1
0
mirror of https://github.com/vlang/v.git synced 2023-08-10 21:13:21 +03:00
v/vlib/math/bits/bits.v
2022-01-04 12:21:12 +03:00

492 lines
16 KiB
V
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

// Copyright (c) 2019-2022 Alexander Medvednikov. All rights reserved.
// Use of this source code is governed by an MIT license
// that can be found in the LICENSE file.
module bits
const (
// See http://supertech.csail.mit.edu/papers/debruijn.pdf
de_bruijn32 = u32(0x077CB531)
de_bruijn32tab = [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]
de_bruijn64 = u64(0x03f79d71b4ca8b09)
de_bruijn64tab = [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 (
m0 = u64(0x5555555555555555) // 01010101 ...
m1 = u64(0x3333333333333333) // 00110011 ...
m2 = u64(0x0f0f0f0f0f0f0f0f) // 00001111 ...
m3 = u64(0x00ff00ff00ff00ff) // etc.
m4 = u64(0x0000ffff0000ffff)
)
const (
// save importing math mod just for these
max_u32 = u32(4294967295)
max_u64 = u64(18446744073709551615)
)
// --- LeadingZeros ---
// leading_zeros_8 returns the number of leading zero bits in x; the result is 8 for x == 0.
pub fn leading_zeros_8(x byte) int {
return 8 - len_8(x)
}
// leading_zeros_16 returns the number of leading zero bits in x; the result is 16 for x == 0.
pub fn leading_zeros_16(x u16) int {
return 16 - len_16(x)
}
// leading_zeros_32 returns the number of leading zero bits in x; the result is 32 for x == 0.
pub fn leading_zeros_32(x u32) int {
return 32 - len_32(x)
}
// leading_zeros_64 returns the number of leading zero bits in x; the result is 64 for x == 0.
pub fn leading_zeros_64(x u64) int {
return 64 - len_64(x)
}
// --- TrailingZeros ---
// trailing_zeros_8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
pub fn trailing_zeros_8(x byte) int {
return int(ntz_8_tab[x])
}
// trailing_zeros_16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
pub fn trailing_zeros_16(x u16) int {
if x == 0 {
return 16
}
// see comment in trailing_zeros_64
return int(bits.de_bruijn32tab[u32(x & -x) * bits.de_bruijn32 >> (32 - 5)])
}
// trailing_zeros_32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
pub fn trailing_zeros_32(x u32) int {
if x == 0 {
return 32
}
// see comment in trailing_zeros_64
return int(bits.de_bruijn32tab[(x & -x) * bits.de_bruijn32 >> (32 - 5)])
}
// trailing_zeros_64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
pub fn trailing_zeros_64(x u64) 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(bits.de_bruijn64tab[(x & -x) * bits.de_bruijn64 >> (64 - 6)])
}
// --- OnesCount ---
// ones_count_8 returns the number of one bits ("population count") in x.
pub fn ones_count_8(x byte) int {
return int(pop_8_tab[x])
}
// ones_count_16 returns the number of one bits ("population count") in x.
pub fn ones_count_16(x u16) int {
return int(pop_8_tab[x >> 8] + pop_8_tab[x & u16(0xff)])
}
// ones_count_32 returns the number of one bits ("population count") in x.
pub fn ones_count_32(x u32) int {
return int(pop_8_tab[x >> 24] + pop_8_tab[x >> 16 & 0xff] + pop_8_tab[x >> 8 & 0xff] +
pop_8_tab[x & u32(0xff)])
}
// ones_count_64 returns the number of one bits ("population count") in x.
pub fn ones_count_64(x u64) 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.
mut y := (x >> u64(1) & (bits.m0 & bits.max_u64)) + (x & (bits.m0 & bits.max_u64))
y = (y >> u64(2) & (bits.m1 & bits.max_u64)) + (y & (bits.m1 & bits.max_u64))
y = ((y >> 4) + y) & (bits.m2 & bits.max_u64)
y += y >> 8
y += y >> 16
y += y >> 32
return int(y) & ((1 << 7) - 1)
}
// --- RotateLeft ---
// rotate_left_8 returns the value of x rotated left by (k mod 8) bits.
// To rotate x right by k bits, call rotate_left_8(x, -k).
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn rotate_left_8(x byte, k int) byte {
n := byte(8)
s := byte(k) & (n - byte(1))
return (x << s) | (x >> (n - s))
}
// rotate_left_16 returns the value of x rotated left by (k mod 16) bits.
// To rotate x right by k bits, call rotate_left_16(x, -k).
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn rotate_left_16(x u16, k int) u16 {
n := u16(16)
s := u16(k) & (n - u16(1))
return (x << s) | (x >> (n - s))
}
// rotate_left_32 returns the value of x rotated left by (k mod 32) bits.
// To rotate x right by k bits, call rotate_left_32(x, -k).
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn rotate_left_32(x u32, k int) u32 {
n := u32(32)
s := u32(k) & (n - u32(1))
return (x << s) | (x >> (n - s))
}
// rotate_left_64 returns the value of x rotated left by (k mod 64) bits.
// To rotate x right by k bits, call rotate_left_64(x, -k).
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn rotate_left_64(x u64, k int) u64 {
n := u64(64)
s := u64(k) & (n - u64(1))
return (x << s) | (x >> (n - s))
}
// --- Reverse ---
// reverse_8 returns the value of x with its bits in reversed order.
[inline]
pub fn reverse_8(x byte) byte {
return rev_8_tab[x]
}
// reverse_16 returns the value of x with its bits in reversed order.
[inline]
pub fn reverse_16(x u16) u16 {
return u16(rev_8_tab[x >> 8]) | (u16(rev_8_tab[x & u16(0xff)]) << 8)
}
// reverse_32 returns the value of x with its bits in reversed order.
[inline]
pub fn reverse_32(x u32) u32 {
mut y := ((x >> u32(1) & (bits.m0 & bits.max_u32)) | ((x & (bits.m0 & bits.max_u32)) << 1))
y = ((y >> u32(2) & (bits.m1 & bits.max_u32)) | ((y & (bits.m1 & bits.max_u32)) << u32(2)))
y = ((y >> u32(4) & (bits.m2 & bits.max_u32)) | ((y & (bits.m2 & bits.max_u32)) << u32(4)))
return reverse_bytes_32(u32(y))
}
// reverse_64 returns the value of x with its bits in reversed order.
[inline]
pub fn reverse_64(x u64) u64 {
mut y := ((x >> u64(1) & (bits.m0 & bits.max_u64)) | ((x & (bits.m0 & bits.max_u64)) << 1))
y = ((y >> u64(2) & (bits.m1 & bits.max_u64)) | ((y & (bits.m1 & bits.max_u64)) << 2))
y = ((y >> u64(4) & (bits.m2 & bits.max_u64)) | ((y & (bits.m2 & bits.max_u64)) << 4))
return reverse_bytes_64(y)
}
// --- ReverseBytes ---
// reverse_bytes_16 returns the value of x with its bytes in reversed order.
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn reverse_bytes_16(x u16) u16 {
return (x >> 8) | (x << 8)
}
// reverse_bytes_32 returns the value of x with its bytes in reversed order.
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn reverse_bytes_32(x u32) u32 {
y := ((x >> u32(8) & (bits.m3 & bits.max_u32)) | ((x & (bits.m3 & bits.max_u32)) << u32(8)))
return u32((y >> 16) | (y << 16))
}
// reverse_bytes_64 returns the value of x with its bytes in reversed order.
//
// This function's execution time does not depend on the inputs.
[inline]
pub fn reverse_bytes_64(x u64) u64 {
mut y := ((x >> u64(8) & (bits.m3 & bits.max_u64)) | ((x & (bits.m3 & bits.max_u64)) << u64(8)))
y = ((y >> u64(16) & (bits.m4 & bits.max_u64)) | ((y & (bits.m4 & bits.max_u64)) << u64(16)))
return (y >> 32) | (y << 32)
}
// --- Len ---
// len_8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
pub fn len_8(x byte) int {
return int(len_8_tab[x])
}
// len_16 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
pub fn len_16(x u16) int {
mut y := x
mut n := 0
if y >= 1 << 8 {
y >>= 8
n = 8
}
return n + int(len_8_tab[y])
}
// len_32 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
pub fn len_32(x u32) int {
mut y := x
mut n := 0
if y >= (1 << 16) {
y >>= 16
n = 16
}
if y >= (1 << 8) {
y >>= 8
n += 8
}
return n + int(len_8_tab[y])
}
// len_64 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
pub fn len_64(x u64) int {
mut y := x
mut n := 0
if y >= u64(1) << u64(32) {
y >>= 32
n = 32
}
if y >= u64(1) << u64(16) {
y >>= 16
n += 16
}
if y >= u64(1) << u64(8) {
y >>= 8
n += 8
}
return n + int(len_8_tab[y])
}
// --- Add with carry ---
// Add returns the sum with carry of x, y and carry: sum = x + y + carry.
// The carry input must be 0 or 1; otherwise the behavior is undefined.
// The carryOut output is guaranteed to be 0 or 1.
//
// add_32 returns the sum with carry of x, y and carry: sum = x + y + carry.
// The carry input must be 0 or 1; otherwise the behavior is undefined.
// The carryOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
pub fn add_32(x u32, y u32, carry u32) (u32, u32) {
sum64 := u64(x) + u64(y) + u64(carry)
sum := u32(sum64)
carry_out := u32(sum64 >> 32)
return sum, carry_out
}
// add_64 returns the sum with carry of x, y and carry: sum = x + y + carry.
// The carry input must be 0 or 1; otherwise the behavior is undefined.
// The carryOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
pub fn add_64(x u64, y u64, carry u64) (u64, u64) {
sum := x + y + carry
// The sum will overflow if both top bits are set (x & y) or if one of them
// is (x | y), and a carry from the lower place happened. If such a carry
// happens, the top bit will be 1 + 0 + 1 = 0 (&^ sum).
carry_out := ((x & y) | ((x | y) & ~sum)) >> 63
return sum, carry_out
}
// --- Subtract with borrow ---
// Sub returns the difference of x, y and borrow: diff = x - y - borrow.
// The borrow input must be 0 or 1; otherwise the behavior is undefined.
// The borrowOut output is guaranteed to be 0 or 1.
//
// sub_32 returns the difference of x, y and borrow, diff = x - y - borrow.
// The borrow input must be 0 or 1; otherwise the behavior is undefined.
// The borrowOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
pub fn sub_32(x u32, y u32, borrow u32) (u32, u32) {
diff := x - y - borrow
// The difference will underflow if the top bit of x is not set and the top
// bit of y is set (^x & y) or if they are the same (^(x ^ y)) and a borrow
// from the lower place happens. If that borrow happens, the result will be
// 1 - 1 - 1 = 0 - 0 - 1 = 1 (& diff).
borrow_out := ((~x & y) | (~(x ^ y) & diff)) >> 31
return diff, borrow_out
}
// sub_64 returns the difference of x, y and borrow: diff = x - y - borrow.
// The borrow input must be 0 or 1; otherwise the behavior is undefined.
// The borrowOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
pub fn sub_64(x u64, y u64, borrow u64) (u64, u64) {
diff := x - y - borrow
// See Sub32 for the bit logic.
borrow_out := ((~x & y) | (~(x ^ y) & diff)) >> 63
return diff, borrow_out
}
// --- Full-width multiply ---
const (
two32 = u64(0x100000000)
mask32 = two32 - 1
overflow_error = 'Overflow Error'
divide_error = 'Divide Error'
)
// mul_32 returns the 64-bit product of x and y: (hi, lo) = x * y
// with the product bits' upper half returned in hi and the lower
// half returned in lo.
//
// This function's execution time does not depend on the inputs.
pub fn mul_32(x u32, y u32) (u32, u32) {
tmp := u64(x) * u64(y)
hi := u32(tmp >> 32)
lo := u32(tmp)
return hi, lo
}
// mul_64 returns the 128-bit product of x and y: (hi, lo) = x * y
// with the product bits' upper half returned in hi and the lower
// half returned in lo.
//
// This function's execution time does not depend on the inputs.
pub fn mul_64(x u64, y u64) (u64, u64) {
x0 := x & bits.mask32
x1 := x >> 32
y0 := y & bits.mask32
y1 := y >> 32
w0 := x0 * y0
t := x1 * y0 + (w0 >> 32)
mut w1 := t & bits.mask32
w2 := t >> 32
w1 += x0 * y1
hi := x1 * y1 + w2 + (w1 >> 32)
lo := x * y
return hi, lo
}
// --- Full-width divide ---
// div_32 returns the quotient and remainder of (hi, lo) divided by y:
// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
// half in parameter hi and the lower half in parameter lo.
// div_32 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
pub fn div_32(hi u32, lo u32, y u32) (u32, u32) {
if y != 0 && y <= hi {
panic(bits.overflow_error)
}
z := (u64(hi) << 32) | u64(lo)
quo := u32(z / u64(y))
rem := u32(z % u64(y))
return quo, rem
}
// div_64 returns the quotient and remainder of (hi, lo) divided by y:
// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
// half in parameter hi and the lower half in parameter lo.
// div_64 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
pub fn div_64(hi u64, lo u64, y1 u64) (u64, u64) {
mut y := y1
if y == 0 {
panic(bits.overflow_error)
}
if y <= hi {
panic(bits.overflow_error)
}
s := u32(leading_zeros_64(y))
y <<= s
yn1 := y >> 32
yn0 := y & bits.mask32
un32 := (hi << s) | (lo >> (64 - s))
un10 := lo << s
un1 := un10 >> 32
un0 := un10 & bits.mask32
mut q1 := un32 / yn1
mut rhat := un32 - q1 * yn1
for q1 >= bits.two32 || q1 * yn0 > bits.two32 * rhat + un1 {
q1--
rhat += yn1
if rhat >= bits.two32 {
break
}
}
un21 := un32 * bits.two32 + un1 - q1 * y
mut q0 := un21 / yn1
rhat = un21 - q0 * yn1
for q0 >= bits.two32 || q0 * yn0 > bits.two32 * rhat + un0 {
q0--
rhat += yn1
if rhat >= bits.two32 {
break
}
}
return q1 * bits.two32 + q0, (un21 * bits.two32 + un0 - q0 * y) >> s
}
// rem_32 returns the remainder of (hi, lo) divided by y. Rem32 panics
// for y == 0 (division by zero) but, unlike Div32, it doesn't panic
// on a quotient overflow.
pub fn rem_32(hi u32, lo u32, y u32) u32 {
return u32(((u64(hi) << 32) | u64(lo)) % u64(y))
}
// rem_64 returns the remainder of (hi, lo) divided by y. Rem64 panics
// for y == 0 (division by zero) but, unlike div_64, it doesn't panic
// on a quotient overflow.
pub fn rem_64(hi u64, lo u64, y u64) u64 {
// We scale down hi so that hi < y, then use div_64 to compute the
// rem with the guarantee that it won't panic on quotient overflow.
// Given that
// hi ≡ hi%y (mod y)
// we have
// hi<<64 + lo ≡ (hi%y)<<64 + lo (mod y)
_, rem := div_64(hi % y, lo, y)
return rem
}
// normalize returns a normal number y and exponent exp
// satisfying x == y × 2**exp. It assumes x is finite and non-zero.
pub fn normalize(x f64) (f64, int) {
smallest_normal := 2.2250738585072014e-308 // 2**-1022
if (if x > 0.0 {
x
} else {
-x
}) < smallest_normal {
return x * (u64(1) << u64(52)), -52
}
return x, 0
}