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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::{
ModPowerOf2, ModPowerOf2Assign, ModPowerOf2IsReduced,
};
use malachite_base::polynomial::{ModPowerOf2Derivative, ModPowerOf2DerivativeAssign};
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}"
);
}
// Multiplies the coefficient of x^i, for i at least 1, by i, reduces it modulo 2^pow, and moves it
// to x^(i-1). The products can be zero, so the result is trimmed.
fn mod_power_of_2_derivative_ref(p: &NaturalPolynomial, pow: u64) -> NaturalPolynomial {
assert_reduced(p, pow);
let mut q = NaturalPolynomial {
coefficients: p
.coefficients
.iter()
.enumerate()
.skip(1)
.map(|(i, c)| (c * Natural::from(i)).mod_power_of_2(pow))
.collect(),
};
q.trim();
q
}
fn mod_power_of_2_derivative_in_place(p: &mut NaturalPolynomial, pow: u64) {
assert_reduced(p, pow);
if p.coefficients.is_empty() {
return;
}
p.coefficients.remove(0);
for (i, c) in p.coefficients.iter_mut().enumerate() {
*c *= Natural::from(i + 1);
c.mod_power_of_2_assign(pow);
}
p.trim();
}
impl ModPowerOf2Derivative for NaturalPolynomial {
type Output = Self;
/// Computes the derivative of a [`NaturalPolynomial`] modulo $2^k$, taking the polynomial by
/// value. The coefficients must already be reduced modulo $2^k$.
///
/// $$
/// f(p, k) = p' \bmod 2^k.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$, reduced, and moved to $x^{i-1}$. Since $ia_i$
/// can be divisible by the modulus even when $a_i$ is not zero, the derivative can lose any
/// number of degrees. A constant polynomial, including zero, has derivative zero.
///
/// # 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::polynomial::ModPowerOf2Derivative;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+1").unwrap();
/// assert_eq!(p.mod_power_of_2_derivative(2).to_string(), "3*x^2+2*x+2");
///
/// let p = NaturalPolynomial::from_str("x^5+x").unwrap();
/// assert_eq!(p.mod_power_of_2_derivative(1).to_string(), "x^4+1");
///
/// // The derivative can lose more than one degree.
/// let p = NaturalPolynomial::from_str("x^4+x^3+1").unwrap();
/// assert_eq!(p.mod_power_of_2_derivative(1).to_string(), "x^2");
/// ```
///
/// This is equivalent to `fmpz_mod_poly_derivative` from `fmpz_mod_poly/derivative.c`, FLINT
/// 3.6.0, with the modulus $2^k$.
#[inline]
fn mod_power_of_2_derivative(mut self, pow: u64) -> Self {
mod_power_of_2_derivative_in_place(&mut self, pow);
self
}
}
impl ModPowerOf2Derivative for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Computes the derivative of a [`NaturalPolynomial`] modulo $2^k$, taking the polynomial by
/// reference. The coefficients must already be reduced modulo $2^k$.
///
/// $$
/// f(p, k) = p' \bmod 2^k.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$, reduced, and moved to $x^{i-1}$. Since $ia_i$
/// can be divisible by the modulus even when $a_i$ is not zero, the derivative can lose any
/// number of degrees. A constant polynomial, including zero, has derivative zero.
///
/// # 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::polynomial::ModPowerOf2Derivative;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+1").unwrap();
/// assert_eq!((&p).mod_power_of_2_derivative(2).to_string(), "3*x^2+2*x+2");
///
/// let p = NaturalPolynomial::from_str("x^5+x").unwrap();
/// assert_eq!((&p).mod_power_of_2_derivative(1).to_string(), "x^4+1");
///
/// // The derivative can lose more than one degree.
/// let p = NaturalPolynomial::from_str("x^4+x^3+1").unwrap();
/// assert_eq!((&p).mod_power_of_2_derivative(1).to_string(), "x^2");
/// ```
///
/// This is equivalent to `fmpz_mod_poly_derivative` from `fmpz_mod_poly/derivative.c`, FLINT
/// 3.6.0, with the modulus $2^k$.
#[inline]
fn mod_power_of_2_derivative(self, pow: u64) -> NaturalPolynomial {
mod_power_of_2_derivative_ref(self, pow)
}
}
impl ModPowerOf2DerivativeAssign for NaturalPolynomial {
/// Replaces a [`NaturalPolynomial`] with its derivative modulo $2^k$, in place. The
/// coefficients must already be reduced modulo $2^k$.
///
/// $$
/// p \gets p' \bmod 2^k.
/// $$
///
/// The coefficient of $x^i$ is multiplied by $i$, reduced, and moved to $x^{i-1}$. Since $ia_i$
/// can be divisible by the modulus even when $a_i$ is not zero, the derivative can lose any
/// number of degrees. A constant polynomial, including zero, has derivative zero.
///
/// # 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::polynomial::ModPowerOf2DerivativeAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^3+3*x^2+2*x+1").unwrap();
/// p.mod_power_of_2_derivative_assign(2);
/// assert_eq!(p.to_string(), "3*x^2+2*x+2");
///
/// let mut p = NaturalPolynomial::from_str("x^5+x").unwrap();
/// p.mod_power_of_2_derivative_assign(1);
/// assert_eq!(p.to_string(), "x^4+1");
///
/// // The derivative can lose more than one degree.
/// let mut p = NaturalPolynomial::from_str("x^4+x^3+1").unwrap();
/// p.mod_power_of_2_derivative_assign(1);
/// assert_eq!(p.to_string(), "x^2");
/// ```
///
/// This is equivalent to `fmpz_mod_poly_derivative` from `fmpz_mod_poly/derivative.c`, FLINT
/// 3.6.0, with the modulus $2^k$.
#[inline]
fn mod_power_of_2_derivative_assign(&mut self, pow: u64) {
mod_power_of_2_derivative_in_place(self, pow);
}
}