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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, ModShl, ModShlAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
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 every coefficient by 2^bits mod m, which is computed once. A nonzero polynomial
// reduced modulo m has a leading coefficient that is at least 1 and less than m, so m is at least 2
// and 1 is reduced modulo m. Since m need not be odd, a product can be zero, so the result is
// trimmed.
fn mod_shl_assign<T: PrimitiveUnsigned + ModShl<U, T, Output = T>, U: PrimitiveUnsigned>(
p: &mut UnsignedPolynomial<T>,
bits: U,
m: T,
) {
assert_reduced(p, m);
if bits == U::ZERO || p.coefficients.is_empty() {
return;
}
let factor = T::ONE.mod_shl(bits, m);
for c in &mut p.coefficients {
*c = c.mod_mul(factor, m);
}
p.trim();
}
fn mod_shl_ref<T: PrimitiveUnsigned + ModShl<U, T, Output = T>, U: PrimitiveUnsigned>(
p: &UnsignedPolynomial<T>,
bits: U,
m: T,
) -> UnsignedPolynomial<T> {
assert_reduced(p, m);
if bits == U::ZERO || p.coefficients.is_empty() {
return p.clone();
}
let factor = T::ONE.mod_shl(bits, m);
let mut q = UnsignedPolynomial {
coefficients: p
.coefficients
.iter()
.map(|&c| c.mod_mul(factor, m))
.collect(),
};
q.trim();
q
}
macro_rules! impl_mod_shl_unsigned {
($t:ident) => {
impl<T: PrimitiveUnsigned + ModShl<$t, T, Output = T>> ModShl<$t, T>
for UnsignedPolynomial<T>
{
type Output = UnsignedPolynomial<T>;
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo `m`,
/// taking the polynomial by value. The coefficients must already be reduced modulo `m`.
///
/// $2^k \bmod m$ is computed once, and every coefficient is multiplied by it. Since `m`
/// need not be odd, coefficients can become zero, so the degree can drop.
///
/// $$
/// f(p, k, m) = 2^kp \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is
/// `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(mut self, bits: $t, m: T) -> UnsignedPolynomial<T> {
mod_shl_assign(&mut self, bits, m);
self
}
}
impl<T: PrimitiveUnsigned + ModShl<$t, T, Output = T>> ModShl<$t, T>
for &UnsignedPolynomial<T>
{
type Output = UnsignedPolynomial<T>;
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo `m`,
/// taking the polynomial by reference. The coefficients must already be reduced modulo
/// `m`.
///
/// $2^k \bmod m$ is computed once, and every coefficient is multiplied by it. Since `m`
/// need not be odd, coefficients can become zero, so the degree can drop.
///
/// $$
/// f(p, k, m) = 2^kp \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is
/// `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(self, bits: $t, m: T) -> UnsignedPolynomial<T> {
mod_shl_ref(self, bits, m)
}
}
impl<T: PrimitiveUnsigned + ModShl<$t, T, Output = T>> ModShlAssign<$t, T>
for UnsignedPolynomial<T>
{
/// Left-shifts an [`UnsignedPolynomial`] (multiplies it by a power of 2) modulo `m`, in
/// place. The coefficients must already be reduced modulo `m`.
///
/// $2^k \bmod m$ is computed once, and every coefficient is multiplied by it. Since `m`
/// need not be odd, coefficients can become zero, so the degree can drop.
///
/// $$
/// p \gets 2^kp \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n + m)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.len()`, and $m$ is
/// `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl_assign).
#[inline]
fn mod_shl_assign(&mut self, bits: $t, m: T) {
mod_shl_assign(self, bits, m);
}
}
};
}
apply_to_unsigneds!(impl_mod_shl_unsigned);