tahoma2d/toonz/sources/common/expressions/tgrammar.cpp

// TnzCore includes
#include "trandom.h"
#include "tutil.h"
#include "tconvert.h"

// TnzBase includes
#include "ttokenizer.h"
#include "tunit.h"
#include "tparser.h"
#include "tdoubleparam.h"
#include "tdoublekeyframe.h"

// STD includes
#include <map>
#include <math.h>
#include <functional>

// Qt includes
#include <QString>

#include "tgrammar.h"

const double PI = 4 * atan(1.0);
const double toDeg(double rad) { return rad * 180.0 / PI; }
const double toRad(double deg) { return deg / 180.0 * PI; }

namespace TSyntax
{

//===================================================================
//
// RandomManager
//
//   es. x = RandomManager::instance()->getValue(seed, frame);
//
//-------------------------------------------------------------------

class RandomSequence
{
	TRandom m_rnd;
	std::vector<double> m_values;

public:
	RandomSequence(UINT seed) : m_rnd(seed) {}
	double getValue(int i)
	{
		assert(i >= 0);
		if (i >= (int)m_values.size()) {
			m_values.reserve(i + 1);
			while (i >= (int)m_values.size())
				m_values.push_back(m_rnd.getDouble());
		}
		return m_values[i];
	}
};

//-------------------------------------------------------------------

class RandomManager
{ // singleton
	typedef std::map<UINT, RandomSequence *> Table;
	Table m_table;
	RandomManager() {}
public:
	~RandomManager()
	{
		for (Table::iterator i = m_table.begin(); i != m_table.end(); ++i)
			delete i->second;
	}
	static RandomManager *instance()
	{
		static RandomManager _instance;
		return &_instance;
	}

	RandomSequence *getSequence(UINT seed)
	{
		Table::iterator i = m_table.find(seed);
		if (i == m_table.end()) {
			RandomSequence *seq = new RandomSequence(seed);
			m_table[seed] = seq;
			return seq;
		} else
			return i->second;
	}

	double getValue(UINT seed, double t)
	{
		RandomSequence *seq = getSequence(seed);
		return seq->getValue(t > 0 ? tfloor(t) : 0);
	}
};

//===================================================================
// Calculator
//-------------------------------------------------------------------

Calculator::Calculator()
	: m_rootNode(0), m_param(0), m_unit(0)
{
}

//-------------------------------------------------------------------

Calculator::~Calculator()
{
	delete m_rootNode;
}

//-------------------------------------------------------------------

void Calculator::setRootNode(CalculatorNode *node)
{
	if (node != m_rootNode) {
		delete m_rootNode;
		m_rootNode = node;
	}
}

//===================================================================
// Nodes
//-------------------------------------------------------------------

template <class Op>
class Op0Node : public CalculatorNode
{
public:
	Op0Node(Calculator *calc)
		: CalculatorNode(calc) {}

	double compute(double vars[3]) const
	{
		Op op;
		return op();
	}
};

//-------------------------------------------------------------------

template <class Op>
class Op1Node : public CalculatorNode
{
protected:
	std::auto_ptr<CalculatorNode> m_a;

public:
	Op1Node(Calculator *calc, CalculatorNode *a)
		: CalculatorNode(calc), m_a(a) {}

	double compute(double vars[3]) const
	{
		Op op;
		return op(m_a->compute(vars));
	}

	void accept(CalculatorNodeVisitor &visitor) { m_a->accept(visitor); }
};

//-------------------------------------------------------------------

template <class Op>
class Op2Node : public CalculatorNode
{
protected:
	std::auto_ptr<CalculatorNode> m_a, m_b;

public:
	Op2Node(Calculator *calc, CalculatorNode *a, CalculatorNode *b)
		: CalculatorNode(calc), m_a(a), m_b(b) {}

	double compute(double vars[3]) const
	{
		Op op;
		return op(m_a->compute(vars), m_b->compute(vars));
	}

	void accept(CalculatorNodeVisitor &visitor)
	{
		m_a->accept(visitor), m_b->accept(visitor);
	}
};

//-------------------------------------------------------------------

template <class Op>
class Op3Node : public CalculatorNode
{
protected:
	std::auto_ptr<CalculatorNode> m_a, m_b, m_c;

public:
	Op3Node(Calculator *calc, CalculatorNode *a, CalculatorNode *b, CalculatorNode *c)
		: CalculatorNode(calc), m_a(a), m_b(b), m_c(c) {}

	double compute(double vars[3]) const
	{
		Op op;
		return op(m_a->compute(vars), m_b->compute(vars), m_c->compute(vars));
	}

	void accept(CalculatorNodeVisitor &visitor)
	{
		m_a->accept(visitor), m_b->accept(visitor), m_c->accept(visitor);
	}
};

//-------------------------------------------------------------------

class ChsNode : public CalculatorNode
{
	std::auto_ptr<CalculatorNode> m_a;

public:
	ChsNode(Calculator *calc, CalculatorNode *a) : CalculatorNode(calc), m_a(a) {}

	double compute(double vars[3]) const { return -m_a->compute(vars); }
	void accept(CalculatorNodeVisitor &visitor) { m_a->accept(visitor); }
};

//-------------------------------------------------------------------

class QuestionNode : public CalculatorNode
{
	std::auto_ptr<CalculatorNode> m_a, m_b, m_c;

public:
	QuestionNode(Calculator *calc, CalculatorNode *a, CalculatorNode *b, CalculatorNode *c)
		: CalculatorNode(calc), m_a(a), m_b(b), m_c(c) {}

	double compute(double vars[3]) const
	{
		return (m_a->compute(vars) != 0) ? m_b->compute(vars) : m_c->compute(vars);
	}

	void accept(CalculatorNodeVisitor &visitor)
	{
		m_a->accept(visitor), m_b->accept(visitor), m_c->accept(visitor);
	}
};

//-------------------------------------------------------------------

class NotNode : public CalculatorNode
{
	std::auto_ptr<CalculatorNode> m_a;

public:
	NotNode(Calculator *calc, CalculatorNode *a) : CalculatorNode(calc), m_a(a) {}

	double compute(double vars[3]) const { return m_a->compute(vars) == 0; }
	void accept(CalculatorNodeVisitor &visitor) { m_a->accept(visitor); }
};
//-------------------------------------------------------------------

class CycleNode : public CalculatorNode
{
	std::auto_ptr<CalculatorNode> m_a;

public:
	CycleNode(Calculator *calc, CalculatorNode *a) : CalculatorNode(calc), m_a(a) {}

	double compute(double vars[3]) const
	{
		struct locals {
			static inline double compute(const TDoubleParam &param, double f)
			{
				if (param.getKeyframeCount() >= 2 && f < param.keyframeIndexToFrame(0)) {
					TDoubleKeyframe kf = param.getKeyframe(0);
					if (kf.m_type == TDoubleKeyframe::Expression || kf.m_type == TDoubleKeyframe::SimilarShape)
						return param.getDefaultValue();
				}

				double value = param.getValue(f);
				return value;
			}
		};

		double delta = tmax(1.0, m_a->compute(vars));

		const TDoubleParam *ownerParam = getCalculator()->getOwnerParameter();
		if (!ownerParam)
			return 0;

		double value = locals::compute(*ownerParam, vars[FRAME] - 1 - delta);
		if (getCalculator()->getUnit())
			value = getCalculator()->getUnit()->convertTo(value);

		return value;
	}

	void accept(CalculatorNodeVisitor &visitor) { m_a->accept(visitor); }
};

//-------------------------------------------------------------------

class RandomNode : public CalculatorNode
{
	std::auto_ptr<CalculatorNode> m_seed, m_min, m_max, m_arg;

public:
	RandomNode(Calculator *calc) : CalculatorNode(calc), m_seed(0), m_min(0), m_max(0)
	{
		m_arg.reset(new VariableNode(calc, CalculatorNode::FRAME));
	}

	void setSeed(CalculatorNode *arg)
	{
		assert(m_seed.get() == 0);
		m_seed.reset(arg);
	}
	void setMax(CalculatorNode *arg)
	{
		assert(m_max.get() == 0);
		m_max.reset(arg);
	}
	void setMin(CalculatorNode *arg)
	{
		assert(m_min.get() == 0);
		m_min.reset(arg);
	}

	double compute(double vars[3]) const
	{
		double s = (m_seed.get() != 0) ? m_seed->compute(vars) : 0;
		double r = RandomManager::instance()->getValue(s, fabs(m_arg->compute(vars)));
		if (m_min.get() == 0)
			if (m_max.get() == 0)
				return r;
			else
				return m_max->compute(vars) * r;
		else
			return (1 - r) * m_min->compute(vars) + r * m_max->compute(vars);
	}

	void accept(CalculatorNodeVisitor &visitor)
	{
		m_arg->accept(visitor);
		if (m_seed.get())
			m_seed->accept(visitor);
		if (m_min.get())
			m_min->accept(visitor);
		if (m_max.get())
			m_max->accept(visitor);
	}
};

//===================================================================
// Patterns
//-------------------------------------------------------------------

CalculatorNode *Pattern::popNode(std::vector<CalculatorNode *> &stack) const
{
	CalculatorNode *node = stack.back();
	stack.pop_back();
	return node;
}

//===================================================================

class NumberPattern : public Pattern
{
public:
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getType() == Token::Number;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 1;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return Number;
	}
	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 1);
		assert(tokens[0].getType() == Token::Number);
		stack.push_back(new NumberNode(calc, tokens[0].getDoubleValue()));
	}
};

//-------------------------------------------------------------------

class ConstantPattern : public Pattern
{
	string m_constantName;
	double m_value;

public:
	ConstantPattern(string constantName, double value, string description = "")
		: m_constantName(constantName), m_value(value)
	{
		setDescription(description);
	}

	string getFirstKeyword() const { return m_constantName; }
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getText() == m_constantName;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 1;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return Constant;
	}

	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 1);
		stack.push_back(new NumberNode(calc, m_value));
	}
};

//-------------------------------------------------------------------

class VariablePattern : public Pattern
{
	string m_variableName;
	int m_varIdx;

public:
	VariablePattern(string variableName, int varIdx, string description = "")
		: m_variableName(variableName), m_varIdx(varIdx)
	{
		setDescription(description);
	}

	string getFirstKeyword() const { return m_variableName; }
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getText() == m_variableName;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 1;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return Variable;
	}

	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 1);
		assert(tokens[0].getText() == m_variableName);
		stack.push_back(new VariableNode(calc, m_varIdx));
	}
};

//-------------------------------------------------------------------

template <class Op>
class Op2Pattern : public Pattern
{
	string m_opName;
	int m_priority;

public:
	Op2Pattern(string opName, int priority)
		: m_opName(opName), m_priority(priority) {}
	int getPriority() const { return m_priority; }
	string getFirstKeyword() const { return m_opName; }
	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		return previousTokens.empty() || previousTokens.size() == 2;
	}
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 1 && token.getText() == m_opName;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 3;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 1 ? Operator : InternalError;
	}
	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 3);
		assert(tokens[1].getText() == m_opName);
		CalculatorNode *b = popNode(stack);
		CalculatorNode *a = popNode(stack);
		stack.push_back(new Op2Node<Op>(calc, a, b));
	}
};

//-------------------------------------------------------------------

class UnaryMinusPattern : public Pattern
{
public:
	UnaryMinusPattern() {}
	int getPriority() const { return 50; }
	string getFirstKeyword() const { return "-"; }

	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		return previousTokens.size() == 1;
	}
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getText() == "-";
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 2;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return Operator;
	}

	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 2);
		assert(tokens[0].getText() == "-");
		stack.push_back(new ChsNode(calc, popNode(stack)));
	}
};

//-------------------------------------------------------------------

class NotPattern : public Pattern
{
	string m_prefix;

public:
	NotPattern(string prefix, string description) : m_prefix(prefix)
	{
		setDescription(description);
	}
	int getPriority() const { return 5; }
	string getFirstKeyword() const { return m_prefix; }

	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		return previousTokens.size() == 1;
	}
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getText() == m_prefix;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 2;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return Operator;
	}
	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 2);
		assert(tokens[0].getText() == m_prefix);
		stack.push_back(new NotNode(calc, popNode(stack)));
	}
};

//-------------------------------------------------------------------

class QuestionTernaryPattern : public Pattern
{
public:
	QuestionTernaryPattern() {}
	int getPriority() const { return 5; }
	string getFirstKeyword() const { return "?"; }

	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		int i = (int)previousTokens.size();
		return i == 0 || i == 2 || i == 4;
	}
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		int i = (int)previousTokens.size();
		return i == 1 && token.getText() == "?" || i == 3 && token.getText() == ":";
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 5;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		int i = (int)previousTokens.size();
		return (i == 1 || i == 3) ? Operator : InternalError;
	}
	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		CalculatorNode *node1 = popNode(stack);
		CalculatorNode *node2 = popNode(stack);
		CalculatorNode *node3 = popNode(stack);
		stack.push_back(new QuestionNode(calc, node3, node2, node1));
	}
};
//-------------------------------------------------------------------

class BraketPattern : public Pattern
{
public:
	BraketPattern() {}
	int getPriority() const { return 5; }
	string getFirstKeyword() const { return "("; }

	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		return previousTokens.size() == 1;
	}
	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.empty() && token.getText() == "(" ||
			   previousTokens.size() == 2 && token.getText() == ")";
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() == 3;
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		return previousTokens.size() != 1 ? Parenthesis : InternalError;
	}
	void createNode(
		Calculator *calc,
		std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{
		assert(tokens.size() == 3);
		assert(tokens[0].getText() == "(");
		assert(tokens[2].getText() == ")");
	}
};

//-------------------------------------------------------------------

class FunctionPattern : public Pattern
{
protected:
	string m_functionName;
	bool m_implicitArgAllowed;
	// if m_implicitArgAllowed == true then the first argument is the frame number
	// e.g. f(5) means f(frame,5)
	// to use a different first argument (e.g. t*10) you have to write f(t*10;5)

	int m_minArgCount;
	std::vector<double> m_optionalArgDefaults;

public:
	FunctionPattern(string functionName, int minArgCount)
		: m_functionName(functionName), m_implicitArgAllowed(false), m_minArgCount(minArgCount)
	{
	}

	void allowImplicitArg(bool allowed) { m_implicitArgAllowed = allowed; }
	void addOptionalArg(double value) { m_optionalArgDefaults.push_back(value); }

	string getFirstKeyword() const { return m_functionName; }
	bool expressionExpected(const std::vector<Token> &previousTokens) const
	{
		int n = (int)previousTokens.size();
		return 2 <= n && (n & 1) == 0;
	}

	bool matchToken(const std::vector<Token> &previousTokens, const Token &token) const
	{
		int i = (int)previousTokens.size();
		string s = toLower(token.getText());
		if (i == 0)
			return s == toLower(m_functionName);
		else if (i == 1)
			return s == "(";
		else if ((i & 1) == 0)
			return true;
		else if (s == ",")
			return true;
		else if (s == ";")
			return i == 3 && m_implicitArgAllowed;
		else if (s == ")") {
			int n = (i - 1) / 2;
			if (previousTokens.size() > 3 && previousTokens[3].getText() == ";")
				n--;
			if (n < m_minArgCount || n > m_minArgCount + (int)m_optionalArgDefaults.size())
				return false;
			else
				return true;
		} else
			return false;
	}
	bool isFinished(const std::vector<Token> &previousTokens, const Token &token) const
	{
		if (previousTokens.empty())
			return false;
		return m_minArgCount == 0 && previousTokens.size() == 1 && token.getText() != "(" ||
			   previousTokens.back().getText() == ")";
	}
	TokenType getTokenType(const std::vector<Token> &previousTokens, const Token &token) const
	{
		int i = (int)previousTokens.size();
		if (i == 0)
			return Function;
		else if (i == 1 || token.getText() == ")")
			return Function;
		else if (i == 3)
			return token.getText() == ";" ? Comma : Comma;
		else if (i & 1)
			return Comma;
		else
			return InternalError;
	}

	void getArgs(
		std::vector<CalculatorNode *> &nodes,
		Calculator *calc, std::vector<CalculatorNode *> &stack,
		const std::vector<Token> &tokens) const
	{

		bool implicitArgUsed = m_implicitArgAllowed && tokens.size() > 3 && tokens[3].getText() == ";";

		// n = number of arguments to provide (mandatory + optional + implicit)
		int n = m_minArgCount + (int)m_optionalArgDefaults.size() + (m_implicitArgAllowed ? 1 : 0);

		// m = number of default arguments to assign (with their default value)
		int m = n - (tokens.size() - 2) / 2;
		if (m_implicitArgAllowed && !implicitArgUsed)
			m--;

		assert(m <= (int)m_optionalArgDefaults.size());
		if (m > (int)m_optionalArgDefaults.size())
			m = (int)m_optionalArgDefaults.size();

		nodes.resize(n);

		// fetch arguments from the stack
		int k = n - m;
		if (implicitArgUsed) {
			while (k > 0)
				nodes[--k] = popNode(stack);
		} else {
			while (k > 1)
				nodes[--k] = popNode(stack);
			nodes[0] = new VariableNode(calc, CalculatorNode::FRAME);
		}

		// add default values
		for (int i = 0; i < m; i++)
			nodes[n - m + i] = new NumberNode(calc, m_optionalArgDefaults[i]);
	}
};

//-------------------------------------------------------------------

template <class Function>
class F0Pattern : public FunctionPattern
{
public:
	F0Pattern(string functionName) : FunctionPattern(functionName, 0) {}
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		stack.push_back(new Op0Node<Function>(calc, m_functionName));
	}
};

//-------------------------------------------------------------------

template <class Function>
class F1Pattern : public FunctionPattern
{
public:
	F1Pattern(string functionName, string descr = "") : FunctionPattern(functionName, 1) { setDescription(descr); }
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		stack.push_back(new Op1Node<Function>(calc, popNode(stack)));
	}
};

//-------------------------------------------------------------------

template <class Function>
class F2Pattern : public FunctionPattern
{
public:
	F2Pattern(string functionName, string descr = "") : FunctionPattern(functionName, 2) { setDescription(descr); }
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		CalculatorNode *b = popNode(stack);
		CalculatorNode *a = popNode(stack);
		stack.push_back(new Op2Node<Function>(calc, a, b));
	}
};

//-------------------------------------------------------------------

template <class Function>
class F3Pattern : public FunctionPattern
{
public:
	F3Pattern(string functionName, string descr = "") : FunctionPattern(functionName, 3) { setDescription(descr); }
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		CalculatorNode *c = popNode(stack);
		CalculatorNode *b = popNode(stack);
		CalculatorNode *a = popNode(stack);
		stack.push_back(new Op3Node<Function>(calc, a, b, c));
	}
};

//-------------------------------------------------------------------

template <class Function>
class Fs2Pattern : public FunctionPattern
{
public:
	Fs2Pattern(string functionName, string description)
		: FunctionPattern(functionName, 1)
	{
		allowImplicitArg(true);
		setDescription(description);
	}
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{

		std::vector<CalculatorNode *> nodes;
		getArgs(nodes, calc, stack, tokens);
		stack.push_back(new Op2Node<Function>(calc, nodes[0], nodes[1]));
	}
};

//-------------------------------------------------------------------

template <class Function>
class Fs3Pattern : public FunctionPattern
{
public:
	Fs3Pattern(string functionName, double defVal, string descr)
		: FunctionPattern(functionName, 1)
	{
		allowImplicitArg(true);
		addOptionalArg(defVal);
		setDescription(descr);
	}
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{

		std::vector<CalculatorNode *> nodes;
		getArgs(nodes, calc, stack, tokens);
		stack.push_back(new Op3Node<Function>(calc, nodes[0], nodes[1], nodes[2]));
	}
};

//-------------------------------------------------------------------

class CyclePattern : public FunctionPattern
{
public:
	CyclePattern(string functionName) : FunctionPattern(functionName, 1)
	{
		setDescription("cycle(period)\nCycles the transitions of the period previous frames to the selected range");
	}
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		CalculatorNode *a = popNode(stack);
		stack.push_back(new CycleNode(calc, a));
	}
};

//-------------------------------------------------------------------

class RandomPattern : public FunctionPattern
{
	bool m_seed;

public:
	RandomPattern(string functionName, bool seed, string description)
		: FunctionPattern(functionName, seed ? 1 : 0), m_seed(seed)
	{
		allowImplicitArg(true);
		addOptionalArg(0);
		addOptionalArg(0);
		setDescription(description);
	}
	void createNode(Calculator *calc, std::vector<CalculatorNode *> &stack,
					const std::vector<Token> &tokens) const
	{
		int n = ((int)tokens.size() - 1) / 2;
		if (m_seed)
			n--;
		RandomNode *randomNode = new RandomNode(calc);
		if (n > 0) {
			randomNode->setMax(popNode(stack));
			if (n > 1)
				randomNode->setMin(popNode(stack));
		}
		if (m_seed)
			randomNode->setSeed(popNode(stack));
		stack.push_back(randomNode);
	}
};

//===================================================================

class PatternTable
{
	std::map<string, Pattern *> m_kTable;
	std::vector<Pattern *> m_uTable;
	Grammar::Position m_position;

public:
	PatternTable(Grammar::Position position) : m_position(position) {}

	~PatternTable()
	{
		for (std::map<string, Pattern *>::iterator
				 it = m_kTable.begin();
			 it != m_kTable.end(); ++it)
			delete it->second;
		for (std::vector<Pattern *>::iterator
				 it = m_uTable.begin();
			 it != m_uTable.end(); ++it)
			delete *it;
	}

	void addPattern(Pattern *pattern)
	{
		string keyword = pattern->getFirstKeyword();
		if (keyword != "") {
			// first keyword should be unique
			assert(m_kTable.count(keyword) == 0);
			m_kTable[keyword] = pattern;
		} else
			m_uTable.push_back(pattern);
	}

	const Pattern *getPattern(const Token &token) const
	{
		std::vector<Token> tokens;
		if (m_position == Grammar::ExpressionEnd)
			tokens.push_back(Token());
		if (token.getType() == Token::Punct || token.getType() == Token::Ident) {
			string keyword = token.getText();
			std::map<string, Pattern *>::const_iterator it = m_kTable.find(keyword);
			if (it != m_kTable.end()) {
				Pattern *pattern = it->second;
				if (pattern->matchToken(tokens, token)) {
					return pattern;
				}
			}
		}
		for (int i = 0; i < (int)m_uTable.size(); i++) {
			Pattern *pattern = m_uTable[i];
			if (pattern->matchToken(tokens, token)) {
				return pattern;
			}
		}
		return 0;
	}

	void getSuggestions(Grammar::Suggestions &suggestions) const
	{
		std::map<string, Pattern *>::const_iterator it;
		for (it = m_kTable.begin(); it != m_kTable.end(); ++it) {
			suggestions.push_back(std::make_pair(it->first, it->second->getDescription()));
		}
		for (int i = 0; i < (int)m_uTable.size(); i++) {
			std::vector<std::string> keywords;
			m_uTable[i]->getAcceptableKeywords(keywords);
			for (int j = 0; j < (int)keywords.size(); j++)
				suggestions.push_back(std::make_pair(keywords[j], m_uTable[i]->getDescription()));
		}
	}
};

//===================================================================
//
// funzioni trigonometriche, log, exp, ecc.
//
//-------------------------------------------------------------------

class Pow
{
public:
	double operator()(double x, double y) const { return pow(x, y); }
};
// class Mod   {public: double operator()(double x, double y) const {return (int)x % (int)y;} };
class Sin
{
public:
	double operator()(double x) const { return sin(toRad(x)); }
};
class Cos
{
public:
	double operator()(double x) const { return cos(toRad(x)); }
};
class Tan
{
public:
	double operator()(double x) const { return tan(toRad(x)); }
};
class Sinh
{
public:
	double operator()(double x) const { return sinh(toRad(x)); }
};
class Cosh
{
public:
	double operator()(double x) const { return cosh(toRad(x)); }
};
class Tanh
{
public:
	double operator()(double x) const { return tanh(toRad(x)); }
};
class Atan
{
public:
	double operator()(double x) const { return toDeg(atan(x)); }
};
class Atan2
{
public:
	double operator()(double x, double y) const { return toDeg(atan2(x, y)); }
};
class Log
{
public:
	double operator()(double x) const { return log(x); }
};
class Exp
{
public:
	double operator()(double x) const { return exp(x); }
};
class Floor
{
public:
	double operator()(double x) const { return tfloor(x); }
};
class Ceil
{
public:
	double operator()(double x) const { return tceil(x); }
};
class Round
{
public:
	double operator()(double x) const { return tround(x); }
};
class Abs
{
public:
	double operator()(double x) const { return fabs(x); }
};
class Sign
{
public:
	double operator()(double x) const { return x > 0 ? 1 : x < 0 ? -1 : 0; }
};
class Sqrt
{
public:
	double operator()(double x) const { return x >= 0.0 ? sqrt(x) : 0; }
};
class Sqr
{
public:
	double operator()(double x) const { return x * x; }
};
class Crop
{
public:
	double operator()(double x, double a, double b) const { return tcrop(x, a, b); }
};
class Step
{
public:
	double operator()(double x, double y) const { return x < y ? 0 : 1; }
};

class Mod
{
public:
	double operator()(double x, double y) const
	{
		if (y == 0.0)
			return 0;
		return x - y * floor(x / y);
	}
};

class Min
{
public:
	double operator()(double x, double y) const { return x < y ? x : y; }
};
class Max
{
public:
	double operator()(double x, double y) const { return x > y ? x : y; }
};

class Gt
{
public:
	double operator()(double x, double y) const { return x > y ? 1 : 0; }
};
class Ge
{
public:
	double operator()(double x, double y) const { return x >= y ? 1 : 0; }
};
class Lt
{
public:
	double operator()(double x, double y) const { return x < y ? 1 : 0; }
};
class Le
{
public:
	double operator()(double x, double y) const { return x <= y ? 1 : 0; }
};
class Ne
{
public:
	double operator()(double x, double y) const { return x != y ? 1 : 0; }
};
class Eq
{
public:
	double operator()(double x, double y) const { return x == y ? 1 : 0; }
};
class And
{
public:
	double operator()(double x, double y) const { return (x != 0) && (y != 0) ? 1 : 0; }
};
class Or
{
public:
	double operator()(double x, double y) const { return (x != 0) || (y != 0) ? 1 : 0; }
};
class Not
{
public:
	double operator()(double x) const { return x == 0; }
};

class Smoothstep
{
public:
	double operator()(double v, double min, double max) const
	{
		if (v <= min)
			return 0;
		else if (v >= max)
			return 1;
		double t = (v - min) / (max - min);
		return -2 * t * t * t + 3 * t * t;
	}
};
class Pulse
{
public:
	double operator()(double x, double x0, double length) const
	{
		// double length=5.0;
		double b = (.69315 * 4.0) / (length * length);
		x -= x0;
		return exp(-x * x * b);
	}
};
class Saw
{
public:
	double operator()(double x, double length, double height) const
	{
		if (length <= 0.0)
			return 0.0;
		if (height <= 0.0)
			height = length;
		double q = x / length;
		return height * (q - floor(q));
	}
};
class Wave
{
public:
	double operator()(double x, double length) const
	{
		if (length <= 0.0)
			return 0.0;
		return sin(x * 2 * PI / length);
	}
};

//===================================================================

class Grammar::Imp
{
public:
	PatternTable m_prePatterns, m_postPatterns;

	Imp()
		: m_prePatterns(Grammar::ExpressionStart), m_postPatterns(Grammar::ExpressionEnd)
	{
	}
	~Imp() {}
};

Grammar::Grammar()
	: m_imp(new Imp())
{
	addPattern(new NumberPattern());
	addPattern(new ConstantPattern("pi", PI, "3.14159265..."));
	addPattern(new VariablePattern("t", CalculatorNode::T, "ranges from 0.0 to 1.0 along the transition"));
	const string f_desc = "the current frame number";
	addPattern(new VariablePattern("f", CalculatorNode::FRAME, f_desc));
	addPattern(new VariablePattern("frame", CalculatorNode::FRAME, f_desc));
	const string r_desc = "the current frame number, relative to the transition";
	addPattern(new VariablePattern("r", CalculatorNode::RFRAME, r_desc));
	addPattern(new VariablePattern("rframe", CalculatorNode::RFRAME, r_desc));
	addPattern(new Op2Pattern<std::plus<double>>("+", 10));
	addPattern(new Op2Pattern<std::multiplies<double>>("*", 20));
	addPattern(new Op2Pattern<Pow>("^", 30));
	addPattern(new Op2Pattern<std::minus<double>>("-", 10));
	addPattern(new Op2Pattern<std::divides<double>>("/", 20));
	addPattern(new Op2Pattern<Mod>("%", 8));
	addPattern(new Op2Pattern<Gt>(">", 6));
	addPattern(new Op2Pattern<Ge>(">=", 6));
	addPattern(new Op2Pattern<Lt>("<", 6));
	addPattern(new Op2Pattern<Le>("<=", 6));
	addPattern(new Op2Pattern<Eq>("==", 6));
	addPattern(new Op2Pattern<Ne>("!=", 6));
	addPattern(new Op2Pattern<And>("&&", 3));
	addPattern(new Op2Pattern<Or>("||", 2));
	addPattern(new Op2Pattern<And>("and", 3));
	addPattern(new Op2Pattern<Or>("or", 2));
	addPattern(new NotPattern("!", "not"));
	addPattern(new NotPattern("not", ""));
	addPattern(new UnaryMinusPattern());
	addPattern(new BraketPattern());
	addPattern(new QuestionTernaryPattern());
	addPattern(new F1Pattern<Sin>("sin", "sin(degree)"));
	addPattern(new F1Pattern<Cos>("cos", "cos(degree)"));
	addPattern(new F1Pattern<Tan>("tan", "tan(degree)"));
	addPattern(new F1Pattern<Sinh>("sinh", "sinh(degree)\nHyperbolic sine"));
	addPattern(new F1Pattern<Cosh>("cosh", "cosh(degree)\nHyperbolic cosine"));
	addPattern(new F1Pattern<Tanh>("tanh", "tanh(degree)\nHyperbolic tangent"));
	addPattern(new F1Pattern<Atan>("atan", "atan(x)\nArctangent : the inverse of tan()"));
	addPattern(new F2Pattern<Atan2>("atan2", "atan2(y,x)\nThe counter-clockwise angle in degree between the x-axis and the point(x,y)"));
	addPattern(new F1Pattern<Log>("log", "log(x)\nThe natural logarithm of x (base e)"));
	addPattern(new F1Pattern<Exp>("exp", "exp(x)\nThe base-e exponential of x"));
	addPattern(new F1Pattern<Floor>("floor", "floor(x)\nThe greatest integer <= x"));
	const string ceil_desc = "The smallest integer >= x";
	addPattern(new F1Pattern<Ceil>("ceil", "ceil(x)\n" + ceil_desc));
	addPattern(new F1Pattern<Ceil>("ceiling", "ceiling(x)\n" + ceil_desc));
	addPattern(new F1Pattern<Round>("round", "round(x)\nThe integer nearest to x"));
	addPattern(new F1Pattern<Abs>("abs", "abs(x)\nThe absolute value of x"));
	addPattern(new F1Pattern<Sign>("sign", "sign(x)\n-1 if x<0, 1 if x>0 and 0 if x=0"));
	const string sqrt_desc = "Square root of x";
	addPattern(new F1Pattern<Sqrt>("sqrt", "sqrt(x)\n" + sqrt_desc));
	addPattern(new F1Pattern<Sqr>("sqr", "sqr(x)\n" + sqrt_desc));
	addPattern(new F3Pattern<Crop>("crop", "crop(x,a,b)\na if x<a, b if x>b, x if x in [a,b]"));
	addPattern(new F3Pattern<Crop>("clamp", "clamp(x,a,b)\na if x<a, b if x>b, x if x in [a,b]"));
	addPattern(new F2Pattern<Min>("min", "min(a,b)"));
	addPattern(new F2Pattern<Max>("max", "max(a,b)"));
	addPattern(new F2Pattern<Step>("step", "min(x,x0)\n0 if x<x0, 1 if x>=x0"));
	addPattern(new F3Pattern<Smoothstep>("smoothstep", "smoothstep(x,x0)\n0 if x<x0, 1 if x>=x0\nas step, but with smooth transition"));
	const string pulse_desc = "Generates a bump ranging from 0.0 to 1.0 set at position pos";
	addPattern(new Fs3Pattern<Pulse>("pulse", 0.5, "pulse(pos)\npulse(pos,length)\npulse(arg; pos)\npulse(arg;pos,length)\n" + pulse_desc));
	addPattern(new Fs3Pattern<Pulse>("bump", 0.5, "bump(pos)\nbump(pos,length)\nbump(arg; pos)\nbump(arg;pos,length)\n" + pulse_desc));
	const string saw_desc = "Generates a periodic sawtooth shaped curve";
	addPattern(new Fs3Pattern<Saw>("sawtooth", 0.0, "sawtooth(length)\nsawtooth(length, height)\nsawtooth(arg; length)\nsawtooth(arg; length, height)\n" + saw_desc));
	addPattern(new Fs3Pattern<Saw>("saw", 0.0, "saw(length)\nsaw(length, height)\nsaw(arg; length)\nsaw(arg; length, height)\n" + saw_desc));
	addPattern(new Fs2Pattern<Wave>("wave", "wave(_length)\nwave(_arg;_length)\nsame as sin(f*180/length)"));
	const string rnd_desc = "Generates random number between min and max";
	addPattern(new RandomPattern("random", false, "random = random(0,1)\nrandom(max) = random(0,max)\nrandom(min,max)\n" + rnd_desc));
	addPattern(new RandomPattern("rnd", false, "rnd = rnd(0,1)\nrnd(max) = rnd(0,max)\nrnd(min,max)\n" + rnd_desc));
	const string rnd_s_desc = rnd_desc + "; seed select different random sequences";
	addPattern(new RandomPattern("random_s", true, "random_s(seed) = random_s(seed, 0,1)\nrandom_s(seed,max) = random_s(seed, 0,max)\nrandom_s(seed,min,max)\n" + rnd_s_desc));
	addPattern(new RandomPattern("rnd_s", true, "rnd_s(seed) = rnd_s(seed, 0,1)\nrnd_s(seed,max) = rnd_s(seed, 0,max)\nrnd_s(seed,min,max)\n" + rnd_s_desc));

	addPattern(new CyclePattern("cycle"));
}

Grammar::~Grammar()
{
}

void Grammar::addPattern(Pattern *pattern)
{
	std::vector<Token> noTokens;
	if (pattern->expressionExpected(noTokens))
		m_imp->m_postPatterns.addPattern(pattern);
	else
		m_imp->m_prePatterns.addPattern(pattern);
}

const Pattern *Grammar::getPattern(Position position, const Token &token) const
{
	Pattern *pattern = 0;
	if (position == ExpressionStart)
		return m_imp->m_prePatterns.getPattern(token);
	else
		return m_imp->m_postPatterns.getPattern(token);
}

void Grammar::getSuggestions(Grammar::Suggestions &suggestions, Position position) const
{
	if (position == ExpressionStart)
		return m_imp->m_prePatterns.getSuggestions(suggestions);
	else
		return m_imp->m_postPatterns.getSuggestions(suggestions);
}

//===================================================================

} // namespace TSyntax