1 #include "FEATURE/uwin"
2
3 #if !_UWIN
4
_STUB_exp__E()5 void _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
39 static 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
95 vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A)
96 vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173)
97 vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45)
98 vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7)
99 vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395)
100
101 ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF)
102 ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4)
103 ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597)
104 ic(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
114 double __exp__E(x,c)
115 double 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