s_log1pf.c revision 2117 
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
17static char rcsid[] = "$Id: s_log1pf.c,v 1.2 1994/08/18 23:07:02 jtc Exp $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23#ifdef __STDC__
24static const float
25#else
26static float
27#endif
28ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
29ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
30two25 =    3.355443200e+07,	/* 0x4c000000 */
31Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
32Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
33Lp3 = 2.8571429849e-01, /* 3E924925 */
34Lp4 = 2.2222198546e-01, /* 3E638E29 */
35Lp5 = 1.8183572590e-01, /* 3E3A3325 */
36Lp6 = 1.5313838422e-01, /* 3E1CD04F */
37Lp7 = 1.4798198640e-01; /* 3E178897 */
38
39#ifdef __STDC__
40static const float zero = 0.0;
41#else
42static float zero = 0.0;
43#endif
44
45#ifdef __STDC__
46	float log1pf(float x)
47#else
48	float log1pf(x)
49	float x;
50#endif
51{
52	float hfsq,f,c,s,z,R,u;
53	int32_t k,hx,hu,ax;
54
55	GET_FLOAT_WORD(hx,x);
56	ax = hx&0x7fffffff;
57
58	k = 1;
59	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
60	    if(ax>=0x3f800000) {		/* x <= -1.0 */
61		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
62		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
63	    }
64	    if(ax<0x31000000) {			/* |x| < 2**-29 */
65		if(two25+x>zero			/* raise inexact */
66	            &&ax<0x24800000) 		/* |x| < 2**-54 */
67		    return x;
68		else
69		    return x - x*x*(float)0.5;
70	    }
71	    if(hx>0||hx<=((int32_t)0xbe95f61f)) {
72		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
73	}
74	if (hx >= 0x7f800000) return x+x;
75	if(k!=0) {
76	    if(hx<0x5a000000) {
77		u  = (float)1.0+x;
78		GET_FLOAT_WORD(hu,u);
79	        k  = (hu>>23)-127;
80		/* correction term */
81	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
82		c /= u;
83	    } else {
84		u  = x;
85		GET_FLOAT_WORD(hu,u);
86	        k  = (hu>>23)-127;
87		c  = 0;
88	    }
89	    hu &= 0x007fffff;
90	    if(hu<0x3504f7) {
91	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
92	    } else {
93	        k += 1;
94		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
95	        hu = (0x00800000-hu)>>2;
96	    }
97	    f = u-(float)1.0;
98	}
99	hfsq=(float)0.5*f*f;
100	if(hu==0) {	/* |f| < 2**-20 */
101	    if(f==zero) if(k==0) return zero;
102			else {c += k*ln2_lo; return k*ln2_hi+c;}
103	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
104	    if(k==0) return f-R; else
105	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
106	}
107 	s = f/((float)2.0+f);
108	z = s*s;
109	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
110	if(k==0) return f-(hfsq-s*(hfsq+R)); else
111		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
112}
113