malachite_q/comparison/
eq_abs_natural.rs

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// Copyright © 2025 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::Rational;
use malachite_base::num::comparison::traits::EqAbs;
use malachite_nz::natural::Natural;

impl EqAbs<Natural> for Rational {
    /// Determines whether the absolute values of a [`Rational`] and a [`Natural`] are equal.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(1)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `min(self.significant_bits(),
    /// other.significant_bits())`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::comparison::traits::EqAbs;
    /// use malachite_nz::natural::Natural;
    /// use malachite_q::Rational;
    ///
    /// assert_eq!(Rational::from(-123).eq_abs(&Natural::from(122u32)), false);
    /// assert_eq!(Rational::from(-123).eq_abs(&Natural::from(124u32)), false);
    /// assert_eq!(
    ///     Rational::from_signeds(22, 7).eq_abs(&Natural::from(123u32)),
    ///     false
    /// );
    /// assert_eq!(
    ///     Rational::from_signeds(-22, 7).eq_abs(&Natural::from(123u32)),
    ///     false
    /// );
    /// assert_eq!(Rational::from(123).eq_abs(&Natural::from(123u32)), true);
    /// assert_eq!(Rational::from(-123).eq_abs(&Natural::from(123u32)), true);
    /// assert_eq!(
    ///     Rational::from_signeds(22, 7).eq_abs(&Natural::from(123u32)),
    ///     false
    /// );
    /// assert_eq!(
    ///     Rational::from_signeds(22, 7).eq_abs(&Natural::from(123u32)),
    ///     false
    /// );
    /// ```
    #[inline]
    fn eq_abs(&self, other: &Natural) -> bool {
        self.denominator == 1 && self.numerator == *other
    }
}

impl EqAbs<Rational> for Natural {
    /// Determines whether the absolute values of a [`Rational`] and a [`Natural`] are equal.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(1)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `min(self.significant_bits(),
    /// other.significant_bits())`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::comparison::traits::EqAbs;
    /// use malachite_nz::natural::Natural;
    /// use malachite_q::Rational;
    ///
    /// assert_eq!(Natural::from(122u32).eq_abs(&Rational::from(-123)), false);
    /// assert_eq!(Natural::from(124u32).eq_abs(&Rational::from(-123)), false);
    /// assert_eq!(
    ///     Natural::from(124u32).eq_abs(&Rational::from_signeds(22, 7)),
    ///     false
    /// );
    /// assert_eq!(
    ///     Natural::from(124u32).eq_abs(&Rational::from_signeds(-22, 7)),
    ///     false
    /// );
    /// assert_eq!(Natural::from(123u32).eq_abs(&Rational::from(123)), true);
    /// assert_eq!(Natural::from(123u32).eq_abs(&Rational::from(-123)), true);
    /// assert_eq!(
    ///     Natural::from(123u32).eq_abs(&Rational::from_signeds(22, 7)),
    ///     false
    /// );
    /// assert_eq!(
    ///     Natural::from(123u32).eq_abs(&Rational::from_signeds(-22, 7)),
    ///     false
    /// );
    /// ```
    #[inline]
    fn eq_abs(&self, other: &Rational) -> bool {
        other.denominator == 1 && other.numerator == *self
    }
}