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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 2009, 2016 William Hart
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::num::arithmetic::traits::ModInverse;
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::WrappingFrom;
use crate::rounding_modes::RoundingMode::*;
// This is a variation of `n_xgcd` from `ulong_extras/xgcd.c`, FLINT 2.7.1.
pub_test! {mod_inverse_binary<
U: WrappingFrom<S> + PrimitiveUnsigned,
S: PrimitiveSigned + WrappingFrom<U>,
>(
x: U,
m: U,
) -> Option<U> {
assert_ne!(x, U::ZERO);
assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
let mut u1 = S::ONE;
let mut v2 = S::ONE;
let mut u2 = S::ZERO;
let mut v1 = S::ZERO;
let mut u3 = m;
let mut v3 = x;
let mut d;
let mut t2;
let mut t1;
if (m & x).get_highest_bit() {
d = u3 - v3;
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
}
while v3.get_bit(U::WIDTH - 2) {
d = u3 - v3;
if d < v3 {
// quot = 1
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
} else if d < (v3 << 1) {
// quot = 2
t1 = u2;
u2 = u1 - (u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - (v2 << 1);
v1 = t2;
v3 = d - u3;
} else {
// quot = 3
t1 = u2;
u2 = u1 - S::wrapping_from(3) * u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - S::wrapping_from(3) * v2;
v1 = t2;
v3 = d - (u3 << 1);
}
}
while v3 != U::ZERO {
d = u3 - v3;
// overflow not possible, top 2 bits of v3 not set
if u3 < (v3 << 2) {
if d < v3 {
// quot = 1
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
} else if d < (v3 << 1) {
// quot = 2
t1 = u2;
u2 = u1.wrapping_sub(u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1.wrapping_sub(v2 << 1);
v1 = t2;
v3 = d - u3;
} else {
// quot = 3
t1 = u2;
u2 = u1.wrapping_sub(S::wrapping_from(3).wrapping_mul(u2));
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1.wrapping_sub(S::wrapping_from(3).wrapping_mul(v2));
v1 = t2;
v3 = d.wrapping_sub(u3 << 1);
}
} else {
let (quot, rem) = u3.div_rem(v3);
t1 = u2;
u2 = u1.wrapping_sub(S::wrapping_from(quot).wrapping_mul(u2));
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1.wrapping_sub(S::wrapping_from(quot).wrapping_mul(v2));
v1 = t2;
v3 = rem;
}
}
if u3 != U::ONE {
return None;
}
let mut inverse = U::wrapping_from(v1);
if u1 <= S::ZERO {
inverse.wrapping_sub_assign(m);
}
let limit = (m >> 1u32).wrapping_neg();
if inverse < limit {
let k = (limit - inverse).div_round(m, Ceiling).0;
inverse.wrapping_add_assign(m.wrapping_mul(k));
}
Some(if inverse.get_highest_bit() {
inverse.wrapping_add(m)
} else {
inverse
})
}}
macro_rules! impl_mod_inverse {
($u:ident, $s:ident) => {
impl ModInverse<$u> for $u {
type Output = $u;
/// Computes the multiplicative inverse of a number modulo another number $m$. The input
/// must be already reduced modulo $m$.
///
/// Returns `None` if $x$ and $m$ are not coprime.
///
/// $f(x, m) = y$, where $x, y < m$, $\gcd(x, y) = 1$, and $xy \equiv 1 \mod m$.
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), m.significant_bits())`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_inverse#mod_inverse).
#[inline]
fn mod_inverse(self, m: $u) -> Option<$u> {
mod_inverse_binary::<$u, $s>(self, m)
}
}
};
}
apply_to_unsigned_signed_pairs!(impl_mod_inverse);