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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 core::cmp::Ordering::Equal;
use malachite_base::num::comparison::traits::{EqAbs, OrdAbs};
impl EqAbs for GaussianRational {
/// Determines whether the absolute values of two [`GaussianRational`]s are equal.
///
/// The absolute value of a complex number is its distance from the origin, so this is
/// equivalent to comparing squared absolute values. The comparison delegates to [`OrdAbs`],
/// whose componentwise and crosswise screens usually decide the answer without computing the
/// squared absolute values.
///
/// # 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 `other`.
///
/// # Examples
/// ```
/// use malachite_base::num::comparison::traits::EqAbs;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("1/2+i").unwrap();
/// let y = GaussianRational::from_str("-1+i/2").unwrap();
/// assert!(x.eq_abs(&y));
///
/// let x = GaussianRational::from_str("1+i").unwrap();
/// let y = GaussianRational::from_str("3i/2").unwrap();
/// // |1+i|^2 = 2 and |3i/2|^2 = 9/4
/// assert_eq!(x.eq_abs(&y), false);
/// ```
#[inline]
fn eq_abs(&self, other: &Self) -> bool {
self.cmp_abs(other) == Equal
}
}