compiler/mlib/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 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_logf.c,v 1.9 2006/07/07 04:33:08 bde Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float
  24 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  25 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  26 two25 =    3.355443200e+07,     /* 0x4c000000 */
  27 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
  28 Lg1 =      0xaaaaaa.0p-24,      /* 0.66666662693 */
  29 Lg2 =      0xccce13.0p-25,      /* 0.40000972152 */
  30 Lg3 =      0x91e9ee.0p-25,      /* 0.28498786688 */
  31 Lg4 =      0xf89e26.0p-26;      /* 0.24279078841 */
  32
  33 static const float zero   =  0.0;
  34
  35 float
  36 __ieee754_logf(float x)
  37 {
  38         float hfsq,f,s,z,R,w,t1,t2,dk;
  39         int32_t k,ix,i,j;
  40
  41         GET_FLOAT_WORD(ix,x);
  42
  43         k=0;
  44         if (ix < 0x00800000) {                  /* x < 2**-126  */
  45             if ((ix&0x7fffffff)==0)
  46                 return -two25/zero;             /* log(+-0)=-inf */
  47             if (ix<0) return (x-x)/zero;        /* log(-#) = NaN */
  48             k -= 25; x *= two25; /* subnormal number, scale up x */
  49             GET_FLOAT_WORD(ix,x);
  50         }
  51         if (ix >= 0x7f800000) return x+x;
  52         k += (ix>>23)-127;
  53         ix &= 0x007fffff;
  54         i = (ix+(0x95f64<<3))&0x800000;
  55         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  56         k += (i>>23);
  57         f = x-(float)1.0;
  58         if((0x007fffff&(0x8000+ix))<0xc000) {   /* -2**-9 <= f < 2**-9 */
  59             if(f==zero) if(k==0) return zero;  else {dk=(float)k;
  60                                  return dk*ln2_hi+dk*ln2_lo;}
  61             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  62             if(k==0) return f-R; else {dk=(float)k;
  63                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  64         }
  65         s = f/((float)2.0+f);
  66         dk = (float)k;
  67         z = s*s;
  68         i = ix-(0x6147a<<3);
  69         w = z*z;
  70         j = (0x6b851<<3)-ix;
  71         t1= w*(Lg2+w*Lg4);
  72         t2= z*(Lg1+w*Lg3);
  73         i |= j;
  74         R = t2+t1;
  75         if(i>0) {
  76             hfsq=(float)0.5*f*f;
  77             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  78                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  79         } else {
  80             if(k==0) return f-s*(f-R); else
  81                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  82         }
  83 }