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// Copyright © 2016–2023 Trevor Spiteri
// This program is free software: you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License as published by the Free
// Software Foundation, either version 3 of the License, or (at your option) any
// later version.
//
// This program is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
// details.
//
// You should have received a copy of the GNU Lesser General Public License and
// a copy of the GNU General Public License along with this program. If not, see
// <https://www.gnu.org/licenses/>.
use crate::ext::xmpq;
use crate::integer::small::Mpz;
use crate::integer::ToSmall;
use crate::{Assign, Rational};
use az::Cast;
use core::cell::UnsafeCell;
use core::ffi::c_int;
use core::mem;
use core::mem::MaybeUninit;
use core::ops::Deref;
use core::ptr::NonNull;
use gmp_mpfr_sys::gmp;
use gmp_mpfr_sys::gmp::{limb_t, mpq_t};
const LIMBS_IN_SMALL: usize = (128 / gmp::LIMB_BITS) as usize;
type Limbs = [MaybeUninit<limb_t>; LIMBS_IN_SMALL];
/**
A small rational number that does not require any memory allocation.
This can be useful when you have a numerator and denominator that are primitive
integer-types such as [`i64`] or [`u8`], and you need a reference to a
[`Rational`].
Although no allocation is required, setting the value of a `SmallRational` does
require some computation, as the numerator and denominator need to be
canonicalized.
The `SmallRational` type can be coerced to a [`Rational`], as it implements
<code>[Deref]\<[Target][Deref::Target] = [Rational]></code>.
# Examples
```rust
use rug::rational::SmallRational;
use rug::Rational;
// `a` requires a heap allocation
let mut a = Rational::from((100, 13));
// `b` can reside on the stack
let b = SmallRational::from((-100, 21));
a /= &*b;
assert_eq!(*a.numer(), -21);
assert_eq!(*a.denom(), 13);
```
*/
#[derive(Clone)]
pub struct SmallRational {
inner: Mpq,
// numerator is first in limbs if inner.num.d <= inner.den.d
first_limbs: Limbs,
last_limbs: Limbs,
}
// Safety: SmallRational cannot be Sync because it contains an
// UnsafeCell which is written to then read without further
// protection, so it could lead to data races. But SmallRational can
// be Send because if it is owned, no other reference can be used to
// modify the UnsafeCell.
unsafe impl Send for SmallRational {}
// Safety: Mpz has a repr equivalent to mpz_t, so Mpq has a repr equivalent to
// mpq_t. The difference in the repr(C) types Mpz and mpz_t is that Mpz uses
// UnsafeCell<NonNull<limb_t>> instead of NonNull<limb_t>, but UnsafeCell is
// repr(transparent). The difference in the repr(C) types Mpq and mpq_t is that
// Mpq uses Mpz instead of mpz_t.
#[derive(Clone)]
#[repr(C)]
struct Mpq {
num: Mpz,
den: Mpz,
}
static_assert_same_layout!(Mpq, mpq_t);
impl Default for SmallRational {
#[inline]
fn default() -> Self {
SmallRational::new()
}
}
impl SmallRational {
/// Creates a [`SmallRational`] with value 0.
///
/// # Examples
///
/// ```rust
/// use rug::rational::SmallRational;
/// let r = SmallRational::new();
/// // Use r as if it were Rational.
/// assert_eq!(*r.numer(), 0);
/// assert_eq!(*r.denom(), 1);
/// ```
#[inline]
pub const fn new() -> Self {
SmallRational {
inner: Mpq {
num: Mpz {
alloc: LIMBS_IN_SMALL as c_int,
size: 0,
d: UnsafeCell::new(NonNull::dangling()),
},
den: Mpz {
alloc: LIMBS_IN_SMALL as c_int,
size: 1,
d: UnsafeCell::new(NonNull::dangling()),
},
},
first_limbs: small_limbs![0],
last_limbs: small_limbs![1],
}
}
/// Returns a mutable reference to a [`Rational`] number for simple
/// operations that do not need to allocate more space for the numerator or
/// denominator.
///
/// # Safety
///
/// It is undefined behavior to perform operations that reallocate the
/// internal data of the referenced [`Rational`] number or to swap it with
/// another number, although it is allowed to swap the numerator and
/// denominator allocations, such as in the reciprocal operation
/// [`recip_mut`].
///
/// Some GMP functions swap the allocations of their target operands;
/// calling such functions with the mutable reference returned by this
/// method can lead to undefined behavior.
///
/// # Examples
///
/// ```rust
/// use rug::rational::SmallRational;
/// let mut r = SmallRational::from((-15i32, 47i32));
/// let num_capacity = r.numer().capacity();
/// let den_capacity = r.denom().capacity();
/// // reciprocating this will not require reallocations
/// unsafe {
/// r.as_nonreallocating_rational().recip_mut();
/// }
/// assert_eq!(*r, (-47, 15));
/// assert_eq!(r.numer().capacity(), num_capacity);
/// assert_eq!(r.denom().capacity(), den_capacity);
/// ```
///
/// [`recip_mut`]: `Rational::recip_mut`
#[inline]
// Safety: after calling update_d(), self.inner.d points to the
// limbs so it is in a consistent state.
pub unsafe fn as_nonreallocating_rational(&mut self) -> &mut Rational {
self.update_d();
let ptr = cast_ptr_mut!(&mut self.inner, Rational);
unsafe { &mut *ptr }
}
/// Creates a [`SmallRational`] from a numerator and denominator, assuming
/// they are in canonical form.
///
/// # Safety
///
/// This method leads to undefined behavior if `den` is zero or if `num` and
/// `den` have common factors.
///
/// # Examples
///
/// ```rust
/// use rug::rational::SmallRational;
/// let from_unsafe = unsafe { SmallRational::from_canonical(-13, 10) };
/// // from_safe is canonicalized to the same form as from_unsafe
/// let from_safe = SmallRational::from((130, -100));
/// assert_eq!(from_unsafe.numer(), from_safe.numer());
/// assert_eq!(from_unsafe.denom(), from_safe.denom());
/// ```
pub unsafe fn from_canonical<Num: ToSmall, Den: ToSmall>(num: Num, den: Den) -> Self {
let mut num_size = 0;
let mut den_size = 0;
let mut num_limbs: Limbs = small_limbs![0];
let mut den_limbs: Limbs = small_limbs![0];
num.copy(&mut num_size, &mut num_limbs);
den.copy(&mut den_size, &mut den_limbs);
// since inner.num.d == inner.den.d, first_limbs are num_limbs
SmallRational {
inner: Mpq {
num: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: num_size,
d: UnsafeCell::new(NonNull::dangling()),
},
den: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: den_size,
d: UnsafeCell::new(NonNull::dangling()),
},
},
first_limbs: num_limbs,
last_limbs: den_limbs,
}
}
/// Assigns a numerator and denominator to a [`SmallRational`], assuming
/// they are in canonical form.
///
/// # Safety
///
/// This method leads to undefined behavior if `den` is zero or negative, or
/// if `num` and `den` have common factors.
///
/// # Examples
///
/// ```rust
/// use rug::rational::SmallRational;
/// use rug::Assign;
/// let mut a = SmallRational::new();
/// unsafe {
/// a.assign_canonical(-13, 10);
/// }
/// // b is canonicalized to the same form as a
/// let mut b = SmallRational::new();
/// b.assign((130, -100));
/// assert_eq!(a.numer(), b.numer());
/// assert_eq!(a.denom(), b.denom());
/// ```
pub unsafe fn assign_canonical<Num: ToSmall, Den: ToSmall>(&mut self, num: Num, den: Den) {
let (num_limbs, den_limbs) = if self.num_is_first() {
(&mut self.first_limbs, &mut self.last_limbs)
} else {
(&mut self.last_limbs, &mut self.first_limbs)
};
num.copy(&mut self.inner.num.size, num_limbs);
den.copy(&mut self.inner.den.size, den_limbs);
}
#[inline]
// Safety: self is not Sync, so reading d does not cause a data race.
fn num_is_first(&self) -> bool {
unsafe { *self.inner.num.d.get() <= *self.inner.den.d.get() }
}
// To be used when offsetting num and den in case the struct has
// been displaced in memory; if currently num.d <= den.d then
// num.d points to first_limbs and den.d points to last_limbs,
// otherwise num.d points to last_limbs and den.d points to
// first_limbs.
#[inline]
fn update_d(&self) {
// Since this is borrowed, the limbs won't move around, and we can set
// the d fields.
//
// However, if there already exists a reference created with Deref, we
// must not set the d fields as that reference contains its d fields
// without the UnsafeCell wrapping. So we first check whether the d
// fields are already set correctly. If not, then there is no existing
// reference created with Deref yet, so we can set the d fields.
let first = NonNull::<[MaybeUninit<limb_t>]>::from(&self.first_limbs[..]).cast();
let last = NonNull::<[MaybeUninit<limb_t>]>::from(&self.last_limbs[..]).cast();
let (num_d, den_d) = if self.num_is_first() {
(first, last)
} else {
(last, first)
};
// Safety: self is not Sync, so we can write to d without causing a data race.
unsafe {
if *self.inner.num.d.get() != num_d {
*self.inner.num.d.get() = num_d;
}
if *self.inner.den.d.get() != den_d {
*self.inner.den.d.get() = den_d;
}
}
}
}
impl Deref for SmallRational {
type Target = Rational;
#[inline]
fn deref(&self) -> &Rational {
self.update_d();
let ptr = cast_ptr!(&self.inner, Rational);
// Safety: since we called update_d, the inner pointer is pointing
// to the limbs and the rational number is in a consistent state.
unsafe { &*ptr }
}
}
impl<Num: ToSmall> Assign<Num> for SmallRational {
#[inline]
fn assign(&mut self, src: Num) {
let (num_limbs, den_limbs) = if self.num_is_first() {
(&mut self.first_limbs, &mut self.last_limbs)
} else {
(&mut self.last_limbs, &mut self.first_limbs)
};
src.copy(&mut self.inner.num.size, num_limbs);
self.inner.den.size = 1;
den_limbs[0] = MaybeUninit::new(1);
}
}
impl<Num: ToSmall> From<Num> for SmallRational {
fn from(src: Num) -> Self {
let mut num_size = 0;
let mut num_limbs = small_limbs![0];
src.copy(&mut num_size, &mut num_limbs);
// since inner.num.d == inner.den.d, first_limbs are num_limbs
SmallRational {
inner: Mpq {
num: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: num_size,
d: UnsafeCell::new(NonNull::dangling()),
},
den: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: 1,
d: UnsafeCell::new(NonNull::dangling()),
},
},
first_limbs: num_limbs,
last_limbs: small_limbs![1],
}
}
}
impl<Num: ToSmall, Den: ToSmall> Assign<(Num, Den)> for SmallRational {
fn assign(&mut self, src: (Num, Den)) {
assert!(!src.1.is_zero(), "division by zero");
{
let (num_limbs, den_limbs) = if self.num_is_first() {
(&mut self.first_limbs, &mut self.last_limbs)
} else {
(&mut self.last_limbs, &mut self.first_limbs)
};
src.0.copy(&mut self.inner.num.size, num_limbs);
src.1.copy(&mut self.inner.den.size, den_limbs);
}
// Safety: canonicalization will never need to make a number larger.
xmpq::canonicalize(unsafe { self.as_nonreallocating_rational() });
}
}
impl<Num: ToSmall, Den: ToSmall> From<(Num, Den)> for SmallRational {
fn from(src: (Num, Den)) -> Self {
assert!(!src.1.is_zero(), "division by zero");
let mut inner = Mpq {
num: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: 0,
d: UnsafeCell::new(NonNull::dangling()),
},
den: Mpz {
alloc: LIMBS_IN_SMALL.cast(),
size: 0,
d: UnsafeCell::new(NonNull::dangling()),
},
};
let mut num_limbs: Limbs = small_limbs![0];
let mut den_limbs: Limbs = small_limbs![0];
src.0.copy(&mut inner.num.size, &mut num_limbs);
src.1.copy(&mut inner.den.size, &mut den_limbs);
inner.num.d =
UnsafeCell::new(NonNull::<[MaybeUninit<limb_t>]>::from(&mut num_limbs[..]).cast());
inner.den.d =
UnsafeCell::new(NonNull::<[MaybeUninit<limb_t>]>::from(&mut den_limbs[..]).cast());
unsafe {
gmp::mpq_canonicalize(cast_ptr_mut!(&mut inner, mpq_t));
}
// order of limbs is important as inner.num.d != inner.den.d
if num_limbs.as_ptr() <= den_limbs.as_ptr() {
SmallRational {
inner,
first_limbs: num_limbs,
last_limbs: den_limbs,
}
} else {
SmallRational {
inner,
first_limbs: den_limbs,
last_limbs: num_limbs,
}
}
}
}
impl Assign<&Self> for SmallRational {
#[inline]
fn assign(&mut self, other: &Self) {
self.clone_from(other);
}
}
impl Assign for SmallRational {
#[inline]
fn assign(&mut self, other: Self) {
drop(mem::replace(self, other));
}
}
#[cfg(test)]
mod tests {
use crate::rational::SmallRational;
use crate::Assign;
#[test]
fn check_assign() {
let mut r = SmallRational::from((1, 2));
assert_eq!(*r, (1, 2));
r.assign(3);
assert_eq!(*r, 3);
let other = SmallRational::from((4, 5));
r.assign(&other);
assert_eq!(*r, (4, 5));
r.assign((6, 7));
assert_eq!(*r, (6, 7));
r.assign(other);
assert_eq!(*r, (4, 5));
}
fn swapped_parts(small: &SmallRational) -> bool {
unsafe {
let num = (*small.numer().as_raw()).d;
let den = (*small.denom().as_raw()).d;
num > den
}
}
#[test]
fn check_swapped_parts() {
let mut r = SmallRational::from((2, 3));
assert_eq!(*r, (2, 3));
assert_eq!(*r.clone(), *r);
let mut orig_swapped_parts = swapped_parts(&r);
unsafe {
r.as_nonreallocating_rational().recip_mut();
}
assert_eq!(*r, (3, 2));
assert_eq!(*r.clone(), *r);
assert!(swapped_parts(&r) != orig_swapped_parts);
unsafe {
r.assign_canonical(5, 7);
}
assert_eq!(*r, (5, 7));
assert_eq!(*r.clone(), *r);
orig_swapped_parts = swapped_parts(&r);
unsafe {
r.as_nonreallocating_rational().recip_mut();
}
assert_eq!(*r, (7, 5));
assert_eq!(*r.clone(), *r);
assert!(swapped_parts(&r) != orig_swapped_parts);
r.assign(2);
assert_eq!(*r, 2);
assert_eq!(*r.clone(), *r);
orig_swapped_parts = swapped_parts(&r);
unsafe {
r.as_nonreallocating_rational().recip_mut();
}
assert_eq!(*r, (1, 2));
assert_eq!(*r.clone(), *r);
assert!(swapped_parts(&r) != orig_swapped_parts);
r.assign((3, -5));
assert_eq!(*r, (-3, 5));
assert_eq!(*r.clone(), *r);
orig_swapped_parts = swapped_parts(&r);
unsafe {
r.as_nonreallocating_rational().recip_mut();
}
assert_eq!(*r, (-5, 3));
assert_eq!(*r.clone(), *r);
assert!(swapped_parts(&r) != orig_swapped_parts);
}
}