2 Contributed by Paolo Bonzini
4 Copyright 2002-2003, 2007, 2009-2012 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 3 of the License, or
11 (at your option) any later version.
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
19 along with this program. If not, see <http://www.gnu.org/licenses/>. */
26 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
36 /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_expl.c. */
40 static const long double C[] = {
41 /* Chebyshev polynomial coefficients for (exp(x)-1)/x */
49 1.66666666666666666666666666666666683E-01L,
50 4.16666666666666666666654902320001674E-02L,
51 8.33333333333333333333314659767198461E-03L,
52 1.38888888889899438565058018857254025E-03L,
53 1.98412698413981650382436541785404286E-04L,
55 /* Smallest integer x for which e^x overflows. */
57 11356.523406294143949491931077970765L,
59 /* Largest integer x for which e^x underflows. */
61 -11433.4627433362978788372438434526231L,
63 /* very small number */
68 # define TWO16383 C[9]
69 5.94865747678615882542879663314003565E+4931L};
74 /* Check for usual case. */
75 if (x < himark && x > lomark)
80 long double result = 1.0;
82 /* Compute an integer power of e with a granularity of 0.125. */
83 exponent = (int) floorl (x * 8.0L);
94 t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
98 t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
111 /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
112 with maximum error in [-2^-16-2^-53,2^-16+2^-53]
113 less than 4.8e-39. */
114 x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
116 return result + result * x22;
118 /* Exceptional cases: */
122 /* e^-inf == 0, with no error. */
129 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
139 printf ("%.16Lg\n", expl (1.0L));
140 printf ("%.16Lg\n", expl (-1.0L));
141 printf ("%.16Lg\n", expl (2.0L));
142 printf ("%.16Lg\n", expl (4.0L));
143 printf ("%.16Lg\n", expl (-2.0L));
144 printf ("%.16Lg\n", expl (-4.0L));
145 printf ("%.16Lg\n", expl (0.0625L));
146 printf ("%.16Lg\n", expl (0.3L));
147 printf ("%.16Lg\n", expl (0.6L));