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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::num::arithmetic::traits::ModPowerOf2Product;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
// Since $2^k$ divides $2^W$, where $W$ is the width of `T`, wrapping multiplication followed by
// reduction gives the product modulo $2^k$. The partial product is reduced after every step so that
// a zero residue is seen at once: from then on the product stays zero, so the factors after the one
// that made it zero are not examined. Starting from 1 reduced modulo $2^k$ makes the product of no
// numbers correct even when $k = 0$.
fn mod_power_of_2_product<T: PrimitiveUnsigned, I: Iterator<Item = T>>(xs: I, pow: u64) -> T {
assert!(pow <= T::WIDTH);
let mut product = T::ONE.mod_power_of_2(pow);
for x in xs {
assert!(
x.significant_bits() <= pow,
"x must be reduced mod 2^pow, but {x} >= 2^{pow}"
);
product = product.wrapping_mul(x).mod_power_of_2(pow);
if product == T::ZERO {
break;
}
}
product
}
macro_rules! impl_mod_power_of_2_product {
($t:ident) => {
impl ModPowerOf2Product for $t {
/// Multiplies together all the numbers in an iterator, modulo $2^k$. Every number must
/// be already reduced modulo $2^k$.
///
/// $f((x_i)_ {i=0}^{n-1}, k) = y$, where $y < 2^k$ and $\prod_ {i=0}^{n-1} x_i \equiv y
/// \mod 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `xs.count()`.
///
/// # Panics
/// Panics if `pow` is greater than `Self::WIDTH` or if any number is greater than or
/// equal to $2^k$. As soon as the partial product is zero, the remaining numbers are
/// not examined, so an unreduced number after that point is not detected.
///
/// # Examples
/// See [here](super::mod_power_of_2_product#mod_power_of_2_product).
#[inline]
fn mod_power_of_2_product<I: Iterator<Item = $t>>(xs: I, pow: u64) -> $t {
mod_power_of_2_product(xs, pow)
}
}
impl<'a> ModPowerOf2Product<&'a $t> for $t {
/// Multiplies together all the numbers in an iterator of references, modulo $2^k$.
/// Every number must be already reduced modulo $2^k$.
///
/// $f((x_i)_ {i=0}^{n-1}, k) = y$, where $y < 2^k$ and $\prod_ {i=0}^{n-1} x_i \equiv y
/// \mod 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `xs.count()`.
///
/// # Panics
/// Panics if `pow` is greater than `Self::WIDTH` or if any number is greater than or
/// equal to $2^k$. As soon as the partial product is zero, the remaining numbers are
/// not examined, so an unreduced number after that point is not detected.
///
/// # Examples
/// See [here](super::mod_power_of_2_product#mod_power_of_2_product).
#[inline]
fn mod_power_of_2_product<I: Iterator<Item = &'a $t>>(xs: I, pow: u64) -> $t {
mod_power_of_2_product(xs.copied(), pow)
}
}
};
}
apply_to_unsigneds!(impl_mod_power_of_2_product);