malachite_float/float/comparison/
partial_cmp_abs_gaussian_integer.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::Float;
10use core::cmp::Ordering::{self, Greater, Less};
11use malachite_base::num::arithmetic::traits::AbsSquared;
12use malachite_base::num::comparison::traits::PartialOrdAbs;
13use malachite_base::num::conversion::traits::ExactFrom;
14use malachite_nz::gaussian_integer::GaussianInteger;
15use malachite_q::Rational;
16
17impl PartialOrdAbs<GaussianInteger> for Float {
18    /// Compares the absolute values of a [`Float`] and a [`GaussianInteger`].
19    ///
20    /// The absolute value of a complex number is its distance from the origin, so this is
21    /// equivalent to comparing squared absolute values. The [`Float`] is smaller in absolute value
22    /// unless it exceeds both components in absolute value, so the squared absolute values are only
23    /// computed in that case. NaN is not comparable to any [`GaussianInteger`]; $\infty$ and
24    /// $-\infty$ are greater in absolute value than any [`GaussianInteger`].
25    ///
26    /// # Worst-case complexity
27    /// $T(n) = O(n \log n \log\log n)$
28    ///
29    /// $M(n) = O(n \log n)$
30    ///
31    /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
32    /// bits of `self` and of the real and imaginary parts of `other`.
33    ///
34    /// # Examples
35    /// ```
36    /// use malachite_base::num::basic::traits::Infinity;
37    /// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
38    /// use malachite_float::Float;
39    /// use malachite_nz::gaussian_integer::GaussianInteger;
40    /// use std::str::FromStr;
41    ///
42    /// let y = GaussianInteger::from_str("3+4i").unwrap();
43    /// assert!(Float::from(-5).eq_abs(&y));
44    /// assert!(Float::from(4).lt_abs(&y));
45    /// assert!(Float::from(-6).gt_abs(&y));
46    /// assert!(Float::INFINITY.gt_abs(&y));
47    /// ```
48    fn partial_cmp_abs(&self, other: &GaussianInteger) -> Option<Ordering> {
49        if self.is_nan() {
50            None
51        } else if !self.is_finite() {
52            Some(Greater)
53        } else if other.imaginary == 0u32 {
54            self.partial_cmp_abs(&other.real)
55        } else if other.real == 0u32 {
56            self.partial_cmp_abs(&other.imaginary)
57        } else if !self.gt_abs(&other.real) || !self.gt_abs(&other.imaginary) {
58            Some(Less)
59        } else {
60            Rational::exact_from(self)
61                .abs_squared()
62                .partial_cmp(&other.abs_squared())
63        }
64    }
65}
66
67impl PartialOrdAbs<Float> for GaussianInteger {
68    /// Compares the absolute values of a [`GaussianInteger`] and a [`Float`].
69    ///
70    /// No [`GaussianInteger`] is comparable to NaN, and every [`GaussianInteger`] is smaller in
71    /// absolute value than $\infty$ and $-\infty$.
72    ///
73    /// # Worst-case complexity
74    /// $T(n) = O(n \log n \log\log n)$
75    ///
76    /// $M(n) = O(n \log n)$
77    ///
78    /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
79    /// bits of `other` and of the real and imaginary parts of `self`.
80    ///
81    /// # Examples
82    /// ```
83    /// use malachite_base::num::basic::traits::Infinity;
84    /// use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
85    /// use malachite_float::Float;
86    /// use malachite_nz::gaussian_integer::GaussianInteger;
87    /// use std::str::FromStr;
88    ///
89    /// let x = GaussianInteger::from_str("3+4i").unwrap();
90    /// assert!(x.eq_abs(&Float::from(-5)));
91    /// assert!(x.gt_abs(&Float::from(4)));
92    /// assert!(x.lt_abs(&Float::from(-6)));
93    /// assert!(x.lt_abs(&Float::INFINITY));
94    /// ```
95    #[inline]
96    fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
97        other.partial_cmp_abs(self).map(Ordering::reverse)
98    }
99}
malachite_float/float/comparison/partial_cmp_abs_gaussian_integer.rs

malachite_float/float/comparison/
partial_cmp_abs_gaussian_integer.rs
