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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_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $");
     19 #endif
     20 
     21 #include "math.h"
     22 #include "math_private.h"
     23 
     24 static const float
     25 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
     26 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
     27 two25 =    3.355443200e+07,	/* 0x4c000000 */
     28 Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
     29 Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
     30 Lg3 = 2.8571429849e-01, /* 3E924925 */
     31 Lg4 = 2.2222198546e-01, /* 3E638E29 */
     32 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
     33 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
     34 Lg7 = 1.4798198640e-01; /* 3E178897 */
     35 
     36 static const float zero   =  0.0;
     37 
     38 float
     39 __ieee754_logf(float x)
     40 {
     41 	float hfsq,f,s,z,R,w,t1,t2,dk;
     42 	int32_t k,ix,i,j;
     43 
     44 	GET_FLOAT_WORD(ix,x);
     45 
     46 	k=0;
     47 	if (ix < 0x00800000) {			/* x < 2**-126  */
     48 	    if ((ix&0x7fffffff)==0)
     49 		return -two25/zero;		/* log(+-0)=-inf */
     50 	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
     51 	    k -= 25; x *= two25; /* subnormal number, scale up x */
     52 	    GET_FLOAT_WORD(ix,x);
     53 	}
     54 	if (ix >= 0x7f800000) return x+x;
     55 	k += (ix>>23)-127;
     56 	ix &= 0x007fffff;
     57 	i = (ix+(0x95f64<<3))&0x800000;
     58 	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
     59 	k += (i>>23);
     60 	f = x-(float)1.0;
     61 	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
     62 	    if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
     63 				   return dk*ln2_hi+dk*ln2_lo;}
     64 	    }
     65 	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
     66 	    if(k==0) return f-R; else {dk=(float)k;
     67 	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
     68 	}
     69  	s = f/((float)2.0+f);
     70 	dk = (float)k;
     71 	z = s*s;
     72 	i = ix-(0x6147a<<3);
     73 	w = z*z;
     74 	j = (0x6b851<<3)-ix;
     75 	t1= w*(Lg2+w*(Lg4+w*Lg6));
     76 	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
     77 	i |= j;
     78 	R = t2+t1;
     79 	if(i>0) {
     80 	    hfsq=(float)0.5*f*f;
     81 	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
     82 		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
     83 	} else {
     84 	    if(k==0) return f-s*(f-R); else
     85 		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
     86 	}
     87 }
     88