ClickHouse/dbms/src/Storages/MergeTree/PKCondition.cpp

#include <DB/Storages/MergeTree/PKCondition.h>
#include <DB/Storages/MergeTree/BoolMask.h>
#include <DB/DataTypes/DataTypesNumber.h>
#include <DB/Interpreters/ExpressionAnalyzer.h>
#include <DB/Interpreters/ExpressionActions.h>
#include <DB/DataTypes/DataTypeEnum.h>
#include <DB/DataTypes/DataTypeDate.h>
#include <DB/DataTypes/DataTypeDateTime.h>
#include <DB/DataTypes/DataTypeString.h>
#include <DB/Columns/ColumnSet.h>
#include <DB/Columns/ColumnTuple.h>
#include <DB/Parsers/ASTSet.h>
#include <DB/Functions/FunctionFactory.h>
#include <DB/Functions/IFunction.h>
#include <DB/Core/FieldVisitors.h>
#include <DB/Interpreters/convertFieldToType.h>
#include <DB/Interpreters/Set.h>


namespace DB
{

String Range::toString() const
{
	std::stringstream str;

	if (!left_bounded)
		str << "(-inf, ";
	else
		str << (left_included ? '[' : '(') << applyVisitor(FieldVisitorToString(), left) << ", ";

	if (!right_bounded)
		str << "+inf)";
	else
		str << applyVisitor(FieldVisitorToString(), right) << (right_included ? ']' : ')');

	return str.str();
}


/// Example: for `Hello\_World% ...` string it returns `Hello_World`, and for `%test%` returns an empty string.
static String extractFixedPrefixFromLikePattern(const String & like_pattern)
{
	String fixed_prefix;

	const char * pos = like_pattern.data();
	const char * end = pos + like_pattern.size();
	while (pos < end)
	{
		switch (*pos)
		{
			case '%':
			case '_':
				return fixed_prefix;

			case '\\':
				++pos;
				if (pos == end)
					break;
			default:
				fixed_prefix += *pos;
				break;
		}

		++pos;
	}

	return fixed_prefix;
}


/** For a given string, get a minimum string that is strictly greater than all strings with this prefix,
  *  or return an empty string if there are no such strings.
  */
static String firstStringThatIsGreaterThanAllStringsWithPrefix(const String & prefix)
{
    /** Increment the last byte of the prefix by one. But if it is 255, then remove it and increase the previous one.
      * Example (for convenience, suppose that the maximum value of byte is `z`)
	  * abcx -> abcy
	  * abcz -> abd
	  * zzz -> empty string
	  * z -> empty string
	  */

	String res = prefix;

	while (!res.empty() && static_cast<UInt8>(res.back()) == 255)
		res.pop_back();

	if (res.empty())
		return res;

	res.back() = static_cast<char>(1 + static_cast<UInt8>(res.back()));
	return res;
}


/// A dictionary containing actions to the corresponding functions to turn them into `RPNElement`
const PKCondition::AtomMap PKCondition::atom_map
{
	{
		"notEquals",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_NOT_IN_RANGE;
			out.range = Range(value);
			return true;
		}
	},
	{
		"equals",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = Range(value);
			return true;
		}
	},
	{
		"less",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = Range::createRightBounded(value, false);
			return true;
		}
	},
	{
		"greater",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = Range::createLeftBounded(value, false);
			return true;
		}
	},
	{
		"lessOrEquals",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = Range::createRightBounded(value, true);
			return true;
		}
	},
	{
		"greaterOrEquals",
		[] (RPNElement & out, const Field & value, ASTPtr &)
		{
			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = Range::createLeftBounded(value, true);
			return true;
		}
	},
	{
		"in",
		[] (RPNElement & out, const Field &, ASTPtr & node)
		{
			out.function = RPNElement::FUNCTION_IN_SET;
			out.in_function = node;
			return true;
		}
	},
	{
		"notIn",
		[] (RPNElement & out, const Field &, ASTPtr & node)
		{
			out.function = RPNElement::FUNCTION_NOT_IN_SET;
			out.in_function = node;
			return true;
		}
	},
	{
		"like",
		[] (RPNElement & out, const Field & value, ASTPtr & node)
		{
			if (value.getType() != Field::Types::String)
				return false;

			String prefix = extractFixedPrefixFromLikePattern(value.get<const String &>());
			if (prefix.empty())
				return false;

			String right_bound = firstStringThatIsGreaterThanAllStringsWithPrefix(prefix);

			out.function = RPNElement::FUNCTION_IN_RANGE;
			out.range = !right_bound.empty()
				? Range(prefix, true, right_bound, false)
				: Range::createLeftBounded(prefix, true);

			return true;
		}
	}
};


inline bool Range::equals(const Field & lhs, const Field & rhs) { return applyVisitor(FieldVisitorAccurateEquals(), lhs, rhs); }
inline bool Range::less(const Field & lhs, const Field & rhs) { return applyVisitor(FieldVisitorAccurateLess(), lhs, rhs); }


/** Calculate expressions, that depend only on constants.
  * For index to work when something like "WHERE Date = toDate(now())" is written.
  */
Block PKCondition::getBlockWithConstants(
	const ASTPtr & query, const Context & context, const NamesAndTypesList & all_columns)
{
	Block result
	{
		{ std::make_shared<ColumnConstUInt8>(1, 0), std::make_shared<DataTypeUInt8>(), "_dummy" }
	};

	const auto expr_for_constant_folding = ExpressionAnalyzer{query, context, nullptr, all_columns}
		.getConstActions();

	expr_for_constant_folding->execute(result);

	return result;
}


PKCondition::PKCondition(ASTPtr & query, const Context & context, const NamesAndTypesList & all_columns,
						 const SortDescription & sort_descr_, const Block & pk_sample_block_)
	: sort_descr(sort_descr_), pk_sample_block(pk_sample_block_)
{
	for (size_t i = 0; i < sort_descr.size(); ++i)
	{
		std::string name = sort_descr[i].column_name;
		if (!pk_columns.count(name))
			pk_columns[name] = i;
	}

    /** Evaluation of expressions that depend only on constants.
      * For the index to be used, if it is written, for example `WHERE Date = toDate(now())`.
	  */
	Block block_with_constants = getBlockWithConstants(query, context, all_columns);

	/// Trasform WHERE section to Reverse Polish notation
	ASTSelectQuery & select = typeid_cast<ASTSelectQuery &>(*query);
	if (select.where_expression)
	{
		traverseAST(select.where_expression, context, block_with_constants);

		if (select.prewhere_expression)
		{
			traverseAST(select.prewhere_expression, context, block_with_constants);
			rpn.emplace_back(RPNElement::FUNCTION_AND);
		}
	}
	else if (select.prewhere_expression)
	{
		traverseAST(select.prewhere_expression, context, block_with_constants);
	}
	else
	{
		rpn.emplace_back(RPNElement::FUNCTION_UNKNOWN);
	}
}

bool PKCondition::addCondition(const String & column, const Range & range)
{
	if (!pk_columns.count(column))
		return false;
	rpn.emplace_back(RPNElement::FUNCTION_IN_RANGE, pk_columns[column], range);
	rpn.emplace_back(RPNElement::FUNCTION_AND);
	return true;
}

/** Computes value of constant expression and it data type.
  * Returns false, if expression isn't constant.
  */
static bool getConstant(const ASTPtr & expr, Block & block_with_constants, Field & out_value, DataTypePtr & out_type)
{
	String column_name = expr->getColumnName();

	if (const ASTLiteral * lit = typeid_cast<const ASTLiteral *>(expr.get()))
	{
		/// By default block_with_constants has only one column named "_dummy".
		/// If block contains only constants it's may not be preprocessed by
		//  ExpressionAnalyzer, so try to look up in the default column.
		if (!block_with_constants.has(column_name))
			column_name = "_dummy";

		/// Simple literal
		out_value = lit->value;
		out_type = block_with_constants.getByName(column_name).type;
		return true;
	}
	else if (block_with_constants.has(column_name) && block_with_constants.getByName(column_name).column->isConst())
	{
		/// An expression which is dependent on constants only
		const auto & expr_info = block_with_constants.getByName(column_name);
		out_value = (*expr_info.column)[0];
		out_type = expr_info.type;
		return true;
	}
	else
		return false;
}

void PKCondition::traverseAST(ASTPtr & node, const Context & context, Block & block_with_constants)
{
	RPNElement element;

	if (ASTFunction * func = typeid_cast<ASTFunction *>(&*node))
	{
		if (operatorFromAST(func, element))
		{
			auto & args = typeid_cast<ASTExpressionList &>(*func->arguments).children;
			for (size_t i = 0, size = args.size(); i < size; ++i)
			{
				traverseAST(args[i], context, block_with_constants);

                /** The first part of the condition is for the correct support of `and` and `or` functions of arbitrary arity
                  * - in this case `n - 1` elements are added (where `n` is the number of arguments).
				  */
				if (i != 0 || element.function == RPNElement::FUNCTION_NOT)
					rpn.push_back(element);
			}

			return;
		}
	}

	if (!atomFromAST(node, context, block_with_constants, element))
	{
		element.function = RPNElement::FUNCTION_UNKNOWN;
	}

	rpn.push_back(element);
}


bool PKCondition::isPrimaryKeyPossiblyWrappedByMonotonicFunctions(
	const ASTPtr & node,
	const Context & context,
	size_t & out_primary_key_column_num,
	DataTypePtr & out_primary_key_res_column_type,
	RPNElement::MonotonicFunctionsChain & out_functions_chain)
{
	std::vector<const ASTFunction *> chain_not_tested_for_monotonicity;
	DataTypePtr primary_key_column_type;

	if (!isPrimaryKeyPossiblyWrappedByMonotonicFunctionsImpl(node, out_primary_key_column_num, primary_key_column_type, chain_not_tested_for_monotonicity))
		return false;

	for (auto it = chain_not_tested_for_monotonicity.rbegin(); it != chain_not_tested_for_monotonicity.rend(); ++it)
	{
		FunctionPtr func = FunctionFactory::instance().tryGet((*it)->name, context);
		if (!func || !func->hasInformationAboutMonotonicity())
			return false;

		primary_key_column_type = func->getReturnType({primary_key_column_type});
		out_functions_chain.push_back(func);
	}

	out_primary_key_res_column_type = primary_key_column_type;

	return true;
}


bool PKCondition::isPrimaryKeyPossiblyWrappedByMonotonicFunctionsImpl(
	const ASTPtr & node,
	size_t & out_primary_key_column_num,
	DataTypePtr & out_primary_key_column_type,
	std::vector<const ASTFunction *> & out_functions_chain)
{
    /** By itself, the primary key column can be a functional expression. for example, `intHash32(UserID)`.
      * Therefore, use the full name of the expression for search.
	  */
	String name = node->getColumnName();

	auto it = pk_columns.find(name);
	if (pk_columns.end() != it)
	{
		out_primary_key_column_num = it->second;
		out_primary_key_column_type = pk_sample_block.getByName(name).type;
		return true;
	}

	if (const ASTFunction * func = typeid_cast<const ASTFunction *>(node.get()))
	{
		const auto & args = func->arguments->children;
		if (args.size() != 1)
			return false;

		out_functions_chain.push_back(func);

		if (!isPrimaryKeyPossiblyWrappedByMonotonicFunctionsImpl(args[0], out_primary_key_column_num, out_primary_key_column_type,
																 out_functions_chain))
			return false;

		return true;
	}

	return false;
}


static void castValueToType(const DataTypePtr & desired_type, Field & src_value, const DataTypePtr & src_type, const ASTPtr & node)
{
	if (desired_type->equals(*src_type))
		return;

	try
	{
		/// NOTE: We don't need accurate info about src_type at this moment
		src_value = convertFieldToType(src_value, *desired_type);
	}
	catch (...)
	{
		throw Exception("Primary key expression contains comparison between inconvertible types: " +
			desired_type->getName() + " and " + src_type->getName() +
			" inside " + DB::toString(node->range),
			ErrorCodes::BAD_TYPE_OF_FIELD);
	}
}


bool PKCondition::atomFromAST(ASTPtr & node, const Context & context, Block & block_with_constants, RPNElement & out)
{
    /** Functions < > = != <= >= in `notIn`, where one argument is a constant, and the other is one of columns of primary key,
      *  or itself, wrapped in a chain of possibly-monotone functions,
      *  or constant expression - number.
	  */
	Field const_value;
	DataTypePtr const_type;
	if (const ASTFunction * func = typeid_cast<const ASTFunction *>(node.get()))
	{
		const ASTs & args = typeid_cast<const ASTExpressionList &>(*func->arguments).children;

		if (args.size() != 2)
			return false;

		DataTypePtr key_expr_type;	/// Type of expression containing primary key column
		size_t key_arg_pos;			/// Position of argument with primary key column (non-const argument)
		size_t key_column_num;		/// Number of a primary key column (inside sort_descr array)
		RPNElement::MonotonicFunctionsChain chain;
		bool is_set_const = false;

		if (getConstant(args[1], block_with_constants, const_value, const_type)
			&& isPrimaryKeyPossiblyWrappedByMonotonicFunctions(args[0], context, key_column_num, key_expr_type, chain))
		{
			key_arg_pos = 0;
		}
		else if (getConstant(args[0], block_with_constants, const_value, const_type)
			&& isPrimaryKeyPossiblyWrappedByMonotonicFunctions(args[1], context, key_column_num, key_expr_type, chain))
		{
			key_arg_pos = 1;
		}
		else if (typeid_cast<const ASTSet *>(args[1].get())
			&& isPrimaryKeyPossiblyWrappedByMonotonicFunctions(args[0], context, key_column_num, key_expr_type, chain))
		{
			key_arg_pos = 0;
			is_set_const = true;
		}
		else
			return false;

		std::string func_name = func->name;

		/// Replace <const> <sign> <data> on to <data> <-sign> <const>
		if (key_arg_pos == 1)
		{
			if (func_name == "less")
				func_name = "greater";
			else if (func_name == "greater")
				func_name = "less";
			else if (func_name == "greaterOrEquals")
				func_name = "lessOrEquals";
			else if (func_name == "lessOrEquals")
				func_name = "greaterOrEquals";
			else if (func_name == "in" || func_name == "notIn" || func_name == "like")
			{
				/// "const IN data_column" doesn't make sense (unlike "data_column IN const")
				return false;
			}
		}

		out.key_column = key_column_num;
		out.monotonic_functions_chain = std::move(chain);

		const auto atom_it = atom_map.find(func_name);
		if (atom_it == std::end(atom_map))
			return false;

		if (!is_set_const) /// Set args are already casted inside Set::createFromAST
			castValueToType(key_expr_type, const_value, const_type, node);

		return atom_it->second(out, const_value, node);
	}
	else if (getConstant(node, block_with_constants, const_value, const_type))	/// For cases where it says, for example, `WHERE 0 AND something`
	{
		if (const_value.getType() == Field::Types::UInt64
			|| const_value.getType() == Field::Types::Int64
			|| const_value.getType() == Field::Types::Float64)
		{
            /// Zero in all types is represented in memory the same way as in UInt64.
			out.function = const_value.get<UInt64>()
				? RPNElement::ALWAYS_TRUE
				: RPNElement::ALWAYS_FALSE;

			return true;
		}
	}

	return false;
}

bool PKCondition::operatorFromAST(const ASTFunction * func, RPNElement & out)
{
    /// Functions AND, OR, NOT.
    /** Also a special function `indexHint` - works as if instead of calling a function there are just parentheses
      * (or, the same thing - calling the function `and` from one argument).
	  */
	const ASTs & args = typeid_cast<const ASTExpressionList &>(*func->arguments).children;

	if (func->name == "not")
	{
		if (args.size() != 1)
			return false;

		out.function = RPNElement::FUNCTION_NOT;
	}
	else
	{
		if (func->name == "and" || func->name == "indexHint")
			out.function = RPNElement::FUNCTION_AND;
		else if (func->name == "or")
			out.function = RPNElement::FUNCTION_OR;
		else
			return false;
	}

	return true;
}

String PKCondition::toString() const
{
	String res;
	for (size_t i = 0; i < rpn.size(); ++i)
	{
		if (i)
			res += ", ";
		res += rpn[i].toString();
	}
	return res;
}


static void applyFunction(
	FunctionPtr & func,
	const DataTypePtr & arg_type, const Field & arg_value,
	DataTypePtr & res_type, Field & res_value)
{
	res_type = func->getReturnType({arg_type});

	Block block
	{
		{ arg_type->createConstColumn(1, arg_value), arg_type, "x" },
		{ nullptr, res_type, "y" }
	};

	func->execute(block, {0}, 1);

	block.safeGetByPosition(1).column->get(0, res_value);
}


/** Index is the value of primary key every `index_granularity` rows.
  * This value is called a "mark". That is, the index consists of marks.
  *
  * The primary key is the tuple.
  * The data is sorted by primary key in the sense of lexicographic order over tuples.
  *
  * A pair of marks specifies a segment with respect to the order over the tuples.
  * Denote it like this: [ x1 y1 z1 .. x2 y2 z2 ],
  *  where x1 y1 z1 - tuple - value of primary key in left border of segment;
  *      x2 y2 z2 - tuple - value of primary key in right boundary of segment.
  * In this section there are data between these marks.
  *
  * Or, the last mark specifies the range open on the right: [ a b c .. + inf )
  *
  * The set of all possible tuples can be considered as an n-dimensional space, where n is the size of the tuple.
  * A range of tuples specifies some subset of this space.
  *
  * Parallelograms (you can also find the term "rail")
  *  will be the subrange of an n-dimensional space that is a direct product of one-dimensional ranges.
  * In this case, the one-dimensional range can be: a period, a segment, an interval, a half-interval, unlimited on the left, unlimited on the right ...
  *
  * The range of tuples can always be represented as a combination of parallelograms.
  * For example, the range [ x1 y1 .. x2 y2 ] given x1 != x2 is equal to the union of the following three parallelograms:
  * [x1]       x [y1 .. +inf)
  * (x1 .. x2) x (-inf .. +inf)
  * [x2]       x (-inf .. y2]
  *
  * Or, for example, the range [ x1 y1 .. +inf ] is equal to the union of the following two parallelograms:
  * [x1]         x [y1 .. +inf)
  * (x1 .. +inf) x (-inf .. +inf)
  * It's easy to see that this is a special case of the variant above.
  *
  * This is important because it is easy for us to check the feasibility of the condition over the parallelogram,
  *  and therefore, feasibility of condition on the range of tuples will be checked by feasibility of condition
  *  over at least one parallelogram from which this range consists.
  */

template <typename F>
static bool forAnyParallelogram(
	size_t key_size,
	const Field * key_left,
	const Field * key_right,
	bool left_bounded,
	bool right_bounded,
	std::vector<Range> & parallelogram,
	size_t prefix_size,
	F && callback)
{
	if (!left_bounded && !right_bounded)
		return callback(parallelogram);

	if (left_bounded && right_bounded)
	{
		/// Let's go through the matching elements of the key.
		while (prefix_size < key_size)
		{
			if (key_left[prefix_size] == key_right[prefix_size])
			{
                /// Point ranges.
				parallelogram[prefix_size] = Range(key_left[prefix_size]);
				++prefix_size;
			}
			else
				break;
		}
	}

	if (prefix_size == key_size)
		return callback(parallelogram);

	if (prefix_size + 1 == key_size)
	{
		if (left_bounded && right_bounded)
			parallelogram[prefix_size] = Range(key_left[prefix_size], true, key_right[prefix_size], true);
		else if (left_bounded)
			parallelogram[prefix_size] = Range::createLeftBounded(key_left[prefix_size], true);
		else if (right_bounded)
			parallelogram[prefix_size] = Range::createRightBounded(key_right[prefix_size], true);

		return callback(parallelogram);
	}

	/// (x1 .. x2) x (-inf .. +inf)

	if (left_bounded && right_bounded)
		parallelogram[prefix_size] = Range(key_left[prefix_size], false, key_right[prefix_size], false);
	else if (left_bounded)
		parallelogram[prefix_size] = Range::createLeftBounded(key_left[prefix_size], false);
	else if (right_bounded)
		parallelogram[prefix_size] = Range::createRightBounded(key_right[prefix_size], false);

	for (size_t i = prefix_size + 1; i < key_size; ++i)
		parallelogram[i] = Range();

	if (callback(parallelogram))
		return true;

	/// [x1]       x [y1 .. +inf)

	if (left_bounded)
	{
		parallelogram[prefix_size] = Range(key_left[prefix_size]);
		if (forAnyParallelogram(key_size, key_left, key_right, true, false, parallelogram, prefix_size + 1, callback))
			return true;
	}

	/// [x2]       x (-inf .. y2]

	if (right_bounded)
	{
		parallelogram[prefix_size] = Range(key_right[prefix_size]);
		if (forAnyParallelogram(key_size, key_left, key_right, false, true, parallelogram, prefix_size + 1, callback))
			return true;
	}

	return false;
}


bool PKCondition::mayBeTrueInRange(
	size_t used_key_size,
	const Field * left_pk,
	const Field * right_pk,
	const DataTypes & data_types,
	bool right_bounded) const
{
	std::vector<Range> key_ranges(used_key_size, Range());

/*	std::cerr << "Checking for: [";
	for (size_t i = 0; i != used_key_size; ++i)
		std::cerr << (i != 0 ? ", " : "") << applyVisitor(FieldVisitorToString(), left_pk[i]);
	std::cerr << " ... ";

	if (right_bounded)
	{
		for (size_t i = 0; i != used_key_size; ++i)
			std::cerr << (i != 0 ? ", " : "") << applyVisitor(FieldVisitorToString(), right_pk[i]);
		std::cerr << "]\n";
	}
	else
		std::cerr << "+inf)\n";*/

	return forAnyParallelogram(used_key_size, left_pk, right_pk, true, right_bounded, key_ranges, 0,
		[&] (const std::vector<Range> & key_ranges)
	{
		auto res = mayBeTrueInRangeImpl(key_ranges, data_types);

/*		std::cerr << "Parallelogram: ";
		for (size_t i = 0, size = key_ranges.size(); i != size; ++i)
			std::cerr << (i != 0 ? " x " : "") << key_ranges[i].toString();
		std::cerr << ": " << res << "\n";*/

		return res;
	});
}


bool PKCondition::mayBeTrueInRangeImpl(const std::vector<Range> & key_ranges, const DataTypes & data_types) const
{
	std::vector<BoolMask> rpn_stack;
	for (size_t i = 0; i < rpn.size(); ++i)
	{
		const auto & element = rpn[i];
		if (element.function == RPNElement::FUNCTION_UNKNOWN)
		{
			rpn_stack.emplace_back(true, true);
		}
		else if (element.function == RPNElement::FUNCTION_IN_RANGE
			|| element.function == RPNElement::FUNCTION_NOT_IN_RANGE
			|| element.function == RPNElement::FUNCTION_IN_SET
			|| element.function == RPNElement::FUNCTION_NOT_IN_SET)
		{
			const Range * key_range = &key_ranges[element.key_column];

            /// The case when the column is wrapped in a chain of possibly monotone functions.
			Range key_range_transformed;
			bool evaluation_is_not_possible = false;
			if (!element.monotonic_functions_chain.empty())
			{
				key_range_transformed = *key_range;
				DataTypePtr current_type = data_types[element.key_column];
				for (auto & func : element.monotonic_functions_chain)
				{
                    /// We check the monotonicity of each function on a specific range.
					IFunction::Monotonicity monotonicity = func->getMonotonicityForRange(
						*current_type.get(), key_range_transformed.left, key_range_transformed.right);

				/*	std::cerr << "Function " << func->getName() << " is " << (monotonicity.is_monotonic ? "" : "not ")
						<< "monotonic " << (monotonicity.is_monotonic ? (monotonicity.is_positive ? "(positive) " : "(negative) ") : "")
						<< "in range "
						<< "[" << applyVisitor(FieldVisitorToString(), key_range_transformed.left)
						<< ", " << applyVisitor(FieldVisitorToString(), key_range_transformed.right) << "]\n";*/

					if (!monotonicity.is_monotonic)
					{
						evaluation_is_not_possible = true;
						break;
					}

                    /// Compute the function.
					DataTypePtr new_type;
					if (!key_range_transformed.left.isNull())
						applyFunction(func, current_type, key_range_transformed.left, new_type, key_range_transformed.left);
					if (!key_range_transformed.right.isNull())
						applyFunction(func, current_type, key_range_transformed.right, new_type, key_range_transformed.right);

					if (!new_type)
					{
						evaluation_is_not_possible = true;
						break;
					}

					current_type.swap(new_type);

					if (!monotonicity.is_positive)
						key_range_transformed.swapLeftAndRight();
				}

				if (evaluation_is_not_possible)
				{
					rpn_stack.emplace_back(true, true);
					continue;
				}

				key_range = &key_range_transformed;
			}

			if (element.function == RPNElement::FUNCTION_IN_RANGE
				|| element.function == RPNElement::FUNCTION_NOT_IN_RANGE)
			{
				bool intersects = element.range.intersectsRange(*key_range);
				bool contains = element.range.containsRange(*key_range);

				rpn_stack.emplace_back(intersects, !contains);
				if (element.function == RPNElement::FUNCTION_NOT_IN_RANGE)
					rpn_stack.back() = !rpn_stack.back();
			}
			else	/// Set
			{
				auto in_func = typeid_cast<const ASTFunction *>(element.in_function.get());
				const ASTs & args = typeid_cast<const ASTExpressionList &>(*in_func->arguments).children;
				auto ast_set = typeid_cast<const ASTSet *>(args[1].get());
				if (in_func && ast_set)
				{
					rpn_stack.push_back(ast_set->set->mayBeTrueInRange(*key_range));
					if (element.function == RPNElement::FUNCTION_NOT_IN_SET)
						rpn_stack.back() = !rpn_stack.back();
				}
				else
				{
					throw Exception("Set for IN is not created yet!", ErrorCodes::LOGICAL_ERROR);
				}
			}
		}
		else if (element.function == RPNElement::FUNCTION_NOT)
		{
			rpn_stack.back() = !rpn_stack.back();
		}
		else if (element.function == RPNElement::FUNCTION_AND)
		{
			auto arg1 = rpn_stack.back();
			rpn_stack.pop_back();
			auto arg2 = rpn_stack.back();
			rpn_stack.back() = arg1 & arg2;
		}
		else if (element.function == RPNElement::FUNCTION_OR)
		{
			auto arg1 = rpn_stack.back();
			rpn_stack.pop_back();
			auto arg2 = rpn_stack.back();
			rpn_stack.back() = arg1 | arg2;
		}
		else if (element.function == RPNElement::ALWAYS_FALSE)
		{
			rpn_stack.emplace_back(false, true);
		}
		else if (element.function == RPNElement::ALWAYS_TRUE)
		{
			rpn_stack.emplace_back(true, false);
		}
		else
			throw Exception("Unexpected function type in PKCondition::RPNElement", ErrorCodes::LOGICAL_ERROR);
	}

	if (rpn_stack.size() != 1)
		throw Exception("Unexpected stack size in PkCondition::mayBeTrueInRange", ErrorCodes::LOGICAL_ERROR);

	return rpn_stack[0].can_be_true;
}


bool PKCondition::mayBeTrueInRange(
	size_t used_key_size, const Field * left_pk, const Field * right_pk, const DataTypes & data_types) const
{
	return mayBeTrueInRange(used_key_size, left_pk, right_pk, data_types, true);
}

bool PKCondition::mayBeTrueAfter(
	size_t used_key_size, const Field * left_pk, const DataTypes & data_types) const
{
	return mayBeTrueInRange(used_key_size, left_pk, nullptr, data_types, false);
}


static const ASTSet & inFunctionToSet(const ASTPtr & in_function)
{
	const auto & in_func = typeid_cast<const ASTFunction &>(*in_function);
	const auto & args = typeid_cast<const ASTExpressionList &>(*in_func.arguments).children;
	const auto & ast_set = typeid_cast<const ASTSet &>(*args[1]);
	return ast_set;
}

String PKCondition::RPNElement::toString() const
{
	auto print_wrapped_column = [this](std::ostringstream & ss)
	{
		for (auto it = monotonic_functions_chain.rbegin(); it != monotonic_functions_chain.rend(); ++it)
			ss << (*it)->getName() << "(";

		ss << "column " << key_column;

		for (auto it = monotonic_functions_chain.rbegin(); it != monotonic_functions_chain.rend(); ++it)
			ss << ")";
	};

	std::ostringstream ss;
	switch (function)
	{
		case FUNCTION_AND:
			return "and";
		case FUNCTION_OR:
			return "or";
		case FUNCTION_NOT:
			return "not";
		case FUNCTION_UNKNOWN:
			return "unknown";
		case FUNCTION_NOT_IN_SET:
		case FUNCTION_IN_SET:
		{
			ss << "(";
			print_wrapped_column(ss);
			ss << (function == FUNCTION_IN_SET ? " in " : " notIn ") << inFunctionToSet(in_function).set->describe();
			ss << ")";
			return ss.str();
		}
		case FUNCTION_IN_RANGE:
		case FUNCTION_NOT_IN_RANGE:
		{
			ss << "(";
			print_wrapped_column(ss);
			ss << (function == FUNCTION_NOT_IN_RANGE ? " not" : "") << " in " << range.toString();
			ss << ")";
			return ss.str();
		}
		case ALWAYS_FALSE:
			return "false";
		case ALWAYS_TRUE:
			return "true";
		default:
			throw Exception("Unknown function in RPNElement", ErrorCodes::LOGICAL_ERROR);
	}
}


bool PKCondition::alwaysUnknownOrTrue() const
{
	std::vector<UInt8> rpn_stack;

	for (const auto & element : rpn)
	{
		if (element.function == RPNElement::FUNCTION_UNKNOWN
			|| element.function == RPNElement::ALWAYS_TRUE)
		{
			rpn_stack.push_back(true);
		}
		else if (element.function == RPNElement::FUNCTION_NOT_IN_RANGE
			|| element.function == RPNElement::FUNCTION_IN_RANGE
			|| element.function == RPNElement::FUNCTION_IN_SET
			|| element.function == RPNElement::FUNCTION_NOT_IN_SET
			|| element.function == RPNElement::ALWAYS_FALSE)
		{
			rpn_stack.push_back(false);
		}
		else if (element.function == RPNElement::FUNCTION_NOT)
		{
		}
		else if (element.function == RPNElement::FUNCTION_AND)
		{
			auto arg1 = rpn_stack.back();
			rpn_stack.pop_back();
			auto arg2 = rpn_stack.back();
			rpn_stack.back() = arg1 & arg2;
		}
		else if (element.function == RPNElement::FUNCTION_OR)
		{
			auto arg1 = rpn_stack.back();
			rpn_stack.pop_back();
			auto arg2 = rpn_stack.back();
			rpn_stack.back() = arg1 | arg2;
		}
		else
			throw Exception("Unexpected function type in PKCondition::RPNElement", ErrorCodes::LOGICAL_ERROR);
	}

	return rpn_stack[0];
}


size_t PKCondition::getMaxKeyColumn() const
{
	size_t res = 0;
	for (const auto & element : rpn)
	{
		if (element.function == RPNElement::FUNCTION_NOT_IN_RANGE
			|| element.function == RPNElement::FUNCTION_IN_RANGE
			|| element.function == RPNElement::FUNCTION_IN_SET
			|| element.function == RPNElement::FUNCTION_NOT_IN_SET)
		{
			if (element.key_column > res)
				res = element.key_column;
		}
	}
	return res;
}


}