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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::{RoundToMultiple, RoundToMultipleAssign, UnsignedAbs};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::ExactFrom;
use crate::rounding_modes::RoundingMode::{self, *};
use core::cmp::Ordering::{self, *};
fn round_to_multiple_unsigned<T: PrimitiveUnsigned>(
x: T,
other: T,
rm: RoundingMode,
) -> (T, Ordering) {
match (x, other) {
(x, y) if x == y => (x, Equal),
(x, y) if y == T::ZERO => match rm {
Down | Floor | Nearest => (T::ZERO, Less),
_ => panic!("Cannot round {x} to zero using RoundingMode {rm}"),
},
(x, y) => {
let r = x % y;
if r == T::ZERO {
(x, Equal)
} else {
let floor = x - r;
match rm {
Down | Floor => (floor, Less),
Up | Ceiling => (floor.checked_add(y).unwrap(), Greater),
Nearest => {
match r.cmp(&(y >> 1)) {
Less => (floor, Less),
Greater => (floor.checked_add(y).unwrap(), Greater),
Equal => {
if y.odd() {
(floor, Less)
} else {
// The even multiple of y will have more trailing zeros.
let (ceiling, overflow) = floor.overflowing_add(y);
if floor.trailing_zeros() > ceiling.trailing_zeros() {
(floor, Less)
} else if overflow {
panic!("Cannot round {x} to {y} using RoundingMode {rm}");
} else {
(ceiling, Greater)
}
}
}
}
}
Exact => {
panic!("Cannot round {x} to {y} using RoundingMode {rm}")
}
}
}
}
}
}
macro_rules! impl_round_to_multiple_unsigned {
($t:ident) => {
impl RoundToMultiple<$t> for $t {
type Output = $t;
/// Rounds a number to a multiple of another number, 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 original value.
///
/// The only rounding modes that are guaranteed to return without a panic are `Down` and
/// `Floor`.
///
/// Let $q = \frac{x}{y}$:
///
/// $f(x, y, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = y \lfloor q \rfloor.$
///
/// $f(x, y, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = y \lceil q \rceil.$
///
/// $$
/// f(x, y, \mathrm{Nearest}) = \begin{cases}
/// y \lfloor q \rfloor & \text{if} \\quad
/// q - \lfloor q \rfloor < \frac{1}{2} \\\\
/// y \lceil q \rceil & \text{if} \\quad q - \lfloor q \rfloor > \frac{1}{2} \\\\
/// y \lfloor q \rfloor &
/// \text{if} \\quad q - \lfloor q \rfloor =
/// \frac{1}{2} \\ \text{and} \\ \lfloor q \rfloor
/// \\ \text{is even} \\\\
/// y \lceil q \rceil &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2}
/// \\ \text{and} \\ \lfloor q \rfloor \\ \text{is odd.}
/// \end{cases}
/// $$
///
/// $f(x, y, \mathrm{Exact}) = x$, but panics if $q \notin \N$.
///
/// The following two expressions are equivalent:
/// - `x.round_to_multiple(other, Exact)`
/// - `{ assert!(x.divisible_by(other)); x }`
///
/// but the latter should be used as it is clearer and more efficient.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// - If `rm` is `Exact`, but `self` is not a multiple of `other`.
/// - If the multiple is outside the representable range.
/// - If `self` is nonzero, `other` is zero, and `rm` is trying to round away from zero.
///
/// # Examples
/// See [here](super::round_to_multiple#round_to_multiple).
#[inline]
fn round_to_multiple(self, other: $t, rm: RoundingMode) -> ($t, Ordering) {
round_to_multiple_unsigned(self, other, rm)
}
}
impl RoundToMultipleAssign<$t> for $t {
/// Rounds a number to a multiple of another number in place, according to a specified
/// rounding mode. An [`Ordering`] is returned, indicating whether the returned value is
/// less than, equal to, or greater than the original value.
///
/// The only rounding modes that are guaranteed to return without a panic are `Down` and
/// `Floor`.
///
/// See the [`RoundToMultiple`] documentation for details.
///
/// The following two expressions are equivalent:
/// - `x.round_to_multiple_assign(other, Exact);`
/// - `assert!(x.divisible_by(other));`
///
/// but the latter should be used as it is clearer and more efficient.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// - If `rm` is `Exact`, but `self` is not a multiple of `other`.
/// - If the multiple is outside the representable range.
/// - If `self` is nonzero, `other` is zero, and `rm` is trying to round away from zero.
///
/// # Examples
/// See [here](super::round_to_multiple#round_to_multiple_assign).
#[inline]
fn round_to_multiple_assign(&mut self, other: $t, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = self.round_to_multiple(other, rm);
o
}
}
};
}
apply_to_unsigneds!(impl_round_to_multiple_unsigned);
fn round_to_multiple_signed<
U: PrimitiveUnsigned,
S: ExactFrom<U> + PrimitiveSigned + UnsignedAbs<Output = U>,
>(
x: S,
other: S,
rm: RoundingMode,
) -> (S, Ordering) {
if x >= S::ZERO {
let (m, o) = x.unsigned_abs().round_to_multiple(other.unsigned_abs(), rm);
(S::exact_from(m), o)
} else {
let (abs_result, o) = x
.unsigned_abs()
.round_to_multiple(other.unsigned_abs(), -rm);
(
if abs_result == S::MIN.unsigned_abs() {
S::MIN
} else {
S::exact_from(abs_result).checked_neg().unwrap()
},
o.reverse(),
)
}
}
macro_rules! impl_round_to_multiple_signed {
($t:ident) => {
impl RoundToMultiple<$t> for $t {
type Output = $t;
/// Rounds a number to a multiple of another number, 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 original value.
///
/// The only rounding mode that is guaranteed to return without a panic is `Down`.
///
/// Let $q = \frac{x}{|y|}$:
///
/// $f(x, y, \mathrm{Down}) = \operatorname{sgn}(q) |y| \lfloor |q| \rfloor.$
///
/// $f(x, y, \mathrm{Up}) = \operatorname{sgn}(q) |y| \lceil |q| \rceil.$
///
/// $f(x, y, \mathrm{Floor}) = |y| \lfloor q \rfloor.$
///
/// $f(x, y, \mathrm{Ceiling}) = |y| \lceil q \rceil.$
///
/// $$
/// f(x, y, \mathrm{Nearest}) = \begin{cases}
/// y \lfloor q \rfloor & \text{if} \\quad
/// q - \lfloor q \rfloor < \frac{1}{2} \\\\
/// y \lceil q \rceil & \text{if} \\quad q - \lfloor q \rfloor > \frac{1}{2} \\\\
/// y \lfloor q \rfloor &
/// \text{if} \\quad q - \lfloor q \rfloor =
/// \frac{1}{2} \\ \text{and} \\ \lfloor q \rfloor
/// \\ \text{is even} \\\\
/// y \lceil q \rceil &
/// \text{if} \\quad q - \lfloor q \rfloor = \frac{1}{2}
/// \\ \text{and} \\ \lfloor q \rfloor \\ \text{is odd.}
/// \end{cases}
/// $$
///
/// $f(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
///
/// The following two expressions are equivalent:
/// - `x.round_to_multiple(other, Exact)`
/// - `{ assert!(x.divisible_by(other)); x }`
///
/// but the latter should be used as it is clearer and more efficient.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// - If `rm` is `Exact`, but `self` is not a multiple of `other`.
/// - If the multiple is outside the representable range.
/// - If `self` is nonzero, `other` is zero, and `rm` is trying to round away from zero.
///
/// # Examples
/// See [here](super::round_to_multiple#round_to_multiple).
#[inline]
fn round_to_multiple(self, other: $t, rm: RoundingMode) -> ($t, Ordering) {
round_to_multiple_signed(self, other, rm)
}
}
impl RoundToMultipleAssign<$t> for $t {
/// Rounds a number to a multiple of another number in place, according to a specified
/// rounding mode. An [`Ordering`] is returned, indicating whether the returned value is
/// less than, equal to, or greater than the original value.
///
/// The only rounding mode that is guaranteed to return without a panic is `Down`.
///
/// See the [`RoundToMultiple`] documentation for details.
///
/// The following two expressions are equivalent:
/// - `x.round_to_multiple_assign(other, Exact);`
/// - `assert!(x.divisible_by(other));`
///
/// but the latter should be used as it is clearer and more efficient.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// - If `rm` is `Exact`, but `self` is not a multiple of `other`.
/// - If the multiple is outside the representable range.
/// - If `self` is nonzero, `other` is zero, and `rm` is trying to round away from zero.
///
/// # Examples
/// See [here](super::round_to_multiple#round_to_multiple_assign).
#[inline]
fn round_to_multiple_assign(&mut self, other: $t, rm: RoundingMode) -> Ordering {
let o;
(*self, o) = self.round_to_multiple(other, rm);
o
}
}
};
}
apply_to_signeds!(impl_round_to_multiple_signed);