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/***************************************************************************
* Copyright (c) 2019 Viktor Titov (DeepSOIC) <vv.titov@gmail.com> *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* This library 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 Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#ifndef FREECAD_BASE_DUAL_NUMBER_H
#define FREECAD_BASE_DUAL_NUMBER_H
#include <cmath>
// NOLINTBEGIN(readability-identifier-length)
namespace Base
{
/**
* @brief Dual Numbers are 2-part numbers like complex numbers, but different
* algebra. They are denoted as a + b*eps, where eps^2 = 0. eps, the nilpotent,
* is like imaginary unit of complex numbers. The neat utility of dual numbers
* is that if you use them instead of normal numbers in a function like sin(),
* derivative is implicitly calculated as a multiplier to the dual part.
*/
class DualNumber
{
public:
double re = 0.0;
double du = 0.0;
public:
DualNumber() = default;
DualNumber(double re, double du = 0.0) // NOLINT
: re(re)
, du(du)
{}
DualNumber operator-() const
{
return {-re, -du};
}
};
inline DualNumber operator+(DualNumber a, DualNumber b)
{
return {a.re + b.re, a.du + b.du};
}
inline DualNumber operator+(DualNumber a, double b)
{
return {a.re + b, a.du};
}
inline DualNumber operator+(double a, DualNumber b)
{
return {a + b.re, b.du};
}
inline DualNumber operator-(DualNumber a, DualNumber b)
{
return {a.re - b.re, a.du - b.du};
}
inline DualNumber operator-(DualNumber a, double b)
{
return {a.re - b, a.du};
}
inline DualNumber operator-(double a, DualNumber b)
{
return {a - b.re, -b.du};
}
inline DualNumber operator*(DualNumber a, DualNumber b)
{
return {a.re * b.re, a.re * b.du + a.du * b.re};
}
inline DualNumber operator*(double a, DualNumber b)
{
return {a * b.re, a * b.du};
}
inline DualNumber operator*(DualNumber a, double b)
{
return {a.re * b, a.du * b};
}
inline DualNumber operator/(DualNumber a, DualNumber b)
{
return {a.re / b.re, (a.du * b.re - a.re * b.du) / (b.re * b.re)};
}
inline DualNumber operator/(DualNumber a, double b)
{
return {a.re / b, a.du / b};
}
inline DualNumber pow(DualNumber a, double pw)
{
return {std::pow(a.re, pw), pw * std::pow(a.re, pw - 1.0) * a.du};
}
} // namespace Base
// NOLINTEND(readability-identifier-length)
#endif
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