s_log1pf.c revision 97409 
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[] = "$FreeBSD: head/lib/msun/src/s_log1pf.c 97409 2002-05-28 17:51:46Z alfred $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
25ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
26two25 =    3.355443200e+07,	/* 0x4c000000 */
27Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
28Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
29Lp3 = 2.8571429849e-01, /* 3E924925 */
30Lp4 = 2.2222198546e-01, /* 3E638E29 */
31Lp5 = 1.8183572590e-01, /* 3E3A3325 */
32Lp6 = 1.5313838422e-01, /* 3E1CD04F */
33Lp7 = 1.4798198640e-01; /* 3E178897 */
34
35static const float zero = 0.0;
36
37	float log1pf(float x)
38{
39	float hfsq,f,c,s,z,R,u;
40	int32_t k,hx,hu,ax;
41
42	GET_FLOAT_WORD(hx,x);
43	ax = hx&0x7fffffff;
44
45	k = 1;
46	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
47	    if(ax>=0x3f800000) {		/* x <= -1.0 */
48		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
49		else return (x-x)/(x-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 (hx >= 0x7f800000) return x+x;
62	if(k!=0) {
63	    if(hx<0x5a000000) {
64		u  = (float)1.0+x;
65		GET_FLOAT_WORD(hu,u);
66	        k  = (hu>>23)-127;
67		/* correction term */
68	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
69		c /= u;
70	    } else {
71		u  = x;
72		GET_FLOAT_WORD(hu,u);
73	        k  = (hu>>23)-127;
74		c  = 0;
75	    }
76	    hu &= 0x007fffff;
77	    if(hu<0x3504f7) {
78	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
79	    } else {
80	        k += 1;
81		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
82	        hu = (0x00800000-hu)>>2;
83	    }
84	    f = u-(float)1.0;
85	}
86	hfsq=(float)0.5*f*f;
87	if(hu==0) {	/* |f| < 2**-20 */
88	    if(f==zero) if(k==0) return zero;
89			else {c += k*ln2_lo; return k*ln2_hi+c;}
90	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
91	    if(k==0) return f-R; else
92	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
93	}
94 	s = f/((float)2.0+f);
95	z = s*s;
96	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
97	if(k==0) return f-(hfsq-s*(hfsq+R)); else
98		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
99}
100