mirror of
https://https.git.savannah.gnu.org/git/gnulib.git
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Bruno Haible
137 lines
3.3 KiB
C
137 lines
3.3 KiB
C
/* Emulation for expl.
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Contributed by Paolo Bonzini
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Copyright 2002, 2003, 2007 Free Software Foundation, Inc.
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This file is part of gnulib.
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation,
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Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
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#include <config.h>
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/* Specification. */
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#include <math.h>
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#include <float.h>
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static const long double C[] = {
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/* Chebyshev polynom coeficients for (exp(x)-1)/x */
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#define P1 C[0]
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#define P2 C[1]
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#define P3 C[2]
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#define P4 C[3]
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#define P5 C[4]
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#define P6 C[5]
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0.5L,
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1.66666666666666666666666666666666683E-01L,
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4.16666666666666666666654902320001674E-02L,
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8.33333333333333333333314659767198461E-03L,
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1.38888888889899438565058018857254025E-03L,
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1.98412698413981650382436541785404286E-04L,
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/* Smallest integer x for which e^x overflows. */
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#define himark C[6]
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11356.523406294143949491931077970765L,
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/* Largest integer x for which e^x underflows. */
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#define lomark C[7]
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-11433.4627433362978788372438434526231L,
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/* very small number */
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#define TINY C[8]
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1.0e-4900L,
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/* 2^16383 */
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#define TWO16383 C[9]
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5.94865747678615882542879663314003565E+4931L};
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long double
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expl (long double x)
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{
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/* Check for usual case. */
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if (x < himark && x > lomark)
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{
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int exponent;
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long double t, x22;
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int k = 1;
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long double result = 1.0;
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/* Compute an integer power of e with a granularity of 0.125. */
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exponent = (int) floorl (x * 8.0L);
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x -= exponent / 8.0L;
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if (x > 0.0625)
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{
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exponent++;
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x -= 0.125L;
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}
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if (exponent < 0)
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{
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t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
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exponent = -exponent;
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}
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else
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t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
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while (exponent)
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{
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if (exponent & k)
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{
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result *= t;
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exponent ^= k;
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}
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t *= t;
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k <<= 1;
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}
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/* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
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with maximum error in [-2^-16-2^-53,2^-16+2^-53]
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less than 4.8e-39. */
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x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
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return result + result * x22;
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}
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/* Exceptional cases: */
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else if (x < himark)
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{
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if (x + x == x)
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/* e^-inf == 0, with no error. */
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return 0;
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else
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/* Underflow */
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return TINY * TINY;
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}
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else
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/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
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return TWO16383*x;
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}
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#if 0
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int
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main (void)
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{
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printf ("%.16Lg\n", expl(1.0L));
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printf ("%.16Lg\n", expl(-1.0L));
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printf ("%.16Lg\n", expl(2.0L));
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printf ("%.16Lg\n", expl(4.0L));
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printf ("%.16Lg\n", expl(-2.0L));
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printf ("%.16Lg\n", expl(-4.0L));
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printf ("%.16Lg\n", expl(0.0625L));
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printf ("%.16Lg\n", expl(0.3L));
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printf ("%.16Lg\n", expl(0.6L));
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}
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#endif
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