eigen/src/Core/Numeric.h

// This file is part of gen, a lightweight C++ template library
// for linear algebra. gen itself is part of the KDE project.
//
// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
//
// gen 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.
//
// gen 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 gen; 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 EI_NUMERIC_H
#define EI_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 epsilon() { return 0; }
  static int real(const int& x) { return x; }
  static int imag(const int& x) { EI_UNUSED(x); return 0; }
  static int conj(const int& x) { return x; }
  static double sqrt(const int& x) { return std::sqrt(static_cast<double>(x)); }
  static int abs(const int& x) { return std::abs(x); }
  static int abs2(const int& x) { return x*x; }
  static int rand()
  {
    // "rand()%21" would be bad. always use the high-order bits, not the low-order bits.
    // note: here (gcc 4.1) static_cast<int> seems to round the nearest int.
    // I don't know if that's part of the standard.
    return -10 + static_cast<int>(std::rand() / ((RAND_MAX + 1.0)/20.0));
  }
};

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 epsilon() { return 1e-5f; }
  static float real(const float& x) { return x; }
  static float imag(const float& x) { EI_UNUSED(x); return 0; }
  static float conj(const float& x) { return x; }
  static float sqrt(const float& x) { return std::sqrt(x); }
  static float abs(const float& x) { return std::abs(x); }
  static float abs2(const float& x) { return x*x; }
  static float rand()
  {
    return std::rand() / (RAND_MAX/20.0f) - 10.0f;
  }
};

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 epsilon() { return 1e-11; }
  static double real(const double& x) { return x; }
  static double imag(const double& x) { EI_UNUSED(x); return 0; }
  static double conj(const double& x) { return x; }
  static double sqrt(const double& x) { return std::sqrt(x); }
  static double abs(const double& x) { return std::abs(x); }
  static double abs2(const double& x) { return x*x; }
  static double rand()
  {
    return std::rand() / (RAND_MAX/20.0) - 10.0;
  }
};

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 epsilon() { return NumTraits<Real>::epsilon(); }
  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 FloatingPoint sqrt(const Complex& x)
  { return std::sqrt(static_cast<FloatingPoint>(x)); }
  static RealFloatingPoint abs(const Complex& x)
  { return std::abs(static_cast<FloatingPoint>(x)); }
  static Real abs2(const Complex& x)
  { return std::real(x) * std::real(x) + std::imag(x) * std::imag(x); }
  static Complex rand()
  {
    return Complex(NumTraits<Real>::rand(), NumTraits<Real>::rand());
  }
};

template<typename T> typename NumTraits<T>::Real Real(const T& x)
{ return NumTraits<T>::real(x); }

template<typename T> typename NumTraits<T>::Real Imag(const T& x)
{ return NumTraits<T>::imag(x); }

template<typename T> T Conj(const T& x)
{ return NumTraits<T>::conj(x); }

template<typename T> typename NumTraits<T>::FloatingPoint Sqrt(const T& x)
{ return NumTraits<T>::sqrt(x); }

template<typename T> typename NumTraits<T>::RealFloatingPoint Abs(const T& x)
{ return NumTraits<T>::abs(x); }

template<typename T> typename NumTraits<T>::Real Abs2(const T& x)
{ return NumTraits<T>::abs2(x); }

template<typename T> T Rand()
{ return NumTraits<T>::rand(); }

template<typename T> bool Negligible(const T& a, const T& b)
{
  return(Abs(a) <= Abs(b) * NumTraits<T>::epsilon());
}

template<typename T> bool Approx(const T& a, const T& b)
{
  if(NumTraits<T>::IsFloat)
    return(Abs(a - b) <= std::min(Abs(a), Abs(b)) * NumTraits<T>::epsilon());
  else
    return(a == b);
}

template<typename T> bool LessThanOrApprox(const T& a, const T& b)
{
  if(NumTraits<T>::IsFloat)
    return(a < b || Approx(a, b));
  else
    return(a <= b);
}

#endif // EI_NUMERIC_H