malachite_float/constants/
sqrt_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 the square root of 3, with the given precision and rounded using
15    /// the given [`RoundingMode`]. An [`Ordering`] is also returned, indicating whether the rounded
16    /// value is less than or greater than the exact value of the constant. (Since the constant is
17    /// irrational, the rounded value is never equal to the exact value.)
18    ///
19    /// $$
20    /// x = \sqrt{3}.
21    /// $$
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, o) = Float::sqrt_3_prec_round(100, Floor);
44    /// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341505");
45    /// assert_eq!(o, Less);
46    ///
47    /// let (sqrt_3, o) = Float::sqrt_3_prec_round(100, Ceiling);
48    /// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341506");
49    /// assert_eq!(o, Greater);
50    /// ```
51    #[inline]
52    pub fn sqrt_3_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
53        Self::sqrt_prec_round(const { Self::const_from_unsigned(3) }, prec, rm)
54    }
55
56    /// Returns an approximation to the square root of 3, with the given precision and rounded to
57    /// the nearest [`Float`] of that precision. An [`Ordering`] is also returned, indicating
58    /// whether the rounded value is less than or greater than the exact value of the constant.
59    /// (Since the constant is irrational, the rounded value is never equal to the exact value.)
60    ///
61    /// $$
62    /// x = \sqrt{3}.
63    /// $$
64    ///
65    /// The constant is irrational and algebraic.
66    ///
67    /// The output has precision `prec`.
68    ///
69    /// # Worst-case complexity
70    /// $T(n) = O(n \log n \log\log n)$
71    ///
72    /// $M(n) = O(n \log n)$
73    ///
74    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
75    ///
76    /// # Panics
77    /// Panics if `prec` is zero.
78    ///
79    /// # Examples
80    /// ```
81    /// use malachite_float::Float;
82    /// use std::cmp::Ordering::*;
83    ///
84    /// let (sqrt_3, o) = Float::sqrt_3_prec(1);
85    /// assert_eq!(sqrt_3.to_string(), "2.0");
86    /// assert_eq!(o, Greater);
87    ///
88    /// let (sqrt_3, o) = Float::sqrt_3_prec(10);
89    /// assert_eq!(sqrt_3.to_string(), "1.732");
90    /// assert_eq!(o, Greater);
91    ///
92    /// let (sqrt_3, o) = Float::sqrt_3_prec(100);
93    /// assert_eq!(sqrt_3.to_string(), "1.732050807568877293527446341506");
94    /// assert_eq!(o, Greater);
95    /// ```
96    #[inline]
97    pub fn sqrt_3_prec(prec: u64) -> (Self, Ordering) {
98        Self::sqrt_3_prec_round(prec, Nearest)
99    }
100}
malachite_float/constants/sqrt_3.rs

malachite_float/constants/
sqrt_3.rs
