bjoernager/rust
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Optimize udiv_1e19() function

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Kogia-sima 2021-01-29 02:27:20 +09:00
parent 643a79af3d
commit ada714d9ce
1 changed files with 34 additions and 17 deletions
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51
library/core/src/fmt/num.rs
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@ -643,25 +643,42 @@ fn fmt_u128(n: u128, is_nonnegative: bool, f: &mut fmt::Formatter<'_>) -> fmt::R
}
/// Partition of `n` into n > 1e19 and rem <= 1e19
///
/// Integer division algorithm is based on the following paper:
///
/// T. Granlund and P. Montgomery, “Division by Invariant Integers Using Multiplication”
/// in Proc. of the SIGPLAN94 Conference on Programming Language Design and
/// Implementation, 1994, pp. 61–72
///
fn udiv_1e19(n: u128) -> (u128, u64) {
const DIV: u64 = 1e19 as u64;
let high = (n >> 64) as u64;
if high == 0 {
let low = n as u64;
return ((low / DIV) as u128, low % DIV);
}
let sr = 65 - high.leading_zeros();
let mut q = n << (128 - sr);
let mut r = n >> sr;
let mut carry = 0;
const FACTOR: u128 = 156927543384667019095894735580191660403;
for _ in 0..sr {
r = (r << 1) | (q >> 127);
q = (q << 1) | carry as u128;
let quot = if n < 1 << 83 {
((n >> 19) as u64 / (DIV >> 19)) as u128
} else {
u128_mulhi(n, FACTOR) >> 62
};
let s = (DIV as u128).wrapping_sub(r).wrapping_sub(1) as i128 >> 127;
carry = (s & 1) as u64;
r -= (DIV as u128) & s as u128;
}
((q << 1) | carry as u128, r as u64)
let rem = (n - quot * DIV as u128) as u64;
(quot, rem)
}
/// Multiply unsigned 128 bit integers, return upper 128 bits of the result
#[inline]
fn u128_mulhi(x: u128, y: u128) -> u128 {
let x_lo = x as u64;
let x_hi = (x >> 64) as u64;
let y_lo = y as u64;
let y_hi = (y >> 64) as u64;
// handle possibility of overflow
let carry = (x_lo as u128 * y_lo as u128) >> 64;
let m = x_lo as u128 * y_hi as u128 + carry;
let high1 = m >> 64;
let m_lo = m as u64;
let high2 = (x_hi as u128 * y_lo as u128 + m_lo as u128) >> 64;
x_hi as u128 * y_hi as u128 + high1 + high2
}