// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen 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 or (at your option) any later version.
//
// Eigen 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 Eigen; if not, write to the Free Software Foundation, Inc., 51
// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. This exception does not invalidate any other reasons why a work
// based on this file might be covered by the GNU General Public License.

#ifndef EIGEN_NUMERIC_H
#define EIGEN_NUMERIC_H

template<typename T> struct NumTraits;

template<> struct NumTraits<int>
{
  typedef int Real;
  typedef double FloatingPoint;
  typedef double RealFloatingPoint;
  
  static const bool IsComplex = false;
  static const bool HasFloatingPoint = false;
  
  static int precision() { return 0; }
  static int real(const int& x) { return x; }
  static int imag(const int& x) { EIGEN_UNUSED(x); return 0; }
  static int conj(const int& x) { return x; }
  static int abs2(const int& x) { return x*x; }
  static int random()
  {
    // "random() % n" is bad, they say, because the low-order bits are not random enough.
    // However here, 21 is odd, so random() % 21 uses the high-order bits
    // as well, so there's no problem.
    return (std::rand() % 21) - 10;
  }
  static bool isMuchSmallerThan(const int& a, const int& b, const int& prec = precision())
  {
    EIGEN_UNUSED(b);
    EIGEN_UNUSED(prec);
    return a == 0;
  }
  static bool isApprox(const int& a, const int& b, const int& prec = precision())
  {
    EIGEN_UNUSED(prec);
    return a == b;
  }
  static bool isApproxOrLessThan(const int& a, const int& b, const int& prec = precision())
  {
    EIGEN_UNUSED(prec);
    return a <= b;
  }
};

template<> struct NumTraits<float>
{
  typedef float Real;
  typedef float FloatingPoint;
  typedef float RealFloatingPoint;
  
  static const bool IsComplex = false;
  static const bool HasFloatingPoint = true;
  
  static float precision() { return 1e-5f; }
  static float real(const float& x) { return x; }
  static float imag(const float& x) { EIGEN_UNUSED(x); return 0; }
  static float conj(const float& x) { return x; }
  static float abs2(const float& x) { return x*x; }
  static float random()
  {
    return std::rand() / (RAND_MAX/20.0f) - 10.0f;
  }
  static bool isMuchSmallerThan(const float& a, const float& b, const float& prec = precision())
  {
    return std::abs(a) <= std::abs(b) * prec;
  }
  static bool isApprox(const float& a, const float& b, const float& prec = precision())
  {
    return std::abs(a - b) <= std::min(std::abs(a), std::abs(b)) * prec;
  }
  static bool isApproxOrLessThan(const float& a, const float& b, const float& prec = precision())
  {
    return a <= b || isApprox(a, b, prec);
  }
};

template<> struct NumTraits<double>
{
  typedef double Real;
  typedef double FloatingPoint;
  typedef double RealFloatingPoint;
  
  static const bool IsComplex = false;
  static const bool HasFloatingPoint = true;
  
  static double precision() { return 1e-11; }
  static double real(const double& x) { return x; }
  static double imag(const double& x) { EIGEN_UNUSED(x); return 0; }
  static double conj(const double& x) { return x; }
  static double abs2(const double& x) { return x*x; }
  static double random()
  {
    return std::rand() / (RAND_MAX/20.0) - 10.0;
  }
  static bool isMuchSmallerThan(const double& a, const double& b, const double& prec = precision())
  {
    return std::abs(a) <= std::abs(b) * prec;
  }
  static bool isApprox(const double& a, const double& b, const double& prec = precision())
  {
    return std::abs(a - b) <= std::min(std::abs(a), std::abs(b)) * prec;
  }
  static bool isApproxOrLessThan(const double& a, const double& b, const double& prec = precision())
  {
    return a <= b || isApprox(a, b, prec);
  }
};

template<typename _Real> struct NumTraits<std::complex<_Real> >
{
  typedef _Real Real;
  typedef std::complex<Real> Complex;
  typedef std::complex<double> FloatingPoint;
  typedef typename NumTraits<Real>::FloatingPoint RealFloatingPoint;
  
  static const bool IsComplex = true;
  static const bool HasFloatingPoint = NumTraits<Real>::HasFloatingPoint;
  
  static Real precision() { return NumTraits<Real>::precision(); }
  static Real real(const Complex& x) { return std::real(x); }
  static Real imag(const Complex& x) { return std::imag(x); }
  static Complex conj(const Complex& x) { return std::conj(x); }
  static Real abs2(const Complex& x)
  { return std::norm(x); }
  static Complex random()
  {
    return Complex(NumTraits<Real>::random(), NumTraits<Real>::random());
  }
  static bool isMuchSmallerThan(const Complex& a, const Complex& b, const Real& prec = precision())
  {
    return abs2(a) <= abs2(b) * prec * prec;
  }
  static bool isApprox(const Complex& a, const Complex& b, const Real& prec = precision())
  {
    return NumTraits<Real>::isApprox(std::real(a), std::real(b), prec)
        && NumTraits<Real>::isApprox(std::imag(a), std::imag(b), prec);
  }
  // isApproxOrLessThan wouldn't make sense for complex numbers
};

#endif // EIGEN_NUMERIC_H