File indexing completed on 2024-05-12 05:55:09

 // cmath.h
 // Complex number support : type definition and function for complex numbers.
 //
 // This file is part of the SpeedCrunch project
 // Copyright (C) 2013, 2015-2016 Hadrien Theveneau <theveneau@gmail.com>.
 // Copyright (C) 2015-2016 Pol Welter.
 // Copyright (C) 2016 @heldercorreia
 //
 // This program 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
 // of the License, or (at your option) any later version.
 //
 // This program 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 this program; see the file COPYING.  If not, write to
 // the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 // Boston, MA 02110-1301, USA.
 
 #ifndef MATH_CMATH_H
 #define MATH_CMATH_H
 
 #include "hmath.h"
 #include "rational.h"
 
 #include <QMap>
 #include <QString>
 
 class CMath;
 
 class CNumber {
     friend class CMath;
     friend CNumber operator-(const CNumber&);
     friend CNumber operator-(const CNumber&, const CNumber&);
     friend bool operator>(const CNumber&, const CNumber&);
     friend bool operator<(const CNumber&, const CNumber&);
     friend bool operator>=(const CNumber&, const CNumber&);
     friend bool operator<=(const CNumber&, const CNumber&);
     friend bool operator==(const CNumber&, const CNumber&);
     friend bool operator!=(const CNumber&, const CNumber&);
 
 public:
     CNumber();
     CNumber(const HNumber&);
     CNumber(const HNumber&, const HNumber&);
     CNumber(const CNumber&);
     CNumber(int);
     CNumber(const char*);
     CNumber(const QJsonObject&);
     ~CNumber() { }
 
     bool isNan() const;
     bool isZero() const;
     bool isPositive() const;
     bool isNegative() const;
     bool isInteger() const;
     bool isGaussian() const;
     bool isReal() const;
     bool isNearReal() const;
 
     void serialize(QJsonObject&) const;
     static CNumber deSerialize(const QJsonObject&);
 
     int toInt() const; // Removed, too problematic for complex numbers.
     Error error() const;
 
     CNumber& operator=(const CNumber&);
     CNumber operator+(const CNumber&) const;
     CNumber& operator+=(const CNumber&);
     CNumber& operator-=(const CNumber&);
     CNumber operator*(const CNumber&) const;
     CNumber operator*(const HNumber&) const;
     CNumber operator*(int x) { return operator * (HNumber(x)); } // Overload ambiguity resolution.
     CNumber& operator*=(const CNumber&);
     CNumber operator/(const CNumber&) const;
     CNumber operator/(const HNumber&) const;
     CNumber operator/(int x) { return operator / (HNumber(x)); } // Overload ambiguity resolution.
     CNumber& operator/=(const CNumber&);
     CNumber operator%(const CNumber&) const;
     CNumber operator&(const CNumber&) const;
     CNumber& operator&=(const CNumber&);
     CNumber operator|(const CNumber&) const;
     CNumber& operator|=(const CNumber&);
     CNumber operator^(const CNumber&) const;
     CNumber& operator^=(const CNumber&);
     CNumber operator~() const;
     CNumber operator>>(const CNumber&) const;
     CNumber operator<<(const CNumber&) const;
 
 private:
     int compare(const CNumber&) const;
 
 public:
     HNumber real;
     HNumber imag;
 
     // FIXME: Better access control to real and imag.
 
     // Invariants:
     // - real and imag are neither or both NaN.
     // - real and imag have the same NaN error.
 
     struct Format : public HNumber::Format  {
         enum class Notation {Null, Cartesian, Polar};
         Notation notation;
 
         Format();
         Format(const Format&);
         Format(const HNumber::Format&);
         Format operator+(const Format&) const;
 
         static Format Polar();
         static Format Cartesian();
     };
 };
 
 class CMath {
 public:
     // FORMAT
     static QString format(const CNumber&, CNumber::Format = CNumber::Format());
     // CONSTANTS
     static CNumber e();
     static CNumber phi();
     static CNumber pi();
     static CNumber nan(Error error = Success);
     static CNumber i();
     // GENERAL MATH
     static CNumber rad2deg(const CNumber&);
     static CNumber deg2rad(const CNumber&);
     static CNumber rad2gon(const CNumber&);
     static CNumber gon2rad(const CNumber&);
     static CNumber abs(const CNumber&);
     static CNumber integer(const CNumber&);
     static CNumber frac(const CNumber&);
     static CNumber floor(const CNumber&);
     static CNumber ceil(const CNumber&);
     static CNumber gcd(const CNumber&, const CNumber&);
     static CNumber idiv(const CNumber&, const CNumber&);
     static CNumber round(const CNumber&, int prec = 0);
     static CNumber trunc(const CNumber&, int prec = 0);
     static CNumber sqrt(const CNumber&);
     static CNumber cbrt(const CNumber&);
     static CNumber raise(const CNumber&, int);
     static CNumber raise(const CNumber&, const CNumber&);
     static CNumber sgn(const CNumber&);
     // EXPONENTIAL FUNCTION AND RELATED
     static CNumber exp(const CNumber&);
     static CNumber ln(const CNumber&);
     static CNumber lg(const CNumber&);
     static CNumber lb(const CNumber&);
     static CNumber log(const CNumber& base, const CNumber& x);
     static CNumber sinh(const CNumber&);
     static CNumber cosh(const CNumber&);
     static CNumber tanh(const CNumber&);
     static CNumber arsinh(const CNumber&);
     static CNumber arcosh(const CNumber&);
     static CNumber artanh(const CNumber&);
     // COMPLEX SPECIFIC
     static CNumber real(const CNumber& x) {return x.real;}
     static CNumber imag(const CNumber& x) {return x.imag;}
     static CNumber conj(const CNumber& x);
     static CNumber phase(const CNumber&);
     // TRIGONOMETRY
     static CNumber sin(const CNumber&);
     static CNumber cos(const CNumber&);
     static CNumber tan(const CNumber&);
     static CNumber cot(const CNumber&);
     static CNumber sec(const CNumber&);
     static CNumber csc(const CNumber&);
     static CNumber arcsin(const CNumber&);
     static CNumber arccos(const CNumber&);
     static CNumber arctan(const CNumber&);
     static CNumber arctan2(const CNumber&, const CNumber&);
     // HIGHER MATH FUNCTIONS
     static CNumber factorial(const CNumber&, const CNumber& base = CNumber(1));
     static CNumber gamma(const CNumber&);
     static CNumber lnGamma(const CNumber&);
     static CNumber erf(const CNumber&);
     static CNumber erfc(const CNumber&);
     // PROBABILITY
     static CNumber nCr(const CNumber&, const CNumber&);
     static CNumber nPr(const CNumber&, const CNumber&);
     static CNumber binomialPmf(const CNumber& k, const CNumber& n, const CNumber& p);
     static CNumber binomialCdf(const CNumber& k, const CNumber& n, const CNumber& p);
     static CNumber binomialMean(const CNumber& n, const CNumber& p);
     static CNumber binomialVariance(const CNumber& n, const CNumber& p);
     static CNumber hypergeometricPmf(const CNumber& k, const CNumber& N, const CNumber& M, const CNumber& n);
     static CNumber hypergeometricCdf(const CNumber& k, const CNumber& N, const CNumber& M, const CNumber& n);
     static CNumber hypergeometricMean(const CNumber& N, const CNumber& M, const CNumber& n);
     static CNumber hypergeometricVariance(const CNumber& N, const CNumber& M, const CNumber& n);
     static CNumber poissonPmf(const CNumber& k, const CNumber& l);
     static CNumber poissonCdf(const CNumber& k, const CNumber& l);
     static CNumber poissonMean(const CNumber& l);
     static CNumber poissonVariance(const CNumber& l);
     // LOGIC
     static CNumber mask(const CNumber&, const CNumber& bits);
     static CNumber sgnext(const CNumber&, const CNumber& bits);
     static CNumber ashr(const CNumber&, const CNumber& bits);
     // IEEE-754 CONVERSION
     static CNumber decodeIeee754(const CNumber&, const CNumber& exp_bits, const CNumber& significand_bits);
     static CNumber decodeIeee754(const CNumber&, const CNumber& exp_bits, const CNumber& significand_bits,
                                  const CNumber& exp_bias);
     static CNumber encodeIeee754(const CNumber&, const CNumber& exp_bits, const CNumber& significand_bits);
     static CNumber encodeIeee754(const CNumber&, const CNumber& exp_bits, const CNumber& significand_bits,
                                  const CNumber& exp_bias);
 };
 
 std::ostream& operator<<(std::ostream&, const CNumber&);
 
 #endif // CMATH_CMATH_H