malachite_float/float/conversion/is_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::conversion::traits::{IsGaussianInteger, IsInteger};
11
12impl IsGaussianInteger for &Float {
13 /// Determines whether a [`Float`] is a Gaussian integer.
14 ///
15 /// A [`Float`] is real (or `NaN` or infinite), so it is a Gaussian integer if and only if it is
16 /// an integer.
17 ///
18 /// $f(x) = x \in \Z\[i\]$.
19 ///
20 /// # Worst-case complexity
21 /// Constant time and additional memory.
22 ///
23 /// # Examples
24 /// ```
25 /// use malachite_base::num::basic::traits::{Infinity, NaN, One, OneHalf, Zero};
26 /// use malachite_base::num::conversion::traits::IsGaussianInteger;
27 /// use malachite_float::Float;
28 ///
29 /// assert_eq!(Float::ZERO.is_gaussian_integer(), true);
30 /// assert_eq!(Float::ONE.is_gaussian_integer(), true);
31 /// assert_eq!(Float::from(-100).is_gaussian_integer(), true);
32 /// assert_eq!(Float::ONE_HALF.is_gaussian_integer(), false);
33 /// assert_eq!(Float::NAN.is_gaussian_integer(), false);
34 /// assert_eq!(Float::INFINITY.is_gaussian_integer(), false);
35 /// ```
36 #[inline]
37 fn is_gaussian_integer(self) -> bool {
38 self.is_integer()
39 }
40}