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fn gcd(mut a: u128, mut b: u128) -> u128 {
while b != 0 {
let (na, nb) = (b, a % b);
a = na;
b = nb;
}
a
}
fn modpow(mut n: u128, mut e: u128, m: u128) -> u128 {
if m == 1 {
return 0;
}
let mut result = 1;
n %= m;
while e > 0 {
if e % 2 == 1 {
result = (result * n) % m;
}
e >>= 1;
n = (n * n) % m;
}
result
}
#[allow(clippy::many_single_char_names)]
pub fn factorize(pq: u64) -> (u64, u64) {
if pq % 2 == 0 {
return (2, pq);
}
let pq = pq as u128;
fn abs_sub(a: u128, b: u128) -> u128 {
a.max(b) - a.min(b)
}
let mut y = pq / 4;
let c = 2 * pq / 4;
let m = 3 * pq / 4;
let mut g = 1u128;
let mut r = 1u128;
let mut q = 1u128;
let mut x = 0u128;
let mut ys = 0u128;
while g == 1 {
x = y;
for _ in 0..r {
y = (modpow(y, 2, pq) + c) % pq;
}
let mut k = 0;
while k < r && g == 1 {
ys = y;
for _ in 0..m.min(r - k) {
y = (modpow(y, 2, pq) + c) % pq;
q = (q * abs_sub(x, y)) % pq;
}
g = gcd(q, pq);
k += m;
}
r *= 2;
}
if g == pq {
loop {
ys = (modpow(ys, 2, pq) + c) % pq;
g = gcd(abs_sub(x, ys), pq);
if g > 1 {
break;
}
}
}
let (p, q) = (g as u64, (pq / g) as u64);
(p.min(q), p.max(q))
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_factorization_1() {
let pq = factorize(1470626929934143021);
assert_eq!(pq, (1206429347, 1218991343));
}
#[test]
fn test_factorization_2() {
let pq = factorize(2363612107535801713);
assert_eq!(pq, (1518968219, 1556064227));
}
}