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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 core::cmp::Ordering::*;
use core::ops::{Shr, ShrAssign};
use malachite_base::num::arithmetic::traits::{
ModMul, ModMulAssign, ModPow, ModShr, ModShrAssign, UnsignedAbs,
};
use malachite_base::num::basic::signeds::PrimitiveSigned;
use malachite_base::num::basic::traits::{One, Two, Zero};
fn mod_shr_ref_val<'a, U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
x: &'a Natural,
bits: S,
m: Natural,
) -> Natural
where
Natural: From<U>,
&'a Natural: Shr<U, Output = Natural>,
{
assert!(*x < m, "x must be reduced mod m, but {x} >= {m}");
let bits_abs = bits.unsigned_abs();
match bits.cmp(&S::ZERO) {
Equal => x.clone(),
Greater => x >> bits_abs,
Less => match m {
Natural::ONE | Natural::TWO => Natural::ZERO,
_ => x.mod_mul(Natural::TWO.mod_pow(Natural::from(bits_abs), &m), m),
},
}
}
fn mod_shr_ref_ref<'a, U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
x: &'a Natural,
bits: S,
m: &Natural,
) -> Natural
where
Natural: From<U>,
&'a Natural: Shr<U, Output = Natural>,
{
assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
let bits_abs = bits.unsigned_abs();
match bits.cmp(&S::ZERO) {
Equal => x.clone(),
Greater => x >> bits_abs,
Less => match m {
&Natural::ONE | &Natural::TWO => Natural::ZERO,
_ => x.mod_mul(Natural::TWO.mod_pow(Natural::from(bits_abs), m), m),
},
}
}
fn mod_shr_assign<U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
x: &mut Natural,
bits: S,
m: Natural,
) where
Natural: From<U> + ShrAssign<U>,
{
assert!(*x < m, "x must be reduced mod m, but {x} >= {m}");
let bits_abs = bits.unsigned_abs();
match bits.cmp(&S::ZERO) {
Equal => {}
Greater => *x >>= bits_abs,
Less => match m {
Natural::ONE | Natural::TWO => *x = Natural::ZERO,
_ => x.mod_mul_assign(Natural::TWO.mod_pow(Natural::from(bits_abs), &m), m),
},
}
}
fn mod_shr_assign_ref<U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
x: &mut Natural,
bits: S,
m: &Natural,
) where
Natural: From<U> + ShrAssign<U>,
{
assert!(*x < *m, "x must be reduced mod m, but {x} >= {m}");
let bits_abs = bits.unsigned_abs();
match bits.cmp(&S::ZERO) {
Equal => {}
Greater => *x >>= bits_abs,
Less => match m {
&Natural::ONE | &Natural::TWO => *x = Natural::ZERO,
_ => x.mod_mul_assign(Natural::TWO.mod_pow(Natural::from(bits_abs), m), m),
},
}
}
macro_rules! impl_mod_shr {
($t:ident) => {
impl ModShr<$t, Natural> for Natural {
type Output = Natural;
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$. The first [`Natural`] must be already reduced modulo $m$. Both [`Natural`]s are
/// taken by value.
///
/// $f(x, n, m) = y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr).
#[inline]
fn mod_shr(mut self, bits: $t, m: Natural) -> Natural {
self.mod_shr_assign(bits, m);
self
}
}
impl<'a> ModShr<$t, &'a Natural> for Natural {
type Output = Natural;
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$. The first [`Natural`] must be already reduced modulo $m$. The first [`Natural`]
/// is taken by value and the second by reference.
///
/// $f(x, n, m) = y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr).
#[inline]
fn mod_shr(mut self, bits: $t, m: &'a Natural) -> Natural {
self.mod_shr_assign(bits, m);
self
}
}
impl ModShr<$t, Natural> for &Natural {
type Output = Natural;
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$. The first [`Natural`] must be already reduced modulo $m$. The first [`Natural`]
/// is taken by reference and the second by value.
///
/// $f(x, n, m) = y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr).
#[inline]
fn mod_shr(self, bits: $t, m: Natural) -> Natural {
mod_shr_ref_val(self, bits, m)
}
}
impl ModShr<$t, &Natural> for &Natural {
type Output = Natural;
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$. The first [`Natural`] must be already reduced modulo $m$. Both [`Natural`]s are
/// taken by reference.
///
/// $f(x, n, m) = y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr).
#[inline]
fn mod_shr(self, bits: $t, m: &Natural) -> Natural {
mod_shr_ref_ref(self, bits, m)
}
}
impl ModShrAssign<$t, Natural> for Natural {
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$, in place. The first [`Natural`] must be already reduced modulo $m$. The
/// [`Natural`] on the right-hand side is taken by value.
///
/// $x \gets y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr_assign).
#[inline]
fn mod_shr_assign(&mut self, bits: $t, m: Natural) {
mod_shr_assign(self, bits, m);
}
}
impl<'a> ModShrAssign<$t, &'a Natural> for Natural {
/// Right-shifts a [`Natural`] (divides it by a power of 2) modulo another [`Natural`]
/// $m$, in place. The first [`Natural`] must be already reduced modulo $m$. The
/// [`Natural`] on the right-hand side is taken by reference.
///
/// $x \gets y$, where $x, y < m$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod m$.
///
/// # Worst-case complexity
/// $T(n, m) = O(mn \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `m.significant_bits()`, and $m$
/// is `bits`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// See [here](super::mod_shr#mod_shr_assign).
#[inline]
fn mod_shr_assign(&mut self, bits: $t, m: &'a Natural) {
mod_shr_assign_ref(self, bits, m);
}
}
};
}
apply_to_signeds!(impl_mod_shr);