| // 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. |
| |
| //go:generate go run make_tables.go |
| |
| // Package bits implements bit counting and manipulation |
| // functions for the predeclared unsigned integer types. |
| package bits |
| |
| const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64 |
| |
| // UintSize is the size of a uint in bits. |
| const UintSize = uintSize |
| |
| // --- LeadingZeros --- |
| |
| // LeadingZeros returns the number of leading zero bits in x; the result is UintSize for x == 0. |
| func LeadingZeros(x uint) int { return UintSize - Len(x) } |
| |
| // LeadingZeros8 returns the number of leading zero bits in x; the result is 8 for x == 0. |
| func LeadingZeros8(x uint8) int { return 8 - Len8(x) } |
| |
| // LeadingZeros16 returns the number of leading zero bits in x; the result is 16 for x == 0. |
| func LeadingZeros16(x uint16) int { return 16 - Len16(x) } |
| |
| // LeadingZeros32 returns the number of leading zero bits in x; the result is 32 for x == 0. |
| func LeadingZeros32(x uint32) int { return 32 - Len32(x) } |
| |
| // LeadingZeros64 returns the number of leading zero bits in x; the result is 64 for x == 0. |
| func LeadingZeros64(x uint64) int { return 64 - Len64(x) } |
| |
| // --- TrailingZeros --- |
| |
| // 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, |
| } |
| |
| 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, |
| } |
| |
| // TrailingZeros returns the number of trailing zero bits in x; the result is UintSize for x == 0. |
| func TrailingZeros(x uint) int { |
| if UintSize == 32 { |
| return TrailingZeros32(uint32(x)) |
| } |
| return TrailingZeros64(uint64(x)) |
| } |
| |
| // TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0. |
| func TrailingZeros8(x uint8) int { |
| return int(ntz8tab[x]) |
| } |
| |
| // TrailingZeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0. |
| func TrailingZeros16(x uint16) (n int) { |
| if x == 0 { |
| return 16 |
| } |
| // see comment in TrailingZeros64 |
| return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)]) |
| } |
| |
| // TrailingZeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0. |
| func TrailingZeros32(x uint32) int { |
| if x == 0 { |
| return 32 |
| } |
| // see comment in TrailingZeros64 |
| return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)]) |
| } |
| |
| // TrailingZeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0. |
| func TrailingZeros64(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)]) |
| } |
| |
| // --- OnesCount --- |
| |
| const m0 = 0x5555555555555555 // 01010101 ... |
| const m1 = 0x3333333333333333 // 00110011 ... |
| const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ... |
| const m3 = 0x00ff00ff00ff00ff // etc. |
| const m4 = 0x0000ffff0000ffff |
| |
| // OnesCount returns the number of one bits ("population count") in x. |
| func OnesCount(x uint) int { |
| if UintSize == 32 { |
| return OnesCount32(uint32(x)) |
| } |
| return OnesCount64(uint64(x)) |
| } |
| |
| // OnesCount8 returns the number of one bits ("population count") in x. |
| func OnesCount8(x uint8) int { |
| return int(pop8tab[x]) |
| } |
| |
| // OnesCount16 returns the number of one bits ("population count") in x. |
| func OnesCount16(x uint16) int { |
| return int(pop8tab[x>>8] + pop8tab[x&0xff]) |
| } |
| |
| // OnesCount32 returns the number of one bits ("population count") in x. |
| func OnesCount32(x uint32) int { |
| return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff]) |
| } |
| |
| // OnesCount64 returns the number of one bits ("population count") in x. |
| func OnesCount64(x uint64) int { |
| // Implementation: Parallel summing of adjacent bits. |
| // See "Hacker's Delight", Chap. 5: Counting Bits. |
| // The following pattern shows the general approach: |
| // |
| // x = x>>1&(m0&m) + x&(m0&m) |
| // x = x>>2&(m1&m) + x&(m1&m) |
| // x = x>>4&(m2&m) + x&(m2&m) |
| // x = x>>8&(m3&m) + x&(m3&m) |
| // x = x>>16&(m4&m) + x&(m4&m) |
| // x = x>>32&(m5&m) + x&(m5&m) |
| // return int(x) |
| // |
| // Masking (& operations) can be left away when there's no |
| // danger that a field's sum will carry over into the next |
| // field: Since the result cannot be > 64, 8 bits is enough |
| // and we can ignore the masks for the shifts by 8 and up. |
| // Per "Hacker's Delight", the first line can be simplified |
| // more, but it saves at best one instruction, so we leave |
| // it alone for clarity. |
| const m = 1<<64 - 1 |
| x = x>>1&(m0&m) + x&(m0&m) |
| x = x>>2&(m1&m) + x&(m1&m) |
| x = (x>>4 + x) & (m2 & m) |
| x += x >> 8 |
| x += x >> 16 |
| x += x >> 32 |
| return int(x) & (1<<7 - 1) |
| } |
| |
| // --- RotateLeft --- |
| |
| // RotateLeft returns the value of x rotated left by (k mod UintSize) bits. |
| // To rotate x right by k bits, call RotateLeft(x, -k). |
| func RotateLeft(x uint, k int) uint { |
| if UintSize == 32 { |
| return uint(RotateLeft32(uint32(x), k)) |
| } |
| return uint(RotateLeft64(uint64(x), k)) |
| } |
| |
| // RotateLeft8 returns the value of x rotated left by (k mod 8) bits. |
| // To rotate x right by k bits, call RotateLeft8(x, -k). |
| func RotateLeft8(x uint8, k int) uint8 { |
| const n = 8 |
| s := uint(k) & (n - 1) |
| return x<<s | x>>(n-s) |
| } |
| |
| // RotateLeft16 returns the value of x rotated left by (k mod 16) bits. |
| // To rotate x right by k bits, call RotateLeft16(x, -k). |
| func RotateLeft16(x uint16, k int) uint16 { |
| const n = 16 |
| s := uint(k) & (n - 1) |
| return x<<s | x>>(n-s) |
| } |
| |
| // RotateLeft32 returns the value of x rotated left by (k mod 32) bits. |
| // To rotate x right by k bits, call RotateLeft32(x, -k). |
| func RotateLeft32(x uint32, k int) uint32 { |
| const n = 32 |
| s := uint(k) & (n - 1) |
| return x<<s | x>>(n-s) |
| } |
| |
| // RotateLeft64 returns the value of x rotated left by (k mod 64) bits. |
| // To rotate x right by k bits, call RotateLeft64(x, -k). |
| func RotateLeft64(x uint64, k int) uint64 { |
| const n = 64 |
| s := uint(k) & (n - 1) |
| return x<<s | x>>(n-s) |
| } |
| |
| // --- Reverse --- |
| |
| // Reverse returns the value of x with its bits in reversed order. |
| func Reverse(x uint) uint { |
| if UintSize == 32 { |
| return uint(Reverse32(uint32(x))) |
| } |
| return uint(Reverse64(uint64(x))) |
| } |
| |
| // Reverse8 returns the value of x with its bits in reversed order. |
| func Reverse8(x uint8) uint8 { |
| return rev8tab[x] |
| } |
| |
| // Reverse16 returns the value of x with its bits in reversed order. |
| func Reverse16(x uint16) uint16 { |
| return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8 |
| } |
| |
| // Reverse32 returns the value of x with its bits in reversed order. |
| func Reverse32(x uint32) uint32 { |
| const m = 1<<32 - 1 |
| x = x>>1&(m0&m) | x&(m0&m)<<1 |
| x = x>>2&(m1&m) | x&(m1&m)<<2 |
| x = x>>4&(m2&m) | x&(m2&m)<<4 |
| x = x>>8&(m3&m) | x&(m3&m)<<8 |
| return x>>16 | x<<16 |
| } |
| |
| // Reverse64 returns the value of x with its bits in reversed order. |
| func Reverse64(x uint64) uint64 { |
| const m = 1<<64 - 1 |
| x = x>>1&(m0&m) | x&(m0&m)<<1 |
| x = x>>2&(m1&m) | x&(m1&m)<<2 |
| x = x>>4&(m2&m) | x&(m2&m)<<4 |
| x = x>>8&(m3&m) | x&(m3&m)<<8 |
| x = x>>16&(m4&m) | x&(m4&m)<<16 |
| return x>>32 | x<<32 |
| } |
| |
| // --- ReverseBytes --- |
| |
| // ReverseBytes returns the value of x with its bytes in reversed order. |
| func ReverseBytes(x uint) uint { |
| if UintSize == 32 { |
| return uint(ReverseBytes32(uint32(x))) |
| } |
| return uint(ReverseBytes64(uint64(x))) |
| } |
| |
| // ReverseBytes16 returns the value of x with its bytes in reversed order. |
| func ReverseBytes16(x uint16) uint16 { |
| return x>>8 | x<<8 |
| } |
| |
| // ReverseBytes32 returns the value of x with its bytes in reversed order. |
| func ReverseBytes32(x uint32) uint32 { |
| const m = 1<<32 - 1 |
| x = x>>8&(m3&m) | x&(m3&m)<<8 |
| return x>>16 | x<<16 |
| } |
| |
| // ReverseBytes64 returns the value of x with its bytes in reversed order. |
| func ReverseBytes64(x uint64) uint64 { |
| const m = 1<<64 - 1 |
| x = x>>8&(m3&m) | x&(m3&m)<<8 |
| x = x>>16&(m4&m) | x&(m4&m)<<16 |
| return x>>32 | x<<32 |
| } |
| |
| // --- Len --- |
| |
| // Len returns the minimum number of bits required to represent x; the result is 0 for x == 0. |
| func Len(x uint) int { |
| if UintSize == 32 { |
| return Len32(uint32(x)) |
| } |
| return Len64(uint64(x)) |
| } |
| |
| // Len8 returns the minimum number of bits required to represent x; the result is 0 for x == 0. |
| func Len8(x uint8) int { |
| return int(len8tab[x]) |
| } |
| |
| // Len16 returns the minimum number of bits required to represent x; the result is 0 for x == 0. |
| func Len16(x uint16) (n int) { |
| if x >= 1<<8 { |
| x >>= 8 |
| n = 8 |
| } |
| return n + int(len8tab[x]) |
| } |
| |
| // Len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0. |
| func Len32(x uint32) (n int) { |
| if x >= 1<<16 { |
| x >>= 16 |
| n = 16 |
| } |
| if x >= 1<<8 { |
| x >>= 8 |
| n += 8 |
| } |
| return n + int(len8tab[x]) |
| } |
| |
| // Len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0. |
| func Len64(x uint64) (n int) { |
| if x >= 1<<32 { |
| x >>= 32 |
| n = 32 |
| } |
| if x >= 1<<16 { |
| x >>= 16 |
| n += 16 |
| } |
| if x >= 1<<8 { |
| x >>= 8 |
| n += 8 |
| } |
| return n + int(len8tab[x]) |
| } |