Home | History | Annotate | Download | only in Math 
      1 
      2 /* @(#)e_log.c 1.3 95/01/18 */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 #include  <LibConfig.h>
     14 #include  <sys/EfiCdefs.h>
     15 #if defined(LIBM_SCCS) && !defined(lint)
     16 __RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
     17 #endif
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
     23   // potential divide by 0 -- near line 53, (x-x)/zero is on purpose
     24   #pragma warning ( disable : 4723 )
     25 #endif
     26 
     27 static const double
     28 ln2 = 0.6931471805599452862268,
     29 two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
     30 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
     31 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
     32 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
     33 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
     34 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
     35 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
     36 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
     37 
     38 static const double zero   =  0.0;
     39 
     40 double
     41 __ieee754_log2(double x)
     42 {
     43   double hfsq,f,s,z,R,w,t1,t2,dk;
     44   int32_t k,hx,i,j;
     45   u_int32_t lx;
     46 
     47   EXTRACT_WORDS(hx,lx,x);
     48 
     49   k=0;
     50   if (hx < 0x00100000) {      /* x < 2**-1022  */
     51       if (((hx&0x7fffffff)|lx)==0)
     52     return -two54/zero;   /* log(+-0)=-inf */
     53       if (hx<0) return (x-x)/zero;  /* log(-#) = NaN */
     54       k -= 54; x *= two54; /* subnormal number, scale up x */
     55       GET_HIGH_WORD(hx,x);
     56   }
     57   if (hx >= 0x7ff00000) return x+x;
     58   k += (hx>>20)-1023;
     59   hx &= 0x000fffff;
     60   i = (hx+0x95f64)&0x100000;
     61   SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
     62   k += (i>>20);
     63   f = x-1.0;
     64   dk = (double)k;
     65   if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
     66       if (f==zero)
     67         return (dk);
     68       R = f*f*(0.5-0.33333333333333333*f);
     69       return (dk-(R-f)/ln2);
     70   }
     71   s = f/(2.0+f);
     72   z = s*s;
     73   i = hx-0x6147a;
     74   w = z*z;
     75   j = 0x6b851-hx;
     76   t1= w*(Lg2+w*(Lg4+w*Lg6));
     77   t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
     78   i |= j;
     79   R = t2+t1;
     80   if(i>0) {
     81       hfsq=0.5*f*f;
     82       return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
     83   } else
     84     return (dk-((s*(f-R))-f)/ln2);
     85 }
     86