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 #include "math.h"
17 #include "math_private.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
34 log1pf(float x)
35 {
36 	float hfsq,f,c,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 (hx < 0x3ed413d7) {			/* x < 0.41422  */
44 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
45 		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
46 		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
47 	    }
48 	    if(ax<0x31000000) {			/* |x| < 2**-29 */
49 		if(two25+x>zero			/* raise inexact */
50 	            &&ax<0x24800000) 		/* |x| < 2**-54 */
51 		    return x;
52 		else
53 		    return x - x*x*(float)0.5;
54 	    }
55 	    if(hx>0||hx<=((int32_t)0xbe95f61f)) {
56 		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
57 	}
58 	if (hx >= 0x7f800000) return x+x;
59 	if(k!=0) {
60 	    if(hx<0x5a000000) {
61 		u  = (float)1.0+x;
62 		GET_FLOAT_WORD(hu,u);
63 	        k  = (hu>>23)-127;
64 		/* correction term */
65 	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
66 		c /= u;
67 	    } else {
68 		u  = x;
69 		GET_FLOAT_WORD(hu,u);
70 	        k  = (hu>>23)-127;
71 		c  = 0;
72 	    }
73 	    hu &= 0x007fffff;
74 	    if(hu<0x3504f7) {
75 	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
76 	    } else {
77 	        k += 1;
78 		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
79 	        hu = (0x00800000-hu)>>2;
80 	    }
81 	    f = u-(float)1.0;
82 	}
83 	hfsq=(float)0.5*f*f;
84 	if(hu==0) {	/* |f| < 2**-20 */
85 	    if(f==zero) if(k==0) return zero;
86 			else {c += k*ln2_lo; return k*ln2_hi+c;}
87 	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
88 	    if(k==0) return f-R; else
89 	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
90 	}
91  	s = f/((float)2.0+f);
92 	z = s*s;
93 	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
94 	if(k==0) return f-(hfsq-s*(hfsq+R)); else
95 		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
96 }
97