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use malachite_base::num::arithmetic::traits::Sign;
use malachite_base::num::comparison::traits::{OrdAbs, PartialOrdAbs};
use std::cmp::Ordering;
use Rational;
impl PartialOrdAbs for Rational {
/// Compares the absolute values of two [`Rational`]s.
///
/// See the documentation for the
/// [`OrdAbs`](malachite_base::num::comparison::traits::OrdAbs) implementation.
#[inline]
fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
Some(self.cmp_abs(other))
}
}
impl OrdAbs for Rational {
/// Compares the absolute values of two [`Rational`]s.
///
/// # 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
/// `max(self.significant_bits(), other.significant_bits())`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_base::num::comparison::traits::OrdAbs;
/// use malachite_q::Rational;
/// use std::cmp::Ordering;
/// use std::str::FromStr;
///
/// assert_eq!(
/// Rational::from_str("2/3").unwrap().cmp_abs(&Rational::ONE_HALF),
/// Ordering::Greater
/// );
/// assert_eq!(
/// Rational::from_str("-2/3").unwrap().cmp_abs(&Rational::ONE_HALF),
/// Ordering::Greater
/// );
/// ```
fn cmp_abs(&self, other: &Rational) -> Ordering {
if std::ptr::eq(self, other) {
return Ordering::Equal;
}
// First check if either value is zero
let self_sign = self.numerator_ref().sign();
let other_sign = other.numerator_ref().sign();
let sign_cmp = self_sign.cmp(&other_sign);
if sign_cmp != Ordering::Equal || self_sign == Ordering::Equal {
return sign_cmp;
}
// Then check if one is < 1 and the other is > 1
let self_cmp_one = self.numerator.cmp(&self.denominator);
let other_cmp_one = other.numerator.cmp(&other.denominator);
let one_cmp = self_cmp_one.cmp(&other_cmp_one);
if one_cmp != Ordering::Equal {
return one_cmp;
}
// Then compare numerators and denominators
let n_cmp = self.numerator.cmp(&other.numerator);
let d_cmp = self.denominator.cmp(&other.denominator);
if n_cmp == Ordering::Equal && d_cmp == Ordering::Equal {
return Ordering::Equal;
} else {
let nd_cmp = n_cmp.cmp(&d_cmp);
if nd_cmp != Ordering::Equal {
return nd_cmp;
}
}
// Then compare floor ∘ log_2 ∘ abs
let log_cmp = self
.floor_log_base_2_of_abs()
.cmp(&other.floor_log_base_2_of_abs());
if log_cmp != Ordering::Equal {
return log_cmp;
}
// Finally, cross-multiply.
(&self.numerator * &other.denominator).cmp(&(&self.denominator * &other.numerator))
}
}