xref: /titanic_41/usr/src/lib/libast/common/uwin/exp.c (revision 67e96bdfbca5b789a8c03fa34eaaa6c9aec7a629)
1 #include "FEATURE/uwin"
2 
3 #if !_UWIN
4 
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 
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