Implement complex number and ImaginaryUnit

include/fintamath/core/MathObjectTypes.hpp

@@ -48,6 +48,7 @@ enum class MathObjectType : MathObjectTypeId {
 
   Rational,
   Real,
+  Complex,
 
   IInteger = 8000,
 
@@ -68,6 +69,7 @@ enum class MathObjectType : MathObjectTypeId {
   NegInf,
   ComplexInf,
   Undefined,
+  ImaginaryUnit,
 
   IFunction = 11000,
 

include/fintamath/literals/constants/ImaginaryUnit.hpp

@@ -0,0 +1,23 @@
+#pragma once
+
+#include "fintamath/literals/Boolean.hpp"
+#include "fintamath/literals/constants/IConstant.hpp"
+#include "fintamath/numbers/Complex.hpp"
+
+namespace fintamath {
+
+class ImaginaryUnit : public IConstantCRTP<Boolean, ImaginaryUnit> {
+public:
+  std::string toString() const override {
+    return Complex(Integer(0), Integer(1)).toString();
+  }
+
+  static MathObjectTypeId getTypeIdStatic() {
+    return MathObjectTypeId(MathObjectType::ImaginaryUnit);
+  }
+
+protected:
+  std::unique_ptr<IMathObject> call() const override;
+};
+
+}

include/fintamath/numbers/Complex.hpp

@@ -0,0 +1,69 @@
+#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);
+
+  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;
+
+  Complex precise(uint8_t precision) const;
+
+  const Integer &real() const;
+
+  const Integer &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);
+};
+
+}

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 std::make_unique<Real>(value);
     });
+
+    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>();
 
@@ -173,6 +173,7 @@ struct ParserConfig {
     IConstant::registerType<NegInf>();
     IConstant::registerType<ComplexInf>();
     IConstant::registerType<Undefined>();
+    IConstant::registerType<ImaginaryUnit>();
 
     IFunction::registerType<Abs>();
     IFunction::registerType<Log>();

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 +1,135 @@
+#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) {
+  re = INumber::parse(str);
+}
+
+Complex::Complex(const INumber &inReal, const INumber &inImaginary) {
+  if (is<Complex>(inReal) || is<Complex>(inImaginary)) {
+    throw InvalidInputException("Nested complex numbers are not allowed");
+  }
+
+  re = cast<INumber>(inReal.clone());
+  im = cast<INumber>(inImaginary.clone());
+}
+
+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)) {
+    if (!res.empty()) {
+      res += " + ";
+    }
+
+    res += im->toString() + "I";
+  }
+
+  if (res.empty()) {
+    res = "0";
+  }
+
+  return res;
+}
+
+std::unique_ptr<IMathObject> Complex::toMinimalObject() const {
+  if (*im == Integer(0)) {
+    return re->clone();
+  }
+  return clone();
+}
+
+Complex Complex::precise(uint8_t precision) const {
+  Complex res = *this;
+  res.re = std::make_unique<Real>(convert<Real>(*re).precise(precision));
+  res.im = std::make_unique<Real>(convert<Real>(*im).precise(precision));
+  return res;
+}
+
+bool Complex::equals(const Complex &rhs) const {
+  return re == rhs.re && im == rhs.im;
+}
+
+bool Complex::less(const Complex &rhs) const {
+  // TODO!!! See symengine
+  throw InvalidInputBinaryOperatorException("<", toString(), rhs.toString());
+}
+
+bool Complex::more(const Complex &rhs) const {
+  // TODO!!! See symengine
+  throw InvalidInputBinaryOperatorException(">", toString(), rhs.toString());
+}
+
+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) {
+  auto lhsRe = cast<INumber>(re->clone());
+  auto lhsIm = cast<INumber>(im->clone());
+  re = *(*lhsRe * *rhs.re) + *(*lhsIm * *rhs.im);
+  im = *(*lhsRe * *rhs.im) + *(*lhsIm * *rhs.re);
+  return *this;
+}
+
+// https://en.wikipedia.org/wiki/Complex_number#Reciprocal_and_division
+Complex &Complex::divide(const Complex &rhs) {
+  auto lhsRe = cast<INumber>(re->clone());
+  auto lhsIm = cast<INumber>(im->clone());
+  auto divisor = *(*rhs.re * *rhs.re) + *(*rhs.im * *rhs.im);
+  re = *(*(*lhsRe * *rhs.re) + *(*lhsIm * *rhs.im)) / *divisor;
+  im = *(*(*lhsIm * *rhs.re) - *(*lhsRe * *rhs.im)) / *divisor;
+  return *this;
+}
+
+Complex &Complex::negate() {
+  re = -(*re);
+  im = -(*im);
+  return *this;
+}
+
+}