1*4887Schin #include "FEATURE/uwin"
2*4887Schin
3*4887Schin #if !_UWIN
4*4887Schin
_STUB_exp()5*4887Schin void _STUB_exp(){}
6*4887Schin
7*4887Schin #else
8*4887Schin
9*4887Schin /*
10*4887Schin * Copyright (c) 1985, 1993
11*4887Schin * The Regents of the University of California. All rights reserved.
12*4887Schin *
13*4887Schin * Redistribution and use in source and binary forms, with or without
14*4887Schin * modification, are permitted provided that the following conditions
15*4887Schin * are met:
16*4887Schin * 1. Redistributions of source code must retain the above copyright
17*4887Schin * notice, this list of conditions and the following disclaimer.
18*4887Schin * 2. Redistributions in binary form must reproduce the above copyright
19*4887Schin * notice, this list of conditions and the following disclaimer in the
20*4887Schin * documentation and/or other materials provided with the distribution.
21*4887Schin * 3. Neither the name of the University nor the names of its contributors
22*4887Schin * may be used to endorse or promote products derived from this software
23*4887Schin * without specific prior written permission.
24*4887Schin *
25*4887Schin * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26*4887Schin * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27*4887Schin * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28*4887Schin * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29*4887Schin * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30*4887Schin * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31*4887Schin * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32*4887Schin * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33*4887Schin * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34*4887Schin * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35*4887Schin * SUCH DAMAGE.
36*4887Schin */
37*4887Schin
38*4887Schin #ifndef lint
39*4887Schin static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
40*4887Schin #endif /* not lint */
41*4887Schin
42*4887Schin /* EXP(X)
43*4887Schin * RETURN THE EXPONENTIAL OF X
44*4887Schin * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
45*4887Schin * CODED IN C BY K.C. NG, 1/19/85;
46*4887Schin * 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*4887Schin *
48*4887Schin * Required system supported functions:
49*4887Schin * scalb(x,n)
50*4887Schin * copysign(x,y)
51*4887Schin * finite(x)
52*4887Schin *
53*4887Schin * Method:
54*4887Schin * 1. Argument Reduction: given the input x, find r and integer k such
55*4887Schin * that
56*4887Schin * x = k*ln2 + r, |r| <= 0.5*ln2 .
57*4887Schin * r will be represented as r := z+c for better accuracy.
58*4887Schin *
59*4887Schin * 2. Compute exp(r) by
60*4887Schin *
61*4887Schin * exp(r) = 1 + r + r*R1/(2-R1),
62*4887Schin * where
63*4887Schin * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
64*4887Schin *
65*4887Schin * 3. exp(x) = 2^k * exp(r) .
66*4887Schin *
67*4887Schin * Special cases:
68*4887Schin * exp(INF) is INF, exp(NaN) is NaN;
69*4887Schin * exp(-INF)= 0;
70*4887Schin * for finite argument, only exp(0)=1 is exact.
71*4887Schin *
72*4887Schin * Accuracy:
73*4887Schin * exp(x) returns the exponential of x nearly rounded. In a test run
74*4887Schin * with 1,156,000 random arguments on a VAX, the maximum observed
75*4887Schin * error was 0.869 ulps (units in the last place).
76*4887Schin *
77*4887Schin * Constants:
78*4887Schin * The hexadecimal values are the intended ones for the following constants.
79*4887Schin * The decimal values may be used, provided that the compiler will convert
80*4887Schin * from decimal to binary accurately enough to produce the hexadecimal values
81*4887Schin * shown.
82*4887Schin */
83*4887Schin
84*4887Schin #include "mathimpl.h"
85*4887Schin
86*4887Schin vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
87*4887Schin vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
88*4887Schin vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
89*4887Schin vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
90*4887Schin vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
91*4887Schin vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
92*4887Schin vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
93*4887Schin vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
94*4887Schin vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
95*4887Schin vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
96*4887Schin
97*4887Schin #ifdef vccast
98*4887Schin #define ln2hi vccast(ln2hi)
99*4887Schin #define ln2lo vccast(ln2lo)
100*4887Schin #define lnhuge vccast(lnhuge)
101*4887Schin #define lntiny vccast(lntiny)
102*4887Schin #define invln2 vccast(invln2)
103*4887Schin #define p1 vccast(p1)
104*4887Schin #define p2 vccast(p2)
105*4887Schin #define p3 vccast(p3)
106*4887Schin #define p4 vccast(p4)
107*4887Schin #define p5 vccast(p5)
108*4887Schin #endif
109*4887Schin
110*4887Schin ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
111*4887Schin ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
112*4887Schin ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
113*4887Schin ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
114*4887Schin ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
115*4887Schin ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
116*4887Schin ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
117*4887Schin ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
118*4887Schin ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
119*4887Schin ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
120*4887Schin
121*4887Schin #if !_lib_exp
122*4887Schin
123*4887Schin extern double exp(x)
124*4887Schin double x;
125*4887Schin {
126*4887Schin double z,hi,lo,c;
127*4887Schin int k;
128*4887Schin
129*4887Schin #if !defined(vax)&&!defined(tahoe)
130*4887Schin if(x!=x) return(x); /* x is NaN */
131*4887Schin #endif /* !defined(vax)&&!defined(tahoe) */
132*4887Schin if( x <= lnhuge ) {
133*4887Schin if( x >= lntiny ) {
134*4887Schin
135*4887Schin /* argument reduction : x --> x - k*ln2 */
136*4887Schin
137*4887Schin k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
138*4887Schin
139*4887Schin /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
140*4887Schin
141*4887Schin hi=x-k*ln2hi;
142*4887Schin x=hi-(lo=k*ln2lo);
143*4887Schin
144*4887Schin /* return 2^k*[1+x+x*c/(2+c)] */
145*4887Schin z=x*x;
146*4887Schin c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
147*4887Schin return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
148*4887Schin
149*4887Schin }
150*4887Schin /* end of x > lntiny */
151*4887Schin
152*4887Schin else
153*4887Schin /* exp(-big#) underflows to zero */
154*4887Schin if(finite(x)) return(scalb(1.0,-5000));
155*4887Schin
156*4887Schin /* exp(-INF) is zero */
157*4887Schin else return(0.0);
158*4887Schin }
159*4887Schin /* end of x < lnhuge */
160*4887Schin
161*4887Schin else
162*4887Schin /* exp(INF) is INF, exp(+big#) overflows to INF */
163*4887Schin return( finite(x) ? scalb(1.0,5000) : x);
164*4887Schin }
165*4887Schin
166*4887Schin #endif
167*4887Schin
168*4887Schin /* returns exp(r = x + c) for |c| < |x| with no overlap. */
169*4887Schin
__exp__D(x,c)170*4887Schin double __exp__D(x, c)
171*4887Schin double x, c;
172*4887Schin {
173*4887Schin double z,hi,lo;
174*4887Schin int k;
175*4887Schin
176*4887Schin #if !defined(vax)&&!defined(tahoe)
177*4887Schin if (x!=x) return(x); /* x is NaN */
178*4887Schin #endif /* !defined(vax)&&!defined(tahoe) */
179*4887Schin if ( x <= lnhuge ) {
180*4887Schin if ( x >= lntiny ) {
181*4887Schin
182*4887Schin /* argument reduction : x --> x - k*ln2 */
183*4887Schin z = invln2*x;
184*4887Schin k = (int)z + copysign(.5, x);
185*4887Schin
186*4887Schin /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
187*4887Schin
188*4887Schin hi=(x-k*ln2hi); /* Exact. */
189*4887Schin x= hi - (lo = k*ln2lo-c);
190*4887Schin /* return 2^k*[1+x+x*c/(2+c)] */
191*4887Schin z=x*x;
192*4887Schin c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
193*4887Schin c = (x*c)/(2.0-c);
194*4887Schin
195*4887Schin return scalb(1.+(hi-(lo - c)), k);
196*4887Schin }
197*4887Schin /* end of x > lntiny */
198*4887Schin
199*4887Schin else
200*4887Schin /* exp(-big#) underflows to zero */
201*4887Schin if(finite(x)) return(scalb(1.0,-5000));
202*4887Schin
203*4887Schin /* exp(-INF) is zero */
204*4887Schin else return(0.0);
205*4887Schin }
206*4887Schin /* end of x < lnhuge */
207*4887Schin
208*4887Schin else
209*4887Schin /* exp(INF) is INF, exp(+big#) overflows to INF */
210*4887Schin return( finite(x) ? scalb(1.0,5000) : x);
211*4887Schin }
212*4887Schin
213*4887Schin #endif
214