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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
mPool sync.Pool
}
// 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
}
// buildXorMatrix can be used to build a matrix with pure XOR
// operations if there is only one parity shard.
func buildXorMatrix(dataShards, totalShards int) (matrix, error) {
if dataShards+1 != totalShards {
return nil, errors.New("internal 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.
if r < dataShards {
result[r][r] = 1
} else {
// Set all values to 1 (XOR)
for c := range row {
result[r][c] = 1
}
}
}
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.fastOneParity && parityShards == 1:
r.m, err = buildXorMatrix(dataShards, r.Shards)
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
}
// Calculate what we want per round
r.o.perRound = cpuid.CPU.Cache.L2
if r.o.perRound <= 0 {
// Set to 128K if undetectable.
r.o.perRound = 128 << 10
}
if cpuid.CPU.ThreadsPerCore > 1 && r.o.maxGoroutines > cpuid.CPU.PhysicalCores {
// If multiple threads per core, make sure they don't contend for cache.
r.o.perRound /= cpuid.CPU.ThreadsPerCore
}
// 1 input + parity must fit in cache, and we add one more to be safer.
r.o.perRound = r.o.perRound / (1 + parityShards)
// Align to 64 bytes.
r.o.perRound = ((r.o.perRound + 63) / 64) * 64
if r.o.minSplitSize <= 0 {
// Set minsplit as high as we can, but still have parity in L1.
cacheSize := cpuid.CPU.Cache.L1D
if cacheSize <= 0 {
cacheSize = 32 << 10
}
r.o.minSplitSize = cacheSize / (parityShards + 1)
// Min 1K
if r.o.minSplitSize < 1024 {
r.o.minSplitSize = 1024
}
}
if r.o.perRound < r.o.minSplitSize {
r.o.perRound = r.o.minSplitSize
}
if r.o.shardSize > 0 {
p := runtime.GOMAXPROCS(0)
if p == 1 || r.o.shardSize <= r.o.minSplitSize*2 {
// Not worth it.
r.o.maxGoroutines = 1
} else {
g := r.o.shardSize / r.o.perRound
// Overprovision by a factor of 2.
if g < p*2 && r.o.perRound > r.o.minSplitSize*2 {
g = p * 2
r.o.perRound /= 2
}
// 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]
}
if avx2CodeGen && r.o.useAVX2 {
r.mPool.New = func() interface{} {
return make([]byte, r.Shards*2*32)
}
}
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)
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)
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 len(outputs) == 0 {
return
}
switch {
case r.o.useAVX512 && r.o.maxGoroutines > 1 && byteCount > r.o.minSplitSize && len(inputs) >= 4 && len(outputs) >= 2:
r.codeSomeShardsAvx512P(matrixRows, inputs, outputs, outputCount, byteCount)
return
case r.o.useAVX512 && len(inputs) >= 4 && len(outputs) >= 2:
r.codeSomeShardsAvx512(matrixRows, inputs, outputs, outputCount, byteCount)
return
case r.o.maxGoroutines > 1 && byteCount > r.o.minSplitSize:
r.codeSomeShardsP(matrixRows, inputs, outputs, outputCount, byteCount)
return
}
// Process using no goroutines
start, end := 0, r.o.perRound
if end > len(inputs[0]) {
end = len(inputs[0])
}
if avx2CodeGen && r.o.useAVX2 && byteCount >= 32 && len(inputs) > 1 && len(outputs) > 1 && len(inputs) <= maxAvx2Inputs && len(outputs) <= maxAvx2Outputs {
m := genAvx2Matrix(matrixRows, len(inputs), len(outputs), r.mPool.Get().([]byte))
start += galMulSlicesAvx2(m, inputs, outputs, 0, byteCount)
r.mPool.Put(m)
end = len(inputs[0])
}
for start < len(inputs[0]) {
for c := 0; c < r.DataShards; c++ {
in := inputs[c][start:end]
for iRow := 0; iRow < outputCount; iRow++ {
if c == 0 {
galMulSlice(matrixRows[iRow][c], in, outputs[iRow][start:end], &r.o)
} else {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow][start:end], &r.o)
}
}
}
start = end
end += r.o.perRound
if end > len(inputs[0]) {
end = len(inputs[0])
}
}
}
// 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 64
do = (do + 63) & (^63)
start := 0
var avx2Matrix []byte
if avx2CodeGen && r.o.useAVX2 && byteCount >= 32 && len(inputs) > 1 && len(outputs) > 1 && len(inputs) <= maxAvx2Inputs && len(outputs) <= maxAvx2Outputs {
avx2Matrix = genAvx2Matrix(matrixRows, len(inputs), len(outputs), r.mPool.Get().([]byte))
defer r.mPool.Put(avx2Matrix)
}
for start < byteCount {
if start+do > byteCount {
do = byteCount - start
}
wg.Add(1)
go func(start, stop int) {
if avx2CodeGen && r.o.useAVX2 && stop-start >= 32 && len(inputs) > 1 && len(outputs) > 1 && len(inputs) <= maxAvx2Inputs && len(outputs) <= maxAvx2Outputs {
start += galMulSlicesAvx2(avx2Matrix, inputs, outputs, start, stop)
}
lstart, lstop := start, start+r.o.perRound
if lstop > stop {
lstop = stop
}
for lstart < stop {
for c := 0; c < r.DataShards; c++ {
in := inputs[c][lstart:lstop]
for iRow := 0; iRow < outputCount; iRow++ {
if c == 0 {
galMulSlice(matrixRows[iRow][c], in, outputs[iRow][lstart:lstop], &r.o)
} else {
galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow][lstart:lstop], &r.o)
}
}
}
lstart = lstop
lstop += r.o.perRound
if lstop > stop {
lstop = stop
}
}
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 64
do = (do + 63) & (^63)
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
dataPresent := 0
for i := 0; i < r.Shards; i++ {
if len(shards[i]) != 0 {
numberPresent++
if i < r.DataShards {
dataPresent++
}
}
}
if numberPresent == r.Shards || dataOnly && dataPresent == r.DataShards {
// 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
var padding []byte
if len(data) < (r.Shards * perShard) {
// calculate maximum number of full shards in `data` slice
fullShards := len(data) / perShard
padding = make([]byte, r.Shards*perShard-perShard*fullShards)
copy(padding, data[perShard*fullShards:])
data = data[0 : perShard*fullShards]
}
// Split into equal-length shards.
dst := make([][]byte, r.Shards)
i := 0
for ; i < len(dst) && len(data) >= perShard; i++ {
dst[i] = data[:perShard:perShard]
data = data[perShard:]
}
for j := 0; i+j < len(dst); j++ {
dst[i+j] = padding[:perShard:perShard]
padding = padding[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
}
