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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, ModPowerOf2Shl, ModPowerOf2ShlAssign};
use crate::num::basic::traits::Zero;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::unsigned_polynomial::UnsignedPolynomial;
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 shift amount as a `u64`, or `None` if it is at least `pow`, in which case every coefficient
// becomes zero. `pow` is at most `T::WIDTH`, which is at most 128, so it fits in every unsigned
// type.
fn shift_below_pow<U: PrimitiveUnsigned>(bits: U, pow: u64) -> Option<u64> {
if bits >= U::exact_from(pow) {
None
} else {
Some(bits.exact_into())
}
}
// Shifts every coefficient left by `bits` modulo 2^pow: only the low `pow - bits` bits of each
// survive, so the shift cannot overflow, a coefficient can become zero, and the result is trimmed.
fn mod_power_of_2_shl_ref<T: PrimitiveUnsigned, U: PrimitiveUnsigned>(
p: &UnsignedPolynomial<T>,
bits: U,
pow: u64,
) -> UnsignedPolynomial<T> {
assert_reduced(p, pow);
let Some(bits) = shift_below_pow(bits, pow) else {
return UnsignedPolynomial::ZERO;
};
let mut q = UnsignedPolynomial {
coefficients: p
.coefficients
.iter()
.map(|&c| c.mod_power_of_2(pow - bits) << bits)
.collect(),
};
q.trim();
q
}
fn mod_power_of_2_shl_assign<T: PrimitiveUnsigned, U: PrimitiveUnsigned>(
p: &mut UnsignedPolynomial<T>,
bits: U,
pow: u64,
) {
assert_reduced(p, pow);
let Some(bits) = shift_below_pow(bits, pow) else {
p.coefficients.clear();
return;
};
if bits != 0 {
for c in &mut p.coefficients {
*c = c.mod_power_of_2(pow - bits) << bits;
}
p.trim();
}
}
macro_rules! impl_mod_power_of_2_shl_unsigned {
($t:ident) => {
impl<T: PrimitiveUnsigned> ModPowerOf2Shl<$t> for UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo $2^k$,
/// taking the polynomial by value. The coefficients must already be reduced modulo
/// $2^k$.
///
/// Every coefficient is shifted and reduced. Coefficients can become zero, so the
/// degree can drop; if `bits` is at least `pow`, the result is zero.
///
/// $$
/// f(p, m, k) = 2^mp \bmod 2^k.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is
/// greater than or equal to $2^k$.
///
/// # Examples
/// See [here](super::mod_power_of_2_shl#mod_power_of_2_shl).
#[inline]
fn mod_power_of_2_shl(mut self, bits: $t, pow: u64) -> UnsignedPolynomial<T> {
mod_power_of_2_shl_assign(&mut self, bits, pow);
self
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2Shl<$t> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo $2^k$,
/// taking the polynomial by reference. The coefficients must already be reduced modulo
/// $2^k$.
///
/// Every coefficient is shifted and reduced. Coefficients can become zero, so the
/// degree can drop; if `bits` is at least `pow`, the result is zero.
///
/// $$
/// f(p, m, k) = 2^mp \bmod 2^k.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is
/// greater than or equal to $2^k$.
///
/// # Examples
/// See [here](super::mod_power_of_2_shl#mod_power_of_2_shl).
#[inline]
fn mod_power_of_2_shl(self, bits: $t, pow: u64) -> UnsignedPolynomial<T> {
mod_power_of_2_shl_ref(self, bits, pow)
}
}
impl<T: PrimitiveUnsigned> ModPowerOf2ShlAssign<$t> for UnsignedPolynomial<T> {
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo $2^k$,
/// in place. The coefficients must already be reduced modulo $2^k$.
///
/// Every coefficient is shifted and reduced. Coefficients can become zero, so the
/// degree can drop; if `bits` is at least `pow`, the result is zero.
///
/// $$
/// p \gets 2^mp \bmod 2^k.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `pow` is greater than `T::WIDTH`, or if any coefficient of `self` is
/// greater than or equal to $2^k$.
///
/// # Examples
/// See [here](super::mod_power_of_2_shl#mod_power_of_2_shl_assign).
#[inline]
fn mod_power_of_2_shl_assign(&mut self, bits: $t, pow: u64) {
mod_power_of_2_shl_assign(self, bits, pow);
}
}
};
}
apply_to_unsigneds!(impl_mod_power_of_2_shl_unsigned);