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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 2009, 2015 William Hart
//
// Copyright © 2019 Daniel Schultz
//
// 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::ModDiv;
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::WrappingFrom;
// Computes `(gcd(x, y), s)`, where `s < y` and `sx ≡ gcd(x, y) mod y`. `x` must be reduced mod
// `y`.
//
// This is n_gcdinv from ulong_extras/gcdinv.c, FLINT 3.6.0, where the GCD is returned along with
// the cofactor.
crate_test_fn! {gcdinv<
U: WrappingFrom<S> + PrimitiveUnsigned,
S: PrimitiveSigned + WrappingFrom<U>,
>(
x: U,
y: U,
) -> (U, U) {
assert!(x < y, "x must be reduced mod y, but {x} >= {y}");
let mut v1 = S::ZERO;
let mut v2 = S::ONE;
let mut r = x;
let mut x = y;
let mut d;
let mut t2;
// y and x both have their highest bit set
if (x & r).get_highest_bit() {
d = x - r;
t2 = v2;
x = r;
v2 = v1 - v2;
v1 = t2;
r = d;
}
// second value has its second-highest bit set
while r.get_bit(U::WIDTH - 2) {
d = x - r;
r = if d < r {
// quot = 1
t2 = v2;
x = r;
v2 = v1 - v2;
v1 = t2;
d
} else if d < (r << 1) {
// quot = 2
x = r;
t2 = v2;
v2 = v1 - (v2 << 1);
v1 = t2;
d - x
} else {
// quot = 3
x = r;
t2 = v2;
v2 = v1 - S::wrapping_from(3) * v2;
v1 = t2;
d - (x << 1)
};
}
while r != U::ZERO {
// overflow not possible, top 2 bits of r not set
r = if x < (r << 2) {
// quot < 4
d = x - r;
if d < r {
// quot = 1
t2 = v2;
x = r;
v2 = v1 - v2;
v1 = t2;
d
} else if d < (r << 1) {
// quot = 2
x = r;
t2 = v2;
v2 = v1.wrapping_sub(v2 << 1);
v1 = t2;
d - x
} else {
// quot = 3
x = r;
t2 = v2;
v2 = v1.wrapping_sub(S::wrapping_from(3).wrapping_mul(v2));
v1 = t2;
d.wrapping_sub(x << 1)
}
} else {
let (quot, rem) = x.div_rem(r);
x = r;
t2 = v2;
v2 = v1.wrapping_sub(S::wrapping_from(quot).wrapping_mul(v2));
v1 = t2;
rem
};
}
let mut s = U::wrapping_from(v1);
if v1 < S::ZERO {
s.wrapping_add_assign(y);
}
(x, s)
}}
// Computes a quotient of `b` and `c` modulo `m`: a `q` such that `qc ≡ b mod m`. `b` and `c` must
// be reduced mod `m`.
//
// This is fmpz_mod_divides from fmpz_mod/divides.c, FLINT 3.6.0, where b and c are word-sized and
// reduced mod the modulus, and the quotient is returned as an Option.
private_test_fn! {mod_div_unsigned<
U: WrappingFrom<S> + PrimitiveUnsigned,
S: PrimitiveSigned + WrappingFrom<U>,
>(
b: U,
c: U,
m: U,
) -> Option<U> {
assert!(b < m, "b must be reduced mod m, but {b} >= {m}");
assert!(c < m, "c must be reduced mod m, but {c} >= {m}");
if c == U::ZERO {
return if b == U::ZERO {
Some(U::ZERO)
} else {
None
};
}
if b == U::ZERO {
return Some(U::ZERO);
}
// b and c are both nonzero now, so m >= 2. Solve g = cx + my, where g = gcd(c, m).
let (g, x) = gcdinv::<U, S>(c, m);
let (q, r) = b.div_rem(g);
if r == U::ZERO {
Some(q.mod_mul(x, m))
} else {
None
}
}}
macro_rules! impl_mod_div {
($u:ident, $s:ident) => {
impl ModDiv<$u> for $u {
type Output = $u;
/// Divides a number by another number modulo a third number $m$, returning `None` if no
/// quotient exists. The inputs must be already reduced modulo $m$.
///
/// A quotient exists if and only if $\gcd(y, m)$ divides $x$. If $y$ is not invertible
/// modulo $m$, the quotient is not unique; all quotients differ by multiples of
/// $m/\gcd(y, m)$, and this function returns one of them.
///
/// $f(x, y, m) = \operatorname{Some}(q)$, where $x, y, q < m$ and $qy \equiv x \mod m$,
/// if such a $q$ exists.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `m.significant_bits()`: the
/// extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost
/// word operations, with no allocation.
///
/// # Panics
/// Panics if `self` or `other` are greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_div#mod_div).
#[inline]
fn mod_div(self, other: $u, m: $u) -> Option<$u> {
mod_div_unsigned::<$u, $s>(self, other, m)
}
}
};
}
apply_to_unsigned_signed_pairs!(impl_mod_div);