Optimise simplification rules (sort into bins).

4 files changed, 514 insertions, 394 deletions

diff --git a/libevmasm/ExpressionClasses.cpp b/libevmasm/ExpressionClasses.cpp
index fccac1b0..fc283b0b 100644
--- a/libevmasm/ExpressionClasses.cpp
+++ b/libevmasm/ExpressionClasses.cpp
@@ -29,6 +29,7 @@
 #include <boost/noncopyable.hpp>
 #include <libevmasm/Assembly.h>
 #include <libevmasm/CommonSubexpressionEliminator.h>
+#include <libevmasm/SimplificationRules.h>
 
 using namespace std;
 using namespace dev;
@@ -180,191 +181,6 @@ string ExpressionClasses::fullDAGToString(ExpressionClasses::Id _id) const
 	return str.str();
 }
 
-class Rules: public boost::noncopyable
-{
-public:
-	Rules();
-	void resetMatchGroups() { m_matchGroups.clear(); }
-	vector<pair<Pattern, function<Pattern()>>> const& rules() const { return m_rules; }
-
-private:
-	using Expression = ExpressionClasses::Expression;
-	map<unsigned, Expression const*> m_matchGroups;
-	vector<pair<Pattern, function<Pattern()>>> m_rules;
-};
-
-template <class S> S divWorkaround(S const& _a, S const& _b)
-{
-	return (S)(bigint(_a) / bigint(_b));
-}
-
-template <class S> S modWorkaround(S const& _a, S const& _b)
-{
-	return (S)(bigint(_a) % bigint(_b));
-}
-
-Rules::Rules()
-{
-	// Multiple occurences of one of these inside one rule must match the same equivalence class.
-	// Constants.
-	Pattern A(Push);
-	Pattern B(Push);
-	Pattern C(Push);
-	// Anything.
-	Pattern X;
-	Pattern Y;
-	Pattern Z;
-	A.setMatchGroup(1, m_matchGroups);
-	B.setMatchGroup(2, m_matchGroups);
-	C.setMatchGroup(3, m_matchGroups);
-	X.setMatchGroup(4, m_matchGroups);
-	Y.setMatchGroup(5, m_matchGroups);
-	Z.setMatchGroup(6, m_matchGroups);
-
-	m_rules = vector<pair<Pattern, function<Pattern()>>>{
-		// arithmetics on constants
-		{{Instruction::ADD, {A, B}}, [=]{ return A.d() + B.d(); }},
-		{{Instruction::MUL, {A, B}}, [=]{ return A.d() * B.d(); }},
-		{{Instruction::SUB, {A, B}}, [=]{ return A.d() - B.d(); }},
-		{{Instruction::DIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : divWorkaround(A.d(), B.d()); }},
-		{{Instruction::SDIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(divWorkaround(u2s(A.d()), u2s(B.d()))); }},
-		{{Instruction::MOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : modWorkaround(A.d(), B.d()); }},
-		{{Instruction::SMOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(modWorkaround(u2s(A.d()), u2s(B.d()))); }},
-		{{Instruction::EXP, {A, B}}, [=]{ return u256(boost::multiprecision::powm(bigint(A.d()), bigint(B.d()), bigint(1) << 256)); }},
-		{{Instruction::NOT, {A}}, [=]{ return ~A.d(); }},
-		{{Instruction::LT, {A, B}}, [=]() { return A.d() < B.d() ? u256(1) : 0; }},
-		{{Instruction::GT, {A, B}}, [=]() -> u256 { return A.d() > B.d() ? 1 : 0; }},
-		{{Instruction::SLT, {A, B}}, [=]() -> u256 { return u2s(A.d()) < u2s(B.d()) ? 1 : 0; }},
-		{{Instruction::SGT, {A, B}}, [=]() -> u256 { return u2s(A.d()) > u2s(B.d()) ? 1 : 0; }},
-		{{Instruction::EQ, {A, B}}, [=]() -> u256 { return A.d() == B.d() ? 1 : 0; }},
-		{{Instruction::ISZERO, {A}}, [=]() -> u256 { return A.d() == 0 ? 1 : 0; }},
-		{{Instruction::AND, {A, B}}, [=]{ return A.d() & B.d(); }},
-		{{Instruction::OR, {A, B}}, [=]{ return A.d() | B.d(); }},
-		{{Instruction::XOR, {A, B}}, [=]{ return A.d() ^ B.d(); }},
-		{{Instruction::BYTE, {A, B}}, [=]{ return A.d() >= 32 ? 0 : (B.d() >> unsigned(8 * (31 - A.d()))) & 0xff; }},
-		{{Instruction::ADDMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) + bigint(B.d())) % C.d()); }},
-		{{Instruction::MULMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) * bigint(B.d())) % C.d()); }},
-		{{Instruction::MULMOD, {A, B, C}}, [=]{ return A.d() * B.d(); }},
-		{{Instruction::SIGNEXTEND, {A, B}}, [=]() -> u256 {
-			if (A.d() >= 31)
-				return B.d();
-			unsigned testBit = unsigned(A.d()) * 8 + 7;
-			u256 mask = (u256(1) << testBit) - 1;
-			return u256(boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask);
-		}},
-
-		// invariants involving known constants
-		{{Instruction::ADD, {X, 0}}, [=]{ return X; }},
-		{{Instruction::SUB, {X, 0}}, [=]{ return X; }},
-		{{Instruction::MUL, {X, 1}}, [=]{ return X; }},
-		{{Instruction::DIV, {X, 1}}, [=]{ return X; }},
-		{{Instruction::SDIV, {X, 1}}, [=]{ return X; }},
-		{{Instruction::OR, {X, 0}}, [=]{ return X; }},
-		{{Instruction::XOR, {X, 0}}, [=]{ return X; }},
-		{{Instruction::AND, {X, ~u256(0)}}, [=]{ return X; }},
-		{{Instruction::AND, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::MUL, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::DIV, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::DIV, {0, X}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {0, X}}, [=]{ return u256(0); }},
-		{{Instruction::OR, {X, ~u256(0)}}, [=]{ return ~u256(0); }},
-		{{Instruction::EQ, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; } },
-		// operations involving an expression and itself
-		{{Instruction::AND, {X, X}}, [=]{ return X; }},
-		{{Instruction::OR, {X, X}}, [=]{ return X; }},
-		{{Instruction::XOR, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SUB, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::EQ, {X, X}}, [=]{ return u256(1); }},
-		{{Instruction::LT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SLT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::GT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SGT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {X, X}}, [=]{ return u256(0); }},
-
-		{{Instruction::NOT, {{Instruction::NOT, {X}}}}, [=]{ return X; }},
-		{{Instruction::XOR, {{{X}, {Instruction::XOR, {X, Y}}}}}, [=]{ return Y; }},
-		{{Instruction::OR, {{{X}, {Instruction::AND, {X, Y}}}}}, [=]{ return X; }},
-		{{Instruction::AND, {{{X}, {Instruction::OR, {X, Y}}}}}, [=]{ return X; }},
-		{{Instruction::AND, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return u256(0); }},
-		{{Instruction::OR, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return ~u256(0); }},
-	};
-	// Double negation of opcodes with binary result
-	for (auto const& op: vector<Instruction>{
-		Instruction::EQ,
-		Instruction::LT,
-		Instruction::SLT,
-		Instruction::GT,
-		Instruction::SGT
-	})
-		m_rules.push_back({
-			{Instruction::ISZERO, {{Instruction::ISZERO, {{op, {X, Y}}}}}},
-			[=]() -> Pattern { return {op, {X, Y}}; }
-		});
-	m_rules.push_back({
-		{Instruction::ISZERO, {{Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}}},
-		[=]() -> Pattern { return {Instruction::ISZERO, {X}}; }
-	});
-	m_rules.push_back({
-		{Instruction::ISZERO, {{Instruction::XOR, {X, Y}}}},
-		[=]() -> Pattern { return { Instruction::EQ, {X, Y} }; }
-	});
-	// Associative operations
-	for (auto const& opFun: vector<pair<Instruction,function<u256(u256 const&,u256 const&)>>>{
-		{Instruction::ADD, plus<u256>()},
-		{Instruction::MUL, multiplies<u256>()},
-		{Instruction::AND, bit_and<u256>()},
-		{Instruction::OR, bit_or<u256>()},
-		{Instruction::XOR, bit_xor<u256>()}
-	})
-	{
-		auto op = opFun.first;
-		auto fun = opFun.second;
-		// Moving constants to the outside, order matters here!
-		// we need actions that return expressions (or patterns?) here, and we need also reversed rules
-		// (X+A)+B -> X+(A+B)
-		m_rules += vector<pair<Pattern, function<Pattern()>>>{{
-			{op, {{op, {X, A}}, B}},
-			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
-		}, {
-		// X+(Y+A) -> (X+Y)+A
-			{op, {{op, {X, A}}, Y}},
-			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
-		}, {
-		// For now, we still need explicit commutativity for the inner pattern
-			{op, {{op, {A, X}}, B}},
-			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
-		}, {
-			{op, {{op, {A, X}}, Y}},
-			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
-		}};
-	}
-	// move constants across subtractions
-	m_rules += vector<pair<Pattern, function<Pattern()>>>{
-		{
-			// X - A -> X + (-A)
-			{Instruction::SUB, {X, A}},
-			[=]() -> Pattern { return {Instruction::ADD, {X, 0 - A.d()}}; }
-		}, {
-			// (X + A) - Y -> (X - Y) + A
-			{Instruction::SUB, {{Instruction::ADD, {X, A}}, Y}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
-		}, {
-			// (A + X) - Y -> (X - Y) + A
-			{Instruction::SUB, {{Instruction::ADD, {A, X}}, Y}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
-		}, {
-			// X - (Y + A) -> (X - Y) + (-A)
-			{Instruction::SUB, {X, {Instruction::ADD, {Y, A}}}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
-		}, {
-			// X - (A + Y) -> (X - Y) + (-A)
-			{Instruction::SUB, {X, {Instruction::ADD, {A, Y}}}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
-		}
-	};
-}
-
 ExpressionClasses::Id ExpressionClasses::tryToSimplify(Expression const& _expr, bool _secondRun)
 {
 	static Rules rules;
@@ -376,21 +192,17 @@ ExpressionClasses::Id ExpressionClasses::tryToSimplify(Expression const& _expr,
 	)
 		return -1;
 
-	for (auto const& rule: rules.rules())
+	if (auto match = rules.findFirstMatch(_expr, *this))
 	{
-		rules.resetMatchGroups();
-		if (rule.first.matches(_expr, *this))
-		{
-			// Debug info
-			//cout << "Simplifying " << *_expr.item << "(";
-			//for (Id arg: _expr.arguments)
-			//	cout << fullDAGToString(arg) << ", ";
-			//cout << ")" << endl;
-			//cout << "with rule " << rule.first.toString() << endl;
-			//ExpressionTemplate t(rule.second());
-			//cout << "to " << rule.second().toString() << endl;
-			return rebuildExpression(ExpressionTemplate(rule.second(), _expr.item->location()));
-		}
+		// Debug info
+		//cout << "Simplifying " << *_expr.item << "(";
+		//for (Id arg: _expr.arguments)
+		//	cout << fullDAGToString(arg) << ", ";
+		//cout << ")" << endl;
+		//cout << "with rule " << match->first.toString() << endl;
+		//ExpressionTemplate t(match->second());
+		//cout << "to " << match->second().toString() << endl;
+		return rebuildExpression(ExpressionTemplate(match->second(), _expr.item->location()));
 	}
 
 	if (!_secondRun && _expr.arguments.size() == 2 && SemanticInformation::isCommutativeOperation(*_expr.item))
@@ -413,131 +225,3 @@ ExpressionClasses::Id ExpressionClasses::rebuildExpression(ExpressionTemplate co
 		arguments.push_back(rebuildExpression(t));
 	return find(_template.item, arguments);
 }
-
-
-Pattern::Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments):
-	m_type(Operation),
-	m_instruction(_instruction),
-	m_arguments(_arguments)
-{
-}
-
-void Pattern::setMatchGroup(unsigned _group, map<unsigned, Expression const*>& _matchGroups)
-{
-	m_matchGroup = _group;
-	m_matchGroups = &_matchGroups;
-}
-
-bool Pattern::matches(Expression const& _expr, ExpressionClasses const& _classes) const
-{
-	if (!matchesBaseItem(_expr.item))
-		return false;
-	if (m_matchGroup)
-	{
-		if (!m_matchGroups->count(m_matchGroup))
-			(*m_matchGroups)[m_matchGroup] = &_expr;
-		else if ((*m_matchGroups)[m_matchGroup]->id != _expr.id)
-			return false;
-	}
-	assertThrow(m_arguments.size() == 0 || _expr.arguments.size() == m_arguments.size(), OptimizerException, "");
-	for (size_t i = 0; i < m_arguments.size(); ++i)
-		if (!m_arguments[i].matches(_classes.representative(_expr.arguments[i]), _classes))
-			return false;
-	return true;
-}
-
-AssemblyItem Pattern::toAssemblyItem(SourceLocation const& _location) const
-{
-	if (m_type == Operation)
-		return AssemblyItem(m_instruction, _location);
-	else
-		return AssemblyItem(m_type, data(), _location);
-}
-
-string Pattern::toString() const
-{
-	stringstream s;
-	switch (m_type)
-	{
-	case Operation:
-		s << instructionInfo(m_instruction).name;
-		break;
-	case Push:
-		s << "PUSH " << hex << data();
-		break;
-	case UndefinedItem:
-		s << "ANY";
-		break;
-	default:
-		s << "t=" << dec << m_type << " d=" << hex << data();
-		break;
-	}
-	if (!m_requireDataMatch)
-		s << " ~";
-	if (m_matchGroup)
-		s << "[" << dec << m_matchGroup << "]";
-	s << "(";
-	for (Pattern const& p: m_arguments)
-		s << p.toString() << ", ";
-	s << ")";
-	return s.str();
-}
-
-bool Pattern::matchesBaseItem(AssemblyItem const* _item) const
-{
-	if (m_type == UndefinedItem)
-		return true;
-	if (!_item)
-		return false;
-	if (m_type != _item->type())
-		return false;
-	else if (m_type == Operation)
-		return m_instruction == _item->instruction();
-	else if (m_requireDataMatch)
-		return data() == _item->data();
-	return true;
-}
-
-Pattern::Expression const& Pattern::matchGroupValue() const
-{
-	assertThrow(m_matchGroup > 0, OptimizerException, "");
-	assertThrow(!!m_matchGroups, OptimizerException, "");
-	assertThrow((*m_matchGroups)[m_matchGroup], OptimizerException, "");
-	return *(*m_matchGroups)[m_matchGroup];
-}
-
-u256 const& Pattern::data() const
-{
-	assertThrow(m_data, OptimizerException, "");
-	return *m_data;
-}
-
-ExpressionTemplate::ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location)
-{
-	if (_pattern.matchGroup())
-	{
-		hasId = true;
-		id = _pattern.id();
-	}
-	else
-	{
-		hasId = false;
-		item = _pattern.toAssemblyItem(_location);
-	}
-	for (auto const& arg: _pattern.arguments())
-		arguments.push_back(ExpressionTemplate(arg, _location));
-}
-
-string ExpressionTemplate::toString() const
-{
-	stringstream s;
-	if (hasId)
-		s << id;
-	else
-		s << item;
-	s << "(";
-	for (auto const& arg: arguments)
-		s << arg.toString();
-	s << ")";
-	return s.str();
-}
diff --git a/libevmasm/ExpressionClasses.h b/libevmasm/ExpressionClasses.h
index c91b227f..5d53b292 100644
--- a/libevmasm/ExpressionClasses.h
+++ b/libevmasm/ExpressionClasses.h
@@ -121,72 +121,5 @@ private:
 	std::vector<std::shared_ptr<AssemblyItem>> m_spareAssemblyItems;
 };
 
-/**
- * Pattern to match against an expression.
- * Also stores matched expressions to retrieve them later, for constructing new expressions using
- * ExpressionTemplate.
- */
-class Pattern
-{
-public:
-	using Expression = ExpressionClasses::Expression;
-	using Id = ExpressionClasses::Id;
-
-	// Matches a specific constant value.
-	Pattern(unsigned _value): Pattern(u256(_value)) {}
-	// Matches a specific constant value.
-	Pattern(u256 const& _value): m_type(Push), m_requireDataMatch(true), m_data(std::make_shared<u256>(_value)) {}
-	// Matches a specific assembly item type or anything if not given.
-	Pattern(AssemblyItemType _type = UndefinedItem): m_type(_type) {}
-	// Matches a given instruction with given arguments
-	Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments = {});
-	/// Sets this pattern to be part of the match group with the identifier @a _group.
-	/// Inside one rule, all patterns in the same match group have to match expressions from the
-	/// same expression equivalence class.
-	void setMatchGroup(unsigned _group, std::map<unsigned, Expression const*>& _matchGroups);
-	unsigned matchGroup() const { return m_matchGroup; }
-	bool matches(Expression const& _expr, ExpressionClasses const& _classes) const;
-
-	AssemblyItem toAssemblyItem(SourceLocation const& _location) const;
-	std::vector<Pattern> arguments() const { return m_arguments; }
-
-	/// @returns the id of the matched expression if this pattern is part of a match group.
-	Id id() const { return matchGroupValue().id; }
-	/// @returns the data of the matched expression if this pattern is part of a match group.
-	u256 const& d() const { return matchGroupValue().item->data(); }
-
-	std::string toString() const;
-
-private:
-	bool matchesBaseItem(AssemblyItem const* _item) const;
-	Expression const& matchGroupValue() const;
-	u256 const& data() const;
-
-	AssemblyItemType m_type;
-	bool m_requireDataMatch = false;
-	Instruction m_instruction; ///< Only valid if m_type is Operation
-	std::shared_ptr<u256> m_data; ///< Only valid if m_type is not Operation
-	std::vector<Pattern> m_arguments;
-	unsigned m_matchGroup = 0;
-	std::map<unsigned, Expression const*>* m_matchGroups = nullptr;
-};
-
-/**
- * Template for a new expression that can be built from matched patterns.
- */
-struct ExpressionTemplate
-{
-	using Expression = ExpressionClasses::Expression;
-	using Id = ExpressionClasses::Id;
-	explicit ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location);
-	std::string toString() const;
-	bool hasId = false;
-	/// Id of the matched expression, if available.
-	Id id = Id(-1);
-	// Otherwise, assembly item.
-	AssemblyItem item = UndefinedItem;
-	std::vector<ExpressionTemplate> arguments;
-};
-
 }
 }
diff --git a/libevmasm/SimplificationRules.cpp b/libevmasm/SimplificationRules.cpp
new file mode 100644
index 00000000..bb950400
--- /dev/null
+++ b/libevmasm/SimplificationRules.cpp
@@ -0,0 +1,363 @@
+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * @file ExpressionClasses.cpp
+ * @author Christian <c@ethdev.com>
+ * @date 2015
+ * Container for equivalence classes of expressions for use in common subexpression elimination.
+ */
+
+#include <libevmasm/ExpressionClasses.h>
+#include <utility>
+#include <tuple>
+#include <functional>
+#include <boost/range/adaptor/reversed.hpp>
+#include <boost/noncopyable.hpp>
+#include <libevmasm/Assembly.h>
+#include <libevmasm/CommonSubexpressionEliminator.h>
+#include <libevmasm/SimplificationRules.h>
+
+using namespace std;
+using namespace dev;
+using namespace dev::eth;
+
+
+pair<Pattern, function<Pattern()> > const* Rules::findFirstMatch(
+	Expression const& _expr,
+	ExpressionClasses const& _classes
+)
+{
+	resetMatchGroups();
+
+	assertThrow(_expr.item, OptimizerException, "");
+	for (auto const& rule: m_rules[byte(_expr.item->instruction())])
+	{
+		if (rule.first.matches(_expr, _classes))
+			return &rule;
+	}
+	return nullptr;
+}
+
+void Rules::addRules(std::vector<std::pair<Pattern, std::function<Pattern ()> > > const& _rules)
+{
+	for (auto const& r: _rules)
+		addRule(r);
+}
+
+void Rules::addRule(std::pair<Pattern, std::function<Pattern()> > const& _rule)
+{
+	m_rules[byte(_rule.first.instruction())].push_back(_rule);
+}
+
+template <class S> S divWorkaround(S const& _a, S const& _b)
+{
+	return (S)(bigint(_a) / bigint(_b));
+}
+
+template <class S> S modWorkaround(S const& _a, S const& _b)
+{
+	return (S)(bigint(_a) % bigint(_b));
+}
+
+Rules::Rules()
+{
+	// Multiple occurences of one of these inside one rule must match the same equivalence class.
+	// Constants.
+	Pattern A(Push);
+	Pattern B(Push);
+	Pattern C(Push);
+	// Anything.
+	Pattern X;
+	Pattern Y;
+	Pattern Z;
+	A.setMatchGroup(1, m_matchGroups);
+	B.setMatchGroup(2, m_matchGroups);
+	C.setMatchGroup(3, m_matchGroups);
+	X.setMatchGroup(4, m_matchGroups);
+	Y.setMatchGroup(5, m_matchGroups);
+	Z.setMatchGroup(6, m_matchGroups);
+
+	addRules(vector<pair<Pattern, function<Pattern()>>>{
+		// arithmetics on constants
+		{{Instruction::ADD, {A, B}}, [=]{ return A.d() + B.d(); }},
+		{{Instruction::MUL, {A, B}}, [=]{ return A.d() * B.d(); }},
+		{{Instruction::SUB, {A, B}}, [=]{ return A.d() - B.d(); }},
+		{{Instruction::DIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : divWorkaround(A.d(), B.d()); }},
+		{{Instruction::SDIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(divWorkaround(u2s(A.d()), u2s(B.d()))); }},
+		{{Instruction::MOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : modWorkaround(A.d(), B.d()); }},
+		{{Instruction::SMOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(modWorkaround(u2s(A.d()), u2s(B.d()))); }},
+		{{Instruction::EXP, {A, B}}, [=]{ return u256(boost::multiprecision::powm(bigint(A.d()), bigint(B.d()), bigint(1) << 256)); }},
+		{{Instruction::NOT, {A}}, [=]{ return ~A.d(); }},
+		{{Instruction::LT, {A, B}}, [=]() { return A.d() < B.d() ? u256(1) : 0; }},
+		{{Instruction::GT, {A, B}}, [=]() -> u256 { return A.d() > B.d() ? 1 : 0; }},
+		{{Instruction::SLT, {A, B}}, [=]() -> u256 { return u2s(A.d()) < u2s(B.d()) ? 1 : 0; }},
+		{{Instruction::SGT, {A, B}}, [=]() -> u256 { return u2s(A.d()) > u2s(B.d()) ? 1 : 0; }},
+		{{Instruction::EQ, {A, B}}, [=]() -> u256 { return A.d() == B.d() ? 1 : 0; }},
+		{{Instruction::ISZERO, {A}}, [=]() -> u256 { return A.d() == 0 ? 1 : 0; }},
+		{{Instruction::AND, {A, B}}, [=]{ return A.d() & B.d(); }},
+		{{Instruction::OR, {A, B}}, [=]{ return A.d() | B.d(); }},
+		{{Instruction::XOR, {A, B}}, [=]{ return A.d() ^ B.d(); }},
+		{{Instruction::BYTE, {A, B}}, [=]{ return A.d() >= 32 ? 0 : (B.d() >> unsigned(8 * (31 - A.d()))) & 0xff; }},
+		{{Instruction::ADDMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) + bigint(B.d())) % C.d()); }},
+		{{Instruction::MULMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) * bigint(B.d())) % C.d()); }},
+		{{Instruction::MULMOD, {A, B, C}}, [=]{ return A.d() * B.d(); }},
+		{{Instruction::SIGNEXTEND, {A, B}}, [=]() -> u256 {
+			if (A.d() >= 31)
+				return B.d();
+			unsigned testBit = unsigned(A.d()) * 8 + 7;
+			u256 mask = (u256(1) << testBit) - 1;
+			return u256(boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask);
+		}},
+
+		// invariants involving known constants
+		{{Instruction::ADD, {X, 0}}, [=]{ return X; }},
+		{{Instruction::SUB, {X, 0}}, [=]{ return X; }},
+		{{Instruction::MUL, {X, 1}}, [=]{ return X; }},
+		{{Instruction::DIV, {X, 1}}, [=]{ return X; }},
+		{{Instruction::SDIV, {X, 1}}, [=]{ return X; }},
+		{{Instruction::OR, {X, 0}}, [=]{ return X; }},
+		{{Instruction::XOR, {X, 0}}, [=]{ return X; }},
+		{{Instruction::AND, {X, ~u256(0)}}, [=]{ return X; }},
+		{{Instruction::AND, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::MUL, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::DIV, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::DIV, {0, X}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {0, X}}, [=]{ return u256(0); }},
+		{{Instruction::OR, {X, ~u256(0)}}, [=]{ return ~u256(0); }},
+		{{Instruction::EQ, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; } },
+		// operations involving an expression and itself
+		{{Instruction::AND, {X, X}}, [=]{ return X; }},
+		{{Instruction::OR, {X, X}}, [=]{ return X; }},
+		{{Instruction::XOR, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SUB, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::EQ, {X, X}}, [=]{ return u256(1); }},
+		{{Instruction::LT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SLT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::GT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SGT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {X, X}}, [=]{ return u256(0); }},
+
+		{{Instruction::NOT, {{Instruction::NOT, {X}}}}, [=]{ return X; }},
+		{{Instruction::XOR, {{{X}, {Instruction::XOR, {X, Y}}}}}, [=]{ return Y; }},
+		{{Instruction::OR, {{{X}, {Instruction::AND, {X, Y}}}}}, [=]{ return X; }},
+		{{Instruction::AND, {{{X}, {Instruction::OR, {X, Y}}}}}, [=]{ return X; }},
+		{{Instruction::AND, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return u256(0); }},
+		{{Instruction::OR, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return ~u256(0); }},
+	});
+	// Double negation of opcodes with binary result
+	for (auto const& op: vector<Instruction>{
+		Instruction::EQ,
+		Instruction::LT,
+		Instruction::SLT,
+		Instruction::GT,
+		Instruction::SGT
+	})
+		addRule({
+			{Instruction::ISZERO, {{Instruction::ISZERO, {{op, {X, Y}}}}}},
+			[=]() -> Pattern { return {op, {X, Y}}; }
+		});
+	addRule({
+		{Instruction::ISZERO, {{Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}}},
+		[=]() -> Pattern { return {Instruction::ISZERO, {X}}; }
+	});
+	addRule({
+		{Instruction::ISZERO, {{Instruction::XOR, {X, Y}}}},
+		[=]() -> Pattern { return { Instruction::EQ, {X, Y} }; }
+	});
+	// Associative operations
+	for (auto const& opFun: vector<pair<Instruction,function<u256(u256 const&,u256 const&)>>>{
+		{Instruction::ADD, plus<u256>()},
+		{Instruction::MUL, multiplies<u256>()},
+		{Instruction::AND, bit_and<u256>()},
+		{Instruction::OR, bit_or<u256>()},
+		{Instruction::XOR, bit_xor<u256>()}
+	})
+	{
+		auto op = opFun.first;
+		auto fun = opFun.second;
+		// Moving constants to the outside, order matters here!
+		// we need actions that return expressions (or patterns?) here, and we need also reversed rules
+		// (X+A)+B -> X+(A+B)
+		addRules(vector<pair<Pattern, function<Pattern()>>>{{
+			{op, {{op, {X, A}}, B}},
+			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
+		}, {
+		// X+(Y+A) -> (X+Y)+A
+			{op, {{op, {X, A}}, Y}},
+			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
+		}, {
+		// For now, we still need explicit commutativity for the inner pattern
+			{op, {{op, {A, X}}, B}},
+			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
+		}, {
+			{op, {{op, {A, X}}, Y}},
+			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
+		}});
+	}
+	// move constants across subtractions
+	addRules(vector<pair<Pattern, function<Pattern()>>>{
+		{
+			// X - A -> X + (-A)
+			{Instruction::SUB, {X, A}},
+			[=]() -> Pattern { return {Instruction::ADD, {X, 0 - A.d()}}; }
+		}, {
+			// (X + A) - Y -> (X - Y) + A
+			{Instruction::SUB, {{Instruction::ADD, {X, A}}, Y}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
+		}, {
+			// (A + X) - Y -> (X - Y) + A
+			{Instruction::SUB, {{Instruction::ADD, {A, X}}, Y}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
+		}, {
+			// X - (Y + A) -> (X - Y) + (-A)
+			{Instruction::SUB, {X, {Instruction::ADD, {Y, A}}}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
+		}, {
+			// X - (A + Y) -> (X - Y) + (-A)
+			{Instruction::SUB, {X, {Instruction::ADD, {A, Y}}}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
+		}
+	});
+}
+
+Pattern::Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments):
+	m_type(Operation),
+	m_instruction(_instruction),
+	m_arguments(_arguments)
+{
+}
+
+void Pattern::setMatchGroup(unsigned _group, map<unsigned, Expression const*>& _matchGroups)
+{
+	m_matchGroup = _group;
+	m_matchGroups = &_matchGroups;
+}
+
+bool Pattern::matches(Expression const& _expr, ExpressionClasses const& _classes) const
+{
+	if (!matchesBaseItem(_expr.item))
+		return false;
+	if (m_matchGroup)
+	{
+		if (!m_matchGroups->count(m_matchGroup))
+			(*m_matchGroups)[m_matchGroup] = &_expr;
+		else if ((*m_matchGroups)[m_matchGroup]->id != _expr.id)
+			return false;
+	}
+	assertThrow(m_arguments.size() == 0 || _expr.arguments.size() == m_arguments.size(), OptimizerException, "");
+	for (size_t i = 0; i < m_arguments.size(); ++i)
+		if (!m_arguments[i].matches(_classes.representative(_expr.arguments[i]), _classes))
+			return false;
+	return true;
+}
+
+AssemblyItem Pattern::toAssemblyItem(SourceLocation const& _location) const
+{
+	if (m_type == Operation)
+		return AssemblyItem(m_instruction, _location);
+	else
+		return AssemblyItem(m_type, data(), _location);
+}
+
+string Pattern::toString() const
+{
+	stringstream s;
+	switch (m_type)
+	{
+	case Operation:
+		s << instructionInfo(m_instruction).name;
+		break;
+	case Push:
+		s << "PUSH " << hex << data();
+		break;
+	case UndefinedItem:
+		s << "ANY";
+		break;
+	default:
+		s << "t=" << dec << m_type << " d=" << hex << data();
+		break;
+	}
+	if (!m_requireDataMatch)
+		s << " ~";
+	if (m_matchGroup)
+		s << "[" << dec << m_matchGroup << "]";
+	s << "(";
+	for (Pattern const& p: m_arguments)
+		s << p.toString() << ", ";
+	s << ")";
+	return s.str();
+}
+
+bool Pattern::matchesBaseItem(AssemblyItem const* _item) const
+{
+	if (m_type == UndefinedItem)
+		return true;
+	if (!_item)
+		return false;
+	if (m_type != _item->type())
+		return false;
+	else if (m_type == Operation)
+		return m_instruction == _item->instruction();
+	else if (m_requireDataMatch)
+		return data() == _item->data();
+	return true;
+}
+
+Pattern::Expression const& Pattern::matchGroupValue() const
+{
+	assertThrow(m_matchGroup > 0, OptimizerException, "");
+	assertThrow(!!m_matchGroups, OptimizerException, "");
+	assertThrow((*m_matchGroups)[m_matchGroup], OptimizerException, "");
+	return *(*m_matchGroups)[m_matchGroup];
+}
+
+u256 const& Pattern::data() const
+{
+	assertThrow(m_data, OptimizerException, "");
+	return *m_data;
+}
+
+ExpressionTemplate::ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location)
+{
+	if (_pattern.matchGroup())
+	{
+		hasId = true;
+		id = _pattern.id();
+	}
+	else
+	{
+		hasId = false;
+		item = _pattern.toAssemblyItem(_location);
+	}
+	for (auto const& arg: _pattern.arguments())
+		arguments.push_back(ExpressionTemplate(arg, _location));
+}
+
+string ExpressionTemplate::toString() const
+{
+	stringstream s;
+	if (hasId)
+		s << id;
+	else
+		s << item;
+	s << "(";
+	for (auto const& arg: arguments)
+		s << arg.toString();
+	s << ")";
+	return s.str();
+}
diff --git a/libevmasm/SimplificationRules.h b/libevmasm/SimplificationRules.h
new file mode 100644
index 00000000..a4da5849
--- /dev/null
+++ b/libevmasm/SimplificationRules.h
@@ -0,0 +1,140 @@
+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * @file SimplificationRules
+ * @author Christian <chris@ethereum.org>
+ * @date 2017
+ * Module for applying replacement rules against Expressions.
+ */
+
+#pragma once
+
+#include <libevmasm/ExpressionClasses.h>
+
+#include <functional>
+#include <vector>
+
+namespace dev
+{
+namespace eth
+{
+
+class Pattern;
+
+/**
+ * Container for all simplification rules.
+ */
+class Rules: public boost::noncopyable
+{
+public:
+	using Expression = ExpressionClasses::Expression;
+
+	Rules();
+
+	/// @returns a pointer to the first matching pattern and sets the match
+	/// groups accordingly.
+	std::pair<Pattern, std::function<Pattern()>> const* findFirstMatch(
+		Expression const& _expr,
+		ExpressionClasses const& _classes
+	);
+
+private:
+	void addRules(std::vector<std::pair<Pattern, std::function<Pattern()>>> const& _rules);
+	void addRule(std::pair<Pattern, std::function<Pattern()>> const& _rule);
+
+	void resetMatchGroups() { m_matchGroups.clear(); }
+
+	std::map<unsigned, Expression const*> m_matchGroups;
+	std::vector<std::pair<Pattern, std::function<Pattern()>>> m_rules[256];
+};
+
+/**
+ * Pattern to match against an expression.
+ * Also stores matched expressions to retrieve them later, for constructing new expressions using
+ * ExpressionTemplate.
+ */
+class Pattern
+{
+public:
+	using Expression = ExpressionClasses::Expression;
+	using Id = ExpressionClasses::Id;
+
+	// Matches a specific constant value.
+	Pattern(unsigned _value): Pattern(u256(_value)) {}
+	// Matches a specific constant value.
+	Pattern(u256 const& _value): m_type(Push), m_requireDataMatch(true), m_data(std::make_shared<u256>(_value)) {}
+	// Matches a specific assembly item type or anything if not given.
+	Pattern(AssemblyItemType _type = UndefinedItem): m_type(_type) {}
+	// Matches a given instruction with given arguments
+	Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments = {});
+	/// Sets this pattern to be part of the match group with the identifier @a _group.
+	/// Inside one rule, all patterns in the same match group have to match expressions from the
+	/// same expression equivalence class.
+	void setMatchGroup(unsigned _group, std::map<unsigned, Expression const*>& _matchGroups);
+	unsigned matchGroup() const { return m_matchGroup; }
+	bool matches(Expression const& _expr, ExpressionClasses const& _classes) const;
+
+	AssemblyItem toAssemblyItem(SourceLocation const& _location) const;
+	std::vector<Pattern> arguments() const { return m_arguments; }
+
+	/// @returns the id of the matched expression if this pattern is part of a match group.
+	Id id() const { return matchGroupValue().id; }
+	/// @returns the data of the matched expression if this pattern is part of a match group.
+	u256 const& d() const { return matchGroupValue().item->data(); }
+
+	std::string toString() const;
+
+	AssemblyItemType type() const { return m_type; }
+	Instruction instruction() const
+	{
+		assertThrow(type() == Operation, OptimizerException, "");
+		return m_instruction;
+	}
+
+private:
+	bool matchesBaseItem(AssemblyItem const* _item) const;
+	Expression const& matchGroupValue() const;
+	u256 const& data() const;
+
+	AssemblyItemType m_type;
+	bool m_requireDataMatch = false;
+	Instruction m_instruction; ///< Only valid if m_type is Operation
+	std::shared_ptr<u256> m_data; ///< Only valid if m_type is not Operation
+	std::vector<Pattern> m_arguments;
+	unsigned m_matchGroup = 0;
+	std::map<unsigned, Expression const*>* m_matchGroups = nullptr;
+};
+
+/**
+ * Template for a new expression that can be built from matched patterns.
+ */
+struct ExpressionTemplate
+{
+	using Expression = ExpressionClasses::Expression;
+	using Id = ExpressionClasses::Id;
+	explicit ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location);
+	std::string toString() const;
+	bool hasId = false;
+	/// Id of the matched expression, if available.
+	Id id = Id(-1);
+	// Otherwise, assembly item.
+	AssemblyItem item = UndefinedItem;
+	std::vector<ExpressionTemplate> arguments;
+};
+
+}
+}