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/// The natural logarithm of 1+`x` (f32).
24#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
25pub fn log1pf(x: f32) -> f32 {
26 let mut ui: u32 = x.to_bits();
27 let hfsq: f32;
28 let mut f: f32 = 0.;
29 let mut c: f32 = 0.;
30 let s: f32;
31 let z: f32;
32 let r: f32;
33 let w: f32;
34 let t1: f32;
35 let t2: f32;
36 let dk: f32;
37 let ix: u32;
38 let mut iu: u32;
39 let mut k: i32;
40
41 ix = ui;
42 k = 1;
43 if ix < 0x3ed413d0 || (ix >> 31) > 0 {
44 /* 1+x < sqrt(2)+ */
45 if ix >= 0xbf800000 {
46 /* x <= -1.0 */
47 if x == -1. {
48 return x / 0.0; /* log1p(-1)=+inf */
49 }
50 return (x - x) / 0.0; /* log1p(x<-1)=NaN */
51 }
52 if ix << 1 < 0x33800000 << 1 {
53 /* |x| < 2**-24 */
54 /* underflow if subnormal */
55 if (ix & 0x7f800000) == 0 {
56 force_eval!(x * x);
57 }
58 return x;
59 }
60 if ix <= 0xbe95f619 {
61 /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
62 k = 0;
63 c = 0.;
64 f = x;
65 }
66 } else if ix >= 0x7f800000 {
67 return x;
68 }
69 if k > 0 {
70 ui = (1. + x).to_bits();
71 iu = ui;
72 iu += 0x3f800000 - 0x3f3504f3;
73 k = (iu >> 23) as i32 - 0x7f;
74 /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
75 if k < 25 {
76 c = if k >= 2 { 1. - (f32::from_bits(ui) - x) } else { x - (f32::from_bits(ui) - 1.) };
77 c /= f32::from_bits(ui);
78 } else {
79 c = 0.;
80 }
81 /* reduce u into [sqrt(2)/2, sqrt(2)] */
82 iu = (iu & 0x007fffff) + 0x3f3504f3;
83 ui = iu;
84 f = f32::from_bits(ui) - 1.;
85 }
86 s = f / (2.0 + f);
87 z = s * s;
88 w = z * z;
89 t1 = w * (LG2 + w * LG4);
90 t2 = z * (LG1 + w * LG3);
91 r = t2 + t1;
92 hfsq = 0.5 * f * f;
93 dk = k as f32;
94 s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
95}
96