itoa/src/udiv128.rs

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// Copyright 2009-2016 compiler-builtins Developers
//
// The compiler-builtins crate is dual licensed under both the University of
// Illinois "BSD-Like" license and the MIT license. As a user of this code you may
// choose to use it under either license. As a contributor, you agree to allow
// your code to be used under both.
//
// Full text of the relevant licenses is found here:
// https://github.com/rust-lang-nursery/compiler-builtins/blob/master/LICENSE.TXT
//
//
//
// The following code is based on Rusts [compiler-builtins crate]
// (https://github.com/rust-lang-nursery/compiler-builtins) which
// provides runtime functions for the Rust programs. The Rust
// compiler will automatically link your programs against this crate.
//
// We copied the implementation of '__udivmodti4()' which is an intrinsic
// implementing division with remainder for architectures without 128-bit integer support.
// We have done this two reasons, to work around [bad optimization by LLVM]
// (https://github.com/rust-lang/rust/issues/44545) and to allow function
// inlining which doesnt happen with the intrinsic.
const BITS: u32 = 128;
const BITS_HALF: u32 = 64;
trait LargeInt {
fn low(self) -> u64;
fn high(self) -> u64;
fn from_parts(low: u64, high: u64) -> Self;
}
trait Int {
fn aborting_div(self, other: Self) -> Self;
fn aborting_rem(self, other: Self) -> Self;
}
impl LargeInt for u128 {
fn low(self) -> u64 {
self as u64
}
fn high(self) -> u64 {
(self >> 64) as u64
}
fn from_parts(low: u64, high: u64) -> u128 {
low as u128 | ((high as u128) << 64)
}
}
impl Int for u64 {
fn aborting_div(self, other: u64) -> u64 {
<u64>::checked_div(self, other).unwrap()
}
fn aborting_rem(self, other: u64) -> u64 {
<u64>::checked_rem(self, other).unwrap()
}
}
pub fn udivmodti4(n: u128, d: u128, rem: Option<&mut u128>) -> u128 {
// NOTE X is unknown, K != 0
if n.high() == 0 {
if d.high() == 0 {
// 0 X
// ---
// 0 X
if let Some(rem) = rem {
*rem = <u128>::from(n.low().aborting_rem(d.low()));
}
return <u128>::from(n.low().aborting_div(d.low()))
} else {
// 0 X
// ---
// K X
if let Some(rem) = rem {
*rem = n;
}
return 0;
};
}
let mut sr;
let mut q;
let mut r;
if d.low() == 0 {
if d.high() == 0 {
// K X
// ---
// 0 0
// NOTE This should be unreachable in safe Rust because the program will panic before
// this intrinsic is called
unreachable!();
}
if n.low() == 0 {
// K 0
// ---
// K 0
if let Some(rem) = rem {
*rem = <u128>::from_parts(0, n.high().aborting_rem(d.high()));
}
return <u128>::from(n.high().aborting_div(d.high()))
}
// K K
// ---
// K 0
if d.high().is_power_of_two() {
if let Some(rem) = rem {
*rem = <u128>::from_parts(n.low(), n.high() & (d.high() - 1));
}
return <u128>::from(n.high() >> d.high().trailing_zeros());
}
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > BITS_HALF - 2 {
if let Some(rem) = rem {
*rem = n;
}
return 0;
}
sr += 1;
// 1 <= sr <= BITS_HALF - 1
q = n << (BITS - sr);
r = n >> sr;
} else if d.high() == 0 {
// K X
// ---
// 0 K
if d.low().is_power_of_two() {
if let Some(rem) = rem {
*rem = <u128>::from(n.low() & (d.low() - 1));
}
if d.low() == 1 {
return n;
} else {
let sr = d.low().trailing_zeros();
return n >> sr;
};
}
sr = 1 + BITS_HALF + d.low().leading_zeros() - n.high().leading_zeros();
// 2 <= sr <= u64::BITS - 1
q = n << (BITS - sr);
r = n >> sr;
} else {
// K X
// ---
// K K
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > BITS_HALF - 1 {
if let Some(rem) = rem {
*rem = n;
}
return 0;
}
sr += 1;
// 1 <= sr <= BITS_HALF
q = n << (BITS - sr);
r = n >> sr;
}
// Not a special case
// q and r are initialized with
// q = n << (u64::BITS - sr)
// r = n >> sr
// 1 <= sr <= u64::BITS - 1
let mut carry = 0;
// Don't use a range because they may generate references to memcpy in unoptimized code
let mut i = 0;
while i < sr {
i += 1;
// r:q = ((r:q) << 1) | carry
r = (r << 1) | (q >> (BITS - 1));
q = (q << 1) | carry as u128;
// carry = 0
// if r >= d {
// r -= d;
// carry = 1;
// }
let s = (d.wrapping_sub(r).wrapping_sub(1)) as i128 >> (BITS - 1);
carry = (s & 1) as u64;
r -= d & s as u128;
}
if let Some(rem) = rem {
*rem = r;
}
(q << 1) | carry as u128
}
#[cfg(test)]
#[test]
fn test_udivmodti4() {
let primes = [
3, 7, 31, 73, 127, 179, 233, 283, 353,
419, 467, 547, 607, 661, 739, 811, 877, 947,
];
for (i, d) in (0..128).cycle().zip(primes.iter().cycle()).take(1_000) {
let n = 1u128 << i;
let mut rem = 0;
let q = udivmodti4(n, *d, Some(&mut rem));
assert_eq!(q, n / d);
assert_eq!(rem, n % d);
}
}