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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 __FBSDID("$FreeBSD$");
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 static const float
     23 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
     24 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
     25 two25 =    3.355443200e+07,	/* 0x4c000000 */
     26 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
     27 Lg1 =      0xaaaaaa.0p-24,	/* 0.66666662693 */
     28 Lg2 =      0xccce13.0p-25,	/* 0.40000972152 */
     29 Lg3 =      0x91e9ee.0p-25,	/* 0.28498786688 */
     30 Lg4 =      0xf89e26.0p-26;	/* 0.24279078841 */
     31 
     32 static const float zero   =  0.0;
     33 static volatile float vzero = 0.0;
     34 
     35 float
     36 __ieee754_logf(float x)
     37 {
     38 	float hfsq,f,s,z,R,w,t1,t2,dk;
     39 	int32_t k,ix,i,j;
     40 
     41 	GET_FLOAT_WORD(ix,x);
     42 
     43 	k=0;
     44 	if (ix < 0x00800000) {			/* x < 2**-126  */
     45 	    if ((ix&0x7fffffff)==0)
     46 		return -two25/vzero;		/* log(+-0)=-inf */
     47 	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
     48 	    k -= 25; x *= two25; /* subnormal number, scale up x */
     49 	    GET_FLOAT_WORD(ix,x);
     50 	}
     51 	if (ix >= 0x7f800000) return x+x;
     52 	k += (ix>>23)-127;
     53 	ix &= 0x007fffff;
     54 	i = (ix+(0x95f64<<3))&0x800000;
     55 	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
     56 	k += (i>>23);
     57 	f = x-(float)1.0;
     58 	if((0x007fffff&(0x8000+ix))<0xc000) {	/* -2**-9 <= f < 2**-9 */
     59 	    if(f==zero) {
     60 		if(k==0) {
     61 		    return zero;
     62 		} else {
     63 		    dk=(float)k;
     64 		    return dk*ln2_hi+dk*ln2_lo;
     65 		}
     66 	    }
     67 	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
     68 	    if(k==0) return f-R; else {dk=(float)k;
     69 	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
     70 	}
     71  	s = f/((float)2.0+f);
     72 	dk = (float)k;
     73 	z = s*s;
     74 	i = ix-(0x6147a<<3);
     75 	w = z*z;
     76 	j = (0x6b851<<3)-ix;
     77 	t1= w*(Lg2+w*Lg4);
     78 	t2= z*(Lg1+w*Lg3);
     79 	i |= j;
     80 	R = t2+t1;
     81 	if(i>0) {
     82 	    hfsq=(float)0.5*f*f;
     83 	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
     84 		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
     85 	} else {
     86 	    if(k==0) return f-s*(f-R); else
     87 		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
     88 	}
     89 }
     90