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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 malachite_base::num::arithmetic::traits::{ModElementProduct, ModProduct};
impl ModElementProduct<Natural> for NaturalVector {
type Output = Natural;
/// Returns the product of the elements of a [`NaturalVector`] modulo another number $m$, taking
/// the vector by reference and the modulus by value. The elements must already be reduced.
///
/// The 0-dimensional vector has no elements, and their product is 1, reduced: 0 when $m = 1$.
///
/// $$
/// f(v, m) = \prod_i v_i \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero, or if any element is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining elements are not examined, so an unreduced element
/// after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModElementProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(3, 5, 7)").unwrap();
/// assert_eq!(v.to_mod_element_product(Natural::from(10u32)), 5);
/// let v = NaturalVector::from_str("()").unwrap();
/// assert_eq!(v.to_mod_element_product(Natural::from(10u32)), 1);
/// ```
#[inline]
fn to_mod_element_product(&self, m: Natural) -> Natural {
Natural::mod_product(self.elements.iter(), m)
}
/// Returns the product of the elements of a [`NaturalVector`] modulo another number $m$, taking
/// the vector by value and the modulus by value. The elements must already be reduced.
///
/// The 0-dimensional vector has no elements, and their product is 1, reduced: 0 when $m = 1$.
///
/// $$
/// f(v, m) = \prod_i v_i \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero, or if any element is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining elements are not examined, so an unreduced element
/// after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModElementProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(3, 5, 7)").unwrap();
/// assert_eq!(v.into_mod_element_product(Natural::from(10u32)), 5);
/// let v = NaturalVector::from_str("()").unwrap();
/// assert_eq!(v.into_mod_element_product(Natural::from(10u32)), 1);
/// ```
#[inline]
fn into_mod_element_product(self, m: Natural) -> Natural {
Natural::mod_product(self.elements.into_iter(), m)
}
}
impl ModElementProduct<&Natural> for NaturalVector {
type Output = Natural;
/// Returns the product of the elements of a [`NaturalVector`] modulo another number $m$, taking
/// the vector by reference and the modulus by reference. The elements must already be reduced.
///
/// The 0-dimensional vector has no elements, and their product is 1, reduced: 0 when $m = 1$.
///
/// $$
/// f(v, m) = \prod_i v_i \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero, or if any element is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining elements are not examined, so an unreduced element
/// after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModElementProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(3, 5, 7)").unwrap();
/// assert_eq!(v.to_mod_element_product(&Natural::from(10u32)), 5);
/// let v = NaturalVector::from_str("()").unwrap();
/// assert_eq!(v.to_mod_element_product(&Natural::from(10u32)), 1);
/// ```
#[inline]
fn to_mod_element_product(&self, m: &Natural) -> Natural {
Natural::mod_product(self.elements.iter(), m)
}
/// Returns the product of the elements of a [`NaturalVector`] modulo another number $m$, taking
/// the vector by value and the modulus by reference. The elements must already be reduced.
///
/// The 0-dimensional vector has no elements, and their product is 1, reduced: 0 when $m = 1$.
///
/// $$
/// f(v, m) = \prod_i v_i \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero, or if any element is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining elements are not examined, so an unreduced element
/// after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModElementProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(3, 5, 7)").unwrap();
/// assert_eq!(v.into_mod_element_product(&Natural::from(10u32)), 5);
/// let v = NaturalVector::from_str("()").unwrap();
/// assert_eq!(v.into_mod_element_product(&Natural::from(10u32)), 1);
/// ```
#[inline]
fn into_mod_element_product(self, m: &Natural) -> Natural {
Natural::mod_product(self.elements.into_iter(), m)
}
}