1 #include "FEATURE/uwin"
2
3 #if !_UWIN
4
_STUB_exp()5 void _STUB_exp(){}
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.c 8.1 (Berkeley) 6/4/93";
40 #endif /* not lint */
41
42 /* EXP(X)
43 * RETURN THE EXPONENTIAL OF X
44 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
45 * CODED IN C BY K.C. NG, 1/19/85;
46 * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
47 *
48 * Required system supported functions:
49 * scalb(x,n)
50 * copysign(x,y)
51 * finite(x)
52 *
53 * Method:
54 * 1. Argument Reduction: given the input x, find r and integer k such
55 * that
56 * x = k*ln2 + r, |r| <= 0.5*ln2 .
57 * r will be represented as r := z+c for better accuracy.
58 *
59 * 2. Compute exp(r) by
60 *
61 * exp(r) = 1 + r + r*R1/(2-R1),
62 * where
63 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
64 *
65 * 3. exp(x) = 2^k * exp(r) .
66 *
67 * Special cases:
68 * exp(INF) is INF, exp(NaN) is NaN;
69 * exp(-INF)= 0;
70 * for finite argument, only exp(0)=1 is exact.
71 *
72 * Accuracy:
73 * exp(x) returns the exponential of x nearly rounded. In a test run
74 * with 1,156,000 random arguments on a VAX, the maximum observed
75 * error was 0.869 ulps (units in the last place).
76 *
77 * Constants:
78 * The hexadecimal values are the intended ones for the following constants.
79 * The decimal values may be used, provided that the compiler will convert
80 * from decimal to binary accurately enough to produce the hexadecimal values
81 * shown.
82 */
83
84 #include "mathimpl.h"
85
86 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
87 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
88 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
89 vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
90 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
91 vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
92 vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
93 vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
94 vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
95 vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
96
97 #ifdef vccast
98 #define ln2hi vccast(ln2hi)
99 #define ln2lo vccast(ln2lo)
100 #define lnhuge vccast(lnhuge)
101 #define lntiny vccast(lntiny)
102 #define invln2 vccast(invln2)
103 #define p1 vccast(p1)
104 #define p2 vccast(p2)
105 #define p3 vccast(p3)
106 #define p4 vccast(p4)
107 #define p5 vccast(p5)
108 #endif
109
110 ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
111 ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
112 ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
113 ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
114 ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
115 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
116 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
117 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
118 ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
119 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
120
121 #if !_lib_exp
122
123 extern double exp(x)
124 double x;
125 {
126 double z,hi,lo,c;
127 int k;
128
129 #if !defined(vax)&&!defined(tahoe)
130 if(x!=x) return(x); /* x is NaN */
131 #endif /* !defined(vax)&&!defined(tahoe) */
132 if( x <= lnhuge ) {
133 if( x >= lntiny ) {
134
135 /* argument reduction : x --> x - k*ln2 */
136
137 k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
138
139 /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
140
141 hi=x-k*ln2hi;
142 x=hi-(lo=k*ln2lo);
143
144 /* return 2^k*[1+x+x*c/(2+c)] */
145 z=x*x;
146 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
147 return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
148
149 }
150 /* end of x > lntiny */
151
152 else
153 /* exp(-big#) underflows to zero */
154 if(finite(x)) return(scalb(1.0,-5000));
155
156 /* exp(-INF) is zero */
157 else return(0.0);
158 }
159 /* end of x < lnhuge */
160
161 else
162 /* exp(INF) is INF, exp(+big#) overflows to INF */
163 return( finite(x) ? scalb(1.0,5000) : x);
164 }
165
166 #endif
167
168 /* returns exp(r = x + c) for |c| < |x| with no overlap. */
169
__exp__D(x,c)170 double __exp__D(x, c)
171 double x, c;
172 {
173 double z,hi,lo;
174 int k;
175
176 #if !defined(vax)&&!defined(tahoe)
177 if (x!=x) return(x); /* x is NaN */
178 #endif /* !defined(vax)&&!defined(tahoe) */
179 if ( x <= lnhuge ) {
180 if ( x >= lntiny ) {
181
182 /* argument reduction : x --> x - k*ln2 */
183 z = invln2*x;
184 k = (int)z + copysign(.5, x);
185
186 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
187
188 hi=(x-k*ln2hi); /* Exact. */
189 x= hi - (lo = k*ln2lo-c);
190 /* return 2^k*[1+x+x*c/(2+c)] */
191 z=x*x;
192 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
193 c = (x*c)/(2.0-c);
194
195 return scalb(1.+(hi-(lo - c)), k);
196 }
197 /* end of x > lntiny */
198
199 else
200 /* exp(-big#) underflows to zero */
201 if(finite(x)) return(scalb(1.0,-5000));
202
203 /* exp(-INF) is zero */
204 else return(0.0);
205 }
206 /* end of x < lnhuge */
207
208 else
209 /* exp(INF) is INF, exp(+big#) overflows to INF */
210 return( finite(x) ? scalb(1.0,5000) : x);
211 }
212
213 #endif
214