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s_log1pf.c (2813B)
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1 /* s_log1pf.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 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
18 #endif
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const float
24 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
25 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
26 two25 = 3.355443200e+07, /* 0x4c000000 */
27 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
28 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
29 Lp3 = 2.8571429849e-01, /* 3E924925 */
30 Lp4 = 2.2222198546e-01, /* 3E638E29 */
31 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
32 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
33 Lp7 = 1.4798198640e-01; /* 3E178897 */
34
35 static const float zero = 0.0;
36
37 float
38 log1pf(float x)
39 {
40 float hfsq,f,c,s,z,R,u;
41 int32_t k,hx,hu,ax;
42
43 GET_FLOAT_WORD(hx,x);
44 ax = hx&0x7fffffff;
45
46 k = 1;
47 if (hx < 0x3ed413d7) { /* x < 0.41422 */
48 if(ax>=0x3f800000) { /* x <= -1.0 */
49 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
50 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
51 }
52 if(ax<0x31000000) { /* |x| < 2**-29 */
53 if(two25+x>zero /* raise inexact */
54 &&ax<0x24800000) /* |x| < 2**-54 */
55 return x;
56 else
57 return x - x*x*(float)0.5;
58 }
59 if(hx>0||hx<=((int32_t)0xbe95f61f)) {
60 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
61 }
62 if (hx >= 0x7f800000) return x+x;
63 if(k!=0) {
64 if(hx<0x5a000000) {
65 u = (float)1.0+x;
66 GET_FLOAT_WORD(hu,u);
67 k = (hu>>23)-127;
68 /* correction term */
69 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
70 c /= u;
71 } else {
72 u = x;
73 GET_FLOAT_WORD(hu,u);
74 k = (hu>>23)-127;
75 c = 0;
76 }
77 hu &= 0x007fffff;
78 if(hu<0x3504f7) {
79 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
80 } else {
81 k += 1;
82 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
83 hu = (0x00800000-hu)>>2;
84 }
85 f = u-(float)1.0;
86 }
87 hfsq=(float)0.5*f*f;
88 if(hu==0) { /* |f| < 2**-20 */
89 if(f==zero) if(k==0) return zero;
90 else {c += k*ln2_lo; return k*ln2_hi+c;}
91 R = hfsq*((float)1.0-(float)0.66666666666666666*f);
92 if(k==0) return f-R; else
93 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
94 }
95 s = f/((float)2.0+f);
96 z = s*s;
97 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
98 if(k==0) return f-(hfsq-s*(hfsq+R)); else
99 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
100 }