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/************************************************************************
* lib/math/lib_exp.c
*
* This file is a part of NuttX:
*
* Copyright (C) 2012 Gregory Nutt. All rights reserved.
* Ported by: Darcy Gong
*
* It derives from the Rhombs OS math library by Nick Johnson which has
* a compatibile, MIT-style license:
*
* Copyright (C) 2009-2011 Nick Johnson <nickbjohnson4224 at gmail.com>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*
************************************************************************/
/************************************************************************
* Included Files
************************************************************************/
#include <nuttx/config.h>
#include <nuttx/compiler.h>
#include <sys/types.h>
#include <math.h>
#include "lib_internal.h"
#ifdef CONFIG_HAVE_DOUBLE
/************************************************************************
* Private Data
************************************************************************/
static double _dbl_inv_fact[] =
{
1.0 / 1.0, // 1 / 0!
1.0 / 1.0, // 1 / 1!
1.0 / 2.0, // 1 / 2!
1.0 / 6.0, // 1 / 3!
1.0 / 24.0, // 1 / 4!
1.0 / 120.0, // 1 / 5!
1.0 / 720.0, // 1 / 6!
1.0 / 5040.0, // 1 / 7!
1.0 / 40320.0, // 1 / 8!
1.0 / 362880.0, // 1 / 9!
1.0 / 3628800.0, // 1 / 10!
1.0 / 39916800.0, // 1 / 11!
1.0 / 479001600.0, // 1 / 12!
1.0 / 6227020800.0, // 1 / 13!
1.0 / 87178291200.0, // 1 / 14!
1.0 / 1307674368000.0, // 1 / 15!
1.0 / 20922789888000.0, // 1 / 16!
1.0 / 355687428096000.0, // 1 / 17!
1.0 / 6402373705728000.0, // 1 / 18!
};
/************************************************************************
* Public Functions
************************************************************************/
double exp(double x)
{
size_t int_part;
bool invert;
double value;
double x0;
size_t i;
if (x == 0)
{
return 1;
}
else if (x < 0)
{
invert = true;
x = -x;
}
else
{
invert = false;
}
/* Extract integer component */
int_part = (size_t) x;
/* Set x to fractional component */
x -= (double)int_part;
/* Perform Taylor series approximation with nineteen terms */
value = 0.0;
x0 = 1.0;
for (i = 0; i < 19; i++)
{
value += x0 * _dbl_inv_fact[i];
x0 *= x;
}
/* Multiply by exp of the integer component */
value *= lib_expi(int_part);
if (invert)
{
return (1.0 / value);
}
else
{
return value;
}
}
#endif
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