1/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
17const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
18/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
19const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24*/
20const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
21const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
22const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
23
24/// The natural logarithm of `x` (f32).
25#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
26pub fn logf(mut x: f32) -> f32 {
27 let x1p25 = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
28
29 let mut ix = x.to_bits();
30 let mut k = 0i32;
31
32 if (ix < 0x00800000) || ((ix >> 31) != 0) {
33 /* x < 2**-126 */
34 if ix << 1 == 0 {
35 return -1. / (x * x); /* log(+-0)=-inf */
36 }
37 if (ix >> 31) != 0 {
38 return (x - x) / 0.; /* log(-#) = NaN */
39 }
40 /* subnormal number, scale up x */
41 k -= 25;
42 x *= x1p25;
43 ix = x.to_bits();
44 } else if ix >= 0x7f800000 {
45 return x;
46 } else if ix == 0x3f800000 {
47 return 0.;
48 }
49
50 /* reduce x into [sqrt(2)/2, sqrt(2)] */
51 ix += 0x3f800000 - 0x3f3504f3;
52 k += ((ix >> 23) as i32) - 0x7f;
53 ix = (ix & 0x007fffff) + 0x3f3504f3;
54 x = f32::from_bits(ix);
55
56 let f = x - 1.;
57 let s = f / (2. + f);
58 let z = s * s;
59 let w = z * z;
60 let t1 = w * (LG2 + w * LG4);
61 let t2 = z * (LG1 + w * LG3);
62 let r = t2 + t1;
63 let hfsq = 0.5 * f * f;
64 let dk = k as f32;
65 s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
66}
67