diff --git a/src/math/bits/bits.go b/src/math/bits/bits.go new file mode 100644 index 0000000000..b342d3e727 --- /dev/null +++ b/src/math/bits/bits.go @@ -0,0 +1,77 @@ +// Copyright 2017 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 bits implements bit counting and manipulation +// functions for the predeclared unsigned integer types. +package bits + +// UintSize is the size of a uint in bits. +const UintSize = uintSize + +// LeadingZerosN returns the number of leading zero bits in x. +// N is absent for uint, or one of 8, 16, 32, 64. +// The result is the size of x in bits for x == 0. +func LeadingZeros(x uint) int { return UintSize - blen(uint64(x)) } +func LeadingZeros8(x uint8) int { return 8 - blen(uint64(x)) } +func LeadingZeros16(x uint16) int { return 16 - blen(uint64(x)) } +func LeadingZeros32(x uint32) int { return 32 - blen(uint64(x)) } +func LeadingZeros64(x uint64) int { return 64 - blen(uint64(x)) } + +// TrailingZerosN returns the number of trailing zero bits in x. +// N is absent for uint, or one of 8, 16, 32, 64. +// The result is the size of x in bits for x == 0. +func TrailingZeros(x uint) int { return ntz(x) } +func TrailingZeros8(x uint8) int { return ntz8(x) } +func TrailingZeros16(x uint16) int { return ntz16(x) } +func TrailingZeros32(x uint32) int { return ntz32(x) } +func TrailingZeros64(x uint64) int { return ntz64(x) } + +// OnesCountN returns the number of one bits ("population count") in x. +// N is absent for uint, or one of 8, 16, 32, 64. +func OnesCount(x uint) int { return pop(uint64(x)) } +func OnesCount8(x uint8) int { return pop(uint64(x)) } +func OnesCount16(x uint16) int { return pop(uint64(x)) } +func OnesCount32(x uint32) int { return pop(uint64(x)) } +func OnesCount64(x uint64) int { return pop(uint64(x)) } + +// RotateLeftN returns the value of x rotated left by k bits; k must not be negative. +// N is absent for uint, or one of 8, 16, 32, 64. +func RotateLeft(x uint, k int) uint { return uint(rot(uint64(x), UintSize, pos(k)%UintSize)) } +func RotateLeft8(x uint8, k int) uint8 { return uint8(rot(uint64(x), 8, pos(k)%8)) } +func RotateLeft16(x uint16, k int) uint16 { return uint16(rot(uint64(x), 16, pos(k)%16)) } +func RotateLeft32(x uint32, k int) uint32 { return uint32(rot(uint64(x), 32, pos(k)%32)) } +func RotateLeft64(x uint64, k int) uint64 { return uint64(rot(uint64(x), 64, pos(k)%64)) } + +// RotateRightN returns the value of x rotated right by k bits; k must not be negative. +// N is absent for uint, or one of 8, 16, 32, 64. +func RotateRight(x uint, k int) uint { return uint(rot(uint64(x), UintSize, UintSize-pos(k)%UintSize)) } +func RotateRight8(x uint8, k int) uint8 { return uint8(rot(uint64(x), 8, 8-pos(k)%8)) } +func RotateRight16(x uint16, k int) uint16 { return uint16(rot(uint64(x), 16, 16-pos(k)%16)) } +func RotateRight32(x uint32, k int) uint32 { return uint32(rot(uint64(x), 32, 32-pos(k)%32)) } +func RotateRight64(x uint64, k int) uint64 { return uint64(rot(uint64(x), 64, 64-pos(k)%64)) } + +// ReverseN returns the value of x with its bits in reversed order. +// N is absent for uint, or one of 8, 16, 32, 64. +func Reverse(x uint) uint { return uint(rev(uint64(x), UintSize)) } +func Reverse8(x uint8) uint8 { return uint8(rev(uint64(x), 8)) } +func Reverse16(x uint16) uint16 { return uint16(rev(uint64(x), 16)) } +func Reverse32(x uint32) uint32 { return uint32(rev(uint64(x), 32)) } +func Reverse64(x uint64) uint64 { return uint64(rev(uint64(x), 64)) } + +// ReverseBytesN returns the value of x with its bytes in reversed order. +// N is absent for uint, or one of 8, 16, 32, 64. +func ReverseBytes(x uint) uint { return uint(swap(uint64(x), UintSize)) } +func ReverseBytes16(x uint16) uint16 { return uint16(swap(uint64(x), 16)) } +func ReverseBytes32(x uint32) uint32 { return uint32(swap(uint64(x), 32)) } +func ReverseBytes64(x uint64) uint64 { return uint64(swap(uint64(x), 64)) } + +// LenN returns the minimum number of bits required to represent x. +// LenN(x) - 1 is the index of the most significant bit of x. +// N is absent for uint, or one of 8, 16, 32, 64. +// The result is 0 for x == 0. +func Len(x uint) int { return blen(uint64(x)) } +func Len8(x uint8) int { return blen(uint64(x)) } +func Len16(x uint16) int { return blen(uint64(x)) } +func Len32(x uint32) int { return blen(uint64(x)) } +func Len64(x uint64) int { return blen(uint64(x)) } diff --git a/src/math/bits/bits_impl.go b/src/math/bits/bits_impl.go new file mode 100644 index 0000000000..6f7a49b943 --- /dev/null +++ b/src/math/bits/bits_impl.go @@ -0,0 +1,132 @@ +// Copyright 2017 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. + +// This file provides basic implementations of the bits functions. + +package bits + +const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64 + +func ntz(x uint) (n int) { + if UintSize == 32 { + return ntz32(uint32(x)) + } + return ntz64(uint64(x)) +} + +// See http://supertech.csail.mit.edu/papers/debruijn.pdf +const deBruijn32 = 0x077CB531 + +var deBruijn32tab = [32]byte{ + 0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8, + 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9, +} + +func ntz8(x uint8) (n int) { + if x == 0 { + return 8 + } + // see comment in ntz64 + return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)]) +} + +func ntz16(x uint16) (n int) { + if x == 0 { + return 16 + } + // see comment in ntz64 + return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)]) +} + +func ntz32(x uint32) int { + if x == 0 { + return 32 + } + // see comment in ntz64 + return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)]) +} + +const deBruijn64 = 0x03f79d71b4ca8b09 + +var deBruijn64tab = [64]byte{ + 0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4, + 62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5, + 63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11, + 54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6, +} + +func ntz64(x uint64) int { + if x == 0 { + return 64 + } + // If popcount is fast, replace code below with return popcount(^x & (x - 1)). + // + // x & -x leaves only the right-most bit set in the word. Let k be the + // index of that bit. Since only a single bit is set, the value is two + // to the power of k. Multiplying by a power of two is equivalent to + // left shifting, in this case by k bits. The de Bruijn (64 bit) constant + // is such that all six bit, consecutive substrings are distinct. + // Therefore, if we have a left shifted version of this constant we can + // find by how many bits it was shifted by looking at which six bit + // substring ended up at the top of the word. + // (Knuth, volume 4, section 7.3.1) + return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)]) +} + +func pop(x uint64) (n int) { + for x != 0 { + n++ + x &= x - 1 + } + return +} + +func pos(k int) uint { + if k < 0 { + panic("negative rotation count") + } + return uint(k) +} + +func rot(x uint64, size, k uint) uint64 { + return x<>(size-k)&(1< 0; i-- { + r = r<<1 | x&1 + x >>= 1 + } + return +} + +func swap(x uint64, size uint) (r uint64) { + for i := size / 8; i > 0; i-- { + r = r<<8 | x&0xff + x >>= 8 + } + return +} + +func blen(x uint64) (i int) { + for ; x >= 1<<(16-1); x >>= 16 { + i += 16 + } + if x >= 1<<(8-1) { + x >>= 8 + i += 8 + } + if x >= 1<<(4-1) { + x >>= 4 + i += 4 + } + if x >= 1<<(2-1) { + x >>= 2 + i += 2 + } + if x >= 1<<(1-1) { + i++ + } + return +} diff --git a/src/math/bits/bits_test.go b/src/math/bits/bits_test.go new file mode 100644 index 0000000000..b930300036 --- /dev/null +++ b/src/math/bits/bits_test.go @@ -0,0 +1,518 @@ +// Copyright 2017 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 bits + +import ( + "testing" + "unsafe" +) + +func TestUintSize(t *testing.T) { + var x uint + if want := unsafe.Sizeof(x) * 8; UintSize != want { + t.Fatalf("UintSize = %d; want %d", UintSize, want) + } +} + +func TestLeadingZeros(t *testing.T) { + for i := 0; i < 256; i++ { + nlz := tab[i].nlz + for k := 0; k < 64-8; k++ { + x := uint64(i) << uint(k) + if x <= 1<<8-1 { + got := LeadingZeros8(uint8(x)) + want := nlz - k + (8 - 8) + if x == 0 { + want = 8 + } + if got != want { + t.Fatalf("LeadingZeros8(%#02x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<16-1 { + got := LeadingZeros16(uint16(x)) + want := nlz - k + (16 - 8) + if x == 0 { + want = 16 + } + if got != want { + t.Fatalf("LeadingZeros16(%#04x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<32-1 { + got := LeadingZeros32(uint32(x)) + want := nlz - k + (32 - 8) + if x == 0 { + want = 32 + } + if got != want { + t.Fatalf("LeadingZeros32(%#08x) == %d; want %d", x, got, want) + } + if UintSize == 32 { + got = LeadingZeros(uint(x)) + if got != want { + t.Fatalf("LeadingZeros(%#08x) == %d; want %d", x, got, want) + } + } + } + + if x <= 1<<64-1 { + got := LeadingZeros64(uint64(x)) + want := nlz - k + (64 - 8) + if x == 0 { + want = 64 + } + if got != want { + t.Fatalf("LeadingZeros64(%#016x) == %d; want %d", x, got, want) + } + if UintSize == 64 { + got = LeadingZeros(uint(x)) + if got != want { + t.Fatalf("LeadingZeros(%#016x) == %d; want %d", x, got, want) + } + } + } + } + } +} + +func TestTrailingZeros(t *testing.T) { + for i := 0; i < 256; i++ { + ntz := tab[i].ntz + for k := 0; k < 64-8; k++ { + x := uint64(i) << uint(k) + want := ntz + k + if x <= 1<<8-1 { + got := TrailingZeros8(uint8(x)) + if x == 0 { + want = 8 + } + if got != want { + t.Fatalf("TrailingZeros8(%#02x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<16-1 { + got := TrailingZeros16(uint16(x)) + if x == 0 { + want = 16 + } + if got != want { + t.Fatalf("TrailingZeros16(%#04x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<32-1 { + got := TrailingZeros32(uint32(x)) + if x == 0 { + want = 32 + } + if got != want { + t.Fatalf("TrailingZeros32(%#08x) == %d; want %d", x, got, want) + } + if UintSize == 32 { + got = TrailingZeros(uint(x)) + if got != want { + t.Fatalf("TrailingZeros(%#08x) == %d; want %d", x, got, want) + } + } + } + + if x <= 1<<64-1 { + got := TrailingZeros64(uint64(x)) + if x == 0 { + want = 64 + } + if got != want { + t.Fatalf("TrailingZeros64(%#016x) == %d; want %d", x, got, want) + } + if UintSize == 64 { + got = TrailingZeros(uint(x)) + if got != want { + t.Fatalf("TrailingZeros(%#016x) == %d; want %d", x, got, want) + } + } + } + } + } +} + +func TestOnesCount(t *testing.T) { + for i := 0; i < 256; i++ { + want := tab[i].pop + for k := 0; k < 64-8; k++ { + x := uint64(i) << uint(k) + if x <= 1<<8-1 { + got := OnesCount8(uint8(x)) + if got != want { + t.Fatalf("OnesCount8(%#02x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<16-1 { + got := OnesCount16(uint16(x)) + if got != want { + t.Fatalf("OnesCount16(%#04x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<32-1 { + got := OnesCount32(uint32(x)) + if got != want { + t.Fatalf("OnesCount32(%#08x) == %d; want %d", x, got, want) + } + if UintSize == 32 { + got = OnesCount(uint(x)) + if got != want { + t.Fatalf("OnesCount(%#08x) == %d; want %d", x, got, want) + } + } + } + + if x <= 1<<64-1 { + got := OnesCount64(uint64(x)) + if got != want { + t.Fatalf("OnesCount64(%#016x) == %d; want %d", x, got, want) + } + if UintSize == 64 { + got = OnesCount(uint(x)) + if got != want { + t.Fatalf("OnesCount(%#016x) == %d; want %d", x, got, want) + } + } + } + } + } +} + +func TestRotateLeft(t *testing.T) { + var m uint64 = deBruijn64 + + for k := uint(0); k < 128; k++ { + x8 := uint8(m) + got8 := RotateLeft8(x8, int(k)) + want8 := x8<<(k&0x7) | x8>>(8-k&0x7) + if got8 != want8 { + t.Fatalf("RotateLeft8(%#02x, %d) == %#02x; want %#02x", x8, k, got8, want8) + } + + x16 := uint16(m) + got16 := RotateLeft16(x16, int(k)) + want16 := x16<<(k&0xf) | x16>>(16-k&0xf) + if got16 != want16 { + t.Fatalf("RotateLeft16(%#04x, %d) == %#04x; want %#04x", x16, k, got16, want16) + } + + x32 := uint32(m) + got32 := RotateLeft32(x32, int(k)) + want32 := x32<<(k&0x1f) | x32>>(32-k&0x1f) + if got32 != want32 { + t.Fatalf("RotateLeft32(%#08x, %d) == %#08x; want %#08x", x32, k, got32, want32) + } + if UintSize == 32 { + x := uint(m) + got := RotateLeft(x, int(k)) + want := x<<(k&0x1f) | x>>(32-k&0x1f) + if got != want { + t.Fatalf("RotateLeft(%#08x, %d) == %#08x; want %#08x", x, k, got, want) + } + } + + x64 := uint64(m) + got64 := RotateLeft64(x64, int(k)) + want64 := x64<<(k&0x3f) | x64>>(64-k&0x3f) + if got64 != want64 { + t.Fatalf("RotateLeft64(%#016x, %d) == %#016x; want %#016x", x64, k, got64, want64) + } + if UintSize == 64 { + x := uint(m) + got := RotateLeft(x, int(k)) + want := x<<(k&0x3f) | x>>(64-k&0x3f) + if got != want { + t.Fatalf("RotateLeft(%#016x, %d) == %#016x; want %#016x", x, k, got, want) + } + } + } +} + +func TestRotateRight(t *testing.T) { + var m uint64 = deBruijn64 + + for k := uint(0); k < 128; k++ { + x8 := uint8(m) + got8 := RotateRight8(x8, int(k)) + want8 := x8>>(k&0x7) | x8<<(8-k&0x7) + if got8 != want8 { + t.Fatalf("RotateRight8(%#02x, %d) == %#02x; want %#02x", x8, k, got8, want8) + } + + x16 := uint16(m) + got16 := RotateRight16(x16, int(k)) + want16 := x16>>(k&0xf) | x16<<(16-k&0xf) + if got16 != want16 { + t.Fatalf("RotateRight16(%#04x, %d) == %#04x; want %#04x", x16, k, got16, want16) + } + + x32 := uint32(m) + got32 := RotateRight32(x32, int(k)) + want32 := x32>>(k&0x1f) | x32<<(32-k&0x1f) + if got32 != want32 { + t.Fatalf("RotateRight32(%#08x, %d) == %#08x; want %#08x", x32, k, got32, want32) + } + if UintSize == 32 { + x := uint(m) + got := RotateRight(x, int(k)) + want := x>>(k&0x1f) | x<<(32-k&0x1f) + if got != want { + t.Fatalf("RotateRight(%#08x, %d) == %#08x; want %#08x", x, k, got, want) + } + } + + x64 := uint64(m) + got64 := RotateRight64(x64, int(k)) + want64 := x64>>(k&0x3f) | x64<<(64-k&0x3f) + if got64 != want64 { + t.Fatalf("RotateRight64(%#016x, %d) == %#016x; want %#016x", x64, k, got64, want64) + } + if UintSize == 64 { + x := uint(m) + got := RotateRight(x, int(k)) + want := x>>(k&0x3f) | x<<(64-k&0x3f) + if got != want { + t.Fatalf("RotateRight(%#016x, %d) == %#016x; want %#016x", x, k, got, want) + } + } + } +} + +func TestReverse(t *testing.T) { + // test each bit + for i := uint(0); i < 64; i++ { + testReverse(t, uint64(1)<> (64 - 8)) + if got8 != want8 { + t.Fatalf("Reverse8(%#02x) == %#02x; want %#02x", x8, got8, want8) + } + + x16 := uint16(x64) + got16 := Reverse16(x16) + want16 := uint16(want64 >> (64 - 16)) + if got16 != want16 { + t.Fatalf("Reverse16(%#04x) == %#04x; want %#04x", x16, got16, want16) + } + + x32 := uint32(x64) + got32 := Reverse32(x32) + want32 := uint32(want64 >> (64 - 32)) + if got32 != want32 { + t.Fatalf("Reverse32(%#08x) == %#08x; want %#08x", x32, got32, want32) + } + if UintSize == 32 { + x := uint(x32) + got := Reverse(x) + want := uint(want32) + if got != want { + t.Fatalf("Reverse(%#08x) == %#08x; want %#08x", x, got, want) + } + } + + got64 := Reverse64(x64) + if got64 != want64 { + t.Fatalf("Reverse64(%#016x) == %#016x; want %#016x", x64, got64, want64) + } + if UintSize == 64 { + x := uint(x64) + got := Reverse(x) + want := uint(want64) + if got != want { + t.Fatalf("Reverse(%#08x) == %#016x; want %#016x", x, got, want) + } + } +} + +func TestReverseBytes(t *testing.T) { + for _, test := range []struct { + x, r uint64 + }{ + {0, 0}, + {0x01, 0x01 << 56}, + {0x0123, 0x2301 << 48}, + {0x012345, 0x452301 << 40}, + {0x01234567, 0x67452301 << 32}, + {0x0123456789, 0x8967452301 << 24}, + {0x0123456789ab, 0xab8967452301 << 16}, + {0x0123456789abcd, 0xcdab8967452301 << 8}, + {0x0123456789abcdef, 0xefcdab8967452301 << 0}, + } { + testReverseBytes(t, test.x, test.r) + testReverseBytes(t, test.r, test.x) + } +} + +func testReverseBytes(t *testing.T, x64, want64 uint64) { + x16 := uint16(x64) + got16 := ReverseBytes16(x16) + want16 := uint16(want64 >> (64 - 16)) + if got16 != want16 { + t.Fatalf("ReverseBytes16(%#04x) == %#04x; want %#04x", x16, got16, want16) + } + + x32 := uint32(x64) + got32 := ReverseBytes32(x32) + want32 := uint32(want64 >> (64 - 32)) + if got32 != want32 { + t.Fatalf("ReverseBytes32(%#08x) == %#08x; want %#08x", x32, got32, want32) + } + if UintSize == 32 { + x := uint(x32) + got := ReverseBytes(x) + want := uint(want32) + if got != want { + t.Fatalf("ReverseBytes(%#08x) == %#08x; want %#08x", x, got, want) + } + } + + got64 := ReverseBytes64(x64) + if got64 != want64 { + t.Fatalf("ReverseBytes64(%#016x) == %#016x; want %#016x", x64, got64, want64) + } + if UintSize == 64 { + x := uint(x64) + got := ReverseBytes(x) + want := uint(want64) + if got != want { + t.Fatalf("ReverseBytes(%#016x) == %#016x; want %#016x", x, got, want) + } + } +} + +func TestLen(t *testing.T) { + for i := 0; i < 256; i++ { + len := 8 - tab[i].nlz + for k := 0; k < 64-8; k++ { + x := uint64(i) << uint(k) + want := 0 + if x != 0 { + want = len + k + } + if x <= 1<<8-1 { + got := Len8(uint8(x)) + if got != want { + t.Fatalf("Len8(%#02x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<16-1 { + got := Len16(uint16(x)) + if got != want { + t.Fatalf("Len16(%#04x) == %d; want %d", x, got, want) + } + } + + if x <= 1<<32-1 { + got := Len32(uint32(x)) + if got != want { + t.Fatalf("Len32(%#08x) == %d; want %d", x, got, want) + } + if UintSize == 32 { + got := Len(uint(x)) + if got != want { + t.Fatalf("Len(%#08x) == %d; want %d", x, got, want) + } + } + } + + if x <= 1<<64-1 { + got := Len64(uint64(x)) + if got != want { + t.Fatalf("Len64(%#016x) == %d; want %d", x, got, want) + } + if UintSize == 64 { + got := Len(uint(x)) + if got != want { + t.Fatalf("Len(%#016x) == %d; want %d", x, got, want) + } + } + } + } + } +} + +// ---------------------------------------------------------------------------- +// Testing support + +type entry = struct { + nlz, ntz, pop int +} + +// tab contains results for all uint8 values +var tab [256]entry + +func init() { + tab[0] = entry{8, 8, 0} + for i := 1; i < len(tab); i++ { + // nlz + x := i // x != 0 + n := 0 + for x&0x80 == 0 { + n++ + x <<= 1 + } + tab[i].nlz = n + + // ntz + x = i // x != 0 + n = 0 + for x&1 == 0 { + n++ + x >>= 1 + } + tab[i].ntz = n + + // pop + x = i // x != 0 + n = 0 + for x != 0 { + n += int(x & 1) + x >>= 1 + } + tab[i].pop = n + } +}