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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::natural::Natural;
#[cfg(feature = "test_build")]
use malachite_base::num::arithmetic::traits::DivisibleBy;
use malachite_base::num::arithmetic::traits::{CoprimeWith, Gcd, Parity};
pub_test! {coprime_with_check_2(x: Natural, y: Natural) -> bool {
(x.odd() || y.odd()) && x.gcd(y) == 1u32
}}
#[cfg(feature = "test_build")]
pub fn coprime_with_check_2_3(x: Natural, y: Natural) -> bool {
(x.odd() || y.odd())
&& (!(&x).divisible_by(Natural::from(3u32)) || !(&y).divisible_by(Natural::from(3u32)))
&& x.gcd(y) == 1u32
}
#[cfg(feature = "test_build")]
pub fn coprime_with_check_2_3_5(x: Natural, y: Natural) -> bool {
if x.even() && y.even() {
false
} else {
let x15 = &x % Natural::from(15u32);
let y15 = &y % Natural::from(15u32);
if (x15 == 0u32 || x15 == 3u32 || x15 == 6u32 || x15 == 9u32 || x15 == 12u32)
&& (y15 == 0u32 || y15 == 3u32 || y15 == 6u32 || y15 == 9u32 || y15 == 12u32)
{
return false;
}
if (x15 == 0u32 || x15 == 5u32 || x15 == 10u32)
&& (y15 == 0u32 || y15 == 5u32 || y15 == 10u32)
{
return false;
}
x.gcd(y) == 1u32
}
}
pub_test! {coprime_with_check_2_val_ref(x: Natural, y: &Natural) -> bool {
(x.odd() || y.odd()) && x.gcd(y) == 1u32
}}
pub_test! {coprime_with_check_2_ref_val(x: &Natural, y: Natural) -> bool {
(x.odd() || y.odd()) && x.gcd(y) == 1u32
}}
pub_test! {coprime_with_check_2_ref_ref(x: &Natural, y: &Natural) -> bool {
(x.odd() || y.odd()) && x.gcd(y) == 1u32
}}
impl CoprimeWith<Self> for Natural {
/// Returns whether two [`Natural`]s are coprime; that is, whether they have no common factor
/// other than 1. Both [`Natural`]s are taken by value.
///
/// Every [`Natural`] is coprime with 1. No [`Natural`] is coprime with 0, except 1.
///
/// $f(x, y) = (\gcd(x, y) = 1)$.
///
/// $f(x, y) = ((k,m,n \in \N \land x=km \land y=kn) \implies k=1)$.
///
/// # 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::CoprimeWith;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(3u32).coprime_with(Natural::from(5u32)), true);
/// assert_eq!(
/// Natural::from(12u32).coprime_with(Natural::from(90u32)),
/// false
/// );
/// ```
#[inline]
fn coprime_with(self, other: Self) -> bool {
coprime_with_check_2(self, other)
}
}
impl<'a> CoprimeWith<&'a Self> for Natural {
/// Returns whether two [`Natural`]s are coprime; that is, whether they have no common factor
/// other than 1. The first [`Natural`] is taken by value and the second by reference.
///
/// Every [`Natural`] is coprime with 1. No [`Natural`] is coprime with 0, except 1.
///
/// $f(x, y) = (\gcd(x, y) = 1)$.
///
/// $f(x, y) = ((k,m,n \in \N \land x=km \land y=kn) \implies k=1)$.
///
/// # 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::CoprimeWith;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(3u32).coprime_with(&Natural::from(5u32)), true);
/// assert_eq!(
/// Natural::from(12u32).coprime_with(&Natural::from(90u32)),
/// false
/// );
/// ```
#[inline]
fn coprime_with(self, other: &'a Self) -> bool {
coprime_with_check_2_val_ref(self, other)
}
}
impl CoprimeWith<Natural> for &Natural {
/// Returns whether two [`Natural`]s are coprime; that is, whether they have no common factor
/// other than 1. The first [`Natural`] is taken by reference and the second by value.
///
/// Every [`Natural`] is coprime with 1. No [`Natural`] is coprime with 0, except 1.
///
/// $f(x, y) = (\gcd(x, y) = 1)$.
///
/// $f(x, y) = ((k,m,n \in \N \land x=km \land y=kn) \implies k=1)$.
///
/// # 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::CoprimeWith;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(3u32)).coprime_with(Natural::from(5u32)),
/// true
/// );
/// assert_eq!(
/// (&Natural::from(12u32)).coprime_with(Natural::from(90u32)),
/// false
/// );
/// ```
#[inline]
fn coprime_with(self, other: Natural) -> bool {
coprime_with_check_2_ref_val(self, other)
}
}
impl CoprimeWith<&Natural> for &Natural {
/// Returns whether two [`Natural`]s are coprime; that is, whether they have no common factor
/// other than 1. Both [`Natural`]s are taken by reference.
///
/// Every [`Natural`] is coprime with 1. No [`Natural`] is coprime with 0, except 1.
///
/// $f(x, y) = (\gcd(x, y) = 1)$.
///
/// $f(x, y) = ((k,m,n \in \N \land x=km \land y=kn) \implies k=1)$.
///
/// # 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::CoprimeWith;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(3u32)).coprime_with(Natural::from(5u32)),
/// true
/// );
/// assert_eq!(
/// (&Natural::from(12u32)).coprime_with(Natural::from(90u32)),
/// false
/// );
/// ```
fn coprime_with(self, other: &Natural) -> bool {
coprime_with_check_2_ref_ref(self, other)
}
}