1 /* sf_log1p.c -- float version of s_log1p.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
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
16 #include "fdlibm.h"
17 #include "math_config.h"
18
19 static const float
20 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
21 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
22 two25 = 3.355443200e+07, /* 0x4c000000 */
23 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
24 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
25 Lp3 = 2.8571429849e-01, /* 3E924925 */
26 Lp4 = 2.2222198546e-01, /* 3E638E29 */
27 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
28 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
29 Lp7 = 1.4798198640e-01; /* 3E178897 */
30
31 static const float zero = 0.0;
32
33 float
log1pf(float x)34 log1pf(float x)
35 {
36 float hfsq,f,c=0,s,z,R,u;
37 __int32_t k,hx,hu,ax;
38
39 GET_FLOAT_WORD(hx,x);
40 ax = hx&0x7fffffff;
41
42 k = 1;
43 if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
44 if (hx < 0x3ed413d7) { /* x < 0.41422 */
45 if(ax>=0x3f800000) { /* x <= -1.0 */
46 if(x==(float)-1.0)
47 return __math_divzerof (1); /* log1p(-1)=-inf */
48 else
49 return __math_invalidf (x); /* log1p(x<-1)=NaN */
50 }
51 if(ax<0x31000000) { /* |x| < 2**-29 */
52 if(two25+x>zero /* raise inexact */
53 &&ax<0x24800000) /* |x| < 2**-54 */
54 return x;
55 else
56 return x - x*x*(float)0.5;
57 }
58 if(hx>0||hx<=((__int32_t)0xbe95f61f)) {
59 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
60 }
61 if(k!=0) {
62 if(hx<0x5a000000) {
63 u = (float)1.0+x;
64 GET_FLOAT_WORD(hu,u);
65 k = (hu>>23)-127;
66 /* correction term */
67 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
68 c /= u;
69 } else {
70 u = x;
71 GET_FLOAT_WORD(hu,u);
72 k = (hu>>23)-127;
73 c = 0;
74 }
75 hu &= 0x007fffff;
76 if(hu<0x3504f7) {
77 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
78 } else {
79 k += 1;
80 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
81 hu = (0x00800000-hu)>>2;
82 }
83 f = u-(float)1.0;
84 }
85 hfsq=(float)0.5*f*f;
86 if(hu==0) { /* |f| < 2**-20 */
87 if(f==zero) { if(k==0) return zero;
88 else {c += k*ln2_lo; return k*ln2_hi+c;}}
89 R = hfsq*((float)1.0-(float)0.66666666666666666*f);
90 if(k==0) return f-R; else
91 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
92 }
93 s = f/((float)2.0+f);
94 z = s*s;
95 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
96 if(k==0) return f-(hfsq-s*(hfsq+R)); else
97 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
98 }
99
100 _MATH_ALIAS_f_f(log1p)
101
