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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 crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, CanonicalPrimitivePartAssign, CanonicalizeUnit, CanonicalizeUnitAssign,
ContentAndCanonicalPrimitivePart, ContentAndPrimitivePart, PrimitivePart, PrimitivePartAssign,
};
impl CanonicalPrimitivePart for GaussianInteger {
type Output = Self;
/// Computes the canonical primitive part of a [`GaussianInteger`], taking the
/// [`GaussianInteger`] by value.
///
/// This is the [`primitive_part`](PrimitivePart::primitive_part), multiplied by the power of
/// $i$ that brings it into canonical unit form, as
/// [`canonicalize_unit`](CanonicalizeUnit::canonicalize_unit) chooses it: the associate whose
/// argument lies in $(-\pi/4, \pi/4]$. So the four associates of a Gaussian integer all have
/// the same canonical primitive part. Zero's is zero.
///
/// $$
/// x = i^k \operatorname{cont}(x) \operatorname{cpp}(x)
/// $$
///
/// for some $k \in \\{0, 1, 2, 3\\}$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("-6+9i").unwrap();
/// assert_eq!(x.canonical_primitive_part().to_string(), "3+2i");
/// ```
#[inline]
fn canonical_primitive_part(self) -> Self {
self.primitive_part().canonicalize_unit()
}
}
impl CanonicalPrimitivePart for &GaussianInteger {
type Output = GaussianInteger;
/// Computes the canonical primitive part of a [`GaussianInteger`], taking the
/// [`GaussianInteger`] by reference.
///
/// This is the [`primitive_part`](PrimitivePart::primitive_part), multiplied by the power of
/// $i$ that brings it into canonical unit form, as
/// [`canonicalize_unit`](CanonicalizeUnit::canonicalize_unit) chooses it: the associate whose
/// argument lies in $(-\pi/4, \pi/4]$. So the four associates of a Gaussian integer all have
/// the same canonical primitive part. Zero's is zero.
///
/// $$
/// x = i^k \operatorname{cont}(x) \operatorname{cpp}(x)
/// $$
///
/// for some $k \in \\{0, 1, 2, 3\\}$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("-6+9i").unwrap();
/// assert_eq!((&x).canonical_primitive_part().to_string(), "3+2i");
/// ```
#[inline]
fn canonical_primitive_part(self) -> GaussianInteger {
self.primitive_part().canonicalize_unit()
}
}
impl CanonicalPrimitivePartAssign for GaussianInteger {
/// Replaces a [`GaussianInteger`] with its canonical primitive part.
///
/// See [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part).
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePartAssign;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let mut x = GaussianInteger::from_str("-6+9i").unwrap();
/// x.canonical_primitive_part_assign();
/// assert_eq!(x.to_string(), "3+2i");
/// ```
#[inline]
fn canonical_primitive_part_assign(&mut self) {
self.primitive_part_assign();
self.canonicalize_unit_assign();
}
}
impl ContentAndCanonicalPrimitivePart for GaussianInteger {
type Content = Natural;
type CanonicalPrimitivePart = Self;
/// Splits a [`GaussianInteger`] into its content and its canonical primitive part, taking the
/// [`GaussianInteger`] by value.
///
/// See [`content_and_primitive_part`](ContentAndPrimitivePart::content_and_primitive_part) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let (content, primitive) = GaussianInteger::from_str("-6+9i")
/// .unwrap()
/// .content_and_canonical_primitive_part();
/// assert_eq!(content, 3);
/// assert_eq!(primitive.to_string(), "3+2i");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Natural, Self) {
let (content, primitive) = self.content_and_primitive_part();
(content, primitive.canonicalize_unit())
}
}
impl ContentAndCanonicalPrimitivePart for &GaussianInteger {
type Content = Natural;
type CanonicalPrimitivePart = GaussianInteger;
/// Splits a [`GaussianInteger`] into its content and its canonical primitive part, taking the
/// [`GaussianInteger`] by reference.
///
/// See [`content_and_primitive_part`](ContentAndPrimitivePart::content_and_primitive_part) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("-6+9i").unwrap();
/// let (content, primitive) = (&x).content_and_canonical_primitive_part();
/// assert_eq!(content, 3);
/// assert_eq!(primitive.to_string(), "3+2i");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Natural, GaussianInteger) {
let (content, primitive) = self.content_and_primitive_part();
(content, primitive.canonicalize_unit())
}
}