numeric.h

/* ********************************************************************
    itom software
    URL: http://www.uni-stuttgart.de/ito
    Copyright (C) 2020, Institut für Technische Optik (ITO),
    Universität Stuttgart, Germany
 
    This file is part of itom and its software development toolkit (SDK).
 
    itom is free software; you can redistribute it and/or modify it
    under the terms of the GNU Library General Public Licence as published by
    the Free Software Foundation; either version 2 of the Licence, or (at
    your option) any later version.
 
    In addition, as a special exception, the Institut für Technische
    Optik (ITO) gives you certain additional rights.
    These rights are described in the ITO LGPL Exception version 1.0,
    which can be found in the file LGPL_EXCEPTION.txt in this package.
 
    itom 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 Licence for more details.
 
    You should have received a copy of the GNU Library General Public License
    along with itom. If not, see <http://www.gnu.org/licenses/>.
*********************************************************************** */
 
#ifndef NUMERIC_H
#define NUMERIC_H
 
#include "typeDefs.h"
#include "color.h"
#include <limits>
 
namespace ito
{
 
    template<typename _Tp> inline bool isNotZero(_Tp value)
    {
        return !(value == 0);
    }
 
    template<> inline bool isNotZero<float32>(float32 value)
    {
        if (fabs(value) < std::numeric_limits<float32>::epsilon())
            return false;
        else
            return true;
    }
 
    template<> inline bool isNotZero<float64>(float64 value)
    {
        if (fabs(value) < std::numeric_limits<float64>::epsilon())
            return false;
        else
            return true;
    }
 
    template<> inline bool isNotZero<complex64>(complex64 value)
    {
        if (fabs(value.real()) < std::numeric_limits<float32>::epsilon() &&
            fabs(value.imag()) < std::numeric_limits<float32>::epsilon())
            return false;
        else
            return true;
    }
 
    template<> inline bool isNotZero<complex128>(complex128 value)
    {
        if (fabs(value.real()) < std::numeric_limits<float64>::epsilon() &&
            fabs(value.imag()) < std::numeric_limits<float64>::epsilon())
            return false;
        else
            return true;
    }
 
 
 
    template<typename _Tp> inline bool isFinite(_Tp /*value*/)
    {
        return true;
    }
 
    template<> inline bool isFinite<float32>(float32 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[3] & 0x7f) != 0x7f || (ch[2] & 0x80) != 0x80;
    }
 
    template<> inline bool isFinite<float64>(float64 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[7] & 0x7f) != 0x7f || (ch[6] & 0xf0) != 0xf0;
    }
 
    template<> inline bool isFinite<complex64>(complex64 value)
    {
        float32 realVal = value.real();
        float32 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[3] & 0x7f) != 0x7f || (chreal[2] & 0x80) != 0x80) && ((chimag[3] & 0x7f) != 0x7f || (chimag[2] & 0x80) != 0x80);
    }
 
    template<> inline bool isFinite<complex128>(complex128 value)
    {
        float64 realVal = value.real();
        float64 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[7] & 0x7f) != 0x7f || (chreal[6] & 0xf0) != 0xf0) && ((chimag[7] & 0x7f) != 0x7f || (chimag[6] & 0xf0) != 0xf0);
    }
 
 
    template<typename _Tp> inline bool isNaN(_Tp value)
    {
        return false;
    }
 
    template<> inline bool isNaN<float32>(float32 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[3] & 0x7f) == 0x7f && ch[2] > 0x80;
    }
    template<> inline bool isNaN<float64>(float64 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[7] & 0x7f) == 0x7f && ch[6] > 0xf0;
    }
 
    template<> inline bool isNaN<complex64>(complex64 value)
    {
        float32 realVal = value.real();
        float32 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[3] & 0x7f) == 0x7f && chreal[2] > 0x80) || ((chimag[3] & 0x7f) == 0x7f && chimag[2] > 0x80);
    }
 
    template<> inline bool isNaN<complex128>(complex128 value)
    {
        float64 realVal = value.real();
        float64 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[7] & 0x7f) == 0x7f && chreal[6] > 0xf0) || ((chimag[7] & 0x7f) == 0x7f && chimag[6] > 0xf0);
    }
 
 
    template<typename _Tp> inline bool isInf(_Tp /*value*/)
    {
        return false;
    }
 
    template<> inline bool isInf<float32>(float32 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[3] & 0x7f) == 0x7f && ch[2] == 0x80;
    }
 
    template<> inline bool isInf<float64>(float64 value)
    {
        unsigned char *ch = (unsigned char *)&value;
        return (ch[7] & 0x7f) == 0x7f && ch[6] == 0xf0;
    }
 
    template<> inline bool isInf<complex64>(complex64 value)
    {
        float32 realVal = value.real();
        float32 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[3] & 0x7f) == 0x7f && chreal[2] == 0x80) || ((chimag[3] & 0x7f) == 0x7f && chimag[2] == 0x80);
    }
 
    template<> inline bool isInf<complex128>(complex128 value)
    {
        float64 realVal = value.real();
        float64 imagVal = value.imag();
        unsigned char *chreal = (unsigned char *)&realVal;
        unsigned char *chimag = (unsigned char *)&imagVal;
        return ((chreal[7] & 0x7f) == 0x7f && chreal[6] == 0xf0) || ((chimag[7] & 0x7f) == 0x7f && chimag[6] == 0xf0);
    }
 
 
        template<typename _Tp> inline bool isZeroValue(_Tp v, _Tp /*epsilon*/)
        {
                return v == 0;
        }
 
        template<> inline bool isZeroValue(Rgba32 v, Rgba32 /*epsilon*/)
        {
                return v == Rgba32::zeros();
        }
 
        template<> inline bool isZeroValue(float32 v, float32 epsilon)
        {
                return v >= epsilon ? false : (v <= -epsilon ? false : true);
        }
 
        template<> inline bool isZeroValue(float64 v, float64 epsilon)
        {
                return v >= epsilon ? false : (v <= -epsilon ? false : true);
        }
 
        template<> inline bool isZeroValue(std::complex<ito::float32> v, std::complex<ito::float32> epsilon)
        {
                return isZeroValue<ito::float32>(v.real(), epsilon.real()) && isZeroValue<ito::float32>(v.imag(), epsilon.real());
        }
 
        template<> inline bool isZeroValue(std::complex<ito::float64> v, std::complex<ito::float64> epsilon)
        {
                return isZeroValue<ito::float64>(v.real(), epsilon.real()) && isZeroValue<ito::float64>(v.imag(), epsilon.real());
        }
 
 
 
    template<typename _Tp> inline bool areEqual(_Tp a, _Tp b)
    {
        //for fixed-point and Rgba32 data types
        return a == b;
    }
 
    template<> inline bool areEqual(float32 a, float32 b)
    {
        return fabs(a - b) < std::numeric_limits<float32>::epsilon();
    }
 
    template<> inline bool areEqual(float64 a, float64 b)
    {
        return fabs(a - b) < std::numeric_limits<float64>::epsilon();
    }
 
    template<> inline bool areEqual(complex64 a, complex64 b)
    {
        return areEqual<ito::float32>(a.real(), b.real()) && areEqual<ito::float32>(a.imag(), b.imag());
    }
 
    template<> inline bool areEqual(complex128 a, complex128 b)
    {
        return areEqual<ito::float64>(a.real(), b.real()) && areEqual<ito::float64>(a.imag(), b.imag());
    }
 
 
} // namespace ito
 
#endif // NUMERIC_H