malachite_nz/gaussian_integer/comparison/
eq_abs_primitive_float.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::gaussian_integer::GaussianInteger;
10use crate::integer::Integer;
11use malachite_base::num::arithmetic::traits::AbsSquared;
12use malachite_base::num::comparison::traits::{EqAbs, PartialOrdAbs};
13
14macro_rules! impl_float {
15    ($t: ident) => {
16        impl EqAbs<$t> for GaussianInteger {
17            /// Determines whether the absolute values of a [`GaussianInteger`] and a primitive
18            /// float are equal.
19            ///
20            /// No [`GaussianInteger`] is equal in absolute value to an infinity or NaN. If the
21            /// float is not an integer, its square is not an integer either (its odd mantissa
22            /// contributes an odd square), so it cannot equal the absolute value of any
23            /// [`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
31            /// significant bits of the real and imaginary parts of `self`.
32            ///
33            /// # Examples
34            /// See [here](super::eq_abs_primitive_float#eq_abs).
35            fn eq_abs(&self, other: &$t) -> bool {
36                if self.imaginary == 0u32 {
37                    self.real.eq_abs(other)
38                } else if self.real == 0u32 {
39                    self.imaginary.eq_abs(other)
40                } else if !self.real.lt_abs(other) || !self.imaginary.lt_abs(other) {
41                    false
42                } else if let Ok(y) = Integer::try_from(*other) {
43                    self.abs_squared() == y.abs_squared()
44                } else {
45                    false
46                }
47            }
48        }
49
50        impl EqAbs<GaussianInteger> for $t {
51            /// Determines whether the absolute values of a primitive float and a
52            /// [`GaussianInteger`] are equal.
53            ///
54            /// No infinity or NaN is equal in absolute value to a [`GaussianInteger`].
55            ///
56            /// # Worst-case complexity
57            /// $T(n) = O(n \log n \log\log n)$
58            ///
59            /// $M(n) = O(n \log n)$
60            ///
61            /// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of
62            /// significant bits of the real and imaginary parts of `other`.
63            ///
64            /// # Examples
65            /// See [here](super::eq_abs_primitive_float#eq_abs).
66            #[inline]
67            fn eq_abs(&self, other: &GaussianInteger) -> bool {
68                other.eq_abs(self)
69            }
70        }
71    };
72}
73apply_to_primitive_floats!(impl_float);
malachite_nz/gaussian_integer/comparison/eq_abs_primitive_float.rs

malachite_nz/gaussian_integer/comparison/
eq_abs_primitive_float.rs
