1 /* $NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $ */
2
3 /*
4 * Copyright (c) 1985, 1993
5 * The Regents of the University of California. All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 * 3. All advertising materials mentioning features or use of this software
16 * must display the following acknowledgement:
17 * This product includes software developed by the University of
18 * California, Berkeley and its contributors.
19 * 4. Neither the name of the University nor the names of its contributors
20 * may be used to endorse or promote products derived from this software
21 * without specific prior written permission.
22 *
23 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
24 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
25 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
26 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
27 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
28 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
29 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
30 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
31 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
32 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
33 * SUCH DAMAGE.
34 */
35
36 /* @(#)exp.c 8.1 (Berkeley) 6/4/93 */
37 #include <sys/cdefs.h>
38 #if 0
39 __FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_exp.c 176449 2008-02-22 02:26:51Z das $");
40 #else
41 __RCSID("$NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
42 #endif
43
44
45 /* EXP(X)
46 * RETURN THE EXPONENTIAL OF X
47 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
48 * CODED IN C BY K.C. NG, 1/19/85;
49 * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
50 *
51 * Required system supported functions:
52 * scalb(x,n)
53 * copysign(x,y)
54 * finite(x)
55 *
56 * Method:
57 * 1. Argument Reduction: given the input x, find r and integer k such
58 * that
59 * x = k*ln2 + r, |r| <= 0.5*ln2 .
60 * r will be represented as r := z+c for better accuracy.
61 *
62 * 2. Compute exp(r) by
63 *
64 * exp(r) = 1 + r + r*R1/(2-R1),
65 * where
66 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
67 *
68 * 3. exp(x) = 2^k * exp(r) .
69 *
70 * Special cases:
71 * exp(INF) is INF, exp(NaN) is NaN;
72 * exp(-INF)= 0;
73 * for finite argument, only exp(0)=1 is exact.
74 *
75 * Accuracy:
76 * exp(x) returns the exponential of x nearly rounded. In a test run
77 * with 1,156,000 random arguments on a VAX, the maximum observed
78 * error was 0.869 ulps (units in the last place).
79 */
80
81 #include "math.h"
82 #include "math_private.h"
83
84 static const double p1 = 0x1.555555555553ep-3;
85 static const double p2 = -0x1.6c16c16bebd93p-9;
86 static const double p3 = 0x1.1566aaf25de2cp-14;
87 static const double p4 = -0x1.bbd41c5d26bf1p-20;
88 static const double p5 = 0x1.6376972bea4d0p-25;
89 static const double ln2hi = 0x1.62e42fee00000p-1;
90 static const double ln2lo = 0x1.a39ef35793c76p-33;
91 static const double lnhuge = 0x1.6602b15b7ecf2p9;
92 static const double lntiny = -0x1.77af8ebeae354p9;
93 static const double invln2 = 0x1.71547652b82fep0;
94
95 /* returns exp(r = x + c) for |c| < |x| with no overlap. */
96
97 double
__exp__D(double x,double c)98 __exp__D(double x, double c)
99 {
100 double z,hi,lo;
101 int k;
102
103 if (x != x) /* x is NaN */
104 return(x);
105 if ( x <= lnhuge ) {
106 if ( x >= lntiny ) {
107
108 /* argument reduction : x --> x - k*ln2 */
109 z = invln2*x;
110 k = z + copysign(.5, x);
111
112 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
113
114 hi=(x-k*ln2hi); /* Exact. */
115 x= hi - (lo = k*ln2lo-c);
116 /* return 2^k*[1+x+x*c/(2+c)] */
117 z=x*x;
118 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
119 c = (x*c)/(2.0-c);
120
121 return scalb(1.+(hi-(lo - c)), k);
122 }
123 /* end of x > lntiny */
124
125 else
126 /* exp(-big#) underflows to zero */
127 if(finite(x)) return(scalb(1.0,-5000));
128
129 /* exp(-INF) is zero */
130 else return(0.0);
131 }
132 /* end of x < lnhuge */
133
134 else
135 /* exp(INF) is INF, exp(+big#) overflows to INF */
136 return( finite(x) ? scalb(1.0,5000) : x);
137 }
138