malachite_float/constants/
prime_constant.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::factorization::primes::prime_indicator_sequence_less_than_or_equal_to;
12use malachite_base::rounding_modes::RoundingMode::{self, *};
13
14impl Float {
15    /// Returns an approximation to the prime constant, with the given precision and rounded using
16    /// the given [`RoundingMode`]. An [`Ordering`] is also returned, indicating whether the rounded
17    /// value is less than or greater than the exact value of the constant. (Since the constant is
18    /// irrational, the rounded value is never equal to the exact value.)
19    ///
20    /// The prime constant is the real number whose $n$th bit is prime if and only if $n$ is prime.
21    /// That is,
22    /// $$
23    /// P = \sum_{p\ text{prime}\}2^{-p}.
24    /// $$
25    ///
26    /// The constant is irrational.
27    ///
28    /// The output has precision `prec`.
29    ///
30    /// # Worst-case complexity
31    /// $T(n) = O(n)$
32    ///
33    /// $M(n) = O(n)$
34    ///
35    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
36    ///
37    /// # Panics
38    /// Panics if `prec` is zero or if `rm` is `Exact`.
39    ///
40    /// # Examples
41    /// ```
42    /// use malachite_base::rounding_modes::RoundingMode::*;
43    /// use malachite_float::Float;
44    /// use std::cmp::Ordering::*;
45    ///
46    /// let (pc, o) = Float::prime_constant_prec_round(100, Floor);
47    /// assert_eq!(pc.to_string(), "0.4146825098511116602481096221542");
48    /// assert_eq!(o, Less);
49    ///
50    /// let (pc, o) = Float::prime_constant_prec_round(100, Ceiling);
51    /// assert_eq!(pc.to_string(), "0.4146825098511116602481096221546");
52    /// assert_eq!(o, Greater);
53    /// ```
54    pub fn prime_constant_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
55        // Strictly speaking, this call violates the preconditions for
56        // `non_dyadic_from_bits_prec_round`, because the iterator passed in is finite. But since we
57        // know exactly how many bits `non_dyadic_from_bits_prec_round` will read, we can get away
58        // with this.
59        Self::non_dyadic_from_bits_prec_round(
60            prime_indicator_sequence_less_than_or_equal_to(if rm == Nearest {
61                prec + 2
62            } else {
63                prec + 1
64            }),
65            prec,
66            rm,
67        )
68    }
69
70    /// Returns an approximation to the prime constant, with the given precision and rounded to the
71    /// nearest [`Float`] of that precision. An [`Ordering`] is also returned, indicating whether
72    /// the rounded value is less than or greater than the exact value of the constant. (Since the
73    /// constant is irrational, the rounded value is never equal to the exact value.)
74    ///
75    /// The prime constant is the real number whose $n$th bit is prime if and only if $n$ is prime.
76    /// That is,
77    /// $$
78    /// P = \sum_{p\ text{prime}\}2^{-p}.
79    /// $$
80    ///
81    /// The constant is irrational.
82    ///
83    /// The output has precision `prec`.
84    ///
85    /// # Worst-case complexity
86    /// $T(n) = O(n)$
87    ///
88    /// $M(n) = O(n)$
89    ///
90    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
91    ///
92    /// # Panics
93    /// Panics if `prec` is zero.
94    ///
95    /// # Examples
96    /// ```
97    /// use malachite_float::Float;
98    /// use std::cmp::Ordering::*;
99    ///
100    /// let (pc, o) = Float::prime_constant_prec(1);
101    /// assert_eq!(pc.to_string(), "0.5");
102    /// assert_eq!(o, Greater);
103    ///
104    /// let (pc, o) = Float::prime_constant_prec(10);
105    /// assert_eq!(pc.to_string(), "0.4146");
106    /// assert_eq!(o, Less);
107    ///
108    /// let (pc, o) = Float::prime_constant_prec(100);
109    /// assert_eq!(pc.to_string(), "0.4146825098511116602481096221542");
110    /// assert_eq!(o, Less);
111    /// ```
112    #[inline]
113    pub fn prime_constant_prec(prec: u64) -> (Self, Ordering) {
114        Self::prime_constant_prec_round(prec, Nearest)
115    }
116}
malachite_float/constants/prime_constant.rs

malachite_float/constants/
prime_constant.rs
