lib/libm/src/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  * $NetBSD: e_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/e_logf.c,v 1.2 2007/06/24 05:17:51 pavalos Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static const float
  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 static const float zero   =  0.0;
  35
  36 float
  37 logf(float x)
  38 {
  39         float hfsq,f,s,z,R,w,t1,t2,dk;
  40         int32_t k,ix,i,j;
  41
  42         GET_FLOAT_WORD(ix,x);
  43
  44         k=0;
  45         if (ix < 0x00800000) {                  /* x < 2**-126  */
  46             if ((ix&0x7fffffff)==0)
  47                 return -two25/zero;             /* log(+-0)=-inf */
  48             if (ix<0) return (x-x)/zero;        /* log(-#) = NaN */
  49             k -= 25; x *= two25; /* subnormal number, scale up x */
  50             GET_FLOAT_WORD(ix,x);
  51         }
  52         if (ix >= 0x7f800000) return x+x;
  53         k += (ix>>23)-127;
  54         ix &= 0x007fffff;
  55         i = (ix+(0x95f64<<3))&0x800000;
  56         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  57         k += (i>>23);
  58         f = x-(float)1.0;
  59         if((0x007fffff&(0x8000+ix))<0xc000) {   /* -2**-9 <= f < 2**-9 */
  60             if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
  61                                    return dk*ln2_hi+dk*ln2_lo;}
  62             }
  63             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  64             if(k==0) return f-R; else {dk=(float)k;
  65                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  66         }
  67         s = f/((float)2.0+f);
  68         dk = (float)k;
  69         z = s*s;
  70         i = ix-(0x6147a<<3);
  71         w = z*z;
  72         j = (0x6b851<<3)-ix;
  73         t1= w*(Lg2+w*(Lg4+w*Lg6));
  74         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  75         i |= j;
  76         R = t2+t1;
  77         if(i>0) {
  78             hfsq=(float)0.5*f*f;
  79             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  80                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  81         } else {
  82             if(k==0) return f-s*(f-R); else
  83                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  84         }
  85 }