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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 core::borrow::Borrow;
use malachite_base::num::arithmetic::traits::{ModIsReduced, ModSum};
fn assert_reduced(v: &NaturalVector, m: &Natural) {
assert!(
v.mod_is_reduced(m),
"every vector must be reduced mod m, but {v} has an element >= {m}"
);
}
const EMPTY: &str = "cannot sum an empty iterator of vectors: the dimension is unknown";
// Adds the remaining vectors to `sum`, the first, entry by entry and exactly, and then reduces each
// entry once: every entry of the exact sum is less than `m` times the number of vectors, so each
// final division has a short quotient.
fn finish<B: Borrow<NaturalVector>, I: Iterator<Item = B>>(
mut sum: NaturalVector,
xs: I,
m: &Natural,
) -> NaturalVector {
assert_ne!(*m, 0u32, "m cannot be zero");
assert_reduced(&sum, m);
for v in xs {
let v = v.borrow();
assert_eq!(
v.elements.len(),
sum.elements.len(),
"cannot sum vectors of different dimensions"
);
assert_reduced(v, m);
for (s, x) in sum.elements.iter_mut().zip(&v.elements) {
*s += x;
}
}
for s in &mut sum.elements {
*s %= m;
}
sum
}
impl ModSum<Self, Natural> for NaturalVector {
/// Adds up all the [`NaturalVector`]s in an iterator, entry by entry, modulo another
/// [`Natural`] $m$, taking the vectors by value and the modulus by value. The vectors must all
/// have the same dimension, and their elements must already be reduced modulo $m$.
///
/// $f((v_i)_ {i=0}^{n-1}, m) = w$, where every element of $w$ is less than $m$ and $\sum_
/// {i=0}^{n-1} v_i \equiv w \mod m$, entry by entry.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk)$
///
/// $M(d, k) = O(dk)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of elements of all the
/// vectors, $d$ is the dimension of the vectors, and $k$ is `m.significant_bits()`.
///
/// # Panics
/// Panics if the iterator is empty, if the vectors do not all have the same dimension, if `m`
/// is zero, or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModSum;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let vs =
/// ["(5, 1, 3)", "(2, 6, 4)", "(6, 2, 5)"].map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.into_iter(), Natural::from(7u32)).to_string(),
/// "(6, 2, 5)"
/// );
///
/// let m = Natural::from_str("1000000000000000000000000000057").unwrap();
/// let vs = [
/// "(1000000000000000000000000000056, 1)",
/// "(1000000000000000000000000000056, 1000000000000000000000000000055)",
/// ]
/// .map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.into_iter(), m).to_string(),
/// "(1000000000000000000000000000055, 1000000000000000000000000000056)"
/// );
/// ```
fn mod_sum<I: Iterator<Item = Self>>(mut xs: I, m: Natural) -> Self {
let first = xs.next().expect(EMPTY);
finish(first, xs, &m)
}
}
impl<'b> ModSum<Self, &'b Natural> for NaturalVector {
/// Adds up all the [`NaturalVector`]s in an iterator, entry by entry, modulo another
/// [`Natural`] $m$, taking the vectors by value and the modulus by reference. The vectors must
/// all have the same dimension, and their elements must already be reduced modulo $m$.
///
/// $f((v_i)_ {i=0}^{n-1}, m) = w$, where every element of $w$ is less than $m$ and $\sum_
/// {i=0}^{n-1} v_i \equiv w \mod m$, entry by entry.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk)$
///
/// $M(d, k) = O(dk)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of elements of all the
/// vectors, $d$ is the dimension of the vectors, and $k$ is `m.significant_bits()`.
///
/// # Panics
/// Panics if the iterator is empty, if the vectors do not all have the same dimension, if `m`
/// is zero, or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModSum;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let vs =
/// ["(5, 1, 3)", "(2, 6, 4)", "(6, 2, 5)"].map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.into_iter(), &Natural::from(7u32)).to_string(),
/// "(6, 2, 5)"
/// );
///
/// let m = Natural::from_str("1000000000000000000000000000057").unwrap();
/// let vs = [
/// "(1000000000000000000000000000056, 1)",
/// "(1000000000000000000000000000056, 1000000000000000000000000000055)",
/// ]
/// .map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.into_iter(), &m).to_string(),
/// "(1000000000000000000000000000055, 1000000000000000000000000000056)"
/// );
/// ```
fn mod_sum<I: Iterator<Item = Self>>(mut xs: I, m: &'b Natural) -> Self {
let first = xs.next().expect(EMPTY);
finish(first, xs, m)
}
}
impl<'a> ModSum<&'a Self, Natural> for NaturalVector {
/// Adds up all the [`NaturalVector`]s in an iterator, entry by entry, modulo another
/// [`Natural`] $m$, taking the vectors by reference and the modulus by value. The vectors must
/// all have the same dimension, and their elements must already be reduced modulo $m$.
///
/// $f((v_i)_ {i=0}^{n-1}, m) = w$, where every element of $w$ is less than $m$ and $\sum_
/// {i=0}^{n-1} v_i \equiv w \mod m$, entry by entry.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk)$
///
/// $M(d, k) = O(dk)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of elements of all the
/// vectors, $d$ is the dimension of the vectors, and $k$ is `m.significant_bits()`.
///
/// # Panics
/// Panics if the iterator is empty, if the vectors do not all have the same dimension, if `m`
/// is zero, or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModSum;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let vs =
/// ["(5, 1, 3)", "(2, 6, 4)", "(6, 2, 5)"].map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.iter(), Natural::from(7u32)).to_string(),
/// "(6, 2, 5)"
/// );
///
/// let m = Natural::from_str("1000000000000000000000000000057").unwrap();
/// let vs = [
/// "(1000000000000000000000000000056, 1)",
/// "(1000000000000000000000000000056, 1000000000000000000000000000055)",
/// ]
/// .map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.iter(), m).to_string(),
/// "(1000000000000000000000000000055, 1000000000000000000000000000056)"
/// );
/// ```
fn mod_sum<I: Iterator<Item = &'a Self>>(mut xs: I, m: Natural) -> Self {
let first = xs.next().expect(EMPTY);
finish(first.clone(), xs, &m)
}
}
impl<'a, 'b> ModSum<&'a Self, &'b Natural> for NaturalVector {
/// Adds up all the [`NaturalVector`]s in an iterator, entry by entry, modulo another
/// [`Natural`] $m$, taking the vectors by reference and the modulus by reference. The vectors
/// must all have the same dimension, and their elements must already be reduced modulo $m$.
///
/// $f((v_i)_ {i=0}^{n-1}, m) = w$, where every element of $w$ is less than $m$ and $\sum_
/// {i=0}^{n-1} v_i \equiv w \mod m$, entry by entry.
///
/// # Worst-case complexity
/// $T(n, k) = O(nk)$
///
/// $M(d, k) = O(dk)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of elements of all the
/// vectors, $d$ is the dimension of the vectors, and $k$ is `m.significant_bits()`.
///
/// # Panics
/// Panics if the iterator is empty, if the vectors do not all have the same dimension, if `m`
/// is zero, or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModSum;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let vs =
/// ["(5, 1, 3)", "(2, 6, 4)", "(6, 2, 5)"].map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.iter(), &Natural::from(7u32)).to_string(),
/// "(6, 2, 5)"
/// );
///
/// let m = Natural::from_str("1000000000000000000000000000057").unwrap();
/// let vs = [
/// "(1000000000000000000000000000056, 1)",
/// "(1000000000000000000000000000056, 1000000000000000000000000000055)",
/// ]
/// .map(|s| NaturalVector::from_str(s).unwrap());
/// assert_eq!(
/// NaturalVector::mod_sum(vs.iter(), &m).to_string(),
/// "(1000000000000000000000000000055, 1000000000000000000000000000056)"
/// );
/// ```
fn mod_sum<I: Iterator<Item = &'a Self>>(mut xs: I, m: &'b Natural) -> Self {
let first = xs.next().expect(EMPTY);
finish(first.clone(), xs, m)
}
}