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// Copyright © 2024 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::Rational;
use core::cmp::Ordering;
use malachite_base::num::arithmetic::traits::Sign;
impl PartialOrd for Rational {
/// Compares two [`Rational`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp(&self, other: &Rational) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for Rational {
/// Compares 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
/// ```
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert!(Rational::from_str("2/3").unwrap() > Rational::ONE_HALF);
/// assert!(Rational::from_str("-2/3").unwrap() < Rational::ONE_HALF);
/// ```
fn cmp(&self, other: &Rational) -> Ordering {
if core::ptr::eq(self, other) {
return Ordering::Equal;
}
// First check signs
let self_sign = self.sign();
let other_sign = other.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 if self.sign {
one_cmp
} else {
one_cmp.reverse()
};
}
// 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 if self.sign { nd_cmp } else { nd_cmp.reverse() };
}
}
// Then compare floor ∘ log_2 ∘ abs
let log_cmp = self
.floor_log_base_2_abs()
.cmp(&other.floor_log_base_2_abs());
if log_cmp != Ordering::Equal {
return if self.sign {
log_cmp
} else {
log_cmp.reverse()
};
}
// Finally, cross-multiply.
let prod_cmp =
(&self.numerator * &other.denominator).cmp(&(&self.denominator * &other.numerator));
if self.sign {
prod_cmp
} else {
prod_cmp.reverse()
}
}
}