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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_rational::GaussianRational;
use malachite_base::num::arithmetic::traits::{
CanonicalUnitIPow, CanonicalizeGaussianUnit, CanonicalizeGaussianUnitAssign, MulIPowAssign,
};
impl CanonicalizeGaussianUnit for GaussianRational {
type Output = Self;
/// Brings a [`GaussianRational`] into canonical Gaussian-unit form, taking it by value.
///
/// The result is the Gaussian associate $x i^k$ whose argument lies in $(-\pi/4, \pi/4]$, where
/// $k$ is given by
/// [`canonical_unit_i_pow`](malachite_base::num::arithmetic::traits::CanonicalUnitIPow); zero
/// is its own canonical form. This differs from
/// [`canonicalize_unit`](malachite_base::num::arithmetic::traits::CanonicalizeUnit), which
/// gives 1 for every nonzero [`GaussianRational`], since the Gaussian rationals form a field.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeGaussianUnit;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// assert_eq!(
/// GaussianRational::from_str("-1/2+3i/4")
/// .unwrap()
/// .canonicalize_gaussian_unit()
/// .to_string(),
/// "3/4+i/2"
/// );
/// assert_eq!(
/// GaussianRational::from_str("-3i")
/// .unwrap()
/// .canonicalize_gaussian_unit()
/// .to_string(),
/// "3"
/// );
/// ```
#[inline]
fn canonicalize_gaussian_unit(mut self) -> Self {
self.canonicalize_gaussian_unit_assign();
self
}
}
impl CanonicalizeGaussianUnit for &GaussianRational {
type Output = GaussianRational;
/// Brings a [`GaussianRational`] into canonical Gaussian-unit form, taking it by reference.
///
/// The result is the Gaussian associate $x i^k$ whose argument lies in $(-\pi/4, \pi/4]$, where
/// $k$ is given by
/// [`canonical_unit_i_pow`](malachite_base::num::arithmetic::traits::CanonicalUnitIPow); zero
/// is its own canonical form. This differs from
/// [`canonicalize_unit`](malachite_base::num::arithmetic::traits::CanonicalizeUnit), which
/// gives 1 for every nonzero [`GaussianRational`], since the Gaussian rationals form a field.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeGaussianUnit;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("-1/2+3i/4").unwrap();
/// assert_eq!((&x).canonicalize_gaussian_unit().to_string(), "3/4+i/2");
/// ```
#[inline]
fn canonicalize_gaussian_unit(self) -> GaussianRational {
self.clone().canonicalize_gaussian_unit()
}
}
impl CanonicalizeGaussianUnitAssign for GaussianRational {
/// Replaces a [`GaussianRational`] with its canonical Gaussian-unit form.
///
/// See [`canonicalize_gaussian_unit`](CanonicalizeGaussianUnit::canonicalize_gaussian_unit).
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeGaussianUnitAssign;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let mut x = GaussianRational::from_str("-1/2+3i/4").unwrap();
/// x.canonicalize_gaussian_unit_assign();
/// assert_eq!(x.to_string(), "3/4+i/2");
/// ```
fn canonicalize_gaussian_unit_assign(&mut self) {
let k = self.canonical_unit_i_pow();
self.mul_i_pow_assign(k);
}
}