Created
April 14, 2022 19:36
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fat muldiv
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| fn lo128(a: u128) -> u128 { | |
| a & ((1<<64)-1) | |
| } | |
| /// Returns the most significant 64 bits of a | |
| fn hi128(a: u128) -> u128 { | |
| a >> 64 | |
| } | |
| /// Returns 2^128 - a (two's complement) | |
| fn neg128(a: u128) -> u128 { | |
| (!a).wrapping_add(1) | |
| } | |
| /// Returns 2^128 / a | |
| fn div128(a: u128) -> Option<u128> { | |
| Some((neg128(a).checked_div(a)?).wrapping_add(1)) | |
| } | |
| /// Returns 2^128 % a | |
| fn mod128(a: u128) -> Option<u128> { | |
| neg128(a).checked_rem(a) | |
| } | |
| /// Returns a+b (wrapping) | |
| fn add256(a0: u128, a1: u128, b0: u128, b1: u128) -> (u128, u128) { | |
| let (r0, overflow) = a0.overflowing_add(b0); | |
| let r1 = a1.wrapping_add(b1).wrapping_add(overflow as u128); | |
| (r0, r1) | |
| } | |
| /// Returns a*b (in 256 bits) | |
| fn mul128(a: u128, b: u128) -> (u128, u128) { | |
| // Split a and b into hi and lo 64-bit parts | |
| // a*b = (a1<<64 + a0)*(b1<<64 + b0) | |
| // = (a1*b1)<<128 + (a1*b0 + b1*a0)<<64 + a0*b0 | |
| let (a0, a1) = (lo128(a), hi128(a)); | |
| let (b0, b1) = (lo128(b), hi128(b)); | |
| let (x, y) = (a1*b0, b1*a0); | |
| let (r0, r1) = (a0*b0, a1*b1); | |
| let (r0, r1) = add256(r0, r1, lo128(x)<<64, hi128(x)); | |
| let (r0, r1) = add256(r0, r1, lo128(y)<<64, hi128(y)); | |
| (r0, r1) | |
| } | |
| /// Returns a/b | |
| fn div256_128(mut a0: u128, mut a1: u128, b: u128) -> Option<(u128, u128)> { | |
| if b == 1 { | |
| return Some((a0, a1)); | |
| } | |
| // Calculate a/b | |
| // = (a0<<128 + a1)/b | |
| // let (q, r) = (div128(b), mod128(b)); | |
| // = (a1*(q*b + r)) + a0)/b | |
| // = (a1*q*b + a1*r + a0)/b | |
| // = (a1*r + a0)/b + a1*q | |
| let (q, r) = (div128(b)?, mod128(b)?); | |
| // x = current result | |
| // a = next number | |
| // t = temp | |
| let (mut x0, mut x1) = (0, 0); | |
| while a1 != 0 { | |
| // x += a1*q | |
| let (t0, t1) = mul128(a1, q); | |
| let (new_x0, new_x1) = add256(x0, x1, t0, t1); | |
| x0 = new_x0; | |
| x1 = new_x1; | |
| // a = a1*r + a0 | |
| let (t0, t1) = mul128(a1, r); | |
| let (new_a0, new_a1) = add256(t0, t1, a0, 0); | |
| a0 = new_a0; | |
| a1 = new_a1; | |
| } | |
| Some(add256(x0, x1, a0.checked_div(b)?, 0)) | |
| } | |
| /// Returns a*b/c (wrapping to 128 bits) | |
| pub fn muldiv128(a: u128, b: u128, c: u128) -> Option<u128> { | |
| let (t0, t1) = mul128(a, b); | |
| Some(div256_128(t0, t1, c)?.0) | |
| } |
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