e_logf.c

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/* e_logf.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 "math.h"
#include "math_private.h"

static const float
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 */

static const float zero   =  0.0;

float
logf(float x)
{
    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);
    }
}