malachite_nz/gaussian_integer/conversion/is_real.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 malachite_base::num::conversion::traits::IsReal;
11
12impl IsReal for &GaussianInteger {
13 /// Determines whether a [`GaussianInteger`] is a real number: that is, whether its imaginary
14 /// part is zero.
15 ///
16 /// $f(x) = x \in \R$.
17 ///
18 /// # Worst-case complexity
19 /// Constant time and additional memory.
20 ///
21 /// # Examples
22 /// ```
23 /// use malachite_base::num::basic::traits::{I, One, Zero};
24 /// use malachite_base::num::conversion::traits::IsReal;
25 /// use malachite_nz::gaussian_integer::GaussianInteger;
26 ///
27 /// assert_eq!(GaussianInteger::ZERO.is_real(), true);
28 /// assert_eq!(GaussianInteger::ONE.is_real(), true);
29 /// assert_eq!(GaussianInteger::I.is_real(), false);
30 /// assert_eq!(GaussianInteger::from(-100).is_real(), true);
31 /// ```
32 #[inline]
33 fn is_real(self) -> bool {
34 self.imaginary == 0u32
35 }
36}