numerics.h

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/*
 *  numerics.h
 *
 *  This file is part of NEST.
 *
 *  Copyright (C) 2004 The NEST Initiative
 *
 *  NEST 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.
 *
 *  NEST 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 NEST.  If not, see <http://www.gnu.org/licenses/>.
 *
 */

#ifndef NUMERICS_H
#define NUMERICS_H

#include <limits>
#include <cmath>

#if HAVE_EXPM1
#  include <math.h>
#endif

namespace numerics {

  extern  const double e;
  extern  const double pi;

  inline
  double expm1(double x)
  { 
#if HAVE_EXPM1
    return ::expm1(x);  // use library implementation if available
#else
    // compute using Taylor series, see GSL
    // e^x-1 = x + x^2/2! + x^3/3! + ...
    if ( x == 0 )
      return 0;
    if ( std::abs(x) > std::log(2.0) )
      return std::exp(x) - 1;
    else
    {
      double sum = x;
      double term = x*x/2;
      long n = 2;
      
      while ( std::abs(term) > 
          std::abs(sum) * std::numeric_limits<double>::epsilon() )
      {
    sum += term;
    ++n;
    term *= x/n; 
      }

      return sum;
    }
#endif
  }

}


// later also in namespace
long   ld_round(double);

double dround(double);

double dtruncate(double);


# endif