malachite_float/constants/
sqrt_2_over_2.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::Float;
10use core::cmp::Ordering;
11use malachite_base::num::basic::traits::Two;
12use malachite_base::rounding_modes::RoundingMode::{self, *};
13
14impl Float {
15    /// Returns an approximation to half of the square root of 2, with the given precision and
16    /// rounded using the given [`RoundingMode`]. An [`Ordering`] is also returned, indicating
17    /// whether the rounded value is less than or greater than the exact value of the constant.
18    /// (Since the constant is irrational, the rounded value is never equal to the exact value.)
19    ///
20    /// $$
21    /// x = \sqrt{2}/2=\sqrt{1/2}=1/\sqrt{2}.
22    /// $$
23    ///
24    /// The constant is irrational and algebraic.
25    ///
26    /// The output has precision `prec`.
27    ///
28    /// # Worst-case complexity
29    /// $T(n) = O(n \log n \log\log n)$
30    ///
31    /// $M(n) = O(n \log n)$
32    ///
33    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
34    ///
35    /// # Panics
36    /// Panics if `prec` is zero or if `rm` is `Exact`.
37    ///
38    /// # Examples
39    /// ```
40    /// use malachite_base::rounding_modes::RoundingMode::*;
41    /// use malachite_float::Float;
42    /// use std::cmp::Ordering::*;
43    ///
44    /// let (sqrt_2_over_2, o) = Float::sqrt_2_over_2_prec_round(100, Floor);
45    /// assert_eq!(
46    ///     sqrt_2_over_2.to_string(),
47    ///     "0.7071067811865475244008443621046"
48    /// );
49    /// assert_eq!(o, Less);
50    ///
51    /// let (sqrt_2_over_2, o) = Float::sqrt_2_over_2_prec_round(100, Ceiling);
52    /// assert_eq!(
53    ///     sqrt_2_over_2.to_string(),
54    ///     "0.7071067811865475244008443621054"
55    /// );
56    /// assert_eq!(o, Greater);
57    /// ```
58    #[inline]
59    pub fn sqrt_2_over_2_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
60        let (sqrt_2, o) = Self::sqrt_prec_round(Self::TWO, prec, rm);
61        (sqrt_2 >> 1u32, o)
62    }
63
64    /// Returns an approximation to half of the square root of 2, with the given precision and
65    /// rounded to the nearest [`Float`] of that precision. An [`Ordering`] is also returned,
66    /// indicating whether the rounded value is less than or greater than the exact value of the
67    /// constant. (Since the constant is irrational, the rounded value is never equal to the exact
68    /// value.)
69    ///
70    /// $$
71    /// x = \sqrt{2}/2=\sqrt{1/2}=1/\sqrt{2}.
72    /// $$
73    ///
74    /// The constant is irrational and algebraic.
75    ///
76    /// The output has precision `prec`.
77    ///
78    /// # Worst-case complexity
79    /// $T(n) = O(n \log n \log\log n)$
80    ///
81    /// $M(n) = O(n \log n)$
82    ///
83    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
84    ///
85    /// # Panics
86    /// Panics if `prec` is zero.
87    ///
88    /// # Examples
89    /// ```
90    /// use malachite_float::Float;
91    /// use std::cmp::Ordering::*;
92    ///
93    /// let (sqrt_2_over_2, o) = Float::sqrt_2_over_2_prec(1);
94    /// assert_eq!(sqrt_2_over_2.to_string(), "0.5");
95    /// assert_eq!(o, Less);
96    ///
97    /// let (sqrt_2_over_2, o) = Float::sqrt_2_over_2_prec(10);
98    /// assert_eq!(sqrt_2_over_2.to_string(), "0.707");
99    /// assert_eq!(o, Less);
100    ///
101    /// let (sqrt_2_over_2, o) = Float::sqrt_2_over_2_prec(100);
102    /// assert_eq!(
103    ///     sqrt_2_over_2.to_string(),
104    ///     "0.7071067811865475244008443621046"
105    /// );
106    /// assert_eq!(o, Less);
107    /// ```
108    #[inline]
109    pub fn sqrt_2_over_2_prec(prec: u64) -> (Self, Ordering) {
110        Self::sqrt_2_over_2_prec_round(prec, Nearest)
111    }
112}
malachite_float/constants/sqrt_2_over_2.rs

malachite_float/constants/
sqrt_2_over_2.rs
