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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::integer_vector::IntegerVector;
use crate::integer_vector::arithmetic::content::{content, normalize_in_place, normalized};
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, CanonicalPrimitivePartAssign, ContentAndCanonicalPrimitivePart,
};
use malachite_base::vector::Vector;
// Whether the canonical primitive part must be negated: when the pivot, the first nonzero element,
// is negative.
fn negate(v: &IntegerVector) -> bool {
v.pivot().is_some_and(|x| !x.sign)
}
impl CanonicalPrimitivePart for IntegerVector {
type Output = Self;
/// Computes the canonical primitive part of an [`IntegerVector`], taking the vector by value.
///
/// This is the
/// [`primitive_part`](malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part),
/// negated if its first nonzero element is negative, so that the first nonzero element is
/// positive. A vector and its negation have the same canonical primitive part. The canonical
/// primitive part of a vector of zeros is itself, keeping its dimension.
///
/// $$
/// v = \pm \operatorname{cont}(v) \operatorname{cpp}(v).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let v = IntegerVector::from_str("(-6, 4, -10)").unwrap();
/// assert_eq!(v.canonical_primitive_part().to_string(), "(3, -2, 5)");
///
/// // Leading zeros are skipped: the first nonzero element is made positive.
/// let v = IntegerVector::from_str("(0, -2, 4)").unwrap();
/// assert_eq!(v.canonical_primitive_part().to_string(), "(0, 1, -2)");
/// ```
#[inline]
fn canonical_primitive_part(mut self) -> Self {
self.canonical_primitive_part_assign();
self
}
}
impl CanonicalPrimitivePart for &IntegerVector {
type Output = IntegerVector;
/// Computes the canonical primitive part of an [`IntegerVector`], taking the vector by
/// reference.
///
/// This is the
/// [`primitive_part`](malachite_base::num::arithmetic::traits::PrimitivePart::primitive_part),
/// negated if its first nonzero element is negative, so that the first nonzero element is
/// positive. A vector and its negation have the same canonical primitive part. The canonical
/// primitive part of a vector of zeros is itself, keeping its dimension.
///
/// $$
/// v = \pm \operatorname{cont}(v) \operatorname{cpp}(v).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let v = IntegerVector::from_str("(-6, 4, -10)").unwrap();
/// assert_eq!((&v).canonical_primitive_part().to_string(), "(3, -2, 5)");
/// ```
#[inline]
fn canonical_primitive_part(self) -> IntegerVector {
let content = content(&self.elements);
IntegerVector {
elements: normalized(&self.elements, &content, negate(self)),
}
}
}
impl CanonicalPrimitivePartAssign for IntegerVector {
/// Replaces an [`IntegerVector`] with its canonical primitive part.
///
/// See [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part).
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePartAssign;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let mut v = IntegerVector::from_str("(-6, 4, -10)").unwrap();
/// v.canonical_primitive_part_assign();
/// assert_eq!(v.to_string(), "(3, -2, 5)");
/// ```
#[inline]
fn canonical_primitive_part_assign(&mut self) {
let content = content(&self.elements);
let negate = negate(self);
normalize_in_place(&mut self.elements, &content, negate);
}
}
impl ContentAndCanonicalPrimitivePart for IntegerVector {
type Content = Natural;
type CanonicalPrimitivePart = Self;
/// Computes the content and the canonical primitive part of an [`IntegerVector`] together,
/// taking the vector by value.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let v = IntegerVector::from_str("(-6, 4, -10)").unwrap();
/// let (content, primitive_part) = v.content_and_canonical_primitive_part();
/// assert_eq!(content, 2u32);
/// assert_eq!(primitive_part.to_string(), "(3, -2, 5)");
/// ```
#[inline]
fn content_and_canonical_primitive_part(mut self) -> (Natural, Self) {
let content = content(&self.elements);
let negate = negate(&self);
normalize_in_place(&mut self.elements, &content, negate);
(content, self)
}
}
impl ContentAndCanonicalPrimitivePart for &IntegerVector {
type Content = Natural;
type CanonicalPrimitivePart = IntegerVector;
/// Computes the content and the canonical primitive part of an [`IntegerVector`] together,
/// taking the vector by reference.
///
/// See [`content`](malachite_base::num::arithmetic::traits::Content::content) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let v = IntegerVector::from_str("(-6, 4, -10)").unwrap();
/// let (content, primitive_part) = (&v).content_and_canonical_primitive_part();
/// assert_eq!(content, 2u32);
/// assert_eq!(primitive_part.to_string(), "(3, -2, 5)");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Natural, IntegerVector) {
let content = content(&self.elements);
let elements = normalized(&self.elements, &content, negate(self));
(content, IntegerVector { elements })
}
}