1#include "FEATURE/uwin"
2
3#if !_UWIN
4
5void _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
39static 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
86vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
87vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
88vc(lnhuge, 9.4961163736712506989E1   ,ec1d,43bd,9010,a73e,   7, .BDEC1DA73E9010)
89vc(lntiny,-9.5654310917272452386E1   ,4f01,c3bf,33af,d72e,   7,-.BF4F01D72E33AF)
90vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)
91vc(p1,     1.6666666666666602251E-1  ,aaaa,3f2a,a9f1,aaaa,  -2, .AAAAAAAAAAA9F1)
92vc(p2,    -2.7777777777015591216E-3  ,0b60,bc36,ec94,b5f5,  -8,-.B60B60B5F5EC94)
93vc(p3,     6.6137563214379341918E-5  ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
94vc(p4,    -1.6533902205465250480E-6  ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
95vc(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
110ic(p1,     1.6666666666666601904E-1,  -3,  1.555555555553E)
111ic(p2,    -2.7777777777015593384E-3,  -9, -1.6C16C16BEBD93)
112ic(p3,     6.6137563214379343612E-5, -14,  1.1566AAF25DE2C)
113ic(p4,    -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
114ic(p5,     4.1381367970572384604E-8, -25,  1.6376972BEA4D0)
115ic(ln2hi,  6.9314718036912381649E-1,  -1,  1.62E42FEE00000)
116ic(ln2lo,  1.9082149292705877000E-10,-33,  1.A39EF35793C76)
117ic(lnhuge, 7.1602103751842355450E2,    9,  1.6602B15B7ECF2)
118ic(lntiny,-7.5137154372698068983E2,    9, -1.77AF8EBEAE354)
119ic(invln2, 1.4426950408889633870E0,    0,  1.71547652B82FE)
120
121#if !_lib_exp
122
123extern double exp(x)
124double 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
170double __exp__D(x, c)
171double 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