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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::gaussian_integer::GaussianInteger;
use malachite_base::num::arithmetic::traits::IsUnit;
impl IsUnit for GaussianInteger {
/// Determines whether a [`GaussianInteger`] is a unit: one of $1$, $-1$, $i$, and $-i$, the
/// four elements of $\mathbb{Z}\[i\]$ with a multiplicative inverse in $\mathbb{Z}\[i\]$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::IsUnit;
/// use malachite_base::num::basic::traits::{I, NegativeI, NegativeOne, One, Two, Zero};
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianInteger::ONE.is_unit(), true);
/// assert_eq!(GaussianInteger::NEGATIVE_ONE.is_unit(), true);
/// assert_eq!(GaussianInteger::I.is_unit(), true);
/// assert_eq!(GaussianInteger::NEGATIVE_I.is_unit(), true);
/// assert_eq!(GaussianInteger::ZERO.is_unit(), false);
/// assert_eq!(GaussianInteger::from_str("1+i").unwrap().is_unit(), false);
/// assert_eq!(GaussianInteger::TWO.is_unit(), false);
/// ```
fn is_unit(&self) -> bool {
if self.imaginary == 0u32 {
self.real == 1u32 || self.real == -1i32
} else if self.real == 0u32 {
self.imaginary == 1u32 || self.imaginary == -1i32
} else {
false
}
}
}