lib/libm/src/e_log2f.c

   1 /* e_logf.c -- float version of e_log.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include "math.h"
  17 #include "math_private.h"
  18
  19 static const float
  20 ln2 = 0.6931471805599452862268,
  21 two25 =    3.355443200e+07,     /* 0x4c000000 */
  22 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
  23 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
  24 Lg3 = 2.8571429849e-01, /* 3E924925 */
  25 Lg4 = 2.2222198546e-01, /* 3E638E29 */
  26 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
  27 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
  28 Lg7 = 1.4798198640e-01; /* 3E178897 */
  29
  30 static const float zero   =  0.0;
  31
  32 float
  33 log2f(float x)
  34 {
  35         float hfsq,f,s,z,R,w,t1,t2,dk;
  36         int32_t k,ix,i,j;
  37
  38         GET_FLOAT_WORD(ix,x);
  39
  40         k=0;
  41         if (ix < 0x00800000) {                  /* x < 2**-126  */
  42             if ((ix&0x7fffffff)==0)
  43                 return -two25/zero;             /* log(+-0)=-inf */
  44             if (ix<0) return (x-x)/zero;        /* log(-#) = NaN */
  45             k -= 25; x *= two25; /* subnormal number, scale up x */
  46             GET_FLOAT_WORD(ix,x);
  47         }
  48         if (ix >= 0x7f800000) return x+x;
  49         k += (ix>>23)-127;
  50         ix &= 0x007fffff;
  51         i = (ix+(0x95f64<<3))&0x800000;
  52         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  53         k += (i>>23);
  54         dk = (float)k;
  55         f = x-(float)1.0;
  56         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  57             if (f==zero)
  58                     return (dk);
  59             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  60             return (dk-(R-f)/ln2);
  61         }
  62         s = f/((float)2.0+f);
  63         z = s*s;
  64         i = ix-(0x6147a<<3);
  65         w = z*z;
  66         j = (0x6b851<<3)-ix;
  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=(float)0.5*f*f;
  73             return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
  74         } else
  75                 return (dk-((s*(f-R))-f)/ln2);
  76 }