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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::rational_polynomial::RationalPolynomial;
use core::mem::replace;
use core::ops::{Shl, ShlAssign, Shr, ShrAssign};
use malachite_base::num::arithmetic::traits::{Parity, UnsignedAbs};
use malachite_base::num::basic::signeds::PrimitiveSigned;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::polynomial::Polynomial;
use malachite_nz::integer::Integer;
use malachite_nz::integer_polynomial::IntegerPolynomial;
// The number of factors of 2 that every coefficient of a nonzero numerator shares, stopping at
// `bits`, since no more are needed. When the denominator is even, the numerator's content is odd,
// so there are none.
fn numerator_shared_zeros(p: &RationalPolynomial, bits: u64) -> u64 {
if p.denominator.even() {
return 0;
}
let mut zeros = bits;
for c in p.numerator.coefficients_asc() {
if let Some(c_zeros) = c.trailing_zeros() {
zeros = zeros.min(c_zeros);
if zeros == 0 {
break;
}
}
}
zeros
}
// Shifts every coefficient of a numerator right by `bits`, which divides each of them exactly.
fn numerator_shr(coefficients: &[Integer], bits: u64) -> IntegerPolynomial {
IntegerPolynomial::from_coefficients_asc(coefficients.iter().map(|c| c >> bits).collect())
}
// Divides a polynomial by 2 to the power of `bits`. The factors of 2 shared by the numerator's
// coefficients are cancelled first, and only what is left shifts the denominator; since the
// denominator was coprime to the numerator's content, what is left of that content is odd or the
// denominator is unchanged, so the two stay coprime.
fn shr_assign_u64(p: &mut RationalPolynomial, bits: u64) {
if bits == 0 || p.numerator == IntegerPolynomial::ZERO {
return;
}
let numerator_zeros = numerator_shared_zeros(p, bits);
if numerator_zeros != 0 {
let numerator = replace(&mut p.numerator, IntegerPolynomial::ZERO);
p.numerator = numerator_shr(&numerator.into_coefficients_asc(), numerator_zeros);
}
p.denominator <<= bits - numerator_zeros;
}
fn shr_ref_u64(p: &RationalPolynomial, bits: u64) -> RationalPolynomial {
if bits == 0 || p.numerator == IntegerPolynomial::ZERO {
return p.clone();
}
let numerator_zeros = numerator_shared_zeros(p, bits);
RationalPolynomial {
numerator: if numerator_zeros == 0 {
p.numerator.clone()
} else {
numerator_shr(p.numerator.coefficients_asc(), numerator_zeros)
},
denominator: &p.denominator << (bits - numerator_zeros),
}
}
fn shr_ref_signed<'a, U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
p: &'a RationalPolynomial,
bits: S,
) -> RationalPolynomial
where
&'a RationalPolynomial:
Shl<U, Output = RationalPolynomial> + Shr<U, Output = RationalPolynomial>,
{
if bits >= S::ZERO {
p >> bits.unsigned_abs()
} else {
p << bits.unsigned_abs()
}
}
fn shr_assign_signed<U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
p: &mut RationalPolynomial,
bits: S,
) where
RationalPolynomial: ShlAssign<U> + ShrAssign<U>,
{
if bits >= S::ZERO {
*p >>= bits.unsigned_abs();
} else {
*p <<= bits.unsigned_abs();
}
}
macro_rules! impl_rational_polynomial_shr_unsigned {
($t:ident) => {
impl Shr<$t> for RationalPolynomial {
type Output = RationalPolynomial;
/// Right-shifts a [`RationalPolynomial`] (divides it by a power of 2), taking it by
/// value.
///
/// $$
/// f(p, k) = p/2^k.
/// $$
///
/// Factors of 2 shared by the numerator's coefficients are cancelled first, and only
/// the rest of the power shifts the denominator, so the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits`, and $k$ is
/// `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr).
#[inline]
fn shr(mut self, bits: $t) -> RationalPolynomial {
self >>= bits;
self
}
}
impl Shr<$t> for &RationalPolynomial {
type Output = RationalPolynomial;
/// Right-shifts a [`RationalPolynomial`] (divides it by a power of 2), taking it by
/// reference.
///
/// $$
/// f(p, k) = p/2^k.
/// $$
///
/// Factors of 2 shared by the numerator's coefficients are cancelled first, and only
/// the rest of the power shifts the denominator, so the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits`, and $k$ is
/// `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr).
#[inline]
fn shr(self, bits: $t) -> RationalPolynomial {
shr_ref_u64(self, u64::exact_from(bits))
}
}
impl ShrAssign<$t> for RationalPolynomial {
/// Right-shifts a [`RationalPolynomial`] (divides it by a power of 2), in place.
///
/// $$
/// p \gets p/2^k.
/// $$
///
/// Factors of 2 shared by the numerator's coefficients are cancelled first, and only
/// the rest of the power shifts the denominator, so the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits`, and $k$ is
/// `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr_assign).
#[inline]
fn shr_assign(&mut self, bits: $t) {
shr_assign_u64(self, u64::exact_from(bits));
}
}
};
}
apply_to_unsigneds!(impl_rational_polynomial_shr_unsigned);
macro_rules! impl_rational_polynomial_shr_signed {
($t:ident) => {
impl Shr<$t> for RationalPolynomial {
type Output = RationalPolynomial;
/// Right-shifts a [`RationalPolynomial`] (divides it or multiplies it by a power of 2),
/// taking it by value.
///
/// $$
/// f(p, k) = p/2^k.
/// $$
///
/// A negative `bits` multiplies by $2^{-k}$: factors of 2 in the denominator are
/// cancelled first, and only the rest of the power shifts the numerator's coefficients.
/// A positive `bits` cancels factors of 2 shared by the numerator's coefficients first.
/// Either way, the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits.unsigned_abs()`, and $k$
/// is `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr).
#[inline]
fn shr(mut self, bits: $t) -> RationalPolynomial {
self >>= bits;
self
}
}
impl Shr<$t> for &RationalPolynomial {
type Output = RationalPolynomial;
/// Right-shifts a [`RationalPolynomial`] (divides it or multiplies it by a power of 2),
/// taking it by reference.
///
/// $$
/// f(p, k) = p/2^k.
/// $$
///
/// A negative `bits` multiplies by $2^{-k}$: factors of 2 in the denominator are
/// cancelled first, and only the rest of the power shifts the numerator's coefficients.
/// A positive `bits` cancels factors of 2 shared by the numerator's coefficients first.
/// Either way, the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits.unsigned_abs()`, and $k$
/// is `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr).
#[inline]
fn shr(self, bits: $t) -> RationalPolynomial {
shr_ref_signed(self, bits)
}
}
impl ShrAssign<$t> for RationalPolynomial {
/// Right-shifts a [`RationalPolynomial`] (divides it or multiplies it by a power of 2),
/// in place.
///
/// $$
/// p \gets p/2^k.
/// $$
///
/// A negative `bits` multiplies by $2^{-k}$: factors of 2 in the denominator are
/// cancelled first, and only the rest of the power shifts the numerator's coefficients.
/// A positive `bits` cancels factors of 2 shared by the numerator's coefficients first.
/// Either way, the result stays in lowest terms.
///
/// # Worst-case complexity
/// $T(n, m, k) = O(n + km)$
///
/// $M(n, m, k) = O(n + km)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// numerator's coefficients and the denominator, $m$ is `bits.unsigned_abs()`, and $k$
/// is `self.len()`.
///
/// # Examples
/// See [here](super::shr#shr_assign).
#[inline]
fn shr_assign(&mut self, bits: $t) {
shr_assign_signed(self, bits);
}
}
};
}
apply_to_signeds!(impl_rational_polynomial_shr_signed);