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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::platform::Limb;
use core::borrow::Borrow;
use malachite_base::num::arithmetic::traits::{ModPowerOf2MulAssign, ModPowerOf2Product};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::One;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
fn assert_reduced(x: &Natural, pow: u64) {
assert!(
x.significant_bits() <= pow,
"x must be reduced mod 2^pow, but {x} >= 2^{pow}"
);
}
// When `pow` is at most `Limb::WIDTH`, every reduced factor fits in a `Limb`, and the `Limb`
// implementation multiplies them with wrapping multiplications. Otherwise the product is reduced
// after every multiplication: an exact product would grow with every factor, while
// `mod_power_of_2_mul` keeps it at `pow` bits and computes only the low half of each product. Since
// `pow` exceeds `Limb::WIDTH` here, the product of no factors is 1. Once the product is zero it
// stays zero, so the factors after the one that made it zero are not examined.
fn mod_power_of_2_product_helper<B: Borrow<Natural>, I: Iterator<Item = B>>(
xs: I,
pow: u64,
) -> Natural {
if pow <= Limb::WIDTH {
Natural::from(Limb::mod_power_of_2_product(
xs.map(|x| {
let x = x.borrow();
assert_reduced(x, pow);
Limb::exact_from(x)
}),
pow,
))
} else {
let mut product = Natural::ONE;
for x in xs {
let x = x.borrow();
assert_reduced(x, pow);
product.mod_power_of_2_mul_assign(x, pow);
if product == 0u32 {
break;
}
}
product
}
}
impl ModPowerOf2Product for Natural {
/// Multiplies together all the [`Natural`]s in an iterator, modulo $2^k$. Every [`Natural`]
/// must be already reduced modulo $2^k$.
///
/// The product of no [`Natural`]s is 1 reduced modulo $2^k$, which is 0 when $k = 0$.
///
/// $f((x_i)_ {i=0}^{n-1}, k) = y$, where $y < 2^k$ and $\prod_ {i=0}^{n-1} x_i \equiv y \mod
/// 2^k$.
///
/// # 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 `xs.count()`, and $m$ is `pow`.
///
/// # Panics
/// Panics if any [`Natural`] is greater than or equal to $2^k$. As soon as the partial product
/// is zero, the remaining [`Natural`]s are not examined, so an unreduced one after that point
/// is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Product;
/// use malachite_base::vecs::vec_from_str;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::mod_power_of_2_product(
/// vec_from_str::<Natural>("[2, 3, 5, 7]").unwrap().into_iter(),
/// 4
/// ),
/// 2
/// );
/// assert_eq!(
/// Natural::mod_power_of_2_product(
/// vec_from_str::<Natural>("[18446744073709551615, 18446744073709551617, 3]")
/// .unwrap()
/// .into_iter(),
/// 65
/// ),
/// Natural::from_str("36893488147419103229").unwrap()
/// );
/// ```
#[inline]
fn mod_power_of_2_product<I: Iterator<Item = Self>>(xs: I, pow: u64) -> Self {
mod_power_of_2_product_helper(xs, pow)
}
}
impl<'a> ModPowerOf2Product<&'a Self> for Natural {
/// Multiplies together all the [`Natural`]s in an iterator of [`Natural`] references, modulo
/// $2^k$. Every [`Natural`] must be already reduced modulo $2^k$.
///
/// The product of no [`Natural`]s is 1 reduced modulo $2^k$, which is 0 when $k = 0$.
///
/// $f((x_i)_ {i=0}^{n-1}, k) = y$, where $y < 2^k$ and $\prod_ {i=0}^{n-1} x_i \equiv y \mod
/// 2^k$.
///
/// # 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 `xs.count()`, and $m$ is `pow`.
///
/// # Panics
/// Panics if any [`Natural`] is greater than or equal to $2^k$. As soon as the partial product
/// is zero, the remaining [`Natural`]s are not examined, so an unreduced one after that point
/// is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Product;
/// use malachite_base::vecs::vec_from_str;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::mod_power_of_2_product(
/// vec_from_str::<Natural>("[2, 3, 5, 7]").unwrap().iter(),
/// 4
/// ),
/// 2
/// );
/// assert_eq!(
/// Natural::mod_power_of_2_product(
/// vec_from_str::<Natural>("[18446744073709551615, 18446744073709551617, 3]")
/// .unwrap()
/// .iter(),
/// 65
/// ),
/// Natural::from_str("36893488147419103229").unwrap()
/// );
/// ```
#[inline]
fn mod_power_of_2_product<I: Iterator<Item = &'a Self>>(xs: I, pow: u64) -> Self {
mod_power_of_2_product_helper(xs, pow)
}
}