malachite-nz 0.13.0

// 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_polynomial::NaturalPolynomial;
use alloc::vec::Vec;
use core::cmp::min;
use core::mem::swap;
use malachite_base::num::arithmetic::traits::{
    ModPowerOf2Add, ModPowerOf2AddAssign, ModPowerOf2IsReduced,
};

pub(crate) fn assert_reduced(p: &NaturalPolynomial, q: &NaturalPolynomial, pow: u64) {
    assert!(
        p.mod_power_of_2_is_reduced(pow),
        "self must be reduced mod 2^pow, but {p} has a coefficient >= 2^{pow}"
    );
    assert!(
        q.mod_power_of_2_is_reduced(pow),
        "other must be reduced mod 2^pow, but {q} has a coefficient >= 2^{pow}"
    );
}

// Adds `ys` into `xs` modulo 2^pow, cloning the coefficients of `ys` past the end of `xs`. The
// caller trims, since leading coefficients can cancel.
pub(crate) fn add_assign_ref(xs: &mut Vec<Natural>, ys: &[Natural], pow: u64) {
    let common = min(xs.len(), ys.len());
    for (x, y) in xs.iter_mut().zip(&ys[..common]) {
        x.mod_power_of_2_add_assign(y, pow);
    }
    if ys.len() > common {
        xs.extend_from_slice(&ys[common..]);
    }
}

// Adds `ys` into `xs` modulo 2^pow, reusing whichever of the two is longer. The caller trims.
pub(crate) fn add_assign_val(xs: &mut Vec<Natural>, mut ys: Vec<Natural>, pow: u64) {
    if ys.len() > xs.len() {
        swap(xs, &mut ys);
    }
    for (x, y) in xs.iter_mut().zip(ys) {
        x.mod_power_of_2_add_assign(y, pow);
    }
}

impl ModPowerOf2Add<Self> for NaturalPolynomial {
    type Output = Self;

    /// Adds two [`NaturalPolynomial`]s modulo $2^k$, taking both by value. The coefficients of both
    /// must already be reduced modulo $2^k$.
    ///
    /// $$
    /// f(p, q, k) = p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(1)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2Add;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// assert_eq!(
    ///     NaturalPolynomial::from_str("5*x^2+x+3")
    ///         .unwrap()
    ///         .mod_power_of_2_add(NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3)
    ///         .to_string(),
    ///     "4"
    /// );
    /// // Wrapping around makes the constant term 1.
    /// assert_eq!(
    ///     NaturalPolynomial::from_str("x+3")
    ///         .unwrap()
    ///         .mod_power_of_2_add(NaturalPolynomial::from_str("x^2+6").unwrap(), 3)
    ///         .to_string(),
    ///     "x^2+x+1"
    /// );
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add(mut self, other: Self, pow: u64) -> Self {
        assert_reduced(&self, &other, pow);
        add_assign_val(&mut self.coefficients, other.coefficients, pow);
        self.trim();
        self
    }
}

impl ModPowerOf2Add<&Self> for NaturalPolynomial {
    type Output = Self;

    /// Adds two [`NaturalPolynomial`]s modulo $2^k$, taking the first by value and the second by
    /// reference. The coefficients of both must already be reduced modulo $2^k$.
    ///
    /// $$
    /// f(p, q, k) = p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2Add;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// assert_eq!(
    ///     NaturalPolynomial::from_str("5*x^2+x+3")
    ///         .unwrap()
    ///         .mod_power_of_2_add(&NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3)
    ///         .to_string(),
    ///     "4"
    /// );
    /// // Wrapping around makes the constant term 1.
    /// assert_eq!(
    ///     NaturalPolynomial::from_str("x+3")
    ///         .unwrap()
    ///         .mod_power_of_2_add(&NaturalPolynomial::from_str("x^2+6").unwrap(), 3)
    ///         .to_string(),
    ///     "x^2+x+1"
    /// );
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add(mut self, other: &Self, pow: u64) -> Self {
        assert_reduced(&self, other, pow);
        add_assign_ref(&mut self.coefficients, &other.coefficients, pow);
        self.trim();
        self
    }
}

impl ModPowerOf2Add<NaturalPolynomial> for &NaturalPolynomial {
    type Output = NaturalPolynomial;

    /// Adds two [`NaturalPolynomial`]s modulo $2^k$, taking the first by reference and the second
    /// by value. The coefficients of both must already be reduced modulo $2^k$.
    ///
    /// $$
    /// f(p, q, k) = p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2Add;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// assert_eq!(
    ///     (&NaturalPolynomial::from_str("5*x^2+x+3").unwrap())
    ///         .mod_power_of_2_add(NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3)
    ///         .to_string(),
    ///     "4"
    /// );
    /// // Wrapping around makes the constant term 1.
    /// assert_eq!(
    ///     (&NaturalPolynomial::from_str("x+3").unwrap())
    ///         .mod_power_of_2_add(NaturalPolynomial::from_str("x^2+6").unwrap(), 3)
    ///         .to_string(),
    ///     "x^2+x+1"
    /// );
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add(self, mut other: NaturalPolynomial, pow: u64) -> NaturalPolynomial {
        assert_reduced(self, &other, pow);
        add_assign_ref(&mut other.coefficients, &self.coefficients, pow);
        other.trim();
        other
    }
}

impl ModPowerOf2Add<&NaturalPolynomial> for &NaturalPolynomial {
    type Output = NaturalPolynomial;

    /// Adds two [`NaturalPolynomial`]s modulo $2^k$, taking both by reference. The coefficients of
    /// both must already be reduced modulo $2^k$.
    ///
    /// $$
    /// f(p, q, k) = p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2Add;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// assert_eq!(
    ///     (&NaturalPolynomial::from_str("5*x^2+x+3").unwrap())
    ///         .mod_power_of_2_add(&NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3)
    ///         .to_string(),
    ///     "4"
    /// );
    /// // Wrapping around makes the constant term 1.
    /// assert_eq!(
    ///     (&NaturalPolynomial::from_str("x+3").unwrap())
    ///         .mod_power_of_2_add(&NaturalPolynomial::from_str("x^2+6").unwrap(), 3)
    ///         .to_string(),
    ///     "x^2+x+1"
    /// );
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add(self, other: &NaturalPolynomial, pow: u64) -> NaturalPolynomial {
        assert_reduced(self, other, pow);
        let mut coefficients = self.coefficients.clone();
        add_assign_ref(&mut coefficients, &other.coefficients, pow);
        let mut result = NaturalPolynomial { coefficients };
        result.trim();
        result
    }
}

impl ModPowerOf2AddAssign<Self> for NaturalPolynomial {
    /// Adds a [`NaturalPolynomial`] to a [`NaturalPolynomial`] modulo $2^k$, in place, taking the
    /// second by value. The coefficients of both must already be reduced modulo $2^k$.
    ///
    /// $$
    /// p \gets p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(1)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2AddAssign;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// let mut p = NaturalPolynomial::from_str("5*x^2+x+3").unwrap();
    /// p.mod_power_of_2_add_assign(NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3);
    /// assert_eq!(p.to_string(), "4");
    ///
    /// // Wrapping around makes the constant term 1.
    /// let mut p = NaturalPolynomial::from_str("x+3").unwrap();
    /// p.mod_power_of_2_add_assign(NaturalPolynomial::from_str("x^2+6").unwrap(), 3);
    /// assert_eq!(p.to_string(), "x^2+x+1");
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add_assign(&mut self, other: Self, pow: u64) {
        assert_reduced(self, &other, pow);
        add_assign_val(&mut self.coefficients, other.coefficients, pow);
        self.trim();
    }
}

impl ModPowerOf2AddAssign<&Self> for NaturalPolynomial {
    /// Adds a [`NaturalPolynomial`] to a [`NaturalPolynomial`] modulo $2^k$, in place, taking the
    /// second by reference. The coefficients of both must already be reduced modulo $2^k$.
    ///
    /// $$
    /// p \gets p + q \bmod 2^k.
    /// $$
    ///
    /// Coefficients past the end of the shorter polynomial are taken to be zero. When the two
    /// polynomials have the same degree, their leading coefficients can cancel modulo $2^k$, and
    /// then the degree of the sum is lower.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(n)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients of the
    /// longer polynomial times `pow`.
    ///
    /// # Panics
    /// Panics if any coefficient of `self` or `other` is greater than or equal to $2^k$.
    ///
    /// # Examples
    /// ```
    /// use core::str::FromStr;
    /// use malachite_base::num::arithmetic::traits::ModPowerOf2AddAssign;
    /// use malachite_nz::natural_polynomial::NaturalPolynomial;
    ///
    /// // The leading coefficients cancel, and so do the linear ones.
    /// let mut p = NaturalPolynomial::from_str("5*x^2+x+3").unwrap();
    /// p.mod_power_of_2_add_assign(&NaturalPolynomial::from_str("3*x^2+7*x+1").unwrap(), 3);
    /// assert_eq!(p.to_string(), "4");
    ///
    /// // Wrapping around makes the constant term 1.
    /// let mut p = NaturalPolynomial::from_str("x+3").unwrap();
    /// p.mod_power_of_2_add_assign(&NaturalPolynomial::from_str("x^2+6").unwrap(), 3);
    /// assert_eq!(p.to_string(), "x^2+x+1");
    /// ```
    ///
    /// This is equivalent to `fmpz_mod_poly_add` from `fmpz_mod_poly/add.c`, FLINT 3.6.0, with the
    /// modulus $2^k$.
    fn mod_power_of_2_add_assign(&mut self, other: &Self, pow: u64) {
        assert_reduced(self, other, pow);
        add_assign_ref(&mut self.coefficients, &other.coefficients, pow);
        self.trim();
    }
}