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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;
use malachite_base::num::basic::traits::One;
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::natural::Natural;
impl PartialOrdAbs<Natural> for Rational {
/// Compares the absolute values of a [`Rational`] and 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_base::num::comparison::traits::PartialOrdAbs;
/// use malachite_nz::natural::Natural;
/// use malachite_q::Rational;
/// use std::cmp::Ordering;
///
/// assert_eq!(
/// Rational::from_signeds(22, 7).partial_cmp_abs(&Natural::from(3u32)),
/// Some(Ordering::Greater)
/// );
/// assert_eq!(
/// Rational::from_signeds(-22, 7).partial_cmp_abs(&Natural::from(3u32)),
/// Some(Ordering::Greater)
/// );
/// ```
fn partial_cmp_abs(&self, other: &Natural) -> Option<Ordering> {
// First check if either value is zero
let self_sign = self.numerator_ref().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);
}
}
// Then compare floor ∘ log_2 ∘ abs
let log_cmp = self
.floor_log_base_2_abs()
.cmp(&i64::exact_from(other.significant_bits() - 1));
if log_cmp != Ordering::Equal {
return Some(log_cmp);
}
// Finally, cross-multiply.
Some(self.numerator.cmp(&(&self.denominator * other)))
}
}
impl PartialOrdAbs<Rational> for Natural {
/// Compares the absolute values of a [`Natural`] and 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_base::num::comparison::traits::PartialOrdAbs;
/// use malachite_nz::natural::Natural;
/// use malachite_q::Rational;
/// use std::cmp::Ordering;
///
/// assert_eq!(
/// Natural::from(3u32).partial_cmp_abs(&Rational::from_signeds(22, 7)),
/// Some(Ordering::Less)
/// );
/// assert_eq!(
/// Natural::from(3u32).partial_cmp_abs(&Rational::from_signeds(-22, 7)),
/// Some(Ordering::Less)
/// );
/// ```
#[inline]
fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
other.partial_cmp_abs(self).map(Ordering::reverse)
}
}