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// 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 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 precision() { 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 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())
{
EI_UNUSED(b);
EI_UNUSED(prec);
return a == 0;
}
static bool isApprox(const int& a, const int& b, const int& prec = precision())
{
EI_UNUSED(prec);
return a == b;
}
static bool isApproxOrLessThan(const int& a, const int& b, const int& prec = precision())
{
EI_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) { 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 random()
{
return std::rand() / (RAND_MAX/20.0f) - 10.0f;
}
static bool isMuchSmallerThan(const float& a, const float& b, const float& prec = precision())
{
return abs(a) <= abs(b) * prec;
}
static bool isApprox(const float& a, const float& b, const float& prec = precision())
{
return abs(a - b) <= std::min(abs(a), 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) { 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 random()
{
return std::rand() / (RAND_MAX/20.0) - 10.0;
}
static bool isMuchSmallerThan(const double& a, const double& b, const double& prec = precision())
{
return abs(a) <= abs(b) * prec;
}
static bool isApprox(const double& a, const double& b, const double& prec = precision())
{
return abs(a - b) <= std::min(abs(a), 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 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 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 // EI_NUMERIC_H
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