lib/libm/src/e_log2.c

   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  * $NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $
  14  * $DragonFly: src/lib/libm/src/e_log2.c,v 1.1 2007/06/16 22:26:53 pavalos Exp $
  15  */
  16
  17 #include <math.h>
  18 #include "math_private.h"
  19
  20 static const double
  21 ln2 = 0.6931471805599452862268,
  22 two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
  23 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
  24 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
  25 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
  26 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
  27 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
  28 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
  29 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
  30
  31 static const double zero   =  0.0;
  32
  33 double
  34 log2(double x)
  35 {
  36         double hfsq,f,s,z,R,w,t1,t2,dk;
  37         int32_t k,hx,i,j;
  38         u_int32_t lx;
  39
  40         EXTRACT_WORDS(hx,lx,x);
  41
  42         k=0;
  43         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  44             if (((hx&0x7fffffff)|lx)==0)
  45                 return -two54/zero;             /* log(+-0)=-inf */
  46             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  47             k -= 54; x *= two54; /* subnormal number, scale up x */
  48             GET_HIGH_WORD(hx,x);
  49         }
  50         if (hx >= 0x7ff00000) return x+x;
  51         k += (hx>>20)-1023;
  52         hx &= 0x000fffff;
  53         i = (hx+0x95f64)&0x100000;
  54         SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
  55         k += (i>>20);
  56         f = x-1.0;
  57         dk = (double)k;
  58         if((0x000fffff&(2+hx))<3) {     /* |f| < 2**-20 */
  59             if (f==zero)
  60                     return (dk);
  61             R = f*f*(0.5-0.33333333333333333*f);
  62             return (dk-(R-f)/ln2);
  63         }
  64         s = f/(2.0+f);
  65         z = s*s;
  66         i = hx-0x6147a;
  67         w = z*z;
  68         j = 0x6b851-hx;
  69         t1= w*(Lg2+w*(Lg4+w*Lg6));
  70         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  71         i |= j;
  72         R = t2+t1;
  73         if(i>0) {
  74             hfsq=0.5*f*f;
  75             return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
  76         } else
  77                 return (dk-((s*(f-R))-f)/ln2);
  78 }