pxfm/gamma/
gamma_pf.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::common::f_fmla;
30use crate::exponents::core_expdf;
31use crate::gamma::lgamma_rf::lgamma_coref;
32use crate::logs::fast_logf;
33
34/// Regularized lower incomplete gamma
35pub fn f_gamma_pf(a: f32, x: f32) -> f32 {
36    let aa = a.to_bits();
37    let ax = x.to_bits();
38
39    if aa >= 0xffu32 << 23 || aa == 0 || ax >= 0xffu32 << 23 || ax == 0 {
40        if (aa >> 31) != 0 || (ax >> 31) != 0 {
41            // |a| < 0 or |b| < 0
42            return f32::NAN;
43        }
44        if aa.wrapping_shl(1) == 0 {
45            // |a| == 0
46            return 1.0;
47        }
48        if ax.wrapping_shl(1) == 0 {
49            // |x| == 0
50            return 0.;
51        }
52        if a.is_infinite() {
53            // |a| == infinity
54            return f32::INFINITY;
55        }
56        if x.is_infinite() {
57            // |x| == infinity
58            return f32::INFINITY;
59        }
60        return a + f32::NAN;
61    }
62    core_gamma_pf(a, x) as f32
63}
64
65#[inline]
66pub(crate) fn core_gamma_pf(a: f32, x: f32) -> f64 {
67    const BIG: f64 = 4503599627370496.0;
68    const BIG_INV: f64 = 2.22044604925031308085e-16;
69
70    const EPS: f64 = 1e-9;
71
72    let da = a as f64;
73    let dx = x as f64;
74
75    let ax = f_fmla(da, fast_logf(x), -dx - lgamma_coref(a).0);
76    if ax <= -104. {
77        if a < x {
78            return 1.0;
79        }
80        return 0.0;
81    }
82    if ax >= 89. {
83        return f64::INFINITY;
84    }
85
86    if x <= 1.0 || x <= a {
87        let mut r2 = da;
88        let mut c2 = 1.0;
89        let mut ans2 = 1.0;
90        for _ in 0..200 {
91            r2 += 1.0;
92            c2 *= dx / r2;
93            ans2 += c2;
94
95            if c2 / ans2 <= EPS {
96                break;
97            }
98        }
99        return core_expdf(ax) * ans2 / da;
100    }
101
102    let mut y = 1.0 - da;
103    let mut z = dx + y + 1.0;
104    let mut c = 0i32;
105
106    let mut p3 = 1.0;
107    let mut q3 = dx;
108    let mut p2 = dx + 1.0;
109    let mut q2 = z * dx;
110    let mut ans = p2 / q2;
111
112    for _ in 0..200 {
113        y += 1.0;
114        z += 2.0;
115        c += 1;
116        let yc = y * c as f64;
117
118        let p = p2 * z - p3 * yc;
119        let q = q2 * z - q3 * yc;
120
121        p3 = p2;
122        p2 = p;
123        q3 = q2;
124        q2 = q;
125
126        if p.abs() > BIG {
127            p3 *= BIG_INV;
128            p2 *= BIG_INV;
129            q3 *= BIG_INV;
130            q2 *= BIG_INV;
131        }
132
133        if q != 0.0 {
134            let nextans = p / q;
135            let error = ((ans - nextans) / nextans).abs();
136            ans = nextans;
137
138            if error <= EPS {
139                break;
140            }
141        }
142    }
143
144    f_fmla(-core_expdf(ax), ans, 1.0)
145}
146
147#[cfg(test)]
148mod tests {
149    use super::*;
150    #[test]
151    fn test_f_beta_pf() {
152        assert_eq!(f_gamma_pf(23.421, 41.), 0.9988695);
153        assert_eq!(f_gamma_pf(0.764, 0.432123), 0.47752997);
154        assert_eq!(f_gamma_pf(0.421, 1.), 0.8727869);
155        assert!(f_gamma_pf(-1., 12.).is_nan());
156        assert!(f_gamma_pf(1., -12.).is_nan());
157        assert!(f_gamma_pf(f32::NAN, 12.).is_nan());
158        assert!(f_gamma_pf(1., f32::NAN).is_nan());
159        assert_eq!(f_gamma_pf(1., f32::INFINITY), f32::INFINITY);
160        assert_eq!(f_gamma_pf(f32::INFINITY, f32::INFINITY), f32::INFINITY);
161        assert_eq!(f_gamma_pf(f32::INFINITY, 5.32), f32::INFINITY);
162    }
163}
pxfm/gamma/gamma_pf.rs

pxfm/gamma/
gamma_pf.rs
