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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::gaussian_rational::GaussianRational;
use malachite_base::num::arithmetic::traits::AbsSquared;
use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
use malachite_nz::natural::Natural;
impl EqAbs<Natural> for GaussianRational {
/// Determines whether the absolute values of a [`GaussianRational`] and a [`Natural`] are
/// equal.
///
/// The absolute value of a complex number is its distance from the origin, so two values are
/// equal in absolute value exactly when their squared absolute values are equal. Purely real
/// and purely imaginary values are handled by comparing single components. Otherwise, equality
/// is impossible unless both components are smaller in absolute value than the real operand, so
/// the squared absolute values are only computed in that case.
///
/// # 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 the maximum number of significant
/// bits of the real and imaginary parts of `self` and of `other`.
///
/// # Examples
/// ```
/// use malachite_base::num::comparison::traits::EqAbs;
/// use malachite_nz::natural::Natural;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// // |3/5+4i/5| = 1
/// let x = GaussianRational::from_str("3/5+4i/5").unwrap();
/// assert!(x.eq_abs(&Natural::from(1u32)));
/// assert_eq!(x.eq_abs(&Natural::from(2u32)), false);
/// ```
fn eq_abs(&self, other: &Natural) -> bool {
if self.imaginary == 0u32 {
self.real.eq_abs(other)
} else if self.real == 0u32 {
self.imaginary.eq_abs(other)
} else {
self.real.lt_abs(other)
&& self.imaginary.lt_abs(other)
&& self.abs_squared() == other.abs_squared()
}
}
}
impl EqAbs<GaussianRational> for Natural {
/// Determines whether the absolute values of a [`Natural`] and a [`GaussianRational`] are
/// equal.
///
/// # 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 the maximum number of significant
/// bits of the real and imaginary parts of `other` and of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::comparison::traits::EqAbs;
/// use malachite_nz::natural::Natural;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// // |3/5+4i/5| = 1
/// let y = GaussianRational::from_str("3/5+4i/5").unwrap();
/// assert!(Natural::from(1u32).eq_abs(&y));
/// assert_eq!(Natural::from(2u32).eq_abs(&y), false);
/// ```
#[inline]
fn eq_abs(&self, other: &GaussianRational) -> bool {
other.eq_abs(self)
}
}