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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::Natural;
use crate::natural_vector::NaturalVector;
use crate::platform::Limb;
use malachite_base::num::arithmetic::traits::{
Dot, ModPowerOf2, ModPowerOf2Dot, ModPowerOf2IsReduced, WrappingAddAssign,
};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::conversion::traits::WrappingFrom;
// The dot product of two vectors modulo $2^k$. When $k$ is at most the width of a limb, every
// element fits in a limb, and the products are summed in wrapping limb arithmetic, since $2^k$
// divides the limb modulus; otherwise the exact dot product is reduced once.
fn mod_power_of_2_dot(v: &NaturalVector, w: &NaturalVector, pow: u64) -> Natural {
assert_eq!(
v.elements.len(),
w.elements.len(),
"the vectors must have the same dimension"
);
assert!(
v.mod_power_of_2_is_reduced(pow),
"self must be reduced mod 2^{pow}, but {v} has an element >= 2^{pow}"
);
assert!(
w.mod_power_of_2_is_reduced(pow),
"other must be reduced mod 2^{pow}, but {w} has an element >= 2^{pow}"
);
if pow <= Limb::WIDTH {
let mut sum: Limb = 0;
for (x, y) in v.elements.iter().zip(&w.elements) {
sum.wrapping_add_assign(Limb::wrapping_from(x).wrapping_mul(Limb::wrapping_from(y)));
}
Natural::from(sum.mod_power_of_2(pow))
} else {
v.dot(w).mod_power_of_2(pow)
}
}
impl ModPowerOf2Dot<Self> for NaturalVector {
type Output = Natural;
/// Computes the dot product of two [`NaturalVector`]s modulo $2^k$, taking the first by value
/// and the second by value. The elements of both must already be reduced.
///
/// The dot product of two 0-dimensional vectors is 0.
///
/// $$
/// f(v, w, k) = \sum_{i=0}^{n-1} v_iw_i \bmod 2^k,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk \log k \log\log k)$
///
/// $M(k) = O(k \log k)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $k$ is
/// `pow`.
///
/// # Panics
/// Panics if the vectors have different dimensions, or if any element is greater than or equal
/// to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Dot;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// let w = NaturalVector::from_str("(4, 5, 7)").unwrap();
/// assert_eq!(v.clone().mod_power_of_2_dot(w.clone(), 4), 3);
/// ```
#[inline]
fn mod_power_of_2_dot(self, other: Self, pow: u64) -> Natural {
mod_power_of_2_dot(&self, &other, pow)
}
}
impl ModPowerOf2Dot<&Self> for NaturalVector {
type Output = Natural;
/// Computes the dot product of two [`NaturalVector`]s modulo $2^k$, taking the first by value
/// and the second by reference. The elements of both must already be reduced.
///
/// The dot product of two 0-dimensional vectors is 0.
///
/// $$
/// f(v, w, k) = \sum_{i=0}^{n-1} v_iw_i \bmod 2^k,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk \log k \log\log k)$
///
/// $M(k) = O(k \log k)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $k$ is
/// `pow`.
///
/// # Panics
/// Panics if the vectors have different dimensions, or if any element is greater than or equal
/// to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Dot;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// let w = NaturalVector::from_str("(4, 5, 7)").unwrap();
/// assert_eq!(v.clone().mod_power_of_2_dot(&w, 4), 3);
/// ```
#[inline]
fn mod_power_of_2_dot(self, other: &Self, pow: u64) -> Natural {
mod_power_of_2_dot(&self, other, pow)
}
}
impl ModPowerOf2Dot<NaturalVector> for &NaturalVector {
type Output = Natural;
/// Computes the dot product of two [`NaturalVector`]s modulo $2^k$, taking the first by
/// reference and the second by value. The elements of both must already be reduced.
///
/// The dot product of two 0-dimensional vectors is 0.
///
/// $$
/// f(v, w, k) = \sum_{i=0}^{n-1} v_iw_i \bmod 2^k,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk \log k \log\log k)$
///
/// $M(k) = O(k \log k)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $k$ is
/// `pow`.
///
/// # Panics
/// Panics if the vectors have different dimensions, or if any element is greater than or equal
/// to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Dot;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// let w = NaturalVector::from_str("(4, 5, 7)").unwrap();
/// assert_eq!((&v).mod_power_of_2_dot(w.clone(), 4), 3);
/// ```
#[inline]
fn mod_power_of_2_dot(self, other: NaturalVector, pow: u64) -> Natural {
mod_power_of_2_dot(self, &other, pow)
}
}
impl ModPowerOf2Dot<&NaturalVector> for &NaturalVector {
type Output = Natural;
/// Computes the dot product of two [`NaturalVector`]s modulo $2^k$, taking the first by
/// reference and the second by reference. The elements of both must already be reduced.
///
/// The dot product of two 0-dimensional vectors is 0.
///
/// $$
/// f(v, w, k) = \sum_{i=0}^{n-1} v_iw_i \bmod 2^k,
/// $$
///
/// where $n$ is the dimension of $v$ and $w$.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk \log k \log\log k)$
///
/// $M(k) = O(k \log k)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vectors, and $k$ is
/// `pow`.
///
/// # Panics
/// Panics if the vectors have different dimensions, or if any element is greater than or equal
/// to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Dot;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// let w = NaturalVector::from_str("(4, 5, 7)").unwrap();
/// assert_eq!((&v).mod_power_of_2_dot(&w, 4), 3);
/// ```
#[inline]
fn mod_power_of_2_dot(self, other: &NaturalVector, pow: u64) -> Natural {
mod_power_of_2_dot(self, other, pow)
}
}