diff --git a/Changelog.md b/Changelog.md
index b32b6e00b..c50b395ae 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -24,8 +24,10 @@ Breaking Changes:
 Language Features:
  * Super constructors can now be called using the member notation e.g. ``M.C(123)``.
 
+Bugfixes:
+ * Type Checker: Perform proper integer arithmetic when using constants in array length expressions.
 
- AST Changes:
+AST Changes:
  * New AST Node ``IdentifierPath`` replacing in many places the ``UserDefinedTypeName``
 
 
diff --git a/docs/080-breaking-changes.rst b/docs/080-breaking-changes.rst
index 0139047fc..e9c206701 100644
--- a/docs/080-breaking-changes.rst
+++ b/docs/080-breaking-changes.rst
@@ -35,6 +35,10 @@ the compiler notifying you about it.
 * If a byte array in storage is accessed whose length is encoded incorrectly, a panic is caused.
   A contract cannot get into this situation unless inline assembly is used to modify the raw representation of storage byte arrays.
 
+* If constants are used in array length expressions, previous versions of Solidity would use arbitrary precision
+  in all branches of the evaluation tree. Now, if constant variables are used as intermediate expressions,
+  their values will be properly rounded in the same way as when they are used in run-time expressions.
+
 New Restrictions
 ================
 
diff --git a/libsolidity/analysis/ConstantEvaluator.cpp b/libsolidity/analysis/ConstantEvaluator.cpp
index d00affb91..fdb414c5e 100644
--- a/libsolidity/analysis/ConstantEvaluator.cpp
+++ b/libsolidity/analysis/ConstantEvaluator.cpp
@@ -32,85 +32,357 @@ using namespace solidity;
 using namespace solidity::frontend;
 using namespace solidity::langutil;
 
+using TypedRational = ConstantEvaluator::TypedRational;
+
+namespace
+{
+
+/// Check whether (_base ** _exp) fits into 4096 bits.
+bool fitsPrecisionExp(bigint const& _base, bigint const& _exp)
+{
+	if (_base == 0)
+		return true;
+
+	solAssert(_base > 0, "");
+
+	size_t const bitsMax = 4096;
+
+	unsigned mostSignificantBaseBit = boost::multiprecision::msb(_base);
+	if (mostSignificantBaseBit == 0) // _base == 1
+		return true;
+	if (mostSignificantBaseBit > bitsMax) // _base >= 2 ^ 4096
+		return false;
+
+	bigint bitsNeeded = _exp * (mostSignificantBaseBit + 1);
+
+	return bitsNeeded <= bitsMax;
+}
+
+/// Checks whether _mantissa * (2 ** _expBase10) fits into 4096 bits.
+bool fitsPrecisionBase2(bigint const& _mantissa, uint32_t _expBase2)
+{
+	return fitsPrecisionBaseX(_mantissa, 1.0, _expBase2);
+}
+
+}
+
+optional<rational> ConstantEvaluator::evaluateBinaryOperator(Token _operator, rational const& _left, rational const& _right)
+{
+	bool fractional = _left.denominator() != 1 || _right.denominator() != 1;
+	switch (_operator)
+	{
+	//bit operations will only be enabled for integers and fixed types that resemble integers
+	case Token::BitOr:
+		if (fractional)
+			return nullopt;
+		else
+			return _left.numerator() | _right.numerator();
+	case Token::BitXor:
+		if (fractional)
+			return nullopt;
+		else
+			return _left.numerator() ^ _right.numerator();
+	case Token::BitAnd:
+		if (fractional)
+			return nullopt;
+		else
+			return _left.numerator() & _right.numerator();
+	case Token::Add: return _left + _right;
+	case Token::Sub: return _left - _right;
+	case Token::Mul: return _left * _right;
+	case Token::Div:
+		if (_right == rational(0))
+			return nullopt;
+		else
+			return _left / _right;
+	case Token::Mod:
+		if (_right == rational(0))
+			return nullopt;
+		else if (fractional)
+		{
+			rational tempValue = _left / _right;
+			return _left - (tempValue.numerator() / tempValue.denominator()) * _right;
+		}
+		else
+			return _left.numerator() % _right.numerator();
+		break;
+	case Token::Exp:
+	{
+		if (_right.denominator() != 1)
+			return nullopt;
+		bigint const& exp = _right.numerator();
+
+		// x ** 0 = 1
+		// for 0, 1 and -1 the size of the exponent doesn't have to be restricted
+		if (exp == 0)
+			return 1;
+		else if (_left == 0 || _left == 1)
+			return _left;
+		else if (_left == -1)
+		{
+			bigint isOdd = abs(exp) & bigint(1);
+			return 1 - 2 * isOdd.convert_to<int>();
+		}
+		else
+		{
+			if (abs(exp) > numeric_limits<uint32_t>::max())
+				return nullopt; // This will need too much memory to represent.
+
+			uint32_t absExp = bigint(abs(exp)).convert_to<uint32_t>();
+
+			if (!fitsPrecisionExp(abs(_left.numerator()), absExp) || !fitsPrecisionExp(abs(_left.denominator()), absExp))
+				return nullopt;
+
+			static auto const optimizedPow = [](bigint const& _base, uint32_t _exponent) -> bigint {
+				if (_base == 1)
+					return 1;
+				else if (_base == -1)
+					return 1 - 2 * static_cast<int>(_exponent & 1);
+				else
+					return boost::multiprecision::pow(_base, _exponent);
+			};
+
+			bigint numerator = optimizedPow(_left.numerator(), absExp);
+			bigint denominator = optimizedPow(_left.denominator(), absExp);
+
+			if (exp >= 0)
+				return makeRational(numerator, denominator);
+			else
+				// invert
+				return makeRational(denominator, numerator);
+		}
+		break;
+	}
+	case Token::SHL:
+	{
+		if (fractional)
+			return nullopt;
+		else if (_right < 0)
+			return nullopt;
+		else if (_right > numeric_limits<uint32_t>::max())
+			return nullopt;
+		if (_left.numerator() == 0)
+			return 0;
+		else
+		{
+			uint32_t exponent = _right.numerator().convert_to<uint32_t>();
+			if (!fitsPrecisionBase2(abs(_left.numerator()), exponent))
+				return nullopt;
+			return _left.numerator() * boost::multiprecision::pow(bigint(2), exponent);
+		}
+		break;
+	}
+	// NOTE: we're using >> (SAR) to denote right shifting. The type of the LValue
+	//       determines the resulting type and the type of shift (SAR or SHR).
+	case Token::SAR:
+	{
+		if (fractional)
+			return nullopt;
+		else if (_right < 0)
+			return nullopt;
+		else if (_right > numeric_limits<uint32_t>::max())
+			return nullopt;
+		if (_left.numerator() == 0)
+			return 0;
+		else
+		{
+			uint32_t exponent = _right.numerator().convert_to<uint32_t>();
+			if (exponent > boost::multiprecision::msb(boost::multiprecision::abs(_left.numerator())))
+				return _left.numerator() < 0 ? -1 : 0;
+			else
+			{
+				if (_left.numerator() < 0)
+					// Add 1 to the negative value before dividing to get a result that is strictly too large,
+					// then subtract 1 afterwards to round towards negative infinity.
+					// This is the same algorithm as used in ExpressionCompiler::appendShiftOperatorCode(...).
+					// To see this note that for negative x, xor(x,all_ones) = (-x-1) and
+					// therefore xor(div(xor(x,all_ones), exp(2, shift_amount)), all_ones) is
+					// -(-x - 1) / 2^shift_amount - 1, which is the same as
+					// (x + 1) / 2^shift_amount - 1.
+					return rational((_left.numerator() + 1) / boost::multiprecision::pow(bigint(2), exponent) - bigint(1), 1);
+				else
+					return rational(_left.numerator() / boost::multiprecision::pow(bigint(2), exponent), 1);
+			}
+		}
+		break;
+	}
+	default:
+		return nullopt;
+	}
+}
+
+optional<rational> ConstantEvaluator::evaluateUnaryOperator(Token _operator, rational const& _input)
+{
+	switch (_operator)
+	{
+	case Token::BitNot:
+		if (_input.denominator() != 1)
+			return nullopt;
+		else
+			return ~_input.numerator();
+	case Token::Sub:
+		return -_input;
+	default:
+		return nullopt;
+	}
+}
+
+optional<TypedRational> convertType(rational const& _value, Type const& _type)
+{
+	if (_type.category() == Type::Category::RationalNumber)
+		return TypedRational{TypeProvider::rationalNumber(_value), _value};
+	else if (auto const* integerType = dynamic_cast<IntegerType const*>(&_type))
+	{
+		if (_value > integerType->maxValue() || _value < integerType->minValue())
+			return nullopt;
+		else
+			return TypedRational{&_type, _value.numerator() / _value.denominator()};
+	}
+	else
+		return nullopt;
+}
+
+optional<TypedRational> convertType(optional<TypedRational> const& _value, Type const& _type)
+{
+	return _value ? convertType(_value->value, _type) : nullopt;
+}
+
+optional<TypedRational> constantToTypedValue(Type const& _type)
+{
+	if (_type.category() == Type::Category::RationalNumber)
+		return TypedRational{&_type, dynamic_cast<RationalNumberType const&>(_type).value()};
+	else
+		return nullopt;
+}
+
+optional<TypedRational> ConstantEvaluator::evaluate(
+	langutil::ErrorReporter& _errorReporter,
+	Expression const& _expr
+)
+{
+	return ConstantEvaluator{_errorReporter}.evaluate(_expr);
+}
+
+
+optional<TypedRational> ConstantEvaluator::evaluate(ASTNode const& _node)
+{
+	if (!m_values.count(&_node))
+	{
+		if (auto const* varDecl = dynamic_cast<VariableDeclaration const*>(&_node))
+		{
+			solAssert(varDecl->isConstant(), "");
+			if (!varDecl->value())
+				m_values[&_node] = nullopt;
+			else
+			{
+				m_depth++;
+				if (m_depth > 32)
+					m_errorReporter.fatalTypeError(
+						5210_error,
+						varDecl->location(),
+						"Cyclic constant definition (or maximum recursion depth exhausted)."
+					);
+				m_values[&_node] = convertType(evaluate(*varDecl->value()), *varDecl->type());
+				m_depth--;
+			}
+		}
+		else if (auto const* expression = dynamic_cast<Expression const*>(&_node))
+		{
+			expression->accept(*this);
+			if (!m_values.count(&_node))
+				m_values[&_node] = nullopt;
+		}
+	}
+	return m_values.at(&_node);
+}
+
 void ConstantEvaluator::endVisit(UnaryOperation const& _operation)
 {
-	auto sub = type(_operation.subExpression());
-	if (sub)
-		setType(_operation, sub->unaryOperatorResult(_operation.getOperator()));
+	optional<TypedRational> value = evaluate(_operation.subExpression());
+	if (!value)
+		return;
+
+	TypePointer resultType = value->type->unaryOperatorResult(_operation.getOperator());
+	if (!resultType)
+		return;
+	value = convertType(value, *resultType);
+	if (!value)
+		return;
+
+	if (optional<rational> result = evaluateUnaryOperator(_operation.getOperator(), value->value))
+	{
+		optional<TypedRational> convertedValue = convertType(*result, *resultType);
+		if (!convertedValue)
+			m_errorReporter.fatalTypeError(
+				3667_error,
+				_operation.location(),
+				"Arithmetic error when computing constant value."
+			);
+		m_values[&_operation] = convertedValue;
+	}
 }
 
 void ConstantEvaluator::endVisit(BinaryOperation const& _operation)
 {
-	auto left = type(_operation.leftExpression());
-	auto right = type(_operation.rightExpression());
-	if (left && right)
+	optional<TypedRational> left = evaluate(_operation.leftExpression());
+	optional<TypedRational> right = evaluate(_operation.rightExpression());
+	if (!left || !right)
+		return;
+
+	// If this is implemented in the future: Comparison operators have a "binaryOperatorResult"
+	// that is non-bool, but the result has to be bool.
+	if (TokenTraits::isCompareOp(_operation.getOperator()))
+		return;
+
+	TypePointer resultType = left->type->binaryOperatorResult(_operation.getOperator(), right->type);
+	if (!resultType)
 	{
-		TypePointer commonType = left->binaryOperatorResult(_operation.getOperator(), right);
-		if (!commonType)
-			m_errorReporter.fatalTypeError(
-				6020_error,
-				_operation.location(),
-				"Operator " +
-				string(TokenTraits::toString(_operation.getOperator())) +
-				" not compatible with types " +
-				left->toString() +
-				" and " +
-				right->toString()
+		m_errorReporter.fatalTypeError(
+			6020_error,
+			_operation.location(),
+			"Operator " +
+			string(TokenTraits::toString(_operation.getOperator())) +
+			" not compatible with types " +
+			left->type->toString() +
+			" and " +
+			right->type->toString()
 			);
-		setType(
-			_operation,
-			TokenTraits::isCompareOp(_operation.getOperator()) ?
-			TypeProvider::boolean() :
-			commonType
-		);
+		return;
+	}
+
+	left = convertType(left, *resultType);
+	right = convertType(right, *resultType);
+	if (!left || !right)
+		return;
+
+	if (optional<rational> value = evaluateBinaryOperator(_operation.getOperator(), left->value, right->value))
+	{
+		optional<TypedRational> convertedValue = convertType(*value, *resultType);
+		if (!convertedValue)
+			m_errorReporter.fatalTypeError(
+				2643_error,
+				_operation.location(),
+				"Arithmetic error when computing constant value."
+			);
+		m_values[&_operation] = convertedValue;
 	}
 }
 
 void ConstantEvaluator::endVisit(Literal const& _literal)
 {
-	setType(_literal, TypeProvider::forLiteral(_literal));
+	if (Type const* literalType = TypeProvider::forLiteral(_literal))
+		m_values[&_literal] = constantToTypedValue(*literalType);
 }
 
 void ConstantEvaluator::endVisit(Identifier const& _identifier)
 {
 	VariableDeclaration const* variableDeclaration = dynamic_cast<VariableDeclaration const*>(_identifier.annotation().referencedDeclaration);
-	if (!variableDeclaration)
-		return;
-	if (!variableDeclaration->isConstant())
-		return;
-
-	ASTPointer<Expression> const& value = variableDeclaration->value();
-	if (!value)
-		return;
-	else if (!m_types->count(value.get()))
-	{
-		if (m_depth > 32)
-			m_errorReporter.fatalTypeError(5210_error, _identifier.location(), "Cyclic constant definition (or maximum recursion depth exhausted).");
-		ConstantEvaluator(m_errorReporter, m_depth + 1, m_types).evaluate(*value);
-	}
-
-	setType(_identifier, type(*value));
+	if (variableDeclaration && variableDeclaration->isConstant())
+		m_values[&_identifier] = evaluate(*variableDeclaration);
 }
 
 void ConstantEvaluator::endVisit(TupleExpression const& _tuple)
 {
 	if (!_tuple.isInlineArray() && _tuple.components().size() == 1)
-		setType(_tuple, type(*_tuple.components().front()));
-}
-
-void ConstantEvaluator::setType(ASTNode const& _node, TypePointer const& _type)
-{
-	if (_type && _type->category() == Type::Category::RationalNumber)
-		(*m_types)[&_node] = _type;
-}
-
-TypePointer ConstantEvaluator::type(ASTNode const& _node)
-{
-	return (*m_types)[&_node];
-}
-
-TypePointer ConstantEvaluator::evaluate(Expression const& _expr)
-{
-	_expr.accept(*this);
-	return type(_expr);
+		m_values[&_tuple] = evaluate(*_tuple.components().front());
 }
diff --git a/libsolidity/analysis/ConstantEvaluator.h b/libsolidity/analysis/ConstantEvaluator.h
index 521f46338..7172258c3 100644
--- a/libsolidity/analysis/ConstantEvaluator.h
+++ b/libsolidity/analysis/ConstantEvaluator.h
@@ -39,37 +39,48 @@ class TypeChecker;
 
 /**
  * Small drop-in replacement for TypeChecker to evaluate simple expressions of integer constants.
+ *
+ * Note: This always use "checked arithmetic" in the sense that any over- or underflow
+ * results in "unknown" value.
  */
 class ConstantEvaluator: private ASTConstVisitor
 {
 public:
-	ConstantEvaluator(
-		langutil::ErrorReporter& _errorReporter,
-		size_t _newDepth = 0,
-		std::shared_ptr<std::map<ASTNode const*, TypePointer>> _types = std::make_shared<std::map<ASTNode const*, TypePointer>>()
-	):
-		m_errorReporter(_errorReporter),
-		m_depth(_newDepth),
-		m_types(std::move(_types))
+	struct TypedRational
 	{
-	}
+		TypePointer type;
+		rational value;
+	};
 
-	TypePointer evaluate(Expression const& _expr);
+	static std::optional<TypedRational> evaluate(
+		langutil::ErrorReporter& _errorReporter,
+		Expression const& _expr
+	);
+
+	/// Performs arbitrary-precision evaluation of a binary operator. Returns nullopt on cases like
+	/// division by zero or e.g. bit operators applied to fractional values.
+	static std::optional<rational> evaluateBinaryOperator(Token _operator, rational const& _left, rational const&  _right);
+
+	/// Performs arbitrary-precision evaluation of a unary operator. Returns nullopt on cases like
+	/// bit operators applied to fractional values.
+	static std::optional<rational> evaluateUnaryOperator(Token _operator, rational const& _input);
 
 private:
+	explicit ConstantEvaluator(langutil::ErrorReporter& _errorReporter): m_errorReporter(_errorReporter) {}
+
+	std::optional<TypedRational> evaluate(ASTNode const& _node);
+
 	void endVisit(BinaryOperation const& _operation) override;
 	void endVisit(UnaryOperation const& _operation) override;
 	void endVisit(Literal const& _literal) override;
 	void endVisit(Identifier const& _identifier) override;
 	void endVisit(TupleExpression const& _tuple) override;
 
-	void setType(ASTNode const& _node, TypePointer const& _type);
-	TypePointer type(ASTNode const& _node);
-
 	langutil::ErrorReporter& m_errorReporter;
 	/// Current recursion depth.
 	size_t m_depth = 0;
-	std::shared_ptr<std::map<ASTNode const*, TypePointer>> m_types;
+	/// Values of sub-expressions and variable declarations.
+	std::map<ASTNode const*, std::optional<TypedRational>> m_values;
 };
 
 }
diff --git a/libsolidity/analysis/DeclarationTypeChecker.cpp b/libsolidity/analysis/DeclarationTypeChecker.cpp
index 14ed89a41..5c267b285 100644
--- a/libsolidity/analysis/DeclarationTypeChecker.cpp
+++ b/libsolidity/analysis/DeclarationTypeChecker.cpp
@@ -265,26 +265,30 @@ void DeclarationTypeChecker::endVisit(ArrayTypeName const& _typeName)
 	solAssert(baseType->storageBytes() != 0, "Illegal base type of storage size zero for array.");
 	if (Expression const* length = _typeName.length())
 	{
-		TypePointer& lengthTypeGeneric = length->annotation().type;
-		if (!lengthTypeGeneric)
-			lengthTypeGeneric = ConstantEvaluator(m_errorReporter).evaluate(*length);
-		RationalNumberType const* lengthType = dynamic_cast<RationalNumberType const*>(lengthTypeGeneric);
-		u256 lengthValue = 0;
-		if (!lengthType || !lengthType->mobileType())
+		optional<rational> lengthValue;
+		if (length->annotation().type && length->annotation().type->category() == Type::Category::RationalNumber)
+			lengthValue = dynamic_cast<RationalNumberType const&>(*length->annotation().type).value();
+		else if (optional<ConstantEvaluator::TypedRational> value = ConstantEvaluator::evaluate(m_errorReporter, *length))
+			lengthValue = value->value;
+
+		if (!lengthValue || lengthValue > TypeProvider::uint256()->max())
 			m_errorReporter.typeError(
 				5462_error,
 				length->location(),
 				"Invalid array length, expected integer literal or constant expression."
 			);
-		else if (lengthType->isZero())
+		else if (*lengthValue == 0)
 			m_errorReporter.typeError(1406_error, length->location(), "Array with zero length specified.");
-		else if (lengthType->isFractional())
+		else if (lengthValue->denominator() != 1)
 			m_errorReporter.typeError(3208_error, length->location(), "Array with fractional length specified.");
-		else if (lengthType->isNegative())
+		else if (*lengthValue < 0)
 			m_errorReporter.typeError(3658_error, length->location(), "Array with negative length specified.");
-		else
-			lengthValue = lengthType->literalValue(nullptr);
-		_typeName.annotation().type = TypeProvider::array(DataLocation::Storage, baseType, lengthValue);
+
+		_typeName.annotation().type = TypeProvider::array(
+			DataLocation::Storage,
+			baseType,
+			lengthValue ? u256(lengthValue->numerator()) : u256(0)
+		);
 	}
 	else
 		_typeName.annotation().type = TypeProvider::array(DataLocation::Storage, baseType);
diff --git a/libsolidity/analysis/StaticAnalyzer.cpp b/libsolidity/analysis/StaticAnalyzer.cpp
index abfeae23d..7b828ebce 100644
--- a/libsolidity/analysis/StaticAnalyzer.cpp
+++ b/libsolidity/analysis/StaticAnalyzer.cpp
@@ -290,10 +290,8 @@ bool StaticAnalyzer::visit(BinaryOperation const& _operation)
 		*_operation.rightExpression().annotation().isPure &&
 		(_operation.getOperator() == Token::Div || _operation.getOperator() == Token::Mod)
 	)
-		if (auto rhs = dynamic_cast<RationalNumberType const*>(
-			ConstantEvaluator(m_errorReporter).evaluate(_operation.rightExpression())
-		))
-			if (rhs->isZero())
+		if (auto rhs = ConstantEvaluator::evaluate(m_errorReporter, _operation.rightExpression()))
+			if (rhs->value == 0)
 				m_errorReporter.typeError(
 					1211_error,
 					_operation.location(),
@@ -313,10 +311,8 @@ bool StaticAnalyzer::visit(FunctionCall const& _functionCall)
 		{
 			solAssert(_functionCall.arguments().size() == 3, "");
 			if (*_functionCall.arguments()[2]->annotation().isPure)
-				if (auto lastArg = dynamic_cast<RationalNumberType const*>(
-					ConstantEvaluator(m_errorReporter).evaluate(*(_functionCall.arguments())[2])
-				))
-					if (lastArg->isZero())
+				if (auto lastArg = ConstantEvaluator::evaluate(m_errorReporter, *(_functionCall.arguments())[2]))
+					if (lastArg->value == 0)
 						m_errorReporter.typeError(
 							4195_error,
 							_functionCall.location(),
diff --git a/libsolidity/ast/Types.cpp b/libsolidity/ast/Types.cpp
index 82a80d974..35910ceac 100644
--- a/libsolidity/ast/Types.cpp
+++ b/libsolidity/ast/Types.cpp
@@ -26,6 +26,8 @@
 #include <libsolidity/ast/AST.h>
 #include <libsolidity/ast/TypeProvider.h>
 
+#include <libsolidity/analysis/ConstantEvaluator.h>
+
 #include <libsolutil/Algorithms.h>
 #include <libsolutil/CommonData.h>
 #include <libsolutil/CommonIO.h>
@@ -56,50 +58,6 @@ using namespace solidity::frontend;
 namespace
 {
 
-/// Check whether (_base ** _exp) fits into 4096 bits.
-bool fitsPrecisionExp(bigint const& _base, bigint const& _exp)
-{
-	if (_base == 0)
-		return true;
-
-	solAssert(_base > 0, "");
-
-	size_t const bitsMax = 4096;
-
-	unsigned mostSignificantBaseBit = boost::multiprecision::msb(_base);
-	if (mostSignificantBaseBit == 0) // _base == 1
-		return true;
-	if (mostSignificantBaseBit > bitsMax) // _base >= 2 ^ 4096
-		return false;
-
-	bigint bitsNeeded = _exp * (mostSignificantBaseBit + 1);
-
-	return bitsNeeded <= bitsMax;
-}
-
-/// Checks whether _mantissa * (X ** _exp) fits into 4096 bits,
-/// where X is given indirectly via _log2OfBase = log2(X).
-bool fitsPrecisionBaseX(
-	bigint const& _mantissa,
-	double _log2OfBase,
-	uint32_t _exp
-)
-{
-	if (_mantissa == 0)
-		return true;
-
-	solAssert(_mantissa > 0, "");
-
-	size_t const bitsMax = 4096;
-
-	unsigned mostSignificantMantissaBit = boost::multiprecision::msb(_mantissa);
-	if (mostSignificantMantissaBit > bitsMax) // _mantissa >= 2 ^ 4096
-		return false;
-
-	bigint bitsNeeded = mostSignificantMantissaBit + bigint(floor(double(_exp) * _log2OfBase)) + 1;
-	return bitsNeeded <= bitsMax;
-}
-
 /// Checks whether _mantissa * (10 ** _expBase10) fits into 4096 bits.
 bool fitsPrecisionBase10(bigint const& _mantissa, uint32_t _expBase10)
 {
@@ -107,12 +65,6 @@ bool fitsPrecisionBase10(bigint const& _mantissa, uint32_t _expBase10)
 	return fitsPrecisionBaseX(_mantissa, log2Of10AwayFromZero, _expBase10);
 }
 
-/// Checks whether _mantissa * (2 ** _expBase10) fits into 4096 bits.
-bool fitsPrecisionBase2(bigint const& _mantissa, uint32_t _expBase2)
-{
-	return fitsPrecisionBaseX(_mantissa, 1.0, _expBase2);
-}
-
 /// Checks whether _value fits into IntegerType _type.
 BoolResult fitsIntegerType(bigint const& _value, IntegerType const& _type)
 {
@@ -1000,26 +952,10 @@ BoolResult RationalNumberType::isExplicitlyConvertibleTo(Type const& _convertTo)
 
 TypeResult RationalNumberType::unaryOperatorResult(Token _operator) const
 {
-	rational value;
-	switch (_operator)
-	{
-	case Token::BitNot:
-		if (isFractional())
-			return nullptr;
-		value = ~m_value.numerator();
-		break;
-	case Token::Add:
-		value = +(m_value);
-		break;
-	case Token::Sub:
-		value = -(m_value);
-		break;
-	case Token::After:
-		return this;
-	default:
+	if (optional<rational> value = ConstantEvaluator::evaluateUnaryOperator(_operator, m_value))
+		return TypeResult{TypeProvider::rationalNumber(*value)};
+	else
 		return nullptr;
-	}
-	return TypeResult{TypeProvider::rationalNumber(value)};
 }
 
 TypeResult RationalNumberType::binaryOperatorResult(Token _operator, Type const* _other) const
@@ -1074,165 +1010,16 @@ TypeResult RationalNumberType::binaryOperatorResult(Token _operator, Type const*
 			return nullptr;
 		return thisMobile->binaryOperatorResult(_operator, otherMobile);
 	}
-	else
+	else if (optional<rational> value = ConstantEvaluator::evaluateBinaryOperator(_operator, m_value, other.m_value))
 	{
-		rational value;
-		bool fractional = isFractional() || other.isFractional();
-		switch (_operator)
-		{
-		//bit operations will only be enabled for integers and fixed types that resemble integers
-		case Token::BitOr:
-			if (fractional)
-				return nullptr;
-			value = m_value.numerator() | other.m_value.numerator();
-			break;
-		case Token::BitXor:
-			if (fractional)
-				return nullptr;
-			value = m_value.numerator() ^ other.m_value.numerator();
-			break;
-		case Token::BitAnd:
-			if (fractional)
-				return nullptr;
-			value = m_value.numerator() & other.m_value.numerator();
-			break;
-		case Token::Add:
-			value = m_value + other.m_value;
-			break;
-		case Token::Sub:
-			value = m_value - other.m_value;
-			break;
-		case Token::Mul:
-			value = m_value * other.m_value;
-			break;
-		case Token::Div:
-			if (other.m_value == rational(0))
-				return nullptr;
-			else
-				value = m_value / other.m_value;
-			break;
-		case Token::Mod:
-			if (other.m_value == rational(0))
-				return nullptr;
-			else if (fractional)
-			{
-				rational tempValue = m_value / other.m_value;
-				value = m_value - (tempValue.numerator() / tempValue.denominator()) * other.m_value;
-			}
-			else
-				value = m_value.numerator() % other.m_value.numerator();
-			break;
-		case Token::Exp:
-		{
-			if (other.isFractional())
-				return nullptr;
-			solAssert(other.m_value.denominator() == 1, "");
-			bigint const& exp = other.m_value.numerator();
-
-			// x ** 0 = 1
-			// for 0, 1 and -1 the size of the exponent doesn't have to be restricted
-			if (exp == 0)
-				value = 1;
-			else if (m_value.numerator() == 0 || m_value == 1)
-				value = m_value;
-			else if (m_value == -1)
-			{
-				bigint isOdd = abs(exp) & bigint(1);
-				value = 1 - 2 * isOdd.convert_to<int>();
-			}
-			else
-			{
-				if (abs(exp) > numeric_limits<uint32_t>::max())
-					return nullptr; // This will need too much memory to represent.
-
-				uint32_t absExp = bigint(abs(exp)).convert_to<uint32_t>();
-
-				if (!fitsPrecisionExp(abs(m_value.numerator()), absExp) || !fitsPrecisionExp(abs(m_value.denominator()), absExp))
-					return TypeResult::err("Precision of rational constants is limited to 4096 bits.");
-
-				static auto const optimizedPow = [](bigint const& _base, uint32_t _exponent) -> bigint {
-					if (_base == 1)
-						return 1;
-					else if (_base == -1)
-						return 1 - 2 * static_cast<int>(_exponent & 1);
-					else
-						return boost::multiprecision::pow(_base, _exponent);
-				};
-
-				bigint numerator = optimizedPow(m_value.numerator(), absExp);
-				bigint denominator = optimizedPow(m_value.denominator(), absExp);
-
-				if (exp >= 0)
-					value = makeRational(numerator, denominator);
-				else
-					// invert
-					value = makeRational(denominator, numerator);
-			}
-			break;
-		}
-		case Token::SHL:
-		{
-			if (fractional)
-				return nullptr;
-			else if (other.m_value < 0)
-				return nullptr;
-			else if (other.m_value > numeric_limits<uint32_t>::max())
-				return nullptr;
-			if (m_value.numerator() == 0)
-				value = 0;
-			else
-			{
-				uint32_t exponent = other.m_value.numerator().convert_to<uint32_t>();
-				if (!fitsPrecisionBase2(abs(m_value.numerator()), exponent))
-					return nullptr;
-				value = m_value.numerator() * boost::multiprecision::pow(bigint(2), exponent);
-			}
-			break;
-		}
-		// NOTE: we're using >> (SAR) to denote right shifting. The type of the LValue
-		//       determines the resulting type and the type of shift (SAR or SHR).
-		case Token::SAR:
-		{
-			if (fractional)
-				return nullptr;
-			else if (other.m_value < 0)
-				return nullptr;
-			else if (other.m_value > numeric_limits<uint32_t>::max())
-				return nullptr;
-			if (m_value.numerator() == 0)
-				value = 0;
-			else
-			{
-				uint32_t exponent = other.m_value.numerator().convert_to<uint32_t>();
-				if (exponent > boost::multiprecision::msb(boost::multiprecision::abs(m_value.numerator())))
-					value = m_value.numerator() < 0 ? -1 : 0;
-				else
-				{
-					if (m_value.numerator() < 0)
-						// Add 1 to the negative value before dividing to get a result that is strictly too large,
-						// then subtract 1 afterwards to round towards negative infinity.
-						// This is the same algorithm as used in ExpressionCompiler::appendShiftOperatorCode(...).
-						// To see this note that for negative x, xor(x,all_ones) = (-x-1) and
-						// therefore xor(div(xor(x,all_ones), exp(2, shift_amount)), all_ones) is
-						// -(-x - 1) / 2^shift_amount - 1, which is the same as
-						// (x + 1) / 2^shift_amount - 1.
-						value = rational((m_value.numerator() + 1) / boost::multiprecision::pow(bigint(2), exponent) - bigint(1), 1);
-					else
-						value = rational(m_value.numerator() / boost::multiprecision::pow(bigint(2), exponent), 1);
-				}
-			}
-			break;
-		}
-		default:
-			return nullptr;
-		}
-
 		// verify that numerator and denominator fit into 4096 bit after every operation
-		if (value.numerator() != 0 && max(boost::multiprecision::msb(abs(value.numerator())), boost::multiprecision::msb(abs(value.denominator()))) > 4096)
+		if (value->numerator() != 0 && max(boost::multiprecision::msb(abs(value->numerator())), boost::multiprecision::msb(abs(value->denominator()))) > 4096)
 			return TypeResult::err("Precision of rational constants is limited to 4096 bits.");
 
-		return TypeResult{TypeProvider::rationalNumber(value)};
+		return TypeResult{TypeProvider::rationalNumber(*value)};
 	}
+	else
+		return nullptr;
 }
 
 string RationalNumberType::richIdentifier() const
diff --git a/libsolidity/ast/Types.h b/libsolidity/ast/Types.h
index 60ce4686f..b366df78e 100644
--- a/libsolidity/ast/Types.h
+++ b/libsolidity/ast/Types.h
@@ -568,6 +568,11 @@ public:
 	u256 literalValue(Literal const* _literal) const override;
 	TypePointer mobileType() const override;
 
+	/// @returns the underlying raw literal value.
+	///
+	/// @see literalValue(Literal const*))
+	rational const& value() const noexcept { return m_value; }
+
 	/// @returns the smallest integer type that can hold the value or an empty pointer if not possible.
 	IntegerType const* integerType() const;
 	/// @returns the smallest fixed type that can hold the value or incurs the least precision loss,
diff --git a/libsolutil/CMakeLists.txt b/libsolutil/CMakeLists.txt
index ea8bcdf86..a38df7443 100644
--- a/libsolutil/CMakeLists.txt
+++ b/libsolutil/CMakeLists.txt
@@ -2,6 +2,7 @@ set(sources
 	Algorithms.h
 	AnsiColorized.h
 	Assertions.h
+	Common.cpp
 	Common.h
 	CommonData.cpp
 	CommonData.h
diff --git a/libsolutil/Common.cpp b/libsolutil/Common.cpp
new file mode 100644
index 000000000..3f77e5d25
--- /dev/null
+++ b/libsolutil/Common.cpp
@@ -0,0 +1,40 @@
+/*
+	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/>.
+*/
+// SPDX-License-Identifier: GPL-3.0
+
+#include <libsolutil/Common.h>
+
+#include <liblangutil/Exceptions.h>
+
+using namespace solidity;
+
+bool solidity::fitsPrecisionBaseX(bigint const& _mantissa, double _log2OfBase, uint32_t _exp)
+{
+	if (_mantissa == 0)
+		return true;
+
+	solAssert(_mantissa > 0, "");
+
+	size_t const bitsMax = 4096;
+
+	unsigned mostSignificantMantissaBit = boost::multiprecision::msb(_mantissa);
+	if (mostSignificantMantissaBit > bitsMax) // _mantissa >= 2 ^ 4096
+		return false;
+
+	bigint bitsNeeded = mostSignificantMantissaBit + bigint(floor(double(_exp) * _log2OfBase)) + 1;
+	return bitsNeeded <= bitsMax;
+}
diff --git a/libsolutil/Common.h b/libsolutil/Common.h
index aae2fa859..659ea2e3e 100644
--- a/libsolutil/Common.h
+++ b/libsolutil/Common.h
@@ -107,6 +107,10 @@ inline u256 exp256(u256 _base, u256 _exponent)
 	return result;
 }
 
+/// Checks whether _mantissa * (X ** _exp) fits into 4096 bits,
+/// where X is given indirectly via _log2OfBase = log2(X).
+bool fitsPrecisionBaseX(bigint const& _mantissa, double _log2OfBase, uint32_t _exp);
+
 inline std::ostream& operator<<(std::ostream& os, bytes const& _bytes)
 {
 	std::ostringstream ss;
diff --git a/test/libsolidity/semanticTests/constantEvaluator/negative_fractional_mod.sol b/test/libsolidity/semanticTests/constantEvaluator/negative_fractional_mod.sol
new file mode 100644
index 000000000..21675e51a
--- /dev/null
+++ b/test/libsolidity/semanticTests/constantEvaluator/negative_fractional_mod.sol
@@ -0,0 +1,11 @@
+contract C {
+    function f() public pure returns (int, int) {
+        int x = int((-(-5.2 % 3)) * 5);
+        int t = 5;
+        return (x, (-(-t % 3)) * 5);
+    }
+}
+// ====
+// compileViaYul: also
+// ----
+// f() -> 11, 10
diff --git a/test/libsolidity/semanticTests/constantEvaluator/rounding.sol b/test/libsolidity/semanticTests/constantEvaluator/rounding.sol
new file mode 100644
index 000000000..a640d8676
--- /dev/null
+++ b/test/libsolidity/semanticTests/constantEvaluator/rounding.sol
@@ -0,0 +1,15 @@
+contract C {
+    int constant a = 7;
+    int constant b = 3;
+    int constant c = a / b;
+    int constant d = (-a) / b;
+    function f() public pure returns (uint, int, uint, int) {
+        uint[c] memory x;
+        uint[-d] memory y;
+        return (x.length, c, y.length, -d);
+    }
+}
+// ====
+// compileViaYul: also
+// ----
+// f() -> 2, 2, 2, 2
diff --git a/test/libsolidity/semanticTests/constants/consteval_array_length.sol b/test/libsolidity/semanticTests/constants/consteval_array_length.sol
new file mode 100644
index 000000000..91e929834
--- /dev/null
+++ b/test/libsolidity/semanticTests/constants/consteval_array_length.sol
@@ -0,0 +1,14 @@
+contract C {
+    uint constant a = 12;
+    uint constant b = 10;
+
+    function f() public pure returns (uint, uint) {
+        uint[(a / b) * b] memory x;
+        return (x.length, (a / b) * b);
+    }
+}
+// ====
+// compileViaYul: true
+// ----
+// constructor() ->
+// f() -> 0x0a, 0x0a
diff --git a/test/libsolidity/syntaxTests/array/length/complex_cyclic_constant.sol b/test/libsolidity/syntaxTests/array/length/complex_cyclic_constant.sol
index 38018165c..0710124a1 100644
--- a/test/libsolidity/syntaxTests/array/length/complex_cyclic_constant.sol
+++ b/test/libsolidity/syntaxTests/array/length/complex_cyclic_constant.sol
@@ -7,4 +7,4 @@ contract C {
     }
 }
 // ----
-// TypeError 5210: (36-39): Cyclic constant definition (or maximum recursion depth exhausted).
+// TypeError 5210: (17-44): Cyclic constant definition (or maximum recursion depth exhausted).
diff --git a/test/libsolidity/syntaxTests/array/length/const_cannot_be_fractional.sol b/test/libsolidity/syntaxTests/array/length/const_cannot_be_fractional.sol
index ca200cdd0..2145d7025 100644
--- a/test/libsolidity/syntaxTests/array/length/const_cannot_be_fractional.sol
+++ b/test/libsolidity/syntaxTests/array/length/const_cannot_be_fractional.sol
@@ -3,4 +3,4 @@ contract C {
     uint[L] ids;
 }
 // ----
-// TypeError 3208: (51-52): Array with fractional length specified.
+// TypeError 5462: (51-52): Invalid array length, expected integer literal or constant expression.
diff --git a/test/libsolidity/syntaxTests/array/length/cyclic_constant.sol b/test/libsolidity/syntaxTests/array/length/cyclic_constant.sol
index 08a5f1cf9..dd089e4d0 100644
--- a/test/libsolidity/syntaxTests/array/length/cyclic_constant.sol
+++ b/test/libsolidity/syntaxTests/array/length/cyclic_constant.sol
@@ -5,4 +5,4 @@ contract C {
     }
 }
 // ----
-// TypeError 5210: (37-40): Cyclic constant definition (or maximum recursion depth exhausted).
+// TypeError 5210: (17-40): Cyclic constant definition (or maximum recursion depth exhausted).
diff --git a/test/libsolidity/syntaxTests/constantEvaluator/overflow.sol b/test/libsolidity/syntaxTests/constantEvaluator/overflow.sol
new file mode 100644
index 000000000..55bd27901
--- /dev/null
+++ b/test/libsolidity/syntaxTests/constantEvaluator/overflow.sol
@@ -0,0 +1,9 @@
+contract C {
+    uint8 constant a = 255;
+    uint16 constant b = a + 2;
+    function f() public pure {
+        uint[b] memory x;
+    }
+}
+// ----
+// TypeError 2643: (65-70): Arithmetic error when computing constant value.
diff --git a/test/libsolidity/syntaxTests/constantEvaluator/unary_fine.sol b/test/libsolidity/syntaxTests/constantEvaluator/unary_fine.sol
new file mode 100644
index 000000000..f36c45c0d
--- /dev/null
+++ b/test/libsolidity/syntaxTests/constantEvaluator/unary_fine.sol
@@ -0,0 +1,8 @@
+contract C {
+    int8 constant a = -7;
+    function f() public pure {
+        uint[-a] memory x;
+        x[0] = 2;
+    }
+}
+// ----
diff --git a/test/libsolidity/syntaxTests/constantEvaluator/underflow.sol b/test/libsolidity/syntaxTests/constantEvaluator/underflow.sol
new file mode 100644
index 000000000..6ca25911a
--- /dev/null
+++ b/test/libsolidity/syntaxTests/constantEvaluator/underflow.sol
@@ -0,0 +1,8 @@
+contract C {
+    uint8 constant a = 0;
+    function f() public pure {
+        uint[a - 1] memory x;
+    }
+}
+// ----
+// TypeError 2643: (83-88): Arithmetic error when computing constant value.
diff --git a/test/libsolidity/syntaxTests/constantEvaluator/underflow_unary.sol b/test/libsolidity/syntaxTests/constantEvaluator/underflow_unary.sol
new file mode 100644
index 000000000..5887ab19d
--- /dev/null
+++ b/test/libsolidity/syntaxTests/constantEvaluator/underflow_unary.sol
@@ -0,0 +1,8 @@
+contract C {
+    int8 constant a = -128;
+    function f() public pure {
+        uint[-a] memory x;
+    }
+}
+// ----
+// TypeError 3667: (85-87): Arithmetic error when computing constant value.
diff --git a/test/libsolidity/syntaxTests/nameAndTypeResolution/308_rational_unary_plus_operation.sol b/test/libsolidity/syntaxTests/nameAndTypeResolution/308_rational_unary_plus_operation.sol
index 8b401c1ae..276c6533d 100644
--- a/test/libsolidity/syntaxTests/nameAndTypeResolution/308_rational_unary_plus_operation.sol
+++ b/test/libsolidity/syntaxTests/nameAndTypeResolution/308_rational_unary_plus_operation.sol
@@ -7,3 +7,4 @@ contract test {
 }
 // ----
 // SyntaxError 9636: (70-75): Use of unary + is disallowed.
+// TypeError 4907: (70-75): Unary operator + cannot be applied to type rational_const 13 / 4
diff --git a/test/libsolidity/syntaxTests/nameAndTypeResolution/array_length_fractional_computed.sol b/test/libsolidity/syntaxTests/nameAndTypeResolution/array_length_fractional_computed.sol
new file mode 100644
index 000000000..dd4c8cb83
--- /dev/null
+++ b/test/libsolidity/syntaxTests/nameAndTypeResolution/array_length_fractional_computed.sol
@@ -0,0 +1,10 @@
+contract test {
+    uint constant a = 7;
+    uint constant b = 3;
+    function f() public {
+        uint[a / b] memory x; x[0];
+        uint[7 / 3] memory y; y[0];
+    }
+}
+// ----
+// TypeError 3208: (141-146): Array with fractional length specified.
diff --git a/test/libsolidity/syntaxTests/types/rational_number_exp_limit_fail.sol b/test/libsolidity/syntaxTests/types/rational_number_exp_limit_fail.sol
index 4a9fc7349..2d7fbdfad 100644
--- a/test/libsolidity/syntaxTests/types/rational_number_exp_limit_fail.sol
+++ b/test/libsolidity/syntaxTests/types/rational_number_exp_limit_fail.sol
@@ -19,7 +19,7 @@ contract c {
     }
 }
 // ----
-// TypeError 2271: (71-112): Operator ** not compatible with types int_const 1797...(301 digits omitted)...7216 and int_const 4. Precision of rational constants is limited to 4096 bits.
+// TypeError 2271: (71-112): Operator ** not compatible with types int_const 1797...(301 digits omitted)...7216 and int_const 4
 // TypeError 7407: (71-112): Type int_const 1797...(301 digits omitted)...7216 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
 // TypeError 2271: (135-151): Operator ** not compatible with types int_const 4 and int_const 1157...(70 digits omitted)...9936
 // TypeError 7407: (126-169): Type int_const 1340...(147 digits omitted)...4096 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
@@ -29,13 +29,13 @@ contract c {
 // TypeError 2271: (258-270): Operator ** not compatible with types int_const -2 and int_const 1000...(1226 digits omitted)...0000
 // TypeError 2271: (284-296): Operator ** not compatible with types int_const 2 and int_const -100...(1227 digits omitted)...0000
 // TypeError 2271: (310-323): Operator ** not compatible with types int_const -2 and int_const -100...(1227 digits omitted)...0000
-// TypeError 2271: (337-348): Operator ** not compatible with types int_const 1000...(1226 digits omitted)...0000 and int_const 2. Precision of rational constants is limited to 4096 bits.
+// TypeError 2271: (337-348): Operator ** not compatible with types int_const 1000...(1226 digits omitted)...0000 and int_const 2
 // TypeError 7407: (337-348): Type int_const 1000...(1226 digits omitted)...0000 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
-// TypeError 2271: (362-374): Operator ** not compatible with types int_const -100...(1227 digits omitted)...0000 and int_const 2. Precision of rational constants is limited to 4096 bits.
+// TypeError 2271: (362-374): Operator ** not compatible with types int_const -100...(1227 digits omitted)...0000 and int_const 2
 // TypeError 7407: (362-374): Type int_const -100...(1227 digits omitted)...0000 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
-// TypeError 2271: (388-400): Operator ** not compatible with types int_const 1000...(1226 digits omitted)...0000 and int_const -2. Precision of rational constants is limited to 4096 bits.
+// TypeError 2271: (388-400): Operator ** not compatible with types int_const 1000...(1226 digits omitted)...0000 and int_const -2
 // TypeError 7407: (388-400): Type int_const 1000...(1226 digits omitted)...0000 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
-// TypeError 2271: (414-427): Operator ** not compatible with types int_const -100...(1227 digits omitted)...0000 and int_const -2. Precision of rational constants is limited to 4096 bits.
+// TypeError 2271: (414-427): Operator ** not compatible with types int_const -100...(1227 digits omitted)...0000 and int_const -2
 // TypeError 7407: (414-427): Type int_const -100...(1227 digits omitted)...0000 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.
 // TypeError 2271: (441-457): Operator ** not compatible with types int_const 1000...(1226 digits omitted)...0000 and int_const 1000...(1226 digits omitted)...0000
 // TypeError 7407: (441-457): Type int_const 1000...(1226 digits omitted)...0000 is not implicitly convertible to expected type int256. Literal is too large to fit in int256.