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| Original file line number | Diff line number | Diff line change |
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| #pragma once | ||
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| #include "fintamath/functions/IFunction.hpp" | ||
| #include "fintamath/numbers/INumber.hpp" | ||
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| namespace fintamath { | ||
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| class Integer; | ||
| class Rational; | ||
| class Real; | ||
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| class Root : public IFunctionCRTP<INumber, Root, INumber, INumber> { | ||
| public: | ||
| Root() = default; | ||
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| std::string toString() const override { | ||
| return "root"; | ||
| } | ||
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| protected: | ||
| std::unique_ptr<IMathObject> call(const ArgumentsRefVector &argsVect) const override; | ||
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| private: | ||
| static std::unique_ptr<IMathObject> rootSimpl(const Integer &lhs, const Integer &rhs); | ||
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| static std::unique_ptr<IMathObject> rootSimpl(const Rational &lhs, const Integer &rhs); | ||
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| static std::unique_ptr<IMathObject> rootSimpl(const Real &lhs, const Integer &rhs); | ||
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| static std::map<Integer, Integer> roots(const Integer &lhs, const Integer &rhs); | ||
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| static std::unique_ptr<IMathObject> perfectRoot(const Integer &lhs, const Integer &rhs); | ||
| }; | ||
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| } |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,145 @@ | ||
| #include "fintamath/functions/powers/Root.hpp" | ||
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| #include "fintamath/functions/arithmetic/Add.hpp" | ||
| #include "fintamath/functions/arithmetic/Div.hpp" | ||
| #include "fintamath/functions/arithmetic/Mul.hpp" | ||
| #include "fintamath/functions/powers/Pow.hpp" | ||
| #include "fintamath/numbers/Integer.hpp" | ||
| #include "fintamath/numbers/IntegerFunctions.hpp" | ||
| #include "fintamath/numbers/Rational.hpp" | ||
| #include "fintamath/numbers/Real.hpp" | ||
| #include "fintamath/numbers/RealFunctions.hpp" | ||
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| namespace fintamath { | ||
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| std::unique_ptr<IMathObject> Root::call(const ArgumentsRefVector &argsVect) const { | ||
| static const auto multiRoot = [] { | ||
| static MultiMethod<std::unique_ptr<IMathObject>(const INumber &, const INumber &)> outMultiRoot; | ||
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| outMultiRoot.add<Integer, Integer>([](const Integer &lhs, const Integer &rhs) { | ||
| return rootSimpl(lhs, rhs); | ||
| }); | ||
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| outMultiRoot.add<Rational, Integer>([](const Rational &lhs, const Integer &rhs) { | ||
| return rootSimpl(lhs, rhs); | ||
| }); | ||
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| outMultiRoot.add<Real, Integer>([](const Real &lhs, const Integer &rhs) { | ||
| return rootSimpl(lhs, rhs); | ||
| }); | ||
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| return outMultiRoot; | ||
| }(); | ||
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| const auto &lhs = cast<INumber>(argsVect.front().get()); | ||
| const auto &rhs = cast<INumber>(argsVect.back().get()); | ||
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| if (lhs == Integer(1)) { | ||
| return lhs.clone(); | ||
| } | ||
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| if (const auto *rhsIntPtr = cast<Integer>(&rhs)) { | ||
| const auto &rhsInt = *rhsIntPtr; | ||
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| if (rhsInt > Integer(1)) { | ||
| // TODO: cast to Complex, when it is implemented | ||
| if (lhs < Integer(0)) { | ||
| throw UndefinedFunctionException(toString(), {lhs.toString(), rhs.toString()}); | ||
| } | ||
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| return multiRoot(lhs, rhsInt); | ||
| } | ||
| } | ||
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| return Pow()(lhs, *(Rational(1) / rhs)); | ||
| } | ||
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| std::unique_ptr<IMathObject> Root::rootSimpl(const Integer &lhs, const Integer &rhs) { | ||
| if (auto res = perfectRoot(lhs, rhs)) { | ||
| return res; | ||
| } | ||
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| ArgumentsPtrVector mulChildren; | ||
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| std::map<Integer, Integer> rootFactors = roots(lhs, rhs); | ||
| auto rootFactorIter = rootFactors.begin(); | ||
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| if (rootFactorIter->first == 1) { | ||
| if (rootFactorIter->second != 1) { | ||
| mulChildren.emplace_back(rootFactorIter->second.clone()); | ||
| } | ||
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| rootFactorIter++; | ||
| } | ||
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| for (; rootFactorIter != rootFactors.end(); rootFactorIter++) { | ||
| Integer root = rootFactorIter->first; | ||
| Integer factor = rootFactorIter->second; | ||
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| if (factor != 1) { | ||
| mulChildren.emplace_back(makeExpr(Root(), factor, root)); | ||
| } | ||
| } | ||
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| if (mulChildren.size() == 1) { | ||
| return mulChildren.front()->clone(); | ||
| } | ||
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| return makeExpr(Mul(), mulChildren); | ||
| } | ||
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| std::map<Integer, Integer> Root::roots(const Integer &lhs, const Integer &rhs) { | ||
| static Integer factorLimit = pow(Integer(2), 15); | ||
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| std::map<Integer, Integer> rootFactors{{1, 1}}; | ||
| std::map<Integer, Integer> factorRates = factors(lhs, factorLimit); | ||
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| for (const auto &factorRate : factorRates) { | ||
| Rational power(factorRate.second, rhs); | ||
| Integer factor = factorRate.first; | ||
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| if (power.denominator() == 1) { | ||
| rootFactors[1] *= pow(factor, power.numerator()); | ||
| continue; | ||
| } | ||
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| if (power.numerator() > power.denominator()) { | ||
| rootFactors[1] *= pow(factor, power.numerator() / power.denominator()); | ||
| } | ||
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| factor = pow(factor, power.numerator() % power.denominator()); | ||
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| if (auto rootIter = rootFactors.find(power.denominator()); rootIter != rootFactors.end()) { | ||
| rootIter->second *= factor; | ||
| } | ||
| else { | ||
| rootFactors.insert({power.denominator(), factor}); | ||
| } | ||
| } | ||
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| return rootFactors; | ||
| } | ||
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| std::unique_ptr<IMathObject> Root::perfectRoot(const Integer &lhs, const Integer &rhs) { | ||
| if (rhs == 2) { // TODO: implement perfect nth-roots minimization | ||
| Integer remainder; | ||
| Integer lhsSqrt = sqrt(lhs, remainder); | ||
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| if (remainder == 0) { | ||
| return lhsSqrt.clone(); | ||
| } | ||
| } | ||
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| return {}; | ||
| } | ||
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| std::unique_ptr<IMathObject> Root::rootSimpl(const Rational &lhs, const Integer &rhs) { | ||
| return makeExpr(Div(), makeExpr(Root(), lhs.numerator(), rhs), makeExpr(Root(), lhs.denominator(), rhs)) | ||
| ->toMinimalObject(); | ||
| } | ||
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| std::unique_ptr<IMathObject> Root::rootSimpl(const Real &lhs, const Integer &rhs) { | ||
| return Pow()(lhs, 1 / Rational(rhs)); | ||
| } | ||
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| } |
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