331 lines
9.5 KiB
Go
331 lines
9.5 KiB
Go
// Copyright 2017 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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//go:generate go run make_tables.go
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// Package bits implements bit counting and manipulation
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// functions for the predeclared unsigned integer types.
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package bits
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const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64
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// UintSize is the size of a uint in bits.
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const UintSize = uintSize
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// --- LeadingZeros ---
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// LeadingZeros returns the number of leading zero bits in x; the result is UintSize for x == 0.
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func LeadingZeros(x uint) int { return UintSize - Len(x) }
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// LeadingZeros8 returns the number of leading zero bits in x; the result is 8 for x == 0.
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func LeadingZeros8(x uint8) int { return 8 - Len8(x) }
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// LeadingZeros16 returns the number of leading zero bits in x; the result is 16 for x == 0.
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func LeadingZeros16(x uint16) int { return 16 - Len16(x) }
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// LeadingZeros32 returns the number of leading zero bits in x; the result is 32 for x == 0.
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func LeadingZeros32(x uint32) int { return 32 - Len32(x) }
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// LeadingZeros64 returns the number of leading zero bits in x; the result is 64 for x == 0.
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func LeadingZeros64(x uint64) int { return 64 - Len64(x) }
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// --- TrailingZeros ---
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// See http://supertech.csail.mit.edu/papers/debruijn.pdf
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const deBruijn32 = 0x077CB531
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var deBruijn32tab = [32]byte{
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0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
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31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
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}
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const deBruijn64 = 0x03f79d71b4ca8b09
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var deBruijn64tab = [64]byte{
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0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
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62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
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63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
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54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
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}
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// TrailingZeros returns the number of trailing zero bits in x; the result is UintSize for x == 0.
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func TrailingZeros(x uint) int {
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if UintSize == 32 {
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return TrailingZeros32(uint32(x))
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}
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return TrailingZeros64(uint64(x))
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}
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// TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
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func TrailingZeros8(x uint8) int {
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return int(ntz8tab[x])
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}
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// TrailingZeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
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func TrailingZeros16(x uint16) (n int) {
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if x == 0 {
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return 16
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}
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// see comment in TrailingZeros64
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return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
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}
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// TrailingZeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
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func TrailingZeros32(x uint32) int {
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if x == 0 {
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return 32
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}
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// see comment in TrailingZeros64
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return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)])
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}
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// TrailingZeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
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func TrailingZeros64(x uint64) int {
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if x == 0 {
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return 64
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}
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// If popcount is fast, replace code below with return popcount(^x & (x - 1)).
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//
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// x & -x leaves only the right-most bit set in the word. Let k be the
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// index of that bit. Since only a single bit is set, the value is two
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// to the power of k. Multiplying by a power of two is equivalent to
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// left shifting, in this case by k bits. The de Bruijn (64 bit) constant
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// is such that all six bit, consecutive substrings are distinct.
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// Therefore, if we have a left shifted version of this constant we can
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// find by how many bits it was shifted by looking at which six bit
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// substring ended up at the top of the word.
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// (Knuth, volume 4, section 7.3.1)
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return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)])
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}
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// --- OnesCount ---
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const m0 = 0x5555555555555555 // 01010101 ...
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const m1 = 0x3333333333333333 // 00110011 ...
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const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...
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const m3 = 0x00ff00ff00ff00ff // etc.
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const m4 = 0x0000ffff0000ffff
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// OnesCount returns the number of one bits ("population count") in x.
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func OnesCount(x uint) int {
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if UintSize == 32 {
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return OnesCount32(uint32(x))
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}
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return OnesCount64(uint64(x))
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}
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// OnesCount8 returns the number of one bits ("population count") in x.
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func OnesCount8(x uint8) int {
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return int(pop8tab[x])
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}
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// OnesCount16 returns the number of one bits ("population count") in x.
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func OnesCount16(x uint16) int {
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return int(pop8tab[x>>8] + pop8tab[x&0xff])
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}
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// OnesCount32 returns the number of one bits ("population count") in x.
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func OnesCount32(x uint32) int {
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return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff])
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}
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// OnesCount64 returns the number of one bits ("population count") in x.
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func OnesCount64(x uint64) int {
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// Implementation: Parallel summing of adjacent bits.
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// See "Hacker's Delight", Chap. 5: Counting Bits.
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// The following pattern shows the general approach:
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//
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// x = x>>1&(m0&m) + x&(m0&m)
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// x = x>>2&(m1&m) + x&(m1&m)
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// x = x>>4&(m2&m) + x&(m2&m)
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// x = x>>8&(m3&m) + x&(m3&m)
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// x = x>>16&(m4&m) + x&(m4&m)
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// x = x>>32&(m5&m) + x&(m5&m)
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// return int(x)
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//
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// Masking (& operations) can be left away when there's no
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// danger that a field's sum will carry over into the next
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// field: Since the result cannot be > 64, 8 bits is enough
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// and we can ignore the masks for the shifts by 8 and up.
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// Per "Hacker's Delight", the first line can be simplified
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// more, but it saves at best one instruction, so we leave
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// it alone for clarity.
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const m = 1<<64 - 1
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x = x>>1&(m0&m) + x&(m0&m)
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x = x>>2&(m1&m) + x&(m1&m)
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x = (x>>4 + x) & (m2 & m)
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x += x >> 8
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x += x >> 16
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x += x >> 32
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return int(x) & (1<<7 - 1)
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}
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// --- RotateLeft ---
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// RotateLeft returns the value of x rotated left by (k mod UintSize) bits.
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// To rotate x right by k bits, call RotateLeft(x, -k).
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func RotateLeft(x uint, k int) uint {
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if UintSize == 32 {
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return uint(RotateLeft32(uint32(x), k))
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}
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return uint(RotateLeft64(uint64(x), k))
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}
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// RotateLeft8 returns the value of x rotated left by (k mod 8) bits.
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// To rotate x right by k bits, call RotateLeft8(x, -k).
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func RotateLeft8(x uint8, k int) uint8 {
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const n = 8
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s := uint(k) & (n - 1)
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return x<<s | x>>(n-s)
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}
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// RotateLeft16 returns the value of x rotated left by (k mod 16) bits.
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// To rotate x right by k bits, call RotateLeft16(x, -k).
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func RotateLeft16(x uint16, k int) uint16 {
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const n = 16
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s := uint(k) & (n - 1)
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return x<<s | x>>(n-s)
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}
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// RotateLeft32 returns the value of x rotated left by (k mod 32) bits.
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// To rotate x right by k bits, call RotateLeft32(x, -k).
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func RotateLeft32(x uint32, k int) uint32 {
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const n = 32
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s := uint(k) & (n - 1)
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return x<<s | x>>(n-s)
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}
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// RotateLeft64 returns the value of x rotated left by (k mod 64) bits.
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// To rotate x right by k bits, call RotateLeft64(x, -k).
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func RotateLeft64(x uint64, k int) uint64 {
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const n = 64
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s := uint(k) & (n - 1)
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return x<<s | x>>(n-s)
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}
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// --- Reverse ---
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// Reverse returns the value of x with its bits in reversed order.
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func Reverse(x uint) uint {
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if UintSize == 32 {
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return uint(Reverse32(uint32(x)))
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}
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return uint(Reverse64(uint64(x)))
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}
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// Reverse8 returns the value of x with its bits in reversed order.
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func Reverse8(x uint8) uint8 {
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return rev8tab[x]
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}
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// Reverse16 returns the value of x with its bits in reversed order.
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func Reverse16(x uint16) uint16 {
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return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8
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}
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// Reverse32 returns the value of x with its bits in reversed order.
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func Reverse32(x uint32) uint32 {
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const m = 1<<32 - 1
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x = x>>1&(m0&m) | x&(m0&m)<<1
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x = x>>2&(m1&m) | x&(m1&m)<<2
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x = x>>4&(m2&m) | x&(m2&m)<<4
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x = x>>8&(m3&m) | x&(m3&m)<<8
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return x>>16 | x<<16
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}
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// Reverse64 returns the value of x with its bits in reversed order.
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func Reverse64(x uint64) uint64 {
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const m = 1<<64 - 1
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x = x>>1&(m0&m) | x&(m0&m)<<1
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x = x>>2&(m1&m) | x&(m1&m)<<2
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x = x>>4&(m2&m) | x&(m2&m)<<4
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x = x>>8&(m3&m) | x&(m3&m)<<8
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x = x>>16&(m4&m) | x&(m4&m)<<16
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return x>>32 | x<<32
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}
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// --- ReverseBytes ---
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// ReverseBytes returns the value of x with its bytes in reversed order.
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func ReverseBytes(x uint) uint {
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if UintSize == 32 {
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return uint(ReverseBytes32(uint32(x)))
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}
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return uint(ReverseBytes64(uint64(x)))
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}
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// ReverseBytes16 returns the value of x with its bytes in reversed order.
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func ReverseBytes16(x uint16) uint16 {
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return x>>8 | x<<8
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}
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// ReverseBytes32 returns the value of x with its bytes in reversed order.
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func ReverseBytes32(x uint32) uint32 {
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const m = 1<<32 - 1
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x = x>>8&(m3&m) | x&(m3&m)<<8
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return x>>16 | x<<16
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}
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// ReverseBytes64 returns the value of x with its bytes in reversed order.
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func ReverseBytes64(x uint64) uint64 {
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const m = 1<<64 - 1
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x = x>>8&(m3&m) | x&(m3&m)<<8
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x = x>>16&(m4&m) | x&(m4&m)<<16
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return x>>32 | x<<32
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}
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// --- Len ---
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// Len returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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func Len(x uint) int {
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if UintSize == 32 {
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return Len32(uint32(x))
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}
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return Len64(uint64(x))
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}
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// Len8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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func Len8(x uint8) int {
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return int(len8tab[x])
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}
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// Len16 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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func Len16(x uint16) (n int) {
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if x >= 1<<8 {
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x >>= 8
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n = 8
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}
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return n + int(len8tab[x])
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}
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// Len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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func Len32(x uint32) (n int) {
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if x >= 1<<16 {
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x >>= 16
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n = 16
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}
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if x >= 1<<8 {
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x >>= 8
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n += 8
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}
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return n + int(len8tab[x])
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}
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// Len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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func Len64(x uint64) (n int) {
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if x >= 1<<32 {
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x >>= 32
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n = 32
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}
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if x >= 1<<16 {
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x >>= 16
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n += 16
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}
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if x >= 1<<8 {
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x >>= 8
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n += 8
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}
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return n + int(len8tab[x])
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}
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