2 Contributed by Paolo Bonzini
4 Copyright 2002, 2003 Free Software Foundation, Inc.
6 This file is part of gnulib.
8 gnulib is free software; you can redistribute it and/or modify it
9 under the terms of the GNU Lesser General Public License as published
10 by the Free Software Foundation; either version 2.1, or (at your option)
13 gnulib is distributed in the hope that it will be useful, but WITHOUT
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
18 You should have received a copy of the GNU Lesser General Public License
19 along with gnulib; see the file COPYING.LIB. If not, write to the Free
20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
29 static const long double C[] = {
30 /* Chebyshev polynom coeficients for (exp(x)-1)/x */
38 1.66666666666666666666666666666666683E-01L,
39 4.16666666666666666666654902320001674E-02L,
40 8.33333333333333333333314659767198461E-03L,
41 1.38888888889899438565058018857254025E-03L,
42 1.98412698413981650382436541785404286E-04L,
44 /* Smallest integer x for which e^x overflows. */
46 11356.523406294143949491931077970765L,
48 /* Largest integer x for which e^x underflows. */
50 -11433.4627433362978788372438434526231L,
52 /* very small number */
58 5.94865747678615882542879663314003565E+4931L};
63 /* Check for usual case. */
64 if (x < himark && x > lomark)
69 long double result = 1.0;
71 /* Compute an integer power of e with a granularity of 0.125. */
72 exponent = (int) floorl (x * 8.0L);
83 t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
87 t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
100 /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
101 with maximum error in [-2^-16-2^-53,2^-16+2^-53]
102 less than 4.8e-39. */
103 x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
105 return result + result * x22;
107 /* Exceptional cases: */
111 /* e^-inf == 0, with no error. */
118 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
126 printf ("%.16Lg\n", expl(1.0L));
127 printf ("%.16Lg\n", expl(-1.0L));
128 printf ("%.16Lg\n", expl(2.0L));
129 printf ("%.16Lg\n", expl(4.0L));
130 printf ("%.16Lg\n", expl(-2.0L));
131 printf ("%.16Lg\n", expl(-4.0L));
132 printf ("%.16Lg\n", expl(0.0625L));
133 printf ("%.16Lg\n", expl(0.3L));
134 printf ("%.16Lg\n", expl(0.6L));