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// Copyright © 2026 Mikhail Hogrefe
//
// 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::{CheckedLcm, Lcm, LcmAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
#[inline]
fn lcm<T: PrimitiveUnsigned>(x: T, y: T) -> T {
checked_lcm(x, y).unwrap()
}
fn checked_lcm<T: PrimitiveUnsigned>(x: T, y: T) -> Option<T> {
if x == T::ZERO && y == T::ZERO {
Some(T::ZERO)
} else {
(x / x.gcd(y)).checked_mul(y)
}
}
macro_rules! impl_lcm {
($t:ident) => {
impl Lcm<$t> for $t {
type Output = $t;
/// Computes the LCM (least common multiple) of two numbers.
///
/// $$
/// f(x, y) = \operatorname{lcm}(x, y).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`.
///
/// # Panics
/// Panics if the result is too large to be represented.
///
/// # Examples
/// See [here](super::lcm#lcm).
#[inline]
fn lcm(self, other: $t) -> $t {
lcm(self, other)
}
}
impl LcmAssign<$t> for $t {
/// Replaces a number with the LCM (least common multiple) of it and another number.
///
/// $$
/// x \gets \operatorname{lcm}(x, y).
/// $$
///
/// # 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(), other.significant_bits())`.
///
/// # Panics
/// Panics if the result is too large to be represented.
///
/// # Examples
/// See [here](super::lcm#lcm_assign).
#[inline]
fn lcm_assign(&mut self, other: $t) {
*self = lcm(*self, other);
}
}
impl CheckedLcm<$t> for $t {
type Output = $t;
/// Computes the LCM (least common multiple) of two numbers, returning `None` if the
/// result is too large to represent.
///
/// $$
/// f(x, y) = \\begin{cases}
/// \operatorname{Some}(\operatorname{lcm}(x, y)) &
/// \text{if} \\quad \operatorname{lcm}(x, y) < 2^W, \\\\
/// \operatorname{None} & \text{if} \\quad \operatorname{lcm}(x, y) \geq 2^W,
/// \\end{cases}
/// $$
/// where $W$ is `Self::WIDTH`.
///
/// # 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(), other.significant_bits())`.
///
/// # Examples
/// See [here](super::lcm#checked_lcm).
#[inline]
fn checked_lcm(self, other: $t) -> Option<$t> {
checked_lcm(self, other)
}
}
};
}
apply_to_unsigneds!(impl_lcm);