xref: /onnv-gate/usr/src/lib/libast/common/uwin/exp.c (revision 4887:feebf9260c2e)
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