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 
18 #ifdef __STDC__
19 static const float
20 #else
21 static float
22 #endif
23 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
24 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
25 two25 =    3.355443200e+07,	/* 0x4c000000 */
26 Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
27 Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
28 Lp3 = 2.8571429849e-01, /* 3E924925 */
29 Lp4 = 2.2222198546e-01, /* 3E638E29 */
30 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
31 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
32 Lp7 = 1.4798198640e-01; /* 3E178897 */
33 
34 #ifdef __STDC__
35 static const float zero = 0.0;
36 #else
37 static float zero = 0.0;
38 #endif
39 
40 #ifdef __STDC__
log1pf(float x)41 	float log1pf(float x)
42 #else
43 	float log1pf(x)
44 	float x;
45 #endif
46 {
47 	float hfsq,f,c,s,z,R,u;
48 	__int32_t k,hx,hu,ax;
49 
50 	GET_FLOAT_WORD(hx,x);
51 	ax = hx&0x7fffffff;
52 
53 	k = 1;
54 	if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
55 	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
56 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
57 		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
58 		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
59 	    }
60 	    if(ax<0x31000000) {			/* |x| < 2**-29 */
61 		if(two25+x>zero			/* raise inexact */
62 	            &&ax<0x24800000) 		/* |x| < 2**-54 */
63 		    return x;
64 		else
65 		    return x - x*x*(float)0.5;
66 	    }
67 	    if(hx>0||hx<=((__int32_t)0xbe95f61f)) {
68 		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
69 	}
70 	if(k!=0) {
71 	    if(hx<0x5a000000) {
72 		u  = (float)1.0+x;
73 		GET_FLOAT_WORD(hu,u);
74 	        k  = (hu>>23)-127;
75 		/* correction term */
76 	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
77 		c /= u;
78 	    } else {
79 		u  = x;
80 		GET_FLOAT_WORD(hu,u);
81 	        k  = (hu>>23)-127;
82 		c  = 0;
83 	    }
84 	    hu &= 0x007fffff;
85 	    if(hu<0x3504f7) {
86 	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
87 	    } else {
88 	        k += 1;
89 		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
90 	        hu = (0x00800000-hu)>>2;
91 	    }
92 	    f = u-(float)1.0;
93 	}
94 	hfsq=(float)0.5*f*f;
95 	if(hu==0) {	/* |f| < 2**-20 */
96            if(f==zero) { if(k==0) return zero;
97                        else {c += k*ln2_lo; return k*ln2_hi+c;}}
98 	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
99 	    if(k==0) return f-R; else
100 	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
101 	}
102  	s = f/((float)2.0+f);
103 	z = s*s;
104 	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
105 	if(k==0) return f-(hfsq-s*(hfsq+R)); else
106 		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
107 }
108 
109 #ifdef _DOUBLE_IS_32BITS
110 
111 #ifdef __STDC__
log1p(double x)112 	double log1p(double x)
113 #else
114 	double log1p(x)
115 	double x;
116 #endif
117 {
118 	return (double) log1pf((float) x);
119 }
120 
121 #endif /* defined(_DOUBLE_IS_32BITS) */
122