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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::{self, Equal};
use malachite_base::num::arithmetic::traits::AbsSquared;
use malachite_base::num::comparison::traits::{OrdAbs, PartialOrdAbs};
// If two component comparisons pull in the same direction (or one is a tie), they decide the
// comparison of the sums of squares; only a strict conflict is indecisive.
fn combine(x: Ordering, y: Ordering) -> Option<Ordering> {
if x == y || y == Equal {
Some(x)
} else if x == Equal {
Some(y)
} else {
None
}
}
impl PartialOrdAbs for GaussianRational {
/// Compares the absolute values of two [`GaussianRational`]s.
///
/// See the documentation for the [`OrdAbs`] implementation.
#[inline]
fn partial_cmp_abs(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp_abs(other))
}
}
impl OrdAbs for GaussianRational {
/// Compares the absolute values of two [`GaussianRational`]s.
///
/// The absolute value of a complex number is its distance from the origin, so this is
/// equivalent to comparing squared absolute values:
///
/// $$
/// f(x, y) = \operatorname{cmp}(|x|, |y|) = \operatorname{cmp}(|x|^2, |y|^2).
/// $$
///
/// The squared absolute values are usually not actually computed: comparing the
/// [`Rational`](crate::Rational) parts componentwise, either directly or crosswise, often
/// decides the ordering, and the [`AbsSquared`] fallback only runs when both pairings strictly
/// conflict.
///
/// # 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::{OrdAbs, PartialOrdAbs};
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::cmp::Ordering::*;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("1/2+i/2").unwrap();
/// let y = GaussianRational::from_str("i").unwrap();
/// // |1/2+i/2|^2 = 1/2 and |i|^2 = 1
/// assert_eq!(x.cmp_abs(&y), Less);
/// assert!(x.lt_abs(&y));
///
/// let x = GaussianRational::from_str("1/2+2i/3").unwrap();
/// let y = GaussianRational::from_str("-2/3+i/2").unwrap();
/// assert_eq!(x.cmp_abs(&y), Equal);
///
/// let x = GaussianRational::from_str("3/2").unwrap();
/// let y = GaussianRational::from_str("1+i").unwrap();
/// // |3/2|^2 = 9/4 and |1+i|^2 = 2
/// assert_eq!(x.cmp_abs(&y), Greater);
/// ```
fn cmp_abs(&self, other: &Self) -> Ordering {
if let Some(o) = combine(
self.real.cmp_abs(&other.real),
self.imaginary.cmp_abs(&other.imaginary),
) {
return o;
}
if let Some(o) = combine(
self.real.cmp_abs(&other.imaginary),
self.imaginary.cmp_abs(&other.real),
) {
return o;
}
self.abs_squared().cmp(&other.abs_squared())
}
}