/*	$OpenBSD: n_exp__E.c,v 1.12 2009/10/27 23:59:29 deraadt Exp $	*/
/*	$NetBSD: n_exp__E.c,v 1.1 1995/10/10 23:36:45 ragge Exp $	*/
/*
 * Copyright (c) 1985, 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

/* exp__E(x,c)
 * ASSUMPTION: c << x  SO THAT  fl(x+c)=x.
 * (c is the correction term for x)
 * exp__E RETURNS
 *
 *			 /  exp(x+c) - 1 - x ,  1E-19 < |x| < .3465736
 *       exp__E(x,c) = 	|
 *			 \  0 ,  |x| < 1E-19.
 *
 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
 * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
 * CODED IN C BY K.C. NG, 1/31/85;
 * REVISED BY K.C. NG on 3/16/85, 4/16/85.
 *
 * Required system supported function:
 *	copysign(x,y)
 *
 * Method:
 *	1. Rational approximation. Let r=x+c.
 *	   Based on
 *                                   2 * sinh(r/2)
 *                exp(r) - 1 =   ----------------------   ,
 *                               cosh(r/2) - sinh(r/2)
 *	   exp__E(r) is computed using
 *                   x*x            (x/2)*W - ( Q - ( 2*P  + x*P ) )
 *                   --- + (c + x*[---------------------------------- + c ])
 *                    2                          1 - W
 * 	   where  P := p1*x^2 + p2*x^4,
 *	          Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
 *	          W := x/2-(Q-x*P),
 *
 *	   (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
 *	    nomials P and Q may be regarded as the approximations to sinh
 *	    and cosh :
 *		sinh(r/2) =  r/2 + r * P  ,  cosh(r/2) =  1 + Q . )
 *
 *         The coefficients were obtained by a special Remes algorithm.
 *
 * Approximation error:
 *
 *   |	exp(x) - 1			   |        2**(-57),  (IEEE double)
 *   | ------------  -  (exp__E(x,0)+x)/x  |  <=
 *   |	     x			           |	    2**(-69).  (VAX D)
 *
 * 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.
 */

#include "math.h"
#include "mathimpl.h"

static const double p1 = 1.5150724356786683059E-2;
static const double p2 = 6.3112487873718332688E-5;
static const double q1 = 1.1363478204690669916E-1;
static const double q2 = 1.2624568129896839182E-3;
static const double q3 = 1.5021856115869022674E-6;

double
__exp__E(double x, double c)
{
	static const double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
	double z,p,q,xp,xh,w;
	if(copysign(x,one)>small) {
           z = x*x  ;
	   p = z*( p1 +z* p2 );
#if defined(__vax__)
           q = z*( q1 +z*( q2 +z* q3 ));
#else	/* defined(__vax__) */
           q = z*( q1 +z*  q2 );
#endif	/* defined(__vax__) */
           xp= x*p     ;
	   xh= x*half  ;
           w = xh-(q-xp)  ;
	   p = p+p;
	   c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
	   return(z*half+c);
	}
	/* end of |x| > small */

	else {
	    if(x != zero) {
		if (one + small >= 1.0)	/* raise the inexact flag */
			return(copysign(zero,x));
	    }
	    else
		return(copysign(zero,x));
	}

	/* NOTREACHED */
}