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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::natural::Natural;
use crate::natural_vector::NaturalVector;
use crate::natural_vector::arithmetic::mod_mul::{mod_mul_assign_unchecked, mod_mul_unchecked};
use malachite_base::num::arithmetic::traits::{ModIsReduced, ModShl, ModShlAssign};
use malachite_base::num::basic::traits::One;
use malachite_base::num::basic::unsigneds::PrimitiveUnsigned;
fn assert_reduced(v: &NaturalVector, m: &Natural) {
assert!(
v.mod_is_reduced(m),
"self must be reduced mod m, but {v} has an element >= {m}"
);
}
// Whether shifting changes nothing: a shift by 0, an empty vector, or a modulus of 1, modulo which
// every element is 0. Otherwise the vector has an element, which is less than `m`, so `m` is at
// least 2 and 1 is reduced modulo `m`.
fn is_unchanged<T: PrimitiveUnsigned>(v: &NaturalVector, bits: T, m: &Natural) -> bool {
bits == T::ZERO || v.elements.is_empty() || *m == 1u32
}
// Multiplies every element by 2^bits mod m, which is computed once.
fn mod_shl_assign<T: PrimitiveUnsigned>(v: &mut NaturalVector, bits: T, m: &Natural)
where
for<'a> Natural: ModShl<T, &'a Natural, Output = Natural>,
{
assert_reduced(v, m);
if !is_unchanged(v, bits, m) {
mod_mul_assign_unchecked(v, &Natural::ONE.mod_shl(bits, m), m);
}
}
fn mod_shl_ref<T: PrimitiveUnsigned>(v: &NaturalVector, bits: T, m: &Natural) -> NaturalVector
where
for<'a> Natural: ModShl<T, &'a Natural, Output = Natural>,
{
assert_reduced(v, m);
if is_unchanged(v, bits, m) {
return v.clone();
}
mod_mul_unchecked(v, &Natural::ONE.mod_shl(bits, m), m)
}
macro_rules! impl_mod_shl_unsigned {
($t:ident) => {
impl ModShl<$t, Natural> for NaturalVector {
type Output = NaturalVector;
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, taking
/// the vector by value and the modulus by value. The elements must already be reduced
/// modulo $m$.
///
/// $2^k \bmod m$ is computed once, and every element is multiplied by it, with the data
/// for multiplying modulo $m$ also computed once. Since $m$ need not be odd, elements
/// can become zero; the dimension is unchanged.
///
/// $$
/// f(v, k, m) = 2^kv \bmod m.
/// $$
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(m \\log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(mut self, bits: $t, m: Natural) -> NaturalVector {
mod_shl_assign(&mut self, bits, &m);
self
}
}
impl ModShl<$t, &Natural> for NaturalVector {
type Output = NaturalVector;
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, taking
/// the vector by value and the modulus by reference. The elements must already be
/// reduced modulo $m$.
///
/// See the documentation for the [`ModShl`] implementation that takes everything by
/// value for details.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(m \\log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(mut self, bits: $t, m: &Natural) -> NaturalVector {
mod_shl_assign(&mut self, bits, m);
self
}
}
impl ModShl<$t, Natural> for &NaturalVector {
type Output = NaturalVector;
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, taking
/// the vector by reference and the modulus by value. The elements must already be
/// reduced modulo $m$.
///
/// See the documentation for the [`ModShl`] implementation that takes everything by
/// value for details.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(self, bits: $t, m: Natural) -> NaturalVector {
mod_shl_ref(self, bits, &m)
}
}
impl ModShl<$t, &Natural> for &NaturalVector {
type Output = NaturalVector;
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, taking
/// the vector by reference and the modulus by reference. The elements must already be
/// reduced modulo $m$.
///
/// See the documentation for the [`ModShl`] implementation that takes everything by
/// value for details.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element of `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shl#mod_shl).
#[inline]
fn mod_shl(self, bits: $t, m: &Natural) -> NaturalVector {
mod_shl_ref(self, bits, m)
}
}
impl ModShlAssign<$t, Natural> for NaturalVector {
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, in
/// place, taking the modulus by value. The elements must already be reduced modulo $m$.
///
/// See the documentation for the [`ModShl`] implementation that takes everything by
/// value for details.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(m \\log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element 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: $t, m: Natural) {
mod_shl_assign(self, bits, &m);
}
}
impl ModShlAssign<$t, &Natural> for NaturalVector {
/// Left-shifts a [`NaturalVector`] (multiplies it by a power of 2) modulo $m$, in
/// place, taking the modulus by reference. The elements must already be reduced modulo
/// $m$.
///
/// See the documentation for the [`ModShl`] implementation that takes everything by
/// value for details.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(nm \log m \log\log m + km^2)$
///
/// $M(n, m) = O(m \\log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `self.dimension()`, $m$ is
/// `m.significant_bits()`, and $k$ is `bits.significant_bits()`.
///
/// # Panics
/// Panics if `m` is 0, or if any element 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: &Natural) {
mod_shl_assign(self, bits, m);
}
}
};
}
apply_to_unsigneds!(impl_mod_shl_unsigned);