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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::natural_vector::NaturalVector;
use core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::DotSign;
// `Greater` if some coordinate is nonzero in both vectors, which have the same dimension, and
// `Equal` otherwise.
fn dot_sign(v: &NaturalVector, w: &NaturalVector) -> Ordering {
assert_eq!(
v.elements.len(),
w.elements.len(),
"the vectors must have the same dimension"
);
if v.elements
.iter()
.zip(&w.elements)
.any(|(x, y)| *x != 0u32 && *y != 0u32)
{
Greater
} else {
Equal
}
}
impl DotSign<Self> for NaturalVector {
/// Determines the sign of the dot product of two [`NaturalVector`]s, taking the first by value
/// and the second by value.
///
/// Every term $v_iw_i$ is non-negative, so the dot product is positive exactly when some
/// coordinate is nonzero in both vectors, and zero otherwise; no product or sum is computed.
/// The result is the ordering of the dot product against 0: `Greater` or `Equal`.
///
/// $$
/// f(v, w) = \operatorname{sgn}\left ( \sum_{i=0}^{n-1} v_iw_i \right ),
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the dimension of the vectors.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::cmp::Ordering::*;
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DotSign;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 0, 3)").unwrap();
/// let w = NaturalVector::from_str("(0, 5, 7)").unwrap();
/// assert_eq!(v.clone().dot_sign(w.clone()), Greater);
/// let w = NaturalVector::from_str("(0, 5, 0)").unwrap();
/// assert_eq!(v.clone().dot_sign(w.clone()), Equal);
/// ```
///
/// This is equivalent to `dotSign` from `AzVector/DotSign.lean`, Azurite.
#[inline]
fn dot_sign(self, other: Self) -> Ordering {
dot_sign(&self, &other)
}
}
impl DotSign<&Self> for NaturalVector {
/// Determines the sign of the dot product of two [`NaturalVector`]s, taking the first by value
/// and the second by reference.
///
/// Every term $v_iw_i$ is non-negative, so the dot product is positive exactly when some
/// coordinate is nonzero in both vectors, and zero otherwise; no product or sum is computed.
/// The result is the ordering of the dot product against 0: `Greater` or `Equal`.
///
/// $$
/// f(v, w) = \operatorname{sgn}\left ( \sum_{i=0}^{n-1} v_iw_i \right ),
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the dimension of the vectors.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::cmp::Ordering::*;
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DotSign;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 0, 3)").unwrap();
/// let w = NaturalVector::from_str("(0, 5, 7)").unwrap();
/// assert_eq!(v.clone().dot_sign(&w), Greater);
/// let w = NaturalVector::from_str("(0, 5, 0)").unwrap();
/// assert_eq!(v.clone().dot_sign(&w), Equal);
/// ```
///
/// This is equivalent to `dotSign` from `AzVector/DotSign.lean`, Azurite.
#[inline]
fn dot_sign(self, other: &Self) -> Ordering {
dot_sign(&self, other)
}
}
impl DotSign<NaturalVector> for &NaturalVector {
/// Determines the sign of the dot product of two [`NaturalVector`]s, taking the first by
/// reference and the second by value.
///
/// Every term $v_iw_i$ is non-negative, so the dot product is positive exactly when some
/// coordinate is nonzero in both vectors, and zero otherwise; no product or sum is computed.
/// The result is the ordering of the dot product against 0: `Greater` or `Equal`.
///
/// $$
/// f(v, w) = \operatorname{sgn}\left ( \sum_{i=0}^{n-1} v_iw_i \right ),
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the dimension of the vectors.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::cmp::Ordering::*;
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DotSign;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 0, 3)").unwrap();
/// let w = NaturalVector::from_str("(0, 5, 7)").unwrap();
/// assert_eq!((&v).dot_sign(w.clone()), Greater);
/// let w = NaturalVector::from_str("(0, 5, 0)").unwrap();
/// assert_eq!((&v).dot_sign(w.clone()), Equal);
/// ```
///
/// This is equivalent to `dotSign` from `AzVector/DotSign.lean`, Azurite.
#[inline]
fn dot_sign(self, other: NaturalVector) -> Ordering {
dot_sign(self, &other)
}
}
impl DotSign<&NaturalVector> for &NaturalVector {
/// Determines the sign of the dot product of two [`NaturalVector`]s, taking the first by
/// reference and the second by reference.
///
/// Every term $v_iw_i$ is non-negative, so the dot product is positive exactly when some
/// coordinate is nonzero in both vectors, and zero otherwise; no product or sum is computed.
/// The result is the ordering of the dot product against 0: `Greater` or `Equal`.
///
/// $$
/// f(v, w) = \operatorname{sgn}\left ( \sum_{i=0}^{n-1} v_iw_i \right ),
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the dimension of the vectors.
///
/// # Panics
/// Panics if the vectors have different dimensions.
///
/// # Examples
/// ```
/// use core::cmp::Ordering::*;
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::DotSign;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 0, 3)").unwrap();
/// let w = NaturalVector::from_str("(0, 5, 7)").unwrap();
/// assert_eq!((&v).dot_sign(&w), Greater);
/// let w = NaturalVector::from_str("(0, 5, 0)").unwrap();
/// assert_eq!((&v).dot_sign(&w), Equal);
/// ```
///
/// This is equivalent to `dotSign` from `AzVector/DotSign.lean`, Azurite.
#[inline]
fn dot_sign(self, other: &NaturalVector) -> Ordering {
dot_sign(self, other)
}
}