File indexing completed on 2024-05-12 17:22:39 

0001 // HMath: C++ high precision math routines
0002 // Copyright (C) 2004 Ariya Hidayat <ariya.hidayat@gmail.com>
0003 // Copyright (C) 2007-2008, 2014, 2016 @heldercorreia
0004 // Copyright (C) 2008 Wolf Lammen
0005 //
0006 // This program is free software; you can redistribute it and/or
0007 // modify it under the terms of the GNU General Public License
0008 // as published by the Free Software Foundation; either version 2
0009 // of the License, or (at your option) any later version.
0010 //
0011 // This program is distributed in the hope that it will be useful,
0012 // but WITHOUT ANY WARRANTY; without even the implied warranty of
0013 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0014 // GNU General Public License for more details.
0015 //
0016 // You should have received a copy of the GNU General Public License
0017 // along with this program; see the file COPYING.  If not, write to
0018 // the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
0019 // Boston, MA 02110-1301, USA.
0020 
0021 #ifndef MATH_HMATH_H
0022 #define MATH_HMATH_H
0023 
0024 #include "errors.h"
0025 
0026 #include <QJsonObject>
0027 #include <QString>
0028 
0029 #include <ostream>
0030 
0031 class HMath;
0032 class HNumberPrivate;
0033 class CNumber;
0034 class CMath;
0035 class Rational;
0036 
0037 class HNumber {
0038     friend class HMath;
0039     friend class CNumber;
0040     friend class CMath;
0041     friend HNumber operator-(const HNumber&);
0042     friend HNumber operator-(const HNumber&, const HNumber&);
0043     friend bool operator>(const HNumber&, const HNumber&);
0044     friend bool operator<(const HNumber&, const HNumber&);
0045     friend bool operator>=(const HNumber&, const HNumber&);
0046     friend bool operator<=(const HNumber&, const HNumber&);
0047     friend bool operator==(const HNumber&, const HNumber&);
0048     friend bool operator!=(const HNumber&, const HNumber&);
0049 
0050 public:
0051     HNumber();
0052     HNumber(const HNumber&);
0053     HNumber(int);
0054     HNumber(const char*);
0055     HNumber(const QJsonObject&);
0056     ~HNumber();
0057 
0058     bool isNan() const;
0059     bool isZero() const;
0060     bool isNearZero() const;
0061     bool isPositive() const;
0062     bool isNegative() const;
0063     bool isInteger() const;
0064 
0065     void serialize(QJsonObject&) const;
0066     static HNumber deSerialize(const QJsonObject&);
0067 
0068     int toInt() const;
0069     Error error() const;
0070 
0071     HNumber& operator=(const HNumber&);
0072     HNumber operator+(const HNumber&) const;
0073     HNumber& operator+=(const HNumber&);
0074     HNumber& operator-=(const HNumber&);
0075     HNumber operator*(const HNumber&) const;
0076     HNumber& operator*=(const HNumber&);
0077     HNumber operator/(const HNumber&) const;
0078     HNumber& operator/=(const HNumber&);
0079     HNumber operator%(const HNumber&) const;
0080     HNumber operator&(const HNumber&) const;
0081     HNumber& operator&=(const HNumber&);
0082     HNumber operator|(const HNumber&) const;
0083     HNumber& operator|=(const HNumber&);
0084     HNumber operator^(const HNumber&) const;
0085     HNumber& operator^=(const HNumber&);
0086     HNumber operator~() const;
0087     HNumber operator>>(const HNumber&) const;
0088     HNumber operator<<(const HNumber&) const;
0089 
0090 private:
0091     HNumberPrivate* d;
0092 
0093     int compare(const HNumber&) const;
0094 
0095 public:
0096     struct Format {
0097         enum class Base {Null, Binary, Decimal, Octal, Hexadecimal};
0098         enum class RadixChar {Null, Point, Comma};
0099         enum class Mode {Null, General, Fixed, Scientific, Engineering};
0100 
0101         Base base;
0102         RadixChar radixChar;
0103         Mode mode;
0104         int precision;  // -1 means 'auto'
0105         static const int PrecisionNull = -1000;
0106 
0107         Format();
0108         Format(const Format&);
0109         Format operator+(const Format&) const;
0110 
0111         static Format Binary();
0112         static Format Octal();
0113         static Format Decimal();
0114         static Format Hexadecimal();
0115 
0116         static Format Precision(int);
0117 
0118         static Format Point();
0119         static Format Comma();
0120 
0121         static Format General();
0122         static Format Fixed();
0123         static Format Scientific();
0124         static Format Engineering();
0125     };
0126 };
0127 
0128 class HMath {
0129 public:
0130     // FORMAT
0131     static QString format(const HNumber&, HNumber::Format = HNumber::Format());
0132     // PARSING
0133     static HNumber parse_str(const char*, const char** out);
0134     // CONSTANTS
0135     static HNumber e();
0136     static HNumber phi();
0137     static HNumber pi();
0138     static HNumber nan(Error = Success);
0139     // GENERAL MATH
0140     static HNumber rad2deg(const HNumber&);
0141     static HNumber deg2rad(const HNumber&);
0142     static HNumber rad2gon(const HNumber&);
0143     static HNumber gon2rad(const HNumber&);
0144     static HNumber max(const HNumber&, const HNumber&);
0145     static HNumber min(const HNumber&, const HNumber&);
0146     static HNumber abs(const HNumber&);
0147     static HNumber integer(const HNumber&);
0148     static HNumber frac(const HNumber&);
0149     static HNumber floor(const HNumber&);
0150     static HNumber ceil(const HNumber&);
0151     static HNumber gcd(const HNumber&, const HNumber&);
0152     static HNumber idiv(const HNumber&, const HNumber&);
0153     static HNumber round(const HNumber&, int prec = 0);
0154     static HNumber trunc(const HNumber&, int prec = 0);
0155     static HNumber sqrt(const HNumber&);
0156     static HNumber cbrt(const HNumber&);
0157     static HNumber raise(const HNumber&, int);
0158     static HNumber raise(const HNumber&, const HNumber&);
0159     static HNumber sgn(const HNumber&);
0160     // EXPONENTIAL FUNCTION AND RELATED
0161     static HNumber exp(const HNumber&);
0162     static HNumber ln(const HNumber&);
0163     static HNumber lg(const HNumber&);
0164     static HNumber lb(const HNumber&);
0165     static HNumber log(const HNumber& base, const HNumber& x);
0166     static HNumber sinh(const HNumber&);
0167     static HNumber cosh(const HNumber&);
0168     static HNumber tanh(const HNumber&);
0169     static HNumber arsinh(const HNumber&);
0170     static HNumber arcosh(const HNumber&);
0171     static HNumber artanh(const HNumber&);
0172     // TRIGONOMETRY
0173     static HNumber sin(const HNumber&);
0174     static HNumber cos(const HNumber&);
0175     static HNumber tan(const HNumber&);
0176     static HNumber cot(const HNumber&);
0177     static HNumber sec(const HNumber&);
0178     static HNumber csc(const HNumber&);
0179     static HNumber arcsin(const HNumber&);
0180     static HNumber arccos(const HNumber&);
0181     static HNumber arctan(const HNumber&);
0182     static HNumber arctan2(const HNumber&, const HNumber&);
0183     // HIGHER MATH FUNCTIONS
0184     static HNumber factorial(const HNumber&, const HNumber& base = HNumber(1));
0185     static HNumber gamma(const HNumber&);
0186     static HNumber lnGamma(const HNumber&);
0187     static HNumber erf(const HNumber&);
0188     static HNumber erfc(const HNumber&);
0189     // PROBABILITY
0190     static HNumber nCr(const HNumber& n, const HNumber& k);
0191     static HNumber nPr(const HNumber& n, const HNumber& r);
0192     static HNumber binomialPmf(const HNumber& k, const HNumber& n, const HNumber& p);
0193     static HNumber binomialCdf(const HNumber& k, const HNumber& n, const HNumber& p);
0194     static HNumber binomialMean(const HNumber& n, const HNumber& p);
0195     static HNumber binomialVariance(const HNumber& n, const HNumber& p);
0196     static HNumber hypergeometricPmf(const HNumber& k, const HNumber& N, const HNumber& M, const HNumber& n);
0197     static HNumber hypergeometricCdf(const HNumber& k, const HNumber& N, const HNumber& M, const HNumber& n);
0198     static HNumber hypergeometricMean(const HNumber& N, const HNumber& M, const HNumber& n);
0199     static HNumber hypergeometricVariance(const HNumber& N, const HNumber& M, const HNumber& n);
0200     static HNumber poissonPmf(const HNumber& k, const HNumber& l);
0201     static HNumber poissonCdf(const HNumber& k, const HNumber& l);
0202     static HNumber poissonMean(const HNumber& l);
0203     static HNumber poissonVariance(const HNumber& l);
0204     // LOGIC
0205     static HNumber mask(const HNumber&, const HNumber& bits);
0206     static HNumber sgnext(const HNumber&, const HNumber& bits);
0207     static HNumber ashr(const HNumber&, const HNumber& bits);
0208     // IEEE-754 CONVERSION
0209     static HNumber decodeIeee754(const HNumber&, const HNumber& exp_bits, const HNumber& significand_bits);
0210     static HNumber decodeIeee754(const HNumber&, const HNumber& exp_bits, const HNumber& significand_bits,
0211                                  const HNumber& exp_bias);
0212     static HNumber encodeIeee754(const HNumber&, const HNumber& exp_bits, const HNumber& significand_bits);
0213     static HNumber encodeIeee754(const HNumber&, const HNumber& exp_bits, const HNumber& significand_bits,
0214                                  const HNumber& exp_bias);
0215 };
0216 
0217 std::ostream& operator<<(std::ostream&, const HNumber&);
0218 
0219 #endif // MATH_HMATH_H