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
  16 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: e_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float
  25 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  26 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  27 two25 =    3.355443200e+07,     /* 0x4c000000 */
  28 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
  29 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
  30 Lg3 = 2.8571429849e-01, /* 3E924925 */
  31 Lg4 = 2.2222198546e-01, /* 3E638E29 */
  32 Lg5 = 1.8183572590e-01, /* 3E3A3325 */
  33 Lg6 = 1.5313838422e-01, /* 3E1CD04F */
  34 Lg7 = 1.4798198640e-01; /* 3E178897 */
  35
  36 static const float zero   =  0.0;
  37
  38 float
  39 __ieee754_logf(float x)
  40 {
  41         float hfsq,f,s,z,R,w,t1,t2,dk;
  42         int32_t k,ix,i,j;
  43
  44         GET_FLOAT_WORD(ix,x);
  45
  46         k=0;
  47         if (ix < 0x00800000) {                  /* x < 2**-126  */
  48             if ((ix&0x7fffffff)==0)
  49                 return -two25/zero;             /* log(+-0)=-inf */
  50             if (ix<0) return (x-x)/zero;        /* log(-#) = NaN */
  51             k -= 25; x *= two25; /* subnormal number, scale up x */
  52             GET_FLOAT_WORD(ix,x);
  53         }
  54         if (ix >= 0x7f800000) return x+x;
  55         k += (ix>>23)-127;
  56         ix &= 0x007fffff;
  57         i = (ix+(0x95f64<<3))&0x800000;
  58         SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
  59         k += (i>>23);
  60         f = x-(float)1.0;
  61         if((0x007fffff&(15+ix))<16) {   /* |f| < 2**-20 */
  62             if(f==zero) { if(k==0) return zero;  else {dk=(float)k;
  63                                    return dk*ln2_hi+dk*ln2_lo;}
  64             }
  65             R = f*f*((float)0.5-(float)0.33333333333333333*f);
  66             if(k==0) return f-R; else {dk=(float)k;
  67                      return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  68         }
  69         s = f/((float)2.0+f);
  70         dk = (float)k;
  71         z = s*s;
  72         i = ix-(0x6147a<<3);
  73         w = z*z;
  74         j = (0x6b851<<3)-ix;
  75         t1= w*(Lg2+w*(Lg4+w*Lg6));
  76         t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  77         i |= j;
  78         R = t2+t1;
  79         if(i>0) {
  80             hfsq=(float)0.5*f*f;
  81             if(k==0) return f-(hfsq-s*(hfsq+R)); else
  82                      return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  83         } else {
  84             if(k==0) return f-s*(f-R); else
  85                      return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  86         }
  87 }