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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 2010 William Hart
//
// Copyright © 2021 Fredrik Johansson
//
// 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::ModProduct;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
// The data for multiplying modulo `m` is computed once and reused for every factor. Once the
// partial product is zero it stays zero, so the factors after the one that made it zero are not
// examined. Starting from 1 reduced modulo `m` makes the product of no numbers correct even when
// `m` is 1.
fn mod_product<T: PrimitiveUnsigned, I: Iterator<Item = T>>(xs: I, m: T) -> T {
assert_ne!(m, T::ZERO, "m cannot be zero");
let data = T::precompute_mod_mul_data(&m);
let mut product = if m == T::ONE { T::ZERO } else { T::ONE };
for x in xs {
assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
product.mod_mul_precomputed_assign(x, m, &data);
if product == T::ZERO {
break;
}
}
product
}
macro_rules! impl_mod_product {
($t:ident) => {
impl ModProduct for $t {
/// Multiplies together all the numbers in an iterator, modulo another number $m$. Every
/// number must be already reduced modulo $m$.
///
/// The product of no numbers is 1 reduced modulo $m$, which is 0 when $m = 1$.
///
/// $f((x_i)_ {i=0}^{n-1}, m) = y$, where $y < m$ and $\prod_ {i=0}^{n-1} x_i \equiv y
/// \mod m$.
///
/// # 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 `m` is zero or if any number is greater than or equal to `m`. 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_product#mod_product).
#[inline]
fn mod_product<I: Iterator<Item = $t>>(xs: I, m: $t) -> $t {
mod_product(xs, m)
}
}
impl<'a> ModProduct<&'a $t, $t> for $t {
/// Multiplies together all the numbers in an iterator of references, modulo another
/// number $m$. Every number must be already reduced modulo $m$.
///
/// The product of no numbers is 1 reduced modulo $m$, which is 0 when $m = 1$.
///
/// $f((x_i)_ {i=0}^{n-1}, m) = y$, where $y < m$ and $\prod_ {i=0}^{n-1} x_i \equiv y
/// \mod m$.
///
/// # 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 `m` is zero or if any number is greater than or equal to `m`. 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_product#mod_product).
#[inline]
fn mod_product<I: Iterator<Item = &'a $t>>(xs: I, m: $t) -> $t {
mod_product(xs.copied(), m)
}
}
};
}
apply_to_unsigneds!(impl_mod_product);