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math.bits: add some more helpers, to be used in upcoming biginteger
This commit is contained in:
joe-conigliaro
Alexander Medvednikov
parent
5a03eaca89
commit
d80a3365c4
@ -5,13 +5,12 @@
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module rand
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import(
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math
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math.bits
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encoding.binary
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)
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pub fn int_u64(max u64) u64? {
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// bitlen := int(math.floor(math.log2(f64(max))+1))
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bitlen := int(math.floor(math.log(f64(max))/math.log(2)) + 1)
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bitlen := bits.len64(max)
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if bitlen == 0 {
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return u64(0)
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}
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@ -4,6 +4,136 @@
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module bits
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const(
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// See http://supertech.csail.mit.edu/papers/debruijn.pdf
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de_bruijn32 = u32(0x077CB531)
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de_bruijn32tab = [
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byte(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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de_bruijn64 = u64(0x03f79d71b4ca8b09)
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de_bruijn64tab = [
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byte(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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)
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const(
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m0 = 0x5555555555555555 // 01010101 ...
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m1 = 0x3333333333333333 // 00110011 ...
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m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...
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m3 = 0x00ff00ff00ff00ff // etc.
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m4 = 0x0000ffff0000ffff
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)
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// --- LeadingZeros ---
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// leading_zeros8 returns the number of leading zero bits in x; the result is 8 for x == 0.
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pub fn leading_zeros8(x byte) int { return 8 - len8(x) }
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// leading_zeros16 returns the number of leading zero bits in x; the result is 16 for x == 0.
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pub fn leading_zeros16(x u16) int { return 16 - len16(x) }
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// leading_zeros32 returns the number of leading zero bits in x; the result is 32 for x == 0.
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pub fn leading_zeros32(x u32) int { return 32 - len32(x) }
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// leading_zeros64 returns the number of leading zero bits in x; the result is 64 for x == 0.
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pub fn leading_zeros64(x u64) int { return 64 - len64(x) }
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// --- TrailingZeros ---
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// trailing_zeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
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pub fn trailing_zeros8(x byte) int {
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return int(ntz8_tab[x])
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}
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// trailing_zeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
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pub fn trailing_zeros16(x u16) int {
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if x == u16(0) {
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return 16
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}
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// see comment in trailing_zeros64
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return int(de_bruijn32tab[u32(x&-x)*de_bruijn32>>u32(32-5)])
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}
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// trailing_zeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
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pub fn trailing_zeros32(x u32) int {
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if x == u32(0) {
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return 32
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}
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// see comment in trailing_zeros64
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return int(de_bruijn32tab[(x&-x)*de_bruijn32>>u32(32-5)])
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}
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// trailing_zeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
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pub fn trailing_zeros64(x u64) int {
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if x == u64(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(de_bruijn64tab[(x&-x)*de_bruijn64>>u64(64-6)])
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}
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// --- OnesCount ---
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// ones_count8 returns the number of one bits ("population count") in x.
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pub fn ones_count8(x byte) int {
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return int(pop8_tab[x])
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}
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// ones_count16 returns the number of one bits ("population count") in x.
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pub fn ones_count16(x u16) int {
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return int(pop8_tab[x>>u16(8)] + pop8_tab[x&u16(0xff)])
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}
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// ones_count32 returns the number of one bits ("population count") in x.
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pub fn ones_count32(x u32) int {
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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)])
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}
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// ones_count64 returns the number of one bits ("population count") in x.
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pub fn ones_count64(x u64) 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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m := u64(u64(1<<64) - u64(1))
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mut y := u64(x>>u64(1)&(m0&m)) + u64(x&(m0&m))
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y = u64(y>>u64(2)&(m1&m)) + u64(y&(m1&m))
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y = u64(u64(y>>u64(4)) + y) & (m2 & m)
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y += u64(y >> u64(8))
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y += u64(y >> u64(16))
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y += u64(y >> u64(32))
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return int(y) & ((1<<7) - 1)
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}
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// --- RotateLeft ---
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// rotate_left_8 returns the value of x rotated left by (k mod 8) bits.
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@ -49,3 +179,120 @@ pub fn rotate_left_64(x u64, k int) u64 {
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s := u64(k) & (n - u64(1))
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return u64(u64(x<<s) | u64(x>>(n-s)))
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}
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// --- Reverse ---
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// reverse8 returns the value of x with its bits in reversed order.
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[inline]
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pub fn reverse8(x byte) byte {
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return rev8_tab[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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[inline]
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pub fn reverse16(x u16) u16 {
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return u16(u16(rev8_tab[x>>u16(8)]) | u16(u16(rev8_tab[x&u16(0xff)])<<u16(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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[inline]
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pub fn reverse32(x u32) u32 {
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m := u64(u64(1<<32) - u64(1))
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mut y := u32(u32(x>>u32(1)&u32(m0&m)) | u32(u32(x&u32(m0&m))<<u32(1)))
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y = u32(u32(y>>u32(2)&u32(m1&m)) | u32(u32(y&u32(m1&m))<<u32(2)))
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y = u32(u32(y>>u32(4)&u32(m2&m)) | u32(u32(y&u32(m2&m))<<u32(4)))
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return reverse_bytes32(y)
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}
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// reverse64 returns the value of x with its bits in reversed order.
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[inline]
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pub fn reverse64(x u64) u64 {
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m := u64(u64(1<<64) - u64(1))
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mut y := u64(u64(x>>u64(1)&(m0&m)) | u64(u64(x&(m0&m))<<u64(1)))
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y = u64(u64(y>>u64(2)&(m1&m)) | u64(u64(y&(m1&m))<<u64(2)))
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y = u64(u64(y>>u64(4)&(m2&m)) | u64(u64(y&(m2&m))<<u64(4)))
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return reverse_bytes64(y)
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}
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// --- ReverseBytes ---
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// reverse_bytes16 returns the value of x with its bytes in reversed order.
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//
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// This function's execution time does not depend on the inputs.
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[inline]
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fn reverse_bytes16(x u16) u16 {
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return u16(x>>u16(8)) | u16(x<<u16(8))
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}
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// reverse_bytes32 returns the value of x with its bytes in reversed order.
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//
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// This function's execution time does not depend on the inputs.
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[inline]
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fn reverse_bytes32(x u32) u32 {
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m := u64(u64(1<<32) - u64(1))
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y := u32(u32(x>>u32(8)&u32(m3&m)) | u32(u32(x&u32(m3&m))<<u32(8)))
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return u32(y>>u32(16)) | u32(y<<u32(16))
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}
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// reverse_bytes64 returns the value of x with its bytes in reversed order.
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//
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// This function's execution time does not depend on the inputs.
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[inline]
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fn reverse_bytes64(x u64) u64 {
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m := u64(u64(1<<64) - u64(1))
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mut y := u64(u64(x>>u64(8)&(m3&m)) | u64(u64(x&(m3&m))<<u64(8)))
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y = u64(u64(y>>u64(16)&(m4&m)) | u64(u64(y&(m4&m))<<u64(16)))
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return u64(y>>u64(32)) | u64(y<<u64(32))
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}
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// --- Len ---
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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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fn len8(x byte) int {
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return int(len8_tab[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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fn len16(x u16) int {
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mut y := x
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mut n := 0
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if y >= u16(u16(1)<<u16(8)) {
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y >>= u16(8)
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n = 8
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}
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return n + int(len8_tab[y])
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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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fn len32(x u32) int {
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mut y := x
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mut n := 0
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if y >= u32(u32(1)<<u32(16)) {
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y >>= u32(16)
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n = 16
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}
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if y >= u32(u32(1)<<u32(8)) {
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y >>= u32(8)
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n += 8
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}
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return n + int(len8_tab[y])
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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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fn len64(x u64) int {
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mut y := x
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mut n := 0
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if y >= u64(u64(1)<<u64(32)) {
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y >>= u64(32)
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n = 32
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}
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if y >= u64(u64(1)<<u64(16)) {
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y >>= u64(16)
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n += 16
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}
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if y >= u64(u64(1)<<u64(8)) {
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y >>= u64(8)
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n += 8
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}
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return n + int(len8_tab[y])
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}
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80
vlib/math/bits/bits_tables.v
Normal file
80
vlib/math/bits/bits_tables.v
Normal file
@ -0,0 +1,80 @@
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// Copyright (c) 2019 Alexander Medvednikov. All rights reserved.
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// Use of this source code is governed by an MIT license
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// that can be found in the LICENSE file.
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module bits
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const(
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ntz8_tab = [
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byte(0x08), 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x07, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
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]
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pop8_tab = [
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byte(0x00), 0x01, 0x01, 0x02, 0x01, 0x02, 0x02, 0x03, 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
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0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
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0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
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0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
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0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
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0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
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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,
|
||||
]
|
||||
)
|
||||
Loading…
Reference in New Issue
Block a user