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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::num::arithmetic::traits::ModIsReduced;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::polynomial::{ModDerivative, ModDerivativeAssign};
use crate::unsigned_polynomial::UnsignedPolynomial;
fn assert_reduced<T: PrimitiveUnsigned>(p: &UnsignedPolynomial<T>, m: T) {
assert!(
p.mod_is_reduced(&m),
"self must be reduced mod m, but {p} has a coefficient >= {m}"
);
}
// Multiplies the coefficient of x^i, for i at least 1, by i mod m, which is kept as a running
// counter so that no index needs converting to `T`, and moves it to x^(i-1). The products can be
// zero, so the result is trimmed.
fn mod_derivative_ref<T: PrimitiveUnsigned>(
p: &UnsignedPolynomial<T>,
m: T,
) -> UnsignedPolynomial<T> {
assert_reduced(p, m);
let mut i = T::ZERO;
let mut q = UnsignedPolynomial {
coefficients: p
.coefficients
.iter()
.skip(1)
.map(|&c| {
i += T::ONE;
if i == m {
i = T::ZERO;
}
c.mod_mul(i, m)
})
.collect(),
};
q.trim();
q
}
fn mod_derivative_in_place<T: PrimitiveUnsigned>(p: &mut UnsignedPolynomial<T>, m: T) {
assert_reduced(p, m);
if p.coefficients.is_empty() {
return;
}
p.coefficients.remove(0);
let mut i = T::ZERO;
for c in &mut p.coefficients {
i += T::ONE;
if i == m {
i = T::ZERO;
}
c.mod_mul_assign(i, m);
}
p.trim();
}
impl<T: PrimitiveUnsigned> ModDerivative<T> for UnsignedPolynomial<T> {
type Output = Self;
/// Computes the derivative of an [`UnsignedPolynomial`] modulo `m`, taking the polynomial by
/// value. The coefficients must already be reduced modulo `m`.
///
/// $$
/// f(p, m) = p' \bmod m.
/// $$
///
/// 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 `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ModDerivative;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!(p.mod_derivative(6).to_string(), "3*x^2+2");
///
/// // The derivative can lose more than one degree.
/// let p = UnsignedPolynomial::<u8>::from_str("x^3+2*x+1").unwrap();
/// assert_eq!(p.mod_derivative(3).to_string(), "2");
/// ```
///
/// This is equivalent to `nmod_poly_derivative` from `nmod_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn mod_derivative(mut self, m: T) -> Self {
mod_derivative_in_place(&mut self, m);
self
}
}
impl<T: PrimitiveUnsigned> ModDerivative<T> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Computes the derivative of an [`UnsignedPolynomial`] modulo `m`, taking the polynomial by
/// reference. The coefficients must already be reduced modulo `m`.
///
/// $$
/// f(p, m) = p' \bmod m.
/// $$
///
/// 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 `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ModDerivative;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u8>::from_str("x^3+3*x^2+2*x+5").unwrap();
/// assert_eq!((&p).mod_derivative(6).to_string(), "3*x^2+2");
///
/// // The derivative can lose more than one degree.
/// let p = UnsignedPolynomial::<u8>::from_str("x^3+2*x+1").unwrap();
/// assert_eq!((&p).mod_derivative(3).to_string(), "2");
/// ```
///
/// This is equivalent to `nmod_poly_derivative` from `nmod_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn mod_derivative(self, m: T) -> UnsignedPolynomial<T> {
mod_derivative_ref(self, m)
}
}
impl<T: PrimitiveUnsigned> ModDerivativeAssign<T> for UnsignedPolynomial<T> {
/// Replaces an [`UnsignedPolynomial`] with its derivative modulo `m`, in place. The
/// coefficients must already be reduced modulo `m`.
///
/// $$
/// p \gets p' \bmod m.
/// $$
///
/// 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 `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ModDerivativeAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("x^3+3*x^2+2*x+5").unwrap();
/// p.mod_derivative_assign(6);
/// assert_eq!(p.to_string(), "3*x^2+2");
///
/// // The derivative can lose more than one degree.
/// let mut p = UnsignedPolynomial::<u8>::from_str("x^3+2*x+1").unwrap();
/// p.mod_derivative_assign(3);
/// assert_eq!(p.to_string(), "2");
/// ```
///
/// This is equivalent to `nmod_poly_derivative` from `nmod_poly/derivative.c`, FLINT 3.6.0.
#[inline]
fn mod_derivative_assign(&mut self, m: T) {
mod_derivative_in_place(self, m);
}
}