vendor.github.com.klauspost.reedsolomon.leopard8.go Maven / Gradle / Ivy
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package reedsolomon
// This is a O(n*log n) implementation of Reed-Solomon
// codes, ported from the C++ library https://github.com/catid/leopard.
//
// The implementation is based on the paper
//
// S.-J. Lin, T. Y. Al-Naffouri, Y. S. Han, and W.-H. Chung,
// "Novel Polynomial Basis with Fast Fourier Transform
// and Its Application to Reed-Solomon Erasure Codes"
// IEEE Trans. on Information Theory, pp. 6284-6299, November, 2016.
import (
"bytes"
"encoding/binary"
"io"
"math/bits"
"sync"
)
// leopardFF8 is like reedSolomon but for the 8-bit "leopard" implementation.
type leopardFF8 struct {
dataShards int // Number of data shards, should not be modified.
parityShards int // Number of parity shards, should not be modified.
totalShards int // Total number of shards. Calculated, and should not be modified.
workPool sync.Pool
inversion map[[inversion8Bytes]byte]leopardGF8cache
inversionMu sync.Mutex
o options
}
const inversion8Bytes = 256 / 8
type leopardGF8cache struct {
errorLocs [256]ffe8
bits *errorBitfield8
}
// newFF8 is like New, but for the 8-bit "leopard" implementation.
func newFF8(dataShards, parityShards int, opt options) (*leopardFF8, error) {
initConstants8()
if dataShards <= 0 || parityShards <= 0 {
return nil, ErrInvShardNum
}
if dataShards+parityShards > 65536 {
return nil, ErrMaxShardNum
}
r := &leopardFF8{
dataShards: dataShards,
parityShards: parityShards,
totalShards: dataShards + parityShards,
o: opt,
}
if opt.inversionCache && (r.totalShards <= 64 || opt.forcedInversionCache) {
// Inversion cache is relatively ineffective for big shard counts and takes up potentially lots of memory
// r.totalShards is not covering the space, but an estimate.
r.inversion = make(map[[inversion8Bytes]byte]leopardGF8cache, r.totalShards)
}
return r, nil
}
var _ = Extensions(&leopardFF8{})
func (r *leopardFF8) ShardSizeMultiple() int {
return 64
}
func (r *leopardFF8) DataShards() int {
return r.dataShards
}
func (r *leopardFF8) ParityShards() int {
return r.parityShards
}
func (r *leopardFF8) TotalShards() int {
return r.totalShards
}
func (r *leopardFF8) AllocAligned(each int) [][]byte {
return AllocAligned(r.totalShards, each)
}
type ffe8 uint8
const (
bitwidth8 = 8
order8 = 1 << bitwidth8
modulus8 = order8 - 1
polynomial8 = 0x11D
// Encode in blocks of this size.
workSize8 = 32 << 10
)
var (
fftSkew8 *[modulus8]ffe8
logWalsh8 *[order8]ffe8
)
// Logarithm Tables
var (
logLUT8 *[order8]ffe8
expLUT8 *[order8]ffe8
)
// Stores the partial products of x * y at offset x + y * 256
// Repeated accesses from the same y value are faster
var mul8LUTs *[order8]mul8LUT
type mul8LUT struct {
Value [256]ffe8
}
// Stores lookup for avx2
var multiply256LUT8 *[order8][2 * 16]byte
func (r *leopardFF8) Encode(shards [][]byte) error {
if len(shards) != r.totalShards {
return ErrTooFewShards
}
if err := checkShards(shards, false); err != nil {
return err
}
return r.encode(shards)
}
func (r *leopardFF8) encode(shards [][]byte) error {
shardSize := shardSize(shards)
if shardSize%64 != 0 {
return ErrInvalidShardSize
}
m := ceilPow2(r.parityShards)
var work [][]byte
if w, ok := r.workPool.Get().([][]byte); ok {
work = w
} else {
work = AllocAligned(m*2, workSize8)
}
if cap(work) >= m*2 {
work = work[:m*2]
for i := range work {
if i >= r.parityShards {
if cap(work[i]) < workSize8 {
work[i] = AllocAligned(1, workSize8)[0]
} else {
work[i] = work[i][:workSize8]
}
}
}
} else {
work = AllocAligned(m*2, workSize8)
}
defer r.workPool.Put(work)
mtrunc := m
if r.dataShards < mtrunc {
mtrunc = r.dataShards
}
skewLUT := fftSkew8[m-1:]
// Split large shards.
// More likely on lower shard count.
off := 0
sh := make([][]byte, len(shards))
// work slice we can modify
wMod := make([][]byte, len(work))
copy(wMod, work)
for off < shardSize {
work := wMod
sh := sh
end := off + workSize8
if end > shardSize {
end = shardSize
sz := shardSize - off
for i := range work {
// Last iteration only...
work[i] = work[i][:sz]
}
}
for i := range shards {
sh[i] = shards[i][off:end]
}
// Replace work slices, so we write directly to output.
// Note that work has parity *before* data shards.
res := shards[r.dataShards:r.totalShards]
for i := range res {
work[i] = res[i][off:end]
}
ifftDITEncoder8(
sh[:r.dataShards],
mtrunc,
work,
nil, // No xor output
m,
skewLUT,
&r.o,
)
lastCount := r.dataShards % m
skewLUT2 := skewLUT
if m >= r.dataShards {
goto skip_body
}
// For sets of m data pieces:
for i := m; i+m <= r.dataShards; i += m {
sh = sh[m:]
skewLUT2 = skewLUT2[m:]
// work <- work xor IFFT(data + i, m, m + i)
ifftDITEncoder8(
sh, // data source
m,
work[m:], // temporary workspace
work, // xor destination
m,
skewLUT2,
&r.o,
)
}
// Handle final partial set of m pieces:
if lastCount != 0 {
sh = sh[m:]
skewLUT2 = skewLUT2[m:]
// work <- work xor IFFT(data + i, m, m + i)
ifftDITEncoder8(
sh, // data source
lastCount,
work[m:], // temporary workspace
work, // xor destination
m,
skewLUT2,
&r.o,
)
}
skip_body:
// work <- FFT(work, m, 0)
fftDIT8(work, r.parityShards, m, fftSkew8[:], &r.o)
off += workSize8
}
return nil
}
func (r *leopardFF8) EncodeIdx(dataShard []byte, idx int, parity [][]byte) error {
return ErrNotSupported
}
func (r *leopardFF8) 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
}
func (r *leopardFF8) Update(shards [][]byte, newDatashards [][]byte) error {
return ErrNotSupported
}
func (r *leopardFF8) Split(data []byte) ([][]byte, error) {
if len(data) == 0 {
return nil, ErrShortData
}
if r.totalShards == 1 && len(data)&63 == 0 {
return [][]byte{data}, nil
}
dataLen := len(data)
// Calculate number of bytes per data shard.
perShard := (len(data) + r.dataShards - 1) / r.dataShards
perShard = ((perShard + 63) / 64) * 64
needTotal := r.totalShards * perShard
if cap(data) > len(data) {
if cap(data) > needTotal {
data = data[:needTotal]
} else {
data = data[:cap(data)]
}
clear := data[dataLen:]
for i := range clear {
clear[i] = 0
}
}
// Only allocate memory if necessary
var padding [][]byte
if len(data) < needTotal {
// calculate maximum number of full shards in `data` slice
fullShards := len(data) / perShard
padding = AllocAligned(r.totalShards-fullShards, perShard)
if dataLen > perShard*fullShards {
// Copy partial shards
copyFrom := data[perShard*fullShards : dataLen]
for i := range padding {
if len(copyFrom) == 0 {
break
}
copyFrom = copyFrom[copy(padding[i], copyFrom):]
}
}
}
// Split into equal-length shards.
dst := make([][]byte, r.totalShards)
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[0]
padding = padding[1:]
}
return dst, nil
}
func (r *leopardFF8) ReconstructSome(shards [][]byte, required []bool) error {
return r.ReconstructData(shards)
}
func (r *leopardFF8) Reconstruct(shards [][]byte) error {
return r.reconstruct(shards, true)
}
func (r *leopardFF8) ReconstructData(shards [][]byte) error {
return r.reconstruct(shards, false)
}
func (r *leopardFF8) Verify(shards [][]byte) (bool, error) {
if len(shards) != r.totalShards {
return false, ErrTooFewShards
}
if err := checkShards(shards, false); err != nil {
return false, err
}
// Re-encode parity shards to temporary storage.
shardSize := len(shards[0])
outputs := make([][]byte, r.totalShards)
copy(outputs, shards[:r.dataShards])
for i := r.dataShards; i < r.totalShards; i++ {
outputs[i] = make([]byte, shardSize)
}
if err := r.Encode(outputs); err != nil {
return false, err
}
// Compare.
for i := r.dataShards; i < r.totalShards; i++ {
if !bytes.Equal(outputs[i], shards[i]) {
return false, nil
}
}
return true, nil
}
func (r *leopardFF8) reconstruct(shards [][]byte, recoverAll bool) error {
if len(shards) != r.totalShards {
return ErrTooFewShards
}
if err := checkShards(shards, true); err != nil {
return err
}
// Quick check: are all of the shards present? If so, there's
// nothing to do.
numberPresent := 0
dataPresent := 0
for i := 0; i < r.totalShards; i++ {
if len(shards[i]) != 0 {
numberPresent++
if i < r.dataShards {
dataPresent++
}
}
}
if numberPresent == r.totalShards || !recoverAll && dataPresent == r.dataShards {
// Cool. All of the shards have data. We don't
// need to do anything.
return nil
}
// Check if we have enough to reconstruct.
if numberPresent < r.dataShards {
return ErrTooFewShards
}
shardSize := shardSize(shards)
if shardSize%64 != 0 {
return ErrInvalidShardSize
}
// Use only if we are missing less than 1/4 parity,
// And we are restoring a significant amount of data.
useBits := r.totalShards-numberPresent <= r.parityShards/4 && shardSize*r.totalShards >= 64<<10
m := ceilPow2(r.parityShards)
n := ceilPow2(m + r.dataShards)
const LEO_ERROR_BITFIELD_OPT = true
// Fill in error locations.
var errorBits errorBitfield8
var errLocs [order8]ffe8
for i := 0; i < r.parityShards; i++ {
if len(shards[i+r.dataShards]) == 0 {
errLocs[i] = 1
if LEO_ERROR_BITFIELD_OPT && recoverAll {
errorBits.set(i)
}
}
}
for i := r.parityShards; i < m; i++ {
errLocs[i] = 1
if LEO_ERROR_BITFIELD_OPT && recoverAll {
errorBits.set(i)
}
}
for i := 0; i < r.dataShards; i++ {
if len(shards[i]) == 0 {
errLocs[i+m] = 1
if LEO_ERROR_BITFIELD_OPT {
errorBits.set(i + m)
}
}
}
var gotInversion bool
if LEO_ERROR_BITFIELD_OPT && r.inversion != nil {
cacheID := errorBits.cacheID()
r.inversionMu.Lock()
if inv, ok := r.inversion[cacheID]; ok {
r.inversionMu.Unlock()
errLocs = inv.errorLocs
if inv.bits != nil && useBits {
errorBits = *inv.bits
useBits = true
} else {
useBits = false
}
gotInversion = true
} else {
r.inversionMu.Unlock()
}
}
if !gotInversion {
// No inversion...
if LEO_ERROR_BITFIELD_OPT && useBits {
errorBits.prepare()
}
// Evaluate error locator polynomial8
fwht8(&errLocs, order8, m+r.dataShards)
for i := 0; i < order8; i++ {
errLocs[i] = ffe8((uint(errLocs[i]) * uint(logWalsh8[i])) % modulus8)
}
fwht8(&errLocs, order8, order8)
if r.inversion != nil {
c := leopardGF8cache{
errorLocs: errLocs,
}
if useBits {
// Heap alloc
var x errorBitfield8
x = errorBits
c.bits = &x
}
r.inversionMu.Lock()
r.inversion[errorBits.cacheID()] = c
r.inversionMu.Unlock()
}
}
var work [][]byte
if w, ok := r.workPool.Get().([][]byte); ok {
work = w
}
if cap(work) >= n {
work = work[:n]
for i := range work {
if cap(work[i]) < workSize8 {
work[i] = make([]byte, workSize8)
} else {
work[i] = work[i][:workSize8]
}
}
} else {
work = make([][]byte, n)
all := make([]byte, n*workSize8)
for i := range work {
work[i] = all[i*workSize8 : i*workSize8+workSize8]
}
}
defer r.workPool.Put(work)
// work <- recovery data
// Split large shards.
// More likely on lower shard count.
sh := make([][]byte, len(shards))
// Copy...
copy(sh, shards)
// Add output
for i, sh := range shards {
if !recoverAll && i >= r.dataShards {
continue
}
if len(sh) == 0 {
if cap(sh) >= shardSize {
shards[i] = sh[:shardSize]
} else {
shards[i] = make([]byte, shardSize)
}
}
}
off := 0
for off < shardSize {
endSlice := off + workSize8
if endSlice > shardSize {
endSlice = shardSize
sz := shardSize - off
// Last iteration only
for i := range work {
work[i] = work[i][:sz]
}
}
for i := range shards {
if len(sh[i]) != 0 {
sh[i] = shards[i][off:endSlice]
}
}
for i := 0; i < r.parityShards; i++ {
if len(sh[i+r.dataShards]) != 0 {
mulgf8(work[i], sh[i+r.dataShards], errLocs[i], &r.o)
} else {
memclr(work[i])
}
}
for i := r.parityShards; i < m; i++ {
memclr(work[i])
}
// work <- original data
for i := 0; i < r.dataShards; i++ {
if len(sh[i]) != 0 {
mulgf8(work[m+i], sh[i], errLocs[m+i], &r.o)
} else {
memclr(work[m+i])
}
}
for i := m + r.dataShards; i < n; i++ {
memclr(work[i])
}
// work <- IFFT(work, n, 0)
ifftDITDecoder8(
m+r.dataShards,
work,
n,
fftSkew8[:],
&r.o,
)
// work <- FormalDerivative(work, n)
for i := 1; i < n; i++ {
width := ((i ^ (i - 1)) + 1) >> 1
slicesXor(work[i-width:i], work[i:i+width], &r.o)
}
// work <- FFT(work, n, 0) truncated to m + dataShards
outputCount := m + r.dataShards
if LEO_ERROR_BITFIELD_OPT && useBits {
errorBits.fftDIT8(work, outputCount, n, fftSkew8[:], &r.o)
} else {
fftDIT8(work, outputCount, n, fftSkew8[:], &r.o)
}
// Reveal erasures
//
// Original = -ErrLocator * FFT( Derivative( IFFT( ErrLocator * ReceivedData ) ) )
// mul_mem(x, y, log_m, ) equals x[] = y[] * log_m
//
// mem layout: [Recovery Data (Power of Two = M)] [Original Data (K)] [Zero Padding out to N]
end := r.dataShards
if recoverAll {
end = r.totalShards
}
// Restore
for i := 0; i < end; i++ {
if len(sh[i]) != 0 {
continue
}
if i >= r.dataShards {
// Parity shard.
mulgf8(shards[i][off:endSlice], work[i-r.dataShards], modulus8-errLocs[i-r.dataShards], &r.o)
} else {
// Data shard.
mulgf8(shards[i][off:endSlice], work[i+m], modulus8-errLocs[i+m], &r.o)
}
}
off += workSize8
}
return nil
}
// Basic no-frills version for decoder
func ifftDITDecoder8(mtrunc int, work [][]byte, m int, skewLUT []ffe8, o *options) {
// Decimation in time: Unroll 2 layers at a time
dist := 1
dist4 := 4
for dist4 <= m {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
iend := r + dist
log_m01 := skewLUT[iend-1]
log_m02 := skewLUT[iend+dist-1]
log_m23 := skewLUT[iend+dist*2-1]
// For each set of dist elements:
for i := r; i < iend; i++ {
ifftDIT48(work[i:], dist, log_m01, log_m23, log_m02, o)
}
}
dist = dist4
dist4 <<= 2
}
// If there is one layer left:
if dist < m {
// Assuming that dist = m / 2
if dist*2 != m {
panic("internal error")
}
log_m := skewLUT[dist-1]
if log_m == modulus8 {
slicesXor(work[dist:2*dist], work[:dist], o)
} else {
for i := 0; i < dist; i++ {
ifftDIT28(
work[i],
work[i+dist],
log_m,
o,
)
}
}
}
}
// In-place FFT for encoder and decoder
func fftDIT8(work [][]byte, mtrunc, m int, skewLUT []ffe8, o *options) {
// Decimation in time: Unroll 2 layers at a time
dist4 := m
dist := m >> 2
for dist != 0 {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
iend := r + dist
log_m01 := skewLUT[iend-1]
log_m02 := skewLUT[iend+dist-1]
log_m23 := skewLUT[iend+dist*2-1]
// For each set of dist elements:
for i := r; i < iend; i++ {
fftDIT48(
work[i:],
dist,
log_m01,
log_m23,
log_m02,
o,
)
}
}
dist4 = dist
dist >>= 2
}
// If there is one layer left:
if dist4 == 2 {
for r := 0; r < mtrunc; r += 2 {
log_m := skewLUT[r+1-1]
if log_m == modulus8 {
sliceXor(work[r], work[r+1], o)
} else {
fftDIT28(work[r], work[r+1], log_m, o)
}
}
}
}
// 4-way butterfly
func fftDIT4Ref8(work [][]byte, dist int, log_m01, log_m23, log_m02 ffe8, o *options) {
// First layer:
if log_m02 == modulus8 {
sliceXor(work[0], work[dist*2], o)
sliceXor(work[dist], work[dist*3], o)
} else {
fftDIT28(work[0], work[dist*2], log_m02, o)
fftDIT28(work[dist], work[dist*3], log_m02, o)
}
// Second layer:
if log_m01 == modulus8 {
sliceXor(work[0], work[dist], o)
} else {
fftDIT28(work[0], work[dist], log_m01, o)
}
if log_m23 == modulus8 {
sliceXor(work[dist*2], work[dist*3], o)
} else {
fftDIT28(work[dist*2], work[dist*3], log_m23, o)
}
}
// Unrolled IFFT for encoder
func ifftDITEncoder8(data [][]byte, mtrunc int, work [][]byte, xorRes [][]byte, m int, skewLUT []ffe8, o *options) {
// I tried rolling the memcpy/memset into the first layer of the FFT and
// found that it only yields a 4% performance improvement, which is not
// worth the extra complexity.
for i := 0; i < mtrunc; i++ {
copy(work[i], data[i])
}
for i := mtrunc; i < m; i++ {
memclr(work[i])
}
// Decimation in time: Unroll 2 layers at a time
dist := 1
dist4 := 4
for dist4 <= m {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
iend := r + dist
log_m01 := skewLUT[iend]
log_m02 := skewLUT[iend+dist]
log_m23 := skewLUT[iend+dist*2]
// For each set of dist elements:
for i := r; i < iend; i++ {
ifftDIT48(
work[i:],
dist,
log_m01,
log_m23,
log_m02,
o,
)
}
}
dist = dist4
dist4 <<= 2
// I tried alternating sweeps left->right and right->left to reduce cache misses.
// It provides about 1% performance boost when done for both FFT and IFFT, so it
// does not seem to be worth the extra complexity.
}
// If there is one layer left:
if dist < m {
// Assuming that dist = m / 2
if dist*2 != m {
panic("internal error")
}
logm := skewLUT[dist]
if logm == modulus8 {
slicesXor(work[dist:dist*2], work[:dist], o)
} else {
for i := 0; i < dist; i++ {
ifftDIT28(work[i], work[i+dist], logm, o)
}
}
}
// I tried unrolling this but it does not provide more than 5% performance
// improvement for 16-bit finite fields, so it's not worth the complexity.
if xorRes != nil {
slicesXor(xorRes[:m], work[:m], o)
}
}
func ifftDIT4Ref8(work [][]byte, dist int, log_m01, log_m23, log_m02 ffe8, o *options) {
// First layer:
if log_m01 == modulus8 {
sliceXor(work[0], work[dist], o)
} else {
ifftDIT28(work[0], work[dist], log_m01, o)
}
if log_m23 == modulus8 {
sliceXor(work[dist*2], work[dist*3], o)
} else {
ifftDIT28(work[dist*2], work[dist*3], log_m23, o)
}
// Second layer:
if log_m02 == modulus8 {
sliceXor(work[0], work[dist*2], o)
sliceXor(work[dist], work[dist*3], o)
} else {
ifftDIT28(work[0], work[dist*2], log_m02, o)
ifftDIT28(work[dist], work[dist*3], log_m02, o)
}
}
// Reference version of muladd: x[] ^= y[] * log_m
func refMulAdd8(x, y []byte, log_m ffe8) {
lut := &mul8LUTs[log_m]
for len(x) >= 64 {
// Assert sizes for no bounds checks in loop
src := y[:64]
dst := x[:len(src)] // Needed, but not checked...
for i, y1 := range src {
dst[i] ^= byte(lut.Value[y1])
}
x = x[64:]
y = y[64:]
}
}
// Reference version of mul: x[] = y[] * log_m
func refMul8(x, y []byte, log_m ffe8) {
lut := &mul8LUTs[log_m]
for off := 0; off < len(x); off += 64 {
src := y[off : off+64]
for i, y1 := range src {
x[off+i] = byte(lut.Value[y1])
}
}
}
// Returns a * Log(b)
func mulLog8(a, log_b ffe8) ffe8 {
/*
Note that this operation is not a normal multiplication in a finite
field because the right operand is already a logarithm. This is done
because it moves K table lookups from the Decode() method into the
initialization step that is less performance critical. The LogWalsh[]
table below contains precalculated logarithms so it is easier to do
all the other multiplies in that form as well.
*/
if a == 0 {
return 0
}
return expLUT8[addMod8(logLUT8[a], log_b)]
}
// z = x + y (mod kModulus)
func addMod8(a, b ffe8) ffe8 {
sum := uint(a) + uint(b)
// Partial reduction step, allowing for kModulus to be returned
return ffe8(sum + sum>>bitwidth8)
}
// z = x - y (mod kModulus)
func subMod8(a, b ffe8) ffe8 {
dif := uint(a) - uint(b)
// Partial reduction step, allowing for kModulus to be returned
return ffe8(dif + dif>>bitwidth8)
}
// Decimation in time (DIT) Fast Walsh-Hadamard Transform
// Unrolls pairs of layers to perform cross-layer operations in registers
// mtrunc: Number of elements that are non-zero at the front of data
func fwht8(data *[order8]ffe8, m, mtrunc int) {
// Decimation in time: Unroll 2 layers at a time
dist := 1
dist4 := 4
for dist4 <= m {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
// For each set of dist elements:
// Use 16 bit indices to avoid bounds check on [65536]ffe8.
dist := uint16(dist)
off := uint16(r)
for i := uint16(0); i < dist; i++ {
// fwht48(data[i:], dist) inlined...
// Reading values appear faster than updating pointers.
// Casting to uint is not faster.
t0 := data[off]
t1 := data[off+dist]
t2 := data[off+dist*2]
t3 := data[off+dist*3]
t0, t1 = fwht2alt8(t0, t1)
t2, t3 = fwht2alt8(t2, t3)
t0, t2 = fwht2alt8(t0, t2)
t1, t3 = fwht2alt8(t1, t3)
data[off] = t0
data[off+dist] = t1
data[off+dist*2] = t2
data[off+dist*3] = t3
off++
}
}
dist = dist4
dist4 <<= 2
}
// If there is one layer left:
if dist < m {
dist := uint16(dist)
for i := uint16(0); i < dist; i++ {
fwht28(&data[i], &data[i+dist])
}
}
}
func fwht48(data []ffe8, s int) {
s2 := s << 1
t0 := &data[0]
t1 := &data[s]
t2 := &data[s2]
t3 := &data[s2+s]
fwht28(t0, t1)
fwht28(t2, t3)
fwht28(t0, t2)
fwht28(t1, t3)
}
// {a, b} = {a + b, a - b} (Mod Q)
func fwht28(a, b *ffe8) {
sum := addMod8(*a, *b)
dif := subMod8(*a, *b)
*a = sum
*b = dif
}
// fwht2alt8 is as fwht28, but returns result.
func fwht2alt8(a, b ffe8) (ffe8, ffe8) {
return addMod8(a, b), subMod8(a, b)
}
var initOnce8 sync.Once
func initConstants8() {
initOnce8.Do(func() {
initLUTs8()
initFFTSkew8()
initMul8LUT()
})
}
// Initialize logLUT8, expLUT8.
func initLUTs8() {
cantorBasis := [bitwidth8]ffe8{
1, 214, 152, 146, 86, 200, 88, 230,
}
expLUT8 = &[order8]ffe8{}
logLUT8 = &[order8]ffe8{}
// LFSR table generation:
state := 1
for i := ffe8(0); i < modulus8; i++ {
expLUT8[state] = i
state <<= 1
if state >= order8 {
state ^= polynomial8
}
}
expLUT8[0] = modulus8
// Conversion to Cantor basis:
logLUT8[0] = 0
for i := 0; i < bitwidth8; i++ {
basis := cantorBasis[i]
width := 1 << i
for j := 0; j < width; j++ {
logLUT8[j+width] = logLUT8[j] ^ basis
}
}
for i := 0; i < order8; i++ {
logLUT8[i] = expLUT8[logLUT8[i]]
}
for i := 0; i < order8; i++ {
expLUT8[logLUT8[i]] = ffe8(i)
}
expLUT8[modulus8] = expLUT8[0]
}
// Initialize fftSkew8.
func initFFTSkew8() {
var temp [bitwidth8 - 1]ffe8
// Generate FFT skew vector {1}:
for i := 1; i < bitwidth8; i++ {
temp[i-1] = ffe8(1 << i)
}
fftSkew8 = &[modulus8]ffe8{}
logWalsh8 = &[order8]ffe8{}
for m := 0; m < bitwidth8-1; m++ {
step := 1 << (m + 1)
fftSkew8[1<>4)+16)]
}
}
// Always initialize assembly tables.
// Not as big resource hog as gf16.
if true {
multiply256LUT8 = &[order8][16 * 2]byte{}
for logM := range multiply256LUT8[:] {
// For each 4 bits of the finite field width in bits:
shift := 0
for i := 0; i < 2; i++ {
// Construct 16 entry LUT for PSHUFB
prod := multiply256LUT8[logM][i*16 : i*16+16]
for x := range prod[:] {
prod[x] = byte(mulLog8(ffe8(x<= 8 || mipLevel <= 0 {
return true
}
return 0 != (e.Words[mipLevel-1][bit/64] & (uint64(1) << (bit & 63)))
}
func (e *errorBitfield8) prepare() {
// First mip level is for final layer of FFT: pairs of data
for i := 0; i < kWords8; i++ {
w_i := e.Words[0][i]
hi2lo0 := w_i | ((w_i & kHiMasks[0]) >> 1)
lo2hi0 := (w_i & (kHiMasks[0] >> 1)) << 1
w_i = hi2lo0 | lo2hi0
e.Words[0][i] = w_i
bits := 2
for j := 1; j < 5; j++ {
hi2lo_j := w_i | ((w_i & kHiMasks[j]) >> bits)
lo2hi_j := (w_i & (kHiMasks[j] >> bits)) << bits
w_i = hi2lo_j | lo2hi_j
e.Words[j][i] = w_i
bits <<= 1
}
}
for i := 0; i < kWords8; i++ {
w := e.Words[4][i]
w |= w >> 32
w |= w << 32
e.Words[5][i] = w
}
for i := 0; i < kWords8; i += 2 {
t := e.Words[5][i] | e.Words[5][i+1]
e.Words[6][i] = t
e.Words[6][i+1] = t
}
}
func (e *errorBitfield8) fftDIT8(work [][]byte, mtrunc, m int, skewLUT []ffe8, o *options) {
// Decimation in time: Unroll 2 layers at a time
mipLevel := bits.Len32(uint32(m)) - 1
dist4 := m
dist := m >> 2
for dist != 0 {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
if !e.isNeeded(mipLevel, r) {
continue
}
iEnd := r + dist
logM01 := skewLUT[iEnd-1]
logM02 := skewLUT[iEnd+dist-1]
logM23 := skewLUT[iEnd+dist*2-1]
// For each set of dist elements:
for i := r; i < iEnd; i++ {
fftDIT48(
work[i:],
dist,
logM01,
logM23,
logM02,
o)
}
}
dist4 = dist
dist >>= 2
mipLevel -= 2
}
// If there is one layer left:
if dist4 == 2 {
for r := 0; r < mtrunc; r += 2 {
if !e.isNeeded(mipLevel, r) {
continue
}
logM := skewLUT[r+1-1]
if logM == modulus8 {
sliceXor(work[r], work[r+1], o)
} else {
fftDIT28(work[r], work[r+1], logM, o)
}
}
}
}