1/* e_logf.c -- float version of e_log.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
19static const float
20ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
21ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
22two25 =    3.355443200e+07,	/* 0x4c000000 */
23Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
24Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
25Lg3 = 2.8571429849e-01, /* 3E924925 */
26Lg4 = 2.2222198546e-01, /* 3E638E29 */
27Lg5 = 1.8183572590e-01, /* 3E3A3325 */
28Lg6 = 1.5313838422e-01, /* 3E1CD04F */
29Lg7 = 1.4798198640e-01; /* 3E178897 */
30
31static const float zero   =  0.0;
32
33float
34logf(float x)
35{
36	float hfsq,f,s,z,R,w,t1,t2,dk;
37	int32_t k,ix,i,j;
38
39	GET_FLOAT_WORD(ix,x);
40
41	k=0;
42	if (ix < 0x00800000) {			/* x < 2**-126  */
43	    if ((ix&0x7fffffff)==0)
44		return -two25/zero;		/* log(+-0)=-inf */
45	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
46	    k -= 25; x *= two25; /* subnormal number, scale up x */
47	    GET_FLOAT_WORD(ix,x);
48	}
49	if (ix >= 0x7f800000) return x+x;
50	k += (ix>>23)-127;
51	ix &= 0x007fffff;
52	i = (ix+(0x95f64<<3))&0x800000;
53	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
54	k += (i>>23);
55	f = x-(float)1.0;
56	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
57	    if(f==zero) {if(k==0) return zero;  else {dk=(float)k;
58				  return dk*ln2_hi+dk*ln2_lo;}}
59	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
60	    if(k==0) return f-R; else {dk=(float)k;
61	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
62	}
63 	s = f/((float)2.0+f);
64	dk = (float)k;
65	z = s*s;
66	i = ix-(0x6147a<<3);
67	w = z*z;
68	j = (0x6b851<<3)-ix;
69	t1= w*(Lg2+w*(Lg4+w*Lg6));
70	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
71	i |= j;
72	R = t2+t1;
73	if(i>0) {
74	    hfsq=(float)0.5*f*f;
75	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
76		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
77	} else {
78	    if(k==0) return f-s*(f-R); else
79		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
80	}
81}
82DEF_STD(logf);
83