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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, Greater};
use malachite_base::num::arithmetic::traits::AbsSquared;
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_nz::integer::Integer;
impl PartialOrdAbs<Integer> for GaussianRational {
/// Compares the absolute values of a [`GaussianRational`] and an [`Integer`].
///
/// The absolute value of a complex number is its distance from the origin, so this is
/// equivalent to comparing squared absolute values. Purely real and purely imaginary values are
/// handled by comparing single components. Otherwise, the complex value is greater in absolute
/// value unless both of its 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::basic::traits::Zero;
/// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
/// use malachite_nz::integer::Integer;
/// 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(&Integer::from(-1)));
/// assert!(x.gt_abs(&Integer::ZERO));
/// assert!(x.lt_abs(&Integer::from(-2)));
/// ```
fn partial_cmp_abs(&self, other: &Integer) -> Option<Ordering> {
if self.imaginary == 0u32 {
self.real.partial_cmp_abs(other)
} else if self.real == 0u32 {
self.imaginary.partial_cmp_abs(other)
} else if !self.real.lt_abs(other) || !self.imaginary.lt_abs(other) {
Some(Greater)
} else {
self.abs_squared().partial_cmp(&other.abs_squared())
}
}
}
impl PartialOrdAbs<GaussianRational> for Integer {
/// Compares the absolute values of an [`Integer`] and a [`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 the real and imaginary parts of `other` and of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
/// use malachite_nz::integer::Integer;
/// 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!(Integer::from(-1).eq_abs(&y));
/// assert!(Integer::ZERO.lt_abs(&y));
/// assert!(Integer::from(-2).gt_abs(&y));
/// ```
#[inline]
fn partial_cmp_abs(&self, other: &GaussianRational) -> Option<Ordering> {
other.partial_cmp_abs(self).map(Ordering::reverse)
}
}