1da2e3ebdSchin #include "FEATURE/uwin"
2da2e3ebdSchin
3da2e3ebdSchin #if !_UWIN
4da2e3ebdSchin
_STUB_exp()5da2e3ebdSchin void _STUB_exp(){}
6da2e3ebdSchin
7da2e3ebdSchin #else
8da2e3ebdSchin
9da2e3ebdSchin /*
10da2e3ebdSchin * Copyright (c) 1985, 1993
11da2e3ebdSchin * The Regents of the University of California. All rights reserved.
12da2e3ebdSchin *
13da2e3ebdSchin * Redistribution and use in source and binary forms, with or without
14da2e3ebdSchin * modification, are permitted provided that the following conditions
15da2e3ebdSchin * are met:
16da2e3ebdSchin * 1. Redistributions of source code must retain the above copyright
17da2e3ebdSchin * notice, this list of conditions and the following disclaimer.
18da2e3ebdSchin * 2. Redistributions in binary form must reproduce the above copyright
19da2e3ebdSchin * notice, this list of conditions and the following disclaimer in the
20da2e3ebdSchin * documentation and/or other materials provided with the distribution.
21da2e3ebdSchin * 3. Neither the name of the University nor the names of its contributors
22da2e3ebdSchin * may be used to endorse or promote products derived from this software
23da2e3ebdSchin * without specific prior written permission.
24da2e3ebdSchin *
25da2e3ebdSchin * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26da2e3ebdSchin * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27da2e3ebdSchin * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28da2e3ebdSchin * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29da2e3ebdSchin * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30da2e3ebdSchin * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31da2e3ebdSchin * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32da2e3ebdSchin * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33da2e3ebdSchin * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34da2e3ebdSchin * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35da2e3ebdSchin * SUCH DAMAGE.
36da2e3ebdSchin */
37da2e3ebdSchin
38da2e3ebdSchin #ifndef lint
39da2e3ebdSchin static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
40da2e3ebdSchin #endif /* not lint */
41da2e3ebdSchin
42da2e3ebdSchin /* EXP(X)
43da2e3ebdSchin * RETURN THE EXPONENTIAL OF X
44da2e3ebdSchin * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
45da2e3ebdSchin * CODED IN C BY K.C. NG, 1/19/85;
46da2e3ebdSchin * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
47da2e3ebdSchin *
48da2e3ebdSchin * Required system supported functions:
49da2e3ebdSchin * scalb(x,n)
50da2e3ebdSchin * copysign(x,y)
51da2e3ebdSchin * finite(x)
52da2e3ebdSchin *
53da2e3ebdSchin * Method:
54da2e3ebdSchin * 1. Argument Reduction: given the input x, find r and integer k such
55da2e3ebdSchin * that
56da2e3ebdSchin * x = k*ln2 + r, |r| <= 0.5*ln2 .
57da2e3ebdSchin * r will be represented as r := z+c for better accuracy.
58da2e3ebdSchin *
59da2e3ebdSchin * 2. Compute exp(r) by
60da2e3ebdSchin *
61da2e3ebdSchin * exp(r) = 1 + r + r*R1/(2-R1),
62da2e3ebdSchin * where
63da2e3ebdSchin * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
64da2e3ebdSchin *
65da2e3ebdSchin * 3. exp(x) = 2^k * exp(r) .
66da2e3ebdSchin *
67da2e3ebdSchin * Special cases:
68da2e3ebdSchin * exp(INF) is INF, exp(NaN) is NaN;
69da2e3ebdSchin * exp(-INF)= 0;
70da2e3ebdSchin * for finite argument, only exp(0)=1 is exact.
71da2e3ebdSchin *
72da2e3ebdSchin * Accuracy:
73da2e3ebdSchin * exp(x) returns the exponential of x nearly rounded. In a test run
74da2e3ebdSchin * with 1,156,000 random arguments on a VAX, the maximum observed
75da2e3ebdSchin * error was 0.869 ulps (units in the last place).
76da2e3ebdSchin *
77da2e3ebdSchin * Constants:
78da2e3ebdSchin * The hexadecimal values are the intended ones for the following constants.
79da2e3ebdSchin * The decimal values may be used, provided that the compiler will convert
80da2e3ebdSchin * from decimal to binary accurately enough to produce the hexadecimal values
81da2e3ebdSchin * shown.
82da2e3ebdSchin */
83da2e3ebdSchin
84da2e3ebdSchin #include "mathimpl.h"
85da2e3ebdSchin
86da2e3ebdSchin vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
87da2e3ebdSchin vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
88da2e3ebdSchin vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
89da2e3ebdSchin vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
90da2e3ebdSchin vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
91da2e3ebdSchin vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
92da2e3ebdSchin vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
93da2e3ebdSchin vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
94da2e3ebdSchin vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
95da2e3ebdSchin vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
96da2e3ebdSchin
97da2e3ebdSchin #ifdef vccast
98da2e3ebdSchin #define ln2hi vccast(ln2hi)
99da2e3ebdSchin #define ln2lo vccast(ln2lo)
100da2e3ebdSchin #define lnhuge vccast(lnhuge)
101da2e3ebdSchin #define lntiny vccast(lntiny)
102da2e3ebdSchin #define invln2 vccast(invln2)
103da2e3ebdSchin #define p1 vccast(p1)
104da2e3ebdSchin #define p2 vccast(p2)
105da2e3ebdSchin #define p3 vccast(p3)
106da2e3ebdSchin #define p4 vccast(p4)
107da2e3ebdSchin #define p5 vccast(p5)
108da2e3ebdSchin #endif
109da2e3ebdSchin
110da2e3ebdSchin ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
111da2e3ebdSchin ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
112da2e3ebdSchin ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
113da2e3ebdSchin ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
114da2e3ebdSchin ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
115da2e3ebdSchin ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
116da2e3ebdSchin ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
117da2e3ebdSchin ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
118da2e3ebdSchin ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
119da2e3ebdSchin ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
120da2e3ebdSchin
121da2e3ebdSchin #if !_lib_exp
122da2e3ebdSchin
123da2e3ebdSchin extern double exp(x)
124da2e3ebdSchin double x;
125da2e3ebdSchin {
126da2e3ebdSchin double z,hi,lo,c;
127da2e3ebdSchin int k;
128da2e3ebdSchin
129da2e3ebdSchin #if !defined(vax)&&!defined(tahoe)
130da2e3ebdSchin if(x!=x) return(x); /* x is NaN */
131da2e3ebdSchin #endif /* !defined(vax)&&!defined(tahoe) */
132da2e3ebdSchin if( x <= lnhuge ) {
133da2e3ebdSchin if( x >= lntiny ) {
134da2e3ebdSchin
135da2e3ebdSchin /* argument reduction : x --> x - k*ln2 */
136da2e3ebdSchin
137da2e3ebdSchin k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
138da2e3ebdSchin
139da2e3ebdSchin /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
140da2e3ebdSchin
141da2e3ebdSchin hi=x-k*ln2hi;
142da2e3ebdSchin x=hi-(lo=k*ln2lo);
143da2e3ebdSchin
144da2e3ebdSchin /* return 2^k*[1+x+x*c/(2+c)] */
145da2e3ebdSchin z=x*x;
146da2e3ebdSchin c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
147da2e3ebdSchin return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
148da2e3ebdSchin
149da2e3ebdSchin }
150da2e3ebdSchin /* end of x > lntiny */
151da2e3ebdSchin
152da2e3ebdSchin else
153da2e3ebdSchin /* exp(-big#) underflows to zero */
154da2e3ebdSchin if(finite(x)) return(scalb(1.0,-5000));
155da2e3ebdSchin
156da2e3ebdSchin /* exp(-INF) is zero */
157da2e3ebdSchin else return(0.0);
158da2e3ebdSchin }
159da2e3ebdSchin /* end of x < lnhuge */
160da2e3ebdSchin
161da2e3ebdSchin else
162da2e3ebdSchin /* exp(INF) is INF, exp(+big#) overflows to INF */
163da2e3ebdSchin return( finite(x) ? scalb(1.0,5000) : x);
164da2e3ebdSchin }
165da2e3ebdSchin
166da2e3ebdSchin #endif
167da2e3ebdSchin
168da2e3ebdSchin /* returns exp(r = x + c) for |c| < |x| with no overlap. */
169da2e3ebdSchin
__exp__D(x,c)170da2e3ebdSchin double __exp__D(x, c)
171da2e3ebdSchin double x, c;
172da2e3ebdSchin {
173da2e3ebdSchin double z,hi,lo;
174da2e3ebdSchin int k;
175da2e3ebdSchin
176da2e3ebdSchin #if !defined(vax)&&!defined(tahoe)
177da2e3ebdSchin if (x!=x) return(x); /* x is NaN */
178da2e3ebdSchin #endif /* !defined(vax)&&!defined(tahoe) */
179da2e3ebdSchin if ( x <= lnhuge ) {
180da2e3ebdSchin if ( x >= lntiny ) {
181da2e3ebdSchin
182da2e3ebdSchin /* argument reduction : x --> x - k*ln2 */
183da2e3ebdSchin z = invln2*x;
184da2e3ebdSchin k = (int)z + copysign(.5, x);
185da2e3ebdSchin
186da2e3ebdSchin /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
187da2e3ebdSchin
188da2e3ebdSchin hi=(x-k*ln2hi); /* Exact. */
189da2e3ebdSchin x= hi - (lo = k*ln2lo-c);
190da2e3ebdSchin /* return 2^k*[1+x+x*c/(2+c)] */
191da2e3ebdSchin z=x*x;
192da2e3ebdSchin c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
193da2e3ebdSchin c = (x*c)/(2.0-c);
194da2e3ebdSchin
195da2e3ebdSchin return scalb(1.+(hi-(lo - c)), k);
196da2e3ebdSchin }
197da2e3ebdSchin /* end of x > lntiny */
198da2e3ebdSchin
199da2e3ebdSchin else
200da2e3ebdSchin /* exp(-big#) underflows to zero */
201da2e3ebdSchin if(finite(x)) return(scalb(1.0,-5000));
202da2e3ebdSchin
203da2e3ebdSchin /* exp(-INF) is zero */
204da2e3ebdSchin else return(0.0);
205da2e3ebdSchin }
206da2e3ebdSchin /* end of x < lnhuge */
207da2e3ebdSchin
208da2e3ebdSchin else
209da2e3ebdSchin /* exp(INF) is INF, exp(+big#) overflows to INF */
210da2e3ebdSchin return( finite(x) ? scalb(1.0,5000) : x);
211da2e3ebdSchin }
212da2e3ebdSchin
213da2e3ebdSchin #endif
214