px4-firmware/nuttx/libc/math/lib_expl.c

/************************************************************************
 * libc/math/lib_expl.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_LONG_DOUBLE

/************************************************************************
 * Private Data
 ************************************************************************/

static long double _ldbl_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
 ************************************************************************/

long double expl(long double x)
{
  size_t int_part;
  bool invert;
  long double value;
  long 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 -= (long double)int_part;

  /* Perform Taylor series approximation with nineteen terms */

  value = 0.0;
  x0 = 1.0;
  for (i = 0; i < 19; i++)
    {
      value += x0 * _ldbl_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