xs/vendor/github.com/klauspost/reedsolomon/leopard.go

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2022-09-21 03:31:53 +00:00
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"
"io"
"math/bits"
"sync"
"unsafe"
"github.com/klauspost/cpuid/v2"
)
// leopardFF16 is like reedSolomon but for more than 256 total shards.
type leopardFF16 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
o options
}
// newFF16 is like New, but for more than 256 total shards.
func newFF16(dataShards, parityShards int, opt options) (*leopardFF16, error) {
initConstants()
if dataShards <= 0 || parityShards <= 0 {
return nil, ErrInvShardNum
}
if dataShards+parityShards > 65536 {
return nil, ErrMaxShardNum
}
r := &leopardFF16{
dataShards: dataShards,
parityShards: parityShards,
totalShards: dataShards + parityShards,
o: opt,
}
return r, nil
}
var _ = Extensions(&leopardFF16{})
func (r *leopardFF16) ShardSizeMultiple() int {
return 64
}
func (r *leopardFF16) DataShards() int {
return r.dataShards
}
func (r *leopardFF16) ParityShards() int {
return r.parityShards
}
func (r *leopardFF16) TotalShards() int {
return r.parityShards
}
type ffe uint16
const (
bitwidth = 16
order = 1 << bitwidth
modulus = order - 1
polynomial = 0x1002D
)
var (
fftSkew *[modulus]ffe
logWalsh *[order]ffe
)
// Logarithm Tables
var (
logLUT *[order]ffe
expLUT *[order]ffe
)
// Stores the partial products of x * y at offset x + y * 65536
// Repeated accesses from the same y value are faster
var mul16LUTs *[order]mul16LUT
type mul16LUT struct {
// Contains Lo product as a single lookup.
// Should be XORed with Hi lookup for result.
Lo [256]ffe
Hi [256]ffe
}
// Stores lookup for avx2
var multiply256LUT *[order][8 * 16]byte
func (r *leopardFF16) 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 *leopardFF16) encode(shards [][]byte) error {
shardSize := shardSize(shards)
if shardSize%64 != 0 {
return ErrShardSize
}
m := ceilPow2(r.parityShards)
var work [][]byte
if w, ok := r.workPool.Get().([][]byte); ok {
work = w
}
if cap(work) >= m*2 {
work = work[:m*2]
} else {
work = make([][]byte, m*2)
}
for i := range work {
if cap(work[i]) < shardSize {
work[i] = make([]byte, shardSize)
} else {
work[i] = work[i][:shardSize]
}
}
defer r.workPool.Put(work)
mtrunc := m
if r.dataShards < mtrunc {
mtrunc = r.dataShards
}
skewLUT := fftSkew[m-1:]
sh := shards
ifftDITEncoder(
sh[:r.dataShards],
mtrunc,
work,
nil, // No xor output
m,
skewLUT,
&r.o,
)
lastCount := r.dataShards % m
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:]
skewLUT = skewLUT[m:]
// work <- work xor IFFT(data + i, m, m + i)
ifftDITEncoder(
sh, // data source
m,
work[m:], // temporary workspace
work, // xor destination
m,
skewLUT,
&r.o,
)
}
// Handle final partial set of m pieces:
if lastCount != 0 {
sh = sh[m:]
skewLUT = skewLUT[m:]
// work <- work xor IFFT(data + i, m, m + i)
ifftDITEncoder(
sh, // data source
lastCount,
work[m:], // temporary workspace
work, // xor destination
m,
skewLUT,
&r.o,
)
}
skip_body:
// work <- FFT(work, m, 0)
fftDIT(work, r.parityShards, m, fftSkew[:], &r.o)
for i, w := range work[:r.parityShards] {
sh := shards[i+r.dataShards]
if cap(sh) >= shardSize {
sh = append(sh[:0], w...)
} else {
sh = w
}
shards[i+r.dataShards] = sh
}
return nil
}
func (r *leopardFF16) EncodeIdx(dataShard []byte, idx int, parity [][]byte) error {
return ErrNotSupported
}
func (r *leopardFF16) 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 *leopardFF16) Update(shards [][]byte, newDatashards [][]byte) error {
return ErrNotSupported
}
func (r *leopardFF16) Split(data []byte) ([][]byte, error) {
if len(data) == 0 {
return nil, ErrShortData
}
dataLen := len(data)
// Calculate number of bytes per data shard.
perShard := (len(data) + r.dataShards - 1) / r.dataShards
perShard = ((perShard + 63) / 64) * 64
if cap(data) > len(data) {
data = data[:cap(data)]
}
// Only allocate memory if necessary
var padding []byte
if len(data) < (r.totalShards * perShard) {
// calculate maximum number of full shards in `data` slice
fullShards := len(data) / perShard
padding = make([]byte, r.totalShards*perShard-perShard*fullShards)
copy(padding, data[perShard*fullShards:])
data = data[0 : perShard*fullShards]
} else {
for i := dataLen; i < dataLen+r.dataShards; i++ {
data[i] = 0
}
}
// 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[:perShard:perShard]
padding = padding[perShard:]
}
return dst, nil
}
func (r *leopardFF16) ReconstructSome(shards [][]byte, required []bool) error {
return r.ReconstructData(shards)
}
func (r *leopardFF16) Reconstruct(shards [][]byte) error {
return r.reconstruct(shards, true)
}
func (r *leopardFF16) ReconstructData(shards [][]byte) error {
return r.reconstruct(shards, false)
}
func (r *leopardFF16) 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 *leopardFF16) 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
}
// Use only if we are missing less than 1/4 parity.
useBits := r.totalShards-numberPresent <= r.parityShards/4
// Check if we have enough to reconstruct.
if numberPresent < r.dataShards {
return ErrTooFewShards
}
shardSize := shardSize(shards)
if shardSize%64 != 0 {
return ErrShardSize
}
m := ceilPow2(r.parityShards)
n := ceilPow2(m + r.dataShards)
const LEO_ERROR_BITFIELD_OPT = true
// Fill in error locations.
var errorBits errorBitfield
var errLocs [order]ffe
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)
}
}
}
if LEO_ERROR_BITFIELD_OPT && useBits {
errorBits.prepare()
}
// Evaluate error locator polynomial
fwht(&errLocs, order, m+r.dataShards)
for i := 0; i < order; i++ {
errLocs[i] = ffe((uint(errLocs[i]) * uint(logWalsh[i])) % modulus)
}
fwht(&errLocs, order, order)
var work [][]byte
if w, ok := r.workPool.Get().([][]byte); ok {
work = w
}
if cap(work) >= n {
work = work[:n]
} else {
work = make([][]byte, n)
}
for i := range work {
if cap(work[i]) < shardSize {
work[i] = make([]byte, shardSize)
} else {
work[i] = work[i][:shardSize]
}
}
defer r.workPool.Put(work)
// work <- recovery data
for i := 0; i < r.parityShards; i++ {
if len(shards[i+r.dataShards]) != 0 {
mulgf16(work[i], shards[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(shards[i]) != 0 {
mulgf16(work[m+i], shards[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)
ifftDITDecoder(
m+r.dataShards,
work,
n,
fftSkew[:],
&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.fftDIT(work, outputCount, n, fftSkew[:], &r.o)
} else {
fftDIT(work, outputCount, n, fftSkew[:], &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
}
for i := 0; i < end; i++ {
if len(shards[i]) != 0 {
continue
}
if cap(shards[i]) >= shardSize {
shards[i] = shards[i][:shardSize]
} else {
shards[i] = make([]byte, shardSize)
}
if i >= r.dataShards {
// Parity shard.
mulgf16(shards[i], work[i-r.dataShards], modulus-errLocs[i-r.dataShards], &r.o)
} else {
// Data shard.
mulgf16(shards[i], work[i+m], modulus-errLocs[i+m], &r.o)
}
}
return nil
}
// Basic no-frills version for decoder
func ifftDITDecoder(mtrunc int, work [][]byte, m int, skewLUT []ffe, 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++ {
ifftDIT4(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 == modulus {
slicesXor(work[dist:2*dist], work[:dist], o)
} else {
for i := 0; i < dist; i++ {
ifftDIT2(
work[i],
work[i+dist],
log_m,
o,
)
}
}
}
}
// In-place FFT for encoder and decoder
func fftDIT(work [][]byte, mtrunc, m int, skewLUT []ffe, 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++ {
fftDIT4(
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 == modulus {
sliceXor(work[r], work[r+1], o)
} else {
fftDIT2(work[r], work[r+1], log_m, o)
}
}
}
}
// 4-way butterfly
func fftDIT4Ref(work [][]byte, dist int, log_m01, log_m23, log_m02 ffe, o *options) {
// First layer:
if log_m02 == modulus {
sliceXor(work[0], work[dist*2], o)
sliceXor(work[dist], work[dist*3], o)
} else {
fftDIT2(work[0], work[dist*2], log_m02, o)
fftDIT2(work[dist], work[dist*3], log_m02, o)
}
// Second layer:
if log_m01 == modulus {
sliceXor(work[0], work[dist], o)
} else {
fftDIT2(work[0], work[dist], log_m01, o)
}
if log_m23 == modulus {
sliceXor(work[dist*2], work[dist*3], o)
} else {
fftDIT2(work[dist*2], work[dist*3], log_m23, o)
}
}
// Unrolled IFFT for encoder
func ifftDITEncoder(data [][]byte, mtrunc int, work [][]byte, xorRes [][]byte, m int, skewLUT []ffe, 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])
}
// I tried splitting up the first few layers into L3-cache sized blocks but
// found that it only provides about 5% performance boost, which is not
// worth the extra complexity.
// 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++ {
ifftDIT4(
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 == modulus {
slicesXor(work[dist:dist*2], work[:dist], o)
} else {
for i := 0; i < dist; i++ {
ifftDIT2(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 ifftDIT4Ref(work [][]byte, dist int, log_m01, log_m23, log_m02 ffe, o *options) {
// First layer:
if log_m01 == modulus {
sliceXor(work[0], work[dist], o)
} else {
ifftDIT2(work[0], work[dist], log_m01, o)
}
if log_m23 == modulus {
sliceXor(work[dist*2], work[dist*3], o)
} else {
ifftDIT2(work[dist*2], work[dist*3], log_m23, o)
}
// Second layer:
if log_m02 == modulus {
sliceXor(work[0], work[dist*2], o)
sliceXor(work[dist], work[dist*3], o)
} else {
ifftDIT2(work[0], work[dist*2], log_m02, o)
ifftDIT2(work[dist], work[dist*3], log_m02, o)
}
}
// Reference version of muladd: x[] ^= y[] * log_m
func refMulAdd(x, y []byte, log_m ffe) {
lut := &mul16LUTs[log_m]
for len(x) >= 64 {
// Assert sizes for no bounds checks in loop
hiA := y[32:64]
loA := y[:32]
dst := x[:64] // Needed, but not checked...
for i, lo := range loA {
hi := hiA[i]
prod := lut.Lo[lo] ^ lut.Hi[hi]
dst[i] ^= byte(prod)
dst[i+32] ^= byte(prod >> 8)
}
x = x[64:]
y = y[64:]
}
}
func memclr(s []byte) {
for i := range s {
s[i] = 0
}
}
// slicesXor calls xor for every slice pair in v1, v2.
func slicesXor(v1, v2 [][]byte, o *options) {
for i, v := range v1 {
sliceXor(v2[i], v, o)
}
}
// Reference version of mul: x[] = y[] * log_m
func refMul(x, y []byte, log_m ffe) {
lut := &mul16LUTs[log_m]
for off := 0; off < len(x); off += 64 {
loA := y[off : off+32]
hiA := y[off+32:]
hiA = hiA[:len(loA)]
for i, lo := range loA {
hi := hiA[i]
prod := lut.Lo[lo] ^ lut.Hi[hi]
x[off+i] = byte(prod)
x[off+i+32] = byte(prod >> 8)
}
}
}
// Returns a * Log(b)
func mulLog(a, log_b ffe) ffe {
/*
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 expLUT[addMod(logLUT[a], log_b)]
}
// z = x + y (mod kModulus)
func addMod(a, b ffe) ffe {
sum := uint(a) + uint(b)
// Partial reduction step, allowing for kModulus to be returned
return ffe(sum + sum>>bitwidth)
}
// z = x - y (mod kModulus)
func subMod(a, b ffe) ffe {
dif := uint(a) - uint(b)
// Partial reduction step, allowing for kModulus to be returned
return ffe(dif + dif>>bitwidth)
}
// ceilPow2 returns power of two at or above n.
func ceilPow2(n int) int {
const w = int(unsafe.Sizeof(n) * 8)
return 1 << (w - bits.LeadingZeros(uint(n-1)))
}
// 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 fwht(data *[order]ffe, 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]ffe.
dist := uint16(dist)
off := uint16(r)
for i := uint16(0); i < dist; i++ {
// fwht4(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 = fwht2alt(t0, t1)
t2, t3 = fwht2alt(t2, t3)
t0, t2 = fwht2alt(t0, t2)
t1, t3 = fwht2alt(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++ {
fwht2(&data[i], &data[i+dist])
}
}
}
func fwht4(data []ffe, s int) {
s2 := s << 1
t0 := &data[0]
t1 := &data[s]
t2 := &data[s2]
t3 := &data[s2+s]
fwht2(t0, t1)
fwht2(t2, t3)
fwht2(t0, t2)
fwht2(t1, t3)
}
// {a, b} = {a + b, a - b} (Mod Q)
func fwht2(a, b *ffe) {
sum := addMod(*a, *b)
dif := subMod(*a, *b)
*a = sum
*b = dif
}
// fwht2alt is as fwht2, but returns result.
func fwht2alt(a, b ffe) (ffe, ffe) {
return addMod(a, b), subMod(a, b)
}
var initOnce sync.Once
func initConstants() {
initOnce.Do(func() {
initLUTs()
initFFTSkew()
initMul16LUT()
})
}
// Initialize logLUT, expLUT.
func initLUTs() {
cantorBasis := [bitwidth]ffe{
0x0001, 0xACCA, 0x3C0E, 0x163E,
0xC582, 0xED2E, 0x914C, 0x4012,
0x6C98, 0x10D8, 0x6A72, 0xB900,
0xFDB8, 0xFB34, 0xFF38, 0x991E,
}
expLUT = &[order]ffe{}
logLUT = &[order]ffe{}
// LFSR table generation:
state := 1
for i := ffe(0); i < modulus; i++ {
expLUT[state] = i
state <<= 1
if state >= order {
state ^= polynomial
}
}
expLUT[0] = modulus
// Conversion to Cantor basis:
logLUT[0] = 0
for i := 0; i < bitwidth; i++ {
basis := cantorBasis[i]
width := 1 << i
for j := 0; j < width; j++ {
logLUT[j+width] = logLUT[j] ^ basis
}
}
for i := 0; i < order; i++ {
logLUT[i] = expLUT[logLUT[i]]
}
for i := 0; i < order; i++ {
expLUT[logLUT[i]] = ffe(i)
}
expLUT[modulus] = expLUT[0]
}
// Initialize fftSkew.
func initFFTSkew() {
var temp [bitwidth - 1]ffe
// Generate FFT skew vector {1}:
for i := 1; i < bitwidth; i++ {
temp[i-1] = ffe(1 << i)
}
fftSkew = &[modulus]ffe{}
logWalsh = &[order]ffe{}
for m := 0; m < bitwidth-1; m++ {
step := 1 << (m + 1)
fftSkew[1<<m-1] = 0
for i := m; i < bitwidth-1; i++ {
s := 1 << (i + 1)
for j := 1<<m - 1; j < s; j += step {
fftSkew[j+s] = fftSkew[j] ^ temp[i]
}
}
temp[m] = modulus - logLUT[mulLog(temp[m], logLUT[temp[m]^1])]
for i := m + 1; i < bitwidth-1; i++ {
sum := addMod(logLUT[temp[i]^1], temp[m])
temp[i] = mulLog(temp[i], sum)
}
}
for i := 0; i < modulus; i++ {
fftSkew[i] = logLUT[fftSkew[i]]
}
// Precalculate FWHT(Log[i]):
for i := 0; i < order; i++ {
logWalsh[i] = logLUT[i]
}
logWalsh[0] = 0
fwht(logWalsh, order, order)
}
func initMul16LUT() {
mul16LUTs = &[order]mul16LUT{}
// For each log_m multiplicand:
for log_m := 0; log_m < order; log_m++ {
var tmp [64]ffe
for nibble, shift := 0, 0; nibble < 4; {
nibble_lut := tmp[nibble*16:]
for xnibble := 0; xnibble < 16; xnibble++ {
prod := mulLog(ffe(xnibble<<shift), ffe(log_m))
nibble_lut[xnibble] = prod
}
nibble++
shift += 4
}
lut := &mul16LUTs[log_m]
for i := range lut.Lo[:] {
lut.Lo[i] = tmp[i&15] ^ tmp[((i>>4)+16)]
lut.Hi[i] = tmp[((i&15)+32)] ^ tmp[((i>>4)+48)]
}
}
if cpuid.CPU.Has(cpuid.SSSE3) || cpuid.CPU.Has(cpuid.AVX2) || cpuid.CPU.Has(cpuid.AVX512F) {
multiply256LUT = &[order][16 * 8]byte{}
for logM := range multiply256LUT[:] {
// For each 4 bits of the finite field width in bits:
shift := 0
for i := 0; i < 4; i++ {
// Construct 16 entry LUT for PSHUFB
prodLo := multiply256LUT[logM][i*16 : i*16+16]
prodHi := multiply256LUT[logM][4*16+i*16 : 4*16+i*16+16]
for x := range prodLo[:] {
prod := mulLog(ffe(x<<shift), ffe(logM))
prodLo[x] = byte(prod)
prodHi[x] = byte(prod >> 8)
}
shift += 4
}
}
}
}
const kWordMips = 5
const kWords = order / 64
const kBigMips = 6
const kBigWords = (kWords + 63) / 64
const kBiggestMips = 4
// errorBitfield contains progressive errors to help indicate which
// shards need reconstruction.
type errorBitfield struct {
Words [kWordMips][kWords]uint64
BigWords [kBigMips][kBigWords]uint64
BiggestWords [kBiggestMips]uint64
}
func (e *errorBitfield) set(i int) {
e.Words[0][i/64] |= uint64(1) << (i & 63)
}
func (e *errorBitfield) isNeededFn(mipLevel int) func(bit int) bool {
if mipLevel >= 16 {
return func(bit int) bool {
return true
}
}
if mipLevel >= 12 {
w := e.BiggestWords[mipLevel-12]
return func(bit int) bool {
bit /= 4096
return 0 != (w & (uint64(1) << bit))
}
}
if mipLevel >= 6 {
w := e.BigWords[mipLevel-6][:]
return func(bit int) bool {
bit /= 64
return 0 != (w[bit/64] & (uint64(1) << (bit & 63)))
}
}
if mipLevel > 0 {
w := e.Words[mipLevel-1][:]
return func(bit int) bool {
return 0 != (w[bit/64] & (uint64(1) << (bit & 63)))
}
}
return nil
}
func (e *errorBitfield) isNeeded(mipLevel int, bit uint) bool {
if mipLevel >= 16 {
return true
}
if mipLevel >= 12 {
bit /= 4096
return 0 != (e.BiggestWords[mipLevel-12] & (uint64(1) << bit))
}
if mipLevel >= 6 {
bit /= 64
return 0 != (e.BigWords[mipLevel-6][bit/64] & (uint64(1) << (bit % 64)))
}
return 0 != (e.Words[mipLevel-1][bit/64] & (uint64(1) << (bit % 64)))
}
var kHiMasks = [5]uint64{
0xAAAAAAAAAAAAAAAA,
0xCCCCCCCCCCCCCCCC,
0xF0F0F0F0F0F0F0F0,
0xFF00FF00FF00FF00,
0xFFFF0000FFFF0000,
}
func (e *errorBitfield) prepare() {
// First mip level is for final layer of FFT: pairs of data
for i := 0; i < kWords; 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 < kWordMips; 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 < kBigWords; i++ {
w_i := uint64(0)
bit := uint64(1)
src := e.Words[kWordMips-1][i*64 : i*64+64]
for _, w := range src {
w_i |= (w | (w >> 32) | (w << 32)) & bit
bit <<= 1
}
e.BigWords[0][i] = w_i
bits := 1
for j := 1; j < kBigMips; j++ {
hi2lo_j := w_i | ((w_i & kHiMasks[j-1]) >> bits)
lo2hi_j := (w_i & (kHiMasks[j-1] >> bits)) << bits
w_i = hi2lo_j | lo2hi_j
e.BigWords[j][i] = w_i
bits <<= 1
}
}
w_i := uint64(0)
bit := uint64(1)
for _, w := range e.BigWords[kBigMips-1][:kBigWords] {
w_i |= (w | (w >> 32) | (w << 32)) & bit
bit <<= 1
}
e.BiggestWords[0] = w_i
bits := uint64(1)
for j := 1; j < kBiggestMips; j++ {
hi2lo_j := w_i | ((w_i & kHiMasks[j-1]) >> bits)
lo2hi_j := (w_i & (kHiMasks[j-1] >> bits)) << bits
w_i = hi2lo_j | lo2hi_j
e.BiggestWords[j] = w_i
bits <<= 1
}
}
func (e *errorBitfield) fftDIT(work [][]byte, mtrunc, m int, skewLUT []ffe, o *options) {
// Decimation in time: Unroll 2 layers at a time
mipLevel := bits.Len32(uint32(m)) - 1
dist4 := m
dist := m >> 2
needed := e.isNeededFn(mipLevel)
for dist != 0 {
// For each set of dist*4 elements:
for r := 0; r < mtrunc; r += dist4 {
if !needed(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++ {
fftDIT4(
work[i:],
dist,
logM01,
logM23,
logM02,
o)
}
}
dist4 = dist
dist >>= 2
mipLevel -= 2
needed = e.isNeededFn(mipLevel)
}
// If there is one layer left:
if dist4 == 2 {
for r := 0; r < mtrunc; r += 2 {
if !needed(r) {
continue
}
logM := skewLUT[r+1-1]
if logM == modulus {
sliceXor(work[r], work[r+1], o)
} else {
fftDIT2(work[r], work[r+1], logM, o)
}
}
}
}