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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::{
AbsSquared, NegAssign, Reciprocal, ReciprocalAssign,
};
impl Reciprocal for GaussianRational {
type Output = Self;
/// Reciprocates a [`GaussianRational`], taking it by value.
///
/// The reciprocal of a complex number is its conjugate divided by its squared absolute value:
/// $$
/// f(x) = \frac{1}{x} = \frac{\overline{x}}{|x|^2}.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Panics
/// Panics if `self` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_base::num::basic::traits::I;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianRational::I.reciprocal().to_string(), "-i");
/// assert_eq!(
/// GaussianRational::from_str("1+i")
/// .unwrap()
/// .reciprocal()
/// .to_string(),
/// "1/2-i/2"
/// );
/// assert_eq!(
/// GaussianRational::from_str("3/5+4i/5")
/// .unwrap()
/// .reciprocal()
/// .to_string(),
/// "3/5-4i/5"
/// );
/// ```
#[inline]
fn reciprocal(mut self) -> Self {
self.reciprocal_assign();
self
}
}
impl Reciprocal for &GaussianRational {
type Output = GaussianRational;
/// Reciprocates a [`GaussianRational`], taking it by reference.
///
/// The reciprocal of a complex number is its conjugate divided by its squared absolute value:
/// $$
/// f(x) = \frac{1}{x} = \frac{\overline{x}}{|x|^2}.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Panics
/// Panics if `self` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("1+i").unwrap();
/// assert_eq!((&x).reciprocal().to_string(), "1/2-i/2");
/// ```
#[inline]
fn reciprocal(self) -> GaussianRational {
assert!(
self.real != 0u32 || self.imaginary != 0u32,
"Cannot take the reciprocal of zero"
);
// Purely real and purely imaginary values reduce to a single Rational reciprocal.
if self.imaginary == 0u32 {
GaussianRational {
real: (&self.real).reciprocal(),
imaginary: self.imaginary.clone(),
}
} else if self.real == 0u32 {
GaussianRational {
real: self.real.clone(),
imaginary: -(&self.imaginary).reciprocal(),
}
} else {
let norm = self.abs_squared();
GaussianRational {
real: (&self.real) / &norm,
imaginary: -(&self.imaginary) / norm,
}
}
}
}
impl ReciprocalAssign for GaussianRational {
/// Reciprocates a [`GaussianRational`] in place.
///
/// The reciprocal of a complex number is its conjugate divided by its squared absolute value:
/// $$
/// x \gets \frac{1}{x} = \frac{\overline{x}}{|x|^2}.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Panics
/// Panics if `self` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ReciprocalAssign;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let mut x = GaussianRational::from_str("1+i").unwrap();
/// x.reciprocal_assign();
/// assert_eq!(x.to_string(), "1/2-i/2");
/// ```
fn reciprocal_assign(&mut self) {
assert!(
self.real != 0u32 || self.imaginary != 0u32,
"Cannot take the reciprocal of zero"
);
// Purely real and purely imaginary values reduce to a single Rational reciprocal.
if self.imaginary == 0u32 {
self.real.reciprocal_assign();
} else if self.real == 0u32 {
self.imaginary.reciprocal_assign();
self.imaginary.neg_assign();
} else {
let norm = AbsSquared::abs_squared(&*self);
self.real /= &norm;
self.imaginary /= norm;
self.imaginary.neg_assign();
}
}
}