gonzui

    1: /* @(#)e_log.c 1.3 95/01/18 */
    2: /*
    3:  * ====================================================
    4:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
    5:  *
    6:  * Developed at SunSoft, a Sun Microsystems, Inc. business.
    7:  * Permission to use, copy, modify, and distribute this
    8:  * software is freely granted, provided that this notice 
    9:  * is preserved.
   10:  * ====================================================
   11:  */
   12: 
   13: /* LINTLIBRARY */
   14: 
   15: #include <sys/cdefs.h>
   16: #include <float.h>
   17: #include <math.h>
   18: 
   19: #include "math_private.h"
   20: 
   21: static const double
   22: ln2 = 0.6931471805599452862268,
   23: two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
   24: Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
   25: Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
   26: Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
   27: Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
   28: Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
   29: Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
   30: Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
   31: 
   32: static const double zero   =  0.0;
   33: 
   34: double
   35: log2(double x)
   36: {
   37:         double hfsq,f,s,z,R,w,t1,t2,dk;
   38:         int32_t k,hx,i,j;
   39:         u_int32_t lx;
   40: 
   41:         EXTRACT_WORDS(hx,lx,x);
   42: 
   43:         k=0;
   44:         if (hx < 0x00100000) {                 /* x < 2**-1022  */
   45:             if (((hx&0x7fffffff)|lx)==0) 
   46:                 return -two54/zero;           /* log(+-0)=-inf */
   47:             if (hx<0) return (x-x)/zero;       /* log(-#) = NaN */
   48:             k -= 54; x *= two54; /* subnormal number, scale up x */
   49:             GET_HIGH_WORD(hx,x);
   50:         } 
   51:         if (hx >= 0x7ff00000) return x+x;
   52:         k += (hx>>20)-1023;
   53:         hx &= 0x000fffff;
   54:         i = (hx+0x95f64)&0x100000;
   55:         SET_HIGH_WORD(x,hx|(i^0x3ff00000));    /* normalize x or x/2 */
   56:         k += (i>>20);
   57:         f = x-1.0;
   58:         dk = (double)k;
   59:         if((0x000fffff&(2+hx))<3) {    /* |f| < 2**-20 */
   60:             if (f==zero) 
   61:                     return (dk);
   62:             R = f*f*(0.5-0.33333333333333333*f);
   63:             return (dk-(R-f)/ln2);
   64:         }
   65:         s = f/(2.0+f); 
   66:         z = s*s;
   67:         i = hx-0x6147a;
   68:         w = z*z;
   69:         j = 0x6b851-hx;
   70:         t1= w*(Lg2+w*(Lg4+w*Lg6)); 
   71:         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
   72:         i |= j;
   73:         R = t2+t1;
   74:         if(i>0) {
   75:             hfsq=0.5*f*f;
   76:             return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
   77:         } else
   78:                 return (dk-((s*(f-R))-f)/ln2);
   79: }
   80: 
   81: #if     LDBL_MANT_DIG == 53
   82: #ifdef  lint
   83: /* PROTOLIB1 */
   84: long double log2l(long double);
   85: #else   /* lint */
   86: __weak_alias(log2l, log2);
   87: #endif  /* lint */
   88: #endif  /* LDBL_MANT_DIG == 53 */