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      1 /* e_logf.c -- float version of e_log.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 #if defined(LIBM_SCCS) && !defined(lint)
     18 __RCSID("$NetBSD: e_log2f.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
     19 #endif
     20 
     21 #include "math.h"
     22 #include "math_private.h"
     23 
     24 static const float
     25 ln2 = 0.6931471805599452862268,
     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 */
     34 
     35 static const float zero   =  0.0;
     36 
     37 float
     38 __ieee754_log2f(float x)
     39 {
     40 	float hfsq,f,s,z,R,w,t1,t2,dk;
     41 	int32_t k,ix,i,j;
     42 
     43 	GET_FLOAT_WORD(ix,x);
     44 
     45 	k=0;
     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 */
     51 	    GET_FLOAT_WORD(ix,x);
     52 	}
     53 	if (ix >= 0x7f800000) return x+x;
     54 	k += (ix>>23)-127;
     55 	ix &= 0x007fffff;
     56 	i = (ix+(0x95f64<<3))&0x800000;
     57 	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
     58 	k += (i>>23);
     59 	dk = (float)k;
     60 	f = x-(float)1.0;
     61 	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
     62 	    if (f==zero)
     63 		    return (dk);
     64 	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
     65 	    return (dk-(R-f)/ln2);
     66 	}
     67  	s = f/((float)2.0+f);
     68 	z = s*s;
     69 	i = ix-(0x6147a<<3);
     70 	w = z*z;
     71 	j = (0x6b851<<3)-ix;
     72 	t1= w*(Lg2+w*(Lg4+w*Lg6));
     73 	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
     74 	i |= j;
     75 	R = t2+t1;
     76 	if(i>0) {
     77 	    hfsq=(float)0.5*f*f;
     78 	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
     79 	} else
     80 		return (dk-((s*(f-R))-f)/ln2);
     81 }
     82