malachite_float/float/comparison/
partial_cmp_abs_rational.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::InnerFloat::{Finite, Infinity, NaN, Zero};
10use crate::{Float, significand_bits};
11use core::cmp::Ordering::{self, *};
12use malachite_base::num::arithmetic::traits::Sign;
13use malachite_base::num::comparison::traits::PartialOrdAbs;
14use malachite_base::num::conversion::traits::ExactFrom;
15use malachite_q::Rational;
16
17impl PartialOrdAbs<Rational> for Float {
18    /// Compares the absolute values of a [`Float`] and a [`Rational`].
19    ///
20    /// NaN is not comparable to any [`Rational`]. $\infty$ and $-\infty$ are greater in absolute
21    /// value than any [`Rational`]. Both the [`Float`] zero and the [`Float`] negative zero are
22    /// equal to the [`Rational`] zero.
23    ///
24    /// # Worst-case complexity
25    /// $T(n) = O(n \log n \log\log n)$
26    ///
27    /// $M(n) = O(n \log n)$
28    ///
29    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
30    /// other.significant_bits())`.
31    ///
32    /// # Examples
33    /// ```
34    /// use malachite_base::num::basic::traits::{Infinity, NegativeInfinity};
35    /// use malachite_base::num::comparison::traits::PartialOrdAbs;
36    /// use malachite_float::Float;
37    /// use malachite_q::Rational;
38    ///
39    /// assert!(Float::from(80).lt_abs(&Rational::from(100)));
40    /// assert!(Float::from(-80).lt_abs(&Rational::from(-100)));
41    /// assert!(Float::INFINITY.gt_abs(&Rational::from(100)));
42    /// assert!(Float::NEGATIVE_INFINITY.gt_abs(&Rational::from(-100)));
43    /// assert!(Float::from(1.0f64 / 3.0).lt_abs(&Rational::from_unsigneds(1u8, 3)));
44    /// ```
45    // The exact exponent comparison above already decides every case the screens of `cmp_product`
46    // could, so the final cross-multiplication is formed directly.
47    #[cfg_attr(dylint_lib = "malachite_lints", allow(use_cmp_product))]
48    fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
49        match (self, other) {
50            (float_nan!(), _) => None,
51            (float_either_infinity!(), _) => Some(Greater),
52            (float_either_zero!(), y) => Some(if *y == 0 { Equal } else { Less }),
53            (
54                Self(Finite {
55                    exponent: e_x,
56                    significand: significand_x,
57                    ..
58                }),
59                y,
60            ) => Some(if *y == 0u32 {
61                Greater
62            } else {
63                let e_x = i64::from(*e_x);
64                let exp_cmp = (e_x - 1).cmp(&y.floor_log_base_2_abs());
65                if exp_cmp != Equal {
66                    return Some(exp_cmp);
67                }
68                let shift = e_x - i64::exact_from(significand_bits(significand_x));
69                let abs_shift = shift.unsigned_abs();
70                match shift.sign() {
71                    Equal => (significand_x * other.denominator_ref()).cmp(other.numerator_ref()),
72                    Greater => ((significand_x * other.denominator_ref()) << abs_shift)
73                        .cmp(other.numerator_ref()),
74                    Less => {
75                        let n_trailing_zeros = significand_x.trailing_zeros().unwrap();
76                        if abs_shift <= n_trailing_zeros {
77                            ((significand_x >> abs_shift) * other.denominator_ref())
78                                .cmp(other.numerator_ref())
79                        } else {
80                            ((significand_x >> n_trailing_zeros) * other.denominator_ref())
81                                .cmp(&(other.numerator_ref() << (abs_shift - n_trailing_zeros)))
82                        }
83                    }
84                }
85            }),
86        }
87    }
88}
89
90impl PartialOrdAbs<Float> for Rational {
91    /// Compares the absolute values of a [`Rational`] and a [`Float`].
92    ///
93    /// No [`Rational`] is comparable to NaN. Every [`Rational`] is smaller in absolute value than
94    /// $\infty$ and $-\infty$. The [`Rational`] zero is equal to both the [`Float`] zero and the
95    /// [`Float`] negative zero.
96    ///
97    /// # Worst-case complexity
98    /// $T(n) = O(n \log n \log\log n)$
99    ///
100    /// $M(n) = O(n \log n)$
101    ///
102    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
103    /// other.significant_bits())`.
104    ///
105    /// # Examples
106    /// ```
107    /// use malachite_base::num::basic::traits::{Infinity, NegativeInfinity};
108    /// use malachite_base::num::comparison::traits::PartialOrdAbs;
109    /// use malachite_float::Float;
110    /// use malachite_q::Rational;
111    ///
112    /// assert!(Rational::from(100).gt_abs(&Float::from(80)));
113    /// assert!(Rational::from(-100).gt_abs(&Float::from(-80)));
114    /// assert!(Rational::from(100).lt_abs(&Float::INFINITY));
115    /// assert!(Rational::from(-100).lt_abs(&Float::NEGATIVE_INFINITY));
116    /// assert!(Rational::from_unsigneds(1u8, 3).gt_abs(&Float::from(1.0f64 / 3.0)));
117    /// ```
118    #[inline]
119    fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
120        other.partial_cmp_abs(self).map(Ordering::reverse)
121    }
122}
malachite_float/float/comparison/partial_cmp_abs_rational.rs

malachite_float/float/comparison/
partial_cmp_abs_rational.rs
