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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::{
DivIAssign, ModPowerOf2, MulIAssign, MulIPow, MulIPowAssign, NegAssign,
};
impl MulIPow for GaussianInteger {
type Output = Self;
/// Multiplies a [`GaussianInteger`] by $i^k$, taking the [`GaussianInteger`] by value.
///
/// Only $k$ modulo 4 matters: $i^0 = 1$, $i^1 = i$, $i^2 = -1$, and $i^3 = -i$, so the result
/// is the number itself, a counterclockwise quarter turn, a half turn, or a clockwise quarter
/// turn. Since $i^{-k} = i^{3k}$, a negative power is a matter of tripling the exponent.
///
/// $$
/// f(x, k) = i^k x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulIPow;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("2+3i").unwrap();
/// assert_eq!(x.clone().mul_i_pow(0).to_string(), "2+3i");
/// assert_eq!(x.clone().mul_i_pow(1).to_string(), "-3+2i");
/// assert_eq!(x.clone().mul_i_pow(2).to_string(), "-2-3i");
/// assert_eq!(x.clone().mul_i_pow(3).to_string(), "3-2i");
/// assert_eq!(x.mul_i_pow(1000000000001).to_string(), "-3+2i");
/// ```
#[inline]
fn mul_i_pow(mut self, k: u64) -> Self {
self.mul_i_pow_assign(k);
self
}
}
impl MulIPow for &GaussianInteger {
type Output = GaussianInteger;
/// Multiplies a [`GaussianInteger`] by $i^k$, taking the [`GaussianInteger`] by reference.
///
/// Only $k$ modulo 4 matters: $i^0 = 1$, $i^1 = i$, $i^2 = -1$, and $i^3 = -i$, so the result
/// is the number itself, a counterclockwise quarter turn, a half turn, or a clockwise quarter
/// turn. Since $i^{-k} = i^{3k}$, a negative power is a matter of tripling the exponent.
///
/// $$
/// f(x, k) = i^k x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulIPow;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("2+3i").unwrap();
/// assert_eq!((&x).mul_i_pow(0).to_string(), "2+3i");
/// assert_eq!((&x).mul_i_pow(1).to_string(), "-3+2i");
/// assert_eq!((&x).mul_i_pow(2).to_string(), "-2-3i");
/// assert_eq!((&x).mul_i_pow(3).to_string(), "3-2i");
/// assert_eq!((&x).mul_i_pow(1000000000001).to_string(), "-3+2i");
/// ```
#[inline]
fn mul_i_pow(self, k: u64) -> GaussianInteger {
self.clone().mul_i_pow(k)
}
}
impl MulIPowAssign for GaussianInteger {
/// Multiplies a [`GaussianInteger`] by $i^k$ in place.
///
/// Only $k$ modulo 4 matters: $i^0 = 1$, $i^1 = i$, $i^2 = -1$, and $i^3 = -i$, so the result
/// is the number itself, a counterclockwise quarter turn, a half turn, or a clockwise quarter
/// turn. Since $i^{-k} = i^{3k}$, a negative power is a matter of tripling the exponent.
///
/// $$
/// x \gets i^k x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulIPowAssign;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let mut x = GaussianInteger::from_str("2+3i").unwrap();
/// x.mul_i_pow_assign(1);
/// assert_eq!(x.to_string(), "-3+2i");
/// x.mul_i_pow_assign(2);
/// assert_eq!(x.to_string(), "3-2i");
/// x.mul_i_pow_assign(1000000000001);
/// assert_eq!(x.to_string(), "2+3i");
/// ```
fn mul_i_pow_assign(&mut self, k: u64) {
match k.mod_power_of_2(2) {
0 => {}
1 => self.mul_i_assign(),
2 => self.neg_assign(),
_ => self.div_i_assign(),
}
}
}