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update kcp-go package

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2019-03-17 17:09:54 +08:00
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# Compiled Object files, Static and Dynamic libs (Shared Objects)
*.o
*.a
*.so
# Folders
_obj
_test
# Architecture specific extensions/prefixes
*.[568vq]
[568vq].out
*.cgo1.go
*.cgo2.c
_cgo_defun.c
_cgo_gotypes.go
_cgo_export.*
_testmain.go
*.exe
*.test
*.prof
.idea

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language: go
sudo: false
os:
- linux
- osx
go:
- 1.9.x
- 1.10.x
- 1.11.x
- 1.12.x
- master
install:
- go get ./...
script:
- go vet ./...
- go test -v -cpu=1,2,4 .
- go test -v -cpu=1,2,4 -short -race .
- go test -tags=noasm -v -cpu=1,2,4 -short -race .
- go build examples/simple-decoder.go
- go build examples/simple-encoder.go
- go build examples/stream-decoder.go
- go build examples/stream-encoder.go
- diff <(gofmt -d .) <("")
matrix:
allow_failures:
- go: 'master'
fast_finish: true

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The MIT License (MIT)
Copyright (c) 2015 Klaus Post
Copyright (c) 2015 Backblaze
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# Reed-Solomon
[![GoDoc][1]][2] [![Build Status][3]][4]
[1]: https://godoc.org/github.com/klauspost/reedsolomon?status.svg
[2]: https://godoc.org/github.com/klauspost/reedsolomon
[3]: https://travis-ci.org/klauspost/reedsolomon.svg?branch=master
[4]: https://travis-ci.org/klauspost/reedsolomon
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](https://github.com/Backblaze/JavaReedSolomon) library released by [Backblaze](http://backblaze.com), with some additional optimizations.
For an introduction on erasure coding, see the post on the [Backblaze blog](https://www.backblaze.com/blog/reed-solomon/).
Package home: https://github.com/klauspost/reedsolomon
Godoc: https://godoc.org/github.com/klauspost/reedsolomon
# Installation
To get the package use the standard:
```bash
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](https://github.com/klauspost/reedsolomon#performance-on-avx512) 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](https://godoc.org/github.com/klauspost/reedsolomon#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](https://godoc.org/github.com/klauspost/reedsolomon#WithCauchyMatrix) is now an option. Thanks to [templexxx](https://github.com/templexxx) for the basis of this.
* Default maximum number of [goroutines](https://godoc.org/github.com/klauspost/reedsolomon#WithMaxGoroutines) 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()`](https://godoc.org/github.com/klauspost/reedsolomon#Encoder) now contains an `Update` function contributed by [chenzhongtao](https://github.com/chenzhongtao).
* [Frank Wessels](https://github.com/fwessels) kindly contributed ARM 64 bit assembly, which gives a huge performance boost on this platform.
## July 20, 2017
`ReconstructData` added to [`Encoder`](https://godoc.org/github.com/klauspost/reedsolomon#Encoder) interface. This can cause compatibility issues if you implement your own Encoder. A simple workaround can be added:
```Go
func (e *YourEnc) ReconstructData(shards [][]byte) error {
return ReconstructData(shards)
}
```
You can of course also do your own implementation. The [`StreamEncoder`](https://godoc.org/github.com/klauspost/reedsolomon#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](https://www.backblaze.com/blog/reed-solomon/).
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):
```Go
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.
```Go
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](https://github.com/edsrzf/mmap-go) to map files.
```Go
// 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.
```Go
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()`:
```Go
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()`:
```Go
// 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()`:
```Go
// 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](https://github.com/klauspost/reedsolomon/tree/master/examples).
# 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.
```Go
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:
```Go
// 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.
```Go
// 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`](https://godoc.org/github.com/klauspost/reedsolomon#NewStream) function to create the encoding/decoding interfaces. You can use [`NewStreamC`](https://godoc.org/github.com/klauspost/reedsolomon#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`](https://godoc.org/github.com/klauspost/reedsolomon#StreamReadError) or [`StreamWriteError`](https://godoc.org/github.com/klauspost/reedsolomon#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](https://github.com/klauspost/reedsolomon/tree/master/examples).
# 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:
```Go
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](https://github.com/fwessels/asm2plan9s) is used for assembling the AVX2 instructions into their BYTE/WORD/LONG equivalents.
# Links
* [Backblaze Open Sources Reed-Solomon Erasure Coding Source Code](https://www.backblaze.com/blog/reed-solomon/).
* [JavaReedSolomon](https://github.com/Backblaze/JavaReedSolomon). Compatible java library by Backblaze.
* [ocaml-reed-solomon-erasure](https://gitlab.com/darrenldl/ocaml-reed-solomon-erasure). Compatible OCaml implementation.
* [reedsolomon-c](https://github.com/jannson/reedsolomon-c). C version, compatible with output from this package.
* [Reed-Solomon Erasure Coding in Haskell](https://github.com/NicolasT/reedsolomon). Haskell port of the package with similar performance.
* [reed-solomon-erasure](https://github.com/darrenldl/reed-solomon-erasure). Compatible Rust implementation.
* [go-erasure](https://github.com/somethingnew2-0/go-erasure). A similar library using cgo, slower in my tests.
* [Screaming Fast Galois Field Arithmetic](http://www.snia.org/sites/default/files2/SDC2013/presentations/NewThinking/EthanMiller_Screaming_Fast_Galois_Field%20Arithmetic_SIMD%20Instructions.pdf). Basis for SSE3 optimizations.
# License
This code, as the original [JavaReedSolomon](https://github.com/Backblaze/JavaReedSolomon) is published under an MIT license. See LICENSE file for more information.

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os: Visual Studio 2015
platform: x64
clone_folder: c:\gopath\src\github.com\klauspost\reedsolomon
# environment variables
environment:
GOPATH: c:\gopath
install:
- echo %PATH%
- echo %GOPATH%
- go version
- go env
- go get -d ./...
build_script:
- go test -v -cpu=2 ./...
- go test -cpu=1,2,4 -short -race ./...

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/**
* 8-bit Galois Field
* Copyright 2015, Klaus Post
* Copyright 2015, Backblaze, Inc. All rights reserved.
*/
package reedsolomon
const (
// The number of elements in the field.
fieldSize = 256
// The polynomial used to generate the logarithm table.
//
// There are a number of polynomials that work to generate
// a Galois field of 256 elements. The choice is arbitrary,
// and we just use the first one.
//
// The possibilities are: 29, 43, 45, 77, 95, 99, 101, 105,
//* 113, 135, 141, 169, 195, 207, 231, and 245.
generatingPolynomial = 29
)
var logTable = [fieldSize]byte{
0, 0, 1, 25, 2, 50, 26, 198,
3, 223, 51, 238, 27, 104, 199, 75,
4, 100, 224, 14, 52, 141, 239, 129,
28, 193, 105, 248, 200, 8, 76, 113,
5, 138, 101, 47, 225, 36, 15, 33,
53, 147, 142, 218, 240, 18, 130, 69,
29, 181, 194, 125, 106, 39, 249, 185,
201, 154, 9, 120, 77, 228, 114, 166,
6, 191, 139, 98, 102, 221, 48, 253,
226, 152, 37, 179, 16, 145, 34, 136,
54, 208, 148, 206, 143, 150, 219, 189,
241, 210, 19, 92, 131, 56, 70, 64,
30, 66, 182, 163, 195, 72, 126, 110,
107, 58, 40, 84, 250, 133, 186, 61,
202, 94, 155, 159, 10, 21, 121, 43,
78, 212, 229, 172, 115, 243, 167, 87,
7, 112, 192, 247, 140, 128, 99, 13,
103, 74, 222, 237, 49, 197, 254, 24,
227, 165, 153, 119, 38, 184, 180, 124,
17, 68, 146, 217, 35, 32, 137, 46,
55, 63, 209, 91, 149, 188, 207, 205,
144, 135, 151, 178, 220, 252, 190, 97,
242, 86, 211, 171, 20, 42, 93, 158,
132, 60, 57, 83, 71, 109, 65, 162,
31, 45, 67, 216, 183, 123, 164, 118,
196, 23, 73, 236, 127, 12, 111, 246,
108, 161, 59, 82, 41, 157, 85, 170,
251, 96, 134, 177, 187, 204, 62, 90,
203, 89, 95, 176, 156, 169, 160, 81,
11, 245, 22, 235, 122, 117, 44, 215,
79, 174, 213, 233, 230, 231, 173, 232,
116, 214, 244, 234, 168, 80, 88, 175,
}
/**
* Inverse of the logarithm table. Maps integer logarithms
* to members of the field. There is no entry for 255
* because the highest log is 254.
*
* This table was generated by `go run gentables.go`
*/
var expTable = []byte{0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c, 0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c, 0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e}
func galAdd(a, b byte) byte {
return a ^ b
}
func galSub(a, b byte) byte {
return a ^ b
}
// Table from https://github.com/templexxx/reedsolomon
var invTable = [256]byte{0x0, 0x1, 0x8e, 0xf4, 0x47, 0xa7, 0x7a, 0xba, 0xad, 0x9d, 0xdd, 0x98, 0x3d, 0xaa, 0x5d, 0x96, 0xd8, 0x72, 0xc0, 0x58, 0xe0, 0x3e, 0x4c, 0x66, 0x90, 0xde, 0x55, 0x80, 0xa0, 0x83, 0x4b, 0x2a, 0x6c, 0xed, 0x39, 0x51, 0x60, 0x56, 0x2c, 0x8a, 0x70, 0xd0, 0x1f, 0x4a, 0x26, 0x8b, 0x33, 0x6e, 0x48, 0x89, 0x6f, 0x2e, 0xa4, 0xc3, 0x40, 0x5e, 0x50, 0x22, 0xcf, 0xa9, 0xab, 0xc, 0x15, 0xe1, 0x36, 0x5f, 0xf8, 0xd5, 0x92, 0x4e, 0xa6, 0x4, 0x30, 0x88, 0x2b, 0x1e, 0x16, 0x67, 0x45, 0x93, 0x38, 0x23, 0x68, 0x8c, 0x81, 0x1a, 0x25, 0x61, 0x13, 0xc1, 0xcb, 0x63, 0x97, 0xe, 0x37, 0x41, 0x24, 0x57, 0xca, 0x5b, 0xb9, 0xc4, 0x17, 0x4d, 0x52, 0x8d, 0xef, 0xb3, 0x20, 0xec, 0x2f, 0x32, 0x28, 0xd1, 0x11, 0xd9, 0xe9, 0xfb, 0xda, 0x79, 0xdb, 0x77, 0x6, 0xbb, 0x84, 0xcd, 0xfe, 0xfc, 0x1b, 0x54, 0xa1, 0x1d, 0x7c, 0xcc, 0xe4, 0xb0, 0x49, 0x31, 0x27, 0x2d, 0x53, 0x69, 0x2, 0xf5, 0x18, 0xdf, 0x44, 0x4f, 0x9b, 0xbc, 0xf, 0x5c, 0xb, 0xdc, 0xbd, 0x94, 0xac, 0x9, 0xc7, 0xa2, 0x1c, 0x82, 0x9f, 0xc6, 0x34, 0xc2, 0x46, 0x5, 0xce, 0x3b, 0xd, 0x3c, 0x9c, 0x8, 0xbe, 0xb7, 0x87, 0xe5, 0xee, 0x6b, 0xeb, 0xf2, 0xbf, 0xaf, 0xc5, 0x64, 0x7, 0x7b, 0x95, 0x9a, 0xae, 0xb6, 0x12, 0x59, 0xa5, 0x35, 0x65, 0xb8, 0xa3, 0x9e, 0xd2, 0xf7, 0x62, 0x5a, 0x85, 0x7d, 0xa8, 0x3a, 0x29, 0x71, 0xc8, 0xf6, 0xf9, 0x43, 0xd7, 0xd6, 0x10, 0x73, 0x76, 0x78, 0x99, 0xa, 0x19, 0x91, 0x14, 0x3f, 0xe6, 0xf0, 0x86, 0xb1, 0xe2, 0xf1, 0xfa, 0x74, 0xf3, 0xb4, 0x6d, 0x21, 0xb2, 0x6a, 0xe3, 0xe7, 0xb5, 0xea, 0x3, 0x8f, 0xd3, 0xc9, 0x42, 0xd4, 0xe8, 0x75, 0x7f, 0xff, 0x7e, 0xfd}
var mulTable = [256][256]uint8{[256]uint8{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},
{0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xa, 0xb, 0xc, 0xd, 0xe, 0xf, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f, 0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f, 0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f, 0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f, 0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f, 0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf, 0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf, 0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf, 0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf, 0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
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{0x0, 0xfe, 0xe1, 0x1f, 0xdf, 0x21, 0x3e, 0xc0, 0xa3, 0x5d, 0x42, 0xbc, 0x7c, 0x82, 0x9d, 0x63, 0x5b, 0xa5, 0xba, 0x44, 0x84, 0x7a, 0x65, 0x9b, 0xf8, 0x6, 0x19, 0xe7, 0x27, 0xd9, 0xc6, 0x38, 0xb6, 0x48, 0x57, 0xa9, 0x69, 0x97, 0x88, 0x76, 0x15, 0xeb, 0xf4, 0xa, 0xca, 0x34, 0x2b, 0xd5, 0xed, 0x13, 0xc, 0xf2, 0x32, 0xcc, 0xd3, 0x2d, 0x4e, 0xb0, 0xaf, 0x51, 0x91, 0x6f, 0x70, 0x8e, 0x71, 0x8f, 0x90, 0x6e, 0xae, 0x50, 0x4f, 0xb1, 0xd2, 0x2c, 0x33, 0xcd, 0xd, 0xf3, 0xec, 0x12, 0x2a, 0xd4, 0xcb, 0x35, 0xf5, 0xb, 0x14, 0xea, 0x89, 0x77, 0x68, 0x96, 0x56, 0xa8, 0xb7, 0x49, 0xc7, 0x39, 0x26, 0xd8, 0x18, 0xe6, 0xf9, 0x7, 0x64, 0x9a, 0x85, 0x7b, 0xbb, 0x45, 0x5a, 0xa4, 0x9c, 0x62, 0x7d, 0x83, 0x43, 0xbd, 0xa2, 0x5c, 0x3f, 0xc1, 0xde, 0x20, 0xe0, 0x1e, 0x1, 0xff, 0xe2, 0x1c, 0x3, 0xfd, 0x3d, 0xc3, 0xdc, 0x22, 0x41, 0xbf, 0xa0, 0x5e, 0x9e, 0x60, 0x7f, 0x81, 0xb9, 0x47, 0x58, 0xa6, 0x66, 0x98, 0x87, 0x79, 0x1a, 0xe4, 0xfb, 0x5, 0xc5, 0x3b, 0x24, 0xda, 0x54, 0xaa, 0xb5, 0x4b, 0x8b, 0x75, 0x6a, 0x94, 0xf7, 0x9, 0x16, 0xe8, 0x28, 0xd6, 0xc9, 0x37, 0xf, 0xf1, 0xee, 0x10, 0xd0, 0x2e, 0x31, 0xcf, 0xac, 0x52, 0x4d, 0xb3, 0x73, 0x8d, 0x92, 0x6c, 0x93, 0x6d, 0x72, 0x8c, 0x4c, 0xb2, 0xad, 0x53, 0x30, 0xce, 0xd1, 0x2f, 0xef, 0x11, 0xe, 0xf0, 0xc8, 0x36, 0x29, 0xd7, 0x17, 0xe9, 0xf6, 0x8, 0x6b, 0x95, 0x8a, 0x74, 0xb4, 0x4a, 0x55, 0xab, 0x25, 0xdb, 0xc4, 0x3a, 0xfa, 0x4, 0x1b, 0xe5, 0x86, 0x78, 0x67, 0x99, 0x59, 0xa7, 0xb8, 0x46, 0x7e, 0x80, 0x9f, 0x61, 0xa1, 0x5f, 0x40, 0xbe, 0xdd, 0x23, 0x3c, 0xc2, 0x2, 0xfc, 0xe3, 0x1d},
{0x0, 0xff, 0xe3, 0x1c, 0xdb, 0x24, 0x38, 0xc7, 0xab, 0x54, 0x48, 0xb7, 0x70, 0x8f, 0x93, 0x6c, 0x4b, 0xb4, 0xa8, 0x57, 0x90, 0x6f, 0x73, 0x8c, 0xe0, 0x1f, 0x3, 0xfc, 0x3b, 0xc4, 0xd8, 0x27, 0x96, 0x69, 0x75, 0x8a, 0x4d, 0xb2, 0xae, 0x51, 0x3d, 0xc2, 0xde, 0x21, 0xe6, 0x19, 0x5, 0xfa, 0xdd, 0x22, 0x3e, 0xc1, 0x6, 0xf9, 0xe5, 0x1a, 0x76, 0x89, 0x95, 0x6a, 0xad, 0x52, 0x4e, 0xb1, 0x31, 0xce, 0xd2, 0x2d, 0xea, 0x15, 0x9, 0xf6, 0x9a, 0x65, 0x79, 0x86, 0x41, 0xbe, 0xa2, 0x5d, 0x7a, 0x85, 0x99, 0x66, 0xa1, 0x5e, 0x42, 0xbd, 0xd1, 0x2e, 0x32, 0xcd, 0xa, 0xf5, 0xe9, 0x16, 0xa7, 0x58, 0x44, 0xbb, 0x7c, 0x83, 0x9f, 0x60, 0xc, 0xf3, 0xef, 0x10, 0xd7, 0x28, 0x34, 0xcb, 0xec, 0x13, 0xf, 0xf0, 0x37, 0xc8, 0xd4, 0x2b, 0x47, 0xb8, 0xa4, 0x5b, 0x9c, 0x63, 0x7f, 0x80, 0x62, 0x9d, 0x81, 0x7e, 0xb9, 0x46, 0x5a, 0xa5, 0xc9, 0x36, 0x2a, 0xd5, 0x12, 0xed, 0xf1, 0xe, 0x29, 0xd6, 0xca, 0x35, 0xf2, 0xd, 0x11, 0xee, 0x82, 0x7d, 0x61, 0x9e, 0x59, 0xa6, 0xba, 0x45, 0xf4, 0xb, 0x17, 0xe8, 0x2f, 0xd0, 0xcc, 0x33, 0x5f, 0xa0, 0xbc, 0x43, 0x84, 0x7b, 0x67, 0x98, 0xbf, 0x40, 0x5c, 0xa3, 0x64, 0x9b, 0x87, 0x78, 0x14, 0xeb, 0xf7, 0x8, 0xcf, 0x30, 0x2c, 0xd3, 0x53, 0xac, 0xb0, 0x4f, 0x88, 0x77, 0x6b, 0x94, 0xf8, 0x7, 0x1b, 0xe4, 0x23, 0xdc, 0xc0, 0x3f, 0x18, 0xe7, 0xfb, 0x4, 0xc3, 0x3c, 0x20, 0xdf, 0xb3, 0x4c, 0x50, 0xaf, 0x68, 0x97, 0x8b, 0x74, 0xc5, 0x3a, 0x26, 0xd9, 0x1e, 0xe1, 0xfd, 0x2, 0x6e, 0x91, 0x8d, 0x72, 0xb5, 0x4a, 0x56, 0xa9, 0x8e, 0x71, 0x6d, 0x92, 0x55, 0xaa, 0xb6, 0x49, 0x25, 0xda, 0xc6, 0x39, 0xfe, 0x1, 0x1d, 0xe2}}
var mulTableLow = [256][16]uint8{{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},
{0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xa, 0xb, 0xc, 0xd, 0xe, 0xf},
{0x0, 0x2, 0x4, 0x6, 0x8, 0xa, 0xc, 0xe, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e},
{0x0, 0x3, 0x6, 0x5, 0xc, 0xf, 0xa, 0x9, 0x18, 0x1b, 0x1e, 0x1d, 0x14, 0x17, 0x12, 0x11},
{0x0, 0x4, 0x8, 0xc, 0x10, 0x14, 0x18, 0x1c, 0x20, 0x24, 0x28, 0x2c, 0x30, 0x34, 0x38, 0x3c},
{0x0, 0x5, 0xa, 0xf, 0x14, 0x11, 0x1e, 0x1b, 0x28, 0x2d, 0x22, 0x27, 0x3c, 0x39, 0x36, 0x33},
{0x0, 0x6, 0xc, 0xa, 0x18, 0x1e, 0x14, 0x12, 0x30, 0x36, 0x3c, 0x3a, 0x28, 0x2e, 0x24, 0x22},
{0x0, 0x7, 0xe, 0x9, 0x1c, 0x1b, 0x12, 0x15, 0x38, 0x3f, 0x36, 0x31, 0x24, 0x23, 0x2a, 0x2d},
{0x0, 0x8, 0x10, 0x18, 0x20, 0x28, 0x30, 0x38, 0x40, 0x48, 0x50, 0x58, 0x60, 0x68, 0x70, 0x78},
{0x0, 0x9, 0x12, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48, 0x41, 0x5a, 0x53, 0x6c, 0x65, 0x7e, 0x77},
{0x0, 0xa, 0x14, 0x1e, 0x28, 0x22, 0x3c, 0x36, 0x50, 0x5a, 0x44, 0x4e, 0x78, 0x72, 0x6c, 0x66},
{0x0, 0xb, 0x16, 0x1d, 0x2c, 0x27, 0x3a, 0x31, 0x58, 0x53, 0x4e, 0x45, 0x74, 0x7f, 0x62, 0x69},
{0x0, 0xc, 0x18, 0x14, 0x30, 0x3c, 0x28, 0x24, 0x60, 0x6c, 0x78, 0x74, 0x50, 0x5c, 0x48, 0x44},
{0x0, 0xd, 0x1a, 0x17, 0x34, 0x39, 0x2e, 0x23, 0x68, 0x65, 0x72, 0x7f, 0x5c, 0x51, 0x46, 0x4b},
{0x0, 0xe, 0x1c, 0x12, 0x38, 0x36, 0x24, 0x2a, 0x70, 0x7e, 0x6c, 0x62, 0x48, 0x46, 0x54, 0x5a},
{0x0, 0xf, 0x1e, 0x11, 0x3c, 0x33, 0x22, 0x2d, 0x78, 0x77, 0x66, 0x69, 0x44, 0x4b, 0x5a, 0x55},
{0x0, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0},
{0x0, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77, 0x88, 0x99, 0xaa, 0xbb, 0xcc, 0xdd, 0xee, 0xff},
{0x0, 0x12, 0x24, 0x36, 0x48, 0x5a, 0x6c, 0x7e, 0x90, 0x82, 0xb4, 0xa6, 0xd8, 0xca, 0xfc, 0xee},
{0x0, 0x13, 0x26, 0x35, 0x4c, 0x5f, 0x6a, 0x79, 0x98, 0x8b, 0xbe, 0xad, 0xd4, 0xc7, 0xf2, 0xe1},
{0x0, 0x14, 0x28, 0x3c, 0x50, 0x44, 0x78, 0x6c, 0xa0, 0xb4, 0x88, 0x9c, 0xf0, 0xe4, 0xd8, 0xcc},
{0x0, 0x15, 0x2a, 0x3f, 0x54, 0x41, 0x7e, 0x6b, 0xa8, 0xbd, 0x82, 0x97, 0xfc, 0xe9, 0xd6, 0xc3},
{0x0, 0x16, 0x2c, 0x3a, 0x58, 0x4e, 0x74, 0x62, 0xb0, 0xa6, 0x9c, 0x8a, 0xe8, 0xfe, 0xc4, 0xd2},
{0x0, 0x17, 0x2e, 0x39, 0x5c, 0x4b, 0x72, 0x65, 0xb8, 0xaf, 0x96, 0x81, 0xe4, 0xf3, 0xca, 0xdd},
{0x0, 0x18, 0x30, 0x28, 0x60, 0x78, 0x50, 0x48, 0xc0, 0xd8, 0xf0, 0xe8, 0xa0, 0xb8, 0x90, 0x88},
{0x0, 0x19, 0x32, 0x2b, 0x64, 0x7d, 0x56, 0x4f, 0xc8, 0xd1, 0xfa, 0xe3, 0xac, 0xb5, 0x9e, 0x87},
{0x0, 0x1a, 0x34, 0x2e, 0x68, 0x72, 0x5c, 0x46, 0xd0, 0xca, 0xe4, 0xfe, 0xb8, 0xa2, 0x8c, 0x96},
{0x0, 0x1b, 0x36, 0x2d, 0x6c, 0x77, 0x5a, 0x41, 0xd8, 0xc3, 0xee, 0xf5, 0xb4, 0xaf, 0x82, 0x99},
{0x0, 0x1c, 0x38, 0x24, 0x70, 0x6c, 0x48, 0x54, 0xe0, 0xfc, 0xd8, 0xc4, 0x90, 0x8c, 0xa8, 0xb4},
{0x0, 0x1d, 0x3a, 0x27, 0x74, 0x69, 0x4e, 0x53, 0xe8, 0xf5, 0xd2, 0xcf, 0x9c, 0x81, 0xa6, 0xbb},
{0x0, 0x1e, 0x3c, 0x22, 0x78, 0x66, 0x44, 0x5a, 0xf0, 0xee, 0xcc, 0xd2, 0x88, 0x96, 0xb4, 0xaa},
{0x0, 0x1f, 0x3e, 0x21, 0x7c, 0x63, 0x42, 0x5d, 0xf8, 0xe7, 0xc6, 0xd9, 0x84, 0x9b, 0xba, 0xa5},
{0x0, 0x20, 0x40, 0x60, 0x80, 0xa0, 0xc0, 0xe0, 0x1d, 0x3d, 0x5d, 0x7d, 0x9d, 0xbd, 0xdd, 0xfd},
{0x0, 0x21, 0x42, 0x63, 0x84, 0xa5, 0xc6, 0xe7, 0x15, 0x34, 0x57, 0x76, 0x91, 0xb0, 0xd3, 0xf2},
{0x0, 0x22, 0x44, 0x66, 0x88, 0xaa, 0xcc, 0xee, 0xd, 0x2f, 0x49, 0x6b, 0x85, 0xa7, 0xc1, 0xe3},
{0x0, 0x23, 0x46, 0x65, 0x8c, 0xaf, 0xca, 0xe9, 0x5, 0x26, 0x43, 0x60, 0x89, 0xaa, 0xcf, 0xec},
{0x0, 0x24, 0x48, 0x6c, 0x90, 0xb4, 0xd8, 0xfc, 0x3d, 0x19, 0x75, 0x51, 0xad, 0x89, 0xe5, 0xc1},
{0x0, 0x25, 0x4a, 0x6f, 0x94, 0xb1, 0xde, 0xfb, 0x35, 0x10, 0x7f, 0x5a, 0xa1, 0x84, 0xeb, 0xce},
{0x0, 0x26, 0x4c, 0x6a, 0x98, 0xbe, 0xd4, 0xf2, 0x2d, 0xb, 0x61, 0x47, 0xb5, 0x93, 0xf9, 0xdf},
{0x0, 0x27, 0x4e, 0x69, 0x9c, 0xbb, 0xd2, 0xf5, 0x25, 0x2, 0x6b, 0x4c, 0xb9, 0x9e, 0xf7, 0xd0},
{0x0, 0x28, 0x50, 0x78, 0xa0, 0x88, 0xf0, 0xd8, 0x5d, 0x75, 0xd, 0x25, 0xfd, 0xd5, 0xad, 0x85},
{0x0, 0x29, 0x52, 0x7b, 0xa4, 0x8d, 0xf6, 0xdf, 0x55, 0x7c, 0x7, 0x2e, 0xf1, 0xd8, 0xa3, 0x8a},
{0x0, 0x2a, 0x54, 0x7e, 0xa8, 0x82, 0xfc, 0xd6, 0x4d, 0x67, 0x19, 0x33, 0xe5, 0xcf, 0xb1, 0x9b},
{0x0, 0x2b, 0x56, 0x7d, 0xac, 0x87, 0xfa, 0xd1, 0x45, 0x6e, 0x13, 0x38, 0xe9, 0xc2, 0xbf, 0x94},
{0x0, 0x2c, 0x58, 0x74, 0xb0, 0x9c, 0xe8, 0xc4, 0x7d, 0x51, 0x25, 0x9, 0xcd, 0xe1, 0x95, 0xb9},
{0x0, 0x2d, 0x5a, 0x77, 0xb4, 0x99, 0xee, 0xc3, 0x75, 0x58, 0x2f, 0x2, 0xc1, 0xec, 0x9b, 0xb6},
{0x0, 0x2e, 0x5c, 0x72, 0xb8, 0x96, 0xe4, 0xca, 0x6d, 0x43, 0x31, 0x1f, 0xd5, 0xfb, 0x89, 0xa7},
{0x0, 0x2f, 0x5e, 0x71, 0xbc, 0x93, 0xe2, 0xcd, 0x65, 0x4a, 0x3b, 0x14, 0xd9, 0xf6, 0x87, 0xa8},
{0x0, 0x30, 0x60, 0x50, 0xc0, 0xf0, 0xa0, 0x90, 0x9d, 0xad, 0xfd, 0xcd, 0x5d, 0x6d, 0x3d, 0xd},
{0x0, 0x31, 0x62, 0x53, 0xc4, 0xf5, 0xa6, 0x97, 0x95, 0xa4, 0xf7, 0xc6, 0x51, 0x60, 0x33, 0x2},
{0x0, 0x32, 0x64, 0x56, 0xc8, 0xfa, 0xac, 0x9e, 0x8d, 0xbf, 0xe9, 0xdb, 0x45, 0x77, 0x21, 0x13},
{0x0, 0x33, 0x66, 0x55, 0xcc, 0xff, 0xaa, 0x99, 0x85, 0xb6, 0xe3, 0xd0, 0x49, 0x7a, 0x2f, 0x1c},
{0x0, 0x34, 0x68, 0x5c, 0xd0, 0xe4, 0xb8, 0x8c, 0xbd, 0x89, 0xd5, 0xe1, 0x6d, 0x59, 0x5, 0x31},
{0x0, 0x35, 0x6a, 0x5f, 0xd4, 0xe1, 0xbe, 0x8b, 0xb5, 0x80, 0xdf, 0xea, 0x61, 0x54, 0xb, 0x3e},
{0x0, 0x36, 0x6c, 0x5a, 0xd8, 0xee, 0xb4, 0x82, 0xad, 0x9b, 0xc1, 0xf7, 0x75, 0x43, 0x19, 0x2f},
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{0x0, 0xa8, 0x4d, 0xe5, 0x9a, 0x32, 0xd7, 0x7f, 0x29, 0x81, 0x64, 0xcc, 0xb3, 0x1b, 0xfe, 0x56},
{0x0, 0xa9, 0x4f, 0xe6, 0x9e, 0x37, 0xd1, 0x78, 0x21, 0x88, 0x6e, 0xc7, 0xbf, 0x16, 0xf0, 0x59},
{0x0, 0xaa, 0x49, 0xe3, 0x92, 0x38, 0xdb, 0x71, 0x39, 0x93, 0x70, 0xda, 0xab, 0x1, 0xe2, 0x48},
{0x0, 0xab, 0x4b, 0xe0, 0x96, 0x3d, 0xdd, 0x76, 0x31, 0x9a, 0x7a, 0xd1, 0xa7, 0xc, 0xec, 0x47},
{0x0, 0xac, 0x45, 0xe9, 0x8a, 0x26, 0xcf, 0x63, 0x9, 0xa5, 0x4c, 0xe0, 0x83, 0x2f, 0xc6, 0x6a},
{0x0, 0xad, 0x47, 0xea, 0x8e, 0x23, 0xc9, 0x64, 0x1, 0xac, 0x46, 0xeb, 0x8f, 0x22, 0xc8, 0x65},
{0x0, 0xae, 0x41, 0xef, 0x82, 0x2c, 0xc3, 0x6d, 0x19, 0xb7, 0x58, 0xf6, 0x9b, 0x35, 0xda, 0x74},
{0x0, 0xaf, 0x43, 0xec, 0x86, 0x29, 0xc5, 0x6a, 0x11, 0xbe, 0x52, 0xfd, 0x97, 0x38, 0xd4, 0x7b},
{0x0, 0xb0, 0x7d, 0xcd, 0xfa, 0x4a, 0x87, 0x37, 0xe9, 0x59, 0x94, 0x24, 0x13, 0xa3, 0x6e, 0xde},
{0x0, 0xb1, 0x7f, 0xce, 0xfe, 0x4f, 0x81, 0x30, 0xe1, 0x50, 0x9e, 0x2f, 0x1f, 0xae, 0x60, 0xd1},
{0x0, 0xb2, 0x79, 0xcb, 0xf2, 0x40, 0x8b, 0x39, 0xf9, 0x4b, 0x80, 0x32, 0xb, 0xb9, 0x72, 0xc0},
{0x0, 0xb3, 0x7b, 0xc8, 0xf6, 0x45, 0x8d, 0x3e, 0xf1, 0x42, 0x8a, 0x39, 0x7, 0xb4, 0x7c, 0xcf},
{0x0, 0xb4, 0x75, 0xc1, 0xea, 0x5e, 0x9f, 0x2b, 0xc9, 0x7d, 0xbc, 0x8, 0x23, 0x97, 0x56, 0xe2},
{0x0, 0xb5, 0x77, 0xc2, 0xee, 0x5b, 0x99, 0x2c, 0xc1, 0x74, 0xb6, 0x3, 0x2f, 0x9a, 0x58, 0xed},
{0x0, 0xb6, 0x71, 0xc7, 0xe2, 0x54, 0x93, 0x25, 0xd9, 0x6f, 0xa8, 0x1e, 0x3b, 0x8d, 0x4a, 0xfc},
{0x0, 0xb7, 0x73, 0xc4, 0xe6, 0x51, 0x95, 0x22, 0xd1, 0x66, 0xa2, 0x15, 0x37, 0x80, 0x44, 0xf3},
{0x0, 0xb8, 0x6d, 0xd5, 0xda, 0x62, 0xb7, 0xf, 0xa9, 0x11, 0xc4, 0x7c, 0x73, 0xcb, 0x1e, 0xa6},
{0x0, 0xb9, 0x6f, 0xd6, 0xde, 0x67, 0xb1, 0x8, 0xa1, 0x18, 0xce, 0x77, 0x7f, 0xc6, 0x10, 0xa9},
{0x0, 0xba, 0x69, 0xd3, 0xd2, 0x68, 0xbb, 0x1, 0xb9, 0x3, 0xd0, 0x6a, 0x6b, 0xd1, 0x2, 0xb8},
{0x0, 0xbb, 0x6b, 0xd0, 0xd6, 0x6d, 0xbd, 0x6, 0xb1, 0xa, 0xda, 0x61, 0x67, 0xdc, 0xc, 0xb7},
{0x0, 0xbc, 0x65, 0xd9, 0xca, 0x76, 0xaf, 0x13, 0x89, 0x35, 0xec, 0x50, 0x43, 0xff, 0x26, 0x9a},
{0x0, 0xbd, 0x67, 0xda, 0xce, 0x73, 0xa9, 0x14, 0x81, 0x3c, 0xe6, 0x5b, 0x4f, 0xf2, 0x28, 0x95},
{0x0, 0xbe, 0x61, 0xdf, 0xc2, 0x7c, 0xa3, 0x1d, 0x99, 0x27, 0xf8, 0x46, 0x5b, 0xe5, 0x3a, 0x84},
{0x0, 0xbf, 0x63, 0xdc, 0xc6, 0x79, 0xa5, 0x1a, 0x91, 0x2e, 0xf2, 0x4d, 0x57, 0xe8, 0x34, 0x8b},
{0x0, 0xc0, 0x9d, 0x5d, 0x27, 0xe7, 0xba, 0x7a, 0x4e, 0x8e, 0xd3, 0x13, 0x69, 0xa9, 0xf4, 0x34},
{0x0, 0xc1, 0x9f, 0x5e, 0x23, 0xe2, 0xbc, 0x7d, 0x46, 0x87, 0xd9, 0x18, 0x65, 0xa4, 0xfa, 0x3b},
{0x0, 0xc2, 0x99, 0x5b, 0x2f, 0xed, 0xb6, 0x74, 0x5e, 0x9c, 0xc7, 0x5, 0x71, 0xb3, 0xe8, 0x2a},
{0x0, 0xc3, 0x9b, 0x58, 0x2b, 0xe8, 0xb0, 0x73, 0x56, 0x95, 0xcd, 0xe, 0x7d, 0xbe, 0xe6, 0x25},
{0x0, 0xc4, 0x95, 0x51, 0x37, 0xf3, 0xa2, 0x66, 0x6e, 0xaa, 0xfb, 0x3f, 0x59, 0x9d, 0xcc, 0x8},
{0x0, 0xc5, 0x97, 0x52, 0x33, 0xf6, 0xa4, 0x61, 0x66, 0xa3, 0xf1, 0x34, 0x55, 0x90, 0xc2, 0x7},
{0x0, 0xc6, 0x91, 0x57, 0x3f, 0xf9, 0xae, 0x68, 0x7e, 0xb8, 0xef, 0x29, 0x41, 0x87, 0xd0, 0x16},
{0x0, 0xc7, 0x93, 0x54, 0x3b, 0xfc, 0xa8, 0x6f, 0x76, 0xb1, 0xe5, 0x22, 0x4d, 0x8a, 0xde, 0x19},
{0x0, 0xc8, 0x8d, 0x45, 0x7, 0xcf, 0x8a, 0x42, 0xe, 0xc6, 0x83, 0x4b, 0x9, 0xc1, 0x84, 0x4c},
{0x0, 0xc9, 0x8f, 0x46, 0x3, 0xca, 0x8c, 0x45, 0x6, 0xcf, 0x89, 0x40, 0x5, 0xcc, 0x8a, 0x43},
{0x0, 0xca, 0x89, 0x43, 0xf, 0xc5, 0x86, 0x4c, 0x1e, 0xd4, 0x97, 0x5d, 0x11, 0xdb, 0x98, 0x52},
{0x0, 0xcb, 0x8b, 0x40, 0xb, 0xc0, 0x80, 0x4b, 0x16, 0xdd, 0x9d, 0x56, 0x1d, 0xd6, 0x96, 0x5d},
{0x0, 0xcc, 0x85, 0x49, 0x17, 0xdb, 0x92, 0x5e, 0x2e, 0xe2, 0xab, 0x67, 0x39, 0xf5, 0xbc, 0x70},
{0x0, 0xcd, 0x87, 0x4a, 0x13, 0xde, 0x94, 0x59, 0x26, 0xeb, 0xa1, 0x6c, 0x35, 0xf8, 0xb2, 0x7f},
{0x0, 0xce, 0x81, 0x4f, 0x1f, 0xd1, 0x9e, 0x50, 0x3e, 0xf0, 0xbf, 0x71, 0x21, 0xef, 0xa0, 0x6e},
{0x0, 0xcf, 0x83, 0x4c, 0x1b, 0xd4, 0x98, 0x57, 0x36, 0xf9, 0xb5, 0x7a, 0x2d, 0xe2, 0xae, 0x61},
{0x0, 0xd0, 0xbd, 0x6d, 0x67, 0xb7, 0xda, 0xa, 0xce, 0x1e, 0x73, 0xa3, 0xa9, 0x79, 0x14, 0xc4},
{0x0, 0xd1, 0xbf, 0x6e, 0x63, 0xb2, 0xdc, 0xd, 0xc6, 0x17, 0x79, 0xa8, 0xa5, 0x74, 0x1a, 0xcb},
{0x0, 0xd2, 0xb9, 0x6b, 0x6f, 0xbd, 0xd6, 0x4, 0xde, 0xc, 0x67, 0xb5, 0xb1, 0x63, 0x8, 0xda},
{0x0, 0xd3, 0xbb, 0x68, 0x6b, 0xb8, 0xd0, 0x3, 0xd6, 0x5, 0x6d, 0xbe, 0xbd, 0x6e, 0x6, 0xd5},
{0x0, 0xd4, 0xb5, 0x61, 0x77, 0xa3, 0xc2, 0x16, 0xee, 0x3a, 0x5b, 0x8f, 0x99, 0x4d, 0x2c, 0xf8},
{0x0, 0xd5, 0xb7, 0x62, 0x73, 0xa6, 0xc4, 0x11, 0xe6, 0x33, 0x51, 0x84, 0x95, 0x40, 0x22, 0xf7},
{0x0, 0xd6, 0xb1, 0x67, 0x7f, 0xa9, 0xce, 0x18, 0xfe, 0x28, 0x4f, 0x99, 0x81, 0x57, 0x30, 0xe6},
{0x0, 0xd7, 0xb3, 0x64, 0x7b, 0xac, 0xc8, 0x1f, 0xf6, 0x21, 0x45, 0x92, 0x8d, 0x5a, 0x3e, 0xe9},
{0x0, 0xd8, 0xad, 0x75, 0x47, 0x9f, 0xea, 0x32, 0x8e, 0x56, 0x23, 0xfb, 0xc9, 0x11, 0x64, 0xbc},
{0x0, 0xd9, 0xaf, 0x76, 0x43, 0x9a, 0xec, 0x35, 0x86, 0x5f, 0x29, 0xf0, 0xc5, 0x1c, 0x6a, 0xb3},
{0x0, 0xda, 0xa9, 0x73, 0x4f, 0x95, 0xe6, 0x3c, 0x9e, 0x44, 0x37, 0xed, 0xd1, 0xb, 0x78, 0xa2},
{0x0, 0xdb, 0xab, 0x70, 0x4b, 0x90, 0xe0, 0x3b, 0x96, 0x4d, 0x3d, 0xe6, 0xdd, 0x6, 0x76, 0xad},
{0x0, 0xdc, 0xa5, 0x79, 0x57, 0x8b, 0xf2, 0x2e, 0xae, 0x72, 0xb, 0xd7, 0xf9, 0x25, 0x5c, 0x80},
{0x0, 0xdd, 0xa7, 0x7a, 0x53, 0x8e, 0xf4, 0x29, 0xa6, 0x7b, 0x1, 0xdc, 0xf5, 0x28, 0x52, 0x8f},
{0x0, 0xde, 0xa1, 0x7f, 0x5f, 0x81, 0xfe, 0x20, 0xbe, 0x60, 0x1f, 0xc1, 0xe1, 0x3f, 0x40, 0x9e},
{0x0, 0xdf, 0xa3, 0x7c, 0x5b, 0x84, 0xf8, 0x27, 0xb6, 0x69, 0x15, 0xca, 0xed, 0x32, 0x4e, 0x91},
{0x0, 0xe0, 0xdd, 0x3d, 0xa7, 0x47, 0x7a, 0x9a, 0x53, 0xb3, 0x8e, 0x6e, 0xf4, 0x14, 0x29, 0xc9},
{0x0, 0xe1, 0xdf, 0x3e, 0xa3, 0x42, 0x7c, 0x9d, 0x5b, 0xba, 0x84, 0x65, 0xf8, 0x19, 0x27, 0xc6},
{0x0, 0xe2, 0xd9, 0x3b, 0xaf, 0x4d, 0x76, 0x94, 0x43, 0xa1, 0x9a, 0x78, 0xec, 0xe, 0x35, 0xd7},
{0x0, 0xe3, 0xdb, 0x38, 0xab, 0x48, 0x70, 0x93, 0x4b, 0xa8, 0x90, 0x73, 0xe0, 0x3, 0x3b, 0xd8},
{0x0, 0xe4, 0xd5, 0x31, 0xb7, 0x53, 0x62, 0x86, 0x73, 0x97, 0xa6, 0x42, 0xc4, 0x20, 0x11, 0xf5},
{0x0, 0xe5, 0xd7, 0x32, 0xb3, 0x56, 0x64, 0x81, 0x7b, 0x9e, 0xac, 0x49, 0xc8, 0x2d, 0x1f, 0xfa},
{0x0, 0xe6, 0xd1, 0x37, 0xbf, 0x59, 0x6e, 0x88, 0x63, 0x85, 0xb2, 0x54, 0xdc, 0x3a, 0xd, 0xeb},
{0x0, 0xe7, 0xd3, 0x34, 0xbb, 0x5c, 0x68, 0x8f, 0x6b, 0x8c, 0xb8, 0x5f, 0xd0, 0x37, 0x3, 0xe4},
{0x0, 0xe8, 0xcd, 0x25, 0x87, 0x6f, 0x4a, 0xa2, 0x13, 0xfb, 0xde, 0x36, 0x94, 0x7c, 0x59, 0xb1},
{0x0, 0xe9, 0xcf, 0x26, 0x83, 0x6a, 0x4c, 0xa5, 0x1b, 0xf2, 0xd4, 0x3d, 0x98, 0x71, 0x57, 0xbe},
{0x0, 0xea, 0xc9, 0x23, 0x8f, 0x65, 0x46, 0xac, 0x3, 0xe9, 0xca, 0x20, 0x8c, 0x66, 0x45, 0xaf},
{0x0, 0xeb, 0xcb, 0x20, 0x8b, 0x60, 0x40, 0xab, 0xb, 0xe0, 0xc0, 0x2b, 0x80, 0x6b, 0x4b, 0xa0},
{0x0, 0xec, 0xc5, 0x29, 0x97, 0x7b, 0x52, 0xbe, 0x33, 0xdf, 0xf6, 0x1a, 0xa4, 0x48, 0x61, 0x8d},
{0x0, 0xed, 0xc7, 0x2a, 0x93, 0x7e, 0x54, 0xb9, 0x3b, 0xd6, 0xfc, 0x11, 0xa8, 0x45, 0x6f, 0x82},
{0x0, 0xee, 0xc1, 0x2f, 0x9f, 0x71, 0x5e, 0xb0, 0x23, 0xcd, 0xe2, 0xc, 0xbc, 0x52, 0x7d, 0x93},
{0x0, 0xef, 0xc3, 0x2c, 0x9b, 0x74, 0x58, 0xb7, 0x2b, 0xc4, 0xe8, 0x7, 0xb0, 0x5f, 0x73, 0x9c},
{0x0, 0xf0, 0xfd, 0xd, 0xe7, 0x17, 0x1a, 0xea, 0xd3, 0x23, 0x2e, 0xde, 0x34, 0xc4, 0xc9, 0x39},
{0x0, 0xf1, 0xff, 0xe, 0xe3, 0x12, 0x1c, 0xed, 0xdb, 0x2a, 0x24, 0xd5, 0x38, 0xc9, 0xc7, 0x36},
{0x0, 0xf2, 0xf9, 0xb, 0xef, 0x1d, 0x16, 0xe4, 0xc3, 0x31, 0x3a, 0xc8, 0x2c, 0xde, 0xd5, 0x27},
{0x0, 0xf3, 0xfb, 0x8, 0xeb, 0x18, 0x10, 0xe3, 0xcb, 0x38, 0x30, 0xc3, 0x20, 0xd3, 0xdb, 0x28},
{0x0, 0xf4, 0xf5, 0x1, 0xf7, 0x3, 0x2, 0xf6, 0xf3, 0x7, 0x6, 0xf2, 0x4, 0xf0, 0xf1, 0x5},
{0x0, 0xf5, 0xf7, 0x2, 0xf3, 0x6, 0x4, 0xf1, 0xfb, 0xe, 0xc, 0xf9, 0x8, 0xfd, 0xff, 0xa},
{0x0, 0xf6, 0xf1, 0x7, 0xff, 0x9, 0xe, 0xf8, 0xe3, 0x15, 0x12, 0xe4, 0x1c, 0xea, 0xed, 0x1b},
{0x0, 0xf7, 0xf3, 0x4, 0xfb, 0xc, 0x8, 0xff, 0xeb, 0x1c, 0x18, 0xef, 0x10, 0xe7, 0xe3, 0x14},
{0x0, 0xf8, 0xed, 0x15, 0xc7, 0x3f, 0x2a, 0xd2, 0x93, 0x6b, 0x7e, 0x86, 0x54, 0xac, 0xb9, 0x41},
{0x0, 0xf9, 0xef, 0x16, 0xc3, 0x3a, 0x2c, 0xd5, 0x9b, 0x62, 0x74, 0x8d, 0x58, 0xa1, 0xb7, 0x4e},
{0x0, 0xfa, 0xe9, 0x13, 0xcf, 0x35, 0x26, 0xdc, 0x83, 0x79, 0x6a, 0x90, 0x4c, 0xb6, 0xa5, 0x5f},
{0x0, 0xfb, 0xeb, 0x10, 0xcb, 0x30, 0x20, 0xdb, 0x8b, 0x70, 0x60, 0x9b, 0x40, 0xbb, 0xab, 0x50},
{0x0, 0xfc, 0xe5, 0x19, 0xd7, 0x2b, 0x32, 0xce, 0xb3, 0x4f, 0x56, 0xaa, 0x64, 0x98, 0x81, 0x7d},
{0x0, 0xfd, 0xe7, 0x1a, 0xd3, 0x2e, 0x34, 0xc9, 0xbb, 0x46, 0x5c, 0xa1, 0x68, 0x95, 0x8f, 0x72},
{0x0, 0xfe, 0xe1, 0x1f, 0xdf, 0x21, 0x3e, 0xc0, 0xa3, 0x5d, 0x42, 0xbc, 0x7c, 0x82, 0x9d, 0x63},
{0x0, 0xff, 0xe3, 0x1c, 0xdb, 0x24, 0x38, 0xc7, 0xab, 0x54, 0x48, 0xb7, 0x70, 0x8f, 0x93, 0x6c}}
var mulTableHigh = [256][16]uint8{{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},
{0x0, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0},
{0x0, 0x20, 0x40, 0x60, 0x80, 0xa0, 0xc0, 0xe0, 0x1d, 0x3d, 0x5d, 0x7d, 0x9d, 0xbd, 0xdd, 0xfd},
{0x0, 0x30, 0x60, 0x50, 0xc0, 0xf0, 0xa0, 0x90, 0x9d, 0xad, 0xfd, 0xcd, 0x5d, 0x6d, 0x3d, 0xd},
{0x0, 0x40, 0x80, 0xc0, 0x1d, 0x5d, 0x9d, 0xdd, 0x3a, 0x7a, 0xba, 0xfa, 0x27, 0x67, 0xa7, 0xe7},
{0x0, 0x50, 0xa0, 0xf0, 0x5d, 0xd, 0xfd, 0xad, 0xba, 0xea, 0x1a, 0x4a, 0xe7, 0xb7, 0x47, 0x17},
{0x0, 0x60, 0xc0, 0xa0, 0x9d, 0xfd, 0x5d, 0x3d, 0x27, 0x47, 0xe7, 0x87, 0xba, 0xda, 0x7a, 0x1a},
{0x0, 0x70, 0xe0, 0x90, 0xdd, 0xad, 0x3d, 0x4d, 0xa7, 0xd7, 0x47, 0x37, 0x7a, 0xa, 0x9a, 0xea},
{0x0, 0x80, 0x1d, 0x9d, 0x3a, 0xba, 0x27, 0xa7, 0x74, 0xf4, 0x69, 0xe9, 0x4e, 0xce, 0x53, 0xd3},
{0x0, 0x90, 0x3d, 0xad, 0x7a, 0xea, 0x47, 0xd7, 0xf4, 0x64, 0xc9, 0x59, 0x8e, 0x1e, 0xb3, 0x23},
{0x0, 0xa0, 0x5d, 0xfd, 0xba, 0x1a, 0xe7, 0x47, 0x69, 0xc9, 0x34, 0x94, 0xd3, 0x73, 0x8e, 0x2e},
{0x0, 0xb0, 0x7d, 0xcd, 0xfa, 0x4a, 0x87, 0x37, 0xe9, 0x59, 0x94, 0x24, 0x13, 0xa3, 0x6e, 0xde},
{0x0, 0xc0, 0x9d, 0x5d, 0x27, 0xe7, 0xba, 0x7a, 0x4e, 0x8e, 0xd3, 0x13, 0x69, 0xa9, 0xf4, 0x34},
{0x0, 0xd0, 0xbd, 0x6d, 0x67, 0xb7, 0xda, 0xa, 0xce, 0x1e, 0x73, 0xa3, 0xa9, 0x79, 0x14, 0xc4},
{0x0, 0xe0, 0xdd, 0x3d, 0xa7, 0x47, 0x7a, 0x9a, 0x53, 0xb3, 0x8e, 0x6e, 0xf4, 0x14, 0x29, 0xc9},
{0x0, 0xf0, 0xfd, 0xd, 0xe7, 0x17, 0x1a, 0xea, 0xd3, 0x23, 0x2e, 0xde, 0x34, 0xc4, 0xc9, 0x39},
{0x0, 0x1d, 0x3a, 0x27, 0x74, 0x69, 0x4e, 0x53, 0xe8, 0xf5, 0xd2, 0xcf, 0x9c, 0x81, 0xa6, 0xbb},
{0x0, 0xd, 0x1a, 0x17, 0x34, 0x39, 0x2e, 0x23, 0x68, 0x65, 0x72, 0x7f, 0x5c, 0x51, 0x46, 0x4b},
{0x0, 0x3d, 0x7a, 0x47, 0xf4, 0xc9, 0x8e, 0xb3, 0xf5, 0xc8, 0x8f, 0xb2, 0x1, 0x3c, 0x7b, 0x46},
{0x0, 0x2d, 0x5a, 0x77, 0xb4, 0x99, 0xee, 0xc3, 0x75, 0x58, 0x2f, 0x2, 0xc1, 0xec, 0x9b, 0xb6},
{0x0, 0x5d, 0xba, 0xe7, 0x69, 0x34, 0xd3, 0x8e, 0xd2, 0x8f, 0x68, 0x35, 0xbb, 0xe6, 0x1, 0x5c},
{0x0, 0x4d, 0x9a, 0xd7, 0x29, 0x64, 0xb3, 0xfe, 0x52, 0x1f, 0xc8, 0x85, 0x7b, 0x36, 0xe1, 0xac},
{0x0, 0x7d, 0xfa, 0x87, 0xe9, 0x94, 0x13, 0x6e, 0xcf, 0xb2, 0x35, 0x48, 0x26, 0x5b, 0xdc, 0xa1},
{0x0, 0x6d, 0xda, 0xb7, 0xa9, 0xc4, 0x73, 0x1e, 0x4f, 0x22, 0x95, 0xf8, 0xe6, 0x8b, 0x3c, 0x51},
{0x0, 0x9d, 0x27, 0xba, 0x4e, 0xd3, 0x69, 0xf4, 0x9c, 0x1, 0xbb, 0x26, 0xd2, 0x4f, 0xf5, 0x68},
{0x0, 0x8d, 0x7, 0x8a, 0xe, 0x83, 0x9, 0x84, 0x1c, 0x91, 0x1b, 0x96, 0x12, 0x9f, 0x15, 0x98},
{0x0, 0xbd, 0x67, 0xda, 0xce, 0x73, 0xa9, 0x14, 0x81, 0x3c, 0xe6, 0x5b, 0x4f, 0xf2, 0x28, 0x95},
{0x0, 0xad, 0x47, 0xea, 0x8e, 0x23, 0xc9, 0x64, 0x1, 0xac, 0x46, 0xeb, 0x8f, 0x22, 0xc8, 0x65},
{0x0, 0xdd, 0xa7, 0x7a, 0x53, 0x8e, 0xf4, 0x29, 0xa6, 0x7b, 0x1, 0xdc, 0xf5, 0x28, 0x52, 0x8f},
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{0x0, 0x8, 0x10, 0x18, 0x20, 0x28, 0x30, 0x38, 0x40, 0x48, 0x50, 0x58, 0x60, 0x68, 0x70, 0x78},
{0x0, 0x18, 0x30, 0x28, 0x60, 0x78, 0x50, 0x48, 0xc0, 0xd8, 0xf0, 0xe8, 0xa0, 0xb8, 0x90, 0x88},
{0x0, 0xf5, 0xf7, 0x2, 0xf3, 0x6, 0x4, 0xf1, 0xfb, 0xe, 0xc, 0xf9, 0x8, 0xfd, 0xff, 0xa},
{0x0, 0xe5, 0xd7, 0x32, 0xb3, 0x56, 0x64, 0x81, 0x7b, 0x9e, 0xac, 0x49, 0xc8, 0x2d, 0x1f, 0xfa},
{0x0, 0xd5, 0xb7, 0x62, 0x73, 0xa6, 0xc4, 0x11, 0xe6, 0x33, 0x51, 0x84, 0x95, 0x40, 0x22, 0xf7},
{0x0, 0xc5, 0x97, 0x52, 0x33, 0xf6, 0xa4, 0x61, 0x66, 0xa3, 0xf1, 0x34, 0x55, 0x90, 0xc2, 0x7},
{0x0, 0xb5, 0x77, 0xc2, 0xee, 0x5b, 0x99, 0x2c, 0xc1, 0x74, 0xb6, 0x3, 0x2f, 0x9a, 0x58, 0xed},
{0x0, 0xa5, 0x57, 0xf2, 0xae, 0xb, 0xf9, 0x5c, 0x41, 0xe4, 0x16, 0xb3, 0xef, 0x4a, 0xb8, 0x1d},
{0x0, 0x95, 0x37, 0xa2, 0x6e, 0xfb, 0x59, 0xcc, 0xdc, 0x49, 0xeb, 0x7e, 0xb2, 0x27, 0x85, 0x10},
{0x0, 0x85, 0x17, 0x92, 0x2e, 0xab, 0x39, 0xbc, 0x5c, 0xd9, 0x4b, 0xce, 0x72, 0xf7, 0x65, 0xe0},
{0x0, 0x75, 0xea, 0x9f, 0xc9, 0xbc, 0x23, 0x56, 0x8f, 0xfa, 0x65, 0x10, 0x46, 0x33, 0xac, 0xd9},
{0x0, 0x65, 0xca, 0xaf, 0x89, 0xec, 0x43, 0x26, 0xf, 0x6a, 0xc5, 0xa0, 0x86, 0xe3, 0x4c, 0x29},
{0x0, 0x55, 0xaa, 0xff, 0x49, 0x1c, 0xe3, 0xb6, 0x92, 0xc7, 0x38, 0x6d, 0xdb, 0x8e, 0x71, 0x24},
{0x0, 0x45, 0x8a, 0xcf, 0x9, 0x4c, 0x83, 0xc6, 0x12, 0x57, 0x98, 0xdd, 0x1b, 0x5e, 0x91, 0xd4},
{0x0, 0x35, 0x6a, 0x5f, 0xd4, 0xe1, 0xbe, 0x8b, 0xb5, 0x80, 0xdf, 0xea, 0x61, 0x54, 0xb, 0x3e},
{0x0, 0x25, 0x4a, 0x6f, 0x94, 0xb1, 0xde, 0xfb, 0x35, 0x10, 0x7f, 0x5a, 0xa1, 0x84, 0xeb, 0xce},
{0x0, 0x15, 0x2a, 0x3f, 0x54, 0x41, 0x7e, 0x6b, 0xa8, 0xbd, 0x82, 0x97, 0xfc, 0xe9, 0xd6, 0xc3},
{0x0, 0x5, 0xa, 0xf, 0x14, 0x11, 0x1e, 0x1b, 0x28, 0x2d, 0x22, 0x27, 0x3c, 0x39, 0x36, 0x33},
{0x0, 0xd2, 0xb9, 0x6b, 0x6f, 0xbd, 0xd6, 0x4, 0xde, 0xc, 0x67, 0xb5, 0xb1, 0x63, 0x8, 0xda},
{0x0, 0xc2, 0x99, 0x5b, 0x2f, 0xed, 0xb6, 0x74, 0x5e, 0x9c, 0xc7, 0x5, 0x71, 0xb3, 0xe8, 0x2a},
{0x0, 0xf2, 0xf9, 0xb, 0xef, 0x1d, 0x16, 0xe4, 0xc3, 0x31, 0x3a, 0xc8, 0x2c, 0xde, 0xd5, 0x27},
{0x0, 0xe2, 0xd9, 0x3b, 0xaf, 0x4d, 0x76, 0x94, 0x43, 0xa1, 0x9a, 0x78, 0xec, 0xe, 0x35, 0xd7},
{0x0, 0x92, 0x39, 0xab, 0x72, 0xe0, 0x4b, 0xd9, 0xe4, 0x76, 0xdd, 0x4f, 0x96, 0x4, 0xaf, 0x3d},
{0x0, 0x82, 0x19, 0x9b, 0x32, 0xb0, 0x2b, 0xa9, 0x64, 0xe6, 0x7d, 0xff, 0x56, 0xd4, 0x4f, 0xcd},
{0x0, 0xb2, 0x79, 0xcb, 0xf2, 0x40, 0x8b, 0x39, 0xf9, 0x4b, 0x80, 0x32, 0xb, 0xb9, 0x72, 0xc0},
{0x0, 0xa2, 0x59, 0xfb, 0xb2, 0x10, 0xeb, 0x49, 0x79, 0xdb, 0x20, 0x82, 0xcb, 0x69, 0x92, 0x30},
{0x0, 0x52, 0xa4, 0xf6, 0x55, 0x7, 0xf1, 0xa3, 0xaa, 0xf8, 0xe, 0x5c, 0xff, 0xad, 0x5b, 0x9},
{0x0, 0x42, 0x84, 0xc6, 0x15, 0x57, 0x91, 0xd3, 0x2a, 0x68, 0xae, 0xec, 0x3f, 0x7d, 0xbb, 0xf9},
{0x0, 0x72, 0xe4, 0x96, 0xd5, 0xa7, 0x31, 0x43, 0xb7, 0xc5, 0x53, 0x21, 0x62, 0x10, 0x86, 0xf4},
{0x0, 0x62, 0xc4, 0xa6, 0x95, 0xf7, 0x51, 0x33, 0x37, 0x55, 0xf3, 0x91, 0xa2, 0xc0, 0x66, 0x4},
{0x0, 0x12, 0x24, 0x36, 0x48, 0x5a, 0x6c, 0x7e, 0x90, 0x82, 0xb4, 0xa6, 0xd8, 0xca, 0xfc, 0xee},
{0x0, 0x2, 0x4, 0x6, 0x8, 0xa, 0xc, 0xe, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e},
{0x0, 0x32, 0x64, 0x56, 0xc8, 0xfa, 0xac, 0x9e, 0x8d, 0xbf, 0xe9, 0xdb, 0x45, 0x77, 0x21, 0x13},
{0x0, 0x22, 0x44, 0x66, 0x88, 0xaa, 0xcc, 0xee, 0xd, 0x2f, 0x49, 0x6b, 0x85, 0xa7, 0xc1, 0xe3},
{0x0, 0xcf, 0x83, 0x4c, 0x1b, 0xd4, 0x98, 0x57, 0x36, 0xf9, 0xb5, 0x7a, 0x2d, 0xe2, 0xae, 0x61},
{0x0, 0xdf, 0xa3, 0x7c, 0x5b, 0x84, 0xf8, 0x27, 0xb6, 0x69, 0x15, 0xca, 0xed, 0x32, 0x4e, 0x91},
{0x0, 0xef, 0xc3, 0x2c, 0x9b, 0x74, 0x58, 0xb7, 0x2b, 0xc4, 0xe8, 0x7, 0xb0, 0x5f, 0x73, 0x9c},
{0x0, 0xff, 0xe3, 0x1c, 0xdb, 0x24, 0x38, 0xc7, 0xab, 0x54, 0x48, 0xb7, 0x70, 0x8f, 0x93, 0x6c},
{0x0, 0x8f, 0x3, 0x8c, 0x6, 0x89, 0x5, 0x8a, 0xc, 0x83, 0xf, 0x80, 0xa, 0x85, 0x9, 0x86},
{0x0, 0x9f, 0x23, 0xbc, 0x46, 0xd9, 0x65, 0xfa, 0x8c, 0x13, 0xaf, 0x30, 0xca, 0x55, 0xe9, 0x76},
{0x0, 0xaf, 0x43, 0xec, 0x86, 0x29, 0xc5, 0x6a, 0x11, 0xbe, 0x52, 0xfd, 0x97, 0x38, 0xd4, 0x7b},
{0x0, 0xbf, 0x63, 0xdc, 0xc6, 0x79, 0xa5, 0x1a, 0x91, 0x2e, 0xf2, 0x4d, 0x57, 0xe8, 0x34, 0x8b},
{0x0, 0x4f, 0x9e, 0xd1, 0x21, 0x6e, 0xbf, 0xf0, 0x42, 0xd, 0xdc, 0x93, 0x63, 0x2c, 0xfd, 0xb2},
{0x0, 0x5f, 0xbe, 0xe1, 0x61, 0x3e, 0xdf, 0x80, 0xc2, 0x9d, 0x7c, 0x23, 0xa3, 0xfc, 0x1d, 0x42},
{0x0, 0x6f, 0xde, 0xb1, 0xa1, 0xce, 0x7f, 0x10, 0x5f, 0x30, 0x81, 0xee, 0xfe, 0x91, 0x20, 0x4f},
{0x0, 0x7f, 0xfe, 0x81, 0xe1, 0x9e, 0x1f, 0x60, 0xdf, 0xa0, 0x21, 0x5e, 0x3e, 0x41, 0xc0, 0xbf},
{0x0, 0xf, 0x1e, 0x11, 0x3c, 0x33, 0x22, 0x2d, 0x78, 0x77, 0x66, 0x69, 0x44, 0x4b, 0x5a, 0x55},
{0x0, 0x1f, 0x3e, 0x21, 0x7c, 0x63, 0x42, 0x5d, 0xf8, 0xe7, 0xc6, 0xd9, 0x84, 0x9b, 0xba, 0xa5},
{0x0, 0x2f, 0x5e, 0x71, 0xbc, 0x93, 0xe2, 0xcd, 0x65, 0x4a, 0x3b, 0x14, 0xd9, 0xf6, 0x87, 0xa8},
{0x0, 0x3f, 0x7e, 0x41, 0xfc, 0xc3, 0x82, 0xbd, 0xe5, 0xda, 0x9b, 0xa4, 0x19, 0x26, 0x67, 0x58},
{0x0, 0x9c, 0x25, 0xb9, 0x4a, 0xd6, 0x6f, 0xf3, 0x94, 0x8, 0xb1, 0x2d, 0xde, 0x42, 0xfb, 0x67},
{0x0, 0x8c, 0x5, 0x89, 0xa, 0x86, 0xf, 0x83, 0x14, 0x98, 0x11, 0x9d, 0x1e, 0x92, 0x1b, 0x97},
{0x0, 0xbc, 0x65, 0xd9, 0xca, 0x76, 0xaf, 0x13, 0x89, 0x35, 0xec, 0x50, 0x43, 0xff, 0x26, 0x9a},
{0x0, 0xac, 0x45, 0xe9, 0x8a, 0x26, 0xcf, 0x63, 0x9, 0xa5, 0x4c, 0xe0, 0x83, 0x2f, 0xc6, 0x6a},
{0x0, 0xdc, 0xa5, 0x79, 0x57, 0x8b, 0xf2, 0x2e, 0xae, 0x72, 0xb, 0xd7, 0xf9, 0x25, 0x5c, 0x80},
{0x0, 0xcc, 0x85, 0x49, 0x17, 0xdb, 0x92, 0x5e, 0x2e, 0xe2, 0xab, 0x67, 0x39, 0xf5, 0xbc, 0x70},
{0x0, 0xfc, 0xe5, 0x19, 0xd7, 0x2b, 0x32, 0xce, 0xb3, 0x4f, 0x56, 0xaa, 0x64, 0x98, 0x81, 0x7d},
{0x0, 0xec, 0xc5, 0x29, 0x97, 0x7b, 0x52, 0xbe, 0x33, 0xdf, 0xf6, 0x1a, 0xa4, 0x48, 0x61, 0x8d},
{0x0, 0x1c, 0x38, 0x24, 0x70, 0x6c, 0x48, 0x54, 0xe0, 0xfc, 0xd8, 0xc4, 0x90, 0x8c, 0xa8, 0xb4},
{0x0, 0xc, 0x18, 0x14, 0x30, 0x3c, 0x28, 0x24, 0x60, 0x6c, 0x78, 0x74, 0x50, 0x5c, 0x48, 0x44},
{0x0, 0x3c, 0x78, 0x44, 0xf0, 0xcc, 0x88, 0xb4, 0xfd, 0xc1, 0x85, 0xb9, 0xd, 0x31, 0x75, 0x49},
{0x0, 0x2c, 0x58, 0x74, 0xb0, 0x9c, 0xe8, 0xc4, 0x7d, 0x51, 0x25, 0x9, 0xcd, 0xe1, 0x95, 0xb9},
{0x0, 0x5c, 0xb8, 0xe4, 0x6d, 0x31, 0xd5, 0x89, 0xda, 0x86, 0x62, 0x3e, 0xb7, 0xeb, 0xf, 0x53},
{0x0, 0x4c, 0x98, 0xd4, 0x2d, 0x61, 0xb5, 0xf9, 0x5a, 0x16, 0xc2, 0x8e, 0x77, 0x3b, 0xef, 0xa3},
{0x0, 0x7c, 0xf8, 0x84, 0xed, 0x91, 0x15, 0x69, 0xc7, 0xbb, 0x3f, 0x43, 0x2a, 0x56, 0xd2, 0xae},
{0x0, 0x6c, 0xd8, 0xb4, 0xad, 0xc1, 0x75, 0x19, 0x47, 0x2b, 0x9f, 0xf3, 0xea, 0x86, 0x32, 0x5e},
{0x0, 0x81, 0x1f, 0x9e, 0x3e, 0xbf, 0x21, 0xa0, 0x7c, 0xfd, 0x63, 0xe2, 0x42, 0xc3, 0x5d, 0xdc},
{0x0, 0x91, 0x3f, 0xae, 0x7e, 0xef, 0x41, 0xd0, 0xfc, 0x6d, 0xc3, 0x52, 0x82, 0x13, 0xbd, 0x2c},
{0x0, 0xa1, 0x5f, 0xfe, 0xbe, 0x1f, 0xe1, 0x40, 0x61, 0xc0, 0x3e, 0x9f, 0xdf, 0x7e, 0x80, 0x21},
{0x0, 0xb1, 0x7f, 0xce, 0xfe, 0x4f, 0x81, 0x30, 0xe1, 0x50, 0x9e, 0x2f, 0x1f, 0xae, 0x60, 0xd1},
{0x0, 0xc1, 0x9f, 0x5e, 0x23, 0xe2, 0xbc, 0x7d, 0x46, 0x87, 0xd9, 0x18, 0x65, 0xa4, 0xfa, 0x3b},
{0x0, 0xd1, 0xbf, 0x6e, 0x63, 0xb2, 0xdc, 0xd, 0xc6, 0x17, 0x79, 0xa8, 0xa5, 0x74, 0x1a, 0xcb},
{0x0, 0xe1, 0xdf, 0x3e, 0xa3, 0x42, 0x7c, 0x9d, 0x5b, 0xba, 0x84, 0x65, 0xf8, 0x19, 0x27, 0xc6},
{0x0, 0xf1, 0xff, 0xe, 0xe3, 0x12, 0x1c, 0xed, 0xdb, 0x2a, 0x24, 0xd5, 0x38, 0xc9, 0xc7, 0x36},
{0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xa, 0xb, 0xc, 0xd, 0xe, 0xf},
{0x0, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77, 0x88, 0x99, 0xaa, 0xbb, 0xcc, 0xdd, 0xee, 0xff},
{0x0, 0x21, 0x42, 0x63, 0x84, 0xa5, 0xc6, 0xe7, 0x15, 0x34, 0x57, 0x76, 0x91, 0xb0, 0xd3, 0xf2},
{0x0, 0x31, 0x62, 0x53, 0xc4, 0xf5, 0xa6, 0x97, 0x95, 0xa4, 0xf7, 0xc6, 0x51, 0x60, 0x33, 0x2},
{0x0, 0x41, 0x82, 0xc3, 0x19, 0x58, 0x9b, 0xda, 0x32, 0x73, 0xb0, 0xf1, 0x2b, 0x6a, 0xa9, 0xe8},
{0x0, 0x51, 0xa2, 0xf3, 0x59, 0x8, 0xfb, 0xaa, 0xb2, 0xe3, 0x10, 0x41, 0xeb, 0xba, 0x49, 0x18},
{0x0, 0x61, 0xc2, 0xa3, 0x99, 0xf8, 0x5b, 0x3a, 0x2f, 0x4e, 0xed, 0x8c, 0xb6, 0xd7, 0x74, 0x15},
{0x0, 0x71, 0xe2, 0x93, 0xd9, 0xa8, 0x3b, 0x4a, 0xaf, 0xde, 0x4d, 0x3c, 0x76, 0x7, 0x94, 0xe5},
{0x0, 0xa6, 0x51, 0xf7, 0xa2, 0x4, 0xf3, 0x55, 0x59, 0xff, 0x8, 0xae, 0xfb, 0x5d, 0xaa, 0xc},
{0x0, 0xb6, 0x71, 0xc7, 0xe2, 0x54, 0x93, 0x25, 0xd9, 0x6f, 0xa8, 0x1e, 0x3b, 0x8d, 0x4a, 0xfc},
{0x0, 0x86, 0x11, 0x97, 0x22, 0xa4, 0x33, 0xb5, 0x44, 0xc2, 0x55, 0xd3, 0x66, 0xe0, 0x77, 0xf1},
{0x0, 0x96, 0x31, 0xa7, 0x62, 0xf4, 0x53, 0xc5, 0xc4, 0x52, 0xf5, 0x63, 0xa6, 0x30, 0x97, 0x1},
{0x0, 0xe6, 0xd1, 0x37, 0xbf, 0x59, 0x6e, 0x88, 0x63, 0x85, 0xb2, 0x54, 0xdc, 0x3a, 0xd, 0xeb},
{0x0, 0xf6, 0xf1, 0x7, 0xff, 0x9, 0xe, 0xf8, 0xe3, 0x15, 0x12, 0xe4, 0x1c, 0xea, 0xed, 0x1b},
{0x0, 0xc6, 0x91, 0x57, 0x3f, 0xf9, 0xae, 0x68, 0x7e, 0xb8, 0xef, 0x29, 0x41, 0x87, 0xd0, 0x16},
{0x0, 0xd6, 0xb1, 0x67, 0x7f, 0xa9, 0xce, 0x18, 0xfe, 0x28, 0x4f, 0x99, 0x81, 0x57, 0x30, 0xe6},
{0x0, 0x26, 0x4c, 0x6a, 0x98, 0xbe, 0xd4, 0xf2, 0x2d, 0xb, 0x61, 0x47, 0xb5, 0x93, 0xf9, 0xdf},
{0x0, 0x36, 0x6c, 0x5a, 0xd8, 0xee, 0xb4, 0x82, 0xad, 0x9b, 0xc1, 0xf7, 0x75, 0x43, 0x19, 0x2f},
{0x0, 0x6, 0xc, 0xa, 0x18, 0x1e, 0x14, 0x12, 0x30, 0x36, 0x3c, 0x3a, 0x28, 0x2e, 0x24, 0x22},
{0x0, 0x16, 0x2c, 0x3a, 0x58, 0x4e, 0x74, 0x62, 0xb0, 0xa6, 0x9c, 0x8a, 0xe8, 0xfe, 0xc4, 0xd2},
{0x0, 0x66, 0xcc, 0xaa, 0x85, 0xe3, 0x49, 0x2f, 0x17, 0x71, 0xdb, 0xbd, 0x92, 0xf4, 0x5e, 0x38},
{0x0, 0x76, 0xec, 0x9a, 0xc5, 0xb3, 0x29, 0x5f, 0x97, 0xe1, 0x7b, 0xd, 0x52, 0x24, 0xbe, 0xc8},
{0x0, 0x46, 0x8c, 0xca, 0x5, 0x43, 0x89, 0xcf, 0xa, 0x4c, 0x86, 0xc0, 0xf, 0x49, 0x83, 0xc5},
{0x0, 0x56, 0xac, 0xfa, 0x45, 0x13, 0xe9, 0xbf, 0x8a, 0xdc, 0x26, 0x70, 0xcf, 0x99, 0x63, 0x35},
{0x0, 0xbb, 0x6b, 0xd0, 0xd6, 0x6d, 0xbd, 0x6, 0xb1, 0xa, 0xda, 0x61, 0x67, 0xdc, 0xc, 0xb7},
{0x0, 0xab, 0x4b, 0xe0, 0x96, 0x3d, 0xdd, 0x76, 0x31, 0x9a, 0x7a, 0xd1, 0xa7, 0xc, 0xec, 0x47},
{0x0, 0x9b, 0x2b, 0xb0, 0x56, 0xcd, 0x7d, 0xe6, 0xac, 0x37, 0x87, 0x1c, 0xfa, 0x61, 0xd1, 0x4a},
{0x0, 0x8b, 0xb, 0x80, 0x16, 0x9d, 0x1d, 0x96, 0x2c, 0xa7, 0x27, 0xac, 0x3a, 0xb1, 0x31, 0xba},
{0x0, 0xfb, 0xeb, 0x10, 0xcb, 0x30, 0x20, 0xdb, 0x8b, 0x70, 0x60, 0x9b, 0x40, 0xbb, 0xab, 0x50},
{0x0, 0xeb, 0xcb, 0x20, 0x8b, 0x60, 0x40, 0xab, 0xb, 0xe0, 0xc0, 0x2b, 0x80, 0x6b, 0x4b, 0xa0},
{0x0, 0xdb, 0xab, 0x70, 0x4b, 0x90, 0xe0, 0x3b, 0x96, 0x4d, 0x3d, 0xe6, 0xdd, 0x6, 0x76, 0xad},
{0x0, 0xcb, 0x8b, 0x40, 0xb, 0xc0, 0x80, 0x4b, 0x16, 0xdd, 0x9d, 0x56, 0x1d, 0xd6, 0x96, 0x5d},
{0x0, 0x3b, 0x76, 0x4d, 0xec, 0xd7, 0x9a, 0xa1, 0xc5, 0xfe, 0xb3, 0x88, 0x29, 0x12, 0x5f, 0x64},
{0x0, 0x2b, 0x56, 0x7d, 0xac, 0x87, 0xfa, 0xd1, 0x45, 0x6e, 0x13, 0x38, 0xe9, 0xc2, 0xbf, 0x94},
{0x0, 0x1b, 0x36, 0x2d, 0x6c, 0x77, 0x5a, 0x41, 0xd8, 0xc3, 0xee, 0xf5, 0xb4, 0xaf, 0x82, 0x99},
{0x0, 0xb, 0x16, 0x1d, 0x2c, 0x27, 0x3a, 0x31, 0x58, 0x53, 0x4e, 0x45, 0x74, 0x7f, 0x62, 0x69},
{0x0, 0x7b, 0xf6, 0x8d, 0xf1, 0x8a, 0x7, 0x7c, 0xff, 0x84, 0x9, 0x72, 0xe, 0x75, 0xf8, 0x83},
{0x0, 0x6b, 0xd6, 0xbd, 0xb1, 0xda, 0x67, 0xc, 0x7f, 0x14, 0xa9, 0xc2, 0xce, 0xa5, 0x18, 0x73},
{0x0, 0x5b, 0xb6, 0xed, 0x71, 0x2a, 0xc7, 0x9c, 0xe2, 0xb9, 0x54, 0xf, 0x93, 0xc8, 0x25, 0x7e},
{0x0, 0x4b, 0x96, 0xdd, 0x31, 0x7a, 0xa7, 0xec, 0x62, 0x29, 0xf4, 0xbf, 0x53, 0x18, 0xc5, 0x8e}}
// galMultiply multiplies to elements of the field.
// Uses lookup table ~40% faster
func galMultiply(a, b byte) byte {
return mulTable[a][b]
}
// Original function:
/*
// galMultiply multiplies to elements of the field.
func galMultiply(a, b byte) byte {
if a == 0 || b == 0 {
return 0
}
logA := int(logTable[a])
logB := int(logTable[b])
return expTable[logA+logB]
}
*/
// galDivide is inverse of galMultiply.
func galDivide(a, b byte) byte {
if a == 0 {
return 0
}
if b == 0 {
panic("Argument 'divisor' is 0")
}
logA := int(logTable[a])
logB := int(logTable[b])
logResult := logA - logB
if logResult < 0 {
logResult += 255
}
return expTable[logResult]
}
// Computes a**n.
//
// The result will be the same as multiplying a times itself n times.
func galExp(a byte, n int) byte {
if n == 0 {
return 1
}
if a == 0 {
return 0
}
logA := logTable[a]
logResult := int(logA) * n
for logResult >= 255 {
logResult -= 255
}
return byte(expTable[logResult])
}

184
vendor/github.com/klauspost/reedsolomon/galoisAvx512_amd64.go generated vendored Normal file
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@@ -0,0 +1,184 @@
//+build !noasm
//+build !appengine
//+build !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2019, Minio, Inc.
package reedsolomon
//go:noescape
func _galMulAVX512Parallel82(in, out [][]byte, matrix *[matrixSize82]byte, addTo bool)
//go:noescape
func _galMulAVX512Parallel84(in, out [][]byte, matrix *[matrixSize84]byte, addTo bool)
const (
dimIn = 8 // Number of input rows processed simultaneously
dimOut82 = 2 // Number of output rows processed simultaneously for x2 routine
dimOut84 = 4 // Number of output rows processed simultaneously for x4 routine
matrixSize82 = (16 + 16) * dimIn * dimOut82 // Dimension of slice of matrix coefficient passed into x2 routine
matrixSize84 = (16 + 16) * dimIn * dimOut84 // Dimension of slice of matrix coefficient passed into x4 routine
)
// Construct block of matrix coefficients for 2 outputs rows in parallel
func setupMatrix82(matrixRows [][]byte, inputOffset, outputOffset int, matrix *[matrixSize82]byte) {
offset := 0
for c := inputOffset; c < inputOffset+dimIn; c++ {
for iRow := outputOffset; iRow < outputOffset+dimOut82; iRow++ {
if c < len(matrixRows[iRow]) {
coeff := matrixRows[iRow][c]
copy(matrix[offset*32:], mulTableLow[coeff][:])
copy(matrix[offset*32+16:], mulTableHigh[coeff][:])
} else {
// coefficients not used for this input shard (so null out)
v := matrix[offset*32 : offset*32+32]
for i := range v {
v[i] = 0
}
}
offset += dimIn
if offset >= dimIn*dimOut82 {
offset -= dimIn*dimOut82 - 1
}
}
}
}
// Construct block of matrix coefficients for 4 outputs rows in parallel
func setupMatrix84(matrixRows [][]byte, inputOffset, outputOffset int, matrix *[matrixSize84]byte) {
offset := 0
for c := inputOffset; c < inputOffset+dimIn; c++ {
for iRow := outputOffset; iRow < outputOffset+dimOut84; iRow++ {
if c < len(matrixRows[iRow]) {
coeff := matrixRows[iRow][c]
copy(matrix[offset*32:], mulTableLow[coeff][:])
copy(matrix[offset*32+16:], mulTableHigh[coeff][:])
} else {
// coefficients not used for this input shard (so null out)
v := matrix[offset*32 : offset*32+32]
for i := range v {
v[i] = 0
}
}
offset += dimIn
if offset >= dimIn*dimOut84 {
offset -= dimIn*dimOut84 - 1
}
}
}
}
// Invoke AVX512 routine for 2 output rows in parallel
func galMulAVX512Parallel82(in, out [][]byte, matrixRows [][]byte, inputOffset, outputOffset int) {
done := len(in[0])
if done == 0 {
return
}
inputEnd := inputOffset + dimIn
if inputEnd > len(in) {
inputEnd = len(in)
}
outputEnd := outputOffset + dimOut82
if outputEnd > len(out) {
outputEnd = len(out)
}
matrix82 := [matrixSize82]byte{}
setupMatrix82(matrixRows, inputOffset, outputOffset, &matrix82)
addTo := inputOffset != 0 // Except for the first input column, add to previous results
_galMulAVX512Parallel82(in[inputOffset:inputEnd], out[outputOffset:outputEnd], &matrix82, addTo)
done = (done >> 6) << 6
if len(in[0])-done == 0 {
return
}
for c := inputOffset; c < inputOffset+dimIn; c++ {
for iRow := outputOffset; iRow < outputOffset+dimOut82; iRow++ {
if c < len(matrixRows[iRow]) {
mt := mulTable[matrixRows[iRow][c]][:256]
for i := done; i < len(in[0]); i++ {
if c == 0 { // only set value for first input column
out[iRow][i] = mt[in[c][i]]
} else { // and add for all others
out[iRow][i] ^= mt[in[c][i]]
}
}
}
}
}
}
// Invoke AVX512 routine for 4 output rows in parallel
func galMulAVX512Parallel84(in, out [][]byte, matrixRows [][]byte, inputOffset, outputOffset int) {
done := len(in[0])
if done == 0 {
return
}
inputEnd := inputOffset + dimIn
if inputEnd > len(in) {
inputEnd = len(in)
}
outputEnd := outputOffset + dimOut84
if outputEnd > len(out) {
outputEnd = len(out)
}
matrix84 := [matrixSize84]byte{}
setupMatrix84(matrixRows, inputOffset, outputOffset, &matrix84)
addTo := inputOffset != 0 // Except for the first input column, add to previous results
_galMulAVX512Parallel84(in[inputOffset:inputEnd], out[outputOffset:outputEnd], &matrix84, addTo)
done = (done >> 6) << 6
if len(in[0])-done == 0 {
return
}
for c := inputOffset; c < inputOffset+dimIn; c++ {
for iRow := outputOffset; iRow < outputOffset+dimOut84; iRow++ {
if c < len(matrixRows[iRow]) {
mt := mulTable[matrixRows[iRow][c]][:256]
for i := done; i < len(in[0]); i++ {
if c == 0 { // only set value for first input column
out[iRow][i] = mt[in[c][i]]
} else { // and add for all others
out[iRow][i] ^= mt[in[c][i]]
}
}
}
}
}
}
// Perform the same as codeSomeShards, but taking advantage of
// AVX512 parallelism for up to 4x faster execution as compared to AVX2
func (r reedSolomon) codeSomeShardsAvx512(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
outputRow := 0
// First process (multiple) batches of 4 output rows in parallel
for ; outputRow+dimOut84 <= len(outputs); outputRow += dimOut84 {
for inputRow := 0; inputRow < len(inputs); inputRow += dimIn {
galMulAVX512Parallel84(inputs, outputs, matrixRows, inputRow, outputRow)
}
}
// Then process a (single) batch of 2 output rows in parallel
if outputRow+dimOut82 <= len(outputs) {
// fmt.Println(outputRow, len(outputs))
for inputRow := 0; inputRow < len(inputs); inputRow += dimIn {
galMulAVX512Parallel82(inputs, outputs, matrixRows, inputRow, outputRow)
}
outputRow += dimOut82
}
// Lastly, we may have a single output row left (for uneven parity)
if outputRow < len(outputs) {
for c := 0; c < r.DataShards; c++ {
if c == 0 {
galMulSlice(matrixRows[outputRow][c], inputs[c], outputs[outputRow], &r.o)
} else {
galMulSliceXor(matrixRows[outputRow][c], inputs[c], outputs[outputRow], &r.o)
}
}
}
}

590
vendor/github.com/klauspost/reedsolomon/galoisAvx512_amd64.s generated vendored Normal file
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@@ -0,0 +1,590 @@
//+build !noasm !appengine !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2019, Minio, Inc.
//
// Process 2 output rows in parallel from a total of 8 input rows
//
// func _galMulAVX512Parallel82(in, out [][]byte, matrix *[matrixSize82]byte, addTo bool)
TEXT ·_galMulAVX512Parallel82(SB), 7, $0
MOVQ in+0(FP), SI //
MOVQ 8(SI), R9 // R9: len(in)
SHRQ $6, R9 // len(in) / 64
TESTQ R9, R9
JZ done_avx512_parallel82
MOVQ matrix+48(FP), SI
LONG $0x48fee162; WORD $0x066f // VMOVDQU64 ZMM16, 0x000[rsi]
LONG $0x48fee162; WORD $0x4e6f; BYTE $0x01 // VMOVDQU64 ZMM17, 0x040[rsi]
LONG $0x48fee162; WORD $0x566f; BYTE $0x02 // VMOVDQU64 ZMM18, 0x080[rsi]
LONG $0x48fee162; WORD $0x5e6f; BYTE $0x03 // VMOVDQU64 ZMM19, 0x0c0[rsi]
LONG $0x48fee162; WORD $0x666f; BYTE $0x04 // VMOVDQU64 ZMM20, 0x100[rsi]
LONG $0x48fee162; WORD $0x6e6f; BYTE $0x05 // VMOVDQU64 ZMM21, 0x140[rsi]
LONG $0x48fee162; WORD $0x766f; BYTE $0x06 // VMOVDQU64 ZMM22, 0x180[rsi]
LONG $0x48fee162; WORD $0x7e6f; BYTE $0x07 // VMOVDQU64 ZMM23, 0x1c0[rsi]
MOVQ $15, BX
MOVQ BX, X5
LONG $0x487df262; WORD $0xd578 // VPBROADCASTB ZMM2, XMM5
MOVB addTo+56(FP), AX
LONG $0xffc0c749; WORD $0xffff; BYTE $0xff // mov r8, -1
WORD $0xf749; BYTE $0xe0 // mul r8
LONG $0x92fbe1c4; BYTE $0xc8 // kmovq k1, rax
MOVQ in+0(FP), SI // SI: &in
MOVQ in_len+8(FP), AX // number of inputs
XORQ R11, R11
MOVQ out+24(FP), DX
MOVQ 24(DX), CX // CX: &out[1][0]
MOVQ (DX), DX // DX: &out[0][0]
loopback_avx512_parallel82:
LONG $0xc9fef162; WORD $0x226f // VMOVDQU64 ZMM4{k1}{z}, [rdx]
LONG $0xc9fef162; WORD $0x296f // VMOVDQU64 ZMM5{k1}{z}, [rcx]
MOVQ (SI), BX // BX: &in[0][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40fd3362; WORD $0xf043; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM16, ZMM16, 0x00
LONG $0x40fd3362; WORD $0xf843; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM16, ZMM16, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40dd3362; WORD $0xe443; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM20, ZMM20, 0x00
LONG $0x40dd3362; WORD $0xec43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM20, ZMM20, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $1
JE skip_avx512_parallel82
MOVQ 24(SI), BX // BX: &in[1][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40fd3362; WORD $0xf043; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM16, ZMM16, 0xaa
LONG $0x40fd3362; WORD $0xf843; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM16, ZMM16, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40dd3362; WORD $0xe443; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM20, ZMM20, 0xaa
LONG $0x40dd3362; WORD $0xec43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM20, ZMM20, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $2
JE skip_avx512_parallel82
MOVQ 48(SI), BX // BX: &in[2][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40f53362; WORD $0xf143; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM17, ZMM17, 0x00
LONG $0x40f53362; WORD $0xf943; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM17, ZMM17, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40d53362; WORD $0xe543; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM21, ZMM21, 0x00
LONG $0x40d53362; WORD $0xed43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM21, ZMM21, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $3
JE skip_avx512_parallel82
MOVQ 72(SI), BX // BX: &in[3][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40f53362; WORD $0xf143; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM17, ZMM17, 0xaa
LONG $0x40f53362; WORD $0xf943; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM17, ZMM17, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40d53362; WORD $0xe543; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM21, ZMM21, 0xaa
LONG $0x40d53362; WORD $0xed43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM21, ZMM21, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $4
JE skip_avx512_parallel82
MOVQ 96(SI), BX // BX: &in[4][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40ed3362; WORD $0xf243; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM18, ZMM18, 0x00
LONG $0x40ed3362; WORD $0xfa43; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM18, ZMM18, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40cd3362; WORD $0xe643; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM22, ZMM22, 0x00
LONG $0x40cd3362; WORD $0xee43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM22, ZMM22, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $5
JE skip_avx512_parallel82
MOVQ 120(SI), BX // BX: &in[5][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40ed3362; WORD $0xf243; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM18, ZMM18, 0xaa
LONG $0x40ed3362; WORD $0xfa43; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM18, ZMM18, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40cd3362; WORD $0xe643; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM22, ZMM22, 0xaa
LONG $0x40cd3362; WORD $0xee43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM22, ZMM22, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $6
JE skip_avx512_parallel82
MOVQ 144(SI), BX // BX: &in[6][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40e53362; WORD $0xf343; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM19, ZMM19, 0x00
LONG $0x40e53362; WORD $0xfb43; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM19, ZMM19, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40c53362; WORD $0xe743; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM23, ZMM23, 0x00
LONG $0x40c53362; WORD $0xef43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM23, ZMM23, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
CMPQ AX, $7
JE skip_avx512_parallel82
MOVQ 168(SI), BX // BX: &in[7][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40e53362; WORD $0xf343; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM19, ZMM19, 0xaa
LONG $0x40e53362; WORD $0xfb43; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM19, ZMM19, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40c53362; WORD $0xe743; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM23, ZMM23, 0xaa
LONG $0x40c53362; WORD $0xef43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM23, ZMM23, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
skip_avx512_parallel82:
LONG $0x48fef162; WORD $0x227f // VMOVDQU64 [rdx], ZMM4
LONG $0x48fef162; WORD $0x297f // VMOVDQU64 [rcx], ZMM5
ADDQ $64, R11 // in4+=64
ADDQ $64, DX // out+=64
ADDQ $64, CX // out2+=64
SUBQ $1, R9
JNZ loopback_avx512_parallel82
done_avx512_parallel82:
VZEROUPPER
RET
//
// Process 4 output rows in parallel from a total of 8 input rows
//
// func _galMulAVX512Parallel84(in, out [][]byte, matrix *[matrixSize84]byte, addTo bool)
TEXT ·_galMulAVX512Parallel84(SB), 7, $0
MOVQ in+0(FP), SI //
MOVQ 8(SI), R9 // R9: len(in)
SHRQ $6, R9 // len(in) / 64
TESTQ R9, R9
JZ done_avx512_parallel84
MOVQ matrix+48(FP), SI
LONG $0x48fee162; WORD $0x066f // VMOVDQU64 ZMM16, 0x000[rsi]
LONG $0x48fee162; WORD $0x4e6f; BYTE $0x01 // VMOVDQU64 ZMM17, 0x040[rsi]
LONG $0x48fee162; WORD $0x566f; BYTE $0x02 // VMOVDQU64 ZMM18, 0x080[rsi]
LONG $0x48fee162; WORD $0x5e6f; BYTE $0x03 // VMOVDQU64 ZMM19, 0x0c0[rsi]
LONG $0x48fee162; WORD $0x666f; BYTE $0x04 // VMOVDQU64 ZMM20, 0x100[rsi]
LONG $0x48fee162; WORD $0x6e6f; BYTE $0x05 // VMOVDQU64 ZMM21, 0x140[rsi]
LONG $0x48fee162; WORD $0x766f; BYTE $0x06 // VMOVDQU64 ZMM22, 0x180[rsi]
LONG $0x48fee162; WORD $0x7e6f; BYTE $0x07 // VMOVDQU64 ZMM23, 0x1c0[rsi]
LONG $0x48fe6162; WORD $0x466f; BYTE $0x08 // VMOVDQU64 ZMM24, 0x200[rsi]
LONG $0x48fe6162; WORD $0x4e6f; BYTE $0x09 // VMOVDQU64 ZMM25, 0x240[rsi]
LONG $0x48fe6162; WORD $0x566f; BYTE $0x0a // VMOVDQU64 ZMM26, 0x280[rsi]
LONG $0x48fe6162; WORD $0x5e6f; BYTE $0x0b // VMOVDQU64 ZMM27, 0x2c0[rsi]
LONG $0x48fe6162; WORD $0x666f; BYTE $0x0c // VMOVDQU64 ZMM28, 0x300[rsi]
LONG $0x48fe6162; WORD $0x6e6f; BYTE $0x0d // VMOVDQU64 ZMM29, 0x340[rsi]
LONG $0x48fe6162; WORD $0x766f; BYTE $0x0e // VMOVDQU64 ZMM30, 0x380[rsi]
LONG $0x48fe6162; WORD $0x7e6f; BYTE $0x0f // VMOVDQU64 ZMM31, 0x3c0[rsi]
MOVQ $15, BX
MOVQ BX, X5
LONG $0x487df262; WORD $0xd578 // VPBROADCASTB ZMM2, XMM5
MOVB addTo+56(FP), AX
LONG $0xffc0c749; WORD $0xffff; BYTE $0xff // mov r8, -1
WORD $0xf749; BYTE $0xe0 // mul r8
LONG $0x92fbe1c4; BYTE $0xc8 // kmovq k1, rax
MOVQ in+0(FP), SI // SI: &in
MOVQ in_len+8(FP), AX // number of inputs
XORQ R11, R11
MOVQ out+24(FP), DX
MOVQ 24(DX), CX // CX: &out[1][0]
MOVQ 48(DX), R10 // R10: &out[2][0]
MOVQ 72(DX), R12 // R12: &out[3][0]
MOVQ (DX), DX // DX: &out[0][0]
loopback_avx512_parallel84:
LONG $0xc9fef162; WORD $0x226f // VMOVDQU64 ZMM4{k1}{z}, [rdx]
LONG $0xc9fef162; WORD $0x296f // VMOVDQU64 ZMM5{k1}{z}, [rcx]
LONG $0xc9fed162; WORD $0x326f // VMOVDQU64 ZMM6{k1}{z}, [r10]
LONG $0xc9fed162; WORD $0x3c6f; BYTE $0x24 // VMOVDQU64 ZMM7{k1}{z}, [r12]
MOVQ (SI), BX // BX: &in[0][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40fd3362; WORD $0xf043; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM16, ZMM16, 0x00
LONG $0x40fd3362; WORD $0xf843; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM16, ZMM16, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40dd3362; WORD $0xe443; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM20, ZMM20, 0x00
LONG $0x40dd3362; WORD $0xec43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM20, ZMM20, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40bd1362; WORD $0xd043; BYTE $0x00 // VSHUFI64x2 ZMM10, ZMM24, ZMM24, 0x00
LONG $0x40bd1362; WORD $0xd843; BYTE $0x55 // VSHUFI64x2 ZMM11, ZMM24, ZMM24, 0x55
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x409d1362; WORD $0xc443; BYTE $0x00 // VSHUFI64x2 ZMM8, ZMM28, ZMM28, 0x00
LONG $0x409d1362; WORD $0xcc43; BYTE $0x55 // VSHUFI64x2 ZMM9, ZMM28, ZMM28, 0x55
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $1
JE skip_avx512_parallel84
MOVQ 24(SI), BX // BX: &in[1][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40fd3362; WORD $0xf043; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM16, ZMM16, 0xaa
LONG $0x40fd3362; WORD $0xf843; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM16, ZMM16, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40dd3362; WORD $0xe443; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM20, ZMM20, 0xaa
LONG $0x40dd3362; WORD $0xec43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM20, ZMM20, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40bd1362; WORD $0xd043; BYTE $0xaa // VSHUFI64x2 ZMM10, ZMM24, ZMM24, 0xaa
LONG $0x40bd1362; WORD $0xd843; BYTE $0xff // VSHUFI64x2 ZMM11, ZMM24, ZMM24, 0xff
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x409d1362; WORD $0xc443; BYTE $0xaa // VSHUFI64x2 ZMM8, ZMM28, ZMM28, 0xaa
LONG $0x409d1362; WORD $0xcc43; BYTE $0xff // VSHUFI64x2 ZMM9, ZMM28, ZMM28, 0xff
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $2
JE skip_avx512_parallel84
MOVQ 48(SI), BX // BX: &in[2][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40f53362; WORD $0xf143; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM17, ZMM17, 0x00
LONG $0x40f53362; WORD $0xf943; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM17, ZMM17, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40d53362; WORD $0xe543; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM21, ZMM21, 0x00
LONG $0x40d53362; WORD $0xed43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM21, ZMM21, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40b51362; WORD $0xd143; BYTE $0x00 // VSHUFI64x2 ZMM10, ZMM25, ZMM25, 0x00
LONG $0x40b51362; WORD $0xd943; BYTE $0x55 // VSHUFI64x2 ZMM11, ZMM25, ZMM25, 0x55
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x40951362; WORD $0xc543; BYTE $0x00 // VSHUFI64x2 ZMM8, ZMM29, ZMM29, 0x00
LONG $0x40951362; WORD $0xcd43; BYTE $0x55 // VSHUFI64x2 ZMM9, ZMM29, ZMM29, 0x55
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $3
JE skip_avx512_parallel84
MOVQ 72(SI), BX // BX: &in[3][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40f53362; WORD $0xf143; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM17, ZMM17, 0xaa
LONG $0x40f53362; WORD $0xf943; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM17, ZMM17, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40d53362; WORD $0xe543; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM21, ZMM21, 0xaa
LONG $0x40d53362; WORD $0xed43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM21, ZMM21, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40b51362; WORD $0xd143; BYTE $0xaa // VSHUFI64x2 ZMM10, ZMM25, ZMM25, 0xaa
LONG $0x40b51362; WORD $0xd943; BYTE $0xff // VSHUFI64x2 ZMM11, ZMM25, ZMM25, 0xff
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x40951362; WORD $0xc543; BYTE $0xaa // VSHUFI64x2 ZMM8, ZMM29, ZMM29, 0xaa
LONG $0x40951362; WORD $0xcd43; BYTE $0xff // VSHUFI64x2 ZMM9, ZMM29, ZMM29, 0xff
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $4
JE skip_avx512_parallel84
MOVQ 96(SI), BX // BX: &in[4][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40ed3362; WORD $0xf243; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM18, ZMM18, 0x00
LONG $0x40ed3362; WORD $0xfa43; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM18, ZMM18, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40cd3362; WORD $0xe643; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM22, ZMM22, 0x00
LONG $0x40cd3362; WORD $0xee43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM22, ZMM22, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40ad1362; WORD $0xd243; BYTE $0x00 // VSHUFI64x2 ZMM10, ZMM26, ZMM26, 0x00
LONG $0x40ad1362; WORD $0xda43; BYTE $0x55 // VSHUFI64x2 ZMM11, ZMM26, ZMM26, 0x55
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x408d1362; WORD $0xc643; BYTE $0x00 // VSHUFI64x2 ZMM8, ZMM30, ZMM30, 0x00
LONG $0x408d1362; WORD $0xce43; BYTE $0x55 // VSHUFI64x2 ZMM9, ZMM30, ZMM30, 0x55
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $5
JE skip_avx512_parallel84
MOVQ 120(SI), BX // BX: &in[5][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40ed3362; WORD $0xf243; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM18, ZMM18, 0xaa
LONG $0x40ed3362; WORD $0xfa43; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM18, ZMM18, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40cd3362; WORD $0xe643; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM22, ZMM22, 0xaa
LONG $0x40cd3362; WORD $0xee43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM22, ZMM22, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40ad1362; WORD $0xd243; BYTE $0xaa // VSHUFI64x2 ZMM10, ZMM26, ZMM26, 0xaa
LONG $0x40ad1362; WORD $0xda43; BYTE $0xff // VSHUFI64x2 ZMM11, ZMM26, ZMM26, 0xff
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x408d1362; WORD $0xc643; BYTE $0xaa // VSHUFI64x2 ZMM8, ZMM30, ZMM30, 0xaa
LONG $0x408d1362; WORD $0xce43; BYTE $0xff // VSHUFI64x2 ZMM9, ZMM30, ZMM30, 0xff
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $6
JE skip_avx512_parallel84
MOVQ 144(SI), BX // BX: &in[6][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40e53362; WORD $0xf343; BYTE $0x00 // VSHUFI64x2 ZMM14, ZMM19, ZMM19, 0x00
LONG $0x40e53362; WORD $0xfb43; BYTE $0x55 // VSHUFI64x2 ZMM15, ZMM19, ZMM19, 0x55
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40c53362; WORD $0xe743; BYTE $0x00 // VSHUFI64x2 ZMM12, ZMM23, ZMM23, 0x00
LONG $0x40c53362; WORD $0xef43; BYTE $0x55 // VSHUFI64x2 ZMM13, ZMM23, ZMM23, 0x55
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40a51362; WORD $0xd343; BYTE $0x00 // VSHUFI64x2 ZMM10, ZMM27, ZMM27, 0x00
LONG $0x40a51362; WORD $0xdb43; BYTE $0x55 // VSHUFI64x2 ZMM11, ZMM27, ZMM27, 0x55
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x40851362; WORD $0xc743; BYTE $0x00 // VSHUFI64x2 ZMM8, ZMM31, ZMM31, 0x00
LONG $0x40851362; WORD $0xcf43; BYTE $0x55 // VSHUFI64x2 ZMM9, ZMM31, ZMM31, 0x55
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
CMPQ AX, $7
JE skip_avx512_parallel84
MOVQ 168(SI), BX // BX: &in[7][0]
LONG $0x48feb162; WORD $0x046f; BYTE $0x1b // VMOVDQU64 ZMM0, [rbx+r11]
LONG $0x40e53362; WORD $0xf343; BYTE $0xaa // VSHUFI64x2 ZMM14, ZMM19, ZMM19, 0xaa
LONG $0x40e53362; WORD $0xfb43; BYTE $0xff // VSHUFI64x2 ZMM15, ZMM19, ZMM19, 0xff
LONG $0x48f5f162; WORD $0xd073; BYTE $0x04 // VPSRLQ ZMM1, ZMM0, 4 ; high input
LONG $0x48fdf162; WORD $0xc2db // VPANDQ ZMM0, ZMM0, ZMM2 ; low input
LONG $0x48f5f162; WORD $0xcadb // VPANDQ ZMM1, ZMM1, ZMM2 ; high input
LONG $0x480d7262; WORD $0xf000 // VPSHUFB ZMM14, ZMM14, ZMM0 ; mul low part
LONG $0x48057262; WORD $0xf900 // VPSHUFB ZMM15, ZMM15, ZMM1 ; mul high part
LONG $0x488d5162; WORD $0xf7ef // VPXORQ ZMM14, ZMM14, ZMM15 ; result
LONG $0x48ddd162; WORD $0xe6ef // VPXORQ ZMM4, ZMM4, ZMM14
LONG $0x40c53362; WORD $0xe743; BYTE $0xaa // VSHUFI64x2 ZMM12, ZMM23, ZMM23, 0xaa
LONG $0x40c53362; WORD $0xef43; BYTE $0xff // VSHUFI64x2 ZMM13, ZMM23, ZMM23, 0xff
LONG $0x481d7262; WORD $0xe000 // VPSHUFB ZMM12, ZMM12, ZMM0 ; mul low part
LONG $0x48157262; WORD $0xe900 // VPSHUFB ZMM13, ZMM13, ZMM1 ; mul high part
LONG $0x489d5162; WORD $0xe5ef // VPXORQ ZMM12, ZMM12, ZMM13 ; result
LONG $0x48d5d162; WORD $0xecef // VPXORQ ZMM5, ZMM5, ZMM12
LONG $0x40a51362; WORD $0xd343; BYTE $0xaa // VSHUFI64x2 ZMM10, ZMM27, ZMM27, 0xaa
LONG $0x40a51362; WORD $0xdb43; BYTE $0xff // VSHUFI64x2 ZMM11, ZMM27, ZMM27, 0xff
LONG $0x482d7262; WORD $0xd000 // VPSHUFB ZMM10, ZMM10, ZMM0 ; mul low part
LONG $0x48257262; WORD $0xd900 // VPSHUFB ZMM11, ZMM11, ZMM1 ; mul high part
LONG $0x48ad5162; WORD $0xd3ef // VPXORQ ZMM10, ZMM10, ZMM11 ; result
LONG $0x48cdd162; WORD $0xf2ef // VPXORQ ZMM6, ZMM6, ZMM10
LONG $0x40851362; WORD $0xc743; BYTE $0xaa // VSHUFI64x2 ZMM8, ZMM31, ZMM31, 0xaa
LONG $0x40851362; WORD $0xcf43; BYTE $0xff // VSHUFI64x2 ZMM9, ZMM31, ZMM31, 0xff
LONG $0x483d7262; WORD $0xc000 // VPSHUFB ZMM8, ZMM8, ZMM0 ; mul low part
LONG $0x48357262; WORD $0xc900 // VPSHUFB ZMM9, ZMM9, ZMM1 ; mul high part
LONG $0x48bd5162; WORD $0xc1ef // VPXORQ ZMM8, ZMM8, ZMM9 ; result
LONG $0x48c5d162; WORD $0xf8ef // VPXORQ ZMM7, ZMM7, ZMM8
skip_avx512_parallel84:
LONG $0x48fef162; WORD $0x227f // VMOVDQU64 [rdx], ZMM4
LONG $0x48fef162; WORD $0x297f // VMOVDQU64 [rcx], ZMM5
LONG $0x48fed162; WORD $0x327f // VMOVDQU64 [r10], ZMM6
LONG $0x48fed162; WORD $0x3c7f; BYTE $0x24 // VMOVDQU64 [r12], ZMM7
ADDQ $64, R11 // in4+=64
ADDQ $64, DX // out+=64
ADDQ $64, CX // out2+=64
ADDQ $64, R10 // out3+=64
ADDQ $64, R12 // out4+=64
SUBQ $1, R9
JNZ loopback_avx512_parallel84
done_avx512_parallel84:
VZEROUPPER
RET

92
vendor/github.com/klauspost/reedsolomon/galois_amd64.go generated vendored Normal file
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//+build !noasm
//+build !appengine
//+build !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
package reedsolomon
//go:noescape
func galMulSSSE3(low, high, in, out []byte)
//go:noescape
func galMulSSSE3Xor(low, high, in, out []byte)
//go:noescape
func galMulAVX2Xor(low, high, in, out []byte)
//go:noescape
func galMulAVX2(low, high, in, out []byte)
//go:noescape
func sSE2XorSlice(in, out []byte)
// This is what the assembler routines do in blocks of 16 bytes:
/*
func galMulSSSE3(low, high, in, out []byte) {
for n, input := range in {
l := input & 0xf
h := input >> 4
out[n] = low[l] ^ high[h]
}
}
func galMulSSSE3Xor(low, high, in, out []byte) {
for n, input := range in {
l := input & 0xf
h := input >> 4
out[n] ^= low[l] ^ high[h]
}
}
*/
func galMulSlice(c byte, in, out []byte, o *options) {
var done int
if o.useAVX2 {
galMulAVX2(mulTableLow[c][:], mulTableHigh[c][:], in, out)
done = (len(in) >> 5) << 5
} else if o.useSSSE3 {
galMulSSSE3(mulTableLow[c][:], mulTableHigh[c][:], in, out)
done = (len(in) >> 4) << 4
}
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] = mt[in[i]]
}
}
}
func galMulSliceXor(c byte, in, out []byte, o *options) {
var done int
if o.useAVX2 {
galMulAVX2Xor(mulTableLow[c][:], mulTableHigh[c][:], in, out)
done = (len(in) >> 5) << 5
} else if o.useSSSE3 {
galMulSSSE3Xor(mulTableLow[c][:], mulTableHigh[c][:], in, out)
done = (len(in) >> 4) << 4
}
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] ^= mt[in[i]]
}
}
}
// slice galois add
func sliceXor(in, out []byte, sse2 bool) {
var done int
if sse2 {
sSE2XorSlice(in, out)
done = (len(in) >> 4) << 4
}
remain := len(in) - done
if remain > 0 {
for i := done; i < len(in); i++ {
out[i] ^= in[i]
}
}
}

236
vendor/github.com/klauspost/reedsolomon/galois_amd64.s generated vendored Normal file
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//+build !noasm !appengine !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Based on http://www.snia.org/sites/default/files2/SDC2013/presentations/NewThinking/EthanMiller_Screaming_Fast_Galois_Field%20Arithmetic_SIMD%20Instructions.pdf
// and http://jerasure.org/jerasure/gf-complete/tree/master
// func galMulSSSE3Xor(low, high, in, out []byte)
TEXT ·galMulSSSE3Xor(SB), 7, $0
MOVQ low+0(FP), SI // SI: &low
MOVQ high+24(FP), DX // DX: &high
MOVOU (SI), X6 // X6 low
MOVOU (DX), X7 // X7: high
MOVQ $15, BX // BX: low mask
MOVQ BX, X8
PXOR X5, X5
MOVQ in+48(FP), SI // R11: &in
MOVQ in_len+56(FP), R9 // R9: len(in)
MOVQ out+72(FP), DX // DX: &out
PSHUFB X5, X8 // X8: lomask (unpacked)
SHRQ $4, R9 // len(in) / 16
MOVQ SI, AX
MOVQ DX, BX
ANDQ $15, AX
ANDQ $15, BX
CMPQ R9, $0
JEQ done_xor
ORQ AX, BX
CMPQ BX, $0
JNZ loopback_xor
loopback_xor_aligned:
MOVOA (SI), X0 // in[x]
MOVOA (DX), X4 // out[x]
MOVOA X0, X1 // in[x]
MOVOA X6, X2 // low copy
MOVOA X7, X3 // high copy
PSRLQ $4, X1 // X1: high input
PAND X8, X0 // X0: low input
PAND X8, X1 // X0: high input
PSHUFB X0, X2 // X2: mul low part
PSHUFB X1, X3 // X3: mul high part
PXOR X2, X3 // X3: Result
PXOR X4, X3 // X3: Result xor existing out
MOVOA X3, (DX) // Store
ADDQ $16, SI // in+=16
ADDQ $16, DX // out+=16
SUBQ $1, R9
JNZ loopback_xor_aligned
JMP done_xor
loopback_xor:
MOVOU (SI), X0 // in[x]
MOVOU (DX), X4 // out[x]
MOVOU X0, X1 // in[x]
MOVOU X6, X2 // low copy
MOVOU X7, X3 // high copy
PSRLQ $4, X1 // X1: high input
PAND X8, X0 // X0: low input
PAND X8, X1 // X0: high input
PSHUFB X0, X2 // X2: mul low part
PSHUFB X1, X3 // X3: mul high part
PXOR X2, X3 // X3: Result
PXOR X4, X3 // X3: Result xor existing out
MOVOU X3, (DX) // Store
ADDQ $16, SI // in+=16
ADDQ $16, DX // out+=16
SUBQ $1, R9
JNZ loopback_xor
done_xor:
RET
// func galMulSSSE3(low, high, in, out []byte)
TEXT ·galMulSSSE3(SB), 7, $0
MOVQ low+0(FP), SI // SI: &low
MOVQ high+24(FP), DX // DX: &high
MOVOU (SI), X6 // X6 low
MOVOU (DX), X7 // X7: high
MOVQ $15, BX // BX: low mask
MOVQ BX, X8
PXOR X5, X5
MOVQ in+48(FP), SI // R11: &in
MOVQ in_len+56(FP), R9 // R9: len(in)
MOVQ out+72(FP), DX // DX: &out
PSHUFB X5, X8 // X8: lomask (unpacked)
MOVQ SI, AX
MOVQ DX, BX
SHRQ $4, R9 // len(in) / 16
ANDQ $15, AX
ANDQ $15, BX
CMPQ R9, $0
JEQ done
ORQ AX, BX
CMPQ BX, $0
JNZ loopback
loopback_aligned:
MOVOA (SI), X0 // in[x]
MOVOA X0, X1 // in[x]
MOVOA X6, X2 // low copy
MOVOA X7, X3 // high copy
PSRLQ $4, X1 // X1: high input
PAND X8, X0 // X0: low input
PAND X8, X1 // X0: high input
PSHUFB X0, X2 // X2: mul low part
PSHUFB X1, X3 // X3: mul high part
PXOR X2, X3 // X3: Result
MOVOA X3, (DX) // Store
ADDQ $16, SI // in+=16
ADDQ $16, DX // out+=16
SUBQ $1, R9
JNZ loopback_aligned
JMP done
loopback:
MOVOU (SI), X0 // in[x]
MOVOU X0, X1 // in[x]
MOVOA X6, X2 // low copy
MOVOA X7, X3 // high copy
PSRLQ $4, X1 // X1: high input
PAND X8, X0 // X0: low input
PAND X8, X1 // X0: high input
PSHUFB X0, X2 // X2: mul low part
PSHUFB X1, X3 // X3: mul high part
PXOR X2, X3 // X3: Result
MOVOU X3, (DX) // Store
ADDQ $16, SI // in+=16
ADDQ $16, DX // out+=16
SUBQ $1, R9
JNZ loopback
done:
RET
// func galMulAVX2Xor(low, high, in, out []byte)
TEXT ·galMulAVX2Xor(SB), 7, $0
MOVQ low+0(FP), SI // SI: &low
MOVQ high+24(FP), DX // DX: &high
MOVQ $15, BX // BX: low mask
MOVQ BX, X5
MOVOU (SI), X6 // X6: low
MOVOU (DX), X7 // X7: high
MOVQ in_len+56(FP), R9 // R9: len(in)
VINSERTI128 $1, X6, Y6, Y6 // low
VINSERTI128 $1, X7, Y7, Y7 // high
VPBROADCASTB X5, Y8 // Y8: lomask (unpacked)
SHRQ $5, R9 // len(in) / 32
MOVQ out+72(FP), DX // DX: &out
MOVQ in+48(FP), SI // SI: &in
TESTQ R9, R9
JZ done_xor_avx2
loopback_xor_avx2:
VMOVDQU (SI), Y0
VMOVDQU (DX), Y4
VPSRLQ $4, Y0, Y1 // Y1: high input
VPAND Y8, Y0, Y0 // Y0: low input
VPAND Y8, Y1, Y1 // Y1: high input
VPSHUFB Y0, Y6, Y2 // Y2: mul low part
VPSHUFB Y1, Y7, Y3 // Y3: mul high part
VPXOR Y3, Y2, Y3 // Y3: Result
VPXOR Y4, Y3, Y4 // Y4: Result
VMOVDQU Y4, (DX)
ADDQ $32, SI // in+=32
ADDQ $32, DX // out+=32
SUBQ $1, R9
JNZ loopback_xor_avx2
done_xor_avx2:
VZEROUPPER
RET
// func galMulAVX2(low, high, in, out []byte)
TEXT ·galMulAVX2(SB), 7, $0
MOVQ low+0(FP), SI // SI: &low
MOVQ high+24(FP), DX // DX: &high
MOVQ $15, BX // BX: low mask
MOVQ BX, X5
MOVOU (SI), X6 // X6: low
MOVOU (DX), X7 // X7: high
MOVQ in_len+56(FP), R9 // R9: len(in)
VINSERTI128 $1, X6, Y6, Y6 // low
VINSERTI128 $1, X7, Y7, Y7 // high
VPBROADCASTB X5, Y8 // Y8: lomask (unpacked)
SHRQ $5, R9 // len(in) / 32
MOVQ out+72(FP), DX // DX: &out
MOVQ in+48(FP), SI // SI: &in
TESTQ R9, R9
JZ done_avx2
loopback_avx2:
VMOVDQU (SI), Y0
VPSRLQ $4, Y0, Y1 // Y1: high input
VPAND Y8, Y0, Y0 // Y0: low input
VPAND Y8, Y1, Y1 // Y1: high input
VPSHUFB Y0, Y6, Y2 // Y2: mul low part
VPSHUFB Y1, Y7, Y3 // Y3: mul high part
VPXOR Y3, Y2, Y4 // Y4: Result
VMOVDQU Y4, (DX)
ADDQ $32, SI // in+=32
ADDQ $32, DX // out+=32
SUBQ $1, R9
JNZ loopback_avx2
done_avx2:
VZEROUPPER
RET
// func sSE2XorSlice(in, out []byte)
TEXT ·sSE2XorSlice(SB), 7, $0
MOVQ in+0(FP), SI // SI: &in
MOVQ in_len+8(FP), R9 // R9: len(in)
MOVQ out+24(FP), DX // DX: &out
SHRQ $4, R9 // len(in) / 16
CMPQ R9, $0
JEQ done_xor_sse2
loopback_xor_sse2:
MOVOU (SI), X0 // in[x]
MOVOU (DX), X1 // out[x]
PXOR X0, X1
MOVOU X1, (DX)
ADDQ $16, SI // in+=16
ADDQ $16, DX // out+=16
SUBQ $1, R9
JNZ loopback_xor_sse2
done_xor_sse2:
RET

52
vendor/github.com/klauspost/reedsolomon/galois_arm64.go generated vendored Normal file
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//+build !noasm
//+build !appengine
//+build !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2017, Minio, Inc.
package reedsolomon
//go:noescape
func galMulNEON(c uint64, in, out []byte)
//go:noescape
func galMulXorNEON(c uint64, in, out []byte)
func galMulSlice(c byte, in, out []byte, o *options) {
var done int
galMulNEON(uint64(c), in, out)
done = (len(in) >> 5) << 5
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] = mt[in[i]]
}
}
}
func galMulSliceXor(c byte, in, out []byte, o *options) {
var done int
galMulXorNEON(uint64(c), in, out)
done = (len(in) >> 5) << 5
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] ^= mt[in[i]]
}
}
}
// slice galois add
func sliceXor(in, out []byte, sse2 bool) {
for n, input := range in {
out[n] ^= input
}
}
func (r reedSolomon) codeSomeShardsAvx512(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
}

141
vendor/github.com/klauspost/reedsolomon/galois_arm64.s generated vendored Normal file
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//+build !noasm !appengine !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2017, Minio, Inc.
// Use github.com/minio/asm2plan9s on this file to assemble ARM instructions to
// the opcodes of their Plan9 equivalents
// polynomial multiplication
#define POLYNOMIAL_MULTIPLICATION \
WORD $0x0e3ce340 \ // pmull v0.8h,v26.8b,v28.8b
WORD $0x4e3ce346 \ // pmull2 v6.8h,v26.16b,v28.16b
WORD $0x0e3ce36c \ // pmull v12.8h,v27.8b,v28.8b
WORD $0x4e3ce372 // pmull2 v18.8h,v27.16b,v28.16b
// first reduction
#define FIRST_REDUCTION \
WORD $0x0f088402 \ // shrn v2.8b, v0.8h, #8
WORD $0x0f0884c8 \ // shrn v8.8b, v6.8h, #8
WORD $0x0f08858e \ // shrn v14.8b, v12.8h, #8
WORD $0x0f088654 \ // shrn v20.8b, v18.8h, #8
WORD $0x0e22e3c3 \ // pmull v3.8h,v30.8b,v2.8b
WORD $0x0e28e3c9 \ // pmull v9.8h,v30.8b,v8.8b
WORD $0x0e2ee3cf \ // pmull v15.8h,v30.8b,v14.8b
WORD $0x0e34e3d5 \ // pmull v21.8h,v30.8b,v20.8b
WORD $0x6e201c60 \ // eor v0.16b,v3.16b,v0.16b
WORD $0x6e261d26 \ // eor v6.16b,v9.16b,v6.16b
WORD $0x6e2c1dec \ // eor v12.16b,v15.16b,v12.16b
WORD $0x6e321eb2 // eor v18.16b,v21.16b,v18.16b
// second reduction
#define SECOND_REDUCTION \
WORD $0x0f088404 \ // shrn v4.8b, v0.8h, #8
WORD $0x0f0884ca \ // shrn v10.8b, v6.8h, #8
WORD $0x0f088590 \ // shrn v16.8b, v12.8h, #8
WORD $0x0f088656 \ // shrn v22.8b, v18.8h, #8
WORD $0x6e241c44 \ // eor v4.16b,v2.16b,v4.16b
WORD $0x6e2a1d0a \ // eor v10.16b,v8.16b,v10.16b
WORD $0x6e301dd0 \ // eor v16.16b,v14.16b,v16.16b
WORD $0x6e361e96 \ // eor v22.16b,v20.16b,v22.16b
WORD $0x0e24e3c5 \ // pmull v5.8h,v30.8b,v4.8b
WORD $0x0e2ae3cb \ // pmull v11.8h,v30.8b,v10.8b
WORD $0x0e30e3d1 \ // pmull v17.8h,v30.8b,v16.8b
WORD $0x0e36e3d7 \ // pmull v23.8h,v30.8b,v22.8b
WORD $0x6e201ca0 \ // eor v0.16b,v5.16b,v0.16b
WORD $0x6e261d61 \ // eor v1.16b,v11.16b,v6.16b
WORD $0x6e2c1e22 \ // eor v2.16b,v17.16b,v12.16b
WORD $0x6e321ee3 // eor v3.16b,v23.16b,v18.16b
// func galMulNEON(c uint64, in, out []byte)
TEXT ·galMulNEON(SB), 7, $0
MOVD c+0(FP), R0
MOVD in_base+8(FP), R1
MOVD in_len+16(FP), R2 // length of message
MOVD out_base+32(FP), R5
SUBS $32, R2
BMI complete
// Load constants table pointer
MOVD $·constants(SB), R3
// and load constants into v30 & v31
WORD $0x4c40a07e // ld1 {v30.16b-v31.16b}, [x3]
WORD $0x4e010c1c // dup v28.16b, w0
loop:
// Main loop
WORD $0x4cdfa83a // ld1 {v26.4s-v27.4s}, [x1], #32
POLYNOMIAL_MULTIPLICATION
FIRST_REDUCTION
SECOND_REDUCTION
// combine results
WORD $0x4e1f2000 // tbl v0.16b,{v0.16b,v1.16b},v31.16b
WORD $0x4e1f2041 // tbl v1.16b,{v2.16b,v3.16b},v31.16b
// Store result
WORD $0x4c9faca0 // st1 {v0.2d-v1.2d}, [x5], #32
SUBS $32, R2
BPL loop
complete:
RET
// func galMulXorNEON(c uint64, in, out []byte)
TEXT ·galMulXorNEON(SB), 7, $0
MOVD c+0(FP), R0
MOVD in_base+8(FP), R1
MOVD in_len+16(FP), R2 // length of message
MOVD out_base+32(FP), R5
SUBS $32, R2
BMI completeXor
// Load constants table pointer
MOVD $·constants(SB), R3
// and load constants into v30 & v31
WORD $0x4c40a07e // ld1 {v30.16b-v31.16b}, [x3]
WORD $0x4e010c1c // dup v28.16b, w0
loopXor:
// Main loop
WORD $0x4cdfa83a // ld1 {v26.4s-v27.4s}, [x1], #32
WORD $0x4c40a8b8 // ld1 {v24.4s-v25.4s}, [x5]
POLYNOMIAL_MULTIPLICATION
FIRST_REDUCTION
SECOND_REDUCTION
// combine results
WORD $0x4e1f2000 // tbl v0.16b,{v0.16b,v1.16b},v31.16b
WORD $0x4e1f2041 // tbl v1.16b,{v2.16b,v3.16b},v31.16b
// Xor result and store
WORD $0x6e381c00 // eor v0.16b,v0.16b,v24.16b
WORD $0x6e391c21 // eor v1.16b,v1.16b,v25.16b
WORD $0x4c9faca0 // st1 {v0.2d-v1.2d}, [x5], #32
SUBS $32, R2
BPL loopXor
completeXor:
RET
// Constants table
// generating polynomial is 29 (= 0x1d)
DATA ·constants+0x0(SB)/8, $0x1d1d1d1d1d1d1d1d
DATA ·constants+0x8(SB)/8, $0x1d1d1d1d1d1d1d1d
// constant for TBL instruction
DATA ·constants+0x10(SB)/8, $0x0e0c0a0806040200
DATA ·constants+0x18(SB)/8, $0x1e1c1a1816141210
GLOBL ·constants(SB), 8, $32

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vendor/github.com/klauspost/reedsolomon/galois_noasm.go generated vendored Normal file
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//+build !amd64 noasm appengine gccgo
//+build !arm64 noasm appengine gccgo
//+build !ppc64le noasm appengine gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
package reedsolomon
func galMulSlice(c byte, in, out []byte, o *options) {
mt := mulTable[c][:256]
out = out[:len(in)]
for n, input := range in {
out[n] = mt[input]
}
}
func galMulSliceXor(c byte, in, out []byte, o *options) {
mt := mulTable[c][:256]
out = out[:len(in)]
for n, input := range in {
out[n] ^= mt[input]
}
}
// slice galois add
func sliceXor(in, out []byte, sse2 bool) {
for n, input := range in {
out[n] ^= input
}
}
func (r reedSolomon) codeSomeShardsAvx512(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
panic("unreachable")
}

70
vendor/github.com/klauspost/reedsolomon/galois_ppc64le.go generated vendored Normal file
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//+build !noasm
//+build !appengine
//+build !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2018, Minio, Inc.
package reedsolomon
//go:noescape
func galMulPpc(low, high, in, out []byte)
//go:noescape
func galMulPpcXor(low, high, in, out []byte)
// This is what the assembler routines do in blocks of 16 bytes:
/*
func galMulPpc(low, high, in, out []byte) {
for n, input := range in {
l := input & 0xf
h := input >> 4
out[n] = low[l] ^ high[h]
}
}
func galMulPpcXor(low, high, in, out []byte) {
for n, input := range in {
l := input & 0xf
h := input >> 4
out[n] ^= low[l] ^ high[h]
}
}
*/
func galMulSlice(c byte, in, out []byte, o *options) {
done := (len(in) >> 4) << 4
if done > 0 {
galMulPpc(mulTableLow[c][:], mulTableHigh[c][:], in[:done], out)
}
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] = mt[in[i]]
}
}
}
func galMulSliceXor(c byte, in, out []byte, o *options) {
done := (len(in) >> 4) << 4
if done > 0 {
galMulPpcXor(mulTableLow[c][:], mulTableHigh[c][:], in[:done], out)
}
remain := len(in) - done
if remain > 0 {
mt := mulTable[c][:256]
for i := done; i < len(in); i++ {
out[i] ^= mt[in[i]]
}
}
}
// slice galois add
func sliceXor(in, out []byte, sse2 bool) {
for n, input := range in {
out[n] ^= input
}
}
func (r reedSolomon) codeSomeShardsAvx512(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
}

126
vendor/github.com/klauspost/reedsolomon/galois_ppc64le.s generated vendored Normal file
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//+build !noasm !appengine !gccgo
// Copyright 2015, Klaus Post, see LICENSE for details.
// Copyright 2018, Minio, Inc.
#include "textflag.h"
#define LOW R3
#define HIGH R4
#define IN R5
#define LEN R6
#define OUT R7
#define CONSTANTS R8
#define OFFSET R9
#define OFFSET1 R10
#define OFFSET2 R11
#define X6 VS34
#define X6_ V2
#define X7 VS35
#define X7_ V3
#define MSG VS36
#define MSG_ V4
#define MSG_HI VS37
#define MSG_HI_ V5
#define RESULT VS38
#define RESULT_ V6
#define ROTATE VS39
#define ROTATE_ V7
#define MASK VS40
#define MASK_ V8
#define FLIP VS41
#define FLIP_ V9
// func galMulPpc(low, high, in, out []byte)
TEXT ·galMulPpc(SB), NOFRAME|NOSPLIT, $0-96
MOVD low+0(FP), LOW
MOVD high+24(FP), HIGH
MOVD in+48(FP), IN
MOVD in_len+56(FP), LEN
MOVD out+72(FP), OUT
MOVD $16, OFFSET1
MOVD $32, OFFSET2
MOVD $·constants(SB), CONSTANTS
LXVD2X (CONSTANTS)(R0), ROTATE
LXVD2X (CONSTANTS)(OFFSET1), MASK
LXVD2X (CONSTANTS)(OFFSET2), FLIP
LXVD2X (LOW)(R0), X6
LXVD2X (HIGH)(R0), X7
VPERM X6_, V31, FLIP_, X6_
VPERM X7_, V31, FLIP_, X7_
MOVD $0, OFFSET
loop:
LXVD2X (IN)(OFFSET), MSG
VSRB MSG_, ROTATE_, MSG_HI_
VAND MSG_, MASK_, MSG_
VPERM X6_, V31, MSG_, MSG_
VPERM X7_, V31, MSG_HI_, MSG_HI_
VXOR MSG_, MSG_HI_, MSG_
STXVD2X MSG, (OUT)(OFFSET)
ADD $16, OFFSET, OFFSET
CMP LEN, OFFSET
BGT loop
RET
// func galMulPpcXorlow, high, in, out []byte)
TEXT ·galMulPpcXor(SB), NOFRAME|NOSPLIT, $0-96
MOVD low+0(FP), LOW
MOVD high+24(FP), HIGH
MOVD in+48(FP), IN
MOVD in_len+56(FP), LEN
MOVD out+72(FP), OUT
MOVD $16, OFFSET1
MOVD $32, OFFSET2
MOVD $·constants(SB), CONSTANTS
LXVD2X (CONSTANTS)(R0), ROTATE
LXVD2X (CONSTANTS)(OFFSET1), MASK
LXVD2X (CONSTANTS)(OFFSET2), FLIP
LXVD2X (LOW)(R0), X6
LXVD2X (HIGH)(R0), X7
VPERM X6_, V31, FLIP_, X6_
VPERM X7_, V31, FLIP_, X7_
MOVD $0, OFFSET
loopXor:
LXVD2X (IN)(OFFSET), MSG
LXVD2X (OUT)(OFFSET), RESULT
VSRB MSG_, ROTATE_, MSG_HI_
VAND MSG_, MASK_, MSG_
VPERM X6_, V31, MSG_, MSG_
VPERM X7_, V31, MSG_HI_, MSG_HI_
VXOR MSG_, MSG_HI_, MSG_
VXOR MSG_, RESULT_, RESULT_
STXVD2X RESULT, (OUT)(OFFSET)
ADD $16, OFFSET, OFFSET
CMP LEN, OFFSET
BGT loopXor
RET
DATA ·constants+0x0(SB)/8, $0x0404040404040404
DATA ·constants+0x8(SB)/8, $0x0404040404040404
DATA ·constants+0x10(SB)/8, $0x0f0f0f0f0f0f0f0f
DATA ·constants+0x18(SB)/8, $0x0f0f0f0f0f0f0f0f
DATA ·constants+0x20(SB)/8, $0x0706050403020100
DATA ·constants+0x28(SB)/8, $0x0f0e0d0c0b0a0908
GLOBL ·constants(SB), 8, $48

132
vendor/github.com/klauspost/reedsolomon/gentables.go generated vendored Normal file
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//+build ignore
package main
import (
"fmt"
)
var logTable = [fieldSize]int16{
-1, 0, 1, 25, 2, 50, 26, 198,
3, 223, 51, 238, 27, 104, 199, 75,
4, 100, 224, 14, 52, 141, 239, 129,
28, 193, 105, 248, 200, 8, 76, 113,
5, 138, 101, 47, 225, 36, 15, 33,
53, 147, 142, 218, 240, 18, 130, 69,
29, 181, 194, 125, 106, 39, 249, 185,
201, 154, 9, 120, 77, 228, 114, 166,
6, 191, 139, 98, 102, 221, 48, 253,
226, 152, 37, 179, 16, 145, 34, 136,
54, 208, 148, 206, 143, 150, 219, 189,
241, 210, 19, 92, 131, 56, 70, 64,
30, 66, 182, 163, 195, 72, 126, 110,
107, 58, 40, 84, 250, 133, 186, 61,
202, 94, 155, 159, 10, 21, 121, 43,
78, 212, 229, 172, 115, 243, 167, 87,
7, 112, 192, 247, 140, 128, 99, 13,
103, 74, 222, 237, 49, 197, 254, 24,
227, 165, 153, 119, 38, 184, 180, 124,
17, 68, 146, 217, 35, 32, 137, 46,
55, 63, 209, 91, 149, 188, 207, 205,
144, 135, 151, 178, 220, 252, 190, 97,
242, 86, 211, 171, 20, 42, 93, 158,
132, 60, 57, 83, 71, 109, 65, 162,
31, 45, 67, 216, 183, 123, 164, 118,
196, 23, 73, 236, 127, 12, 111, 246,
108, 161, 59, 82, 41, 157, 85, 170,
251, 96, 134, 177, 187, 204, 62, 90,
203, 89, 95, 176, 156, 169, 160, 81,
11, 245, 22, 235, 122, 117, 44, 215,
79, 174, 213, 233, 230, 231, 173, 232,
116, 214, 244, 234, 168, 80, 88, 175,
}
const (
// The number of elements in the field.
fieldSize = 256
// The polynomial used to generate the logarithm table.
//
// There are a number of polynomials that work to generate
// a Galois field of 256 elements. The choice is arbitrary,
// and we just use the first one.
//
// The possibilities are: 29, 43, 45, 77, 95, 99, 101, 105,
//* 113, 135, 141, 169, 195, 207, 231, and 245.
generatingPolynomial = 29
)
func main() {
t := generateExpTable()
fmt.Printf("var expTable = %#v\n", t)
//t2 := generateMulTableSplit(t)
//fmt.Printf("var mulTable = %#v\n", t2)
low, high := generateMulTableHalf(t)
fmt.Printf("var mulTableLow = %#v\n", low)
fmt.Printf("var mulTableHigh = %#v\n", high)
}
/**
* Generates the inverse log table.
*/
func generateExpTable() []byte {
result := make([]byte, fieldSize*2-2)
for i := 1; i < fieldSize; i++ {
log := logTable[i]
result[log] = byte(i)
result[log+fieldSize-1] = byte(i)
}
return result
}
func generateMulTable(expTable []byte) []byte {
result := make([]byte, 256*256)
for v := range result {
a := byte(v & 0xff)
b := byte(v >> 8)
if a == 0 || b == 0 {
result[v] = 0
continue
}
logA := int(logTable[a])
logB := int(logTable[b])
result[v] = expTable[logA+logB]
}
return result
}
func generateMulTableSplit(expTable []byte) [256][256]byte {
var result [256][256]byte
for a := range result {
for b := range result[a] {
if a == 0 || b == 0 {
result[a][b] = 0
continue
}
logA := int(logTable[a])
logB := int(logTable[b])
result[a][b] = expTable[logA+logB]
}
}
return result
}
func generateMulTableHalf(expTable []byte) (low [256][16]byte, high [256][16]byte) {
for a := range low {
for b := range low {
result := 0
if !(a == 0 || b == 0) {
logA := int(logTable[a])
logB := int(logTable[b])
result = int(expTable[logA+logB])
}
if (b & 0xf) == b {
low[a][b] = byte(result)
}
if (b & 0xf0) == b {
high[a][b>>4] = byte(result)
}
}
}
return
}

160
vendor/github.com/klauspost/reedsolomon/inversion_tree.go generated vendored Normal file
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/**
* A thread-safe tree which caches inverted matrices.
*
* Copyright 2016, Peter Collins
*/
package reedsolomon
import (
"errors"
"sync"
)
// The tree uses a Reader-Writer mutex to make it thread-safe
// when accessing cached matrices and inserting new ones.
type inversionTree struct {
mutex *sync.RWMutex
root inversionNode
}
type inversionNode struct {
matrix matrix
children []*inversionNode
}
// newInversionTree initializes a tree for storing inverted matrices.
// Note that the root node is the identity matrix as it implies
// there were no errors with the original data.
func newInversionTree(dataShards, parityShards int) inversionTree {
identity, _ := identityMatrix(dataShards)
root := inversionNode{
matrix: identity,
children: make([]*inversionNode, dataShards+parityShards),
}
return inversionTree{
mutex: &sync.RWMutex{},
root: root,
}
}
// GetInvertedMatrix returns the cached inverted matrix or nil if it
// is not found in the tree keyed on the indices of invalid rows.
func (t inversionTree) GetInvertedMatrix(invalidIndices []int) matrix {
// Lock the tree for reading before accessing the tree.
t.mutex.RLock()
defer t.mutex.RUnlock()
// If no invalid indices were give we should return the root
// identity matrix.
if len(invalidIndices) == 0 {
return t.root.matrix
}
// Recursively search for the inverted matrix in the tree, passing in
// 0 as the parent index as we start at the root of the tree.
return t.root.getInvertedMatrix(invalidIndices, 0)
}
// errAlreadySet is returned if the root node matrix is overwritten
var errAlreadySet = errors.New("the root node identity matrix is already set")
// InsertInvertedMatrix inserts a new inverted matrix into the tree
// keyed by the indices of invalid rows. The total number of shards
// is required for creating the proper length lists of child nodes for
// each node.
func (t inversionTree) InsertInvertedMatrix(invalidIndices []int, matrix matrix, shards int) error {
// If no invalid indices were given then we are done because the
// root node is already set with the identity matrix.
if len(invalidIndices) == 0 {
return errAlreadySet
}
if !matrix.IsSquare() {
return errNotSquare
}
// Lock the tree for writing and reading before accessing the tree.
t.mutex.Lock()
defer t.mutex.Unlock()
// Recursively create nodes for the inverted matrix in the tree until
// we reach the node to insert the matrix to. We start by passing in
// 0 as the parent index as we start at the root of the tree.
t.root.insertInvertedMatrix(invalidIndices, matrix, shards, 0)
return nil
}
func (n inversionNode) getInvertedMatrix(invalidIndices []int, parent int) matrix {
// Get the child node to search next from the list of children. The
// list of children starts relative to the parent index passed in
// because the indices of invalid rows is sorted (by default). As we
// search recursively, the first invalid index gets popped off the list,
// so when searching through the list of children, use that first invalid
// index to find the child node.
firstIndex := invalidIndices[0]
node := n.children[firstIndex-parent]
// If the child node doesn't exist in the list yet, fail fast by
// returning, so we can construct and insert the proper inverted matrix.
if node == nil {
return nil
}
// If there's more than one invalid index left in the list we should
// keep searching recursively.
if len(invalidIndices) > 1 {
// Search recursively on the child node by passing in the invalid indices
// with the first index popped off the front. Also the parent index to
// pass down is the first index plus one.
return node.getInvertedMatrix(invalidIndices[1:], firstIndex+1)
}
// If there aren't any more invalid indices to search, we've found our
// node. Return it, however keep in mind that the matrix could still be
// nil because intermediary nodes in the tree are created sometimes with
// their inversion matrices uninitialized.
return node.matrix
}
func (n inversionNode) insertInvertedMatrix(invalidIndices []int, matrix matrix, shards, parent int) {
// As above, get the child node to search next from the list of children.
// The list of children starts relative to the parent index passed in
// because the indices of invalid rows is sorted (by default). As we
// search recursively, the first invalid index gets popped off the list,
// so when searching through the list of children, use that first invalid
// index to find the child node.
firstIndex := invalidIndices[0]
node := n.children[firstIndex-parent]
// If the child node doesn't exist in the list yet, create a new
// node because we have the writer lock and add it to the list
// of children.
if node == nil {
// Make the length of the list of children equal to the number
// of shards minus the first invalid index because the list of
// invalid indices is sorted, so only this length of errors
// are possible in the tree.
node = &inversionNode{
children: make([]*inversionNode, shards-firstIndex),
}
// Insert the new node into the tree at the first index relative
// to the parent index that was given in this recursive call.
n.children[firstIndex-parent] = node
}
// If there's more than one invalid index left in the list we should
// keep searching recursively in order to find the node to add our
// matrix.
if len(invalidIndices) > 1 {
// As above, search recursively on the child node by passing in
// the invalid indices with the first index popped off the front.
// Also the total number of shards and parent index are passed down
// which is equal to the first index plus one.
node.insertInvertedMatrix(invalidIndices[1:], matrix, shards, firstIndex+1)
} else {
// If there aren't any more invalid indices to search, we've found our
// node. Cache the inverted matrix in this node.
node.matrix = matrix
}
}

279
vendor/github.com/klauspost/reedsolomon/matrix.go generated vendored Normal file
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/**
* Matrix Algebra over an 8-bit Galois Field
*
* Copyright 2015, Klaus Post
* Copyright 2015, Backblaze, Inc.
*/
package reedsolomon
import (
"errors"
"fmt"
"strconv"
"strings"
)
// byte[row][col]
type matrix [][]byte
// newMatrix returns a matrix of zeros.
func newMatrix(rows, cols int) (matrix, error) {
if rows <= 0 {
return nil, errInvalidRowSize
}
if cols <= 0 {
return nil, errInvalidColSize
}
m := matrix(make([][]byte, rows))
for i := range m {
m[i] = make([]byte, cols)
}
return m, nil
}
// NewMatrixData initializes a matrix with the given row-major data.
// Note that data is not copied from input.
func newMatrixData(data [][]byte) (matrix, error) {
m := matrix(data)
err := m.Check()
if err != nil {
return nil, err
}
return m, nil
}
// IdentityMatrix returns an identity matrix of the given size.
func identityMatrix(size int) (matrix, error) {
m, err := newMatrix(size, size)
if err != nil {
return nil, err
}
for i := range m {
m[i][i] = 1
}
return m, nil
}
// errInvalidRowSize will be returned if attempting to create a matrix with negative or zero row number.
var errInvalidRowSize = errors.New("invalid row size")
// errInvalidColSize will be returned if attempting to create a matrix with negative or zero column number.
var errInvalidColSize = errors.New("invalid column size")
// errColSizeMismatch is returned if the size of matrix columns mismatch.
var errColSizeMismatch = errors.New("column size is not the same for all rows")
func (m matrix) Check() error {
rows := len(m)
if rows <= 0 {
return errInvalidRowSize
}
cols := len(m[0])
if cols <= 0 {
return errInvalidColSize
}
for _, col := range m {
if len(col) != cols {
return errColSizeMismatch
}
}
return nil
}
// String returns a human-readable string of the matrix contents.
//
// Example: [[1, 2], [3, 4]]
func (m matrix) String() string {
rowOut := make([]string, 0, len(m))
for _, row := range m {
colOut := make([]string, 0, len(row))
for _, col := range row {
colOut = append(colOut, strconv.Itoa(int(col)))
}
rowOut = append(rowOut, "["+strings.Join(colOut, ", ")+"]")
}
return "[" + strings.Join(rowOut, ", ") + "]"
}
// Multiply multiplies this matrix (the one on the left) by another
// matrix (the one on the right) and returns a new matrix with the result.
func (m matrix) Multiply(right matrix) (matrix, error) {
if len(m[0]) != len(right) {
return nil, fmt.Errorf("columns on left (%d) is different than rows on right (%d)", len(m[0]), len(right))
}
result, _ := newMatrix(len(m), len(right[0]))
for r, row := range result {
for c := range row {
var value byte
for i := range m[0] {
value ^= galMultiply(m[r][i], right[i][c])
}
result[r][c] = value
}
}
return result, nil
}
// Augment returns the concatenation of this matrix and the matrix on the right.
func (m matrix) Augment(right matrix) (matrix, error) {
if len(m) != len(right) {
return nil, errMatrixSize
}
result, _ := newMatrix(len(m), len(m[0])+len(right[0]))
for r, row := range m {
for c := range row {
result[r][c] = m[r][c]
}
cols := len(m[0])
for c := range right[0] {
result[r][cols+c] = right[r][c]
}
}
return result, nil
}
// errMatrixSize is returned if matrix dimensions are doesn't match.
var errMatrixSize = errors.New("matrix sizes do not match")
func (m matrix) SameSize(n matrix) error {
if len(m) != len(n) {
return errMatrixSize
}
for i := range m {
if len(m[i]) != len(n[i]) {
return errMatrixSize
}
}
return nil
}
// SubMatrix returns a part of this matrix. Data is copied.
func (m matrix) SubMatrix(rmin, cmin, rmax, cmax int) (matrix, error) {
result, err := newMatrix(rmax-rmin, cmax-cmin)
if err != nil {
return nil, err
}
// OPTME: If used heavily, use copy function to copy slice
for r := rmin; r < rmax; r++ {
for c := cmin; c < cmax; c++ {
result[r-rmin][c-cmin] = m[r][c]
}
}
return result, nil
}
// SwapRows Exchanges two rows in the matrix.
func (m matrix) SwapRows(r1, r2 int) error {
if r1 < 0 || len(m) <= r1 || r2 < 0 || len(m) <= r2 {
return errInvalidRowSize
}
m[r2], m[r1] = m[r1], m[r2]
return nil
}
// IsSquare will return true if the matrix is square
// and nil if the matrix is square
func (m matrix) IsSquare() bool {
return len(m) == len(m[0])
}
// errSingular is returned if the matrix is singular and cannot be inversed
var errSingular = errors.New("matrix is singular")
// errNotSquare is returned if attempting to inverse a non-square matrix.
var errNotSquare = errors.New("only square matrices can be inverted")
// Invert returns the inverse of this matrix.
// Returns ErrSingular when the matrix is singular and doesn't have an inverse.
// The matrix must be square, otherwise ErrNotSquare is returned.
func (m matrix) Invert() (matrix, error) {
if !m.IsSquare() {
return nil, errNotSquare
}
size := len(m)
work, _ := identityMatrix(size)
work, _ = m.Augment(work)
err := work.gaussianElimination()
if err != nil {
return nil, err
}
return work.SubMatrix(0, size, size, size*2)
}
func (m matrix) gaussianElimination() error {
rows := len(m)
columns := len(m[0])
// Clear out the part below the main diagonal and scale the main
// diagonal to be 1.
for r := 0; r < rows; r++ {
// If the element on the diagonal is 0, find a row below
// that has a non-zero and swap them.
if m[r][r] == 0 {
for rowBelow := r + 1; rowBelow < rows; rowBelow++ {
if m[rowBelow][r] != 0 {
m.SwapRows(r, rowBelow)
break
}
}
}
// If we couldn't find one, the matrix is singular.
if m[r][r] == 0 {
return errSingular
}
// Scale to 1.
if m[r][r] != 1 {
scale := galDivide(1, m[r][r])
for c := 0; c < columns; c++ {
m[r][c] = galMultiply(m[r][c], scale)
}
}
// Make everything below the 1 be a 0 by subtracting
// a multiple of it. (Subtraction and addition are
// both exclusive or in the Galois field.)
for rowBelow := r + 1; rowBelow < rows; rowBelow++ {
if m[rowBelow][r] != 0 {
scale := m[rowBelow][r]
for c := 0; c < columns; c++ {
m[rowBelow][c] ^= galMultiply(scale, m[r][c])
}
}
}
}
// Now clear the part above the main diagonal.
for d := 0; d < rows; d++ {
for rowAbove := 0; rowAbove < d; rowAbove++ {
if m[rowAbove][d] != 0 {
scale := m[rowAbove][d]
for c := 0; c < columns; c++ {
m[rowAbove][c] ^= galMultiply(scale, m[d][c])
}
}
}
}
return nil
}
// Create a Vandermonde matrix, which is guaranteed to have the
// property that any subset of rows that forms a square matrix
// is invertible.
func vandermonde(rows, cols int) (matrix, error) {
result, err := newMatrix(rows, cols)
if err != nil {
return nil, err
}
for r, row := range result {
for c := range row {
result[r][c] = galExp(byte(r), c)
}
}
return result, nil
}

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vendor/github.com/klauspost/reedsolomon/options.go generated vendored Normal file
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package reedsolomon
import (
"runtime"
"github.com/klauspost/cpuid"
)
// Option allows to override processing parameters.
type Option func(*options)
type options struct {
maxGoroutines int
minSplitSize int
useAVX512, useAVX2, useSSSE3, useSSE2 bool
usePAR1Matrix bool
useCauchy bool
shardSize int
}
var defaultOptions = options{
maxGoroutines: 384,
minSplitSize: 1024,
}
func init() {
if runtime.GOMAXPROCS(0) <= 1 {
defaultOptions.maxGoroutines = 1
}
// Detect CPU capabilities.
defaultOptions.useSSSE3 = cpuid.CPU.SSSE3()
defaultOptions.useSSE2 = cpuid.CPU.SSE2()
defaultOptions.useAVX2 = cpuid.CPU.AVX2()
defaultOptions.useAVX512 = cpuid.CPU.AVX512F() && cpuid.CPU.AVX512BW()
}
// 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 WithMaxGoroutines(n int) Option {
return func(o *options) {
if n > 0 {
o.maxGoroutines = n
}
}
}
// 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 WithAutoGoroutines(shardSize int) Option {
return func(o *options) {
o.shardSize = shardSize
}
}
// WithMinSplitSize is the minimum encoding size in bytes per goroutine.
// See WithMaxGoroutines on how jobs are split.
// If n <= 0, it is ignored.
func WithMinSplitSize(n int) Option {
return func(o *options) {
if n > 0 {
o.minSplitSize = n
}
}
}
func withSSE3(enabled bool) Option {
return func(o *options) {
o.useSSSE3 = enabled
}
}
func withAVX2(enabled bool) Option {
return func(o *options) {
o.useAVX2 = enabled
}
}
func withSSE2(enabled bool) Option {
return func(o *options) {
o.useSSE2 = enabled
}
}
func withAVX512(enabled bool) Option {
return func(o *options) {
o.useAVX512 = enabled
}
}
// 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 WithPAR1Matrix() Option {
return func(o *options) {
o.usePAR1Matrix = true
o.useCauchy = false
}
}
// 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 WithCauchyMatrix() Option {
return func(o *options) {
o.useCauchy = true
o.usePAR1Matrix = false
}
}

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/**
* Reed-Solomon Coding over 8-bit values.
*
* Copyright 2015, Klaus Post
* Copyright 2015, Backblaze, Inc.
*/
// Package reedsolomon enables Erasure Coding in Go
//
// For usage and examples, see https://github.com/klauspost/reedsolomon
//
package reedsolomon
import (
"bytes"
"errors"
"io"
"runtime"
"sync"
"github.com/klauspost/cpuid"
)
// Encoder is an interface to encode Reed-Salomon parity sets for your data.
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
// 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
// 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.
//
// The data will be split into equally sized shards.
// If the data size isn't dividable by the number of shards,
// the last shard will contain extra zeros.
//
// 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
}
// reedSolomon contains a matrix for a specific
// distribution of datashards and parity shards.
// Construct if using New()
type reedSolomon struct {
DataShards int // Number of data shards, should not be modified.
ParityShards int // Number of parity shards, should not be modified.
Shards int // Total number of shards. Calculated, and should not be modified.
m matrix
tree inversionTree
parity [][]byte
o options
}
// ErrInvShardNum will be returned by New, if you attempt to create
// an Encoder where either data or parity shards is zero or less.
var ErrInvShardNum = errors.New("cannot create Encoder with zero or less 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 ErrMaxShardNum = errors.New("cannot create Encoder with more than 256 data+parity shards")
// buildMatrix creates the matrix to use for encoding, given the
// number of data shards and the number of total shards.
//
// The top square of the matrix is guaranteed to be an identity
// matrix, which means that the data shards are unchanged after
// encoding.
func buildMatrix(dataShards, totalShards int) (matrix, error) {
// Start with a Vandermonde matrix. This matrix would work,
// in theory, but doesn't have the property that the data
// shards are unchanged after encoding.
vm, err := vandermonde(totalShards, dataShards)
if err != nil {
return nil, err
}
// Multiply by the inverse of the top square of the matrix.
// This will make the top square be the identity matrix, but
// preserve the property that any square subset of rows is
// invertible.
top, err := vm.SubMatrix(0, 0, dataShards, dataShards)
if err != nil {
return nil, err
}
topInv, err := top.Invert()
if err != nil {
return nil, err
}
return vm.Multiply(topInv)
}
// buildMatrixPAR1 creates the matrix to use for encoding according to
// the PARv1 spec, given the number of data shards and the number of
// total shards. Note that the method they use is buggy, and may lead
// to cases where recovery is impossible, even if there are enough
// parity shards.
//
// The top square of the matrix is guaranteed to be an identity
// matrix, which means that the data shards are unchanged after
// encoding.
func buildMatrixPAR1(dataShards, totalShards int) (matrix, error) {
result, err := newMatrix(totalShards, dataShards)
if err != nil {
return nil, err
}
for r, row := range result {
// The top portion of the matrix is the identity
// matrix, and the bottom is a transposed Vandermonde
// matrix starting at 1 instead of 0.
if r < dataShards {
result[r][r] = 1
} else {
for c := range row {
result[r][c] = galExp(byte(c+1), r-dataShards)
}
}
}
return result, nil
}
func buildMatrixCauchy(dataShards, totalShards int) (matrix, error) {
result, err := newMatrix(totalShards, dataShards)
if err != nil {
return nil, err
}
for r, row := range result {
// The top portion of the matrix is the identity
// matrix, and the bottom is a transposed Cauchy matrix.
if r < dataShards {
result[r][r] = 1
} else {
for c := range row {
result[r][c] = invTable[(byte(r ^ c))]
}
}
}
return result, nil
}
// 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 256.
// If no options are supplied, default options are used.
func New(dataShards, parityShards int, opts ...Option) (Encoder, error) {
r := reedSolomon{
DataShards: dataShards,
ParityShards: parityShards,
Shards: dataShards + parityShards,
o: defaultOptions,
}
for _, opt := range opts {
opt(&r.o)
}
if dataShards <= 0 || parityShards <= 0 {
return nil, ErrInvShardNum
}
if dataShards+parityShards > 256 {
return nil, ErrMaxShardNum
}
var err error
switch {
case r.o.useCauchy:
r.m, err = buildMatrixCauchy(dataShards, r.Shards)
case r.o.usePAR1Matrix:
r.m, err = buildMatrixPAR1(dataShards, r.Shards)
default:
r.m, err = buildMatrix(dataShards, r.Shards)
}
if err != nil {
return nil, err
}
if r.o.shardSize > 0 {
cacheSize := cpuid.CPU.Cache.L2
if cacheSize <= 0 {
// Set to 128K if undetectable.
cacheSize = 128 << 10
}
p := runtime.NumCPU()
// 1 input + parity must fit in cache, and we add one more to be safer.
shards := 1 + parityShards
g := (r.o.shardSize * shards) / (cacheSize - (cacheSize >> 4))
if cpuid.CPU.ThreadsPerCore > 1 {
// If multiple threads per core, make sure they don't contend for cache.
g *= cpuid.CPU.ThreadsPerCore
}
g *= 2
if g < p {
g = p
}
// Have g be multiple of p
g += p - 1
g -= g % p
r.o.maxGoroutines = g
}
// Inverted matrices are cached in a tree keyed by the indices
// of the invalid rows of the data to reconstruct.
// The inversion root node will have the identity matrix as
// its inversion matrix because it implies there are no errors
// with the original data.
r.tree = newInversionTree(dataShards, parityShards)
r.parity = make([][]byte, parityShards)
for i := range r.parity {
r.parity[i] = r.m[dataShards+i]
}
return &r, err
}
// 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.
var ErrTooFewShards = errors.New("too few shards given")
// Encodes parity for a set of data shards.
// An array '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.
func (r reedSolomon) Encode(shards [][]byte) error {
if len(shards) != r.Shards {
return ErrTooFewShards
}
err := checkShards(shards, false)
if err != nil {
return err
}
// Get the slice of output buffers.
output := shards[r.DataShards:]
// Do the coding.
r.codeSomeShards(r.parity, shards[0:r.DataShards], output, r.ParityShards, len(shards[0]))
return nil
}
// ErrInvalidInput is returned if invalid input parameter of Update.
var ErrInvalidInput = errors.New("invalid input")
func (r reedSolomon) Update(shards [][]byte, newDatashards [][]byte) error {
if len(shards) != r.Shards {
return ErrTooFewShards
}
if len(newDatashards) != r.DataShards {
return ErrTooFewShards
}
err := checkShards(shards, true)
if err != nil {
return err
}
err = checkShards(newDatashards, true)
if err != nil {
return err
}
for i := range newDatashards {
if newDatashards[i] != nil && shards[i] == nil {
return ErrInvalidInput
}
}
for _, p := range shards[r.DataShards:] {
if p == nil {
return ErrInvalidInput
}
}
shardSize := shardSize(shards)
// Get the slice of output buffers.
output := shards[r.DataShards:]
// Do the coding.
r.updateParityShards(r.parity, shards[0:r.DataShards], newDatashards[0:r.DataShards], output, r.ParityShards, shardSize)
return nil
}
func (r reedSolomon) updateParityShards(matrixRows, oldinputs, newinputs, outputs [][]byte, outputCount, byteCount int) {
if r.o.maxGoroutines > 1 && byteCount > r.o.minSplitSize {
r.updateParityShardsP(matrixRows, oldinputs, newinputs, outputs, outputCount, byteCount)
return
}
for c := 0; c < r.DataShards; c++ {
in := newinputs[c]
if in == nil {
continue
}
oldin := oldinputs[c]
// oldinputs data will be change
sliceXor(in, oldin, r.o.useSSE2)
for iRow := 0; iRow < outputCount; iRow++ {
galMulSliceXor(matrixRows[iRow][c], oldin, outputs[iRow], &r.o)
}
}
}
func (r reedSolomon) updateParityShardsP(matrixRows, oldinputs, newinputs, outputs [][]byte, outputCount, byteCount int) {
var wg sync.WaitGroup
do := byteCount / r.o.maxGoroutines
if do < r.o.minSplitSize {
do = r.o.minSplitSize
}
start := 0
for start < byteCount {
if start+do > byteCount {
do = byteCount - start
}
wg.Add(1)
go func(start, stop int) {
for c := 0; c < r.DataShards; c++ {
in := newinputs[c]
if in == nil {
continue
}
oldin := oldinputs[c]
// oldinputs data will be change
sliceXor(in[start:stop], oldin[start:stop], r.o.useSSE2)
for iRow := 0; iRow < outputCount; iRow++ {
galMulSliceXor(matrixRows[iRow][c], oldin[start:stop], outputs[iRow][start:stop], &r.o)
}
}
wg.Done()
}(start, start+do)
start += do
}
wg.Wait()
}
// Verify returns true if the parity shards contain the right data.
// The data is the same format as Encode. No data is modified.
func (r reedSolomon) Verify(shards [][]byte) (bool, error) {
if len(shards) != r.Shards {
return false, ErrTooFewShards
}
err := checkShards(shards, false)
if err != nil {
return false, err
}
// Slice of buffers being checked.
toCheck := shards[r.DataShards:]
// Do the checking.
return r.checkSomeShards(r.parity, shards[0:r.DataShards], toCheck, r.ParityShards, len(shards[0])), nil
}
// Multiplies a subset of rows from a coding matrix by a full set of
// input shards to produce some output shards.
// 'matrixRows' is The rows from the matrix to use.
// 'inputs' An array of byte arrays, each of which is one input shard.
// The number of inputs used is determined by the length of each matrix row.
// outputs Byte arrays where the computed shards are stored.
// The number of outputs computed, and the
// number of matrix rows used, is determined by
// outputCount, which is the number of outputs to compute.
func (r reedSolomon) codeSomeShards(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
if r.o.useAVX512 && len(inputs) >= 4 && len(outputs) >= 2 {
r.codeSomeShardsAvx512(matrixRows, inputs, outputs, outputCount, byteCount)
return
} else if r.o.maxGoroutines > 1 && byteCount > r.o.minSplitSize {
r.codeSomeShardsP(matrixRows, inputs, outputs, outputCount, byteCount)
return
}
for c := 0; c < r.DataShards; c++ {
in := inputs[c]
for iRow := 0; iRow < outputCount; iRow++ {
if c == 0 {
galMulSlice(matrixRows[iRow][c], in, outputs[iRow], &r.o)
} else {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow], &r.o)
}
}
}
}
// Perform the same as codeSomeShards, but split the workload into
// several goroutines.
func (r reedSolomon) codeSomeShardsP(matrixRows, inputs, outputs [][]byte, outputCount, byteCount int) {
var wg sync.WaitGroup
do := byteCount / r.o.maxGoroutines
if do < r.o.minSplitSize {
do = r.o.minSplitSize
}
// Make sizes divisible by 32
do = (do + 31) & (^31)
start := 0
for start < byteCount {
if start+do > byteCount {
do = byteCount - start
}
wg.Add(1)
go func(start, stop int) {
for c := 0; c < r.DataShards; c++ {
in := inputs[c][start:stop]
for iRow := 0; iRow < outputCount; iRow++ {
if c == 0 {
galMulSlice(matrixRows[iRow][c], in, outputs[iRow][start:stop], &r.o)
} else {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow][start:stop], &r.o)
}
}
}
wg.Done()
}(start, start+do)
start += do
}
wg.Wait()
}
// checkSomeShards is mostly the same as codeSomeShards,
// except this will check values and return
// as soon as a difference is found.
func (r reedSolomon) checkSomeShards(matrixRows, inputs, toCheck [][]byte, outputCount, byteCount int) bool {
if r.o.maxGoroutines > 1 && byteCount > r.o.minSplitSize {
return r.checkSomeShardsP(matrixRows, inputs, toCheck, outputCount, byteCount)
}
outputs := make([][]byte, len(toCheck))
for i := range outputs {
outputs[i] = make([]byte, byteCount)
}
for c := 0; c < r.DataShards; c++ {
in := inputs[c]
for iRow := 0; iRow < outputCount; iRow++ {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow], &r.o)
}
}
for i, calc := range outputs {
if !bytes.Equal(calc, toCheck[i]) {
return false
}
}
return true
}
func (r reedSolomon) checkSomeShardsP(matrixRows, inputs, toCheck [][]byte, outputCount, byteCount int) bool {
same := true
var mu sync.RWMutex // For above
var wg sync.WaitGroup
do := byteCount / r.o.maxGoroutines
if do < r.o.minSplitSize {
do = r.o.minSplitSize
}
// Make sizes divisible by 32
do = (do + 31) & (^31)
start := 0
for start < byteCount {
if start+do > byteCount {
do = byteCount - start
}
wg.Add(1)
go func(start, do int) {
defer wg.Done()
outputs := make([][]byte, len(toCheck))
for i := range outputs {
outputs[i] = make([]byte, do)
}
for c := 0; c < r.DataShards; c++ {
mu.RLock()
if !same {
mu.RUnlock()
return
}
mu.RUnlock()
in := inputs[c][start : start+do]
for iRow := 0; iRow < outputCount; iRow++ {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow], &r.o)
}
}
for i, calc := range outputs {
if !bytes.Equal(calc, toCheck[i][start:start+do]) {
mu.Lock()
same = false
mu.Unlock()
return
}
}
}(start, do)
start += do
}
wg.Wait()
return same
}
// ErrShardNoData will be returned if there are no shards,
// or if the length of all shards is zero.
var ErrShardNoData = errors.New("no shard data")
// ErrShardSize is returned if shard length isn't the same for all
// shards.
var ErrShardSize = errors.New("shard sizes do not match")
// checkShards will check if shards are the same size
// or 0, if allowed. An error is returned if this fails.
// An error is also returned if all shards are size 0.
func checkShards(shards [][]byte, nilok bool) error {
size := shardSize(shards)
if size == 0 {
return ErrShardNoData
}
for _, shard := range shards {
if len(shard) != size {
if len(shard) != 0 || !nilok {
return ErrShardSize
}
}
}
return nil
}
// shardSize return the size of a single shard.
// The first non-zero size is returned,
// or 0 if all shards are size 0.
func shardSize(shards [][]byte) int {
for _, shard := range shards {
if len(shard) != 0 {
return len(shard)
}
}
return 0
}
// 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 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.
func (r reedSolomon) Reconstruct(shards [][]byte) error {
return r.reconstruct(shards, false)
}
// 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.
func (r reedSolomon) ReconstructData(shards [][]byte) error {
return r.reconstruct(shards, true)
}
// reconstruct will recreate the missing data shards, and unless
// dataOnly is true, also the missing parity shards
//
// The length of the array must be equal to Shards.
// You indicate that a shard is missing by setting it to nil.
//
// If there are too few shards to reconstruct the missing
// ones, ErrTooFewShards will be returned.
func (r reedSolomon) reconstruct(shards [][]byte, dataOnly bool) error {
if len(shards) != r.Shards {
return ErrTooFewShards
}
// Check arguments.
err := checkShards(shards, true)
if err != nil {
return err
}
shardSize := shardSize(shards)
// Quick check: are all of the shards present? If so, there's
// nothing to do.
numberPresent := 0
for i := 0; i < r.Shards; i++ {
if len(shards[i]) != 0 {
numberPresent++
}
}
if numberPresent == r.Shards {
// Cool. All of the shards data data. We don't
// need to do anything.
return nil
}
// More complete sanity check
if numberPresent < r.DataShards {
return ErrTooFewShards
}
// Pull out an array holding just the shards that
// correspond to the rows of the submatrix. These shards
// will be the input to the decoding process that re-creates
// the missing data shards.
//
// Also, create an array of indices of the valid rows we do have
// and the invalid rows we don't have up until we have enough valid rows.
subShards := make([][]byte, r.DataShards)
validIndices := make([]int, r.DataShards)
invalidIndices := make([]int, 0)
subMatrixRow := 0
for matrixRow := 0; matrixRow < r.Shards && subMatrixRow < r.DataShards; matrixRow++ {
if len(shards[matrixRow]) != 0 {
subShards[subMatrixRow] = shards[matrixRow]
validIndices[subMatrixRow] = matrixRow
subMatrixRow++
} else {
invalidIndices = append(invalidIndices, matrixRow)
}
}
// Attempt to get the cached inverted matrix out of the tree
// based on the indices of the invalid rows.
dataDecodeMatrix := r.tree.GetInvertedMatrix(invalidIndices)
// If the inverted matrix isn't cached in the tree yet we must
// construct it ourselves and insert it into the tree for the
// future. In this way the inversion tree is lazily loaded.
if dataDecodeMatrix == nil {
// Pull out the rows of the matrix that correspond to the
// shards that we have and build a square matrix. This
// matrix could be used to generate the shards that we have
// from the original data.
subMatrix, _ := newMatrix(r.DataShards, r.DataShards)
for subMatrixRow, validIndex := range validIndices {
for c := 0; c < r.DataShards; c++ {
subMatrix[subMatrixRow][c] = r.m[validIndex][c]
}
}
// Invert the matrix, so we can go from the encoded shards
// back to the original data. Then pull out the row that
// generates the shard that we want to decode. Note that
// since this matrix maps back to the original data, it can
// be used to create a data shard, but not a parity shard.
dataDecodeMatrix, err = subMatrix.Invert()
if err != nil {
return err
}
// Cache the inverted matrix in the tree for future use keyed on the
// indices of the invalid rows.
err = r.tree.InsertInvertedMatrix(invalidIndices, dataDecodeMatrix, r.Shards)
if err != nil {
return err
}
}
// Re-create any data shards that were missing.
//
// The input to the coding is all of the shards we actually
// have, and the output is the missing data shards. The computation
// is done using the special decode matrix we just built.
outputs := make([][]byte, r.ParityShards)
matrixRows := make([][]byte, r.ParityShards)
outputCount := 0
for iShard := 0; iShard < r.DataShards; iShard++ {
if len(shards[iShard]) == 0 {
if cap(shards[iShard]) >= shardSize {
shards[iShard] = shards[iShard][0:shardSize]
} else {
shards[iShard] = make([]byte, shardSize)
}
outputs[outputCount] = shards[iShard]
matrixRows[outputCount] = dataDecodeMatrix[iShard]
outputCount++
}
}
r.codeSomeShards(matrixRows, subShards, outputs[:outputCount], outputCount, shardSize)
if dataOnly {
// Exit out early if we are only interested in the data shards
return nil
}
// Now that we have all of the data shards intact, we can
// compute any of the parity that is missing.
//
// The input to the coding is ALL of the data shards, including
// any that we just calculated. The output is whichever of the
// data shards were missing.
outputCount = 0
for iShard := r.DataShards; iShard < r.Shards; iShard++ {
if len(shards[iShard]) == 0 {
if cap(shards[iShard]) >= shardSize {
shards[iShard] = shards[iShard][0:shardSize]
} else {
shards[iShard] = make([]byte, shardSize)
}
outputs[outputCount] = shards[iShard]
matrixRows[outputCount] = r.parity[iShard-r.DataShards]
outputCount++
}
}
r.codeSomeShards(matrixRows, shards[:r.DataShards], outputs[:outputCount], outputCount, shardSize)
return nil
}
// ErrShortData will be returned by Split(), if there isn't enough data
// to fill the number of shards.
var ErrShortData = errors.New("not enough data to fill the number of requested shards")
// 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.
//
// 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.
func (r reedSolomon) Split(data []byte) ([][]byte, error) {
if len(data) == 0 {
return nil, ErrShortData
}
// Calculate number of bytes per data shard.
perShard := (len(data) + r.DataShards - 1) / r.DataShards
if cap(data) > len(data) {
data = data[:cap(data)]
}
// Only allocate memory if necessary
if len(data) < (r.Shards * perShard) {
// Pad data to r.Shards*perShard.
padding := make([]byte, (r.Shards*perShard)-len(data))
data = append(data, padding...)
}
// Split into equal-length shards.
dst := make([][]byte, r.Shards)
for i := range dst {
dst[i] = data[:perShard]
data = data[perShard:]
}
return dst, nil
}
// ErrReconstructRequired is returned if too few data shards are intact and a
// reconstruction is required before you can successfully join the shards.
var ErrReconstructRequired = errors.New("reconstruction required as one or more required data shards are nil")
// 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.
// If one or more required data shards are nil, ErrReconstructRequired will be returned.
func (r reedSolomon) Join(dst io.Writer, shards [][]byte, outSize int) error {
// Do we have enough shards?
if len(shards) < r.DataShards {
return ErrTooFewShards
}
shards = shards[:r.DataShards]
// Do we have enough data?
size := 0
for _, shard := range shards {
if shard == nil {
return ErrReconstructRequired
}
size += len(shard)
// Do we have enough data already?
if size >= outSize {
break
}
}
if size < outSize {
return ErrShortData
}
// Copy data to dst
write := outSize
for _, shard := range shards {
if write < len(shard) {
_, err := dst.Write(shard[:write])
return err
}
n, err := dst.Write(shard)
if err != nil {
return err
}
write -= n
}
return nil
}

584
vendor/github.com/klauspost/reedsolomon/streaming.go generated vendored Normal file
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@@ -0,0 +1,584 @@
/**
* Reed-Solomon Coding over 8-bit values.
*
* Copyright 2015, Klaus Post
* Copyright 2015, Backblaze, Inc.
*/
package reedsolomon
import (
"bytes"
"errors"
"fmt"
"io"
"sync"
)
// StreamEncoder is an interface to encode Reed-Salomon parity sets for your data.
// It provides a fully streaming interface, and processes data in blocks of up to 4MB.
//
// For small shard sizes, 10MB and below, it is recommended to use the in-memory interface,
// since the streaming interface has a start up overhead.
//
// For all operations, no readers and writers should not assume any order/size of
// individual reads/writes.
//
// For usage examples, see "stream-encoder.go" and "streamdecoder.go" in the examples
// folder.
type StreamEncoder interface {
// Encode parity shards for a set of data shards.
//
// Input is 'shards' containing readers for data shards followed by parity shards
// io.Writer.
//
// The number of shards must match the number given to NewStream().
//
// Each reader must supply the same number of bytes.
//
// The parity shards will be written to the writer.
// The number of bytes written will match the input size.
//
// If a data stream returns an error, a StreamReadError type error
// will be returned. If a parity writer returns an error, a
// StreamWriteError will be returned.
Encode(data []io.Reader, parity []io.Writer) error
// Verify returns true if the parity shards contain correct data.
//
// The number of shards must match the number total data+parity shards
// given to NewStream().
//
// Each reader must supply the same number of bytes.
// If a shard stream returns an error, a StreamReadError type error
// will be returned.
Verify(shards []io.Reader) (bool, error)
// Reconstruct will recreate the missing shards if possible.
//
// Given a list of valid shards (to read) and invalid shards (to write)
//
// You indicate that a shard is missing by setting it to nil in the 'valid'
// slice and at the same time setting a non-nil writer in "fill".
// An index cannot contain both non-nil 'valid' and 'fill' entry.
// If both are provided 'ErrReconstructMismatch' is returned.
//
// 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(valid []io.Reader, fill []io.Writer) error
// Split a an input stream into the number of shards given to the encoder.
//
// The data will be split into equally sized shards.
// If the data size isn't dividable by the number of shards,
// the last shard will contain extra zeros.
//
// You must supply the total size of your input.
// 'ErrShortData' will be returned if it is unable to retrieve the
// number of bytes indicated.
Split(data io.Reader, dst []io.Writer, size int64) (err 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 []io.Reader, outSize int64) error
}
// StreamReadError is returned when a read error is encountered
// that relates to a supplied stream.
// This will allow you to find out which reader has failed.
type StreamReadError struct {
Err error // The error
Stream int // The stream number on which the error occurred
}
// Error returns the error as a string
func (s StreamReadError) Error() string {
return fmt.Sprintf("error reading stream %d: %s", s.Stream, s.Err)
}
// String returns the error as a string
func (s StreamReadError) String() string {
return s.Error()
}
// StreamWriteError is returned when a write error is encountered
// that relates to a supplied stream. This will allow you to
// find out which reader has failed.
type StreamWriteError struct {
Err error // The error
Stream int // The stream number on which the error occurred
}
// Error returns the error as a string
func (s StreamWriteError) Error() string {
return fmt.Sprintf("error writing stream %d: %s", s.Stream, s.Err)
}
// String returns the error as a string
func (s StreamWriteError) String() string {
return s.Error()
}
// rsStream contains a matrix for a specific
// distribution of datashards and parity shards.
// Construct if using NewStream()
type rsStream struct {
r *reedSolomon
bs int // Block size
// Shard reader
readShards func(dst [][]byte, in []io.Reader) error
// Shard writer
writeShards func(out []io.Writer, in [][]byte) error
creads bool
cwrites bool
}
// NewStream 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 data shards is 256.
func NewStream(dataShards, parityShards int, o ...Option) (StreamEncoder, error) {
enc, err := New(dataShards, parityShards, o...)
if err != nil {
return nil, err
}
rs := enc.(*reedSolomon)
r := rsStream{r: rs, bs: 4 << 20}
r.readShards = readShards
r.writeShards = writeShards
return &r, err
}
// NewStreamC creates a new encoder and initializes it to
// the number of data shards and parity shards given.
//
// This functions as 'NewStream', but allows you to enable CONCURRENT reads and writes.
func NewStreamC(dataShards, parityShards int, conReads, conWrites bool, o ...Option) (StreamEncoder, error) {
enc, err := New(dataShards, parityShards, o...)
if err != nil {
return nil, err
}
rs := enc.(*reedSolomon)
r := rsStream{r: rs, bs: 4 << 20}
r.readShards = readShards
r.writeShards = writeShards
if conReads {
r.readShards = cReadShards
}
if conWrites {
r.writeShards = cWriteShards
}
return &r, err
}
func createSlice(n, length int) [][]byte {
out := make([][]byte, n)
for i := range out {
out[i] = make([]byte, length)
}
return out
}
// Encodes parity shards for a set of data shards.
//
// Input is 'shards' containing readers for data shards followed by parity shards
// io.Writer.
//
// The number of shards must match the number given to NewStream().
//
// Each reader must supply the same number of bytes.
//
// The parity shards will be written to the writer.
// The number of bytes written will match the input size.
//
// If a data stream returns an error, a StreamReadError type error
// will be returned. If a parity writer returns an error, a
// StreamWriteError will be returned.
func (r rsStream) Encode(data []io.Reader, parity []io.Writer) error {
if len(data) != r.r.DataShards {
return ErrTooFewShards
}
if len(parity) != r.r.ParityShards {
return ErrTooFewShards
}
all := createSlice(r.r.Shards, r.bs)
in := all[:r.r.DataShards]
out := all[r.r.DataShards:]
read := 0
for {
err := r.readShards(in, data)
switch err {
case nil:
case io.EOF:
if read == 0 {
return ErrShardNoData
}
return nil
default:
return err
}
out = trimShards(out, shardSize(in))
read += shardSize(in)
err = r.r.Encode(all)
if err != nil {
return err
}
err = r.writeShards(parity, out)
if err != nil {
return err
}
}
}
// Trim the shards so they are all the same size
func trimShards(in [][]byte, size int) [][]byte {
for i := range in {
if in[i] != nil {
in[i] = in[i][0:size]
}
if len(in[i]) < size {
in[i] = nil
}
}
return in
}
func readShards(dst [][]byte, in []io.Reader) error {
if len(in) != len(dst) {
panic("internal error: in and dst size do not match")
}
size := -1
for i := range in {
if in[i] == nil {
dst[i] = nil
continue
}
n, err := io.ReadFull(in[i], dst[i])
// The error is EOF only if no bytes were read.
// If an EOF happens after reading some but not all the bytes,
// ReadFull returns ErrUnexpectedEOF.
switch err {
case io.ErrUnexpectedEOF, io.EOF:
if size < 0 {
size = n
} else if n != size {
// Shard sizes must match.
return ErrShardSize
}
dst[i] = dst[i][0:n]
case nil:
continue
default:
return StreamReadError{Err: err, Stream: i}
}
}
if size == 0 {
return io.EOF
}
return nil
}
func writeShards(out []io.Writer, in [][]byte) error {
if len(out) != len(in) {
panic("internal error: in and out size do not match")
}
for i := range in {
if out[i] == nil {
continue
}
n, err := out[i].Write(in[i])
if err != nil {
return StreamWriteError{Err: err, Stream: i}
}
//
if n != len(in[i]) {
return StreamWriteError{Err: io.ErrShortWrite, Stream: i}
}
}
return nil
}
type readResult struct {
n int
size int
err error
}
// cReadShards reads shards concurrently
func cReadShards(dst [][]byte, in []io.Reader) error {
if len(in) != len(dst) {
panic("internal error: in and dst size do not match")
}
var wg sync.WaitGroup
wg.Add(len(in))
res := make(chan readResult, len(in))
for i := range in {
if in[i] == nil {
dst[i] = nil
wg.Done()
continue
}
go func(i int) {
defer wg.Done()
n, err := io.ReadFull(in[i], dst[i])
// The error is EOF only if no bytes were read.
// If an EOF happens after reading some but not all the bytes,
// ReadFull returns ErrUnexpectedEOF.
res <- readResult{size: n, err: err, n: i}
}(i)
}
wg.Wait()
close(res)
size := -1
for r := range res {
switch r.err {
case io.ErrUnexpectedEOF, io.EOF:
if size < 0 {
size = r.size
} else if r.size != size {
// Shard sizes must match.
return ErrShardSize
}
dst[r.n] = dst[r.n][0:r.size]
case nil:
default:
return StreamReadError{Err: r.err, Stream: r.n}
}
}
if size == 0 {
return io.EOF
}
return nil
}
// cWriteShards writes shards concurrently
func cWriteShards(out []io.Writer, in [][]byte) error {
if len(out) != len(in) {
panic("internal error: in and out size do not match")
}
var errs = make(chan error, len(out))
var wg sync.WaitGroup
wg.Add(len(out))
for i := range in {
go func(i int) {
defer wg.Done()
if out[i] == nil {
errs <- nil
return
}
n, err := out[i].Write(in[i])
if err != nil {
errs <- StreamWriteError{Err: err, Stream: i}
return
}
if n != len(in[i]) {
errs <- StreamWriteError{Err: io.ErrShortWrite, Stream: i}
}
}(i)
}
wg.Wait()
close(errs)
for err := range errs {
if err != nil {
return err
}
}
return nil
}
// Verify returns true if the parity shards contain correct data.
//
// The number of shards must match the number total data+parity shards
// given to NewStream().
//
// Each reader must supply the same number of bytes.
// If a shard stream returns an error, a StreamReadError type error
// will be returned.
func (r rsStream) Verify(shards []io.Reader) (bool, error) {
if len(shards) != r.r.Shards {
return false, ErrTooFewShards
}
read := 0
all := createSlice(r.r.Shards, r.bs)
for {
err := r.readShards(all, shards)
if err == io.EOF {
if read == 0 {
return false, ErrShardNoData
}
return true, nil
}
if err != nil {
return false, err
}
read += shardSize(all)
ok, err := r.r.Verify(all)
if !ok || err != nil {
return ok, err
}
}
}
// ErrReconstructMismatch is returned by the StreamEncoder, if you supply
// "valid" and "fill" streams on the same index.
// Therefore it is impossible to see if you consider the shard valid
// or would like to have it reconstructed.
var ErrReconstructMismatch = errors.New("valid shards and fill shards are mutually exclusive")
// Reconstruct will recreate the missing shards if possible.
//
// Given a list of valid shards (to read) and invalid shards (to write)
//
// You indicate that a shard is missing by setting it to nil in the 'valid'
// slice and at the same time setting a non-nil writer in "fill".
// An index cannot contain both non-nil 'valid' and 'fill' entry.
//
// If there are too few shards to reconstruct the missing
// ones, ErrTooFewShards will be returned.
//
// The reconstructed shard set is complete when explicitly asked for all missing shards.
// However its integrity is not automatically verified.
// Use the Verify function to check in case the data set is complete.
func (r rsStream) Reconstruct(valid []io.Reader, fill []io.Writer) error {
if len(valid) != r.r.Shards {
return ErrTooFewShards
}
if len(fill) != r.r.Shards {
return ErrTooFewShards
}
all := createSlice(r.r.Shards, r.bs)
reconDataOnly := true
for i := range valid {
if valid[i] != nil && fill[i] != nil {
return ErrReconstructMismatch
}
if i >= r.r.DataShards && fill[i] != nil {
reconDataOnly = false
}
}
read := 0
for {
err := r.readShards(all, valid)
if err == io.EOF {
if read == 0 {
return ErrShardNoData
}
return nil
}
if err != nil {
return err
}
read += shardSize(all)
all = trimShards(all, shardSize(all))
if reconDataOnly {
err = r.r.ReconstructData(all) // just reconstruct missing data shards
} else {
err = r.r.Reconstruct(all) // reconstruct all missing shards
}
if err != nil {
return err
}
err = r.writeShards(fill, all)
if err != nil {
return err
}
}
}
// 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.
func (r rsStream) Join(dst io.Writer, shards []io.Reader, outSize int64) error {
// Do we have enough shards?
if len(shards) < r.r.DataShards {
return ErrTooFewShards
}
// Trim off parity shards if any
shards = shards[:r.r.DataShards]
for i := range shards {
if shards[i] == nil {
return StreamReadError{Err: ErrShardNoData, Stream: i}
}
}
// Join all shards
src := io.MultiReader(shards...)
// Copy data to dst
n, err := io.CopyN(dst, src, outSize)
if err == io.EOF {
return ErrShortData
}
if err != nil {
return err
}
if n != outSize {
return ErrShortData
}
return nil
}
// Split a an input stream into the number of shards given to the encoder.
//
// The data will be split into equally sized shards.
// If the data size isn't dividable by the number of shards,
// the last shard will contain extra zeros.
//
// You must supply the total size of your input.
// 'ErrShortData' will be returned if it is unable to retrieve the
// number of bytes indicated.
func (r rsStream) Split(data io.Reader, dst []io.Writer, size int64) error {
if size == 0 {
return ErrShortData
}
if len(dst) != r.r.DataShards {
return ErrInvShardNum
}
for i := range dst {
if dst[i] == nil {
return StreamWriteError{Err: ErrShardNoData, Stream: i}
}
}
// Calculate number of bytes per shard.
perShard := (size + int64(r.r.DataShards) - 1) / int64(r.r.DataShards)
// Pad data to r.Shards*perShard.
padding := make([]byte, (int64(r.r.Shards)*perShard)-size)
data = io.MultiReader(data, bytes.NewBuffer(padding))
// Split into equal-length shards and copy.
for i := range dst {
n, err := io.CopyN(dst[i], data, perShard)
if err != io.EOF && err != nil {
return err
}
if n != perShard {
return ErrShortData
}
}
return nil
}