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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 2020 Daniel Schultz
//
// Copyright © 2023 Albin Ahlbäck
//
// 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::Rational;
use malachite_base::num::arithmetic::traits::{Gcd, GcdAssign, Lcm, LcmAssign};
// In each impl below, the GCD of two canonical rationals p/q and r/s is gcd(p, r)/lcm(q, s): FLINT
// defines the GCD as the canonical form of gcd(ps, qr)/(qs), which reduces to the component form
// for canonical inputs, as the assertions of _fmpq_gcd_cofactors check. The result is canonical
// outright: a common prime of gcd(p, r) and lcm(q, s) would divide both numerators and one
// denominator, contradicting that input's canonicity.
impl Gcd<Self> for Rational {
type Output = Self;
/// Computes the GCD of two [`Rational`]s, taking both by value.
///
/// The GCD of $p/q$ and $r/s$ in canonical form is $\gcd(p, r)/\operatorname{lcm}(q, s)$: the
/// largest rational that divides both into integers. It is stable under scaling of numerator
/// and denominator, and agrees with the GCD on the integers.
///
/// $$
/// f(p/q, r/s) = \frac{\gcd(p, r)}{\operatorname{lcm}(q, s)}.
/// $$
///
/// The GCD of 0 and 0 is 0, and the GCD of $x$ and 0 is $|x|$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Gcd;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let x = Rational::from_str("2/3").unwrap();
/// let y = Rational::from_str("-3/4").unwrap();
/// assert_eq!(x.gcd(y).to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0.
#[inline]
fn gcd(self, other: Self) -> Self {
Self {
sign: true,
numerator: self.numerator.gcd(other.numerator),
denominator: self.denominator.lcm(other.denominator),
}
}
}
impl Gcd<&Self> for Rational {
type Output = Self;
/// Computes the GCD of two [`Rational`]s, taking the first by value and the second by
/// reference.
///
/// The GCD of $p/q$ and $r/s$ in canonical form is $\gcd(p, r)/\operatorname{lcm}(q, s)$: the
/// largest rational that divides both into integers. It is stable under scaling of numerator
/// and denominator, and agrees with the GCD on the integers.
///
/// $$
/// f(p/q, r/s) = \frac{\gcd(p, r)}{\operatorname{lcm}(q, s)}.
/// $$
///
/// The GCD of 0 and 0 is 0, and the GCD of $x$ and 0 is $|x|$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Gcd;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let x = Rational::from_str("2/3").unwrap();
/// let y = Rational::from_str("-3/4").unwrap();
/// assert_eq!(x.gcd(&y).to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0.
#[inline]
fn gcd(self, other: &Self) -> Self {
Self {
sign: true,
numerator: self.numerator.gcd(&other.numerator),
denominator: self.denominator.lcm(&other.denominator),
}
}
}
impl Gcd<Rational> for &Rational {
type Output = Rational;
/// Computes the GCD of two [`Rational`]s, taking the first by reference and the second by
/// value.
///
/// The GCD of $p/q$ and $r/s$ in canonical form is $\gcd(p, r)/\operatorname{lcm}(q, s)$: the
/// largest rational that divides both into integers. It is stable under scaling of numerator
/// and denominator, and agrees with the GCD on the integers.
///
/// $$
/// f(p/q, r/s) = \frac{\gcd(p, r)}{\operatorname{lcm}(q, s)}.
/// $$
///
/// The GCD of 0 and 0 is 0, and the GCD of $x$ and 0 is $|x|$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Gcd;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let x = Rational::from_str("2/3").unwrap();
/// let y = Rational::from_str("-3/4").unwrap();
/// assert_eq!((&x).gcd(y).to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0.
#[inline]
fn gcd(self, other: Rational) -> Rational {
Rational {
sign: true,
numerator: other.numerator.gcd(&self.numerator),
denominator: other.denominator.lcm(&self.denominator),
}
}
}
impl Gcd<&Rational> for &Rational {
type Output = Rational;
/// Computes the GCD of two [`Rational`]s, taking both by reference.
///
/// The GCD of $p/q$ and $r/s$ in canonical form is $\gcd(p, r)/\operatorname{lcm}(q, s)$: the
/// largest rational that divides both into integers. It is stable under scaling of numerator
/// and denominator, and agrees with the GCD on the integers.
///
/// $$
/// f(p/q, r/s) = \frac{\gcd(p, r)}{\operatorname{lcm}(q, s)}.
/// $$
///
/// The GCD of 0 and 0 is 0, and the GCD of $x$ and 0 is $|x|$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Gcd;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let x = Rational::from_str("2/3").unwrap();
/// let y = Rational::from_str("-3/4").unwrap();
/// assert_eq!((&x).gcd(&y).to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0.
#[inline]
fn gcd(self, other: &Rational) -> Rational {
Rational {
sign: true,
numerator: (&self.numerator).gcd(&other.numerator),
denominator: (&self.denominator).lcm(&other.denominator),
}
}
}
impl GcdAssign<Self> for Rational {
/// Replaces a [`Rational`] with the GCD of it and another [`Rational`], taking the other by
/// value.
///
/// See [`Gcd`] for the definition.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::GcdAssign;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let mut x = Rational::from_str("2/3").unwrap();
/// x.gcd_assign(Rational::from_str("-3/4").unwrap());
/// assert_eq!(x.to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0, where res and op1 are aliased.
#[inline]
fn gcd_assign(&mut self, other: Self) {
self.sign = true;
self.numerator.gcd_assign(other.numerator);
self.denominator.lcm_assign(other.denominator);
}
}
impl GcdAssign<&Self> for Rational {
/// Replaces a [`Rational`] with the GCD of it and another [`Rational`], taking the other by
/// reference.
///
/// See [`Gcd`] for the definition.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::GcdAssign;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let mut x = Rational::from_str("2/3").unwrap();
/// x.gcd_assign(&Rational::from_str("-3/4").unwrap());
/// assert_eq!(x.to_string(), "1/12");
/// ```
///
/// This is fmpq_gcd from fmpq/gcd.c, FLINT 3.6.0, where res and op1 are aliased.
#[inline]
fn gcd_assign(&mut self, other: &Self) {
self.sign = true;
self.numerator.gcd_assign(&other.numerator);
self.denominator.lcm_assign(&other.denominator);
}
}