math.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_MATH_HH
#define DUNE_MATH_HH

/** \file
 * \brief Some useful basic math stuff
 */

#include <cmath>
#include <complex>

namespace Dune
{

  /**
     \brief Provides commonly used mathematical constants.

     a struct that is specialized for types repesenting real or complex
     numbers. I provides commonly used mathematical constants with the
     required accuary for the specified type.
   */
  template< class Field >
  struct MathematicalConstants;

  /**
     \brief Standard implementation of MathematicalConstants.

     This implementation will work with all built-in floating point
     types. It provides

   * e as std::exp(1.0)
   * pi as std::acos(-1.0)

   */
  template< class T >
  struct StandardMathematicalConstants
  {
    static T e ()
    {
      static const T e = std::exp( T( 1 ) );
      return e;
    }

    static T pi ()
    {
      static const T pi = std::acos( T( -1 ) );
      return pi;
    }
  };


#ifndef DOXYGEN
  // MathematicalConstants for float
  // -------------------------------

  template<>
  struct MathematicalConstants< float >
    : public StandardMathematicalConstants< float >
  {};



  // MathematicalConstants for double
  // --------------------------------

  template<>
  struct MathematicalConstants< double >
    : public StandardMathematicalConstants< double >
  {};



  // MathematicalConstants for long double
  // -------------------------------------

  template<>
  struct MathematicalConstants< long double >
    : public StandardMathematicalConstants< long double >
  {};
#endif // DOXYGEN


  //! Calculates the factorial of m at compile time
  template <int m>
  struct Factorial
  {
    //! factorial stores m!
    enum { factorial = m * Factorial<m-1>::factorial };
  };

  //! end of recursion of factorial via specialization
  template <>
  struct Factorial<0>
  {
    // 0! = 1
    enum { factorial = 1 };
  };

  //! compute conjugate complex of x
  // conjugate complex does nothing for non-complex types
  template<class K>
  inline K conjugateComplex (const K& x)
  {
    return x;
  }

#ifndef DOXYGEN
  // specialization for complex
  template<class K>
  inline std::complex<K> conjugateComplex (const std::complex<K>& c)
  {
    return std::complex<K>(c.real(),-c.imag());
  }
#endif

  //! Return the sign of the value
  template <class T>
  int sign(const T& val)
  {
    return (val < 0 ? -1 : 1);
  }

}

#endif // #ifndef DUNE_MATH_HH