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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::{Gcd, GcdAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use core::cmp::min;
#[cfg(feature = "test_build")]
pub fn gcd_euclidean<T: PrimitiveUnsigned>(x: T, y: T) -> T {
if y == T::ZERO {
x
} else {
gcd_euclidean(y, x % y)
}
}
#[cfg(feature = "test_build")]
pub fn gcd_binary<T: PrimitiveUnsigned>(x: T, y: T) -> T {
if x == y {
x
} else if x == T::ZERO {
y
} else if y == T::ZERO {
x
} else if x.even() {
if y.odd() {
gcd_binary(x >> 1, y)
} else {
gcd_binary(x >> 1, y >> 1) << 1
}
} else if y.even() {
gcd_binary(x, y >> 1)
} else if x > y {
gcd_binary((x - y) >> 1, y)
} else {
gcd_binary((y - x) >> 1, x)
}
}
private_test_fn! {gcd_fast_a<T: PrimitiveUnsigned>(mut x: T, mut y: T) -> T {
if x == T::ZERO {
return y;
}
if y == T::ZERO {
return x;
}
let x_zeros = x.trailing_zeros();
let y_zeros = y.trailing_zeros();
let f = min(x_zeros, y_zeros);
x >>= x_zeros;
y >>= y_zeros;
while x != y {
if x < y {
y -= x;
y >>= y.trailing_zeros();
} else {
x -= y;
x >>= x.trailing_zeros();
}
}
x << f
}}
#[cfg(feature = "test_build")]
// This is a modified version of `n_xgcd` from `ulong_extras/xgcd.c`, FLINT 2.7.1.
pub fn gcd_fast_b<T: PrimitiveUnsigned>(x: T, y: T) -> T {
let (mut x, mut v) = if x >= y { (x, y) } else { (y, x) };
// x and y both have their top bit set.
if (x & v).get_highest_bit() {
(x, v) = (v, x - v);
}
// The second value has its second-highest set.
while (v << 1u64).get_highest_bit() {
let d = x - v;
(x, v) = (
v,
if d < v {
d
} else if d < (v << 1) {
d - v
} else {
d - (v << 1)
},
);
}
while v != T::ZERO {
// Overflow is not possible due to top 2 bits of v not being set. Avoid divisions when
// quotient < 4.
(x, v) = if x < (v << 2) {
let d = x - v;
(
v,
if d < v {
d
} else if d < (v << 1) {
d - v
} else {
d - (v << 1)
},
)
} else {
(v, x % v)
};
}
x
}
macro_rules! impl_gcd {
($t:ident) => {
impl Gcd<$t> for $t {
type Output = $t;
/// Computes the GCD (greatest common divisor) of two numbers.
///
/// The GCD of 0 and $n$, for any $n$, is 0. In particular, $\gcd(0, 0) = 0$, which
/// makes sense if we interpret "greatest" to mean "greatest by the divisibility order".
///
/// $$
/// f(x, y) = \gcd(x, y).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`: this is binary GCD, and
/// each subtract-and-shift iteration removes at least one bit from one of the operands,
/// so there are $O(n)$ iterations of constant-cost word operations, with no allocation.
///
/// # Examples
/// See [here](super::gcd#gcd).
#[inline]
fn gcd(self, other: $t) -> $t {
gcd_fast_a(self, other)
}
}
impl GcdAssign<$t> for $t {
/// Replaces another with the GCD (greatest common divisor) of it and another number.
///
/// The GCD of 0 and $n$, for any $n$, is 0. In particular, $\gcd(0, 0) = 0$, which
/// makes sense if we interpret "greatest" to mean "greatest by the divisibility order".
///
/// $$
/// x \gets \gcd(x, y).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`: this is binary GCD, and
/// each subtract-and-shift iteration removes at least one bit from one of the operands,
/// so there are $O(n)$ iterations of constant-cost word operations, with no allocation.
///
/// # Examples
/// See [here](super::gcd#gcd_assign).
#[inline]
fn gcd_assign(&mut self, other: $t) {
*self = gcd_fast_a(*self, other);
}
}
};
}
apply_to_unsigneds!(impl_gcd);