diff --git a/vlib/crypto/rand/utils.v b/vlib/crypto/rand/utils.v index 1f20f272ea..fba5ee0e57 100644 --- a/vlib/crypto/rand/utils.v +++ b/vlib/crypto/rand/utils.v @@ -5,13 +5,12 @@ module rand import( - math + math.bits encoding.binary ) pub fn int_u64(max u64) u64? { - // bitlen := int(math.floor(math.log2(f64(max))+1)) - bitlen := int(math.floor(math.log(f64(max))/math.log(2)) + 1) + bitlen := bits.len64(max) if bitlen == 0 { return u64(0) } diff --git a/vlib/math/bits/bits.v b/vlib/math/bits/bits.v index 9d4b288936..b269cce84b 100644 --- a/vlib/math/bits/bits.v +++ b/vlib/math/bits/bits.v @@ -4,6 +4,136 @@ 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 = 0x5555555555555555 // 01010101 ... + m1 = 0x3333333333333333 // 00110011 ... + m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ... + m3 = 0x00ff00ff00ff00ff // etc. + m4 = 0x0000ffff0000ffff +) + +// --- LeadingZeros --- + +// leading_zeros8 returns the number of leading zero bits in x; the result is 8 for x == 0. +pub fn leading_zeros8(x byte) int { return 8 - len8(x) } + +// leading_zeros16 returns the number of leading zero bits in x; the result is 16 for x == 0. +pub fn leading_zeros16(x u16) int { return 16 - len16(x) } + +// leading_zeros32 returns the number of leading zero bits in x; the result is 32 for x == 0. +pub fn leading_zeros32(x u32) int { return 32 - len32(x) } + +// leading_zeros64 returns the number of leading zero bits in x; the result is 64 for x == 0. +pub fn leading_zeros64(x u64) int { return 64 - len64(x) } + +// --- TrailingZeros --- + +// trailing_zeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0. +pub fn trailing_zeros8(x byte) int { + return int(ntz8_tab[x]) +} + +// trailing_zeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0. +pub fn trailing_zeros16(x u16) int { + if x == u16(0) { + return 16 + } + // see comment in trailing_zeros64 + return int(de_bruijn32tab[u32(x&-x)*de_bruijn32>>u32(32-5)]) +} + +// trailing_zeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0. +pub fn trailing_zeros32(x u32) int { + if x == u32(0) { + return 32 + } + // see comment in trailing_zeros64 + return int(de_bruijn32tab[(x&-x)*de_bruijn32>>u32(32-5)]) +} + +// trailing_zeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0. +pub fn trailing_zeros64(x u64) int { + if x == u64(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(de_bruijn64tab[(x&-x)*de_bruijn64>>u64(64-6)]) +} + +// --- OnesCount --- + +// ones_count8 returns the number of one bits ("population count") in x. +pub fn ones_count8(x byte) int { + return int(pop8_tab[x]) +} + +// ones_count16 returns the number of one bits ("population count") in x. +pub fn ones_count16(x u16) int { + return int(pop8_tab[x>>u16(8)] + pop8_tab[x&u16(0xff)]) +} + +// ones_count32 returns the number of one bits ("population count") in x. +pub fn ones_count32(x u32) int { + return int(pop8_tab[x>>u32(24)] + pop8_tab[x>>u32(16)&u32(0xff)] + pop8_tab[x>>u32(8)&u32(0xff)] + pop8_tab[x&u32(0xff)]) +} + +// ones_count64 returns the number of one bits ("population count") in x. +pub fn ones_count64(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. + m := u64(u64(1<<64) - u64(1)) + mut y := u64(x>>u64(1)&(m0&m)) + u64(x&(m0&m)) + y = u64(y>>u64(2)&(m1&m)) + u64(y&(m1&m)) + y = u64(u64(y>>u64(4)) + y) & (m2 & m) + y += u64(y >> u64(8)) + y += u64(y >> u64(16)) + y += u64(y >> u64(32)) + return int(y) & ((1<<7) - 1) +} + // --- RotateLeft --- // rotate_left_8 returns the value of x rotated left by (k mod 8) bits. @@ -49,3 +179,120 @@ pub fn rotate_left_64(x u64, k int) u64 { s := u64(k) & (n - u64(1)) return u64(u64(x<>(n-s))) } + +// --- Reverse --- + +// reverse8 returns the value of x with its bits in reversed order. +[inline] +pub fn reverse8(x byte) byte { + return rev8_tab[x] +} + +// reverse16 returns the value of x with its bits in reversed order. +[inline] +pub fn reverse16(x u16) u16 { + return u16(u16(rev8_tab[x>>u16(8)]) | u16(u16(rev8_tab[x&u16(0xff)])<>u32(1)&u32(m0&m)) | u32(u32(x&u32(m0&m))<>u32(2)&u32(m1&m)) | u32(u32(y&u32(m1&m))<>u32(4)&u32(m2&m)) | u32(u32(y&u32(m2&m))<>u64(1)&(m0&m)) | u64(u64(x&(m0&m))<>u64(2)&(m1&m)) | u64(u64(y&(m1&m))<>u64(4)&(m2&m)) | u64(u64(y&(m2&m))<>u16(8)) | u16(x<>u32(8)&u32(m3&m)) | u32(u32(x&u32(m3&m))<>u32(16)) | u32(y<>u64(8)&(m3&m)) | u64(u64(x&(m3&m))<>u64(16)&(m4&m)) | u64(u64(y&(m4&m))<>u64(32)) | u64(y<= u16(u16(1)<>= u16(8) + n = 8 + } + return n + int(len8_tab[y]) +} + +// len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0. +fn len32(x u32) int { + mut y := x + mut n := 0 + if y >= u32(u32(1)<>= u32(16) + n = 16 + } + if y >= u32(u32(1)<>= u32(8) + n += 8 + } + return n + int(len8_tab[y]) +} + +// len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0. +fn len64(x u64) int { + mut y := x + mut n := 0 + if y >= u64(u64(1)<>= u64(32) + n = 32 + } + if y >= u64(u64(1)<>= u64(16) + n += 16 + } + if y >= u64(u64(1)<>= u64(8) + n += 8 + } + return n + int(len8_tab[y]) +} diff --git a/vlib/math/bits/bits_tables.v b/vlib/math/bits/bits_tables.v new file mode 100644 index 0000000000..5953d9f355 --- /dev/null +++ b/vlib/math/bits/bits_tables.v @@ -0,0 +1,80 @@ +// Copyright (c) 2019 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( + ntz8_tab = [ + byte(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, + ] + pop8_tab = [ + byte(0x00), 0x01, 0x01, 0x02, 0x01, 0x02, 0x02, 0x03, 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, + 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, + 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, + 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, + 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, + 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, + 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, + 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, 0x05, 0x06, 0x06, 0x07, 0x06, 0x07, 0x07, 0x08, + ] + rev8_tab = [ + byte(0x00), 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0, 0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0, + 0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8, 0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8, + 0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4, 0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4, + 0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec, 0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc, + 0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2, 0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2, + 0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea, 0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa, + 0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6, 0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6, + 0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee, 0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe, + 0x01, 0x81, 0x41, 0xc1, 0x21, 0xa1, 0x61, 0xe1, 0x11, 0x91, 0x51, 0xd1, 0x31, 0xb1, 0x71, 0xf1, + 0x09, 0x89, 0x49, 0xc9, 0x29, 0xa9, 0x69, 0xe9, 0x19, 0x99, 0x59, 0xd9, 0x39, 0xb9, 0x79, 0xf9, + 0x05, 0x85, 0x45, 0xc5, 0x25, 0xa5, 0x65, 0xe5, 0x15, 0x95, 0x55, 0xd5, 0x35, 0xb5, 0x75, 0xf5, + 0x0d, 0x8d, 0x4d, 0xcd, 0x2d, 0xad, 0x6d, 0xed, 0x1d, 0x9d, 0x5d, 0xdd, 0x3d, 0xbd, 0x7d, 0xfd, + 0x03, 0x83, 0x43, 0xc3, 0x23, 0xa3, 0x63, 0xe3, 0x13, 0x93, 0x53, 0xd3, 0x33, 0xb3, 0x73, 0xf3, + 0x0b, 0x8b, 0x4b, 0xcb, 0x2b, 0xab, 0x6b, 0xeb, 0x1b, 0x9b, 0x5b, 0xdb, 0x3b, 0xbb, 0x7b, 0xfb, + 0x07, 0x87, 0x47, 0xc7, 0x27, 0xa7, 0x67, 0xe7, 0x17, 0x97, 0x57, 0xd7, 0x37, 0xb7, 0x77, 0xf7, + 0x0f, 0x8f, 0x4f, 0xcf, 0x2f, 0xaf, 0x6f, 0xef, 0x1f, 0x9f, 0x5f, 0xdf, 0x3f, 0xbf, 0x7f, 0xff, + ] + len8_tab = [ + byte(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, + ] +)