lib/libm/src/e_log2.c

   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 #include <float.h>
  14 #include <math.h>
  15
  16 #include "math_private.h"
  17
  18 static const double
  19 ln2 = 0.6931471805599452862268,
  20 two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
  21 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
  22 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
  23 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
  24 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
  25 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
  26 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
  27 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
  28
  29 static const double zero   =  0.0;
  30
  31 double
  32 log2(double x)
  33 {
  34         double hfsq,f,s,z,R,w,t1,t2,dk;
  35         int32_t k,hx,i,j;
  36         u_int32_t lx;
  37
  38         EXTRACT_WORDS(hx,lx,x);
  39
  40         k=0;
  41         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  42             if (((hx&0x7fffffff)|lx)==0)
  43                 return -two54/zero;             /* log(+-0)=-inf */
  44             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  45             k -= 54; x *= two54; /* subnormal number, scale up x */
  46             GET_HIGH_WORD(hx,x);
  47         }
  48         if (hx >= 0x7ff00000) return x+x;
  49         k += (hx>>20)-1023;
  50         hx &= 0x000fffff;
  51         i = (hx+0x95f64)&0x100000;
  52         SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
  53         k += (i>>20);
  54         f = x-1.0;
  55         dk = (double)k;
  56         if((0x000fffff&(2+hx))<3) {     /* |f| < 2**-20 */
  57             if (f==zero)
  58                     return (dk);
  59             R = f*f*(0.5-0.33333333333333333*f);
  60             return (dk-(R-f)/ln2);
  61         }
  62         s = f/(2.0+f);
  63         z = s*s;
  64         i = hx-0x6147a;
  65         w = z*z;
  66         j = 0x6b851-hx;
  67         t1= w*(Lg2+w*(Lg4+w*Lg6));
  68         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  69         i |= j;
  70         R = t2+t1;
  71         if(i>0) {
  72             hfsq=0.5*f*f;
  73             return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
  74         } else
  75                 return (dk-((s*(f-R))-f)/ln2);
  76 }
  77
  78 #if     LDBL_MANT_DIG == 53
  79 __strong_alias(log2l, log2);
  80 #endif  /* LDBL_MANT_DIG == 53 */