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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::Float;
use malachite_base::num::arithmetic::traits::AbsSquared;
use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_q::Rational;
use malachite_q::gaussian_rational::GaussianRational;
impl EqAbs<GaussianRational> for Float {
/// Determines whether the absolute values of a [`Float`] and a [`GaussianRational`] 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. Equality is
/// impossible unless the float exceeds both components in absolute value, so the squared
/// absolute values are only computed in that case. $\infty$, $-\infty$, and NaN are not equal
/// in absolute value to any [`GaussianRational`].
///
/// # 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 `self` and of the real and imaginary parts of `other`.
///
/// # Examples
/// ```
/// use malachite_base::num::comparison::traits::EqAbs;
/// use malachite_float::Float;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// // |3/2+2i| = 5/2
/// let y = GaussianRational::from_str("3/2+2i").unwrap();
/// assert!(Float::from(2.5).eq_abs(&y));
/// assert_eq!(Float::from(2).eq_abs(&y), false);
/// ```
fn eq_abs(&self, other: &GaussianRational) -> bool {
if other.imaginary == 0u32 {
self.eq_abs(&other.real)
} else if other.real == 0u32 {
self.eq_abs(&other.imaginary)
} else if self.is_finite() {
self.gt_abs(&other.real)
&& self.gt_abs(&other.imaginary)
&& Rational::exact_from(self).abs_squared() == other.abs_squared()
} else {
false
}
}
}
impl EqAbs<Float> for GaussianRational {
/// Determines whether the absolute values of a [`GaussianRational`] and a [`Float`] are equal.
///
/// No [`GaussianRational`] is equal in absolute value to $\infty$, $-\infty$, or NaN.
///
/// # 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 `other` and of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::comparison::traits::EqAbs;
/// use malachite_float::Float;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// // |3/2+2i| = 5/2
/// let x = GaussianRational::from_str("3/2+2i").unwrap();
/// assert!(x.eq_abs(&Float::from(2.5)));
/// assert_eq!(x.eq_abs(&Float::from(2)), false);
/// ```
#[inline]
fn eq_abs(&self, other: &Float) -> bool {
other.eq_abs(self)
}
}