STK_Const_Math.cpp

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/*--------------------------------------------------------------------*/
/*     Copyright (C) 2004-2007  Serge Iovleff

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU Lesser 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 Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with this program; if not, write to the
    Free Software Foundation, Inc.,
    59 Temple Place,
    Suite 330,
    Boston, MA 02111-1307
    USA

    Contact : Serge.Iovleff@stkpp.org
*/

/*
 * Project:  Analysis
 * Purpose:  implementation of the class Const
 * Author:   Serge Iovleff, serge.iovleff@stkpp.org
 **/

#include "../../STKernel/include/STK_Integer.h"
#include "../../STKernel/include/STK_Real.h"
#include "../include/STK_Const_Math.h"
#include "../include/STK_ISerie.h"
#include "../include/STK_Algo.h"

namespace STK
{

namespace Const
{

class SeriePi : public ISerie<SeriePi>
{
  private:
    mutable Real dig16_;
    mutable Integer k4_;

  public:
    inline SeriePi() : dig16_(1.), k4_(0)
    { ;}

    inline Real first() const
    { return 47./15.;}
 
    inline Real next() const
    { 
      dig16_ /= 16.;
      k4_    += 4;
     
      return  dig16_
            * ( 2.0/(k4_+0.5)
              - 1.0/(k4_+2.0)
              - 0.5/(k4_+2.5)
              - 0.5/(k4_+3.0)
              );
    }
 
    inline Real operator[](Integer k) const
    { Integer aux = 4*k;
      return  pow(2, -aux)
            * ( 2.0/(aux+0.5)
              - 1.0/(aux+2.0)
              - 0.5/(aux+2.5)
              - 0.5/(aux+3.0)
              );
  }
};

Real pi()
{
  SeriePi f;
  return sumSerie<SeriePi>(f);
}

class SerieEuler : public ISerie<SerieEuler>
{
  private:
    mutable Real k_;

  public:
    inline SerieEuler() : k_(2.)
    { ;}

    inline Real first() const
    { return (Const::_LN2_/2.);}
 
    inline Real next() const
    { 
      k_    += 1.;
      return  log(k_)/k_;
    }
 
    inline Real operator[](Integer k) const
    { return log(k + 2.)/(Real)(k + 2);}
};

Real euler()
{
  SerieEuler f;
  return Const::_LN2_/2.0 + sumAlternateSerie<SerieEuler>(f)/Const::_LN2_;
}

} // namespace CONST

} // namespace STK