pxfm/gamma/
beta.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 9/2025. All rights reserved.
3 * //
4 * // Redistribution and use in source and binary forms, with or without modification,
5 * // are permitted provided that the following conditions are met:
6 * //
7 * // 1.  Redistributions of source code must retain the above copyright notice, this
8 * // list of conditions and the following disclaimer.
9 * //
10 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
11 * // this list of conditions and the following disclaimer in the documentation
12 * // and/or other materials provided with the distribution.
13 * //
14 * // 3.  Neither the name of the copyright holder nor the names of its
15 * // contributors may be used to endorse or promote products derived from
16 * // this software without specific prior written permission.
17 * //
18 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29use crate::double_double::DoubleDouble;
30use crate::f_exp;
31use crate::gamma::lgamma::lgamma_core;
32
33/// Computes beta function
34pub fn f_beta(a: f64, b: f64) -> f64 {
35    let ax = a.to_bits();
36    let bx = b.to_bits();
37
38    if ax >= 0x7ffu64 << 52 || ax == 0 || bx >= 0x7ffu64 << 52 || bx == 0 {
39        if (ax >> 63) != 0 || (bx >> 63) != 0 {
40            // |a| < 0 or |b| < 0
41            return f64::NAN;
42        }
43        if ax.wrapping_shl(1) == 0 || bx.wrapping_shl(1) == 0 {
44            // |a| == 0 || |b| == 0
45            if ax.wrapping_shl(1) != 0 || bx.wrapping_shl(1) != 0 {
46                return f64::INFINITY;
47            }
48            return f64::NAN;
49        }
50        if a.is_infinite() || b.is_infinite() {
51            // |a| == inf or |b| == inf
52            return 0.;
53        }
54        return a + f64::NAN; // nan
55    }
56
57    let mut sign = 1i32;
58    let (mut y, sgngamf) = lgamma_core(DoubleDouble::from_full_exact_add(a, b).to_f64());
59    sign *= sgngamf; /* keep track of the sign */
60    let (y1, sgngamf) = lgamma_core(b);
61    y = DoubleDouble::quick_dd_sub(y1, y);
62    sign *= sgngamf;
63    let (y1, sgngamf) = lgamma_core(a);
64    y = DoubleDouble::quick_dd_add(y1, y);
65    sign *= sgngamf;
66    f_exp(y.to_f64()) * (sign as f64)
67}
68
69#[cfg(test)]
70mod tests {
71    use crate::f_beta;
72
73    #[test]
74    fn test_beta() {
75        assert!(f_beta(-5., 15.).is_nan());
76        assert!(f_beta(5., -15.).is_nan());
77        assert!(f_beta(f64::NAN, 15.).is_nan());
78        assert!(f_beta(15., f64::NAN).is_nan());
79        assert_eq!(f_beta(f64::INFINITY, 0.), f64::INFINITY);
80        assert_eq!(f_beta(f64::INFINITY, 1.), 0.);
81        assert_eq!(f_beta(1., f64::INFINITY), 0.);
82        assert_eq!(f_beta(5., 3.), 0.009523809523809526);
83        assert_eq!(f_beta(3., 5.), 0.009523809523809526);
84        assert_eq!(f_beta(12., 23.), 1.5196994506201402e-10);
85    }
86}
pxfm/gamma/beta.rs

pxfm/gamma/
beta.rs
