newlib-cygwin/newlib/libm/math/ef_log.c

/* ef_log.c -- float version of e_log.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include "fdlibm.h"

#ifdef __STDC__
static const float
#else
static float
#endif
ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
two25 =    3.355443200e+07,	/* 0x4c000000 */
Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
Lg3 = 2.8571429849e-01, /* 3E924925 */
Lg4 = 2.2222198546e-01, /* 3E638E29 */
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
Lg7 = 1.4798198640e-01; /* 3E178897 */

#ifdef __STDC__
static const float zero   =  0.0;
#else
static float zero   =  0.0;
#endif

#ifdef __STDC__
	float __ieee754_logf(float x)
#else
	float __ieee754_logf(x)
	float x;
#endif
{
	float hfsq,f,s,z,R,w,t1,t2,dk;
	__int32_t k,ix,i,j;

	GET_FLOAT_WORD(ix,x);

	k=0;
	if (ix < 0x00800000) {			/* x < 2**-126  */
	    if ((ix&0x7fffffff)==0) 
		return -two25/zero;		/* log(+-0)=-inf */
	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
	    k -= 25; x *= two25; /* subnormal number, scale up x */
	    GET_FLOAT_WORD(ix,x);
	} 
	if (ix >= 0x7f800000) return x+x;
	k += (ix>>23)-127;
	ix &= 0x007fffff;
	i = (ix+(0x95f64<<3))&0x800000;
	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
	k += (i>>23);
	f = x-(float)1.0;
	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
           if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
                                return dk*ln2_hi+dk*ln2_lo;}}
	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
	    if(k==0) return f-R; else {dk=(float)k;
	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
	}
 	s = f/((float)2.0+f); 
	dk = (float)k;
	z = s*s;
	i = ix-(0x6147a<<3);
	w = z*z;
	j = (0x6b851<<3)-ix;
	t1= w*(Lg2+w*(Lg4+w*Lg6)); 
	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
	i |= j;
	R = t2+t1;
	if(i>0) {
	    hfsq=(float)0.5*f*f;
	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
	} else {
	    if(k==0) return f-s*(f-R); else
		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
	}
}