// 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]) }