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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;
use crate::num::basic::traits::Zero;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::{ExactFrom, SaturatingFrom};
use crate::polynomial::{
ModPowerOf2PowTruncated, ModPowerOf2PowTruncatedAssign, Polynomial, pow_binexp_trimmed,
};
use crate::unsigned_polynomial::UnsignedPolynomial;
use crate::unsigned_polynomial::arithmetic::mod_power_of_2_mul_truncated::*;
use crate::unsigned_polynomial::arithmetic::mod_power_of_2_square_truncated::*;
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, a nonzero first element,
// and coefficients reduced modulo $2^k$, keeping only the coefficients of $x^i$ for $i$ less than
// `len`, which is at least 2, where `e` is at least 3, by binary exponentiation with truncated
// squaring and multiplication, each reduced and trimmed.
//
// This is equivalent to `_nmod_poly_pow_trunc_binexp` from `nmod_poly/pow_trunc.c`, FLINT 3.6.0,
// with the modulus $2^k$, except that the polynomial is not padded to length `len` and the
// intermediate powers are trimmed.
crate_test_fn! {mod_power_of_2_pow_truncated_binexp<T: PrimitiveUnsigned>(
xs: &[T],
e: u64,
len: u64,
pow: u64,
) -> Vec<T> {
pow_binexp_trimmed(
xs,
e,
|r| mod_power_of_2_square_truncated_helper(r, len, pow).into_coefficients_asc(),
|r, xs| mod_power_of_2_mul_truncated_helper(r, xs, len, 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 $2^k$, keeping only the coefficients of
// $x^i$ for $i$ less than `len`.
//
// Writing the polynomial modulo $x^n$ as $x^\ell q$, with $q_0 \neq 0$, its power is $x^{e\ell}
// (q^e \bmod x^{n - e\ell})$, or 0 if $e\ell \geq n$.
//
// This is equivalent to `nmod_poly_pow_trunc` from `nmod_poly/pow_trunc.c`, FLINT 3.6.0, with the
// modulus $2^k$, except for the removal of the factor of $x^\ell$, and except that the zeroth power
// of the zero polynomial is 1, where FLINT gives 0.
fn mod_power_of_2_pow_truncated_helper<T: PrimitiveUnsigned>(
xs: &[T],
e: u64,
len: u64,
pow: u64,
) -> UnsignedPolynomial<T> {
if pow == 0 || len == 0 {
return UnsignedPolynomial::ZERO;
}
if e == 0 {
return UnsignedPolynomial::one();
}
let n = usize::saturating_from(len);
let xs = &xs[..xs.len().min(n)];
let Some(low) = xs.iter().position(|&x| x != T::ZERO) else {
return UnsignedPolynomial::ZERO;
};
let shift = usize::saturating_from(e).saturating_mul(low);
if shift >= n {
return UnsignedPolynomial::ZERO;
}
let q = &xs[low..];
let q_len = n - shift;
let q_len_u64 = u64::exact_from(q_len);
let mut power = match (q.len().min(q_len), e) {
(1, _) => {
let c = q[0].mod_power_of_2_pow(e, pow);
if c == T::ZERO { Vec::new() } else { vec![c] }
}
(m, 1) => {
let mut power = q[..m].to_vec();
while power.last() == Some(&T::ZERO) {
power.pop();
}
power
}
(_, 2) => mod_power_of_2_square_truncated_helper(q, q_len_u64, pow).into_coefficients_asc(),
_ => mod_power_of_2_pow_truncated_binexp(q, e, q_len_u64, pow),
};
if power.is_empty() {
return UnsignedPolynomial::ZERO;
}
power.splice(0..0, core::iter::repeat_n(T::ZERO, shift));
UnsignedPolynomial {
coefficients: power,
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2PowTruncated for UnsignedPolynomial<T> {
type Output = Self;
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$, keeping only the coefficients of
/// $x^i$ for $i$ less than `len`, taking it by value. Its coefficients must already be reduced
/// modulo $2^k$.
///
/// $$
/// f(p, e, n, k) = (p^e \bmod x^n) \bmod 2^k.
/// $$
///
/// The polynomial need not already be truncated: only its first `len` coefficients are read.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0 and reduced to 0
/// when $k$ is 0. The power is computed by repeated truncated 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 `len`, 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::polynomial::ModPowerOf2PowTruncated;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(
/// (UnsignedPolynomial::<u8>::from_str("x+1").unwrap())
/// .mod_power_of_2_pow_truncated(5, 3, 3)
/// .to_string(),
/// "2*x^2+5*x+1"
/// );
/// // The power is a multiple of x^4.
/// assert_eq!(
/// (UnsignedPolynomial::<u8>::from_str("x^2+x").unwrap())
/// .mod_power_of_2_pow_truncated(4, 4, 3)
/// .to_string(),
/// "0"
/// );
/// ```
///
/// This is equivalent to `nmod_poly_pow_trunc` from `nmod_poly/pow_trunc.c`, FLINT 3.6.0, with
/// the modulus $2^k$, except that a factor of $x^\ell$ is removed before powering, that the
/// intermediate powers are trimmed rather than padded to `len`, and that the zeroth power of
/// the zero polynomial is 1 (modulo $2^k$), where FLINT gives 0.
#[inline]
fn mod_power_of_2_pow_truncated(mut self, exp: u64, len: u64, pow: u64) -> Self {
self.mod_power_of_2_pow_truncated_assign(exp, len, pow);
self
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2PowTruncated for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$, keeping only the coefficients of
/// $x^i$ for $i$ less than `len`, taking it by reference. Its coefficients must already be
/// reduced modulo $2^k$.
///
/// $$
/// f(p, e, n, k) = (p^e \bmod x^n) \bmod 2^k.
/// $$
///
/// The polynomial need not already be truncated: only its first `len` coefficients are read.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0 and reduced to 0
/// when $k$ is 0. The power is computed by repeated truncated 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 `len`, 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::polynomial::ModPowerOf2PowTruncated;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::from_str("x+1").unwrap())
/// .mod_power_of_2_pow_truncated(5, 3, 3)
/// .to_string(),
/// "2*x^2+5*x+1"
/// );
/// // The power is a multiple of x^4.
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::from_str("x^2+x").unwrap())
/// .mod_power_of_2_pow_truncated(4, 4, 3)
/// .to_string(),
/// "0"
/// );
/// ```
///
/// This is equivalent to `nmod_poly_pow_trunc` from `nmod_poly/pow_trunc.c`, FLINT 3.6.0, with
/// the modulus $2^k$, except that a factor of $x^\ell$ is removed before powering, that the
/// intermediate powers are trimmed rather than padded to `len`, and that the zeroth power of
/// the zero polynomial is 1 (modulo $2^k$), where FLINT gives 0.
fn mod_power_of_2_pow_truncated(self, exp: u64, len: u64, pow: u64) -> UnsignedPolynomial<T> {
assert_reduced(self, pow);
mod_power_of_2_pow_truncated_helper(&self.coefficients, exp, len, pow)
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2PowTruncatedAssign for UnsignedPolynomial<T> {
/// Raises an [`UnsignedPolynomial`] to a power modulo $2^k$ in place, keeping only the
/// coefficients of $x^i$ for $i$ less than `len`. Its coefficients must already be reduced
/// modulo $2^k$.
///
/// $$
/// p \gets (p^e \bmod x^n) \bmod 2^k.
/// $$
///
/// The polynomial need not already be truncated: only its first `len` coefficients are read.
/// The zeroth power of every polynomial is 1, truncated to 0 when `len` is 0 and reduced to 0
/// when $k$ is 0. The power is computed by repeated truncated 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 `len`, 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::polynomial::ModPowerOf2PowTruncatedAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("x+1").unwrap();
/// p.mod_power_of_2_pow_truncated_assign(5, 3, 3);
/// assert_eq!(p.to_string(), "2*x^2+5*x+1");
///
/// // The power is a multiple of x^4.
/// let mut p = UnsignedPolynomial::<u8>::from_str("x^2+x").unwrap();
/// p.mod_power_of_2_pow_truncated_assign(4, 4, 3);
/// assert_eq!(p.to_string(), "0");
/// ```
///
/// This is equivalent to `nmod_poly_pow_trunc` from `nmod_poly/pow_trunc.c`, FLINT 3.6.0, with
/// the modulus $2^k$, except that a factor of $x^\ell$ is removed before powering, that the
/// intermediate powers are trimmed rather than padded to `len`, and that the zeroth power of
/// the zero polynomial is 1 (modulo $2^k$), where FLINT gives 0.
fn mod_power_of_2_pow_truncated_assign(&mut self, exp: u64, len: u64, pow: u64) {
assert_reduced(self, pow);
let xs = &mut self.coefficients;
match (xs.len(), exp, len, pow) {
(_, _, 0, _) | (_, _, _, 0) => xs.clear(),
(0, 0, _, _) => xs.push(T::ONE),
(_, 0, _, _) => {
xs.truncate(1);
xs[0] = T::ONE;
}
(0, _, _, _) => {}
(_, 1, _, _) => self.truncate_assign(len),
(1, _, _, _) => {
xs[0].mod_power_of_2_pow_assign(exp, pow);
if xs[0] == T::ZERO {
xs.clear();
}
}
_ => *self = mod_power_of_2_pow_truncated_helper(xs, exp, len, pow),
}
}
}