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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_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::{
ModPowerOf2IsReduced, ModPowerOf2Neg, ModPowerOf2NegAssign,
};
fn assert_reduced(p: &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}"
);
}
// Negates every coefficient modulo 2^pow. The coefficients are reduced, so a nonzero one stays
// nonzero and nothing needs trimming.
fn negate(coefficients: &mut [Natural], pow: u64) {
for c in coefficients {
c.mod_power_of_2_neg_assign(pow);
}
}
impl ModPowerOf2Neg for NaturalPolynomial {
type Output = Self;
/// Negates a [`NaturalPolynomial`] modulo $2^k$, taking the polynomial by value. The
/// coefficients must already be reduced modulo $2^k$.
///
/// Each nonzero coefficient $c$ becomes $2^k - c$, which is also nonzero, so the degree is
/// unchanged. The zero polynomial is its own negation.
///
/// $$
/// f(p, k) = -p \bmod 2^k.
/// $$
///
/// # 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 times
/// `pow`.
///
/// # Panics
/// Panics if any coefficient of `self` is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Neg;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("5*x^2+x+3").unwrap();
/// assert_eq!(p.clone().mod_power_of_2_neg(3).to_string(), "3*x^2+7*x+5");
/// let p = NaturalPolynomial::from_str("x").unwrap();
/// assert_eq!(p.clone().mod_power_of_2_neg(8).to_string(), "255*x");
/// assert_eq!(
/// NaturalPolynomial::ZERO.mod_power_of_2_neg(3),
/// NaturalPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `nmod_poly_neg` from `nmod_poly/neg.c`, FLINT 3.6.0, with the modulus
/// $2^k$.
#[inline]
fn mod_power_of_2_neg(mut self, pow: u64) -> Self {
self.mod_power_of_2_neg_assign(pow);
self
}
}
impl ModPowerOf2Neg for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Negates a [`NaturalPolynomial`] modulo $2^k$, taking the polynomial by reference. The
/// coefficients must already be reduced modulo $2^k$.
///
/// Each nonzero coefficient $c$ becomes $2^k - c$, which is also nonzero, so the degree is
/// unchanged. The zero polynomial is its own negation.
///
/// $$
/// f(p, k) = -p \bmod 2^k.
/// $$
///
/// # 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 times
/// `pow`.
///
/// # Panics
/// Panics if any coefficient of `self` is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Neg;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("5*x^2+x+3").unwrap();
/// assert_eq!((&p).mod_power_of_2_neg(3).to_string(), "3*x^2+7*x+5");
/// let p = NaturalPolynomial::from_str("x").unwrap();
/// assert_eq!((&p).mod_power_of_2_neg(8).to_string(), "255*x");
/// assert_eq!(
/// NaturalPolynomial::ZERO.mod_power_of_2_neg(3),
/// NaturalPolynomial::ZERO
/// );
/// ```
///
/// This is equivalent to `nmod_poly_neg` from `nmod_poly/neg.c`, FLINT 3.6.0, with the modulus
/// $2^k$.
#[inline]
fn mod_power_of_2_neg(self, pow: u64) -> NaturalPolynomial {
assert_reduced(self, pow);
let mut coefficients = self.coefficients.clone();
negate(&mut coefficients, pow);
NaturalPolynomial { coefficients }
}
}
impl ModPowerOf2NegAssign for NaturalPolynomial {
/// Negates a [`NaturalPolynomial`] modulo $2^k$, in place. The coefficients must already be
/// reduced modulo $2^k$.
///
/// See [`mod_power_of_2_neg`](ModPowerOf2Neg::mod_power_of_2_neg).
///
/// # 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 times
/// `pow`.
///
/// # Panics
/// Panics if any coefficient of `self` is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2NegAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("5*x^2+x+3").unwrap();
/// p.mod_power_of_2_neg_assign(3);
/// assert_eq!(p.to_string(), "3*x^2+7*x+5");
/// ```
#[inline]
fn mod_power_of_2_neg_assign(&mut self, pow: u64) {
assert_reduced(self, pow);
negate(&mut self.coefficients, pow);
}
}