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use malachite_base::num::arithmetic::traits::{Reciprocal, ReciprocalAssign};
use std::mem::swap;
use Rational;
impl Reciprocal for Rational {
type Output = Rational;
/// Reciprocates a [`Rational`], taking it by value.
///
/// $$
/// f(x) = 1/x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from_signeds(22, 7).reciprocal().to_string(), "7/22");
/// assert_eq!(Rational::from_signeds(7, 22).reciprocal().to_string(), "22/7");
/// ```
#[inline]
fn reciprocal(mut self) -> Rational {
self.reciprocal_assign();
self
}
}
impl<'a> Reciprocal for &'a Rational {
type Output = Rational;
/// Reciprocates a [`Rational`], taking it by reference.
///
/// $$
/// f(x) = 1/x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_q::Rational;
///
/// assert_eq!((&Rational::from_signeds(22, 7)).reciprocal().to_string(), "7/22");
/// assert_eq!((&Rational::from_signeds(7, 22)).reciprocal().to_string(), "22/7");
/// ```
fn reciprocal(self) -> Rational {
assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
Rational {
sign: self.sign,
numerator: self.denominator.clone(),
denominator: self.numerator.clone(),
}
}
}
impl ReciprocalAssign for Rational {
/// Reciprocates a [`Rational`] in place.
///
/// $$
/// x \gets 1/x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::ReciprocalAssign;
/// use malachite_q::Rational;
///
/// let mut x = Rational::from_signeds(22, 7);
/// x.reciprocal_assign();
/// assert_eq!(x.to_string(), "7/22");
///
/// let mut x = Rational::from_signeds(7, 22);
/// x.reciprocal_assign();
/// assert_eq!(x.to_string(), "22/7");
/// ```
fn reciprocal_assign(&mut self) {
assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
swap(&mut self.numerator, &mut self.denominator);
}
}