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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::integer::Integer;
use crate::natural::arithmetic::mul_shr_round::mul_shr_round_ref_ref;
use core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::{MulShrRound, MulShrRoundAssign};
use malachite_base::num::basic::traits::Zero;
use malachite_base::rounding_modes::RoundingMode::{self, *};
// Rounding a negative value with `rm` is rounding its magnitude with `-rm`, and the magnitude's
// `Ordering` flips on the way back. Exactness is checked here rather than left to the `Natural`
// core so that the panic message shows the signed operands.
fn mul_shr_round_integers(
x: &Integer,
y: &Integer,
bits: u64,
rm: RoundingMode,
) -> (Integer, Ordering) {
if *x == 0 || *y == 0 {
return (Integer::ZERO, Equal);
}
if rm == Exact {
let exact = x.unsigned_abs_ref().trailing_zeros().unwrap()
+ y.unsigned_abs_ref().trailing_zeros().unwrap()
>= bits;
assert!(
exact,
"Product right shift is not exact: {x} * {y} >> {bits}"
);
}
let negative = (*x < 0) != (*y < 0);
let (mag, o) = mul_shr_round_ref_ref(
x.unsigned_abs_ref(),
y.unsigned_abs_ref(),
bits,
if negative { -rm } else { rm },
);
if negative {
(Integer::from_sign_and_abs(false, mag), o.reverse())
} else {
(Integer::from(mag), o)
}
}
impl MulShrRound<Self, u64> for Integer {
type Output = Self;
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2),
/// rounding according to a specified rounding mode, taking both [`Integer`]s by value. An
/// [`Ordering`] is also returned, indicating whether the returned value is less than, equal to,
/// or greater than the exact value.
///
/// When most of the product is discarded, the product's low portion is never computed: a short
/// product determines the surviving bits at roughly half the cost of a full multiplication.
/// `Floor` rounds toward negative infinity and `Down` toward zero, so they differ when the
/// product is negative.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRound;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// Integer::from(-100).mul_shr_round(Integer::from(200), 8, Floor),
/// (Integer::from(-79), Less)
/// );
/// assert_eq!(
/// Integer::from(-100).mul_shr_round(Integer::from(200), 8, Down),
/// (Integer::from(-78), Greater)
/// );
/// ```
#[inline]
fn mul_shr_round(self, y: Self, bits: u64, rm: RoundingMode) -> (Self, Ordering) {
mul_shr_round_integers(&self, &y, bits, rm)
}
}
impl MulShrRound<&Self, u64> for Integer {
type Output = Self;
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2),
/// rounding according to a specified rounding mode, taking the first [`Integer`] by value and
/// the second by reference. An [`Ordering`] is also returned, indicating whether the returned
/// value is less than, equal to, or greater than the exact value.
///
/// See the by-value documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRound;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// Integer::from(-100).mul_shr_round(&Integer::from(200), 8, Nearest),
/// (Integer::from(-78), Greater)
/// );
/// ```
#[inline]
fn mul_shr_round(self, y: &Self, bits: u64, rm: RoundingMode) -> (Self, Ordering) {
mul_shr_round_integers(&self, y, bits, rm)
}
}
impl MulShrRound<Integer, u64> for &Integer {
type Output = Integer;
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2),
/// rounding according to a specified rounding mode, taking the first [`Integer`] by reference
/// and the second by value. An [`Ordering`] is also returned, indicating whether the returned
/// value is less than, equal to, or greater than the exact value.
///
/// See the by-value documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRound;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// (&Integer::from(-96)).mul_shr_round(Integer::from(8), 8, Exact),
/// (Integer::from(-3), Equal)
/// );
/// ```
#[inline]
fn mul_shr_round(self, y: Integer, bits: u64, rm: RoundingMode) -> (Integer, Ordering) {
mul_shr_round_integers(self, &y, bits, rm)
}
}
impl MulShrRound<&Integer, u64> for &Integer {
type Output = Integer;
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2),
/// rounding according to a specified rounding mode, taking both [`Integer`]s by reference. An
/// [`Ordering`] is also returned, indicating whether the returned value is less than, equal to,
/// or greater than the exact value.
///
/// See the by-value documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRound;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// (&Integer::from(100)).mul_shr_round(&Integer::from(-200), 8, Ceiling),
/// (Integer::from(-78), Greater)
/// );
/// ```
#[inline]
fn mul_shr_round(self, y: &Integer, bits: u64, rm: RoundingMode) -> (Integer, Ordering) {
mul_shr_round_integers(self, y, bits, rm)
}
}
impl MulShrRoundAssign<Self, u64> for Integer {
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2) in
/// place, rounding according to a specified rounding mode, taking the [`Integer`] on the
/// right-hand side by value. An [`Ordering`] is returned, indicating whether the assigned value
/// is less than, equal to, or greater than the exact value.
///
/// See the [`MulShrRound`] documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRoundAssign;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// let mut x = Integer::from(-100);
/// assert_eq!(x.mul_shr_round_assign(Integer::from(200), 8, Floor), Less);
/// assert_eq!(x, -79);
/// ```
#[inline]
fn mul_shr_round_assign(&mut self, y: Self, bits: u64, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = mul_shr_round_integers(self, &y, bits, rm);
o
}
}
impl MulShrRoundAssign<&Self, u64> for Integer {
/// Multiplies two [`Integer`]s and right-shifts the product (divides it by a power of 2) in
/// place, rounding according to a specified rounding mode, taking the [`Integer`] on the
/// right-hand side by reference. An [`Ordering`] is returned, indicating whether the assigned
/// value is less than, equal to, or greater than the exact value.
///
/// See the [`MulShrRound`] documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// y.significant_bits())`.
///
/// # Panics
/// Panics if `rm` is `Exact` but the shift is not exact.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::MulShrRoundAssign;
/// use malachite_base::rounding_modes::RoundingMode::*;
/// use malachite_nz::integer::Integer;
/// use std::cmp::Ordering::*;
///
/// let mut x = Integer::from(-100);
/// assert_eq!(
/// x.mul_shr_round_assign(&Integer::from(200), 8, Ceiling),
/// Greater
/// );
/// assert_eq!(x, -78);
/// ```
#[inline]
fn mul_shr_round_assign(&mut self, y: &Self, bits: u64, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = mul_shr_round_integers(self, y, bits, rm);
o
}
}