sinc.c

/*
 * Copyright (c) 2002, 2012 Jens Keiner, Stefan Kunis, Daniel Potts
 *
 * 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 2 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, write to the Free Software Foundation, Inc., 51
 * Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

/* $Id: util.c 3483 2010-04-23 19:02:34Z keiner $ */

#include "infft.h"

R X(sinc)(const R x)
{
  /* Based on sinc function from Boost C++ library. */
  const R b =  EPSILON;
  const R bs = SQRT(b);
  const R bs2 = SQRT(bs);

  if (FABS(x) >= bs2)
    return SIN(x)/x;
  else
  {
    R r = K(1.0);

    if (FABS(x) >= b)
    {
      const R x2 = x * x;
      r -= x2 / K(6.0);

      if (FABS(x) >= bs)
        r += (x2 * x2) / K(120.0);
    }

    return r;
  }
}