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// 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 { 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}, }