malachite_float/constants/
phi.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::{self, *};
11use malachite_base::num::basic::traits::{One, Two};
12use malachite_base::rounding_modes::RoundingMode::{self, *};
13
14impl Float {
15    /// Returns an approximation to the golden ratio, with the given precision and rounded using the
16    /// 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    /// $$
21    /// x = \varphi = \frac{1+\sqrt{2}}{2}.
22    /// $$
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 (phi, o) = Float::phi_prec_round(100, Floor);
45    /// assert_eq!(phi.to_string(), "1.618033988749894848204586834364");
46    /// assert_eq!(o, Less);
47    ///
48    /// let (phi, o) = Float::phi_prec_round(100, Ceiling);
49    /// assert_eq!(phi.to_string(), "1.618033988749894848204586834366");
50    /// assert_eq!(o, Greater);
51    /// ```
52    #[inline]
53    pub fn phi_prec_round(prec: u64, rm: RoundingMode) -> (Self, Ordering) {
54        if prec == 1 {
55            match rm {
56                Floor | Down => (Self::ONE, Less),
57                Ceiling | Up | Nearest => (Self::TWO, Greater),
58                Exact => panic!("Inexact float square root"),
59            }
60        } else {
61            let (sqrt_5, o) =
62                Self::sqrt_prec_round(const { Self::const_from_unsigned(5) }, prec, rm);
63            ((sqrt_5 + Self::ONE) >> 1u32, o)
64        }
65    }
66
67    /// Returns an approximation to the golden ratio, with the given precision and rounded to the
68    /// nearest [`Float`] of that precision. An [`Ordering`] is also returned, indicating whether
69    /// the rounded value is less than or greater than the exact value of the constant. (Since the
70    /// constant is irrational, the rounded value is never equal to the exact value.)
71    ///
72    /// $$
73    /// x = \varphi = \frac{1+\sqrt{2}}{2}.
74    /// $$
75    ///
76    /// The constant is irrational and algebraic.
77    ///
78    /// The output has precision `prec`.
79    ///
80    /// # Worst-case complexity
81    /// $T(n) = O(n \log n \log\log n)$
82    ///
83    /// $M(n) = O(n \log n)$
84    ///
85    /// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
86    ///
87    /// # Panics
88    /// Panics if `prec` is zero.
89    ///
90    /// # Examples
91    /// ```
92    /// use malachite_float::Float;
93    /// use std::cmp::Ordering::*;
94    ///
95    /// let (phi, o) = Float::phi_prec(1);
96    /// assert_eq!(phi.to_string(), "2.0");
97    /// assert_eq!(o, Greater);
98    ///
99    /// let (phi, o) = Float::phi_prec(10);
100    /// assert_eq!(phi.to_string(), "1.617");
101    /// assert_eq!(o, Less);
102    ///
103    /// let (phi, o) = Float::phi_prec(100);
104    /// assert_eq!(phi.to_string(), "1.618033988749894848204586834366");
105    /// assert_eq!(o, Greater);
106    /// ```
107    #[inline]
108    pub fn phi_prec(prec: u64) -> (Self, Ordering) {
109        Self::phi_prec_round(prec, Nearest)
110    }
111}
malachite_float/constants/phi.rs

malachite_float/constants/
phi.rs
