Source File
	intrinsics_common.go

Belonging Package
	runtime/internal/sys

// Copyright 2019 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 sys

// Copied from math/bits to avoid dependence.

var len8tab = [256]uint8{
	0x00, 0x01, 0x02, 0x02, 0x03, 0x03, 0x03, 0x03, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04,
	0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05,
	0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
	0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
	0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
	0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
	0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
	0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
	0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
}

var ntz8tab = [256]uint8{
	0x08, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x07, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
}

// 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])
}

// --- OnesCount ---

const m0 = 0x5555555555555555 // 01010101 ...
const m1 = 0x3333333333333333 // 00110011 ...
const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...

// 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)
}

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,
}

const deBruijn64 = 0x03f79d71b4ca8b09

// 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)])
}

// 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) }

// 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) }

// 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])
}

// 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])
}

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