/*
  Implementation of Lambert W function

  Copyright (C) 2009 Darko Veberic, darko.veberic@ung.si

  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 3 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, see <http://www.gnu.org/licenses/>.
*/

#ifndef _LambertW_h_
#define _LambertW_h_

#include <limits>


/**
  \author Darko Veberic
  \version $Id: LambertW.h 14958 2009-10-19 11:11:19Z darko $
  \date 25 Jun 2009
*/


/** Approximate Lambert W function
  Accuracy at least 5 decimal places in all definition range.
  See LambertW() for details.

  \param branch: valid values are 0 and -1
  \param x: real-valued argument \f$\geq-1/e\f$
  \ingroup math
*/

template<int branch>
double LambertWApproximation(const double x);


/** Lambert W function
  \image html LambertW.png

  Lambert function \f$y={\rm W}(x)\f$ is defined as a solution
  to the \f$x=ye^y\f$ expression and is also known as
  "product logarithm". Since the inverse of \f$ye^y\f$ is not
  single-valued, the Lambert function has two real branches
  \f${\rm W}_0\f$ and \f${\rm W}_{-1}\f$.

  \f${\rm W}_0(x)\f$ has real values in the interval
  \f$[-1/e,\infty]\f$ and \f${\rm W}_{-1}(x)\f$ has real values
  in the interval \f$[-1/e,0]\f$.
  Accuracy is the nominal double type resolution
  (16 decimal places).

  \param branch: valid values are 0 and -1
  \param x: real-valued argument \f$\geq-1/e\f$ (range depends on branch)
  \ingroup math
*/

template<int branch>
double LambertW(const double x);


inline
double
LambertW(const int branch, const double x)
{
  switch (branch) {
  case -1: return LambertW<-1>(x);
  case  0: return LambertW<0>(x);
  default: return std::numeric_limits<double>::quiet_NaN();
  }
}


#endif