text: 
  /* @(#)e_exp.c 1.6 04/04/22 */
  /*
   * ====================================================
   * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
   *
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice 
   * is preserved.
   * ====================================================
   */
  
  /* __ieee754_exp(x)
   * Returns the exponential of x.
   *
   * Method
   *   1. Argument reduction:
   *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
   *	Given x, find r and integer k such that
   *
   *               x = k*ln2 + r,  |r| <= 0.5*ln2.  
   *
   *      Here r will be represented as r = hi-lo for better 
   *	accuracy.
   *
   *   2. Approximation of exp(r) by a special rational function on
   *	the interval [0,0.34658]:
   *	Write
   *	    R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
   *      We use a special Remes algorithm on [0,0.34658] to generate 
   * 	a polynomial of degree 5 to approximate R. The maximum error 
   *	of this polynomial approximation is bounded by 2**-59. In
   *	other words,
   *	    R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
   *  	(where z=r*r, and the values of P1 to P5 are listed below)
   *	and
   *	    |                  5          |     -59
   *	    | 2.0+P1*z+...+P5*z   -  R(z) | <= 2 
   *	    |                             |
   *	The computation of exp(r) thus becomes
   *                             2*r
   *		exp(r) = 1 + -------
   *		              R - r
   *                                 r*R1(r)	
   *		       = 1 + r + ----------- (for better accuracy)
   *		                  2 - R1(r)
   *	where
   *			         2       4             10
   *		R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
   *	
   *   3. Scale back to obtain exp(x):
   *	From step 1, we have
   *	   exp(x) = 2^k * exp(r)
   *
   * Special cases:
   *	exp(INF) is INF, exp(NaN) is NaN;
   *	exp(-INF) is 0, and
   *	for finite argument, only exp(0)=1 is exact.
   *
   * Accuracy:
   *	according to an error analysis, the error is always less than
   *	1 ulp (unit in the last place).
   *
   * Misc. info.
   *	For IEEE double 
   *	    if x >  7.09782712893383973096e+02 then exp(x) overflow
   *	    if x < -7.45133219101941108420e+02 then exp(x) underflow
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following 
   * constants. The decimal values may be used, provided that the 
   * compiler will convert from decimal to binary accurately enough
   * to produce the hexadecimal values shown.
   */
  
  #define __HI(x) *(1+(int*)&x)
  #define __LO(x) *(int*)&x
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
  one	= 1.0,
  halF[2]	= {0.5,-0.5,},
  huge	= 1.0e+300,
  twom1000= 9.33263618503218878990e-302,     /* 2**-1000=0x01700000,0*/
  o_threshold=  7.09782712893383973096e+02,  /* 0x40862E42, 0xFEFA39EF */
  u_threshold= -7.45133219101941108420e+02,  /* 0xc0874910, 0xD52D3051 */
  ln2HI[2]   ={ 6.93147180369123816490e-01,  /* 0x3fe62e42, 0xfee00000 */
  	     -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
  ln2LO[2]   ={ 1.90821492927058770002e-10,  /* 0x3dea39ef, 0x35793c76 */
  	     -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
  invln2 =  1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
  P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
  P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
  P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
  P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
  P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
  
  double exp(double x)	/* default IEEE double exp */
  {
  	double y,hi,lo,c,t;
  	int k,xsb;
  	unsigned hx;
  
  	hx  = __HI(x);	/* high word of x */
  	xsb = (hx>>31)&1;		/* sign bit of x */
  	hx &= 0x7fffffff;		/* high word of |x| */
  
      /* filter out non-finite argument */
  	if(hx >= 0x40862E42) {			/* if |x|>=709.78... */
              if(hx>=0x7ff00000) {
  		if(((hx&0xfffff)|__LO(x))!=0) 
  		     return x+x; 		/* NaN */
  		else return (xsb==0)? x:0.0;	/* exp(+-inf)={inf,0} */
  	    }
  	    if(x > o_threshold) return huge*huge; /* overflow */
  	    if(x < u_threshold) return twom1000*twom1000; /* underflow */
  	}
  
      /* argument reduction */
  	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */ 
  	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
  		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  	    } else {
  		k  = (int)(invln2*x+halF[xsb]);
  		t  = k;
  		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
  		lo = t*ln2LO[0];
  	    }
  	    x  = hi - lo;
  	} 
  	else if(hx < 0x3e300000)  {	/* when |x|<2**-28 */
  	    if(huge+x>one) return one+x;/* trigger inexact */
  	}
  	else k = 0;
  
      /* x is now in primary range */
  	t  = x*x;
  	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  	if(k==0) 	return one-((x*c)/(c-2.0)-x); 
  	else 		y = one-((lo-(x*c)/(2.0-c))-hi);
  	if(k >= -1021) {
  	    __HI(y) += (k<<20);	/* add k to y's exponent */
  	    return y;
  	} else {
  	    __HI(y) += ((k+1000)<<20);/* add k to y's exponent */
  	    return y*twom1000;
  	}
  }
  
  