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use crate::Rational;
use malachite_base::num::arithmetic::traits::{Square, SquareAssign};
impl Square for Rational {
type Output = Rational;
/// Squares a [`Rational`], taking it by value.
///
/// $$
/// f(x) = x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::ZERO.square(), 0);
/// assert_eq!(Rational::from_signeds(22, 7).square().to_string(), "484/49");
/// assert_eq!(Rational::from_signeds(-22, 7).square().to_string(), "484/49");
/// ```
#[inline]
fn square(mut self) -> Rational {
self.square_assign();
self
}
}
impl<'a> Square for &'a Rational {
type Output = Rational;
/// Squares a [`Rational`], taking it by reference.
///
/// $$
/// f(x) = x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
///
/// assert_eq!((&Rational::ZERO).square(), 0);
/// assert_eq!((&Rational::from_signeds(22, 7)).square().to_string(), "484/49");
/// assert_eq!((&Rational::from_signeds(-22, 7)).square().to_string(), "484/49");
/// ```
#[inline]
fn square(self) -> Rational {
Rational {
sign: true,
numerator: (&self.numerator).square(),
denominator: (&self.denominator).square(),
}
}
}
impl SquareAssign for Rational {
/// Squares a [`Rational`] in place.
///
/// $$
/// x \gets x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::SquareAssign;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
///
/// let mut x = Rational::ZERO;
/// x.square_assign();
/// assert_eq!(x, 0);
///
/// let mut x = Rational::from_signeds(22, 7);
/// x.square_assign();
/// assert_eq!(x.to_string(), "484/49");
///
/// let mut x = Rational::from_signeds(-22, 7);
/// x.square_assign();
/// assert_eq!(x.to_string(), "484/49");
/// ```
fn square_assign(&mut self) {
self.sign = true;
self.numerator.square_assign();
self.denominator.square_assign();
}
}