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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 core::cmp::Ordering::*;
use malachite_base::num::arithmetic::traits::CanonicalUnitIPow;
use malachite_base::num::comparison::traits::PartialOrdAbs;
impl CanonicalUnitIPow for GaussianInteger {
/// Finds the power of $i$ that brings a [`GaussianInteger`] into canonical unit form.
///
/// A nonzero value has four associates, $x$, $ix$, $-x$, and $-ix$; the canonical one is the
/// associate whose argument lies in $(-\pi/4, \pi/4]$, that is, whose real part $a$ is positive
/// and whose imaginary part $b$ satisfies $-a < b \leq a$. The result is the $k \in \\{0, 1, 2,
/// 3\\}$ such that $x i^k$ is canonical, and 0 for zero. The choice of associate, including the
/// tie on the diagonals, matches FLINT's `fmpzi_canonical_unit_i_pow`.
///
/// # 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 real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalUnitIPow;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(
/// GaussianInteger::from_str("2+i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 0
/// );
/// assert_eq!(
/// GaussianInteger::from_str("-1+2i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 3
/// );
/// assert_eq!(
/// GaussianInteger::from_str("-2-i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 2
/// );
/// assert_eq!(
/// GaussianInteger::from_str("1-2i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 1
/// );
/// assert_eq!(
/// GaussianInteger::from_str("1+i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 0
/// );
/// assert_eq!(
/// GaussianInteger::from_str("1-i")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 1
/// );
/// assert_eq!(
/// GaussianInteger::from_str("0")
/// .unwrap()
/// .canonical_unit_i_pow(),
/// 0
/// );
/// ```
fn canonical_unit_i_pow(&self) -> u64 {
match self.real.cmp(&self.imaginary) {
Equal => u64::from(self.real < 0u32) << 1,
Greater => u64::from(self.real.le_abs(&self.imaginary)),
Less => {
if self.real.le_abs(&self.imaginary) {
3
} else {
2
}
}
}
}
}