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// Copyright © 2026 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::{self, *};
use malachite_base::num::arithmetic::traits::{Sign, UnsignedAbs};
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;
#[allow(clippy::unnecessary_wraps)]
fn partial_cmp_abs_unsigned<T: Copy + One + Ord + Sign + SignificantBits>(
x: &Rational,
other: &T,
) -> Option<Ordering>
where
Natural: From<T> + PartialOrd<T>,
{
// First check if either value is zero
let self_sign = x.numerator_ref().sign();
let other_sign = other.sign();
let sign_cmp = self_sign.cmp(&other_sign);
if sign_cmp != Equal || self_sign == Equal {
return Some(sign_cmp);
}
// Then check if one is < 1 and the other is > 1
let self_cmp_one = x.numerator.cmp(&x.denominator);
let other_cmp_one = other.cmp(&T::ONE);
let one_cmp = self_cmp_one.cmp(&other_cmp_one);
if one_cmp != Equal {
return Some(one_cmp);
}
// Then compare numerators and denominators
let n_cmp = x.numerator.partial_cmp(other).unwrap();
let d_cmp = x.denominator.cmp(&Natural::ONE);
if n_cmp == Equal && d_cmp == Equal {
return Some(Equal);
}
let nd_cmp = n_cmp.cmp(&d_cmp);
if nd_cmp != Equal {
return Some(nd_cmp);
}
// Then compare floor ∘ log_2 ∘ abs
let log_cmp = x
.floor_log_base_2_abs()
.cmp(&i64::exact_from(other.significant_bits() - 1));
if log_cmp != Equal {
return Some(log_cmp);
}
// Finally, cross-multiply.
Some(x.numerator.cmp(&(&x.denominator * Natural::from(*other))))
}
macro_rules! impl_unsigned {
($t: ident) => {
impl PartialOrdAbs<$t> for Rational {
/// Compares the absolute values of a [`Rational`] and an unsigned primitive integer.
///
/// # 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
/// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
#[inline]
fn partial_cmp_abs(&self, other: &$t) -> Option<Ordering> {
partial_cmp_abs_unsigned(self, other)
}
}
impl PartialOrdAbs<Rational> for $t {
/// Compares the absolute values of an unsigned primitive integer 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 `other.significant_bits()`.
///
/// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
#[inline]
fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
other.partial_cmp_abs(self).map(Ordering::reverse)
}
}
};
}
apply_to_unsigneds!(impl_unsigned);
#[allow(clippy::unnecessary_wraps)]
fn partial_cmp_abs_signed<
U: Copy + One + Ord + Sign + SignificantBits,
S: Copy + Sign + SignificantBits + UnsignedAbs<Output = U>,
>(
x: &Rational,
other: &S,
) -> Option<Ordering>
where
Natural: From<U> + PartialOrd<U>,
{
// First check if either value is zero
let self_sign = x.numerator_ref().sign();
let other_abs = other.unsigned_abs();
let other_sign = other_abs.sign();
let sign_cmp = self_sign.cmp(&other_sign);
if sign_cmp != Equal || self_sign == Equal {
return Some(sign_cmp);
}
// Then check if one is < 1 and the other is > 1
let self_cmp_one = x.numerator.cmp(&x.denominator);
let other_cmp_one = other_abs.cmp(&U::ONE);
let one_cmp = self_cmp_one.cmp(&other_cmp_one);
if one_cmp != Equal {
return Some(one_cmp);
}
// Then compare numerators and denominators
let n_cmp = x.numerator.partial_cmp(&other_abs).unwrap();
let d_cmp = x.denominator.cmp(&Natural::ONE);
if n_cmp == Equal && d_cmp == Equal {
return Some(Equal);
}
let nd_cmp = n_cmp.cmp(&d_cmp);
if nd_cmp != Equal {
return Some(nd_cmp);
}
// Then compare floor ∘ log_2 ∘ abs
let log_cmp = x
.floor_log_base_2_abs()
.cmp(&i64::exact_from(other.significant_bits() - 1));
if log_cmp != Equal {
return Some(log_cmp);
}
// Finally, cross-multiply.
Some(
x.numerator
.cmp(&(&x.denominator * Natural::from(other_abs))),
)
}
macro_rules! impl_signed {
($t: ident) => {
impl PartialOrdAbs<$t> for Rational {
/// Compares the absolute values of a [`Rational`] and a signed primitive integer.
///
/// # 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
/// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
#[inline]
fn partial_cmp_abs(&self, other: &$t) -> Option<Ordering> {
partial_cmp_abs_signed(self, other)
}
}
impl PartialOrdAbs<Rational> for $t {
/// Compares the absolute values of a signed primitive integer 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 `other.significant_bits()`.
///
/// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
#[inline]
fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
other.partial_cmp_abs(self).map(Ordering::reverse)
}
}
};
}
apply_to_signeds!(impl_signed);