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math.bits: added missing functions and test
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penguindark
GitHub
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commit
67e7ad13de
@ -96,6 +96,7 @@ pub fn trailing_zeros_64(x u64) int {
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}
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// --- OnesCount ---
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// ones_count_8 returns the number of one bits ("population count") in x.
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pub fn ones_count_8(x byte) int {
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return int(pop_8_tab[x])
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@ -142,6 +143,7 @@ pub fn ones_count_64(x u64) int {
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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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// To rotate x right by k bits, call rotate_left_8(x, -k).
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//
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@ -187,6 +189,7 @@ pub fn rotate_left_64(x u64, k int) u64 {
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}
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// --- Reverse ---
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// reverse_8 returns the value of x with its bits in reversed order.
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[inline]
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pub fn reverse_8(x byte) byte {
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@ -218,6 +221,7 @@ pub fn reverse_64(x u64) u64 {
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}
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// --- ReverseBytes ---
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// reverse_bytes_16 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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@ -246,6 +250,7 @@ pub fn reverse_bytes_64(x u64) u64 {
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}
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// --- Len ---
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// len_8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
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pub fn len_8(x byte) int {
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return int(len_8_tab[x])
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@ -296,3 +301,195 @@ pub fn len_64(x u64) int {
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return n + int(len_8_tab[y])
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}
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// --- Add with carry ---
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// Add returns the sum with carry of x, y and carry: sum = x + y + carry.
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// The carry input must be 0 or 1; otherwise the behavior is undefined.
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// The carryOut output is guaranteed to be 0 or 1.
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//
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// add_32 returns the sum with carry of x, y and carry: sum = x + y + carry.
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// The carry input must be 0 or 1; otherwise the behavior is undefined.
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// The carryOut output is guaranteed to be 0 or 1.
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//
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// This function's execution time does not depend on the inputs.
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fn add_32(x u32, y u32, carry u32) (u32, u32) {
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sum64 := u64(x) + u64(y) + u64(carry)
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sum := u32(sum64)
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carry_out := u32(sum64>>32)
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return sum, carry_out
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}
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// add_64 returns the sum with carry of x, y and carry: sum = x + y + carry.
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// The carry input must be 0 or 1; otherwise the behavior is undefined.
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// The carryOut output is guaranteed to be 0 or 1.
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//
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// This function's execution time does not depend on the inputs.
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fn add_64(x u64, y u64, carry u64) (u64, u64) {
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sum := x + y + carry
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// The sum will overflow if both top bits are set (x & y) or if one of them
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// is (x | y), and a carry from the lower place happened. If such a carry
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// happens, the top bit will be 1 + 0 + 1 = 0 (&^ sum).
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carry_out := ((x & y) | ((x | y) & ~sum ))>>63
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return sum, carry_out
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}
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// --- Subtract with borrow ---
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// Sub returns the difference of x, y and borrow: diff = x - y - borrow.
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// The borrow input must be 0 or 1; otherwise the behavior is undefined.
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// The borrowOut output is guaranteed to be 0 or 1.
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//
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// sub_32 returns the difference of x, y and borrow, diff = x - y - borrow.
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// The borrow input must be 0 or 1; otherwise the behavior is undefined.
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// The borrowOut output is guaranteed to be 0 or 1.
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//
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// This function's execution time does not depend on the inputs.
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fn sub_32(x u32, y u32, borrow u32) (u32, u32) {
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diff := x - y - borrow
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// The difference will underflow if the top bit of x is not set and the top
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// bit of y is set (^x & y) or if they are the same (^(x ^ y)) and a borrow
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// from the lower place happens. If that borrow happens, the result will be
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// 1 - 1 - 1 = 0 - 0 - 1 = 1 (& diff).
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borrow_out := ((~x & y) | (~(x ^ y) & diff))>>31
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return diff, borrow_out
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}
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// sub_64 returns the difference of x, y and borrow: diff = x - y - borrow.
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// The borrow input must be 0 or 1; otherwise the behavior is undefined.
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// The borrowOut output is guaranteed to be 0 or 1.
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//
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// This function's execution time does not depend on the inputs.
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fn sub_64(x u64, y u64, borrow u64) (u64, u64) {
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diff := x - y - borrow
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// See Sub32 for the bit logic.
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borrow_out := ((~x & y) | (~(x ^ y) & diff))>>63
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return diff, borrow_out
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}
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// --- Full-width multiply ---
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const (
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two32 = u64(0x1_0000_0000)
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mask32 = two32 - 1
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overflow_error = "Overflow Error"
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divide_error = "Divide Error"
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)
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// mul_32 returns the 64-bit product of x and y: (hi, lo) = x * y
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// with the product bits' upper half returned in hi and the lower
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// half returned in lo.
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//
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// This function's execution time does not depend on the inputs.
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fn mul_32(x u32, y u32) (u32, u32) {
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tmp := u64(x) * u64(y)
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hi := u32(tmp>>32)
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lo := u32(tmp)
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return hi, lo
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}
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// mul_64 returns the 128-bit product of x and y: (hi, lo) = x * y
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// with the product bits' upper half returned in hi and the lower
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// half returned in lo.
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//
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// This function's execution time does not depend on the inputs.
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fn mul_64(x u64, y u64) (u64, u64) {
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x0 := x & mask32
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x1 := x>>32
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y0 := y & mask32
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y1 := y>>32
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w0 := x0 * y0
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t := x1*y0 + (w0>>32)
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mut w1 := t & mask32
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w2 := t>>32
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w1 += x0 * y1
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hi := x1*y1 + w2 + (w1>>32)
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lo := x * y
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return hi, lo
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}
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// --- Full-width divide ---
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// div_32 returns the quotient and remainder of (hi, lo) divided by y:
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// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
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// half in parameter hi and the lower half in parameter lo.
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// div_32 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
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fn div_32(hi u32, lo u32, y u32) (u32, u32) {
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if y != 0 && y <= hi {
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panic(overflow_error)
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}
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z := (u64(hi)<<32) | u64(lo)
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quo := u32(z/u64(y))
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rem := u32(z%u64(y))
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return quo, rem
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}
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// div_64 returns the quotient and remainder of (hi, lo) divided by y:
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// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
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// half in parameter hi and the lower half in parameter lo.
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// div_64 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
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fn div_64(hi u64, lo u64, y1 u64) (u64, u64) {
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mut y := y1
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if y == 0 {
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panic(overflow_error)
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}
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if y <= hi {
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panic(overflow_error)
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}
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s := u32(leading_zeros_64(y))
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y <<= s
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yn1 := y>>32
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yn0 := y & mask32
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un32 := (hi<<s) | (lo>>(64-s))
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un10 := lo<<s
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un1 := un10>>32
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un0 := un10 & mask32
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mut q1 := un32 / yn1
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mut rhat := un32 - q1*yn1
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for q1 >= two32 || q1*yn0 > two32*rhat+un1 {
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q1--
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rhat += yn1
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if rhat >= two32 {
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break
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}
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}
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un21 := un32*two32 + un1 - q1*y
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mut q0 := un21 / yn1
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rhat = un21 - q0*yn1
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for q0 >= two32 || q0*yn0 > two32*rhat+un0 {
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q0--
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rhat += yn1
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if rhat >= two32 {
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break
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}
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}
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return q1*two32 + q0, (un21*two32 + un0 - q0*y)>>s
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}
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// rem_32 returns the remainder of (hi, lo) divided by y. Rem32 panics
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// for y == 0 (division by zero) but, unlike Div32, it doesn't panic
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// on a quotient overflow.
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fn rem_32(hi u32, lo u32, y u32) u32 {
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return u32((u64(hi)<<32 | u64(lo)) % u64(y))
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}
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// rem_64 returns the remainder of (hi, lo) divided by y. Rem64 panics
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// for y == 0 (division by zero) but, unlike div_64, it doesn't panic
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// on a quotient overflow.
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fn rem_64(hi, lo, y u64) u64 {
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// We scale down hi so that hi < y, then use div_64 to compute the
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// rem with the guarantee that it won't panic on quotient overflow.
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// Given that
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// hi ≡ hi%y (mod y)
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// we have
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// hi<<64 + lo ≡ (hi%y)<<64 + lo (mod y)
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_, rem := div_64(hi%y, lo, y)
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return rem
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}
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@ -1,8 +1,12 @@
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//
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// test suite for bits and bits math functions
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//
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module bits
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fn test_bits(){
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mut i := 0
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mut i1:= u64(0)
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//
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// --- LeadingZeros ---
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//
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@ -10,26 +14,29 @@ fn test_bits(){
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// 8 bit
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i = 1
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for x in 0..8 {
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//C.printf("x:%02x lz: %d cmp: %d\n",i<<x,leading_zeros_8(i<<x), 7-x)
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assert leading_zeros_8(byte(i<<x)) == 7 - x
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//C.printf("x:%02x lz: %d cmp: %d\n", i << x, leading_zeros_8(i << x), 7-x)
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assert leading_zeros_8(byte(i << x)) == 7 - x
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}
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// 16 bit
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i = 1
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for x in 0..16 {
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//C.printf("x:%04x lz: %d cmp: %d\n",u16(i)<<x,leading_zeros_16(u16(i)<<x), 15-x)
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assert leading_zeros_16(u16(i)<<x) == 15 - x
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//C.printf("x:%04x lz: %d cmp: %d\n", u16(i) << x, leading_zeros_16(u16(i) << x), 15-x)
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assert leading_zeros_16(u16(i) << x) == 15 - x
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}
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// 32 bit
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i = 1
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for x in 0..32 {
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//C.printf("x:%08x lz: %d cmp: %d\n",u32(i)<<x,leading_zeros_32(u32(i)<<x), 31-x)
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assert leading_zeros_32(u32(i)<<x) == 31 - x
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//C.printf("x:%08x lz: %d cmp: %d\n", u32(i) << x, leading_zeros_32(u32(i) << x), 31-x)
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assert leading_zeros_32(u32(i) << x) == 31 - x
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}
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// 64 bit
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i = 1
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for x in 0..64 {
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//C.printf("x:%016llx lz: %llu cmp: %d\n",u64(i)<<x,leading_zeros_64(u64(i)<<x), 63-x)
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assert leading_zeros_64(u64(i)<<x) == 63 - x
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//C.printf("x:%016llx lz: %llu cmp: %d\n", u64(i) << x, leading_zeros_64(u64(i) << x), 63-x)
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assert leading_zeros_64(u64(i) << x) == 63 - x
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}
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//
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@ -39,29 +46,32 @@ fn test_bits(){
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// 8 bit
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i = 0
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for x in 0..9 {
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//C.printf("x:%02x lz: %llu cmp: %d\n",byte(i),ones_count_8(byte(i)), x)
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//C.printf("x:%02x lz: %llu cmp: %d\n", byte(i), ones_count_8(byte(i)), x)
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assert ones_count_8(byte(i)) == x
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i = (i << 1) + 1
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}
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// 16 bit
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i = 0
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for x in 0..17 {
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//C.printf("x:%04x lz: %llu cmp: %d\n",u16(i),ones_count_16(u16(i)), x)
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//C.printf("x:%04x lz: %llu cmp: %d\n", u16(i), ones_count_16(u16(i)), x)
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assert ones_count_16(u16(i)) == x
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i = (i << 1) + 1
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}
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// 32 bit
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i = 0
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for x in 0..33 {
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//C.printf("x:%08x lz: %llu cmp: %d\n",u32(i),ones_count_32(u32(i)), x)
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//C.printf("x:%08x lz: %llu cmp: %d\n", u32(i), ones_count_32(u32(i)), x)
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assert ones_count_32(u32(i)) == x
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i = (i << 1) + 1
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}
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// 64 bit
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i1 = 0
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for x in 0..65 {
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//C.printf("x:%016llx lz: %llu cmp: %d\n",u64(i1),ones_count_64(u64(i1)), x)
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assert ones_count_64(u64(i1)) == x
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//C.printf("x:%016llx lz: %llu cmp: %d\n", u64(i1), ones_count_64(u64(i1)), x)
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assert ones_count_64(i1) == x
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i1 = (i1 << 1) + 1
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}
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@ -88,10 +98,11 @@ fn test_bits(){
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bc++
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n = n >> 1
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}
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//C.printf("x:%02x lz: %llu cmp: %d\n",byte(i),reverse_8(byte(i)), rv)
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//C.printf("x:%02x lz: %llu cmp: %d\n", byte(i), reverse_8(byte(i)), rv)
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assert reverse_8(byte(i)) == rv
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i = (i << 1) + 1
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}
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// 16 bit
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i = 0
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for x in 0..17 {
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@ -103,10 +114,11 @@ fn test_bits(){
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bc++
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n = n >> 1
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}
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//C.printf("x:%04x lz: %llu cmp: %d\n",u16(i),reverse_16(u16(i)), rv)
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//C.printf("x:%04x lz: %llu cmp: %d\n", u16(i), reverse_16(u16(i)), rv)
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assert reverse_16(u16(i)) == rv
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i = (i << 1) + 1
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}
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// 32 bit
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i = 0
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for x in 0..33 {
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@ -118,10 +130,11 @@ fn test_bits(){
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bc++
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n = n >> 1
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}
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//C.printf("x:%08x lz: %llu cmp: %d\n",u32(i),reverse_32(u32(i)), rv)
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//C.printf("x:%08x lz: %llu cmp: %d\n", u32(i), reverse_32(u32(i)), rv)
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assert reverse_32(u32(i)) == rv
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i = (i << 1) + 1
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}
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// 64 bit
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i1 = 0
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for x in 0..64 {
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@ -133,8 +146,144 @@ fn test_bits(){
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bc++
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n = n >> 1
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}
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//C.printf("x:%016llx lz: %016llx cmp: %016llx\n",u64(i1),reverse_64(u64(i1)), rv)
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assert reverse_64(u64(i1)) == rv
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//C.printf("x:%016llx lz: %016llx cmp: %016llx\n", u64(i1), reverse_64(u64(i1)), rv)
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assert reverse_64(i1) == rv
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i1 = (i1 << 1) + 1
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}
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}
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//
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// --- add ---
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//
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// 32 bit
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i = 1
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for x in 0..32 {
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v := u32(i) << x
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sum,carry := add_32(v, v, u32(0))
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//C.printf("x:%08x [%llu,%llu] %llu\n", u32(i) << x, sum, carry, u64(v) + u64(v))
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assert ((u64(carry) << 32) | u64(sum)) == u64(v) + u64(v)
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}
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mut sum_32t, mut carry_32t := add_32(0x8000_0000, 0x8000_0000, u32(0))
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assert sum_32t == u32(0)
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assert carry_32t == u32(1)
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sum_32t, carry_32t = add_32(0xFFFF_FFFF, 0xFFFF_FFFF, u32(1))
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assert sum_32t == 0xFFFF_FFFF
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assert carry_32t == u32(1)
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// 64 bit
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i = 1
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for x in 0..63 {
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v := u64(i) << x
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sum,carry := add_64(v, v, u64(0))
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//C.printf("x:%16x [%llu,%llu] %llu\n", u64(i) << x, sum, carry, u64(v >> 32) + u64(v >> 32))
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assert ((carry << 32) | sum) == v + v
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}
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mut sum_64t, mut carry_64t := add_64(0x8000_0000_0000_0000, 0x8000_0000_0000_0000, u64(0))
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assert sum_64t == u64(0)
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assert carry_64t == u64(1)
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sum_64t, carry_64t = add_64(0xFFFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF, u64(1))
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assert sum_64t == 0xFFFF_FFFF_FFFF_FFFF
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assert carry_64t == u64(1)
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//
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||||
// --- sub ---
|
||||
//
|
||||
|
||||
// 32 bit
|
||||
i = 1
|
||||
for x in 1..32 {
|
||||
v0 := u32(i) << x
|
||||
v1 := v0 >> 1
|
||||
mut diff, mut borrow_out := sub_32(v0, v1, u32(0))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v0 - v1)
|
||||
assert diff == v1
|
||||
|
||||
diff, borrow_out = sub_32(v0, v1, u32(1))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v0 - v1)
|
||||
assert diff == (v1 - 1)
|
||||
assert borrow_out == u32(0)
|
||||
|
||||
diff, borrow_out = sub_32(v1, v0, u32(1))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v1 - v0)
|
||||
assert borrow_out == u32(1)
|
||||
}
|
||||
|
||||
// 64 bit
|
||||
i = 1
|
||||
for x in 1..64 {
|
||||
v0 := u64(i) << x
|
||||
v1 := v0 >> 1
|
||||
mut diff, mut borrow_out := sub_64(v0, v1, u64(0))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n", u64(i) << x, diff, borrow_out, v0 - v1)
|
||||
assert diff == v1
|
||||
|
||||
diff, borrow_out = sub_64(v0, v1, u64(1))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n", u64(i) << x, diff, borrow_out, v0 - v1)
|
||||
assert diff == (v1 - 1)
|
||||
assert borrow_out == u64(0)
|
||||
|
||||
diff, borrow_out = sub_64(v1, v0, u64(1))
|
||||
//C.printf("x:%08x [%llu,%llu] %08x\n",u64(i) << x, diff, borrow_out, v1 - v0)
|
||||
assert borrow_out == u64(1)
|
||||
}
|
||||
|
||||
//
|
||||
// --- mul ---
|
||||
//
|
||||
|
||||
// 32 bit
|
||||
i = 1
|
||||
for x in 0..32 {
|
||||
v0 := u32(i) << x
|
||||
v1 := v0 - 1
|
||||
hi, lo := mul_32(v0, v1)
|
||||
//C.printf("x:%08x [%llu,%llu] %llu\n", v0, hi, lo, u64(v0 * v1))
|
||||
assert (u64(hi) << 32) | (u64(lo)) == u64(v0 * v1)
|
||||
}
|
||||
|
||||
// 64 bit
|
||||
i = 1
|
||||
for x in 0..64 {
|
||||
v0 := u64(i) << x
|
||||
v1 := v0 - 1
|
||||
hi, lo := mul_64(v0, v1)
|
||||
//C.printf("v0: %llu v1: %llu [%llu,%llu] tt: %llu\n", v0, v1, hi, lo, (v0 >> 32) * (v1 >> 32))
|
||||
assert (hi & 0xFFFF_FFFF_0000_0000) == (((v0 >> 32)*(v1 >> 32)) & 0xFFFF_FFFF_0000_0000)
|
||||
assert (lo & 0x0000_0000_FFFF_FFFF) == (((v0 & 0x0000_0000_FFFF_FFFF) * (v1 & 0x0000_0000_FFFF_FFFF)) & 0x0000_0000_FFFF_FFFF)
|
||||
}
|
||||
|
||||
//
|
||||
// --- div ---
|
||||
//
|
||||
|
||||
// 32 bit
|
||||
i = 1
|
||||
for x in 0..31 {
|
||||
hi := u32(i) << x
|
||||
lo := hi - 1
|
||||
y := u32(3) << x
|
||||
quo, rem := div_32(hi, lo, y)
|
||||
//C.printf("[%08x_%08x] %08x (%08x,%08x)\n", hi, lo, y, quo, rem)
|
||||
tst := ((u64(hi) << 32) | u64(lo))
|
||||
assert quo == (tst / u64(y))
|
||||
assert rem == (tst % u64(y))
|
||||
assert rem == rem_32(hi, lo, y)
|
||||
}
|
||||
|
||||
// 64 bit
|
||||
i = 1
|
||||
for x in 0..62 {
|
||||
hi := u64(i) << x
|
||||
lo := u64(2) //hi - 1
|
||||
y := 0x4000_0000_0000_0000
|
||||
quo, rem := div_64(hi, lo, y)
|
||||
//C.printf("[%016llx_%016llx] %016llx (%016llx,%016llx)\n", hi, lo, y, quo, rem)
|
||||
assert quo == u64(2)<<(x+1)
|
||||
_, rem1 := div_64(hi%y, lo, y)
|
||||
assert rem == rem1
|
||||
assert rem == rem_64(hi, lo, y)
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user