1 /* e_logf.c -- float version of e_log.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
17 static char rcsid[] = "$FreeBSD$";
21 #include "math_private.h"
24 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
25 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
26 two25 = 3.355443200e+07, /* 0x4c000000 */
27 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
28 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
29 Lg3 = 2.8571429849e-01, /* 3E924925 */
30 Lg4 = 2.2222198546e-01, /* 3E638E29 */
31 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
32 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
33 Lg7 = 1.4798198640e-01; /* 3E178897 */
35 static const float zero = 0.0;
38 __ieee754_logf(float x)
40 float hfsq,f,s,z,R,w,t1,t2,dk;
46 if (ix < 0x00800000) { /* x < 2**-126 */
47 if ((ix&0x7fffffff)==0)
48 return -two25/zero; /* log(+-0)=-inf */
49 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
50 k -= 25; x *= two25; /* subnormal number, scale up x */
53 if (ix >= 0x7f800000) return x+x;
56 i = (ix+(0x95f64<<3))&0x800000;
57 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
60 if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
61 if(f==zero) if(k==0) return zero; else {dk=(float)k;
62 return dk*ln2_hi+dk*ln2_lo;}
63 R = f*f*((float)0.5-(float)0.33333333333333333*f);
64 if(k==0) return f-R; else {dk=(float)k;
65 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
73 t1= w*(Lg2+w*(Lg4+w*Lg6));
74 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
79 if(k==0) return f-(hfsq-s*(hfsq+R)); else
80 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
82 if(k==0) return f-s*(f-R); else
83 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);