numb.h

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/*-
 * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * Project homepage:
 * https://amath.innolan.net
 * 
 */

#ifndef AMATH_NUMBER_H
#define AMATH_NUMBER_H

#if __GNUC__ > 2
#pragma GCC diagnostic ignored "-Wshadow"
#endif

/**
 * @file  numb.h
 * @brief Class base handling of numbers
 */

#include "amath.h"

union FloatUnion64 {
    bool IsNegative() const { return (integer >> 63) != 0; }
    bool IsZero() const { return integer == 0; }
    bool IsInf() const { return GetExponent() == 0x7FF && GetMantissa() == 0; }
    bool IsNaN() const { return GetExponent() == 0x7FF && GetMantissa() != 0; }
    bool IsMaxPositive() const { return integer == 0x7EFFFFFFFFFFFFFFull; }
    bool IsMaxNegative() const { return integer == 0x7FFFFFFFFFFFFFFFull; }
    int32_t GetExponent() const { return (integer >> 52) & 0x7FF; }
    uint64_t GetMantissa() const { return integer & 0xFFFFFFFFFFFFFull; }
    double floatingPoint;
    uint64_t integer;
};

typedef enum
{
    nsysnatural,
    nsysrational,
    nsysreal,
    nsyscomplex,
    nsysnan
} NumberSystem;

struct Number
{
public:
    explicit Number(NumberSystem system) :
        system(system)
    {
    }

    virtual ~Number()
    {
    }

    virtual Number* Clone() = 0;
    virtual int GetIntegerValue() = 0;
    virtual double GetRealValue() = 0;
    virtual bool PureComplexValue() = 0;
    virtual int GetPrecedence() = 0;
    virtual int GetDefaultPrecedence() = 0;
    virtual bool IsNegative() = 0;
    virtual bool IsZero() = 0;
    virtual bool IsNaN() = 0;
    virtual bool IsInfinite() = 0;
    virtual bool IsNotImplemented() = 0;

    virtual Number* Unary() = 0;
    virtual Number* Add(Number* other) = 0;
    virtual Number* Sub(Number* other) = 0;
    virtual Number* Mul(Number* other) = 0;
    virtual Number* Div(Number* other) = 0;
    virtual Number* Raise(Number* exponent) = 0;

    virtual Number* Signum() = 0;
    virtual Number* Trunc() = 0;
    virtual Number* Round() = 0;
    virtual Number* Floor() = 0;
    virtual Number* Ceiling() = 0;
    virtual Number* Absolute() = 0;
    virtual Number* SquareRoot() = 0;
    virtual Number* CubeRoot() = 0;
    virtual Number* Reciprocal() = 0;
    virtual Number* Factorial() = 0;

    virtual Number* Log() = 0;
    virtual Number* Log2() = 0;
    virtual Number* Log10() = 0;

    virtual Number* Sine() = 0;
    virtual Number* Cosine() = 0;
    virtual Number* Tangent() = 0;
    virtual Number* Cosecant() = 0;
    virtual Number* Secant() = 0;
    virtual Number* Cotangent() = 0;
    virtual Number* Chord() = 0;
    virtual Number* ExSecant() = 0;
    virtual Number* ExCosecant() = 0;

    virtual Number* ArcSine() = 0;
    virtual Number* ArcCosine() = 0;
    virtual Number* ArcTangent() = 0;
    virtual Number* ArcCosecant() = 0;
    virtual Number* ArcSecant() = 0;
    virtual Number* ArcCotangent() = 0;
    virtual Number* ArcChord() = 0;
    virtual Number* ArcExSecant() = 0;
    virtual Number* ArcExCosecant() = 0;

    virtual Number* HypSine() = 0;
    virtual Number* HypCosine() = 0;
    virtual Number* HypTangent() = 0;
    virtual Number* HypCosecant() = 0;
    virtual Number* HypSecant() = 0;
    virtual Number* HypCotangent() = 0;

    virtual Number* HypArcSine() = 0;
    virtual Number* HypArcCosine() = 0;
    virtual Number* HypArcTangent() = 0;
    virtual Number* HypArcCosecant() = 0;
    virtual Number* HypArcSecant() = 0;
    virtual Number* HypArcCotangent() = 0;

    virtual Number* VerSine() = 0;
    virtual Number* VerCosine() = 0;
    virtual Number* CoVerSine() = 0;
    virtual Number* CoVerCosine() = 0;
    virtual Number* HaVerSine() = 0;
    virtual Number* HaVerCosine() = 0;
    virtual Number* HaCoVerSine() = 0;
    virtual Number* HaCoVerCosine() = 0;

    virtual Number* ArcVerSine() = 0;
    virtual Number* ArcVerCosine() = 0;
    virtual Number* ArcCoVerSine() = 0;
    virtual Number* ArcCoVerCosine() = 0;
    virtual Number* ArcHaVerSine() = 0;
    virtual Number* ArcHaVerCosine() = 0;
    virtual Number* ArcHaCoVerSine() = 0;
    virtual Number* ArcHaCoVerCosine() = 0;

    friend class PositionalNumeralSystem;
    friend class DecimalSystem;
    friend struct IntegerNumber;
    friend struct RealNumber;
    friend struct ComplexNumber;

protected:
    NumberSystem system;
};

#endif