// Copyright 2023 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package zstd
import (
"math/bits"
)
// fseEntry is one entry in an FSE table.
type fseEntry struct {
sym uint8 // value that this entry records
bits uint8 // number of bits to read to determine next state
base uint16 // add those bits to this state to get the next state
}
// readFSE reads an FSE table from data starting at off.
// maxSym is the maximum symbol value.
// maxBits is the maximum number of bits permitted for symbols in the table.
// The FSE is written into table, which must be at least 1<<maxBits in size.
// This returns the number of bits in the FSE table and the new offset.
// RFC 4.1.1.
func (r *Reader) readFSE(data block, off, maxSym, maxBits int, table []fseEntry) (tableBits, roff int, err error) {
br := r.makeBitReader(data, off)
if err := br.moreBits(); err != nil {
return 0, 0, err
}
accuracyLog := int(br.val(4)) + 5
if accuracyLog > maxBits {
return 0, 0, br.makeError("FSE accuracy log too large")
}
// The number of remaining probabilities, plus 1.
// This determines the number of bits to be read for the next value.
remaining := (1 << accuracyLog) + 1
// The current difference between small and large values,
// which depends on the number of remaining values.
// Small values use 1 less bit.
threshold := 1 << accuracyLog
// The number of bits needed to compute threshold.
bitsNeeded := accuracyLog + 1
// The next character value.
sym := 0
// Whether the last count was 0.
prev0 := false
var norm [256]int16
for remaining > 1 && sym <= maxSym {
if err := br.moreBits(); err != nil {
return 0, 0, err
}
if prev0 {
// Previous count was 0, so there is a 2-bit
// repeat flag. If the 2-bit flag is 0b11,
// it adds 3 and then there is another repeat flag.
zsym := sym
for (br.bits & 0xfff) == 0xfff {
zsym += 3 * 6
br.bits >>= 12
br.cnt -= 12
if err := br.moreBits(); err != nil {
return 0, 0, err
}
}
for (br.bits & 3) == 3 {
zsym += 3
br.bits >>= 2
br.cnt -= 2
if err := br.moreBits(); err != nil {
return 0, 0, err
}
}
// We have at least 14 bits here,
// no need to call moreBits
zsym += int(br.val(2))
if zsym > maxSym {
return 0, 0, br.makeError("FSE symbol index overflow")
}
for ; sym < zsym; sym++ {
norm[uint8(sym)] = 0
}
prev0 = false
continue
}
max := (2*threshold - 1) - remaining
var count int
if int(br.bits&uint32(threshold-1)) < max {
// A small value.
count = int(br.bits & uint32((threshold - 1)))
br.bits >>= bitsNeeded - 1
br.cnt -= uint32(bitsNeeded - 1)
} else {
// A large value.
count = int(br.bits & uint32((2*threshold - 1)))
if count >= threshold {
count -= max
}
br.bits >>= bitsNeeded
br.cnt -= uint32(bitsNeeded)
}
count--
if count >= 0 {
remaining -= count
} else {
remaining--
}
if sym >= 256 {
return 0, 0, br.makeError("FSE sym overflow")
}
norm[uint8(sym)] = int16(count)
sym++
prev0 = count == 0
for remaining < threshold {
bitsNeeded--
threshold >>= 1
}
}
if remaining != 1 {
return 0, 0, br.makeError("too many symbols in FSE table")
}
for ; sym <= maxSym; sym++ {
norm[uint8(sym)] = 0
}
br.backup()
if err := r.buildFSE(off, norm[:maxSym+1], table, accuracyLog); err != nil {
return 0, 0, err
}
return accuracyLog, int(br.off), nil
}
// buildFSE builds an FSE decoding table from a list of probabilities.
// The probabilities are in norm. next is scratch space. The number of bits
// in the table is tableBits.
func (r *Reader) buildFSE(off int, norm []int16, table []fseEntry, tableBits int) error {
tableSize := 1 << tableBits
highThreshold := tableSize - 1
var next [256]uint16
for i, n := range norm {
if n >= 0 {
next[uint8(i)] = uint16(n)
} else {
table[highThreshold].sym = uint8(i)
highThreshold--
next[uint8(i)] = 1
}
}
pos := 0
step := (tableSize >> 1) + (tableSize >> 3) + 3
mask := tableSize - 1
for i, n := range norm {
for j := 0; j < int(n); j++ {
table[pos].sym = uint8(i)
pos = (pos + step) & mask
for pos > highThreshold {
pos = (pos + step) & mask
}
}
}
if pos != 0 {
return r.makeError(off, "FSE count error")
}
for i := 0; i < tableSize; i++ {
sym := table[i].sym
nextState := next[sym]
next[sym]++
if nextState == 0 {
return r.makeError(off, "FSE state error")
}
highBit := 15 - bits.LeadingZeros16(nextState)
bits := tableBits - highBit
table[i].bits = uint8(bits)
table[i].base = (nextState << bits) - uint16(tableSize)
}
return nil
}
// fseBaselineEntry is an entry in an FSE baseline table.
// We use these for literal/match/length values.
// Those require mapping the symbol to a baseline value,
// and then reading zero or more bits and adding the value to the baseline.
// Rather than looking these up in separate tables,
// we convert the FSE table to an FSE baseline table.
type fseBaselineEntry struct {
baseline uint32 // baseline for value that this entry represents
basebits uint8 // number of bits to read to add to baseline
bits uint8 // number of bits to read to determine next state
base uint16 // add the bits to this base to get the next state
}
// Given a literal length code, we need to read a number of bits and
// add that to a baseline. For states 0 to 15 the baseline is the
// state and the number of bits is zero. RFC 3.1.1.3.2.1.1.
const literalLengthOffset = 16
var literalLengthBase = []uint32{
16 | (1 << 24),
18 | (1 << 24),
20 | (1 << 24),
22 | (1 << 24),
24 | (2 << 24),
28 | (2 << 24),
32 | (3 << 24),
40 | (3 << 24),
48 | (4 << 24),
64 | (6 << 24),
128 | (7 << 24),
256 | (8 << 24),
512 | (9 << 24),
1024 | (10 << 24),
2048 | (11 << 24),
4096 | (12 << 24),
8192 | (13 << 24),
16384 | (14 << 24),
32768 | (15 << 24),
65536 | (16 << 24),
}
// makeLiteralBaselineFSE converts the literal length fseTable to baselineTable.
func (r *Reader) makeLiteralBaselineFSE(off int, fseTable []fseEntry, baselineTable []fseBaselineEntry) error {
for i, e := range fseTable {
be := fseBaselineEntry{
bits: e.bits,
base: e.base,
}
if e.sym < literalLengthOffset {
be.baseline = uint32(e.sym)
be.basebits = 0
} else {
if e.sym > 35 {
return r.makeError(off, "FSE baseline symbol overflow")
}
idx := e.sym - literalLengthOffset
basebits := literalLengthBase[idx]
be.baseline = basebits & 0xffffff
be.basebits = uint8(basebits >> 24)
}
baselineTable[i] = be
}
return nil
}
// makeOffsetBaselineFSE converts the offset length fseTable to baselineTable.
func (r *Reader) makeOffsetBaselineFSE(off int, fseTable []fseEntry, baselineTable []fseBaselineEntry) error {
for i, e := range fseTable {
be := fseBaselineEntry{
bits: e.bits,
base: e.base,
}
if e.sym > 31 {
return r.makeError(off, "FSE offset symbol overflow")
}
// The simple way to write this is
// be.baseline = 1 << e.sym
// be.basebits = e.sym
// That would give us an offset value that corresponds to
// the one described in the RFC. However, for offsets > 3
// we have to subtract 3. And for offset values 1, 2, 3
// we use a repeated offset.
//
// The baseline is always a power of 2, and is never 0,
// so for those low values we will see one entry that is
// baseline 1, basebits 0, and one entry that is baseline 2,
// basebits 1. All other entries will have baseline >= 4
// basebits >= 2.
//
// So we can check for RFC offset <= 3 by checking for
// basebits <= 1. That means that we can subtract 3 here
// and not worry about doing it in the hot loop.
be.baseline = 1 << e.sym
if e.sym >= 2 {
be.baseline -= 3
}
be.basebits = e.sym
baselineTable[i] = be
}
return nil
}
// Given a match length code, we need to read a number of bits and add
// that to a baseline. For states 0 to 31 the baseline is state+3 and
// the number of bits is zero. RFC 3.1.1.3.2.1.1.
const matchLengthOffset = 32
var matchLengthBase = []uint32{
35 | (1 << 24),
37 | (1 << 24),
39 | (1 << 24),
41 | (1 << 24),
43 | (2 << 24),
47 | (2 << 24),
51 | (3 << 24),
59 | (3 << 24),
67 | (4 << 24),
83 | (4 << 24),
99 | (5 << 24),
131 | (7 << 24),
259 | (8 << 24),
515 | (9 << 24),
1027 | (10 << 24),
2051 | (11 << 24),
4099 | (12 << 24),
8195 | (13 << 24),
16387 | (14 << 24),
32771 | (15 << 24),
65539 | (16 << 24),
}
// makeMatchBaselineFSE converts the match length fseTable to baselineTable.
func (r *Reader) makeMatchBaselineFSE(off int, fseTable []fseEntry, baselineTable []fseBaselineEntry) error {
for i, e := range fseTable {
be := fseBaselineEntry{
bits: e.bits,
base: e.base,
}
if e.sym < matchLengthOffset {
be.baseline = uint32(e.sym) + 3
be.basebits = 0
} else {
if e.sym > 52 {
return r.makeError(off, "FSE baseline symbol overflow")
}
idx := e.sym - matchLengthOffset
basebits := matchLengthBase[idx]
be.baseline = basebits & 0xffffff
be.basebits = uint8(basebits >> 24)
}
baselineTable[i] = be
}
return nil
}
// predefinedLiteralTable is the predefined table to use for literal lengths.
// Generated from table in RFC 3.1.1.3.2.2.1.
// Checked by TestPredefinedTables.
var predefinedLiteralTable = [...]fseBaselineEntry{
{0, 0, 4, 0}, {0, 0, 4, 16}, {1, 0, 5, 32},
{3, 0, 5, 0}, {4, 0, 5, 0}, {6, 0, 5, 0},
{7, 0, 5, 0}, {9, 0, 5, 0}, {10, 0, 5, 0},
{12, 0, 5, 0}, {14, 0, 6, 0}, {16, 1, 5, 0},
{20, 1, 5, 0}, {22, 1, 5, 0}, {28, 2, 5, 0},
{32, 3, 5, 0}, {48, 4, 5, 0}, {64, 6, 5, 32},
{128, 7, 5, 0}, {256, 8, 6, 0}, {1024, 10, 6, 0},
{4096, 12, 6, 0}, {0, 0, 4, 32}, {1, 0, 4, 0},
{2, 0, 5, 0}, {4, 0, 5, 32}, {5, 0, 5, 0},
{7, 0, 5, 32}, {8, 0, 5, 0}, {10, 0, 5, 32},
{11, 0, 5, 0}, {13, 0, 6, 0}, {16, 1, 5, 32},
{18, 1, 5, 0}, {22, 1, 5, 32}, {24, 2, 5, 0},
{32, 3, 5, 32}, {40, 3, 5, 0}, {64, 6, 4, 0},
{64, 6, 4, 16}, {128, 7, 5, 32}, {512, 9, 6, 0},
{2048, 11, 6, 0}, {0, 0, 4, 48}, {1, 0, 4, 16},
{2, 0, 5, 32}, {3, 0, 5, 32}, {5, 0, 5, 32},
{6, 0, 5, 32}, {8, 0, 5, 32}, {9, 0, 5, 32},
{11, 0, 5, 32}, {12, 0, 5, 32}, {15, 0, 6, 0},
{18, 1, 5, 32}, {20, 1, 5, 32}, {24, 2, 5, 32},
{28, 2, 5, 32}, {40, 3, 5, 32}, {48, 4, 5, 32},
{65536, 16, 6, 0}, {32768, 15, 6, 0}, {16384, 14, 6, 0},
{8192, 13, 6, 0},
}
// predefinedOffsetTable is the predefined table to use for offsets.
// Generated from table in RFC 3.1.1.3.2.2.3.
// Checked by TestPredefinedTables.
var predefinedOffsetTable = [...]fseBaselineEntry{
{1, 0, 5, 0}, {61, 6, 4, 0}, {509, 9, 5, 0},
{32765, 15, 5, 0}, {2097149, 21, 5, 0}, {5, 3, 5, 0},
{125, 7, 4, 0}, {4093, 12, 5, 0}, {262141, 18, 5, 0},
{8388605, 23, 5, 0}, {29, 5, 5, 0}, {253, 8, 4, 0},
{16381, 14, 5, 0}, {1048573, 20, 5, 0}, {1, 2, 5, 0},
{125, 7, 4, 16}, {2045, 11, 5, 0}, {131069, 17, 5, 0},
{4194301, 22, 5, 0}, {13, 4, 5, 0}, {253, 8, 4, 16},
{8189, 13, 5, 0}, {524285, 19, 5, 0}, {2, 1, 5, 0},
{61, 6, 4, 16}, {1021, 10, 5, 0}, {65533, 16, 5, 0},
{268435453, 28, 5, 0}, {134217725, 27, 5, 0}, {67108861, 26, 5, 0},
{33554429, 25, 5, 0}, {16777213, 24, 5, 0},
}
// predefinedMatchTable is the predefined table to use for match lengths.
// Generated from table in RFC 3.1.1.3.2.2.2.
// Checked by TestPredefinedTables.
var predefinedMatchTable = [...]fseBaselineEntry{
{3, 0, 6, 0}, {4, 0, 4, 0}, {5, 0, 5, 32},
{6, 0, 5, 0}, {8, 0, 5, 0}, {9, 0, 5, 0},
{11, 0, 5, 0}, {13, 0, 6, 0}, {16, 0, 6, 0},
{19, 0, 6, 0}, {22, 0, 6, 0}, {25, 0, 6, 0},
{28, 0, 6, 0}, {31, 0, 6, 0}, {34, 0, 6, 0},
{37, 1, 6, 0}, {41, 1, 6, 0}, {47, 2, 6, 0},
{59, 3, 6, 0}, {83, 4, 6, 0}, {131, 7, 6, 0},
{515, 9, 6, 0}, {4, 0, 4, 16}, {5, 0, 4, 0},
{6, 0, 5, 32}, {7, 0, 5, 0}, {9, 0, 5, 32},
{10, 0, 5, 0}, {12, 0, 6, 0}, {15, 0, 6, 0},
{18, 0, 6, 0}, {21, 0, 6, 0}, {24, 0, 6, 0},
{27, 0, 6, 0}, {30, 0, 6, 0}, {33, 0, 6, 0},
{35, 1, 6, 0}, {39, 1, 6, 0}, {43, 2, 6, 0},
{51, 3, 6, 0}, {67, 4, 6, 0}, {99, 5, 6, 0},
{259, 8, 6, 0}, {4, 0, 4, 32}, {4, 0, 4, 48},
{5, 0, 4, 16}, {7, 0, 5, 32}, {8, 0, 5, 32},
{10, 0, 5, 32}, {11, 0, 5, 32}, {14, 0, 6, 0},
{17, 0, 6, 0}, {20, 0, 6, 0}, {23, 0, 6, 0},
{26, 0, 6, 0}, {29, 0, 6, 0}, {32, 0, 6, 0},
{65539, 16, 6, 0}, {32771, 15, 6, 0}, {16387, 14, 6, 0},
{8195, 13, 6, 0}, {4099, 12, 6, 0}, {2051, 11, 6, 0},
{1027, 10, 6, 0},
}