toolchain/gcc/newlib/libm/math/ef_log.c

   1 /* ef_log.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 "fdlibm.h"
  17
  18 #ifdef __STDC__
  19 static const float
  20 #else
  21 static float
  22 #endif
  23 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  24 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  25 two25 =    3.355443200e+07,     /* 0x4c000000 */
  26 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
  27 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
  28 Lg3 = 2.8571429849e-01, /* 3E924925 */
  29 Lg4 = 2.2222198546e-01, /* 3E638E29 */
  30 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
  31 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
  32 Lg7 = 1.4798198640e-01; /* 3E178897 */
  33
  34 #ifdef __STDC__
  35 static const float zero   =  0.0;
  36 #else
  37 static float zero   =  0.0;
  38 #endif
  39
  40 #ifdef __STDC__
  41         float __ieee754_logf(float x)
  42 #else
  43         float __ieee754_logf(x)
  44         float x;
  45 #endif
  46 {
  47         float hfsq,f,s,z,R,w,t1,t2,dk;
  48         __int32_t k,ix,i,j;
  49
  50         GET_FLOAT_WORD(ix,x);
  51
  52         k=0;
  53         if (FLT_UWORD_IS_ZERO(ix&0x7fffffff))
  54             return -two25/zero;         /* log(+-0)=-inf */
  55         if (ix<0) return (x-x)/zero;    /* log(-#) = NaN */
  56         if (!FLT_UWORD_IS_FINITE(ix)) return x+x;
  57         if (FLT_UWORD_IS_SUBNORMAL(ix)) {
  58             k -= 25; x *= two25; /* subnormal number, scale up x */
  59             GET_FLOAT_WORD(ix,x);
  60         }
  61         k += (ix>>23)-127;
  62         ix &= 0x007fffff;
  63         i = (ix+(0x95f64<<3))&0x800000;
  64         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  65         k += (i>>23);
  66         f = x-(float)1.0;
  67         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  68            if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
  69                                 return dk*ln2_hi+dk*ln2_lo;}}
  70             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  71             if(k==0) return f-R; else {dk=(float)k;
  72                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  73         }
  74         s = f/((float)2.0+f);
  75         dk = (float)k;
  76         z = s*s;
  77         i = ix-(0x6147a<<3);
  78         w = z*z;
  79         j = (0x6b851<<3)-ix;
  80         t1= w*(Lg2+w*(Lg4+w*Lg6));
  81         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  82         i |= j;
  83         R = t2+t1;
  84         if(i>0) {
  85             hfsq=(float)0.5*f*f;
  86             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  87                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  88         } else {
  89             if(k==0) return f-s*(f-R); else
  90                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  91         }
  92 }