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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::{DivRound, DivRoundAssign, UnsignedAbs};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::{ExactFrom, WrappingFrom};
use crate::rounding_modes::RoundingMode::{self, *};
use core::cmp::Ordering::{self, *};
fn div_round_unsigned<T: PrimitiveUnsigned>(x: T, other: T, rm: RoundingMode) -> (T, Ordering) {
let quotient = x / other;
let remainder = x - quotient * other;
match rm {
_ if remainder == T::ZERO => (quotient, Equal),
Down | Floor => (quotient, Less),
Up | Ceiling => (quotient + T::ONE, Greater),
Nearest => {
let shifted_other = other >> 1;
if remainder > shifted_other
|| remainder == shifted_other && other.even() && quotient.odd()
{
(quotient + T::ONE, Greater)
} else {
(quotient, Less)
}
}
Exact => {
panic!("Division is not exact: {x} / {other}");
}
}
}
macro_rules! impl_div_round_unsigned {
($t:ident) => {
impl DivRound<$t> for $t {
type Output = $t;
/// Divides a value by another value and rounds according to a specified rounding mode.
/// An [`Ordering`] is also returned, indicating whether the returned value is less
/// than, equal to, or greater than the exact value.
///
/// Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first
/// element of the pair, without the [`Ordering`]:
///
/// $$
/// g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.
/// $$
///
/// $$
/// g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.
/// $$
///
/// $$
/// g(x, y, \mathrm{Nearest}) = \begin{cases}
/// \lfloor q \rfloor & \text{if} \\quad q - \lfloor q \rfloor < \frac{1}{2}, \\\\
/// \lceil q \rceil & \text{if} \\quad q - \lfloor q \rfloor > \frac{1}{2}, \\\\
/// \lfloor q \rfloor &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2}
/// \\ \text{and} \\ \lfloor q \rfloor \\ \text{is even}, \\\\
/// \lceil q \rceil &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2}
/// \\ \text{and} \\ \lfloor q \rfloor \\ \text{is odd.}
/// \end{cases}
/// $$
///
/// $g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
///
/// Then
///
/// $f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `other` is zero, or if `rm` is `Exact` but `self` is not divisible by
/// `other`.
///
/// # Examples
/// See [here](super::div_round#div_round).
#[inline]
fn div_round(self, other: $t, rm: RoundingMode) -> ($t, Ordering) {
div_round_unsigned(self, other, rm)
}
}
impl DivRoundAssign<$t> for $t {
/// Divides a value by another value in place and rounds according to a specified
/// rounding mode. An [`Ordering`] is returned, indicating whether the assigned value is
/// less than, equal to, or greater than the exact value.
///
/// See the [`DivRound`] documentation for details.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `other` is zero, or if `rm` is `Exact` but `self` is not divisible by
/// `other`.
///
/// # Examples
/// See [here](super::div_round#div_round_assign).
#[inline]
fn div_round_assign(&mut self, other: $t, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = self.div_round(other, rm);
o
}
}
};
}
apply_to_unsigneds!(impl_div_round_unsigned);
fn div_round_signed<
U: PrimitiveUnsigned,
S: ExactFrom<U> + PrimitiveSigned + UnsignedAbs<Output = U> + WrappingFrom<U>,
>(
x: S,
other: S,
rm: RoundingMode,
) -> (S, Ordering) {
if (x >= S::ZERO) == (other >= S::ZERO) {
let (q, o) = x.unsigned_abs().div_round(other.unsigned_abs(), rm);
(S::exact_from(q), o)
} else {
// Has to be wrapping so that (self, other) == (T::MIN, 1) works
let (q, o) = x.unsigned_abs().div_round(other.unsigned_abs(), -rm);
(S::wrapping_from(q).wrapping_neg(), o.reverse())
}
}
macro_rules! impl_div_round_signed {
($t:ident) => {
impl DivRound<$t> for $t {
type Output = $t;
/// Divides a value by another value and rounds according to a specified rounding mode.
/// An [`Ordering`] is also returned, indicating whether the returned value is less
/// than, equal to, or greater than the exact value.
///
/// Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first
/// element of the pair, without the [`Ordering`]:
///
/// $$
/// g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.
/// $$
///
/// $$
/// g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.
/// $$
///
/// $$
/// g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.
/// $$
///
/// $$
/// g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.
/// $$
///
/// $$
/// g(x, y, \mathrm{Nearest}) = \begin{cases}
/// \lfloor q \rfloor & \text{if} \\quad q - \lfloor q \rfloor < \frac{1}{2}, \\\\
/// \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\\\
/// \lfloor q \rfloor &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2} \\ \text{and}
/// \\ \lfloor q \rfloor \\ \text{is even}, \\\\
/// \lceil q \rceil &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2} \\ \text{and}
/// \\ \lfloor q \rfloor \\ \text{is odd.}
/// \end{cases}
/// $$
///
/// $g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
///
/// Then
///
/// $f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `other` is zero, if `self` is `Self::MIN` and `other` is `-1`, or if `rm`
/// is `Exact` but `self` is not divisible by `other`.
///
/// # Examples
/// See [here](super::div_round#div_round).
fn div_round(self, other: $t, rm: RoundingMode) -> ($t, Ordering) {
div_round_signed(self, other, rm)
}
}
impl DivRoundAssign<$t> for $t {
/// Divides a value by another value in place and rounds according to a specified
/// rounding mode. An [`Ordering`] is returned, indicating whether the assigned value is
/// less than, equal to, or greater than the exact value.
///
/// See the [`DivRound`] documentation for details.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `other` is zero, if `self` is `Self::MIN` and `other` is `-1`, or if `rm`
/// is `Exact` but `self` is not divisible by `other`.
///
/// # Examples
/// See [here](super::div_round#div_round_assign).
#[inline]
fn div_round_assign(&mut self, other: $t, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = self.div_round(other, rm);
o
}
}
};
}
apply_to_signeds!(impl_div_round_signed);