/** * 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" "sync" ) // Encoder is an interface to encode Reed-Salomon parity sets for your data. type Encoder interface { // Encodes 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. // // 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. // // 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 } // 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 if r.o.usePAR1Matrix { r.m, err = buildMatrixPAR1(dataShards, r.Shards) } else { r.m, err = buildMatrix(dataShards, r.Shards) } if err != nil { return nil, err } // 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.useSSSE3, r.o.useAVX2) } } } 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.useSSSE3, r.o.useAVX2) } } 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.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.useSSSE3, r.o.useAVX2) } else { galMulSliceXor(matrixRows[iRow][c], in, outputs[iRow], r.o.useSSSE3, r.o.useAVX2) } } } } // 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 } 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] for iRow := 0; iRow < outputCount; iRow++ { if c == 0 { galMulSlice(matrixRows[iRow][c], in[start:stop], outputs[iRow][start:stop], r.o.useSSSE3, r.o.useAVX2) } else { galMulSliceXor(matrixRows[iRow][c], in[start:stop], outputs[iRow][start:stop], r.o.useSSSE3, r.o.useAVX2) } } } 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.useSSSE3, r.o.useAVX2) } } 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 } 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.useSSSE3, r.o.useAVX2) } } 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. // // 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. // // 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 { 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 { 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 }