sysdeps/ieee754/flt-32/e_logf.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 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: e_logf.c,v 1.4 1995/05/10 20:45:54 jtc Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 #ifdef __STDC__
  24 static const float
  25 #else
  26 static float
  27 #endif
  28 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  29 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  30 two25 =    3.355443200e+07,     /* 0x4c000000 */
  31 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
  32 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
  33 Lg3 = 2.8571429849e-01, /* 3E924925 */
  34 Lg4 = 2.2222198546e-01, /* 3E638E29 */
  35 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
  36 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
  37 Lg7 = 1.4798198640e-01; /* 3E178897 */
  38
  39 #ifdef __STDC__
  40 static const float zero   =  0.0;
  41 #else
  42 static float zero   =  0.0;
  43 #endif
  44
  45 #ifdef __STDC__
  46         float __ieee754_logf(float x)
  47 #else
  48         float __ieee754_logf(x)
  49         float x;
  50 #endif
  51 {
  52         float hfsq,f,s,z,R,w,t1,t2,dk;
  53         int32_t k,ix,i,j;
  54
  55         GET_FLOAT_WORD(ix,x);
  56
  57         k=0;
  58         if (ix < 0x00800000) {                  /* x < 2**-126  */
  59             if ((ix&0x7fffffff)==0)
  60                 return -two25/(x-x);            /* log(+-0)=-inf */
  61             if (ix<0) return (x-x)/(x-x);       /* log(-#) = NaN */
  62             k -= 25; x *= two25; /* subnormal number, scale up x */
  63             GET_FLOAT_WORD(ix,x);
  64         }
  65         if (ix >= 0x7f800000) return x+x;
  66         k += (ix>>23)-127;
  67         ix &= 0x007fffff;
  68         i = (ix+(0x95f64<<3))&0x800000;
  69         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  70         k += (i>>23);
  71         f = x-(float)1.0;
  72         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  73             if(f==zero) {
  74               if(k==0) return zero;  else {dk=(float)k;
  75                                            return dk*ln2_hi+dk*ln2_lo;}
  76             }
  77             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  78             if(k==0) return f-R; else {dk=(float)k;
  79                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  80         }
  81         s = f/((float)2.0+f);
  82         dk = (float)k;
  83         z = s*s;
  84         i = ix-(0x6147a<<3);
  85         w = z*z;
  86         j = (0x6b851<<3)-ix;
  87         t1= w*(Lg2+w*(Lg4+w*Lg6));
  88         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  89         i |= j;
  90         R = t2+t1;
  91         if(i>0) {
  92             hfsq=(float)0.5*f*f;
  93             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  94                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  95         } else {
  96             if(k==0) return f-s*(f-R); else
  97                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  98         }
  99 }