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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 core::cmp::Ordering::{self, Greater, Less};
use malachite_base::num::arithmetic::traits::AbsSquared;
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_nz::gaussian_integer::GaussianInteger;
use malachite_q::Rational;
impl PartialOrdAbs<GaussianInteger> for Float {
/// Compares the absolute values of a [`Float`] and a [`GaussianInteger`].
///
/// The absolute value of a complex number is its distance from the origin, so this is
/// equivalent to comparing squared absolute values. The [`Float`] is smaller in absolute value
/// unless it exceeds both components in absolute value, so the squared absolute values are only
/// computed in that case. NaN is not comparable to any [`GaussianInteger`]; $\infty$ and
/// $-\infty$ are greater in absolute value than any [`GaussianInteger`].
///
/// # 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::basic::traits::Infinity;
/// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
/// use malachite_float::Float;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let y = GaussianInteger::from_str("3+4i").unwrap();
/// assert!(Float::from(-5).eq_abs(&y));
/// assert!(Float::from(4).lt_abs(&y));
/// assert!(Float::from(-6).gt_abs(&y));
/// assert!(Float::INFINITY.gt_abs(&y));
/// ```
fn partial_cmp_abs(&self, other: &GaussianInteger) -> Option<Ordering> {
if self.is_nan() {
None
} else if !self.is_finite() {
Some(Greater)
} else if other.imaginary == 0u32 {
self.partial_cmp_abs(&other.real)
} else if other.real == 0u32 {
self.partial_cmp_abs(&other.imaginary)
} else if !self.gt_abs(&other.real) || !self.gt_abs(&other.imaginary) {
Some(Less)
} else {
Rational::exact_from(self)
.abs_squared()
.partial_cmp(&other.abs_squared())
}
}
}
impl PartialOrdAbs<Float> for GaussianInteger {
/// Compares the absolute values of a [`GaussianInteger`] and a [`Float`].
///
/// No [`GaussianInteger`] is comparable to NaN, and every [`GaussianInteger`] is smaller in
/// absolute value than $\infty$ and $-\infty$.
///
/// # 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::basic::traits::Infinity;
/// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
/// use malachite_float::Float;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("3+4i").unwrap();
/// assert!(x.eq_abs(&Float::from(-5)));
/// assert!(x.gt_abs(&Float::from(4)));
/// assert!(x.lt_abs(&Float::from(-6)));
/// assert!(x.lt_abs(&Float::INFINITY));
/// ```
#[inline]
fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
other.partial_cmp_abs(self).map(Ordering::reverse)
}
}