ClickHouse/dbms/include/DB/Functions/FunctionsArithmetic.h

#pragma once

#include <DB/DataTypes/DataTypesNumberFixed.h>
#include <DB/DataTypes/DataTypeDate.h>
#include <DB/DataTypes/DataTypeDateTime.h>
#include <DB/Functions/IFunction.h>
#include <DB/Functions/NumberTraits.h>
#include <DB/Functions/AccurateComparison.h>
#include <DB/Core/FieldVisitors.h>


namespace DB
{

namespace ErrorCodes
{
	extern const int ILLEGAL_DIVISION;
}


/** Арифметические функции: +, -, *, /, %,
  * intDiv (целочисленное деление), унарный минус.
  * Битовые функции: |, &, ^, ~.
  */

template<typename A, typename B, typename Op, typename ResultType_ = typename Op::ResultType>
struct BinaryOperationImplBase
{
	using ResultType = ResultType_;

	static void vector_vector(const PaddedPODArray<A> & a, const PaddedPODArray<B> & b, PaddedPODArray<ResultType> & c)
	{
		size_t size = a.size();
		for (size_t i = 0; i < size; ++i)
			c[i] = Op::template apply<ResultType>(a[i], b[i]);
	}

	static void vector_constant(const PaddedPODArray<A> & a, B b, PaddedPODArray<ResultType> & c)
	{
		size_t size = a.size();
		for (size_t i = 0; i < size; ++i)
			c[i] = Op::template apply<ResultType>(a[i], b);
	}

	static void constant_vector(A a, const PaddedPODArray<B> & b, PaddedPODArray<ResultType> & c)
	{
		size_t size = b.size();
		for (size_t i = 0; i < size; ++i)
			c[i] = Op::template apply<ResultType>(a, b[i]);
	}

	static void constant_constant(A a, B b, ResultType & c)
	{
		c = Op::template apply<ResultType>(a, b);
	}
};

template<typename A, typename B, typename Op, typename ResultType = typename Op::ResultType>
struct BinaryOperationImpl : BinaryOperationImplBase<A, B, Op, ResultType>
{
};


template<typename A, typename Op>
struct UnaryOperationImpl
{
	using ResultType = typename Op::ResultType;

	static void vector(const PaddedPODArray<A> & a, PaddedPODArray<ResultType> & c)
	{
		size_t size = a.size();
		for (size_t i = 0; i < size; ++i)
			c[i] = Op::apply(a[i]);
	}

	static void constant(A a, ResultType & c)
	{
		c = Op::apply(a);
	}
};


template<typename A, typename B>
struct PlusImpl
{
	using ResultType = typename NumberTraits::ResultOfAdditionMultiplication<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		/// Далее везде, static_cast - чтобы не было неправильного результата в выражениях вида Int64 c = UInt32(a) * Int32(-1).
		return static_cast<Result>(a) + b;
	}
};


template<typename A, typename B>
struct MultiplyImpl
{
	using ResultType = typename NumberTraits::ResultOfAdditionMultiplication<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a) * b;
	}
};

template<typename A, typename B>
struct MinusImpl
{
	using ResultType = typename NumberTraits::ResultOfSubtraction<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a) - b;
	}
};

template<typename A, typename B>
struct DivideFloatingImpl
{
	using ResultType = typename NumberTraits::ResultOfFloatingPointDivision<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a) / b;
	}
};


#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-compare"

template <typename A, typename B>
inline void throwIfDivisionLeadsToFPE(A a, B b)
{
	/// Возможно, лучше вместо проверок использовать siglongjmp?

	if (unlikely(b == 0))
		throw Exception("Division by zero", ErrorCodes::ILLEGAL_DIVISION);

	/// http://avva.livejournal.com/2548306.html
	if (unlikely(std::is_signed<A>::value && std::is_signed<B>::value && a == std::numeric_limits<A>::min() && b == -1))
		throw Exception("Division of minimal signed number by minus one", ErrorCodes::ILLEGAL_DIVISION);
}

template <typename A, typename B>
inline bool divisionLeadsToFPE(A a, B b)
{
	/// Возможно, лучше вместо проверок использовать siglongjmp?

	if (unlikely(b == 0))
		return true;

	/// http://avva.livejournal.com/2548306.html
	if (unlikely(std::is_signed<A>::value && std::is_signed<B>::value && a == std::numeric_limits<A>::min() && b == -1))
		return true;

	return false;
}


#pragma GCC diagnostic pop


template<typename A, typename B>
struct DivideIntegralImpl
{
	using ResultType = typename NumberTraits::ResultOfIntegerDivision<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		throwIfDivisionLeadsToFPE(a, b);
		return a / b;
	}
};

template<typename A, typename B>
struct DivideIntegralOrZeroImpl
{
	using ResultType = typename NumberTraits::ResultOfIntegerDivision<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return unlikely(divisionLeadsToFPE(a, b)) ? 0 : a / b;
	}
};

template<typename A, typename B>
struct ModuloImpl
{
	using ResultType = typename NumberTraits::ResultOfModulo<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		throwIfDivisionLeadsToFPE(typename NumberTraits::ToInteger<A>::Type(a), typename NumberTraits::ToInteger<A>::Type(b));
		return typename NumberTraits::ToInteger<A>::Type(a)
			% typename NumberTraits::ToInteger<A>::Type(b);
	}
};

template<typename A, typename B>
struct BitAndImpl
{
	using ResultType = typename NumberTraits::ResultOfBit<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a)
			& static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct BitOrImpl
{
	using ResultType = typename NumberTraits::ResultOfBit<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a)
			| static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct BitXorImpl
{
	using ResultType = typename NumberTraits::ResultOfBit<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a)
			^ static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct BitShiftLeftImpl
{
	using ResultType = typename NumberTraits::ResultOfBit<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a)
			<< static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct BitShiftRightImpl
{
	using ResultType = typename NumberTraits::ResultOfBit<A, B>::Type;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a)
			>> static_cast<Result>(b);
	}
};


template<typename A, typename B>
struct LeastBaseImpl
{
	using ResultType = NumberTraits::ResultOfLeast<A, B>;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		/** gcc 4.9.2 успешно векторизует цикл из этой функции. */
		return static_cast<Result>(a) < static_cast<Result>(b) ? static_cast<Result>(a) : static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct LeastSpecialImpl
{
	using ResultType = std::make_signed_t<A>;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		static_assert(std::is_same<Result, ResultType>::value, "ResultType != Result");
		return accurate::lessOp(a, b) ? static_cast<Result>(a) : static_cast<Result>(b);
	}
};

template<typename A, typename B>
using LeastImpl = std::conditional_t<!NumberTraits::LeastGreatestSpecialCase<A, B>::value, LeastBaseImpl<A, B>, LeastSpecialImpl<A, B>>;


template<typename A, typename B>
struct GreatestBaseImpl
{
	using ResultType = NumberTraits::ResultOfGreatest<A, B>;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		return static_cast<Result>(a) > static_cast<Result>(b) ? static_cast<Result>(a) : static_cast<Result>(b);
	}
};

template<typename A, typename B>
struct GreatestSpecialImpl
{
	using ResultType = std::make_unsigned_t<A>;

	template <typename Result = ResultType>
	static inline Result apply(A a, B b)
	{
		static_assert(std::is_same<Result, ResultType>::value, "ResultType != Result");
		return accurate::greaterOp(a, b) ? static_cast<Result>(a) : static_cast<Result>(b);
	}
};

template<typename A, typename B>
using GreatestImpl = std::conditional_t<!NumberTraits::LeastGreatestSpecialCase<A, B>::value, GreatestBaseImpl<A, B>, GreatestSpecialImpl<A, B>>;


template<typename A>
struct NegateImpl
{
	using ResultType = typename NumberTraits::ResultOfNegate<A>::Type;

	static inline ResultType apply(A a)
	{
		return -static_cast<ResultType>(a);
	}
};

template<typename A>
struct BitNotImpl
{
	using ResultType = typename NumberTraits::ResultOfBitNot<A>::Type;

	static inline ResultType apply(A a)
	{
		return ~static_cast<ResultType>(a);
	}
};

template<typename A>
struct AbsImpl
{
	using ResultType = typename NumberTraits::ResultOfAbs<A>::Type;

	template<typename T = A>
	static inline ResultType apply(T a,
		typename std::enable_if<std::is_integral<T>::value && std::is_signed<T>::value, void>::type * = nullptr)
	{
		return a < 0 ? static_cast<ResultType>(~a) + 1 : a;
	}

	template<typename T = A>
	static inline ResultType apply(T a,
		typename std::enable_if<std::is_integral<T>::value && std::is_unsigned<T>::value, void>::type * = nullptr)
	{
		return static_cast<ResultType>(a);
	}

	template<typename T = A>
	static inline ResultType apply(T a, typename std::enable_if<std::is_floating_point<T>::value, void>::type * = nullptr)
	{
		return static_cast<ResultType>(std::abs(a));
	}
};

/// this one is just for convenience
template <bool B, typename T1, typename T2> using If = typename std::conditional<B, T1, T2>::type;
/// these ones for better semantics
template <typename T> using Then = T;
template <typename T> using Else = T;

/// Used to indicate undefined operation
struct InvalidType;

template <>
struct DataTypeFromFieldType<NumberTraits::Error>
{
	using Type = InvalidType;
};

template <typename DataType> struct IsIntegral { static constexpr auto value = false; };
template <> struct IsIntegral<DataTypeUInt8> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeUInt16> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeUInt32> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeUInt64> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeInt8> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeInt16> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeInt32> { static constexpr auto value = true; };
template <> struct IsIntegral<DataTypeInt64> { static constexpr auto value = true; };

template <typename DataType> struct IsFloating { static constexpr auto value = false; };
template <> struct IsFloating<DataTypeFloat32> { static constexpr auto value = true; };
template <> struct IsFloating<DataTypeFloat64> { static constexpr auto value = true; };

template <typename DataType> struct IsNumeric
{
	static constexpr auto value = IsIntegral<DataType>::value || IsFloating<DataType>::value;
};

template <typename DataType> struct IsDateOrDateTime { static constexpr auto value = false; };
template <> struct IsDateOrDateTime<DataTypeDate> { static constexpr auto value = true; };
template <> struct IsDateOrDateTime<DataTypeDateTime> { static constexpr auto value = true; };

/** Returns appropriate result type for binary operator on dates (or datetimes):
 *  Date + Integral -> Date
 *  Integral + Date -> Date
 *  Date - Date     -> Int32
 *  Date - Integral -> Date
 *  least(Date, Date) -> Date
 *  greatest(Date, Date) -> Date
 *  All other operations are not defined and return InvalidType, operations on
 *  distinct date types are also undefined (e.g. DataTypeDate - DataTypeDateTime) */
template <template <typename, typename> class Operation, typename LeftDataType, typename RightDataType>
struct DateBinaryOperationTraits
{
	using T0 = typename LeftDataType::FieldType;
	using T1 = typename RightDataType::FieldType;
	using Op = Operation<T0, T1>;

	using ResultDataType =
		If<std::is_same<Op, PlusImpl<T0, T1>>::value,
			Then<
				If<IsDateOrDateTime<LeftDataType>::value && IsIntegral<RightDataType>::value,
					Then<LeftDataType>,
					Else<
						If<IsIntegral<LeftDataType>::value && IsDateOrDateTime<RightDataType>::value,
							Then<RightDataType>,
							Else<InvalidType>
						>
					>
				>
			>,
			Else<
				If<std::is_same<Op, MinusImpl<T0, T1>>::value,
					Then<
						If<IsDateOrDateTime<LeftDataType>::value,
							Then<
								If<std::is_same<LeftDataType, RightDataType>::value,
									Then<DataTypeInt32>,
									Else<
										If<IsIntegral<RightDataType>::value,
											Then<LeftDataType>,
											Else<InvalidType>
										>
									>
								>
							>,
							Else<InvalidType>
						>
					>,
					Else<
						If<std::is_same<T0, T1>::value
							&& (std::is_same<Op, LeastImpl<T0, T1>>::value || std::is_same<Op, GreatestImpl<T0, T1>>::value),
							Then<LeftDataType>,
							Else<InvalidType>
						>
					>
				>
			>
		>;
};


/// Decides among date and numeric operations
template <template <typename, typename> class Operation, typename LeftDataType, typename RightDataType>
struct BinaryOperationTraits
{
	using ResultDataType =
		If<IsDateOrDateTime<LeftDataType>::value || IsDateOrDateTime<RightDataType>::value,
			Then<
				typename DateBinaryOperationTraits<
					Operation, LeftDataType, RightDataType
				>::ResultDataType
			>,
			Else<
				typename DataTypeFromFieldType<
					typename Operation<
						typename LeftDataType::FieldType,
						typename RightDataType::FieldType
					>::ResultType
				>::Type
			>
		>;
};


template <template <typename, typename> class Op, typename Name>
class FunctionBinaryArithmetic : public IFunction
{
public:
	static constexpr auto name = Name::name;
	static FunctionPtr create(const Context & context) { return std::make_shared<FunctionBinaryArithmetic>(); }

private:
	/// Overload for InvalidType
	template <typename ResultDataType,
			  typename std::enable_if<std::is_same<ResultDataType, InvalidType>::value>::type * = nullptr>
	bool checkRightTypeImpl(DataTypePtr & type_res) const
	{
		return false;
	}

	/// Overload for well-defined operations
	template <typename ResultDataType,
			  typename std::enable_if<!std::is_same<ResultDataType, InvalidType>::value>::type * = nullptr>
	bool checkRightTypeImpl(DataTypePtr & type_res) const
	{
		type_res = std::make_shared<ResultDataType>();
		return true;
	}

	template <typename LeftDataType, typename RightDataType>
	bool checkRightType(const DataTypes & arguments, DataTypePtr & type_res) const
	{
		using ResultDataType = typename BinaryOperationTraits<Op, LeftDataType, RightDataType>::ResultDataType;

		if (typeid_cast<const RightDataType *>(&*arguments[1]))
			return checkRightTypeImpl<ResultDataType>(type_res);

		return false;
	}

	template <typename T0>
	bool checkLeftType(const DataTypes & arguments, DataTypePtr & type_res) const
	{
		if (typeid_cast<const T0 *>(&*arguments[0]))
		{
			if (	checkRightType<T0, DataTypeDate>(arguments, type_res)
				||  checkRightType<T0, DataTypeDateTime>(arguments, type_res)
				||	checkRightType<T0, DataTypeUInt8>(arguments, type_res)
				||	checkRightType<T0, DataTypeUInt16>(arguments, type_res)
				||	checkRightType<T0, DataTypeUInt32>(arguments, type_res)
				||	checkRightType<T0, DataTypeUInt64>(arguments, type_res)
				||	checkRightType<T0, DataTypeInt8>(arguments, type_res)
				||	checkRightType<T0, DataTypeInt16>(arguments, type_res)
				||	checkRightType<T0, DataTypeInt32>(arguments, type_res)
				||	checkRightType<T0, DataTypeInt64>(arguments, type_res)
				||	checkRightType<T0, DataTypeFloat32>(arguments, type_res)
				||	checkRightType<T0, DataTypeFloat64>(arguments, type_res))
				return true;
			else
				throw Exception("Illegal type " + arguments[1]->getName() + " of second argument of function " + getName(),
					ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
		}
		return false;
	}

	/// Overload for date operations
	template <typename LeftDataType, typename RightDataType, typename ColumnType>
	bool executeRightType(Block & block, const ColumnNumbers & arguments, const size_t result, const ColumnType * col_left)
	{
		if (!typeid_cast<const RightDataType *>(block.safeGetByPosition(arguments[1]).type.get()))
			return false;

		using ResultDataType = typename BinaryOperationTraits<Op, LeftDataType, RightDataType>::ResultDataType;

		return executeRightTypeDispatch<LeftDataType, RightDataType, ResultDataType>(
			block, arguments, result, col_left);
	}

	/// Overload for InvalidType
	template <typename LeftDataType, typename RightDataType, typename ResultDataType, typename ColumnType,
			  typename std::enable_if<std::is_same<ResultDataType, InvalidType>::value>::type * = nullptr>
	bool executeRightTypeDispatch(Block & block, const ColumnNumbers & arguments, const size_t result,
								  const ColumnType * col_left)
	{
		throw Exception("Types " + TypeName<typename LeftDataType::FieldType>::get()
			+ " and " + TypeName<typename LeftDataType::FieldType>::get()
			+ " are incompatible for function " + getName() + " or not upscaleable to common type", ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
	}

	/// Overload for well-defined operations
	template <typename LeftDataType, typename RightDataType, typename ResultDataType, typename ColumnType,
			  typename std::enable_if<!std::is_same<ResultDataType, InvalidType>::value>::type * = nullptr>
	bool executeRightTypeDispatch(Block & block, const ColumnNumbers & arguments, const size_t result,
								  const ColumnType * col_left)
	{
		using T0 = typename LeftDataType::FieldType;
		using T1 = typename RightDataType::FieldType;
		using ResultType = typename ResultDataType::FieldType;

		return executeRightTypeImpl<T0, T1, ResultType>(block, arguments, result, col_left);
	}

	/// ColumnVector overload
	template <typename T0, typename T1, typename ResultType = typename Op<T0, T1>::ResultType>
	bool executeRightTypeImpl(Block & block, const ColumnNumbers & arguments, size_t result, const ColumnVector<T0> * col_left)
	{
		if (auto col_right = typeid_cast<const ColumnVector<T1> *>(block.safeGetByPosition(arguments[1]).column.get()))
		{
			auto col_res = std::make_shared<ColumnVector<ResultType>>();
			block.safeGetByPosition(result).column = col_res;

			auto & vec_res = col_res->getData();
			vec_res.resize(col_left->getData().size());
			BinaryOperationImpl<T0, T1, Op<T0, T1>, ResultType>::vector_vector(col_left->getData(), col_right->getData(), vec_res);

			return true;
		}
		else if (auto col_right = typeid_cast<const ColumnConst<T1> *>(block.safeGetByPosition(arguments[1]).column.get()))
		{
			auto col_res = std::make_shared<ColumnVector<ResultType>>();
			block.safeGetByPosition(result).column = col_res;

			auto & vec_res = col_res->getData();
			vec_res.resize(col_left->getData().size());
			BinaryOperationImpl<T0, T1, Op<T0, T1>, ResultType>::vector_constant(col_left->getData(), col_right->getData(), vec_res);

			return true;
		}

		throw Exception("Logical error: unexpected type of column", ErrorCodes::LOGICAL_ERROR);
	}

	/// ColumnConst overload
	template <typename T0, typename T1, typename ResultType = typename Op<T0, T1>::ResultType>
	bool executeRightTypeImpl(Block & block, const ColumnNumbers & arguments, size_t result, const ColumnConst<T0> * col_left)
	{
		if (auto col_right = typeid_cast<const ColumnVector<T1> *>(block.safeGetByPosition(arguments[1]).column.get()))
		{
			auto col_res = std::make_shared<ColumnVector<ResultType>>();
			block.safeGetByPosition(result).column = col_res;

			auto & vec_res = col_res->getData();
			vec_res.resize(col_left->size());
			BinaryOperationImpl<T0, T1, Op<T0, T1>, ResultType>::constant_vector(col_left->getData(), col_right->getData(), vec_res);

			return true;
		}
		else if (auto col_right = typeid_cast<const ColumnConst<T1> *>(block.safeGetByPosition(arguments[1]).column.get()))
		{
			ResultType res = 0;
			BinaryOperationImpl<T0, T1, Op<T0, T1>, ResultType>::constant_constant(col_left->getData(), col_right->getData(), res);

			auto col_res = std::make_shared<ColumnConst<ResultType>>(col_left->size(), res);
			block.safeGetByPosition(result).column = col_res;

			return true;
		}

		return false;
	}

	template <typename LeftDataType>
	bool executeLeftType(Block & block, const ColumnNumbers & arguments, const size_t result)
	{
		if (!typeid_cast<const LeftDataType *>(block.safeGetByPosition(arguments[0]).type.get()))
			return false;

		using T0 = typename LeftDataType::FieldType;

		if (	executeLeftTypeImpl<LeftDataType, ColumnVector<T0>>(block, arguments, result)
			||	executeLeftTypeImpl<LeftDataType, ColumnConst<T0>>(block, arguments, result))
			return true;

		return false;
	}

	template <typename LeftDataType, typename ColumnType>
	bool executeLeftTypeImpl(Block & block, const ColumnNumbers & arguments, const size_t result)
	{
		if (auto col_left = typeid_cast<const ColumnType *>(block.safeGetByPosition(arguments[0]).column.get()))
		{
			if (	executeRightType<LeftDataType, DataTypeDate>(block, arguments, result, col_left)
				||  executeRightType<LeftDataType, DataTypeDateTime>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeUInt8>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeUInt16>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeUInt32>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeUInt64>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeInt8>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeInt16>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeInt32>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeInt64>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeFloat32>(block, arguments, result, col_left)
				||	executeRightType<LeftDataType, DataTypeFloat64>(block, arguments, result, col_left))
				return true;
			else
				throw Exception("Illegal column " + block.safeGetByPosition(arguments[1]).column->getName()
					+ " of second argument of function " + getName(),
					ErrorCodes::ILLEGAL_COLUMN);
		}

		return false;
	}

public:
	/// Получить имя функции.
	String getName() const override
	{
		return name;
	}

	size_t getNumberOfArguments() const override { return 2; }

	/// Получить типы результата по типам аргументов. Если функция неприменима для данных аргументов - кинуть исключение.
	DataTypePtr getReturnTypeImpl(const DataTypes & arguments) const override
	{
		DataTypePtr type_res;

		if (!(	checkLeftType<DataTypeDate>(arguments, type_res)
			||	checkLeftType<DataTypeDateTime>(arguments, type_res)
			||	checkLeftType<DataTypeUInt8>(arguments, type_res)
			||	checkLeftType<DataTypeUInt16>(arguments, type_res)
			||	checkLeftType<DataTypeUInt32>(arguments, type_res)
			||	checkLeftType<DataTypeUInt64>(arguments, type_res)
			||	checkLeftType<DataTypeInt8>(arguments, type_res)
			||	checkLeftType<DataTypeInt16>(arguments, type_res)
			||	checkLeftType<DataTypeInt32>(arguments, type_res)
			||	checkLeftType<DataTypeInt64>(arguments, type_res)
			||	checkLeftType<DataTypeFloat32>(arguments, type_res)
			||	checkLeftType<DataTypeFloat64>(arguments, type_res)))
			throw Exception("Illegal type " + arguments[0]->getName() + " of first argument of function " + getName(),
				ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);

		return type_res;
	}

	/// Выполнить функцию над блоком.
	void executeImpl(Block & block, const ColumnNumbers & arguments, size_t result) override
	{
		if (!(  executeLeftType<DataTypeDate>(block, arguments, result)
			||  executeLeftType<DataTypeDateTime>(block, arguments, result)
			||  executeLeftType<DataTypeUInt8>(block, arguments, result)
			||	executeLeftType<DataTypeUInt16>(block, arguments, result)
			||	executeLeftType<DataTypeUInt32>(block, arguments, result)
			||	executeLeftType<DataTypeUInt64>(block, arguments, result)
			||	executeLeftType<DataTypeInt8>(block, arguments, result)
			||	executeLeftType<DataTypeInt16>(block, arguments, result)
			||	executeLeftType<DataTypeInt32>(block, arguments, result)
			||	executeLeftType<DataTypeInt64>(block, arguments, result)
			||	executeLeftType<DataTypeFloat32>(block, arguments, result)
			||	executeLeftType<DataTypeFloat64>(block, arguments, result)))
		   throw Exception("Illegal column " + block.safeGetByPosition(arguments[0]).column->getName()
				+ " of first argument of function " + getName(),
				ErrorCodes::ILLEGAL_COLUMN);
	}
};


template <typename FunctionName>
struct FunctionUnaryArithmeticMonotonicity;


template <template <typename> class Op, typename Name, bool is_injective>
class FunctionUnaryArithmetic : public IFunction
{
public:
	static constexpr auto name = Name::name;
	static FunctionPtr create(const Context & context) { return std::make_shared<FunctionUnaryArithmetic>(); }

private:
	template <typename T0>
	bool checkType(const DataTypes & arguments, DataTypePtr & result) const
	{
		if (typeid_cast<const T0 *>(&*arguments[0]))
		{
			result = std::make_shared<typename DataTypeFromFieldType<
				typename Op<typename T0::FieldType>::ResultType>::Type>();
			return true;
		}
		return false;
	}

	template <typename T0>
	bool executeType(Block & block, const ColumnNumbers & arguments, size_t result)
	{
		if (const ColumnVector<T0> * col = typeid_cast<const ColumnVector<T0> *>(block.safeGetByPosition(arguments[0]).column.get()))
		{
			using ResultType = typename Op<T0>::ResultType;

			std::shared_ptr<ColumnVector<ResultType>> col_res = std::make_shared<ColumnVector<ResultType>>();
			block.safeGetByPosition(result).column = col_res;

			typename ColumnVector<ResultType>::Container_t & vec_res = col_res->getData();
			vec_res.resize(col->getData().size());
			UnaryOperationImpl<T0, Op<T0> >::vector(col->getData(), vec_res);

			return true;
		}
		else if (const ColumnConst<T0> * col = typeid_cast<const ColumnConst<T0> *>(block.safeGetByPosition(arguments[0]).column.get()))
		{
			using ResultType = typename Op<T0>::ResultType;

			ResultType res = 0;
			UnaryOperationImpl<T0, Op<T0> >::constant(col->getData(), res);

			std::shared_ptr<ColumnConst<ResultType>> col_res = std::make_shared<ColumnConst<ResultType>>(col->size(), res);
			block.safeGetByPosition(result).column = col_res;

			return true;
		}

		return false;
	}

public:
	/// Получить имя функции.
	String getName() const override
	{
		return name;
	}

	size_t getNumberOfArguments() const override { return 1; }
	bool isInjective(const Block &) override { return is_injective; }

	/// Получить типы результата по типам аргументов. Если функция неприменима для данных аргументов - кинуть исключение.
	DataTypePtr getReturnTypeImpl(const DataTypes & arguments) const override
	{
		DataTypePtr result;

		if (!(	checkType<DataTypeUInt8>(arguments, result)
			||	checkType<DataTypeUInt16>(arguments, result)
			||	checkType<DataTypeUInt32>(arguments, result)
			||	checkType<DataTypeUInt64>(arguments, result)
			||	checkType<DataTypeInt8>(arguments, result)
			||	checkType<DataTypeInt16>(arguments, result)
			||	checkType<DataTypeInt32>(arguments, result)
			||	checkType<DataTypeInt64>(arguments, result)
			||	checkType<DataTypeFloat32>(arguments, result)
			||	checkType<DataTypeFloat64>(arguments, result)))
			throw Exception("Illegal type " + arguments[0]->getName() + " of argument of function " + getName(),
				ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);

		return result;
	}

	/// Выполнить функцию над блоком.
	void executeImpl(Block & block, const ColumnNumbers & arguments, size_t result) override
	{
		if (!(	executeType<UInt8>(block, arguments, result)
			||	executeType<UInt16>(block, arguments, result)
			||	executeType<UInt32>(block, arguments, result)
			||	executeType<UInt64>(block, arguments, result)
			||	executeType<Int8>(block, arguments, result)
			||	executeType<Int16>(block, arguments, result)
			||	executeType<Int32>(block, arguments, result)
			||	executeType<Int64>(block, arguments, result)
			||	executeType<Float32>(block, arguments, result)
			||	executeType<Float64>(block, arguments, result)))
		   throw Exception("Illegal column " + block.safeGetByPosition(arguments[0]).column->getName()
				+ " of argument of function " + getName(),
				ErrorCodes::ILLEGAL_COLUMN);
	}

	bool hasInformationAboutMonotonicity() const override
	{
		return FunctionUnaryArithmeticMonotonicity<Name>::has();
	}

	Monotonicity getMonotonicityForRange(const IDataType & type, const Field & left, const Field & right) const override
	{
		return FunctionUnaryArithmeticMonotonicity<Name>::get(left, right);
	}
};


struct NamePlus 			{ static constexpr auto name = "plus"; };
struct NameMinus 			{ static constexpr auto name = "minus"; };
struct NameMultiply 		{ static constexpr auto name = "multiply"; };
struct NameDivideFloating	{ static constexpr auto name = "divide"; };
struct NameDivideIntegral	{ static constexpr auto name = "intDiv"; };
struct NameDivideIntegralOrZero	{ static constexpr auto name = "intDivOrZero"; };
struct NameModulo			{ static constexpr auto name = "modulo"; };
struct NameNegate			{ static constexpr auto name = "negate"; };
struct NameAbs				{ static constexpr auto name = "abs"; };
struct NameBitAnd			{ static constexpr auto name = "bitAnd"; };
struct NameBitOr			{ static constexpr auto name = "bitOr"; };
struct NameBitXor			{ static constexpr auto name = "bitXor"; };
struct NameBitNot			{ static constexpr auto name = "bitNot"; };
struct NameBitShiftLeft		{ static constexpr auto name = "bitShiftLeft"; };
struct NameBitShiftRight	{ static constexpr auto name = "bitShiftRight"; };
struct NameLeast			{ static constexpr auto name = "least"; };
struct NameGreatest			{ static constexpr auto name = "greatest"; };

using FunctionPlus = FunctionBinaryArithmetic<PlusImpl, NamePlus>;
using FunctionMinus = FunctionBinaryArithmetic<MinusImpl, NameMinus>;
using FunctionMultiply = FunctionBinaryArithmetic<MultiplyImpl, NameMultiply>;
using FunctionDivideFloating = FunctionBinaryArithmetic<DivideFloatingImpl, NameDivideFloating>;
using FunctionDivideIntegral = FunctionBinaryArithmetic<DivideIntegralImpl, NameDivideIntegral>;
using FunctionDivideIntegralOrZero = FunctionBinaryArithmetic<DivideIntegralOrZeroImpl, NameDivideIntegralOrZero>;
using FunctionModulo = FunctionBinaryArithmetic<ModuloImpl, NameModulo>;
using FunctionNegate = FunctionUnaryArithmetic<NegateImpl, NameNegate, true>;
using FunctionAbs = FunctionUnaryArithmetic<AbsImpl, NameAbs, false>;
using FunctionBitAnd = FunctionBinaryArithmetic<BitAndImpl,	NameBitAnd>;
using FunctionBitOr = FunctionBinaryArithmetic<BitOrImpl, NameBitOr>;
using FunctionBitXor = FunctionBinaryArithmetic<BitXorImpl, NameBitXor>;
using FunctionBitNot = FunctionUnaryArithmetic<BitNotImpl, NameBitNot, true>;
using FunctionBitShiftLeft = FunctionBinaryArithmetic<BitShiftLeftImpl,	NameBitShiftLeft>;
using FunctionBitShiftRight = FunctionBinaryArithmetic<BitShiftRightImpl, NameBitShiftRight>;
using FunctionLeast = FunctionBinaryArithmetic<LeastImpl, NameLeast>;
using FunctionGreatest = FunctionBinaryArithmetic<GreatestImpl, NameGreatest>;

/// Свойства монотонности для некоторых функций.

template <> struct FunctionUnaryArithmeticMonotonicity<NameNegate>
{
	static bool has() { return true; }
	static IFunction::Monotonicity get(const Field & left, const Field & right)
	{
		return { true, false };
	}
};

template <> struct FunctionUnaryArithmeticMonotonicity<NameAbs>
{
	static bool has() { return true; }
	static IFunction::Monotonicity get(const Field & left, const Field & right)
	{
		Float64 left_float = left.isNull() ? -std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), left);
		Float64 right_float = right.isNull() ? std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), right);

		if ((left_float < 0 && right_float > 0) || (left_float > 0 && right_float < 0))
			return {};

		return { true, (left_float > 0) };
	}
};

template <> struct FunctionUnaryArithmeticMonotonicity<NameBitNot>
{
	static bool has() { return false; }
	static IFunction::Monotonicity get(const Field & left, const Field & right)
	{
		return {};
	}
};


/// Оптимизации для целочисленного деления на константу.

#if defined(__x86_64__)
	#define LIBDIVIDE_USE_SSE2 1
#endif

#include <libdivide.h>


template <typename A, typename B>
struct DivideIntegralByConstantImpl
	: BinaryOperationImplBase<A, B, DivideIntegralImpl<A, B>>
{
	using ResultType = typename DivideIntegralImpl<A, B>::ResultType;

	static void vector_constant(const PaddedPODArray<A> & a, B b, PaddedPODArray<ResultType> & c)
	{
		if (unlikely(b == 0))
			throw Exception("Division by zero", ErrorCodes::ILLEGAL_DIVISION);

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-compare"

		if (unlikely(std::is_signed<B>::value && b == -1))
		{
			size_t size = a.size();
			for (size_t i = 0; i < size; ++i)
				c[i] = -c[i];
			return;
		}

#pragma GCC diagnostic pop

		libdivide::divider<A> divider(b);

		size_t size = a.size();
		const A * a_pos = &a[0];
		const A * a_end = a_pos + size;
		ResultType * c_pos = &c[0];

#if defined(__x86_64__)
		static constexpr size_t values_per_sse_register = 16 / sizeof(A);
		const A * a_end_sse = a_pos + size / values_per_sse_register * values_per_sse_register;

		while (a_pos < a_end_sse)
		{
			_mm_storeu_si128(reinterpret_cast<__m128i *>(c_pos),
				_mm_loadu_si128(reinterpret_cast<const __m128i *>(a_pos)) / divider);

			a_pos += values_per_sse_register;
			c_pos += values_per_sse_register;
		}
#endif

		while (a_pos < a_end)
		{
			*c_pos = *a_pos / divider;
			++a_pos;
			++c_pos;
		}
	}
};

template <typename A, typename B>
struct ModuloByConstantImpl
	: BinaryOperationImplBase<A, B, ModuloImpl<A, B>>
{
	using ResultType = typename ModuloImpl<A, B>::ResultType;

	static void vector_constant(const PaddedPODArray<A> & a, B b, PaddedPODArray<ResultType> & c)
	{
		if (unlikely(b == 0))
			throw Exception("Division by zero", ErrorCodes::ILLEGAL_DIVISION);

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-compare"

		if (unlikely((std::is_signed<B>::value && b == -1) || b == 1))
		{
			size_t size = a.size();
			for (size_t i = 0; i < size; ++i)
				c[i] = 0;
			return;
		}

#pragma GCC diagnostic pop

		libdivide::divider<A> divider(b);

		/// Тут не удалось сделать так, чтобы SSE вариант из libdivide давал преимущество.
		size_t size = a.size();
		for (size_t i = 0; i < size; ++i)
			c[i] = a[i] - (a[i] / divider) * b;	/// NOTE: возможно, не сохраняется семантика деления с остатком отрицательных чисел.
	}
};


/** Прописаны специализации для деления чисел типа UInt64 и UInt32 на числа той же знаковости.
  * Можно дополнить до всех возможных комбинаций, но потребуется больше кода.
  */

template <> struct BinaryOperationImpl<UInt64, UInt8, 	DivideIntegralImpl<UInt64, UInt8>> 	: DivideIntegralByConstantImpl<UInt64, UInt8> {};
template <> struct BinaryOperationImpl<UInt64, UInt16,	DivideIntegralImpl<UInt64, UInt16>> : DivideIntegralByConstantImpl<UInt64, UInt16> {};
template <> struct BinaryOperationImpl<UInt64, UInt32, 	DivideIntegralImpl<UInt64, UInt32>> : DivideIntegralByConstantImpl<UInt64, UInt32> {};
template <> struct BinaryOperationImpl<UInt64, UInt64, 	DivideIntegralImpl<UInt64, UInt64>> : DivideIntegralByConstantImpl<UInt64, UInt64> {};

template <> struct BinaryOperationImpl<UInt32, UInt8, 	DivideIntegralImpl<UInt32, UInt8>> 	: DivideIntegralByConstantImpl<UInt32, UInt8> {};
template <> struct BinaryOperationImpl<UInt32, UInt16, 	DivideIntegralImpl<UInt32, UInt16>> : DivideIntegralByConstantImpl<UInt32, UInt16> {};
template <> struct BinaryOperationImpl<UInt32, UInt32, 	DivideIntegralImpl<UInt32, UInt32>> : DivideIntegralByConstantImpl<UInt32, UInt32> {};
template <> struct BinaryOperationImpl<UInt32, UInt64, 	DivideIntegralImpl<UInt32, UInt64>> : DivideIntegralByConstantImpl<UInt32, UInt64> {};

template <> struct BinaryOperationImpl<Int64, Int8, 	DivideIntegralImpl<Int64, Int8>> 	: DivideIntegralByConstantImpl<Int64, Int8> {};
template <> struct BinaryOperationImpl<Int64, Int16, 	DivideIntegralImpl<Int64, Int16>> 	: DivideIntegralByConstantImpl<Int64, Int16> {};
template <> struct BinaryOperationImpl<Int64, Int32, 	DivideIntegralImpl<Int64, Int32>> 	: DivideIntegralByConstantImpl<Int64, Int32> {};
template <> struct BinaryOperationImpl<Int64, Int64, 	DivideIntegralImpl<Int64, Int64>> 	: DivideIntegralByConstantImpl<Int64, Int64> {};

template <> struct BinaryOperationImpl<Int32, Int8, 	DivideIntegralImpl<Int32, Int8>> 	: DivideIntegralByConstantImpl<Int32, Int8> {};
template <> struct BinaryOperationImpl<Int32, Int16, 	DivideIntegralImpl<Int32, Int16>> 	: DivideIntegralByConstantImpl<Int32, Int16> {};
template <> struct BinaryOperationImpl<Int32, Int32, 	DivideIntegralImpl<Int32, Int32>> 	: DivideIntegralByConstantImpl<Int32, Int32> {};
template <> struct BinaryOperationImpl<Int32, Int64, 	DivideIntegralImpl<Int32, Int64>> 	: DivideIntegralByConstantImpl<Int32, Int64> {};


template <> struct BinaryOperationImpl<UInt64, UInt8, 	ModuloImpl<UInt64, UInt8>> 	: ModuloByConstantImpl<UInt64, UInt8> {};
template <> struct BinaryOperationImpl<UInt64, UInt16,	ModuloImpl<UInt64, UInt16>> : ModuloByConstantImpl<UInt64, UInt16> {};
template <> struct BinaryOperationImpl<UInt64, UInt32, 	ModuloImpl<UInt64, UInt32>> : ModuloByConstantImpl<UInt64, UInt32> {};
template <> struct BinaryOperationImpl<UInt64, UInt64, 	ModuloImpl<UInt64, UInt64>> : ModuloByConstantImpl<UInt64, UInt64> {};

template <> struct BinaryOperationImpl<UInt32, UInt8, 	ModuloImpl<UInt32, UInt8>> 	: ModuloByConstantImpl<UInt32, UInt8> {};
template <> struct BinaryOperationImpl<UInt32, UInt16, 	ModuloImpl<UInt32, UInt16>> : ModuloByConstantImpl<UInt32, UInt16> {};
template <> struct BinaryOperationImpl<UInt32, UInt32, 	ModuloImpl<UInt32, UInt32>> : ModuloByConstantImpl<UInt32, UInt32> {};
template <> struct BinaryOperationImpl<UInt32, UInt64, 	ModuloImpl<UInt32, UInt64>> : ModuloByConstantImpl<UInt32, UInt64> {};

template <> struct BinaryOperationImpl<Int64, Int8, 	ModuloImpl<Int64, Int8>> 	: ModuloByConstantImpl<Int64, Int8> {};
template <> struct BinaryOperationImpl<Int64, Int16, 	ModuloImpl<Int64, Int16>> 	: ModuloByConstantImpl<Int64, Int16> {};
template <> struct BinaryOperationImpl<Int64, Int32, 	ModuloImpl<Int64, Int32>> 	: ModuloByConstantImpl<Int64, Int32> {};
template <> struct BinaryOperationImpl<Int64, Int64, 	ModuloImpl<Int64, Int64>> 	: ModuloByConstantImpl<Int64, Int64> {};

template <> struct BinaryOperationImpl<Int32, Int8, 	ModuloImpl<Int32, Int8>> 	: ModuloByConstantImpl<Int32, Int8> {};
template <> struct BinaryOperationImpl<Int32, Int16, 	ModuloImpl<Int32, Int16>> 	: ModuloByConstantImpl<Int32, Int16> {};
template <> struct BinaryOperationImpl<Int32, Int32, 	ModuloImpl<Int32, Int32>> 	: ModuloByConstantImpl<Int32, Int32> {};
template <> struct BinaryOperationImpl<Int32, Int64, 	ModuloImpl<Int32, Int64>> 	: ModuloByConstantImpl<Int32, Int64> {};

}