s_log1pf.c revision 175494 
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 <sys/cdefs.h>
17__FBSDID("$FreeBSD: head/lib/msun/src/s_log1pf.c 175494 2008-01-19 18:13:21Z bde $");
18
19#include <float.h>
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
26ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
27two25 =    3.355443200e+07,	/* 0x4c000000 */
28Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
29Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
30Lp3 = 2.8571429849e-01, /* 3E924925 */
31Lp4 = 2.2222198546e-01, /* 3E638E29 */
32Lp5 = 1.8183572590e-01, /* 3E3A3325 */
33Lp6 = 1.5313838422e-01, /* 3E1CD04F */
34Lp7 = 1.4798198640e-01; /* 3E178897 */
35
36static const float zero = 0.0;
37
38float
39log1pf(float x)
40{
41	float hfsq,f,c,s,z,R,u;
42	int32_t k,hx,hu,ax;
43
44	GET_FLOAT_WORD(hx,x);
45	ax = hx&0x7fffffff;
46
47	k = 1;
48	if (hx < 0x3ed413d0) {			/* 1+x < sqrt(2)+  */
49	    if(ax>=0x3f800000) {		/* x <= -1.0 */
50		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
51		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
52	    }
53	    if(ax<0x31000000) {			/* |x| < 2**-29 */
54		if(two25+x>zero			/* raise inexact */
55	            &&ax<0x24800000) 		/* |x| < 2**-54 */
56		    return x;
57		else
58		    return x - x*x*(float)0.5;
59	    }
60	    if(hx>0||hx<=((int32_t)0xbe95f619)) {
61		k=0;f=x;hu=1;}		/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
62	}
63	if (hx >= 0x7f800000) return x+x;
64	if(k!=0) {
65	    if(hx<0x5a000000) {
66		STRICT_ASSIGN(float,u,(float)1.0+x);
67		GET_FLOAT_WORD(hu,u);
68	        k  = (hu>>23)-127;
69		/* correction term */
70	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
71		c /= u;
72	    } else {
73		u  = x;
74		GET_FLOAT_WORD(hu,u);
75	        k  = (hu>>23)-127;
76		c  = 0;
77	    }
78	    hu &= 0x007fffff;
79	    /*
80	     * The approximation to sqrt(2) used in thresholds is not
81	     * critical.  However, the ones used above must give less
82	     * strict bounds than the one here so that the k==0 case is
83	     * never reached from here, since here we have committed to
84	     * using the correction term but don't use it if k==0.
85	     */
86	    if(hu<0x3504f4) {			/* u < sqrt(2) */
87	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
88	    } else {
89	        k += 1;
90		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
91	        hu = (0x00800000-hu)>>2;
92	    }
93	    f = u-(float)1.0;
94	}
95	hfsq=(float)0.5*f*f;
96	if(hu==0) {	/* |f| < 2**-20 */
97	    if(f==zero) if(k==0) return zero;
98			else {c += k*ln2_lo; return k*ln2_hi+c;}
99	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
100	    if(k==0) return f-R; else
101	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
102	}
103 	s = f/((float)2.0+f);
104	z = s*s;
105	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
106	if(k==0) return f-(hfsq-s*(hfsq+R)); else
107		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
108}
109