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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::integer::Integer;
use malachite_base::num::arithmetic::traits::DivisibleBy;
impl DivisibleBy<Self> for Integer {
/// Returns whether an [`Integer`] is divisible by another [`Integer`]; in other words, whether
/// the first is a multiple of the second. Both [`Integer`]s are taken by value.
///
/// This means that zero is divisible by any [`Integer`], including zero; but a nonzero
/// [`Integer`] is never divisible by zero.
///
/// It's more efficient to use this function than to compute the remainder and check whether
/// it's zero.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DivisibleBy;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(Integer::ZERO.divisible_by(Integer::ZERO), true);
/// assert_eq!(Integer::from(-100).divisible_by(Integer::from(-3)), false);
/// assert_eq!(Integer::from(102).divisible_by(Integer::from(-3)), true);
/// assert_eq!(
/// Integer::from_str("-1000000000000000000000000")
/// .unwrap()
/// .divisible_by(Integer::from_str("1000000000000").unwrap()),
/// true
/// );
/// ```
fn divisible_by(self, other: Self) -> bool {
self.abs.divisible_by(other.abs)
}
}
impl DivisibleBy<&Self> for Integer {
/// Returns whether an [`Integer`] is divisible by another [`Integer`]; in other words, whether
/// the first is a multiple of the second. The first [`Integer`] is taken by value and the
/// second by reference.
///
/// This means that zero is divisible by any [`Integer`], including zero; but a nonzero
/// [`Integer`] is never divisible by zero.
///
/// It's more efficient to use this function than to compute the remainder and check whether
/// it's zero.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DivisibleBy;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(Integer::ZERO.divisible_by(&Integer::ZERO), true);
/// assert_eq!(Integer::from(-100).divisible_by(&Integer::from(-3)), false);
/// assert_eq!(Integer::from(102).divisible_by(&Integer::from(-3)), true);
/// assert_eq!(
/// Integer::from_str("-1000000000000000000000000")
/// .unwrap()
/// .divisible_by(&Integer::from_str("1000000000000").unwrap()),
/// true
/// );
/// ```
fn divisible_by(self, other: &Self) -> bool {
self.abs.divisible_by(&other.abs)
}
}
impl DivisibleBy<Integer> for &Integer {
/// Returns whether an [`Integer`] is divisible by another [`Integer`]; in other words, whether
/// the first is a multiple of the second. The first [`Integer`] is taken by reference and the
/// second by value.
///
/// This means that zero is divisible by any [`Integer`], including zero; but a nonzero
/// [`Integer`] is never divisible by zero.
///
/// It's more efficient to use this function than to compute the remainder and check whether
/// it's zero.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DivisibleBy;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!((&Integer::ZERO).divisible_by(Integer::ZERO), true);
/// assert_eq!(
/// (&Integer::from(-100)).divisible_by(Integer::from(-3)),
/// false
/// );
/// assert_eq!((&Integer::from(102)).divisible_by(Integer::from(-3)), true);
/// assert_eq!(
/// (&Integer::from_str("-1000000000000000000000000").unwrap())
/// .divisible_by(Integer::from_str("1000000000000").unwrap()),
/// true
/// );
/// ```
fn divisible_by(self, other: Integer) -> bool {
(&self.abs).divisible_by(other.abs)
}
}
impl DivisibleBy<&Integer> for &Integer {
/// Returns whether an [`Integer`] is divisible by another [`Integer`]; in other words, whether
/// the first is a multiple of the second. Both [`Integer`]s are taken by reference.
///
/// This means that zero is divisible by any [`Integer`], including zero; but a nonzero
/// [`Integer`] is never divisible by zero.
///
/// It's more efficient to use this function than to compute the remainder and check whether
/// it's zero.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DivisibleBy;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!((&Integer::ZERO).divisible_by(&Integer::ZERO), true);
/// assert_eq!(
/// (&Integer::from(-100)).divisible_by(&Integer::from(-3)),
/// false
/// );
/// assert_eq!((&Integer::from(102)).divisible_by(&Integer::from(-3)), true);
/// assert_eq!(
/// (&Integer::from_str("-1000000000000000000000000").unwrap())
/// .divisible_by(&Integer::from_str("1000000000000").unwrap()),
/// true
/// );
/// ```
fn divisible_by(self, other: &Integer) -> bool {
(&self.abs).divisible_by(&other.abs)
}
}