reedsolomon

README

Reed-Solomon

Reed-Solomon Erasure Coding in Go, with speeds exceeding 1GB/s/cpu core implemented in pure Go.

This is a Go port of the JavaReedSolomon library released by Backblaze, with some additional optimizations.

For an introduction on erasure coding, see the post on the Backblaze blog.

For encoding high shard counts (>256) a Leopard implementation is used. For most platforms this performs close to the original Leopard implementation in terms of speed.

Package home: https://github.com/klauspost/reedsolomon

Godoc: https://pkg.go.dev/github.com/klauspost/reedsolomon

Installation

To get the package use the standard:

go get -u github.com/klauspost/reedsolomon

Using Go modules is recommended.

Changes

2024

• Auto-generation of SVE and NEON routines for ARM based on AVX2 code. This results in a speedup of 2x for SVE (as measured using Graviton 3 on AWS) and a speedup of 1.5x as compared to the existing NEON-accelerated code.

2022

• GFNI support for amd64, for up to 3x faster processing.
• Leopard GF8 mode added, for faster processing of medium shard counts.
• Leopard GF16 mode added, for up to 65536 shards.
• WithJerasureMatrix allows constructing a Jerasure compatible matrix.

2021

• Use GOAMD64=v4 to enable faster AVX2.
• Add progressive shard encoding.
• Wider AVX2 loops
• Limit concurrency on AVX2, since we are likely memory bound.
• Allow 0 parity shards.
• Allow disabling inversion cache.
• Faster AVX2 encoding.

See older changes

May 2020

• ARM64 optimizations, up to 2.5x faster.
• Added WithFastOneParityMatrix for faster operation with 1 parity shard.
• Much better performance when using a limited number of goroutines.
• AVX512 is now using multiple cores.
• Stream processing overhaul, big speedups in most cases.
• AVX512 optimizations

March 6, 2019

The pure Go implementation is about 30% faster. Minor tweaks to assembler implementations.

February 8, 2019

AVX512 accelerated version added for Intel Skylake CPUs. This can give up to a 4x speed improvement as compared to AVX2. See here for more details.

December 18, 2018

Assembly code for ppc64le has been contributed, this boosts performance by about 10x on this platform.

November 18, 2017

Added WithAutoGoroutines which will attempt to calculate the optimal number of goroutines to use based on your expected shard size and detected CPU.

October 1, 2017

• Cauchy Matrix is now an option. Thanks to templexxx for the basis of this.

• Default maximum number of goroutines has been increased for better multi-core scaling.

• After several requests the Reconstruct and ReconstructData now slices of zero length but sufficient capacity to be used instead of allocating new memory.

August 26, 2017

• The Encoder() now contains an Update function contributed by chenzhongtao.

• Frank Wessels kindly contributed ARM 64 bit assembly, which gives a huge performance boost on this platform.

July 20, 2017

ReconstructData added to Encoder interface. This can cause compatibility issues if you implement your own Encoder. A simple workaround can be added:

func (e *YourEnc) ReconstructData(shards [][]byte) error {
	return ReconstructData(shards)
}

You can of course also do your own implementation. The StreamEncoder handles this without modifying the interface. This is a good lesson on why returning interfaces is not a good design.

Usage

This section assumes you know the basics of Reed-Solomon encoding. A good start is this Backblaze blog post.

This package performs the calculation of the parity sets. The usage is therefore relatively simple.

First of all, you need to choose your distribution of data and parity shards. A 'good' distribution is very subjective, and will depend a lot on your usage scenario.

To create an encoder with 10 data shards (where your data goes) and 3 parity shards (calculated):

    enc, err := reedsolomon.New(10, 3)

This encoder will work for all parity sets with this distribution of data and parity shards.

If you will primarily be using it with one shard size it is recommended to use WithAutoGoroutines(shardSize) as an additional parameter. This will attempt to calculate the optimal number of goroutines to use for the best speed. It is not required that all shards are this size.

Then you send and receive data that is a simple slice of byte slices; [][]byte. In the example above, the top slice must have a length of 13.

    data := make([][]byte, 13)

You should then fill the 10 first slices with equally sized data, and create parity shards that will be populated with parity data. In this case we create the data in memory, but you could for instance also use mmap to map files.

    // Create all shards, size them at 50000 each
    for i := range input {
      data[i] := make([]byte, 50000)
    }
    
    // The above allocations can also be done by the encoder:
    // data := enc.(reedsolomon.Extended).AllocAligned(50000)
    
    // Fill some data into the data shards
    for i, in := range data[:10] {
      for j:= range in {
         in[j] = byte((i+j)&0xff)
      }
    }

To populate the parity shards, you simply call Encode() with your data.

    err = enc.Encode(data)

The only cases where you should get an error is, if the data shards aren't of equal size. The last 3 shards now contain parity data. You can verify this by calling Verify():

    ok, err = enc.Verify(data)

The final (and important) part is to be able to reconstruct missing shards. For this to work, you need to know which parts of your data is missing. The encoder does not know which parts are invalid, so if data corruption is a likely scenario, you need to implement a hash check for each shard.

If a byte has changed in your set, and you don't know which it is, there is no way to reconstruct the data set.

To indicate missing data, you set the shard to nil before calling Reconstruct():

    // Delete two data shards
    data[3] = nil
    data[7] = nil
    
    // Reconstruct the missing shards
    err := enc.Reconstruct(data)

The missing data and parity shards will be recreated. If more than 3 shards are missing, the reconstruction will fail.

If you are only interested in the data shards (for reading purposes) you can call ReconstructData():

    // Delete two data shards
    data[3] = nil
    data[7] = nil
    
    // Reconstruct just the missing data shards
    err := enc.ReconstructData(data)

If you don't need all data shards you can use ReconstructSome():

    // Delete two data shards
    data[3] = nil
    data[7] = nil
    
    // Reconstruct just the shard 3
    err := enc.ReconstructSome(data, []bool{false, false, false, true, false, false, false, false})

So to sum up reconstruction:

• The number of data/parity shards must match the numbers used for encoding.
• The order of shards must be the same as used when encoding.
• You may only supply data you know is valid.
• Invalid shards should be set to nil.

For complete examples of an encoder and decoder see the examples folder.

Splitting/Joining Data

You might have a large slice of data. To help you split this, there are some helper functions that can split and join a single byte slice.

   bigfile, _ := os.Readfile("myfile.data")
   
   // Split the file
   split, err := enc.Split(bigfile)

This will split the file into the number of data shards set when creating the encoder and create empty parity shards.

An important thing to note is that you have to keep track of the exact input size. If the size of the input isn't divisible by the number of data shards, extra zeros will be inserted in the last shard.

To join a data set, use the Join() function, which will join the shards and write it to the io.Writer you supply:

   // Join a data set and write it to io.Discard.
   err = enc.Join(io.Discard, data, len(bigfile))

Aligned Allocations

For AMD64 aligned inputs can make a big speed difference.

This is an example of the speed difference when inputs are unaligned/aligned:

BenchmarkEncode100x20x10000-32    	    7058	    172648 ns/op	6950.57 MB/s
BenchmarkEncode100x20x10000-32    	    8406	    137911 ns/op	8701.24 MB/s

This is mostly the case when dealing with odd-sized shards.

To facilitate this the package provides an AllocAligned(shards, each int) [][]byte. This will allocate a number of shards, each with the size each. Each shard will then be aligned to a 64 byte boundary.

Each encoder also has a AllocAligned(each int) [][]byte as an extended interface which will return the same, but with the shard count configured in the encoder.

It is not possible to re-aligned already allocated slices, for example when using Split. When it is not possible to write to aligned shards, you should not copy to them.

Progressive encoding

It is possible to encode individual shards using EncodeIdx:

	// EncodeIdx will add parity for a single data shard.
	// Parity shards should start out as 0. The caller must zero them.
	// Data shards must be delivered exactly once. There is no check for this.
	// The parity shards will always be updated and the data shards will remain the same.
	EncodeIdx(dataShard []byte, idx int, parity [][]byte) error

This allows progressively encoding the parity by sending individual data shards. There is no requirement on shards being delivered in order, but when sent in order it allows encoding shards one at the time, effectively allowing the operation to be streaming.

The result will be the same as encoding all shards at once. There is a minor speed penalty using this method, so send shards at once if they are available.

Example

func test() {
    // Create an encoder with 7 data and 3 parity slices.
    enc, _ := reedsolomon.New(7, 3)

    // This will be our output parity.
    parity := make([][]byte, 3)
    for i := range parity {
        parity[i] = make([]byte, 10000)
    }

    for i := 0; i < 7; i++ {
        // Send data shards one at the time.
        _ = enc.EncodeIdx(make([]byte, 10000), i, parity)
    }

    // parity now contains parity, as if all data was sent in one call.
}

Streaming/Merging

It might seem like a limitation that all data should be in memory, but an important property is that as long as the number of data/parity shards are the same, you can merge/split data sets, and they will remain valid as a separate set.

    // Split the data set of 50000 elements into two of 25000
    splitA := make([][]byte, 13)
    splitB := make([][]byte, 13)
    
    // Merge into a 100000 element set
    merged := make([][]byte, 13)
    
    for i := range data {
      splitA[i] = data[i][:25000]
      splitB[i] = data[i][25000:]
      
      // Concatenate it to itself
	  merged[i] = append(make([]byte, 0, len(data[i])*2), data[i]...)
	  merged[i] = append(merged[i], data[i]...)
    }
    
    // Each part should still verify as ok.
    ok, err := enc.Verify(splitA)
    if ok && err == nil {
        log.Println("splitA ok")
    }
    
    ok, err = enc.Verify(splitB)
    if ok && err == nil {
        log.Println("splitB ok")
    }
    
    ok, err = enc.Verify(merge)
    if ok && err == nil {
        log.Println("merge ok")
    }

This means that if you have a data set that may not fit into memory, you can split processing into smaller blocks. For the best throughput, don't use too small blocks.

This also means that you can divide big input up into smaller blocks, and do reconstruction on parts of your data. This doesn't give the same flexibility of a higher number of data shards, but it will be much more performant.

Streaming API

There has been added support for a streaming API, to help perform fully streaming operations, which enables you to do the same operations, but on streams. To use the stream API, use NewStream function to create the encoding/decoding interfaces.

You can use WithConcurrentStreams to ready an interface that reads/writes concurrently from the streams.

You can specify the size of each operation using WithStreamBlockSize. This will set the size of each read/write operation.

Input is delivered as []io.Reader, output as []io.Writer, and functionality corresponds to the in-memory API. Each stream must supply the same amount of data, similar to how each slice must be similar size with the in-memory API. If an error occurs in relation to a stream, a StreamReadError or StreamWriteError will help you determine which stream was the offender.

There is no buffering or timeouts/retry specified. If you want to add that, you need to add it to the Reader/Writer.

For complete examples of a streaming encoder and decoder see the examples folder.

GF16 (more than 256 shards) is not supported by the streaming interface.

Advanced Options

You can modify internal options which affects how jobs are split between and processed by goroutines.

To create options, use the WithXXX functions. You can supply options to New, NewStream. If no Options are supplied, default options are used.

Example of how to supply options:

    enc, err := reedsolomon.New(10, 3, WithMaxGoroutines(25))

Leopard Compatible GF16

When you encode more than 256 shards the library will switch to a Leopard-RS implementation.

This allows encoding up to 65536 shards (data+parity) with the following limitations, similar to leopard:

• The original and recovery data must not exceed 65536 pieces.
• The shard size must each be a multiple of 64 bytes.
• Each buffer should have the same number of bytes.
• Even the last shard must be rounded up to the block size.

	Regular	Leopard
Encode	✓	✓
EncodeIdx	✓	-
Verify	✓	✓
Reconstruct	✓	✓
ReconstructData	✓	✓
ReconstructSome	✓	✓ (+)
Update	✓	-
Split	✓	✓
Join	✓	✓

• (+) Same as calling ReconstructData.

The Split/Join functions will help to split an input to the proper sizes.

Speed can be expected to be O(N*log(N)), compared to the O(N*N). Reconstruction matrix calculation is more time-consuming, so be sure to include that as part of any benchmark you run.

For now SSSE3, AVX2 and AVX512 assembly are available on AMD64 platforms.

Leopard mode currently always runs as a single goroutine, since multiple goroutines doesn't provide any worthwhile speedup.

Leopard GF8

It is possible to replace the default reed-solomon encoder with a leopard compatible one. This will typically be faster when dealing with more than 20-30 shards. Note that the limitations listed above also applies to this mode. See table below for speed with different number of shards.

To enable Leopard GF8 mode use WithLeopardGF(true).

Benchmark Encoding and Reconstructing 1KB shards with variable number of shards. All implementation use inversion cache when available. Speed is total shard size for each operation. Data shard throughput is speed/2. AVX2 is used.

Encoder	Shards	Encode	Recover All	Recover One
Cauchy	4+4	23076.83 MB/s	5444.02 MB/s	10834.67 MB/s
Cauchy	8+8	15206.87 MB/s	4223.42 MB/s	16181.62 MB/s
Cauchy	16+16	7427.47 MB/s	3305.84 MB/s	22480.41 MB/s
Cauchy	32+32	3785.64 MB/s	2300.07 MB/s	26181.31 MB/s
Cauchy	64+64	1911.93 MB/s	1368.51 MB/s	27992.93 MB/s
Cauchy	128+128	963.83 MB/s	1327.56 MB/s	32866.86 MB/s
Leopard GF8	4+4	17061.28 MB/s	3099.06 MB/s	4096.78 MB/s
Leopard GF8	8+8	10546.67 MB/s	2925.92 MB/s	3964.00 MB/s
Leopard GF8	16+16	10961.37 MB/s	2328.40 MB/s	3110.22 MB/s
Leopard GF8	32+32	7111.47 MB/s	2374.61 MB/s	3220.75 MB/s
Leopard GF8	64+64	7468.57 MB/s	2055.41 MB/s	3061.81 MB/s
Leopard GF8	128+128	5479.99 MB/s	1953.21 MB/s	2815.15 MB/s
Leopard GF16	256+256	6158.66 MB/s	454.14 MB/s	506.70 MB/s
Leopard GF16	512+512	4418.58 MB/s	685.75 MB/s	801.63 MB/s
Leopard GF16	1024+1024	4778.05 MB/s	814.51 MB/s	1080.19 MB/s
Leopard GF16	2048+2048	3417.05 MB/s	911.64 MB/s	1179.48 MB/s
Leopard GF16	4096+4096	3209.41 MB/s	729.13 MB/s	1135.06 MB/s
Leopard GF16	8192+8192	2034.11 MB/s	604.52 MB/s	842.13 MB/s
Leopard GF16	16384+16384	1525.88 MB/s	486.74 MB/s	750.01 MB/s
Leopard GF16	32768+32768	1138.67 MB/s	482.81 MB/s	712.73 MB/s

"Traditional" encoding is faster until somewhere between 16 and 32 shards. Leopard provides fast encoding in all cases, but shows a significant overhead for reconstruction.

Calculating the reconstruction matrix takes a significant amount of computation. With bigger shards that will be smaller. Arguably, fewer shards typically also means bigger shards. Due to the high shard count caching reconstruction matrices generally isn't feasible for Leopard.

Performance

Performance depends mainly on the number of parity shards. In rough terms, doubling the number of parity shards will double the encoding time.

Here are the throughput numbers with some different selections of data and parity shards. For reference each shard is 1MB random data, and 16 CPU cores are used for encoding.

Data	Parity	Go MB/s	SSSE3 MB/s	AVX2 MB/s
5	2	20,772	66,355	108,755
8	8	6,815	38,338	70,516
10	4	9,245	48,237	93,875
50	20	2,063	12,130	22,828

The throughput numbers here is the size of the encoded data and parity shards.

If runtime.GOMAXPROCS() is set to a value higher than 1, the encoder will use multiple goroutines to perform the calculations in Verify, Encode and Reconstruct.

Benchmarking Reconstruct() followed by a Verify() (=all) versus just calling ReconstructData() (=data) gives the following result:

benchmark                            all MB/s     data MB/s    speedup
BenchmarkReconstruct10x2x10000-8     2011.67      10530.10     5.23x
BenchmarkReconstruct50x5x50000-8     4585.41      14301.60     3.12x
BenchmarkReconstruct10x2x1M-8        8081.15      28216.41     3.49x
BenchmarkReconstruct5x2x1M-8         5780.07      28015.37     4.85x
BenchmarkReconstruct10x4x1M-8        4352.56      14367.61     3.30x
BenchmarkReconstruct50x20x1M-8       1364.35      4189.79      3.07x
BenchmarkReconstruct10x4x16M-8       1484.35      5779.53      3.89x

The package will use GFNI instructions combined with AVX512 when these are available. This further improves speed by up to 3x over AVX2 code paths.

ARM64 NEON

By exploiting NEON instructions the performance for ARM has been accelerated. Below are the performance numbers for a single core on an EC2 m6g.16xlarge (Graviton2) instance (Amazon Linux 2):

BenchmarkGalois128K-64        119562     10028 ns/op        13070.78 MB/s
BenchmarkGalois1M-64           14380     83424 ns/op        12569.22 MB/s
BenchmarkGaloisXor128K-64      96508     12432 ns/op        10543.29 MB/s
BenchmarkGaloisXor1M-64        10000    100322 ns/op        10452.13 MB/s

Performance on ppc64le

The performance for ppc64le has been accelerated. This gives roughly a 10x performance improvement on this architecture as can be seen below:

benchmark                      old MB/s     new MB/s     speedup
BenchmarkGalois128K-160        948.87       8878.85      9.36x
BenchmarkGalois1M-160          968.85       9041.92      9.33x
BenchmarkGaloisXor128K-160     862.02       7905.00      9.17x
BenchmarkGaloisXor1M-160       784.60       6296.65      8.03x

Legal

None of section below is legal advice. Seek your own legal counsel. As stated by the LICENSE the authors will not be held reliable for any use of this library. Users are encouraged to independently verify they comply with all legal requirements.

As can be seen in recent news there has been lawsuits related to possible patents of aspects of erasure coding functionality.

As a possible mitigation it is possible to use the tag nopshufb when compiling any code which includes this package. This will remove all inclusion and use of PSHUFB and equivalent on other platforms.

This is done by adding -tags=nopshufb to go build and similar commands that produce binary output.

The removed code may not be infringing and even after -tags=nopshufb there may still be infringing code left.

Links

• Backblaze Open Sources Reed-Solomon Erasure Coding Source Code.
• JavaReedSolomon. Compatible java library by Backblaze.
• ocaml-reed-solomon-erasure. Compatible OCaml implementation.
• reedsolomon-c. C version, compatible with output from this package.
• Reed-Solomon Erasure Coding in Haskell. Haskell port of the package with similar performance.
• reed-solomon-erasure. Compatible Rust implementation.
• go-erasure. A similar library using cgo, slower in my tests.
• Screaming Fast Galois Field Arithmetic. Basis for SSE3 optimizations.
• Leopard-RS C library used as basis for GF16 implementation.
• reed-solomon-simd Leopard-RS Rust implementation.

License

This code, as the original JavaReedSolomon is published under an MIT license. See LICENSE file for more information.

Documentation

Overview

Package reedsolomon enables Erasure Coding in Go

For usage and examples, see https://github.com/klauspost/reedsolomon

Index

• Variables
• func AllocAligned(shards, each int) [][]byte
• func SetLog(filename string, stderr ...bool)
• type Encoder
  • func New(dataShards, parityShards int, opts ...Option) (Encoder, error)
• type Extensions
• type Option
  • func WithAVX2(enabled bool) Option
  • func WithAVX512(enabled bool) Option
  • func WithAVXGFNI(enabled bool) Option
  • func WithAutoGoroutines(shardSize int) Option
  • func WithCauchyMatrix() Option
  • func WithConcurrentStreamReads(enabled bool) Option
  • func WithConcurrentStreamWrites(enabled bool) Option
  • func WithConcurrentStreams(enabled bool) Option
  • func WithCustomMatrix(customMatrix [][]byte) Option
  • func WithFastOneParityMatrix() Option
  • func WithGFNI(enabled bool) Option
  • func WithInversionCache(enabled bool) Option
  • func WithJerasureMatrix() Option
  • func WithLeopardGF(enabled bool) Option
  • func WithLeopardGF16(enabled bool) Option
  • func WithMaxGoroutines(n int) Option
  • func WithMinSplitSize(n int) Option
  • func WithPAR1Matrix() Option
  • func WithSSE2(enabled bool) Option
  • func WithSSSE3(enabled bool) Option
  • func WithStreamBlockSize(n int) Option
• type StreamEncoder
  • func NewStream(dataShards, parityShards int, o ...Option) (StreamEncoder, error)
  • func NewStreamC(dataShards, parityShards int, conReads, conWrites bool, o ...Option) (StreamEncoder, error)
• type StreamEncoder16
  • func NewStream16(dataShards, parityShards int, opts ...Option) (StreamEncoder16, error)
• type StreamReadError
  • func (s StreamReadError) Error() string
  • func (s StreamReadError) String() string
• type StreamWriteError
  • func (s StreamWriteError) Error() string
  • func (s StreamWriteError) String() string

Examples

• Encoder
• Encoder (Slicing)
• Encoder (Xor)
• StreamEncoder

Variables

var ErrInvShardNum = errors.New("cannot create Encoder with less than one data shard or less than zero parity shards")

ErrInvShardNum will be returned by New, if you attempt to create an Encoder with less than one data shard or less than zero parity shards.

var ErrInvalidInput = errors.New("invalid input")

ErrInvalidInput is returned if invalid input parameter of Update.

var ErrInvalidShardSize = errors.New("invalid shard size")

ErrInvalidShardSize is returned if shard length doesn't meet the requirements, typically a multiple of N.

var ErrMaxShardNum = errors.New("cannot create Encoder with more than 256 data+parity shards")

ErrMaxShardNum will be returned by New, if you attempt to create an Encoder where data and parity shards are bigger than the order of GF(2^8).

var ErrNotSupported = errors.New("operation not supported")

ErrNotSupported is returned when an operation is not supported.

var ErrReconstructMismatch = errors.New("有效分片和填充分片是互斥的")

ErrReconstructMismatch 在StreamEncoder中返回,如果您在同一索引上提供了"valid"和"fill"流。 因此无法判断您是否认为该分片有效或希望重建它。

var ErrReconstructRequired = errors.New("reconstruction required as one or more required data shards are nil")

ErrReconstructRequired is returned if too few data shards are intact and a reconstruction is required before you can successfully join the shards.

var ErrShardNoData = errors.New("no shard data")

ErrShardNoData will be returned if there are no shards, or if the length of all shards is zero.

var ErrShardSize = errors.New("shard sizes do not match")

ErrShardSize is returned if shard length isn't the same for all shards.

var ErrShortData = errors.New("not enough data to fill the number of requested shards")

ErrShortData will be returned by Split(), if there isn't enough data to fill the number of shards.

var ErrTooFewShards = errors.New("too few shards given")

ErrTooFewShards is returned if too few shards where given to Encode/Verify/Reconstruct/Update. It will also be returned from Reconstruct if there were too few shards to reconstruct the missing data.

Functions

func AllocAligned

func AllocAligned(shards, each int) [][]byte

AllocAligned allocates 'shards' slices, with 'each' bytes. Each slice will start on a 64 byte aligned boundary.

func SetLog

func SetLog(filename string, stderr ...bool)

SetLog 设置日志配置 该方法允许自定义日志输出的文件路径和是否输出到标准错误 参数: - filename: 日志文件路径,指定日志输出的目标文件 - stderr: 可选参数,是否同时输出到标准错误,默认为false

Types

type Encoder

type Encoder interface {
	// Encode parity for a set of data shards.
	// Input is 'shards' containing data shards followed by parity shards.
	// The number of shards must match the number given to New().
	// Each shard is a byte array, and they must all be the same size.
	// The parity shards will always be overwritten and the data shards
	// will remain the same, so it is safe for you to read from the
	// data shards while this is running.
	Encode(shards [][]byte) error

	// EncodeIdx will add parity for a single data shard.
	// Parity shards should start out as 0. The caller must zero them.
	// Data shards must be delivered exactly once. There is no check for this.
	// The parity shards will always be updated and the data shards will remain the same.
	EncodeIdx(dataShard []byte, idx int, parity [][]byte) error

	// Verify returns true if the parity shards contain correct data.
	// The data is the same format as Encode. No data is modified, so
	// you are allowed to read from data while this is running.
	Verify(shards [][]byte) (bool, error)

	// Reconstruct will recreate the missing shards if possible.
	//
	// Given a list of shards, some of which contain data, fills in the
	// ones that don't have data.
	//
	// The length of the array must be equal to the total number of shards.
	// You indicate that a shard is missing by setting it to nil or zero-length.
	// If a shard is zero-length but has sufficient capacity, that memory will
	// be used, otherwise a new []byte will be allocated.
	//
	// If there are too few shards to reconstruct the missing
	// ones, ErrTooFewShards will be returned.
	//
	// The reconstructed shard set is complete, but integrity is not verified.
	// Use the Verify function to check if data set is ok.
	Reconstruct(shards [][]byte) error

	// ReconstructData will recreate any missing data shards, if possible.
	//
	// Given a list of shards, some of which contain data, fills in the
	// data shards that don't have data.
	//
	// The length of the array must be equal to Shards.
	// You indicate that a shard is missing by setting it to nil or zero-length.
	// If a shard is zero-length but has sufficient capacity, that memory will
	// be used, otherwise a new []byte will be allocated.
	//
	// If there are too few shards to reconstruct the missing
	// ones, ErrTooFewShards will be returned.
	//
	// As the reconstructed shard set may contain missing parity shards,
	// calling the Verify function is likely to fail.
	ReconstructData(shards [][]byte) error

	// ReconstructSome will recreate only requested shards, if possible.
	//
	// Given a list of shards, some of which contain data, fills in the
	// shards indicated by true values in the "required" parameter.
	// The length of the "required" array must be equal to either Shards or DataShards.
	// If the length is equal to DataShards, the reconstruction of parity shards will be ignored.
	//
	// The length of "shards" array must be equal to Shards.
	// You indicate that a shard is missing by setting it to nil or zero-length.
	// If a shard is zero-length but has sufficient capacity, that memory will
	// be used, otherwise a new []byte will be allocated.
	//
	// If there are too few shards to reconstruct the missing
	// ones, ErrTooFewShards will be returned.
	//
	// As the reconstructed shard set may contain missing parity shards,
	// calling the Verify function is likely to fail.
	ReconstructSome(shards [][]byte, required []bool) error

	// Update parity is use for change a few data shards and update it's parity.
	// Input 'newDatashards' containing data shards changed.
	// Input 'shards' containing old data shards (if data shard not changed, it can be nil) and old parity shards.
	// new parity shards will in shards[DataShards:]
	// Update is very useful if  DataShards much larger than ParityShards and changed data shards is few. It will
	// faster than Encode and not need read all data shards to encode.
	Update(shards [][]byte, newDatashards [][]byte) error

	// Split a data slice into the number of shards given to the encoder,
	// and create empty parity shards if necessary.
	//
	// The data will be split into equally sized shards.
	// If the data size isn't divisible by the number of shards,
	// the last shard will contain extra zeros.
	//
	// If there is extra capacity on the provided data slice
	// it will be used instead of allocating parity shards.
	// It will be zeroed out.
	//
	// There must be at least 1 byte otherwise ErrShortData will be
	// returned.
	//
	// The data will not be copied, except for the last shard, so you
	// should not modify the data of the input slice afterwards.
	Split(data []byte) ([][]byte, error)

	// Join the shards and write the data segment to dst.
	//
	// Only the data shards are considered.
	// You must supply the exact output size you want.
	// If there are to few shards given, ErrTooFewShards will be returned.
	// If the total data size is less than outSize, ErrShortData will be returned.
	Join(dst io.Writer, shards [][]byte, outSize int) error
}

Encoder is an interface to encode Reed-Salomon parity sets for your data.

Example

Simple example of how to use all functions of the Encoder. Note that all error checks have been removed to keep it short.

package main

import (
	"fmt"
	"math/rand"

	"github.com/bpfs/defs/v2/reedsolomon"
)

func fillRandom(p []byte) {
	for i := 0; i < len(p); i += 7 {
		val := rand.Int63()
		for j := 0; i+j < len(p) && j < 7; j++ {
			p[i+j] = byte(val)
			val >>= 8
		}
	}
}

func main() {
	// Create some sample data
	var data = make([]byte, 250000)
	fillRandom(data)

	// Create an encoder with 17 data and 3 parity slices.
	enc, _ := reedsolomon.New(17, 3)

	// Split the data into shards
	shards, _ := enc.Split(data)

	// Encode the parity set
	_ = enc.Encode(shards)

	// Verify the parity set
	ok, _ := enc.Verify(shards)
	if ok {
		fmt.Println("ok")
	}

	// Delete two shards
	shards[10], shards[11] = nil, nil

	// Reconstruct the shards
	_ = enc.Reconstruct(shards)

	// Verify the data set
	ok, _ = enc.Verify(shards)
	if ok {
		fmt.Println("ok")
	}
}

Output:

ok
ok

Example (Slicing)

This demonstrates that shards can be arbitrary sliced and merged and still remain valid.

package main

import (
	"fmt"
	"math/rand"

	"github.com/bpfs/defs/v2/reedsolomon"
)

func fillRandom(p []byte) {
	for i := 0; i < len(p); i += 7 {
		val := rand.Int63()
		for j := 0; i+j < len(p) && j < 7; j++ {
			p[i+j] = byte(val)
			val >>= 8
		}
	}
}

func main() {
	// Create some sample data
	var data = make([]byte, 250000)
	fillRandom(data)

	// Create 5 data slices of 50000 elements each
	enc, _ := reedsolomon.New(5, 3)
	shards, _ := enc.Split(data)
	err := enc.Encode(shards)
	if err != nil {
		panic(err)
	}

	// Check that it verifies
	ok, err := enc.Verify(shards)
	if ok && err == nil {
		fmt.Println("encode ok")
	}

	// Split the data set of 50000 elements into two of 25000
	splitA := make([][]byte, 8)
	splitB := make([][]byte, 8)

	// Merge into a 100000 element set
	merged := make([][]byte, 8)

	// Split/merge the shards
	for i := range shards {
		splitA[i] = shards[i][:25000]
		splitB[i] = shards[i][25000:]

		// Concencate it to itself
		merged[i] = append(make([]byte, 0, len(shards[i])*2), shards[i]...)
		merged[i] = append(merged[i], shards[i]...)
	}

	// Each part should still verify as ok.
	ok, err = enc.Verify(shards)
	if ok && err == nil {
		fmt.Println("splitA ok")
	}

	ok, err = enc.Verify(splitB)
	if ok && err == nil {
		fmt.Println("splitB ok")
	}

	ok, err = enc.Verify(merged)
	if ok && err == nil {
		fmt.Println("merge ok")
	}
}

Output:

encode ok
splitA ok
splitB ok
merge ok

Example (Xor)

This demonstrates that shards can xor'ed and still remain a valid set.

The xor value must be the same for element 'n' in each shard, except if you xor with a similar sized encoded shard set.

package main

import (
	"fmt"
	"math/rand"

	"github.com/bpfs/defs/v2/reedsolomon"
)

func fillRandom(p []byte) {
	for i := 0; i < len(p); i += 7 {
		val := rand.Int63()
		for j := 0; i+j < len(p) && j < 7; j++ {
			p[i+j] = byte(val)
			val >>= 8
		}
	}
}

func main() {
	// Create some sample data
	var data = make([]byte, 25000)
	fillRandom(data)

	// Create 5 data slices of 5000 elements each
	enc, _ := reedsolomon.New(5, 3)
	shards, _ := enc.Split(data)
	err := enc.Encode(shards)
	if err != nil {
		panic(err)
	}

	// Check that it verifies
	ok, err := enc.Verify(shards)
	if !ok || err != nil {
		fmt.Println("falied initial verify", err)
	}

	// Create an xor'ed set
	xored := make([][]byte, 8)

	// We xor by the index, so you can see that the xor can change,
	// It should however be constant vertically through your slices.
	for i := range shards {
		xored[i] = make([]byte, len(shards[i]))
		for j := range xored[i] {
			xored[i][j] = shards[i][j] ^ byte(j&0xff)
		}
	}

	// Each part should still verify as ok.
	ok, err = enc.Verify(xored)
	if ok && err == nil {
		fmt.Println("verified ok after xor")
	}
}

Output:

verified ok after xor

func New

func New(dataShards, parityShards int, opts ...Option) (Encoder, error)

New creates a new encoder and initializes it to the number of data shards and parity shards that you want to use. You can reuse this encoder. Note that the maximum number of total shards is 65536, with some restrictions for a total larger than 256:

• Shard sizes must be multiple of 64
• The methods Join/Split/Update/EncodeIdx are not supported

If no options are supplied, default options are used.

type Extensions

type Extensions interface {
	// ShardSizeMultiple will return the size the shard sizes must be a multiple of.
	ShardSizeMultiple() int

	// DataShards will return the number of data shards.
	DataShards() int

	// ParityShards will return the number of parity shards.
	ParityShards() int

	// TotalShards will return the total number of shards.
	TotalShards() int

	// AllocAligned will allocate TotalShards number of slices,
	// aligned to reasonable memory sizes.
	// Provide the size of each shard.
	AllocAligned(each int) [][]byte
}

Extensions is an optional interface. All returned instances will support this interface.

type Option

type Option func(*options)

Option allows to override processing parameters.

func WithAVX2

func WithAVX2(enabled bool) Option

WithAVX2 allows to enable/disable AVX2 instructions. If not set, AVX will be turned on or off automatically based on CPU ID information. This will also disable AVX GFNI instructions.

func WithAVX512

func WithAVX512(enabled bool) Option

WithAVX512 allows to enable/disable AVX512 (and GFNI) instructions.

func WithAVXGFNI

func WithAVXGFNI(enabled bool) Option

WithAVXGFNI allows to enable/disable GFNI with AVX instructions. If not set, GFNI will be turned on or off automatically based on CPU ID information.

func WithAutoGoroutines

func WithAutoGoroutines(shardSize int) Option

WithAutoGoroutines will adjust the number of goroutines for optimal speed with a specific shard size. Send in the shard size you expect to send. Other shard sizes will work, but may not run at the optimal speed. Overwrites WithMaxGoroutines. If shardSize <= 0, it is ignored.

func WithCauchyMatrix

func WithCauchyMatrix() Option

WithCauchyMatrix will make the encoder build a Cauchy style matrix. The output of this is not compatible with the standard output. A Cauchy matrix is faster to generate. This does not affect data throughput, but will result in slightly faster start-up time.

func WithConcurrentStreamReads

func WithConcurrentStreamReads(enabled bool) Option

WithConcurrentStreamReads will enable concurrent reads from the input streams. Default: Disabled, meaning only one stream will be read at the time. Ignored if not used on a stream input.

func WithConcurrentStreamWrites

func WithConcurrentStreamWrites(enabled bool) Option

WithConcurrentStreamWrites will enable concurrent writes to the the output streams. Default: Disabled, meaning only one stream will be written at the time. Ignored if not used on a stream input.

func WithConcurrentStreams

func WithConcurrentStreams(enabled bool) Option

WithConcurrentStreams will enable concurrent reads and writes on the streams. Default: Disabled, meaning only one stream will be read/written at the time. Ignored if not used on a stream input.

func WithCustomMatrix

func WithCustomMatrix(customMatrix [][]byte) Option

WithCustomMatrix causes the encoder to use the manually specified matrix. customMatrix represents only the parity chunks. customMatrix must have at least ParityShards rows and DataShards columns. It can be used for interoperability with libraries which generate the matrix differently or to implement more complex coding schemes like LRC (locally reconstructible codes).

func WithFastOneParityMatrix

func WithFastOneParityMatrix() Option

WithFastOneParityMatrix will switch the matrix to a simple xor if there is only one parity shard. The PAR1 matrix already has this property so it has little effect there.

func WithGFNI

func WithGFNI(enabled bool) Option

WithGFNI allows to enable/disable AVX512+GFNI instructions. If not set, GFNI will be turned on or off automatically based on CPU ID information.

func WithInversionCache

func WithInversionCache(enabled bool) Option

WithInversionCache allows to control the inversion cache. This will cache reconstruction matrices so they can be reused. Enabled by default, or <= 64 shards for Leopard encoding.

func WithJerasureMatrix

func WithJerasureMatrix() Option

WithJerasureMatrix causes the encoder to build the Reed-Solomon-Vandermonde matrix in the same way as done by the Jerasure library. The first row and column of the coding matrix only contains 1's in this method so the first parity chunk is always equal to XOR of all data chunks.

func WithLeopardGF

func WithLeopardGF(enabled bool) Option

WithLeopardGF will use leopard GF for encoding, even when there are fewer than 256 shards. This will likely improve reconstruction time for some setups. Note that Leopard places certain restrictions on use see other documentation.

func WithLeopardGF16

func WithLeopardGF16(enabled bool) Option

WithLeopardGF16 will always use leopard GF16 for encoding, even when there is less than 256 shards. This will likely improve reconstruction time for some setups. This is not compatible with Leopard output for <= 256 shards. Note that Leopard places certain restrictions on use see other documentation.

func WithMaxGoroutines

func WithMaxGoroutines(n int) Option

WithMaxGoroutines is the maximum number of goroutines number for encoding & decoding. Jobs will be split into this many parts, unless each goroutine would have to process less than minSplitSize bytes (set with WithMinSplitSize). For the best speed, keep this well above the GOMAXPROCS number for more fine grained scheduling. If n <= 0, it is ignored.

func WithMinSplitSize

func WithMinSplitSize(n int) Option

WithMinSplitSize is the minimum encoding size in bytes per goroutine. By default this parameter is determined by CPU cache characteristics. See WithMaxGoroutines on how jobs are split. If n <= 0, it is ignored.

func WithPAR1Matrix

func WithPAR1Matrix() Option

WithPAR1Matrix causes the encoder to build the matrix how PARv1 does. Note that the method they use is buggy, and may lead to cases where recovery is impossible, even if there are enough parity shards.

func WithSSE2

func WithSSE2(enabled bool) Option

WithSSE2 allows to enable/disable SSE2 instructions. If not set, SSE2 will be turned on or off automatically based on CPU ID information.

func WithSSSE3

func WithSSSE3(enabled bool) Option

WithSSSE3 allows to enable/disable SSSE3 instructions. If not set, SSSE3 will be turned on or off automatically based on CPU ID information.

func WithStreamBlockSize

func WithStreamBlockSize(n int) Option

WithStreamBlockSize allows to set a custom block size per round of reads/writes. If not set, any shard size set with WithAutoGoroutines will be used. If WithAutoGoroutines is also unset, 4MB will be used. Ignored if not used on stream.

type StreamEncoder

type StreamEncoder interface {
	// Encode 为一组数据分片生成奇偶校验分片。
	//
	// 输入'shards'包含数据分片的读取器,后跟奇偶校验分片的io.Writer。
	//
	// 分片数量必须与传给NewStream()的数量匹配。
	//
	// 每个读取器必须提供相同数量的字节。
	//
	// 奇偶校验分片将写入写入器。
	// 写入的字节数将与输入大小匹配。
	//
	// 如果数据流返回错误,将返回StreamReadError类型错误。如果奇偶校验写入器返回错误,将返回StreamWriteError。
	Encode(inputs []io.Reader, outputs []io.Writer) error

	// Verify 如果奇偶校验分片包含正确的数据则返回true。
	//
	// 分片数量必须与传给NewStream()的数据+奇偶校验分片总数匹配。
	//
	// 每个读取器必须提供相同数量的字节。
	// 如果分片流返回错误,将返回StreamReadError类型错误。
	Verify(shards []io.Reader) (bool, error)

	// Reconstruct 将在可能的情况下重建丢失的分片。
	//
	// 给定有效分片列表(用于读取)和无效分片列表(用于写入)
	//
	// 通过在'valid'切片中将其设置为nil并同时在"fill"中设置非nil写入器来指示分片丢失。
	// 一个索引不能同时包含非nil的'valid'和'fill'条目。
	// 如果两者都提供了,将返回'ErrReconstructMismatch'。
	//
	// 如果分片太少而无法重建丢失的分片,将返回ErrTooFewShards。
	//
	// 重建的分片集是完整的,但未验证完整性。
	// 使用Verify函数检查数据集是否正常。
	Reconstruct(inputs []io.Reader, outputs []io.Writer) error

	// Split 将输入流分割成给定给编码器的分片数。
	//
	// 数据将被分割成大小相等的分片。
	// 如果数据大小不能被分片数整除,最后一个分片将包含额外的零。
	//
	// 您必须提供输入的总大小。
	// 如果无法检索指定的字节数,将返回'ErrShortData'。
	Split(data io.Reader, dst []io.Writer, size int64) error

	// Join 将分片连接起来并将数据段写入dst。
	//
	// 只考虑数据分片。
	//
	// 您必须提供想要的确切输出大小。
	// 如果给定的分片太少,将返回ErrTooFewShards。
	// 如果总数据大小小于outSize,将返回ErrShortData。
	Join(dst io.Writer, shards []io.Reader, outSize int64) error
}

StreamEncoder 是一个用于对数据进行Reed-Solomon奇偶校验编码的接口。 它提供了完整的流式接口,并以最大4MB的块处理数据。

对于10MB及以下的小分片大小,建议使用内存接口,因为流式接口有启动开销。

对于所有操作,读取器和写入器不应假定任何单个读/写的顺序/大小。

使用示例请参见examples文件夹中的"stream-encoder.go"和"streamdecoder.go"。

Example

This will show a simple stream encoder where we encode from a []io.Reader which contain a reader for each shard.

Input and output can be exchanged with files, network streams or what may suit your needs.

package main

import (
	"bytes"
	"fmt"
	"io"
	"log"
	"math/rand"

	"github.com/bpfs/defs/v2/reedsolomon"
)

func fillRandom(p []byte) {
	for i := 0; i < len(p); i += 7 {
		val := rand.Int63()
		for j := 0; i+j < len(p) && j < 7; j++ {
			p[i+j] = byte(val)
			val >>= 8
		}
	}
}

func main() {
	dataShards := 5
	parityShards := 2

	// Create a StreamEncoder with the number of data andparity shards.
	rs, err := reedsolomon.NewStream(dataShards, parityShards)
	if err != nil {
		log.Fatal(err)
	}

	shardSize := 50000

	// Create input data shards.
	input := make([][]byte, dataShards)
	for s := range input {
		input[s] = make([]byte, shardSize)
		fillRandom(input[s])
	}

	// Convert our buffers to io.Readers
	readers := make([]io.Reader, dataShards)
	for i := range readers {
		readers[i] = io.Reader(bytes.NewBuffer(input[i]))
	}

	// Create our output io.Writers
	out := make([]io.Writer, parityShards)
	for i := range out {
		out[i] = io.Discard
	}

	// Encode from input to output.
	err = rs.Encode(readers, out)
	if err != nil {
		log.Fatal(err)
	}

	fmt.Println("ok")
}

Output:

ok

func NewStream

func NewStream(dataShards, parityShards int, o ...Option) (StreamEncoder, error)

NewStream 创建一个新的编码器并将其初始化为您想要使用的数据分片和奇偶校验分片的数量。您可以重用此编码器。 注意数据分片的最大数量是256。 参数: - dataShards: int 数据分片数量 - parityShards: int 奇偶校验分片数量 - o: 可选参数,可以传递WithConcurrentStreamReads(true)和WithConcurrentStreamWrites(true)来启用并发读取和写入。 返回: - StreamEncoder: 流式编码器 - error: 错误

func NewStreamC

func NewStreamC(dataShards, parityShards int, conReads, conWrites bool, o ...Option) (StreamEncoder, error)

NewStreamC 创建一个新的编码器并将其初始化为给定的数据分片和奇偶校验分片数量。

此函数与'NewStream'功能相同,但允许您启用并发读取和写入。

参数: - dataShards: int 数据分片数量 - parityShards: int 奇偶校验分片数量 - conReads: bool 是否启用并发读取 - conWrites: bool 是否启用并发写入 - o: 可选参数,可以传递WithConcurrentStreamReads(true)和WithConcurrentStreamWrites(true)来启用并发读取和写入。

type StreamEncoder16

type StreamEncoder16 interface {
	// Encode 为一组数据分片生成奇偶校验分片
	Encode(inputs []io.Reader, outputs []io.Writer) error

	// Verify 验证奇偶校验分片的正确性
	Verify(shards []io.Reader) (bool, error)

	// Reconstruct 重建丢失的分片
	Reconstruct(inputs []io.Reader, outputs []io.Writer) error

	// Split 将输入流分割成多个分片
	Split(data io.Reader, dst []io.Writer, size int64) error
}

StreamEncoder16 是一个基于GF(2^16)的Reed-Solomon编码器接口

func NewStream16

func NewStream16(dataShards, parityShards int, opts ...Option) (StreamEncoder16, error)

NewStream16 创建一个新的GF(2^16) Reed-Solomon流式编码器 参数: - dataShards: 数据分片数量 - parityShards: 奇偶校验分片数量 - opts: 可选参数 返回: - StreamEncoder16: 新的流式编码器 - error: 如果发生错误,返回错误信息

type StreamReadError

type StreamReadError struct {
	Err    error // 错误
	Stream int   // 发生错误的流编号
}

StreamReadError 在遇到与提供的流相关的读取错误时返回。 这将让您知道哪个读取器失败了。

func (StreamReadError) Error

func (s StreamReadError) Error() string

Error 以字符串形式返回错误

返回: - string: 错误字符串

func (StreamReadError) String

func (s StreamReadError) String() string

String 以字符串形式返回错误

返回: - string: 错误字符串

type StreamWriteError

type StreamWriteError struct {
	Err    error // 错误
	Stream int   // 发生错误的流编号
}

StreamWriteError 在遇到与提供的流相关的写入错误时返回。 这将让您知道哪个读取器失败了。

func (StreamWriteError) Error

func (s StreamWriteError) Error() string

Error 以字符串形式返回错误

返回: - string: 错误字符串

func (StreamWriteError) String

func (s StreamWriteError) String() string

String 以字符串形式返回错误

返回: - string: 错误字符串