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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 | ||
13 | use core::f32; | |
14 | ||
15 | const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */ | |
16 | const 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]). */ | |
18 | const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */ | |
19 | const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */ | |
20 | const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */ | |
21 | const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */ | |
22 | ||
23 | #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] | |
24 | pub 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 | } |