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 #if __OBSOLETE_MATH
  19 #ifdef __STDC__
  20 static const float
  21 #else
  22 static float
  23 #endif
  24 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  25 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  26 two25 =    3.355443200e+07,     /* 0x4c000000 */
  27 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
  28 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
  29 Lg3 = 2.8571429849e-01, /* 3E924925 */
  30 Lg4 = 2.2222198546e-01, /* 3E638E29 */
  31 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
  32 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
  33 Lg7 = 1.4798198640e-01; /* 3E178897 */
  34
  35 #ifdef __STDC__
  36 static const float zero   =  0.0;
  37 #else
  38 static float zero   =  0.0;
  39 #endif
  40
  41 #ifdef __STDC__
  42         float __ieee754_logf(float x)
  43 #else
  44         float __ieee754_logf(x)
  45         float x;
  46 #endif
  47 {
  48         float hfsq,f,s,z,R,w,t1,t2,dk;
  49         __int32_t k,ix,i,j;
  50
  51         GET_FLOAT_WORD(ix,x);
  52
  53         k=0;
  54         if (FLT_UWORD_IS_ZERO(ix&0x7fffffff))
  55             return -two25/zero;         /* log(+-0)=-inf */
  56         if (ix<0) return (x-x)/zero;    /* log(-#) = NaN */
  57         if (!FLT_UWORD_IS_FINITE(ix)) return x+x;
  58         if (FLT_UWORD_IS_SUBNORMAL(ix)) {
  59             k -= 25; x *= two25; /* subnormal number, scale up x */
  60             GET_FLOAT_WORD(ix,x);
  61         }
  62         k += (ix>>23)-127;
  63         ix &= 0x007fffff;
  64         i = (ix+(0x95f64<<3))&0x800000;
  65         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  66         k += (i>>23);
  67         f = x-(float)1.0;
  68         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  69            if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
  70                                 return dk*ln2_hi+dk*ln2_lo;}}
  71             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  72             if(k==0) return f-R; else {dk=(float)k;
  73                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  74         }
  75         s = f/((float)2.0+f);
  76         dk = (float)k;
  77         z = s*s;
  78         i = ix-(0x6147a<<3);
  79         w = z*z;
  80         j = (0x6b851<<3)-ix;
  81         t1= w*(Lg2+w*(Lg4+w*Lg6));
  82         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  83         i |= j;
  84         R = t2+t1;
  85         if(i>0) {
  86             hfsq=(float)0.5*f*f;
  87             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  88                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  89         } else {
  90             if(k==0) return f-s*(f-R); else
  91                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  92         }
  93 }
  94 #endif /* __OBSOLETE_MATH */