xs/vendor/github.com/klauspost/reedsolomon/README.md

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.

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

Godoc: https://godoc.org/github.com/klauspost/reedsolomon

Installation

To get the package use the standard:

go get -u github.com/klauspost/reedsolomon

Changes

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. A good starting point is above 5 and below 257 data shards (the maximum supported number), and the number of parity shards to be 2 or above, and below the number of data shards.

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. The error will only be set if you specify 0 or negative values in any of the parameters, or if you specify more than 256 data shards.

The you send and receive data 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)
    }
    
    
  // 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)

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, _ := ioutil.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))

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 NewStreamC to ready an interface that reads/writes concurrently from the streams.

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.

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 and NewStreamC. If no Options are supplied, default options are used.

Example of how to supply options:

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

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 2 CPU cores are used for encoding.

Data	Parity	Parity	MB/s	SSSE3 MB/s	SSSE3 Speed	Rel. Speed
5	2	40%	576,11	2599,2	451%	100,00%
10	2	20%	587,73	3100,28	528%	102,02%
10	4	40%	298,38	2470,97	828%	51,79%
50	20	40%	59,81	713,28	1193%	10,38%

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.

Example of performance scaling on Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz - 4 physical cores, 8 logical cores. The example uses 10 blocks with 16MB data each and 4 parity blocks.

Threads	MB/s	Speed
1	1355,11	100%
2	2339,78	172%
4	3179,33	235%
8	4346,18	321%

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

Performance on AVX512

The performance on AVX512 has been accelerated for Intel CPUs. This gives speedups on a per-core basis of up to 4x compared to AVX2 as can be seen in the following table:

$ benchcmp avx2.txt avx512.txt
benchmark                      AVX2 MB/s    AVX512 MB/s   speedup
BenchmarkEncode8x8x1M-72       1681.35      4125.64       2.45x
BenchmarkEncode8x4x8M-72       1529.36      5507.97       3.60x
BenchmarkEncode8x8x8M-72        791.16      2952.29       3.73x
BenchmarkEncode8x8x32M-72       573.26      2168.61       3.78x
BenchmarkEncode12x4x12M-72     1234.41      4912.37       3.98x
BenchmarkEncode16x4x16M-72     1189.59      5138.01       4.32x
BenchmarkEncode24x8x24M-72      690.68      2583.70       3.74x
BenchmarkEncode24x8x48M-72      674.20      2643.31       3.92x

This speedup has been achieved by computing multiple parity blocks in parallel as opposed to one after the other. In doing so it is possible to minimize the memory bandwidth required for loading all data shards. At the same time the calculations are performed in the 512-bit wide ZMM registers and the surplus of ZMM registers (32 in total) is used to keep more data around (most notably the matrix coefficients).

Performance on ARM64 NEON

By exploiting NEON instructions the performance for ARM has been accelerated. Below are the performance numbers for a single core on an ARM Cortex-A53 CPU @ 1.2GHz (Debian 8.0 Jessie running Go: 1.7.4):

Data	Parity	Parity	ARM64 Go MB/s	ARM64 NEON MB/s	NEON Speed
5	2	40%	189	1304	588%
10	2	20%	188	1738	925%
10	4	40%	96	839	877%

Performance on ppc64le

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

asm2plan9s

asm2plan9s is used for assembling the AVX2 instructions into their BYTE/WORD/LONG equivalents.

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.

License

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