malachite_float/float/comparison/
eq_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 malachite_base::num::arithmetic::traits::AbsSquared;
11use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
12use malachite_base::num::conversion::traits::ExactFrom;
13use malachite_nz::gaussian_integer::GaussianInteger;
14use malachite_q::Rational;
15
16impl EqAbs<GaussianInteger> for Float {
17    /// Determines whether the absolute values of a [`Float`] and a [`GaussianInteger`] are equal.
18    ///
19    /// The absolute value of a complex number is its distance from the origin, so two values are
20    /// equal in absolute value exactly when their squared absolute values are equal. Equality is
21    /// impossible unless the float exceeds both components in absolute value, so the squared
22    /// absolute values are only computed in that case. $\infty$, $-\infty$, and NaN are not equal
23    /// in absolute value to any [`GaussianInteger`].
24    ///
25    /// # Worst-case complexity
26    /// $T(n) = O(n \log n \log\log n)$
27    ///
28    /// $M(n) = O(n \log n)$
29    ///
30    /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
31    /// bits of `self` and of the real and imaginary parts of `other`.
32    ///
33    /// # Examples
34    /// ```
35    /// use malachite_base::num::comparison::traits::EqAbs;
36    /// use malachite_float::Float;
37    /// use malachite_nz::gaussian_integer::GaussianInteger;
38    /// use std::str::FromStr;
39    ///
40    /// // |3+4i| = 5
41    /// let y = GaussianInteger::from_str("3+4i").unwrap();
42    /// assert!(Float::from(-5).eq_abs(&y));
43    /// assert_eq!(Float::from(4).eq_abs(&y), false);
44    /// ```
45    fn eq_abs(&self, other: &GaussianInteger) -> bool {
46        if other.imaginary == 0u32 {
47            self.eq_abs(&other.real)
48        } else if other.real == 0u32 {
49            self.eq_abs(&other.imaginary)
50        } else if self.is_finite() {
51            self.gt_abs(&other.real)
52                && self.gt_abs(&other.imaginary)
53                && Rational::exact_from(self).abs_squared() == other.abs_squared()
54        } else {
55            false
56        }
57    }
58}
59
60impl EqAbs<Float> for GaussianInteger {
61    /// Determines whether the absolute values of a [`GaussianInteger`] and a [`Float`] are equal.
62    ///
63    /// No [`GaussianInteger`] is equal in absolute value to $\infty$, $-\infty$, or NaN.
64    ///
65    /// # Worst-case complexity
66    /// $T(n) = O(n \log n \log\log n)$
67    ///
68    /// $M(n) = O(n \log n)$
69    ///
70    /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
71    /// bits of `other` and of the real and imaginary parts of `self`.
72    ///
73    /// # Examples
74    /// ```
75    /// use malachite_base::num::comparison::traits::EqAbs;
76    /// use malachite_float::Float;
77    /// use malachite_nz::gaussian_integer::GaussianInteger;
78    /// use std::str::FromStr;
79    ///
80    /// // |3+4i| = 5
81    /// let x = GaussianInteger::from_str("3+4i").unwrap();
82    /// assert!(x.eq_abs(&Float::from(-5)));
83    /// assert_eq!(x.eq_abs(&Float::from(4)), false);
84    /// ```
85    #[inline]
86    fn eq_abs(&self, other: &Float) -> bool {
87        other.eq_abs(self)
88    }
89}
malachite_float/float/comparison/eq_abs_gaussian_integer.rs

malachite_float/float/comparison/
eq_abs_gaussian_integer.rs
