libm & rtld: Ansify some remaining functions.
[dragonfly.git] / lib / libm / src / b_exp.c
CommitLineData
1a3b704c
JM
1/*
2 * Copyright (c) 1985, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 * 3. All advertising materials mentioning features or use of this software
14 * must display the following acknowledgement:
15 * This product includes software developed by the University of
16 * California, Berkeley and its contributors.
17 * 4. Neither the name of the University nor the names of its contributors
18 * may be used to endorse or promote products derived from this software
19 * without specific prior written permission.
20 *
21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31 * SUCH DAMAGE.
32 *
33 * FreeBSD SVN: 226414 (2011-10-16)
34 */
35
36/* @(#)exp.c 8.1 (Berkeley) 6/4/93 */
37
38/* EXP(X)
39 * RETURN THE EXPONENTIAL OF X
40 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
41 * CODED IN C BY K.C. NG, 1/19/85;
42 * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
43 *
44 * Required system supported functions:
45 * scalb(x,n)
46 * copysign(x,y)
47 * finite(x)
48 *
49 * Method:
50 * 1. Argument Reduction: given the input x, find r and integer k such
51 * that
52 * x = k*ln2 + r, |r| <= 0.5*ln2 .
53 * r will be represented as r := z+c for better accuracy.
54 *
55 * 2. Compute exp(r) by
56 *
57 * exp(r) = 1 + r + r*R1/(2-R1),
58 * where
59 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
60 *
61 * 3. exp(x) = 2^k * exp(r) .
62 *
63 * Special cases:
64 * exp(INF) is INF, exp(NaN) is NaN;
65 * exp(-INF)= 0;
66 * for finite argument, only exp(0)=1 is exact.
67 *
68 * Accuracy:
69 * exp(x) returns the exponential of x nearly rounded. In a test run
70 * with 1,156,000 random arguments on a VAX, the maximum observed
71 * error was 0.869 ulps (units in the last place).
72 */
73
74#include "mathimpl.h"
75
76static const double p1 = 0x1.555555555553ep-3;
77static const double p2 = -0x1.6c16c16bebd93p-9;
78static const double p3 = 0x1.1566aaf25de2cp-14;
79static const double p4 = -0x1.bbd41c5d26bf1p-20;
80static const double p5 = 0x1.6376972bea4d0p-25;
81static const double ln2hi = 0x1.62e42fee00000p-1;
82static const double ln2lo = 0x1.a39ef35793c76p-33;
83static const double lnhuge = 0x1.6602b15b7ecf2p9;
84static const double lntiny = -0x1.77af8ebeae354p9;
85static const double invln2 = 0x1.71547652b82fep0;
86
87
88/* returns exp(r = x + c) for |c| < |x| with no overlap. */
89
472de6d1
SW
90double
91__exp__D(double x, double c)
1a3b704c
JM
92{
93 double z,hi,lo;
94 int k;
95
96 if (x != x) /* x is NaN */
97 return(x);
98 if ( x <= lnhuge ) {
99 if ( x >= lntiny ) {
100
101 /* argument reduction : x --> x - k*ln2 */
102 z = invln2*x;
103 k = z + copysign(.5, x);
104
105 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
106
107 hi=(x-k*ln2hi); /* Exact. */
108 x= hi - (lo = k*ln2lo-c);
109 /* return 2^k*[1+x+x*c/(2+c)] */
110 z=x*x;
111 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
112 c = (x*c)/(2.0-c);
113
114 return scalb(1.+(hi-(lo - c)), k);
115 }
116 /* end of x > lntiny */
117
118 else
119 /* exp(-big#) underflows to zero */
120 if(finite(x)) return(scalb(1.0,-5000));
121
122 /* exp(-INF) is zero */
123 else return(0.0);
124 }
125 /* end of x < lnhuge */
126
127 else
128 /* exp(INF) is INF, exp(+big#) overflows to INF */
129 return( finite(x) ? scalb(1.0,5000) : x);
130}