lib/libm/src/e_expf.c

   1 /* e_expf.c -- float version of e_exp.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_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/e_expf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static const float huge = 1.0e+30;
  23
  24 static const float
  25 one     = 1.0,
  26 halF[2] = {0.5,-0.5,},
  27 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
  28 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
  29 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
  30 ln2HI[2]   ={ 6.9313812256e-01,         /* 0x3f317180 */
  31              -6.9313812256e-01,},       /* 0xbf317180 */
  32 ln2LO[2]   ={ 9.0580006145e-06,         /* 0x3717f7d1 */
  33              -9.0580006145e-06,},       /* 0xb717f7d1 */
  34 invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  35 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  36 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  37 P3   =  6.6137559770e-05, /* 0x388ab355 */
  38 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  39 P5   =  4.1381369442e-08; /* 0x3331bb4c */
  40
  41 float
  42 expf(float x)   /* default IEEE double exp */
  43 {
  44         float y,hi,lo,c,t;
  45         int32_t k,xsb;
  46         u_int32_t hx;
  47
  48         hi = lo = 0;
  49         k = 0;
  50         GET_FLOAT_WORD(hx,x);
  51         xsb = (hx>>31)&1;               /* sign bit of x */
  52         hx &= 0x7fffffff;               /* high word of |x| */
  53
  54     /* filter out non-finite argument */
  55         if(hx >= 0x42b17218) {                  /* if |x|>=88.721... */
  56             if(hx>0x7f800000)
  57                  return x+x;                    /* NaN */
  58             if(hx==0x7f800000)
  59                 return (xsb==0)? x:0.0;         /* exp(+-inf)={inf,0} */
  60             if(x > o_threshold) return huge*huge; /* overflow */
  61             if(x < u_threshold) return twom100*twom100; /* underflow */
  62         }
  63
  64     /* argument reduction */
  65         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  66             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  67                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  68             } else {
  69                 k  = invln2*x+halF[xsb];
  70                 t  = k;
  71                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  72                 lo = t*ln2LO[0];
  73             }
  74             x  = hi - lo;
  75         }
  76         else if(hx < 0x31800000)  {     /* when |x|<2**-28 */
  77             if(huge+x>one) return one+x;/* trigger inexact */
  78         }
  79         else k = 0;
  80
  81     /* x is now in primary range */
  82         t  = x*x;
  83         c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  84         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  85         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  86         if(k >= -125) {
  87             u_int32_t hy;
  88             GET_FLOAT_WORD(hy,y);
  89             SET_FLOAT_WORD(y,hy+(k<<23));       /* add k to y's exponent */
  90             return y;
  91         } else {
  92             u_int32_t hy;
  93             GET_FLOAT_WORD(hy,y);
  94             SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
  95             return y*twom100;
  96         }
  97 }