Quelle e_expf.cpp Sprache: C

/* e_expf.c -- float version of e_exp.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/

/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");

#include <float.h>

#include "math_private.h"

static const float
one = 1.0,
halF[2] = {0.5,-0.5,},
o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
ln2HI[2]   ={ 6.9314575195e-01,  /* 0x3f317200 */
      -6.9314575195e-01,}, /* 0xbf317200 */
ln2LO[2]   ={ 1.4286067653e-06,   /* 0x35bfbe8e */
      -1.4286067653e-06,}, /* 0xb5bfbe8e */
invln2 =  1.4426950216e+00,   /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
*/
P1 =  1.6666625440e-1,  /*  0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3;  /* -0xb55215.0p-32 */

static volatile float
huge = 1.0e+30,
twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */

float
__ieee754_expf(float x)
{
float y,hi=0.0,lo=0.0,c,t,twopk;
int32_t k=0,xsb;
u_int32_t hx;

GET_FLOAT_WORD(hx,x);
xsb = (hx>>31)&1;  /* sign bit of x */
hx &= 0x7fffffff;  /* high word of |x| */

    /* filter out non-finite argument */
if(hx >= 0x42b17218) {   /* if |x|>=88.721... */
     if(hx>0x7f800000)
   return x+x;    /* NaN */
            if(hx==0x7f800000)
  return (xsb==0)? x:0.0;  /* exp(+-inf)={inf,0} */
     if(x > o_threshold) return huge*huge; /* overflow */
     if(x < u_threshold) return twom100*twom100; /* underflow */
}

    /* argument reduction */
if(hx > 0x3eb17218) {  /* if  |x| > 0.5 ln2 */
     if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
  hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
     } else {
  k  = invln2*x+halF[xsb];
  t  = k;
  hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
  lo = t*ln2LO[0];
     }
     STRICT_ASSIGN(float, x, hi - lo);
}
else if(hx < 0x39000000)  { /* when |x|<2**-14 */
     if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;

    /* x is now in primary range */
t  = x*x;
if(k >= -125)
     SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);
else
     SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23);
c  = x - t*(P1+t*P2);
if(k==0)  return one-((x*c)/(c-(float)2.0)-x);
else   y = one-((lo-(x*c)/((float)2.0-c))-hi);
if(k >= -125) {
     if(k==128) return y*2.0F*0x1p127F;
     return y*twopk;
} else {
     return y*twopk*twom100;
}
}

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