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
19 static const float
20 ln2 = 0.6931471805599452862268,
21 two25 = 3.355443200e+07, /* 0x4c000000 */
22 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
23 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
24 Lg3 = 2.8571429849e-01, /* 3E924925 */
25 Lg4 = 2.2222198546e-01, /* 3E638E29 */
26 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
27 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
28 Lg7 = 1.4798198640e-01; /* 3E178897 */
29
30 static const float zero = 0.0;
31
32 float
log2f(float x)33 log2f(float x)
34 {
35 float hfsq,f,s,z,R,w,t1,t2,dk;
36 int32_t k,ix,i,j;
37
38 GET_FLOAT_WORD(ix,x);
39
40 k=0;
41 if (ix < 0x00800000) { /* x < 2**-126 */
42 if ((ix&0x7fffffff)==0)
43 return -two25/zero; /* log(+-0)=-inf */
44 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
45 k -= 25; x *= two25; /* subnormal number, scale up x */
46 GET_FLOAT_WORD(ix,x);
47 }
48 if (ix >= 0x7f800000) return x+x;
49 k += (ix>>23)-127;
50 ix &= 0x007fffff;
51 i = (ix+(0x95f64<<3))&0x800000;
52 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
53 k += (i>>23);
54 dk = (float)k;
55 f = x-(float)1.0;
56 if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
57 if (f==zero)
58 return (dk);
59 R = f*f*((float)0.5-(float)0.33333333333333333*f);
60 return (dk-(R-f)/ln2);
61 }
62 s = f/((float)2.0+f);
63 z = s*s;
64 i = ix-(0x6147a<<3);
65 w = z*z;
66 j = (0x6b851<<3)-ix;
67 t1= w*(Lg2+w*(Lg4+w*Lg6));
68 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
69 i |= j;
70 R = t2+t1;
71 if(i>0) {
72 hfsq=(float)0.5*f*f;
73 return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
74 } else
75 return (dk-((s*(f-R))-f)/ln2);
76 }
77