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#![no_std]
#![feature(asm)]
pub mod reference {
#[inline]
pub fn mulmod_u64(a: u64, b: u64, m: u64) -> u64 {
let aa = a as u128;
let bb = b as u128;
let mm = m as u128;
let rr = aa * bb % mm;
rr as _
}
#[inline]
pub fn mod_u128u64(a: u128, m: u64) -> u64 {
let mm = m as u128;
let rr = a % mm;
rr as _
}
}
#[inline]
pub fn mulmod_u64(a: u64, mut b: u64, m: u64) -> u64 {
unsafe {
asm!(
"mul rdx",
"div {}",
in(reg) m,
in("rax") a,
inout("rdx") b,
);
}
b
}
#[inline]
pub fn mod_u128u64(a: u128, m: u64) -> u64 {
let qb = 65 + m.leading_zeros() - a.leading_zeros();
if qb > 64 {
let s = qb - 64;
let mask = (1 << s) - 1;
let r = mod_u128u64_unchecked(a >> s, m) as u128;
let na = (r << s) + (a & mask);
mod_u128u64_unchecked(na, m)
} else {
mod_u128u64_unchecked(a, m)
}
}
#[inline]
pub fn mod_u128u64_unchecked(a: u128, m: u64) -> u64 {
let hi = (a >> 64) as u64;
let lo = (a & 0xFFFFFFFFFFFFFFFF) as u64;
let r;
unsafe {
asm!(
"div {}",
in(reg) m,
in("rax") lo,
inout("rdx") hi => r,
);
}
r
}
#[cfg(test)]
mod tests {
use crate::*;
#[test]
fn it_works() {
assert_eq!(2 + 2, 4);
}
#[test]
fn modulo_u64() {
use rand::prelude::*;
let mut rng = rand::thread_rng();
for _ in 0..1_000_000 {
let m = rng.gen();
let a = rng.gen::<u64>() % m;
let b = rng.gen::<u64>() % m;
assert_eq!(reference::mulmod_u64(a, b, m), mulmod_u64(a, b, m));
}
}
#[test]
fn modulo_u128u64() {
use rand::prelude::*;
let mut rng = rand::thread_rng();
for _ in 0..1_000_000 {
let m = rng.gen();
let a = rng.gen();
assert_eq!(reference::mod_u128u64(a, m), mod_u128u64(a, m));
}
}
#[test]
fn modulo_u128u64_small_divisor() {
use rand::prelude::*;
let mut rng = rand::thread_rng();
for _ in 0..1_000_000 {
let m = rng.gen::<u32>().into();
let a = rng.gen();
assert_eq!(reference::mod_u128u64(a, m), mod_u128u64(a, m));
}
}
}