Implement complex number and ImaginaryUnit

include/fintamath/core/MathObjectTypes.hpp

@@ -49,6 +49,7 @@ enum class MathObjectType : MathObjectTypeId {
 
   Rational,
   Real,
+  Complex,
 
   IInteger = 8000,
 
@@ -69,6 +70,7 @@ enum class MathObjectType : MathObjectTypeId {
   NegInf,
   ComplexInf,
   Undefined,
+  ImaginaryUnit,
 
   IFunction = 11000,
 

include/fintamath/literals/constants/ImaginaryUnit.hpp

@@ -0,0 +1,22 @@
+#pragma once
+
+#include "fintamath/literals/constants/IConstant.hpp"
+#include "fintamath/numbers/Complex.hpp"
+
+namespace fintamath {
+
+class ImaginaryUnit : public IConstantCRTP<Complex, ImaginaryUnit> {
+public:
+  std::string toString() const override {
+    return "I";
+  }
+
+  static MathObjectTypeId getTypeIdStatic() {
+    return MathObjectTypeId(MathObjectType::ImaginaryUnit);
+  }
+
+protected:
+  std::unique_ptr<IMathObject> call() const override;
+};
+
+}

include/fintamath/numbers/Complex.hpp

@@ -0,0 +1,73 @@
+#pragma once
+
+#include "fintamath/numbers/Integer.hpp"
+#include "fintamath/numbers/Rational.hpp"
+#include "fintamath/numbers/Real.hpp"
+
+namespace fintamath {
+
+class Complex : public INumberCRTP<Complex> {
+public:
+  Complex() = default;
+
+  Complex(const Complex &rhs);
+
+  Complex(Complex &&rhs) noexcept = default;
+
+  Complex &operator=(const Complex &rhs);
+
+  Complex &operator=(Complex &&rhs) noexcept = default;
+
+  explicit Complex(const std::string &str);
+
+  explicit Complex(const INumber &inReal, const INumber &inImag);
+
+  explicit Complex(int64_t inReal, int64_t inImag);
+
+  Complex(const Integer &rhs);
+
+  Complex(const Rational &rhs);
+
+  Complex(const Real &rhs);
+
+  Complex(int64_t rhs);
+
+  std::string toString() const override;
+
+  std::unique_ptr<IMathObject> toMinimalObject() const override;
+
+  bool isPrecise() const override;
+
+  bool isComplex() const override;
+
+  const INumber &real() const;
+
+  const INumber &imag() const;
+
+  static MathObjectTypeId getTypeIdStatic() {
+    return MathObjectTypeId(MathObjectType::Complex);
+  }
+
+protected:
+  bool equals(const Complex &rhs) const override;
+
+  bool less(const Complex &rhs) const override;
+
+  bool more(const Complex &rhs) const override;
+
+  Complex &add(const Complex &rhs) override;
+
+  Complex &substract(const Complex &rhs) override;
+
+  Complex &multiply(const Complex &rhs) override;
+
+  Complex &divide(const Complex &rhs) override;
+
+  Complex &negate() override;
+
+private:
+  std::unique_ptr<INumber> re = std::make_unique<Integer>(0);
+  std::unique_ptr<INumber> im = std::make_unique<Integer>(0);
+};
+
+}

include/fintamath/numbers/INumber.hpp

@@ -14,6 +14,10 @@ class INumber : public IComparable {
     return true;
   }
 
+  virtual bool isComplex() const {
+    return false;
+  }
+
   template <typename T, typename = std::enable_if_t<std::is_base_of_v<INumber, T>>>
   static void registerType() {
     Parser::registerType<T>(getParser());

src/fintamath/config/ConverterConfig.cpp

@@ -1,5 +1,6 @@
 #include "fintamath/core/Converter.hpp"
 
+#include "fintamath/numbers/Complex.hpp"
 #include "fintamath/numbers/Integer.hpp"
 #include "fintamath/numbers/Rational.hpp"
 #include "fintamath/numbers/Real.hpp"
@@ -39,6 +40,19 @@ struct ConverterConfig {
     Converter::add<Real, Rational>([](const Real & /*type*/, const Rational &value) {
       return Real(value).clone();
     });
+
+    Converter::add<Complex, Complex>([](const Complex & /*type*/, const Complex &value) {
+      return std::make_unique<Complex>(value);
+    });
+    Converter::add<Complex, Integer>([](const Complex & /*type*/, const Integer &value) {
+      return std::make_unique<Complex>(value);
+    });
+    Converter::add<Complex, Rational>([](const Complex & /*type*/, const Rational &value) {
+      return std::make_unique<Complex>(value);
+    });
+    Converter::add<Complex, Real>([](const Complex & /*type*/, const Real &value) {
+      return std::make_unique<Complex>(value);
+    });
   }
 };
 

src/fintamath/config/ParserConfig.cpp

@@ -66,6 +66,7 @@
 #include "fintamath/literals/constants/E.hpp"
 #include "fintamath/literals/constants/False.hpp"
 #include "fintamath/literals/constants/IConstant.hpp"
+#include "fintamath/literals/constants/ImaginaryUnit.hpp"
 #include "fintamath/literals/constants/Inf.hpp"
 #include "fintamath/literals/constants/NegInf.hpp"
 #include "fintamath/literals/constants/Pi.hpp"
@@ -157,7 +158,6 @@ struct ParserConfig {
 
     INumber::registerType<IInteger>(&IInteger::parse);
     INumber::registerType<Rational>();
-    INumber::registerType<Real>();
 
     IInteger::registerType<Integer>();
 
@@ -169,6 +169,7 @@ struct ParserConfig {
     IConstant::registerType<Pi>();
     IConstant::registerType<True>();
     IConstant::registerType<False>();
+    IConstant::registerType<ImaginaryUnit>();
     IConstant::registerType<Inf>();
     IConstant::registerType<NegInf>();
     IConstant::registerType<ComplexInf>();

src/fintamath/literals/constants/ImaginaryUnit.cpp

@@ -0,0 +1,9 @@
+#include "fintamath/literals/constants/ImaginaryUnit.hpp"
+
+namespace fintamath {
+
+std::unique_ptr<IMathObject> ImaginaryUnit::call() const {
+  return std::make_unique<Complex>(Integer(0), Integer(1));
+}
+
+}

src/fintamath/numbers/Complex.cpp

@@ -0,0 +1,206 @@
+#include "fintamath/numbers/Complex.hpp"
+
+#include <algorithm>
+#include <stdexcept>
+
+#include "fintamath/exceptions/InvalidInputException.hpp"
+#include "fintamath/exceptions/UndefinedException.hpp"
+
+namespace fintamath {
+
+Complex::Complex(const Complex &rhs) : re(cast<INumber>(rhs.re->clone())), im(cast<INumber>(rhs.im->clone())) {
+}
+
+Complex &Complex::operator=(const Complex &rhs) {
+  if (this != &rhs) {
+    re = cast<INumber>(rhs.re->clone());
+    im = cast<INumber>(rhs.im->clone());
+  }
+
+  return *this;
+}
+
+Complex::Complex(const std::string &str) {
+  if (!str.empty() && str.back() == 'I') {
+    im = INumber::parse(str.substr(0, str.length() - 1));
+  }
+  else {
+    re = INumber::parse(str);
+  }
+
+  if (!re || !im) {
+    throw InvalidInputException(str);
+  }
+}
+
+Complex::Complex(const INumber &inReal, const INumber &inImag) {
+  if (is<Complex>(inReal) || is<Complex>(inImag)) {
+    throw InvalidInputException("Nested complex numbers are not allowed");
+  }
+
+  re = cast<INumber>(inReal.toMinimalObject());
+  im = cast<INumber>(inImag.toMinimalObject());
+}
+
+Complex::Complex(int64_t inReal, int64_t inImag) : re(std::make_unique<Integer>(inReal)),
+                                                   im(std::make_unique<Integer>(inImag)) {
+}
+
+Complex::Complex(const Integer &rhs) : re(cast<INumber>(rhs.toMinimalObject())) {
+}
+
+Complex::Complex(const Rational &rhs) : re(cast<INumber>(rhs.toMinimalObject())) {
+}
+
+Complex::Complex(const Real &rhs) : re(cast<INumber>(rhs.toMinimalObject())) {
+}
+
+Complex::Complex(int64_t rhs) : re(std::make_unique<Integer>(rhs)) {
+}
+
+std::string Complex::toString() const {
+  std::string res;
+
+  if (*re != Integer(0)) {
+    res += re->toString();
+  }
+
+  if (*im != Integer(0)) {
+    std::string imStr = im->toString();
+    bool isImNeg = false;
+
+    if (imStr.front() == '-') {
+      imStr = imStr.substr(1);
+      isImNeg = true;
+    }
+
+    if (imStr == "1") {
+      imStr.clear();
+    }
+    else {
+      imStr += " ";
+    }
+
+    if (!res.empty()) {
+      res += isImNeg ? " - " : " + ";
+    }
+    else if (isImNeg) {
+      res += "-";
+    }
+
+    res += imStr + "I";
+  }
+
+  if (res.empty()) {
+    res = "0";
+  }
+
+  return res;
+}
+
+std::unique_ptr<IMathObject> Complex::toMinimalObject() const {
+  if (*im == Integer(0)) {
+    return re->toMinimalObject();
+  }
+
+  return clone();
+}
+
+bool Complex::isPrecise() const {
+  return !is<Real>(re) && !is<Real>(im);
+}
+
+bool Complex::isComplex() const {
+  return *im != Integer(0);
+}
+
+const INumber &Complex::real() const {
+  return *re;
+}
+
+const INumber &Complex::imag() const {
+  return *im;
+}
+
+bool Complex::equals(const Complex &rhs) const {
+  return *re == *rhs.re && *im == *rhs.im;
+}
+
+bool Complex::less(const Complex &rhs) const {
+  if (*re == *rhs.re) {
+    return *im < *rhs.im;
+  }
+
+  return *re < *rhs.re;
+}
+
+bool Complex::more(const Complex &rhs) const {
+  if (*re == *rhs.re) {
+    return *im > *rhs.im;
+  }
+
+  return *re > *rhs.re;
+}
+
+Complex &Complex::add(const Complex &rhs) {
+  re = *re + *rhs.re;
+  im = *im + *rhs.im;
+
+  return *this;
+}
+
+Complex &Complex::substract(const Complex &rhs) {
+  re = *re - *rhs.re;
+  im = *im - *rhs.im;
+
+  return *this;
+}
+
+// https://en.wikipedia.org/wiki/Complex_number#Multiplication_and_square
+Complex &Complex::multiply(const Complex &rhs) {
+  Complex lhs = *this;
+
+  auto &x = *lhs.re;
+  auto &y = *lhs.im;
+  auto &u = *rhs.re;
+  auto &v = *rhs.im;
+
+  re = *(x * u) - *(y * v);
+  im = *(x * v) + *(y * u);
+
+  return *this;
+}
+
+// https://en.wikipedia.org/wiki/Complex_number#Reciprocal_and_division
+Complex &Complex::divide(const Complex &rhs) {
+  Complex lhs = *this;
+
+  auto &x = *lhs.re;
+  auto &y = *lhs.im;
+  auto &u = *rhs.re;
+  auto &v = *rhs.im;
+
+  auto divisor = *(u * u) + *(v * v);
+
+  if (is<Integer>(divisor)) {
+    divisor = convert<Rational>(*divisor);
+  }
+
+  try {
+    re = *(*(x * u) + *(y * v)) / *divisor;
+    im = *(*(y * u) - *(x * v)) / *divisor;
+  }
+  catch (const UndefinedException &) {
+    throw UndefinedBinaryOperatorException("/", toString(), rhs.toString());
+  }
+
+  return *this;
+}
+
+Complex &Complex::negate() {
+  re = -(*re);
+  im = -(*im);
+  return *this;
+}
+
+}