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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::{ModPowerOf2IsReduced, ModPowerOf2Pow, ModPowerOf2PowAssign};
use crate::num::basic::traits::Zero;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::ExactFrom;
use crate::polynomial::{Polynomial, pow_binexp_trimmed};
use crate::unsigned_polynomial::UnsignedPolynomial;
use crate::unsigned_polynomial::arithmetic::mod_power_of_2_mul::mod_power_of_2_mul_helper;
use crate::unsigned_polynomial::arithmetic::mod_power_of_2_square::mod_power_of_2_square_helper;
use alloc::vec;
use alloc::vec::Vec;
fn assert_reduced<T: PrimitiveUnsigned>(p: &UnsignedPolynomial<T>, pow: u64) {
assert!(pow <= T::WIDTH);
assert!(
p.mod_power_of_2_is_reduced(pow),
"self must be reduced mod 2^pow, but {p} has a coefficient >= 2^{pow}"
);
}
// The coefficients, without zeros at the end, of the `e`th power modulo $2^k$, where $k$ is `pow`,
// of the polynomial with coefficients `xs`, which has length at least 2, nonzero first and last
// elements, and coefficients reduced modulo $2^k$, where `e` is at least 3, by binary
// exponentiation: each square and product is reduced and trimmed, so the intermediate powers shrink
// when leading coefficients vanish modulo $2^k$.
//
// This is equivalent to `_nmod_poly_pow_binexp` from `nmod_poly/pow_binexp.c`, FLINT 3.6.0, with
// the modulus $2^k$, except that the intermediate powers are trimmed.
crate_test_fn! {mod_power_of_2_pow_binexp<T: PrimitiveUnsigned>(
xs: &[T],
e: u64,
pow: u64,
) -> Vec<T> {
pow_binexp_trimmed(
xs,
e,
|r| mod_power_of_2_square_helper(r, pow).into_coefficients_asc(),
|r, xs| mod_power_of_2_mul_helper(r, xs, pow).into_coefficients_asc(),
)
}}
// The `e`th power modulo $2^k$, where $k$ is `pow`, of the polynomial with coefficients `xs`, which
// has no zeros at the end and coefficients reduced modulo $2^k$.
//
// Writing the polynomial as $x^\ell q$, with $q_0 \neq 0$, its power is $x^{e\ell} q^e$.
//
// This is equivalent to `nmod_poly_pow` from `nmod_poly/pow.c`, FLINT 3.6.0, with the modulus
// $2^k$, except for the removal of the factor of $x^\ell$.
fn mod_power_of_2_pow_helper<T: PrimitiveUnsigned>(
xs: &[T],
e: u64,
pow: u64,
) -> UnsignedPolynomial<T> {
if pow == 0 {
return UnsignedPolynomial::ZERO;
}
if e == 0 {
return UnsignedPolynomial::one();
}
let Some(low) = xs.iter().position(|&x| x != T::ZERO) else {
return UnsignedPolynomial::ZERO;
};
let q = &xs[low..];
let mut power = match (q.len(), e) {
(1, _) => {
let c = q[0].mod_power_of_2_pow(e, pow);
if c == T::ZERO { Vec::new() } else { vec![c] }
}
(_, 1) => q.to_vec(),
(_, 2) => mod_power_of_2_square_helper(q, pow).into_coefficients_asc(),
_ => mod_power_of_2_pow_binexp(q, e, pow),
};
if power.is_empty() {
return UnsignedPolynomial::ZERO;
}
if low != 0 {
let shift = usize::exact_from(e)
.checked_mul(low)
.expect("the power has too many coefficients to represent");
power.splice(0..0, core::iter::repeat_n(T::ZERO, shift));
}
UnsignedPolynomial {
coefficients: power,
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2Pow<u64> for UnsignedPolynomial<T> {
type Output = Self;
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$, taking it by value. Its
/// coefficients must already be reduced modulo $2^k$.
///
/// $$
/// f(p, e, k) = p^e \bmod 2^k.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1, which is 0 modulo $2^0$. The
/// leading coefficients of a power can vanish modulo $2^k$, and then its degree is lower than
/// $e$ times the degree of the polynomial. The power is computed by repeated squaring modulo
/// $2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n^{\log_2 3} \log e)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, and $e$ is `exp`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is greater than
/// or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Pow;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(
/// (UnsignedPolynomial::<u8>::from_str("x+1").unwrap())
/// .mod_power_of_2_pow(5, 3)
/// .to_string(),
/// "x^5+5*x^4+2*x^3+2*x^2+5*x+1"
/// );
/// // The square of 2*x+1 is 4*x^2+4*x+1, which is 1 modulo 4.
/// assert_eq!(
/// (UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap())
/// .mod_power_of_2_pow(2, 2)
/// .to_string(),
/// "1"
/// );
/// ```
///
/// This is equivalent to `nmod_poly_pow` from `nmod_poly/pow.c`, FLINT 3.6.0, with the modulus
/// $2^k$, except that a factor of $x^\ell$ is removed before powering and that the intermediate
/// powers are trimmed.
#[inline]
fn mod_power_of_2_pow(mut self, exp: u64, pow: u64) -> Self {
self.mod_power_of_2_pow_assign(exp, pow);
self
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2Pow<u64> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$, taking it by reference. Its
/// coefficients must already be reduced modulo $2^k$.
///
/// $$
/// f(p, e, k) = p^e \bmod 2^k.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1, which is 0 modulo $2^0$. The
/// leading coefficients of a power can vanish modulo $2^k$, and then its degree is lower than
/// $e$ times the degree of the polynomial. The power is computed by repeated squaring modulo
/// $2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n^{\log_2 3} \log e)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, and $e$ is `exp`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is greater than
/// or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Pow;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::from_str("x+1").unwrap())
/// .mod_power_of_2_pow(5, 3)
/// .to_string(),
/// "x^5+5*x^4+2*x^3+2*x^2+5*x+1"
/// );
/// // The square of 2*x+1 is 4*x^2+4*x+1, which is 1 modulo 4.
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap())
/// .mod_power_of_2_pow(2, 2)
/// .to_string(),
/// "1"
/// );
/// ```
///
/// This is equivalent to `nmod_poly_pow` from `nmod_poly/pow.c`, FLINT 3.6.0, with the modulus
/// $2^k$, except that a factor of $x^\ell$ is removed before powering and that the intermediate
/// powers are trimmed.
fn mod_power_of_2_pow(self, exp: u64, pow: u64) -> UnsignedPolynomial<T> {
assert_reduced(self, pow);
mod_power_of_2_pow_helper(&self.coefficients, exp, pow)
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2PowAssign<u64> for UnsignedPolynomial<T> {
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$ in place. Its coefficients must
/// already be reduced modulo $2^k$.
///
/// $$
/// p \gets p^e \bmod 2^k.
/// $$
///
/// The zeroth power of every polynomial, including 0, is 1, which is 0 modulo $2^0$. The
/// leading coefficients of a power can vanish modulo $2^k$, and then its degree is lower than
/// $e$ times the degree of the polynomial. The power is computed by repeated squaring modulo
/// $2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n^{\log_2 3} \log e)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `exp` times the length of the
/// polynomial, and $e$ is `exp`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is greater than
/// or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2PowAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("x+1").unwrap();
/// p.mod_power_of_2_pow_assign(5, 3);
/// assert_eq!(p.to_string(), "x^5+5*x^4+2*x^3+2*x^2+5*x+1");
///
/// // The square of 2*x+1 is 4*x^2+4*x+1, which is 1 modulo 4.
/// let mut p = UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap();
/// p.mod_power_of_2_pow_assign(2, 2);
/// assert_eq!(p.to_string(), "1");
/// ```
///
/// This is equivalent to `nmod_poly_pow` from `nmod_poly/pow.c`, FLINT 3.6.0, with the modulus
/// $2^k$, except that a factor of $x^\ell$ is removed before powering and that the intermediate
/// powers are trimmed.
fn mod_power_of_2_pow_assign(&mut self, exp: u64, pow: u64) {
assert_reduced(self, pow);
let xs = &mut self.coefficients;
match (xs.len(), exp, pow) {
(_, _, 0) => xs.clear(),
(0, 0, _) => xs.push(T::ONE),
(_, 0, _) => {
xs.truncate(1);
xs[0] = T::ONE;
}
(0, _, _) | (_, 1, _) => {}
(1, _, _) => {
xs[0].mod_power_of_2_pow_assign(exp, pow);
if xs[0] == T::ZERO {
xs.clear();
}
}
_ => *self = mod_power_of_2_pow_helper(xs, exp, pow),
}
}
}