e_log2.c

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/* @(#)e_log.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, 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 double
ln2 = 0.6931471805599452862268,
two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

static const double zero   =  0.0;

double
log2(double x)
{
    double hfsq,f,s,z,R,w,t1,t2,dk;
    int32_t k,hx,i,j;
    u_int32_t lx;

    EXTRACT_WORDS(hx,lx,x);

    k=0;
    if (hx < 0x00100000) {          /* x < 2**-1022  */
        if (((hx&0x7fffffff)|lx)==0) 
        return -two54/zero;     /* log(+-0)=-inf */
        if (hx<0) return (x-x)/zero;    /* log(-#) = NaN */
        k -= 54; x *= two54; /* subnormal number, scale up x */
        GET_HIGH_WORD(hx,x);
    } 
    if (hx >= 0x7ff00000) return x+x;
    k += (hx>>20)-1023;
    hx &= 0x000fffff;
    i = (hx+0x95f64)&0x100000;
    SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
    k += (i>>20);
    f = x-1.0;
    dk = (double)k;
    if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
        if (f==zero) 
            return (dk);
        R = f*f*(0.5-0.33333333333333333*f);
        return (dk-(R-f)/ln2);
    }
    s = f/(2.0+f); 
    z = s*s;
    i = hx-0x6147a;
    w = z*z;
    j = 0x6b851-hx;
    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=0.5*f*f;
        return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
    } else
        return (dk-((s*(f-R))-f)/ln2);
}