/* exp__E.c - math routines *//* Copyright 1992 Wind River Systems, Inc. *//*modification history--------------------01b,20sep92,smb  documentation additions.01a,08jul92,smb  documentation.*//*DESCRIPTION* Copyright (c) 1985 Regents of the University of California.* All rights reserved.** Redistribution and use in source and binary forms are permitted* provided that the above copyright notice and this paragraph are* duplicated in all such forms and that any documentation,* advertising materials, and other materials related to such* distribution and use acknowledge that the software was developed* by the University of California, Berkeley.  The name of the* University may not be used to endorse or promote products derived* from this software without specific prior written permission.* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.** All recipients should regard themselves as participants in an ongoing* research project and hence should feel obligated to report their* experiences (good or bad) with these elementary function codes, using* the sendbug(8) program, to the authors.*SEE ALSO: American National Standard X3.159-1989NOMANUAL*/#include "vxWorks.h"#include "math.h"#if defined(vax)||defined(tahoe)	/* VAX D format */#ifdef vax#define _0x(A,B)	0x/**/A/**/B#else	/* vax */#define _0x(A,B)	0x/**/B/**/A#endif	/* vax *//* static double *//* p1     =  1.5150724356786683059E-2    , Hex  2^ -6   *  .F83ABE67E1066A *//* p2     =  6.3112487873718332688E-5    , Hex  2^-13   *  .845B4248CD0173 *//* q1     =  1.1363478204690669916E-1    , Hex  2^ -3   *  .E8B95A44A2EC45 *//* q2     =  1.2624568129896839182E-3    , Hex  2^ -9   *  .A5790572E4F5E7 *//* q3     =  1.5021856115869022674E-6    ; Hex  2^-19   *  .C99EB4604AC395 */static long        p1x[] = { _0x(3abe,3d78), _0x(066a,67e1)};static long        p2x[] = { _0x(5b42,3984), _0x(0173,48cd)};static long        q1x[] = { _0x(b95a,3ee8), _0x(ec45,44a2)};static long        q2x[] = { _0x(7905,3ba5), _0x(f5e7,72e4)};static long        q3x[] = { _0x(9eb4,36c9), _0x(c395,604a)};#define       p1    (*(double*)p1x)#define       p2    (*(double*)p2x)#define       q1    (*(double*)q1x)#define       q2    (*(double*)q2x)#define       q3    (*(double*)q3x)#else	/* defined(vax)||defined(tahoe) */static doublep1     =  1.3887401997267371720E-2    , /*Hex  2^ -7   *  1.C70FF8B3CC2CF */p2     =  3.3044019718331897649E-5    , /*Hex  2^-15   *  1.15317DF4526C4 */q1     =  1.1110813732786649355E-1    , /*Hex  2^ -4   *  1.C719538248597 */q2     =  9.9176615021572857300E-4    ; /*Hex  2^-10   *  1.03FC4CB8C98E8 */#endif	/* defined(vax)||defined(tahoe) *//********************************************************************************* exp_E	- ** 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 Remez 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.NOMANUAL*/double exp__E(x,c)double x,c;{	static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;	double copysign(),z,p,q,xp,xh,w;	if(copysign(x,one)>small) {           z = x*x  ;	   p = z*( p1 +z* p2 );#if defined(vax)||defined(tahoe)           q = z*( q1 +z*( q2 +z* q3 ));#else	/* defined(vax)||defined(tahoe) */           q = z*( q1 +z*  q2 );#endif	/* defined(vax)||defined(tahoe) */           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) one+small;	/* raise the inexact flag */	    return(copysign(zero,x));	}}