1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
// 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;
use malachite_base::num::basic::traits::One;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::natural::Natural;
impl PartialOrd<Natural> for Rational {
/// Compares a [`Rational`] to a [`Natural`].
///
/// # 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_nz::natural::Natural;
/// use malachite_q::Rational;
///
/// assert!(Rational::from_signeds(22, 7) > Natural::from(3u32));
/// assert!(Rational::from_signeds(22, 7) < Natural::from(4u32));
/// ```
fn partial_cmp(&self, other: &Natural) -> Option<Ordering> {
// 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 Some(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.cmp(&Natural::ONE);
let one_cmp = self_cmp_one.cmp(&other_cmp_one);
if one_cmp != Ordering::Equal {
return Some(one_cmp);
}
// Then compare numerators and denominators
let n_cmp = self.numerator.cmp(other);
let d_cmp = self.denominator.cmp(&Natural::ONE);
if n_cmp == Ordering::Equal && d_cmp == Ordering::Equal {
return Some(Ordering::Equal);
} else {
let nd_cmp = n_cmp.cmp(&d_cmp);
if nd_cmp != Ordering::Equal {
return Some(nd_cmp);
}
}
let log_cmp = self
.floor_log_base_2_abs()
.cmp(&i64::exact_from(other.significant_bits() - 1));
if log_cmp != Ordering::Equal {
return Some(if self.sign {
log_cmp
} else {
log_cmp.reverse()
});
}
// Finally, cross-multiply.
Some(self.numerator.cmp(&(&self.denominator * other)))
}
}
impl PartialOrd<Rational> for Natural {
/// Compares a [`Natural`] to a [`Rational`].
///
/// # 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_nz::natural::Natural;
/// use malachite_q::Rational;
///
/// assert!(Natural::from(3u32) < Rational::from_signeds(22, 7));
/// assert!(Natural::from(4u32) > Rational::from_signeds(22, 7));
/// ```
#[inline]
fn partial_cmp(&self, other: &Rational) -> Option<Ordering> {
other.partial_cmp(self).map(Ordering::reverse)
}
}