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/* Emulation for expl.
Contributed by Paolo Bonzini
Copyright 2002, 2003, 2007, 2009 Free Software Foundation, Inc.
This file is part of gnulib.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>. */
#include <config.h>
/* Specification. */
#include <math.h>
#include <float.h>
static const long double C[] = {
/* Chebyshev polynom coeficients for (exp(x)-1)/x */
#define P1 C[0]
#define P2 C[1]
#define P3 C[2]
#define P4 C[3]
#define P5 C[4]
#define P6 C[5]
0.5L,
1.66666666666666666666666666666666683E-01L,
4.16666666666666666666654902320001674E-02L,
8.33333333333333333333314659767198461E-03L,
1.38888888889899438565058018857254025E-03L,
1.98412698413981650382436541785404286E-04L,
/* Smallest integer x for which e^x overflows. */
#define himark C[6]
11356.523406294143949491931077970765L,
/* Largest integer x for which e^x underflows. */
#define lomark C[7]
-11433.4627433362978788372438434526231L,
/* very small number */
#define TINY C[8]
1.0e-4900L,
/* 2^16383 */
#define TWO16383 C[9]
5.94865747678615882542879663314003565E+4931L};
long double
expl (long double x)
{
/* Check for usual case. */
if (x < himark && x > lomark)
{
int exponent;
long double t, x22;
int k = 1;
long double result = 1.0;
/* Compute an integer power of e with a granularity of 0.125. */
exponent = (int) floorl (x * 8.0L);
x -= exponent / 8.0L;
if (x > 0.0625)
{
exponent++;
x -= 0.125L;
}
if (exponent < 0)
{
t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
exponent = -exponent;
}
else
t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
while (exponent)
{
if (exponent & k)
{
result *= t;
exponent ^= k;
}
t *= t;
k <<= 1;
}
/* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
with maximum error in [-2^-16-2^-53,2^-16+2^-53]
less than 4.8e-39. */
x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
return result + result * x22;
}
/* Exceptional cases: */
else if (x < himark)
{
if (x + x == x)
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TINY * TINY;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO16383*x;
}
#if 0
int
main (void)
{
printf ("%.16Lg\n", expl(1.0L));
printf ("%.16Lg\n", expl(-1.0L));
printf ("%.16Lg\n", expl(2.0L));
printf ("%.16Lg\n", expl(4.0L));
printf ("%.16Lg\n", expl(-2.0L));
printf ("%.16Lg\n", expl(-4.0L));
printf ("%.16Lg\n", expl(0.0625L));
printf ("%.16Lg\n", expl(0.3L));
printf ("%.16Lg\n", expl(0.6L));
}
#endif
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