1#include "FEATURE/uwin"
2
3#if !_UWIN
4
5void _STUB_exp__E(){}
6
7#else
8
9/*
10 * Copyright (c) 1985, 1993
11 *	The Regents of the University of California.  All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 *    notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 *    notice, this list of conditions and the following disclaimer in the
20 *    documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 *    may be used to endorse or promote products derived from this software
23 *    without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38#ifndef lint
39static char sccsid[] = "@(#)exp__E.c	8.1 (Berkeley) 6/4/93";
40#endif /* not lint */
41
42/* exp__E(x,c)
43 * ASSUMPTION: c << x  SO THAT  fl(x+c)=x.
44 * (c is the correction term for x)
45 * exp__E RETURNS
46 *
47 *			 /  exp(x+c) - 1 - x ,  1E-19 < |x| < .3465736
48 *       exp__E(x,c) = 	|
49 *			 \  0 ,  |x| < 1E-19.
50 *
51 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
52 * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
53 * CODED IN C BY K.C. NG, 1/31/85;
54 * REVISED BY K.C. NG on 3/16/85, 4/16/85.
55 *
56 * Required system supported function:
57 *	copysign(x,y)
58 *
59 * Method:
60 *	1. Rational approximation. Let r=x+c.
61 *	   Based on
62 *                                   2 * sinh(r/2)
63 *                exp(r) - 1 =   ----------------------   ,
64 *                               cosh(r/2) - sinh(r/2)
65 *	   exp__E(r) is computed using
66 *                   x*x            (x/2)*W - ( Q - ( 2*P  + x*P ) )
67 *                   --- + (c + x*[---------------------------------- + c ])
68 *                    2                          1 - W
69 * 	   where  P := p1*x^2 + p2*x^4,
70 *	          Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
71 *	          W := x/2-(Q-x*P),
72 *
73 *	   (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
74 *	    nomials P and Q may be regarded as the approximations to sinh
75 *	    and cosh :
76 *		sinh(r/2) =  r/2 + r * P  ,  cosh(r/2) =  1 + Q . )
77 *
78 *         The coefficients were obtained by a special Remez algorithm.
79 *
80 * Approximation error:
81 *
82 *   |	exp(x) - 1			   |        2**(-57),  (IEEE double)
83 *   | ------------  -  (exp__E(x,0)+x)/x  |  <=
84 *   |	     x			           |	    2**(-69).  (VAX D)
85 *
86 * Constants:
87 * The hexadecimal values are the intended ones for the following constants.
88 * The decimal values may be used, provided that the compiler will convert
89 * from decimal to binary accurately enough to produce the hexadecimal values
90 * shown.
91 */
92
93#include "mathimpl.h"
94
95vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1,  -6, .F83ABE67E1066A)
96vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173)
97vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2,  -3, .E8B95A44A2EC45)
98vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4,  -9, .A5790572E4F5E7)
99vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395)
100
101ic(p1, 1.3887401997267371720E-2,  -7, 1.C70FF8B3CC2CF)
102ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4)
103ic(q1, 1.1110813732786649355E-1,  -4, 1.C719538248597)
104ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8)
105
106#ifdef vccast
107#define       p1    vccast(p1)
108#define       p2    vccast(p2)
109#define       q1    vccast(q1)
110#define       q2    vccast(q2)
111#define       q3    vccast(q3)
112#endif
113
114double __exp__E(x,c)
115double x,c;
116{
117	const static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
118	double z,p,q,xp,xh,w;
119	if(copysign(x,one)>small) {
120           z = x*x  ;
121	   p = z*( p1 +z* p2 );
122#if defined(vax)||defined(tahoe)
123           q = z*( q1 +z*( q2 +z* q3 ));
124#else	/* defined(vax)||defined(tahoe) */
125           q = z*( q1 +z*  q2 );
126#endif	/* defined(vax)||defined(tahoe) */
127           xp= x*p     ;
128	   xh= x*half  ;
129           w = xh-(q-xp)  ;
130	   p = p+p;
131	   c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
132	   return(z*half+c);
133	}
134	/* end of |x| > small */
135
136	else {
137	    if(x!=zero) one+small;	/* raise the inexact flag */
138	    return(copysign(zero,x));
139	}
140}
141
142#endif
143