libm/math/
log1pf.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13use core::f32;
14
15const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
16const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
17/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
18const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
19const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
20const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
21const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
22
23#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
24pub fn log1pf(x: f32) -> f32 {
25    let mut ui: u32 = x.to_bits();
26    let hfsq: f32;
27    let mut f: f32 = 0.;
28    let mut c: f32 = 0.;
29    let s: f32;
30    let z: f32;
31    let r: f32;
32    let w: f32;
33    let t1: f32;
34    let t2: f32;
35    let dk: f32;
36    let ix: u32;
37    let mut iu: u32;
38    let mut k: i32;
39
40    ix = ui;
41    k = 1;
42    if ix < 0x3ed413d0 || (ix >> 31) > 0 {
43        /* 1+x < sqrt(2)+  */
44        if ix >= 0xbf800000 {
45            /* x <= -1.0 */
46            if x == -1. {
47                return x / 0.0; /* log1p(-1)=+inf */
48            }
49            return (x - x) / 0.0; /* log1p(x<-1)=NaN */
50        }
51        if ix << 1 < 0x33800000 << 1 {
52            /* |x| < 2**-24 */
53            /* underflow if subnormal */
54            if (ix & 0x7f800000) == 0 {
55                force_eval!(x * x);
56            }
57            return x;
58        }
59        if ix <= 0xbe95f619 {
60            /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
61            k = 0;
62            c = 0.;
63            f = x;
64        }
65    } else if ix >= 0x7f800000 {
66        return x;
67    }
68    if k > 0 {
69        ui = (1. + x).to_bits();
70        iu = ui;
71        iu += 0x3f800000 - 0x3f3504f3;
72        k = (iu >> 23) as i32 - 0x7f;
73        /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
74        if k < 25 {
75            c = if k >= 2 {
76                1. - (f32::from_bits(ui) - x)
77            } else {
78                x - (f32::from_bits(ui) - 1.)
79            };
80            c /= f32::from_bits(ui);
81        } else {
82            c = 0.;
83        }
84        /* reduce u into [sqrt(2)/2, sqrt(2)] */
85        iu = (iu & 0x007fffff) + 0x3f3504f3;
86        ui = iu;
87        f = f32::from_bits(ui) - 1.;
88    }
89    s = f / (2.0 + f);
90    z = s * s;
91    w = z * z;
92    t1 = w * (LG2 + w * LG4);
93    t2 = z * (LG1 + w * LG3);
94    r = t2 + t1;
95    hfsq = 0.5 * f * f;
96    dk = k as f32;
97    s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
98}