malachite_q/arithmetic/
floor.rs

1// Copyright © 2025 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::Rational;
10use core::mem::swap;
11use malachite_base::num::arithmetic::traits::{DivRound, DivRoundAssign, Floor, FloorAssign};
12use malachite_base::num::basic::traits::One;
13use malachite_base::rounding_modes::RoundingMode::*;
14use malachite_nz::integer::Integer;
15use malachite_nz::natural::Natural;
16
17impl Floor for Rational {
18    type Output = Integer;
19
20    /// Finds the floor of a [`Rational`], taking the [`Rational`] by value.
21    ///
22    /// $$
23    /// f(x) = \lfloor x \rfloor.
24    /// $$
25    ///
26    /// # Worst-case complexity
27    /// $T(n) = O(n \log n \log\log n)$
28    ///
29    /// $M(n) = O(n \log n)$
30    ///
31    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
32    /// other.significant_bits())`.
33    ///
34    /// # Examples
35    /// ```
36    /// use malachite_base::num::arithmetic::traits::Floor;
37    /// use malachite_base::num::basic::traits::Zero;
38    /// use malachite_q::Rational;
39    ///
40    /// assert_eq!(Rational::ZERO.floor(), 0);
41    /// assert_eq!(Rational::from_signeds(22, 7).floor(), 3);
42    /// assert_eq!(Rational::from_signeds(-22, 7).floor(), -4);
43    /// ```
44    fn floor(self) -> Integer {
45        if self.sign {
46            Integer::from(self.numerator / self.denominator)
47        } else {
48            Integer::from_sign_and_abs(false, self.numerator.div_round(self.denominator, Ceiling).0)
49        }
50    }
51}
52
53impl Floor for &Rational {
54    type Output = Integer;
55
56    /// Finds the floor of a [`Rational`], taking the [`Rational`] by reference.
57    ///
58    /// $$
59    /// f(x) = \lfloor x \rfloor.
60    /// $$
61    ///
62    /// # Worst-case complexity
63    /// $T(n) = O(n \log n \log\log n)$
64    ///
65    /// $M(n) = O(n \log n)$
66    ///
67    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
68    /// other.significant_bits())`.
69    ///
70    /// # Examples
71    /// ```
72    /// use malachite_base::num::arithmetic::traits::Floor;
73    /// use malachite_base::num::basic::traits::Zero;
74    /// use malachite_q::Rational;
75    ///
76    /// assert_eq!((&Rational::ZERO).floor(), 0);
77    /// assert_eq!((&Rational::from_signeds(22, 7)).floor(), 3);
78    /// assert_eq!((&Rational::from_signeds(-22, 7)).floor(), -4);
79    /// ```
80    fn floor(self) -> Integer {
81        if self.sign {
82            Integer::from(&self.numerator / &self.denominator)
83        } else {
84            Integer::from_sign_and_abs(
85                false,
86                (&self.numerator).div_round(&self.denominator, Ceiling).0,
87            )
88        }
89    }
90}
91
92impl FloorAssign for Rational {
93    /// Replaces a [`Rational`] with its floor.
94    ///
95    /// $$
96    /// x \gets \lfloor x \rfloor.
97    /// $$
98    ///
99    /// # Worst-case complexity
100    /// $T(n) = O(n \log n \log\log n)$
101    ///
102    /// $M(n) = O(n \log n)$
103    ///
104    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
105    /// other.significant_bits())`.
106    ///
107    /// # Examples
108    /// ```
109    /// use malachite_base::num::arithmetic::traits::FloorAssign;
110    /// use malachite_base::num::basic::traits::Zero;
111    /// use malachite_q::Rational;
112    ///
113    /// let mut x = Rational::ZERO;
114    /// x.floor_assign();
115    /// assert_eq!(x, 0);
116    ///
117    /// let mut x = Rational::from_signeds(22, 7);
118    /// x.floor_assign();
119    /// assert_eq!(x, 3);
120    ///
121    /// let mut x = Rational::from_signeds(-22, 7);
122    /// x.floor_assign();
123    /// assert_eq!(x, -4);
124    /// ```
125    fn floor_assign(&mut self) {
126        let mut d = Natural::ONE;
127        swap(&mut self.denominator, &mut d);
128        if self.sign {
129            self.numerator /= d;
130        } else {
131            self.numerator.div_round_assign(d, Ceiling);
132            if !self.sign && self.numerator == 0 {
133                self.sign = true;
134            }
135        }
136    }
137}
malachite_q/arithmetic/floor.rs

malachite_q/arithmetic/
floor.rs
