root/lib/math/ef_log.c

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DEFINITIONS

This source file includes following definitions.
  1. logf

   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 static const float
  19 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  20 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  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 extern float logf(float x);
  33 
  34 float logf(float x)
  35 {
  36         float hfsq,f,s,z,R,w,t1,t2,dk;
  37         int k,ix,i,j;
  38 
  39         GET_FLOAT_WORD(ix,x);
  40 
  41         k=0;
  42         if (FLT_UWORD_IS_ZERO(ix&0x7fffffff))
  43             return -two25/zero;         /* log(+-0)=-inf */
  44         if (ix<0) return (x-x)/zero;    /* log(-#) = NaN */
  45         if (!FLT_UWORD_IS_FINITE(ix)) return x+x;
  46         if (FLT_UWORD_IS_SUBNORMAL(ix)) {
  47             k -= 25; x *= two25; /* subnormal number, scale up x */
  48             GET_FLOAT_WORD(ix,x);
  49         } 
  50         k += (ix>>23)-127;
  51         ix &= 0x007fffff;
  52         i = (ix+(0x95f64<<3))&0x800000;
  53         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  54         k += (i>>23);
  55         f = x-(float)1.0;
  56         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  57            if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
  58                                 return dk*ln2_hi+dk*ln2_lo;}}
  59             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  60             if(k==0) return f-R; else {dk=(float)k;
  61                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  62         }
  63         s = f/((float)2.0+f); 
  64         dk = (float)k;
  65         z = s*s;
  66         i = ix-(0x6147a<<3);
  67         w = z*z;
  68         j = (0x6b851<<3)-ix;
  69         t1= w*(Lg2+w*(Lg4+w*Lg6)); 
  70         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
  71         i |= j;
  72         R = t2+t1;
  73         if(i>0) {
  74             hfsq=(float)0.5*f*f;
  75             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  76                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  77         } else {
  78             if(k==0) return f-s*(f-R); else
  79                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  80         }
  81 }

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