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#include "libm.h"
14
15static const float
16ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
17ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
18/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
19Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
20Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
21Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
22Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
23
24float log1pf(float x)
25{
26	union {float f; uint32_t i;} u = {x};
27	float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
28	uint32_t ix,iu;
29	int k;
30
31	ix = u.i;
32	k = 1;
33	if (ix < 0x3ed413d0 || ix>>31) {  /* 1+x < sqrt(2)+  */
34		if (ix >= 0xbf800000) {  /* x <= -1.0 */
35			if (x == -1)
36				return x/0.0f; /* log1p(-1)=+inf */
37			return (x-x)/0.0f;     /* log1p(x<-1)=NaN */
38		}
39		if (ix<<1 < 0x33800000<<1) {   /* |x| < 2**-24 */
40			/* underflow if subnormal */
41			if ((ix&0x7f800000) == 0)
42				FORCE_EVAL(x*x);
43			return x;
44		}
45		if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
46			k = 0;
47			c = 0;
48			f = x;
49		}
50	} else if (ix >= 0x7f800000)
51		return x;
52	if (k) {
53		u.f = 1 + x;
54		iu = u.i;
55		iu += 0x3f800000 - 0x3f3504f3;
56		k = (int)(iu>>23) - 0x7f;
57		/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
58		if (k < 25) {
59			c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
60			c /= u.f;
61		} else
62			c = 0;
63		/* reduce u into [sqrt(2)/2, sqrt(2)] */
64		iu = (iu&0x007fffff) + 0x3f3504f3;
65		u.i = iu;
66		f = u.f - 1;
67	}
68	s = f/(2.0f + f);
69	z = s*s;
70	w = z*z;
71	t1= w*(Lg2+w*Lg4);
72	t2= z*(Lg1+w*Lg3);
73	R = t2 + t1;
74	hfsq = 0.5f*f*f;
75	dk = k;
76	return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
77}
78