malachite_float/constants/
sqrt_3_over_3.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::rounding_modes::RoundingMode::{self, *};
12
13impl Float {
14    /// Returns an approximation to one third of the square root of 3, with the given precision and
15    /// rounded using the given [`RoundingMode`]. An [`Ordering`] is also returned, indicating
16    /// whether the rounded value is less than or greater than the exact value of the constant.
17    /// (Since the constant is irrational, the rounded value is never equal to the exact value.)
18    ///
19    /// $$
20    /// x = \sqrt{3}/3=\sqrt{1/3}=1/\sqrt{3}.
21    /// $$
22    ///
23    /// The constant is irrational and algebraic.
24    ///
25    /// The output has precision `prec`.
26    ///
27    /// # Worst-case complexity
28    /// $T(n) = O(n \log n \log\log n)$
29    ///
30    /// $M(n) = O(n \log n)$
31    ///
32    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
33    ///
34    /// # Panics
35    /// Panics if `prec` is zero or if `rm` is `Exact`.
36    ///
37    /// # Examples
38    /// ```
39    /// use malachite_base::rounding_modes::RoundingMode::*;
40    /// use malachite_float::Float;
41    /// use std::cmp::Ordering::*;
42    ///
43    /// let (sqrt_3_over_3, o) = Float::sqrt_3_over_3_prec_round(100, Floor);
44    /// assert_eq!(
45    ///     sqrt_3_over_3.to_string(),
46    ///     "0.577350269189625764509148780501"
47    /// );
48    /// assert_eq!(o, Less);
49    ///
50    /// let (sqrt_3_over_3, o) = Float::sqrt_3_over_3_prec_round(100, Ceiling);
51    /// assert_eq!(
52    ///     sqrt_3_over_3.to_string(),
53    ///     "0.577350269189625764509148780502"
54    /// );
55    /// assert_eq!(o, Greater);
56    /// ```
57    #[inline]
58    pub fn sqrt_3_over_3_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
59        Self::reciprocal_sqrt_prec_round(const { Self::const_from_unsigned(3) }, prec, rm)
60    }
61
62    /// Returns an approximation to one third of the square root of 3, with the given precision and
63    /// rounded to the nearest [`Float`] of that precision. An [`Ordering`] is also returned,
64    /// indicating whether the rounded value is less than or greater than the exact value of the
65    /// constant. (Since the constant is irrational, the rounded value is never equal to the exact
66    /// value.)
67    ///
68    /// $$
69    /// x = \sqrt{3}/3=\sqrt{1/3}=1/\sqrt{3}.
70    /// $$
71    ///
72    /// The constant is irrational and algebraic.
73    ///
74    /// The output has precision `prec`.
75    ///
76    /// # Worst-case complexity
77    /// $T(n) = O(n \log n \log\log n)$
78    ///
79    /// $M(n) = O(n \log n)$
80    ///
81    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
82    ///
83    /// # Panics
84    /// Panics if `prec` is zero.
85    ///
86    /// # Examples
87    /// ```
88    /// use malachite_float::Float;
89    /// use std::cmp::Ordering::*;
90    ///
91    /// let (sqrt_3_over_3, o) = Float::sqrt_3_over_3_prec(1);
92    /// assert_eq!(sqrt_3_over_3.to_string(), "0.5");
93    /// assert_eq!(o, Less);
94    ///
95    /// let (sqrt_3_over_3, o) = Float::sqrt_3_over_3_prec(10);
96    /// assert_eq!(sqrt_3_over_3.to_string(), "0.577");
97    /// assert_eq!(o, Less);
98    ///
99    /// let (sqrt_3_over_3, o) = Float::sqrt_3_over_3_prec(100);
100    /// assert_eq!(
101    ///     sqrt_3_over_3.to_string(),
102    ///     "0.577350269189625764509148780502"
103    /// );
104    /// assert_eq!(o, Greater);
105    /// ```
106    #[inline]
107    pub fn sqrt_3_over_3_prec(prec: u64) -> (Self, Ordering) {
108        Self::sqrt_3_over_3_prec_round(prec, Nearest)
109    }
110}
malachite_float/constants/sqrt_3_over_3.rs

malachite_float/constants/
sqrt_3_over_3.rs
