  |  1  |  2  |  3  |  4  |

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

##### Huffman Tree header

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

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

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

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

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

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

##### FSE (Finite State Entropy) compression of huffman weights

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

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

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

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


##### Conversion from weights to huffman prefix codes

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


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

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

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

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


#### Literals bitstreams

##### Bitstreams sizes

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

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

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

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

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

##### Bitstreams read and decode

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

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

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

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

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


### Sequences section

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

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

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

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

| Header | [LitLengthTable] | [OffsetTable] | [MatchLengthTable] | bitStream |
| ------ | ---------------- | ------------- | ------------------ | --------- |

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


#### Sequences section header

Consists in 2 items :
- Nb of Sequences
- Flags providing Symbol compression types

__Nb of Sequences__

This is a variable size field, `nbSeqs`, using between 1 and 3 bytes.
Let's call its first byte `byte0`.
- `if (byte0 == 0)` : there are no sequences.
            The sequence section stops there.
            Regenerated content is defined entirely by literals section.
- `if (byte0 < 128)` : `nbSeqs = byte0;` . Uses 1 byte.
- `if (byte0 < 255)` : `nbSeqs = ((byte0-128) << 8) + byte1;` . Uses 2 bytes.
- `if (byte0 == 255)`: `nbSeqs = byte1 + (byte2<<8) + 0x7F00;` . Uses 3 bytes.

__Symbol compression modes__

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

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

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

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

They follow the same enumeration :

|       Value      |    0   |  1  |    2   |  3  |
| ---------------- | ------ | --- | ------ | --- |
| Compression Mode | predef | RLE | Repeat | FSE |

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

#### Symbols decoding

##### Literal Lengths codes

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

|  Code  | 0-15 |
| ------ | ---- |
| length | Code |
| nbBits |   0  |


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

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

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

__Default distribution__

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

Below is its definition. It uses an accuracy of 6 bits (64 states).
```
short literalLengths_defaultDistribution[36] =
        { 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
          2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1, 1, 1,
         -1,-1,-1,-1 };
```

##### Match Lengths codes

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

|  Code  |   0-31   |
| ------ | -------- |
| value  | Code + 3 |
| nbBits |     0    |

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

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

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

__Default distribution__

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

Here is its definition. It uses an accuracy of 6 bits (64 states).
```
short matchLengths_defaultDistribution[53] =
        { 1, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,-1,-1,
         -1,-1,-1,-1,-1 };
```

##### Offset codes

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

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

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

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

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

__Default distribution__

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

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

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

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

#### Distribution tables

Following the header, up to 3 distribution tables can be described.
They are, in order :
- Literal lengthes
- Offsets
- Match Lengthes

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

##### FSE distribution table : condensed format

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

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

The bitstream starts by reporting on which scale it operates.
`AccuracyLog = low4bits + 5;`
In theory, it can define a scale from 5 to 20.
In practice, decoders are allowed to limit the maximum supported `AccuracyLog`.
Recommended maximum are `9` for literal and match lengthes, and `8` for offsets.
The reference decoder uses these limits.

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

- Remaining probabilities + 1 :
  __example__ :
  Presuming an AccuracyLog of 8,
  and presuming 100 probabilities points have already been distributed,
  the decoder may read any value from `0` to `255 - 100 + 1 == 156` (included).<commit_msg>made accuracy limits "hard" instead of "recommended"<commit_after>Zstandard Compression Format
============================

### Notices

Copyright (c) 2016 <NAME>

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

### Version

0.2.0 (22/07/16)


Introduction
------------

The purpose of this document is to define a lossless compressed data format,
that is independent of CPU type, operating system,
file system and character set, suitable for
file compression, pipe and streaming compression,
using the [Zstandard algorithm](http://www.zstandard.org).

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.

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

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

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


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

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


General Structure of Zstandard Frame format
-------------------------------------------

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

__Magic Number__

4 Bytes, Little endian format.
Value : 0xFD2FB527

__Frame Header__

2 to 14 Bytes, detailed in [next part](#frame-header).

__Data Blocks__

Detailed in [next chapter](#data-blocks).
That’s where compressed data is stored.

__EndMark__

The flow of blocks ends when the last block header brings an _end signal_ .
This last block header may optionally host a __Content Checksum__ .

##### __Content Checksum__

Content Checksum verify that frame content has been regenerated correctly.
The content checksum is the result
of [xxh64() hash function](https://www.xxHash.com)
digesting the original (decoded) data as input, and a seed of zero.
Bits from 11 to 32 (included) are extracted to form a 22 bits checksum
stored into the endmark body.
```
mask22bits = (1<<22)-1;
contentChecksum = (XXH64(content, size, 0) >> 11) & mask22bits;
```
Content checksum is only present when its associated flag
is set in the frame descriptor.
Its usage is optional.

__Frame Concatenation__

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

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

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


Frame Header
-------------

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

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

__FHD byte__ (Frame Header Descriptor)

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

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

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

__Frame Content Size flag__

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

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

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

__Single Segment__

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

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

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

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

__Unused bit__

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

__Reserved bit__

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

__Content checksum flag__

If this flag is set, a content checksum will be present into the EndMark.
The checksum is a 22 bits value extracted from the XXH64() of data,
and stored into endMark. See [__Content Checksum__](#content-checksum) .

__Dictionary ID flag__

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

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

__WD byte__ (Window Descriptor)

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

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

|   BitNb   |    7-3   |    0-2   |
| --------- | -------- | -------- |
| FieldName | Exponent | Mantissa |

Maximum distance is given by the following formulae :
```
windowLog = 10 + Exponent;
windowBase = 1 << windowLog;
windowAdd = (windowBase / 8) * Mantissa;
windowSize = windowBase + windowAdd;
```
The minimum window size is 1 KB.
The maximum size is `15*(1<<38)` bytes, which is 1.875 TB.

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

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

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

__Dictionary ID__

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

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

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

_Reserved ranges :_
If the frame is going to be distributed in a private environment,
any dictionary ID can be used.
However, for public distribution of compressed frames using a dictionary,
some ranges are reserved for future use :
- low : 1 - 32767 : reserved
- high : >= (2^31) : reserved


__Frame Content Size__

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

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

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

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


Data Blocks
-----------

| B. Header |  data  |
|:---------:| ------ |
|  3 bytes  |        |


__Block Header__

This field uses 3-bytes, format is __little-endian__.

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

There are 4 block types :

|    Value   |      0     |  1  |  2  |    3    |
| ---------- | ---------- | --- | --- | ------- |
| Block Type | Compressed | Raw | RLE | EndMark |

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

Block sizes must respect a few rules :
- In compressed mode, compressed size if always strictly `< decompressed size`.
- Block decompressed size is always <= maximum back-reference distance .
- Block decompressed size is always <= 128 KB


__Data__

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


Skippable Frames
----------------

| Magic Number | Frame Size | User Data |
|:------------:|:----------:| --------- |
|   4 bytes    |  4 bytes   |           |

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

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

[LZ4]:http://www.lz4.org

__Magic Number__ :

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

__Frame Size__ :

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

__User Data__ :

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


Compressed block format
-----------------------
This specification details the content of a _compressed block_.
A compressed block has a size, which must be known.
It also has a guaranteed maximum regenerated size,
in order to properly allocate destination buffer.
See [Data Blocks](#data-blocks) for more details.

A compressed block consists of 2 sections :
- [Literals section](#literals-section)
- [Sequences section](#sequences-section)

### Prerequisites
To decode a compressed block, the following elements are necessary :
- Previous decoded blocks, up to a distance of `windowSize`,
  or all previous blocks in "single segment" mode.
- List of "recent offsets" from previous compressed block.
- Decoding tables of previous compressed block for each symbol type
  (literals, litLength, matchLength, offset).


### Literals section

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

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

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

#### Literals section header

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

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

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

__Block Type__ :

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

|    Value   |      0     |    1   |  2  |    3    |
| ---------- | ---------- | ------ | --- | ------- |
| Block Type | Compressed | Repeat | Raw |   RLE   |

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

__Sizes format__ :

Sizes format are divided into 2 families :

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

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

__Sizes format for Raw and RLE literals block__ :

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

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

__Sizes format for Compressed literals block__ :

Note : also applicable to "repeat-stats" blocks.
- Value : 00 : _Single stream_.
               Compressed and regenerated sizes use 10 bits (0-1023).
               Total literal header size is 3 bytes.
- Value : 01 : 4 streams.
               Compressed and regenerated sizes use 10 bits (0-1023).
               Total literal header size is 3 bytes.
- Value : 10 : 4 streams.
               Compressed and regenerated sizes use 14 bits (0-16383).
               Total literal header size is 4 bytes.
- Value : 11 : 4 streams.
               Compressed and regenerated sizes use 18 bits (0-262143).
               Total literal header size is 5 bytes.

Compressed and regenerated size fields follow little endian convention.

#### Huffman Tree description

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

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

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

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


##### Representation

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

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

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

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

| weights |  4  |  3  |  2  |  0  |  1  |
| ------- | --- | --- | --- | --- | --- |
| literal |  0  |  1  |  2  |  3  |  4  |

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

##### Huffman Tree header

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

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

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

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

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

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

##### FSE (Finite State Entropy) compression of huffman weights

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

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

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

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


##### Conversion from weights to huffman prefix codes

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


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

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

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

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


#### Literals bitstreams

##### Bitstreams sizes

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

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

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

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

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

##### Bitstreams read and decode

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

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

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

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

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


### Sequences section

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

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

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

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

| Header | [LitLengthTable] | [OffsetTable] | [MatchLengthTable] | bitStream |
| ------ | ---------------- | ------------- | ------------------ | --------- |

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


#### Sequences section header

Consists in 2 items :
- Nb of Sequences
- Flags providing Symbol compression types

__Nb of Sequences__

This is a variable size field, `nbSeqs`, using between 1 and 3 bytes.
Let's call its first byte `byte0`.
- `if (byte0 == 0)` : there are no sequences.
            The sequence section stops there.
            Regenerated content is defined entirely by literals section.
- `if (byte0 < 128)` : `nbSeqs = byte0;` . Uses 1 byte.
- `if (byte0 < 255)` : `nbSeqs = ((byte0-128) << 8) + byte1;` . Uses 2 bytes.
- `if (byte0 == 255)`: `nbSeqs = byte1 + (byte2<<8) + 0x7F00;` . Uses 3 bytes.

__Symbol compression modes__

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

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

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

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

They follow the same enumeration :

|       Value      |    0   |  1  |    2   |  3  |
| ---------------- | ------ | --- | ------ | --- |
| Compression Mode | predef | RLE | Repeat | FSE |

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

#### Symbols decoding

##### Literal Lengths codes

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

|  Code  | 0-15 |
| ------ | ---- |
| length | Code |
| nbBits |   0  |


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

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

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

__Default distribution__

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

Below is its definition. It uses an accuracy of 6 bits (64 states).
```
short literalLengths_defaultDistribution[36] =
        { 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1,
          2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1, 1, 1,
         -1,-1,-1,-1 };
```

##### Match Lengths codes

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

|  Code  |   0-31   |
| ------ | -------- |
| value  | Code + 3 |
| nbBits |     0    |

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

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

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

__Default distribution__

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

Here is its definition. It uses an accuracy of 6 bits (64 states).
```
short matchLengths_defaultDistribution[53] =
        { 1, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
          1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,-1,-1,
         -1,-1,-1,-1,-1 };
```

##### Offset codes

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

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

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

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

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

__Default distribution__

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

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

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

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

#### Distribution tables

Following the header, up to 3 distribution tables can be described.
They are, in order :
- Literal lengthes
- Offsets
- Match Lengthes

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

##### FSE distribution table : condensed format

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

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

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

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

- Remaining probabilities + 1 :
  __example__ :
  Presuming an AccuracyLog of 8,
  and presuming 100 probabilities points have already been distributed,
  the decoder may read any value from `0` to `255 - 100 + 1 == 156` (included).
{'fraction_non_alphanumeric': 0.10476121458076672, 'fraction_numerical': 0.0339589825349663, 'mean_word_length': 2.8493639812541844, 'pattern_counts': {'":': 0, '<': 63, '<?xml version=': 0, '>': 35, 'https://': 2, 'lorem ipsum': 0, 'www.': 8, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 14, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '785458', 'n_tokens_mistral': 21684, 'n_tokens_neox': 19464, 'n_words': 9714}