2 Contributed by Paolo Bonzini
4 Copyright 2002, 2003 Free Software Foundation, Inc.
6 This file is part of gnulib.
8 This program is free software; you can redistribute it and/or modify
9 it under the terms of the GNU General Public License as published by
10 the Free Software Foundation; either version 2, or (at your option)
13 This program is distributed in the hope that it will be useful,
14 but WITHOUT ANY WARRANTY; without even the implied warranty of
15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 GNU General Public License for more details.
18 You should have received a copy of the GNU General Public License along
19 with this program; if not, write to the Free Software Foundation,
20 Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
27 static const long double C[] = {
28 /* Chebyshev polynom coeficients for (exp(x)-1)/x */
36 1.66666666666666666666666666666666683E-01L,
37 4.16666666666666666666654902320001674E-02L,
38 8.33333333333333333333314659767198461E-03L,
39 1.38888888889899438565058018857254025E-03L,
40 1.98412698413981650382436541785404286E-04L,
42 /* Smallest integer x for which e^x overflows. */
44 11356.523406294143949491931077970765L,
46 /* Largest integer x for which e^x underflows. */
48 -11433.4627433362978788372438434526231L,
50 /* very small number */
56 5.94865747678615882542879663314003565E+4931L};
61 /* Check for usual case. */
62 if (x < himark && x > lomark)
67 long double result = 1.0;
69 /* Compute an integer power of e with a granularity of 0.125. */
70 exponent = (int) floorl (x * 8.0L);
81 t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
85 t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
98 /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
99 with maximum error in [-2^-16-2^-53,2^-16+2^-53]
100 less than 4.8e-39. */
101 x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
103 return result + result * x22;
105 /* Exceptional cases: */
109 /* e^-inf == 0, with no error. */
116 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
124 printf ("%.16Lg\n", expl(1.0L));
125 printf ("%.16Lg\n", expl(-1.0L));
126 printf ("%.16Lg\n", expl(2.0L));
127 printf ("%.16Lg\n", expl(4.0L));
128 printf ("%.16Lg\n", expl(-2.0L));
129 printf ("%.16Lg\n", expl(-4.0L));
130 printf ("%.16Lg\n", expl(0.0625L));
131 printf ("%.16Lg\n", expl(0.3L));
132 printf ("%.16Lg\n", expl(0.6L));