#include "storm/storage/dd/sylvan/InternalSylvanBdd.h"

#include <boost/functional/hash.hpp>

#include "storm/storage/dd/sylvan/InternalSylvanDdManager.h"
#include "storm/storage/dd/sylvan/InternalSylvanAdd.h"
#include "storm/storage/dd/sylvan/SylvanAddIterator.h"

#include "storm/storage/BitVector.h"
#include "storm/storage/PairHash.h"

#include "storm/utility/macros.h"
#include "storm/exceptions/InvalidOperationException.h"
#include "storm/exceptions/NotSupportedException.h"

#include "storm/adapters/CarlAdapter.h"
#include "storm-config.h"

namespace storm {
    namespace dd {
        InternalBdd<DdType::Sylvan>::InternalBdd(InternalDdManager<DdType::Sylvan> const* ddManager, sylvan::Bdd const& sylvanBdd) : ddManager(ddManager), sylvanBdd(sylvanBdd) {
            // Intentionally left empty.
        }
        
        template<typename ValueType>
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::fromVector(InternalDdManager<DdType::Sylvan> const* ddManager, std::vector<ValueType> const& values, Odd const& odd, std::vector<uint_fast64_t> const& sortedDdVariableIndices, std::function<bool (ValueType const&)> const& filter) {
            uint_fast64_t offset = 0;
            return InternalBdd<DdType::Sylvan>(ddManager, sylvan::Bdd(fromVectorRec(offset, 0, sortedDdVariableIndices.size(), values, odd, sortedDdVariableIndices, filter)));
        }
        
        template<typename ValueType>
        BDD InternalBdd<DdType::Sylvan>::fromVectorRec(uint_fast64_t& currentOffset, uint_fast64_t currentLevel, uint_fast64_t maxLevel, std::vector<ValueType> const& values, Odd const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::function<bool (ValueType const&)> const& filter) {
            if (currentLevel == maxLevel) {
                // If we are in a terminal node of the ODD, we need to check whether the then-offset of the ODD is one
                // (meaning the encoding is a valid one) or zero (meaning the encoding is not valid). Consequently, we
                // need to copy the next value of the vector iff the then-offset is greater than zero.
                if (odd.getThenOffset() > 0) {
                    if (filter(values[currentOffset++])) {
                        return sylvan_true;
                    } else {
                        return sylvan_false;
                    }
                } else {
                    return sylvan_false;
                }
            } else {
                // If the total offset is zero, we can just return the constant zero DD.
                if (odd.getThenOffset() + odd.getElseOffset() == 0) {
                    return sylvan_false;
                }
                
                // Determine the new else-successor.
                BDD elseSuccessor;
                if (odd.getElseOffset() > 0) {
                    elseSuccessor = fromVectorRec(currentOffset, currentLevel + 1, maxLevel, values, odd.getElseSuccessor(), ddVariableIndices, filter);
                } else {
                    elseSuccessor = sylvan_false;
                }
                bdd_refs_push(elseSuccessor);
                
                // Determine the new then-successor.
                BDD thenSuccessor;
                if (odd.getThenOffset() > 0) {
                    thenSuccessor = fromVectorRec(currentOffset, currentLevel + 1, maxLevel, values, odd.getThenSuccessor(), ddVariableIndices, filter);
                } else {
                    thenSuccessor = sylvan_false;
                }
                bdd_refs_push(thenSuccessor);
                
                // Create a node representing ITE(currentVar, thenSuccessor, elseSuccessor);
                BDD currentVar = sylvan_ithvar(static_cast<BDDVAR>(ddVariableIndices[currentLevel]));
                bdd_refs_push(currentVar);

                LACE_ME;
                BDD result = sylvan_ite(currentVar, thenSuccessor, elseSuccessor);
                
                // Dispose of the intermediate results.
                bdd_refs_pop(3);
                
                return result;
            }
        }
        
        bool InternalBdd<DdType::Sylvan>::operator==(InternalBdd<DdType::Sylvan> const& other) const {
            return sylvanBdd == other.sylvanBdd;
        }
        
        bool InternalBdd<DdType::Sylvan>::operator!=(InternalBdd<DdType::Sylvan> const& other) const {
            return sylvanBdd != other.sylvanBdd;
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::relationalProduct(InternalBdd<DdType::Sylvan> const& relation, std::vector<InternalBdd<DdType::Sylvan>> const&, std::vector<InternalBdd<DdType::Sylvan>> const&) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.RelNext(relation.sylvanBdd, sylvan::Bdd(sylvan_false)));
        }

        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::inverseRelationalProduct(InternalBdd<DdType::Sylvan> const& relation, std::vector<InternalBdd<DdType::Sylvan>> const&, std::vector<InternalBdd<DdType::Sylvan>> const&) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.RelPrev(relation.sylvanBdd, sylvan::Bdd(sylvan_false)));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::inverseRelationalProductWithExtendedRelation(InternalBdd<DdType::Sylvan> const& relation, std::vector<InternalBdd<DdType::Sylvan>> const& rowVariables, std::vector<InternalBdd<DdType::Sylvan>> const& columnVariables) const {
            // Currently, there is no specialized version to perform this operation, so we fall back to the regular operations.
            
            InternalBdd<DdType::Sylvan> columnCube = ddManager->getBddOne();
            for (auto const& variable : columnVariables) {
                columnCube &= variable;
            }

            return this->swapVariables(rowVariables, columnVariables).andExists(relation, columnCube);
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::ite(InternalBdd<DdType::Sylvan> const& thenDd, InternalBdd<DdType::Sylvan> const& elseDd) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.Ite(thenDd.sylvanBdd, elseDd.sylvanBdd));
        }
        
        template<typename ValueType>
        InternalAdd<DdType::Sylvan, ValueType> InternalBdd<DdType::Sylvan>::ite(InternalAdd<DdType::Sylvan, ValueType> const& thenAdd, InternalAdd<DdType::Sylvan, ValueType> const& elseAdd) const {
            return InternalAdd<DdType::Sylvan, ValueType>(ddManager, this->sylvanBdd.Ite(thenAdd.getSylvanMtbdd(), elseAdd.getSylvanMtbdd()));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::operator||(InternalBdd<DdType::Sylvan> const& other) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd | other.sylvanBdd);
        }
        
        InternalBdd<DdType::Sylvan>& InternalBdd<DdType::Sylvan>::operator|=(InternalBdd<DdType::Sylvan> const& other) {
            this->sylvanBdd |= other.sylvanBdd;
            return *this;
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::operator&&(InternalBdd<DdType::Sylvan> const& other) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd & other.sylvanBdd);
        }
        
        InternalBdd<DdType::Sylvan>& InternalBdd<DdType::Sylvan>::operator&=(InternalBdd<DdType::Sylvan> const& other) {
            this->sylvanBdd &= other.sylvanBdd;
            return *this;
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::iff(InternalBdd<DdType::Sylvan> const& other) const {
            return InternalBdd<DdType::Sylvan>(ddManager, !(this->sylvanBdd ^ other.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::exclusiveOr(InternalBdd<DdType::Sylvan> const& other) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd ^ other.sylvanBdd);
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::implies(InternalBdd<DdType::Sylvan> const& other) const {
            return InternalBdd<DdType::Sylvan>(ddManager, (!this->sylvanBdd) | other.sylvanBdd);
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::operator!() const {
            return InternalBdd<DdType::Sylvan>(ddManager, !this->sylvanBdd);
        }
        
        InternalBdd<DdType::Sylvan>& InternalBdd<DdType::Sylvan>::complement() {
            this->sylvanBdd = !this->sylvanBdd;
            return *this;
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::existsAbstract(InternalBdd<DdType::Sylvan> const& cube) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.ExistAbstract(cube.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::existsAbstractRepresentative(InternalBdd<DdType::Sylvan> const& cube) const {
			return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.ExistAbstractRepresentative(cube.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::universalAbstract(InternalBdd<DdType::Sylvan> const& cube) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.UnivAbstract(cube.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::andExists(InternalBdd<DdType::Sylvan> const& other, InternalBdd<DdType::Sylvan> const& cube) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.AndAbstract(other.sylvanBdd, cube.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::constrain(InternalBdd<DdType::Sylvan> const& constraint) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.Constrain(constraint.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::restrict(InternalBdd<DdType::Sylvan> const& constraint) const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.Restrict(constraint.sylvanBdd));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::swapVariables(std::vector<InternalBdd<DdType::Sylvan>> const& from, std::vector<InternalBdd<DdType::Sylvan>> const& to) const {
            std::vector<uint32_t> fromIndices;
            std::vector<uint32_t> toIndices;
            for (auto it1 = from.begin(), ite1 = from.end(), it2 = to.begin(); it1 != ite1; ++it1, ++it2) {
                fromIndices.push_back(it1->getIndex());
                fromIndices.push_back(it2->getIndex());
                toIndices.push_back(it2->getIndex());
                toIndices.push_back(it1->getIndex());
            }
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.Permute(fromIndices, toIndices));
        }
        
        InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::getSupport() const {
            return InternalBdd<DdType::Sylvan>(ddManager, this->sylvanBdd.Support());
        }
        
        uint_fast64_t InternalBdd<DdType::Sylvan>::getNonZeroCount(uint_fast64_t numberOfDdVariables) const {
            if (numberOfDdVariables == 0) {
                return 0;
            }
            return static_cast<uint_fast64_t>(this->sylvanBdd.SatCount(numberOfDdVariables));
        }
        
        uint_fast64_t InternalBdd<DdType::Sylvan>::getLeafCount() const {
            // For BDDs, the leaf count is always one, because the only leaf is the false leaf (and true is represented
            // by a negation edge to false).
            return 1;
        }
        
        uint_fast64_t InternalBdd<DdType::Sylvan>::getNodeCount() const {
            // We have to add one to also count the false-leaf, which is the only leaf appearing in BDDs.
            return static_cast<uint_fast64_t>(this->sylvanBdd.NodeCount()) + 1;
        }
        
        bool InternalBdd<DdType::Sylvan>::isOne() const {
            return this->sylvanBdd.isOne();
        }
        
        bool InternalBdd<DdType::Sylvan>::isZero() const {
            return this->sylvanBdd.isZero();
        }
        
        uint_fast64_t InternalBdd<DdType::Sylvan>::getIndex() const {
            return static_cast<uint_fast64_t>(this->sylvanBdd.TopVar());
        }
        
        uint_fast64_t InternalBdd<DdType::Sylvan>::getLevel() const {
            return this->getIndex();
        }
        
        void InternalBdd<DdType::Sylvan>::exportToDot(std::string const& filename, std::vector<std::string> const&) const {
            FILE* filePointer = fopen(filename.c_str() , "w");
            this->sylvanBdd.PrintDot(filePointer);
            fclose(filePointer);
        }
        
        sylvan::Bdd& InternalBdd<DdType::Sylvan>::getSylvanBdd() {
            return sylvanBdd;
        }
        
        sylvan::Bdd const& InternalBdd<DdType::Sylvan>::getSylvanBdd() const {
            return sylvanBdd;
        }
        
        template<typename ValueType>
        InternalAdd<DdType::Sylvan, ValueType> InternalBdd<DdType::Sylvan>::toAdd() const {
            if (std::is_same<ValueType, double>::value) {
                return InternalAdd<DdType::Sylvan, ValueType>(ddManager, this->sylvanBdd.toDoubleMtbdd());
            } else if (std::is_same<ValueType, uint_fast64_t>::value) {
                return InternalAdd<DdType::Sylvan, ValueType>(ddManager, this->sylvanBdd.toInt64Mtbdd());
			} 
#ifdef STORM_HAVE_CARL
			else if (std::is_same<ValueType, storm::RationalFunction>::value) {
				return InternalAdd<DdType::Sylvan, ValueType>(ddManager, this->sylvanBdd.toStormRationalFunctionMtbdd());
			} 
#endif
			else {
                STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "Illegal ADD type.");
            }
        }
        
        storm::storage::BitVector InternalBdd<DdType::Sylvan>::toVector(storm::dd::Odd const& rowOdd, std::vector<uint_fast64_t> const& ddVariableIndices) const {
            storm::storage::BitVector result(rowOdd.getTotalOffset());
            this->toVectorRec(bdd_regular(this->getSylvanBdd().GetBDD()), result, rowOdd, bdd_isnegated(this->getSylvanBdd().GetBDD()), 0, ddVariableIndices.size(), 0, ddVariableIndices);
            return result;
        }
        
        void InternalBdd<DdType::Sylvan>::toVectorRec(BDD dd, storm::storage::BitVector& result, Odd const& rowOdd, bool complement, uint_fast64_t currentRowLevel, uint_fast64_t maxLevel, uint_fast64_t currentRowOffset, std::vector<uint_fast64_t> const& ddRowVariableIndices) const {
            // If there are no more values to select, we can directly return.
            if (dd == sylvan_false && !complement) {
                return;
            } else if (dd == sylvan_true && complement) {
                return;
            }
            
            // If we are at the maximal level, the value to be set is stored as a constant in the DD.
            if (currentRowLevel == maxLevel) {
                result.set(currentRowOffset, true);
            } else if (ddRowVariableIndices[currentRowLevel] < sylvan_var(dd)) {
                toVectorRec(dd, result, rowOdd.getElseSuccessor(), complement, currentRowLevel + 1, maxLevel, currentRowOffset, ddRowVariableIndices);
                toVectorRec(dd, result, rowOdd.getThenSuccessor(), complement, currentRowLevel + 1, maxLevel, currentRowOffset + rowOdd.getElseOffset(), ddRowVariableIndices);
            } else {
                // Otherwise, we compute the ODDs for both the then- and else successors.
                BDD elseDdNode = sylvan_low(dd);
                BDD thenDdNode = sylvan_high(dd);
                
                // Determine whether we have to evaluate the successors as if they were complemented.
                bool elseComplemented = bdd_isnegated(elseDdNode) ^ complement;
                bool thenComplemented = bdd_isnegated(thenDdNode) ^ complement;
                
                toVectorRec(bdd_regular(elseDdNode), result, rowOdd.getElseSuccessor(), elseComplemented, currentRowLevel + 1, maxLevel, currentRowOffset, ddRowVariableIndices);
                toVectorRec(bdd_regular(thenDdNode), result, rowOdd.getThenSuccessor(), thenComplemented, currentRowLevel + 1, maxLevel, currentRowOffset + rowOdd.getElseOffset(), ddRowVariableIndices);
            }
        }
        
        Odd InternalBdd<DdType::Sylvan>::createOdd(std::vector<uint_fast64_t> const& ddVariableIndices) const {
            // Prepare a unique table for each level that keeps the constructed ODD nodes unique.
            std::vector<std::unordered_map<std::pair<BDD, bool>, std::shared_ptr<Odd>, HashFunctor>> uniqueTableForLevels(ddVariableIndices.size() + 1);
            
            // Now construct the ODD structure from the BDD.
            std::shared_ptr<Odd> rootOdd = createOddRec(bdd_regular(this->getSylvanBdd().GetBDD()), bdd_isnegated(this->getSylvanBdd().GetBDD()), 0, ddVariableIndices.size(), ddVariableIndices, uniqueTableForLevels);
            
            // Return a copy of the root node to remove the shared_ptr encapsulation.
            return Odd(*rootOdd);
        }
        
        std::size_t InternalBdd<DdType::Sylvan>::HashFunctor::operator()(std::pair<BDD, bool> const& key) const {
            std::size_t result = 0;
            boost::hash_combine(result, key.first);
            boost::hash_combine(result, key.second);
            return result;
        }
        
        std::shared_ptr<Odd> InternalBdd<DdType::Sylvan>::createOddRec(BDD dd, bool complement, uint_fast64_t currentLevel, uint_fast64_t maxLevel, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<std::unordered_map<std::pair<BDD, bool>, std::shared_ptr<Odd>, HashFunctor>>& uniqueTableForLevels) {
            // Check whether the ODD for this node has already been computed (for this level) and if so, return this instead.
            auto const& iterator = uniqueTableForLevels[currentLevel].find(std::make_pair(dd, complement));
            if (iterator != uniqueTableForLevels[currentLevel].end()) {
                return iterator->second;
            } else {
                // Otherwise, we need to recursively compute the ODD.
                
                // If we are already at the maximal level that is to be considered, we can simply create an Odd without
                // successors.
                if (currentLevel == maxLevel) {
                    uint_fast64_t elseOffset = 0;
                    uint_fast64_t thenOffset = 0;
                    
                    // If the DD is not the zero leaf, then the then-offset is 1.
                    if (dd != mtbdd_false) {
                        thenOffset = 1;
                    }
                    
                    // If we need to complement the 'terminal' node, we need to negate its offset.
                    if (complement) {
                        thenOffset = 1 - thenOffset;
                    }
                    
                    auto oddNode = std::make_shared<Odd>(nullptr, elseOffset, nullptr, thenOffset);
                    uniqueTableForLevels[currentLevel].emplace(std::make_pair(dd, complement), oddNode);
                    return oddNode;
                } else if (bdd_isterminal(dd) || ddVariableIndices[currentLevel] < sylvan_var(dd)) {
                    // If we skipped the level in the DD, we compute the ODD just for the else-successor and use the same
                    // node for the then-successor as well.
                    std::shared_ptr<Odd> elseNode = createOddRec(dd, complement, currentLevel + 1, maxLevel, ddVariableIndices, uniqueTableForLevels);
                    std::shared_ptr<Odd> thenNode = elseNode;
                    uint_fast64_t totalOffset = elseNode->getElseOffset() + elseNode->getThenOffset();
                    auto oddNode = std::make_shared<Odd>(elseNode, totalOffset, thenNode, totalOffset);
                    uniqueTableForLevels[currentLevel].emplace(std::make_pair(dd, complement), oddNode);
                    return oddNode;
                } else {
                    // Otherwise, we compute the ODDs for both the then- and else successors.
                    BDD thenDdNode = sylvan_high(dd);
                    BDD elseDdNode = sylvan_low(dd);

                    // Determine whether we have to evaluate the successors as if they were complemented.
                    bool elseComplemented = bdd_isnegated(elseDdNode) ^ complement;
                    bool thenComplemented = bdd_isnegated(thenDdNode) ^ complement;
                    
                    std::shared_ptr<Odd> elseNode = createOddRec(bdd_regular(elseDdNode), elseComplemented, currentLevel + 1, maxLevel, ddVariableIndices, uniqueTableForLevels);
                    std::shared_ptr<Odd> thenNode = createOddRec(bdd_regular(thenDdNode), thenComplemented, currentLevel + 1, maxLevel, ddVariableIndices, uniqueTableForLevels);
                    
                    auto oddNode = std::make_shared<Odd>(elseNode, elseNode->getElseOffset() + elseNode->getThenOffset(), thenNode, thenNode->getElseOffset() + thenNode->getThenOffset());
                    uniqueTableForLevels[currentLevel].emplace(std::make_pair(dd, complement), oddNode);
                    return oddNode;
                }
            }
        }
        
        template<typename ValueType>
        void InternalBdd<DdType::Sylvan>::filterExplicitVector(Odd const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<ValueType> const& sourceValues, std::vector<ValueType>& targetValues) const {
            uint_fast64_t currentIndex = 0;
            filterExplicitVectorRec(bdd_regular(this->getSylvanBdd().GetBDD()), 0, bdd_isnegated(this->getSylvanBdd().GetBDD()), ddVariableIndices.size(), ddVariableIndices, 0, odd, targetValues, currentIndex, sourceValues);
        }
        
        template<typename ValueType>
        void InternalBdd<DdType::Sylvan>::filterExplicitVectorRec(BDD dd, uint_fast64_t currentLevel, bool complement, uint_fast64_t maxLevel, std::vector<uint_fast64_t> const& ddVariableIndices, uint_fast64_t currentOffset, storm::dd::Odd const& odd, std::vector<ValueType>& result, uint_fast64_t& currentIndex, std::vector<ValueType> const& values) {
            // If there are no more values to select, we can directly return.
            if (dd == sylvan_false && !complement) {
                return;
            } else if (dd == sylvan_true && complement) {
                return;
            }
            
            if (currentLevel == maxLevel) {
                result[currentIndex++] = values[currentOffset];
            } else if (ddVariableIndices[currentLevel] < sylvan_var(dd)) {
                // If we skipped a level, we need to enumerate the explicit entries for the case in which the bit is set
                // and for the one in which it is not set.
                filterExplicitVectorRec(dd, currentLevel + 1, complement, maxLevel, ddVariableIndices, currentOffset, odd.getElseSuccessor(), result, currentIndex, values);
                filterExplicitVectorRec(dd, currentLevel + 1, complement, maxLevel, ddVariableIndices, currentOffset + odd.getElseOffset(), odd.getThenSuccessor(), result, currentIndex, values);
            } else {
                // Otherwise, we compute the ODDs for both the then- and else successors.
                BDD thenDdNode = sylvan_high(dd);
                BDD elseDdNode = sylvan_low(dd);
                
                // Determine whether we have to evaluate the successors as if they were complemented.
                bool elseComplemented = bdd_isnegated(elseDdNode) ^ complement;
                bool thenComplemented = bdd_isnegated(thenDdNode) ^ complement;
                
                filterExplicitVectorRec(bdd_regular(elseDdNode), currentLevel + 1, elseComplemented, maxLevel, ddVariableIndices, currentOffset, odd.getElseSuccessor(), result, currentIndex, values);
                filterExplicitVectorRec(bdd_regular(thenDdNode), currentLevel + 1, thenComplemented, maxLevel, ddVariableIndices, currentOffset + odd.getElseOffset(), odd.getThenSuccessor(), result, currentIndex, values);
            }
        }
        
        std::pair<std::vector<storm::expressions::Expression>, std::unordered_map<uint_fast64_t, storm::expressions::Variable>> InternalBdd<DdType::Sylvan>::toExpression(storm::expressions::ExpressionManager& manager) const {
            std::pair<std::vector<storm::expressions::Expression>, std::unordered_map<uint_fast64_t, storm::expressions::Variable>> result;
            
            // Create (and maintain) a mapping from the DD nodes to a counter that says the how-many-th node (within the
            // nodes of equal index) the node was.
            std::unordered_map<BDD, uint_fast64_t> nodeToCounterMap;
            std::vector<uint_fast64_t> nextCounterForIndex(ddManager->getNumberOfDdVariables(), 0);
            std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable> countIndexToVariablePair;
            
            bool negated = bdd_isnegated(this->getSylvanBdd().GetBDD());
            
            // Translate from the top node downwards.
            storm::expressions::Variable topVariable = this->toExpressionRec(bdd_regular(this->getSylvanBdd().GetBDD()), manager, result.first, result.second, countIndexToVariablePair, nodeToCounterMap, nextCounterForIndex);
            
            // Create the final expression.
            if (negated) {
                result.first.push_back(!topVariable);
            } else {
                result.first.push_back(topVariable);
            }
            
            return result;
        }
        
        storm::expressions::Variable InternalBdd<DdType::Sylvan>::toExpressionRec(BDD dd, storm::expressions::ExpressionManager& manager, std::vector<storm::expressions::Expression>& expressions, std::unordered_map<uint_fast64_t, storm::expressions::Variable>& indexToVariableMap, std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable>& countIndexToVariablePair, std::unordered_map<BDD, uint_fast64_t>& nodeToCounterMap, std::vector<uint_fast64_t>& nextCounterForIndex) {
            STORM_LOG_ASSERT(!bdd_isnegated(dd), "Expected non-negated BDD node.");
            
            // First, try to look up the current node if it's not a terminal node.
            auto nodeCounterIt = nodeToCounterMap.find(dd);
            if (nodeCounterIt != nodeToCounterMap.end()) {
                // If we have found the node, this means we can look up the counter-index pair and get the corresponding variable.
                auto variableIt = countIndexToVariablePair.find(std::make_pair(nodeCounterIt->second, sylvan_var(dd)));
                STORM_LOG_ASSERT(variableIt != countIndexToVariablePair.end(), "Unable to find node.");
                return variableIt->second;
            }
            
            // If the node was not yet encountered, we create a variable and associate it with the appropriate expression.
            storm::expressions::Variable newNodeVariable = manager.declareFreshBooleanVariable();
            
            // Since we want to reuse the variable whenever possible, we insert the appropriate entries in the hash table.
            if (!bdd_isterminal(dd)) {
                // If we are dealing with a non-terminal node, we count it as a new node with this index.
                nodeToCounterMap[dd] = nextCounterForIndex[sylvan_var(dd)];
                countIndexToVariablePair[std::make_pair(nextCounterForIndex[sylvan_var(dd)], sylvan_var(dd))] = newNodeVariable;
                ++nextCounterForIndex[sylvan_var(dd)];
            } else {
                // If it's a terminal node, it is the one leaf and there's no need to keep track of a counter for this level.
                nodeToCounterMap[dd] = 0;
                countIndexToVariablePair[std::make_pair(0, sylvan_var(dd))] = newNodeVariable;
            }
            
            // In the terminal case, we can only have a one since we are considering non-negated nodes only.
            if (bdd_isterminal(dd)) {
                if (dd == sylvan_true) {
                    expressions.push_back(storm::expressions::iff(manager.boolean(true), newNodeVariable));
                } else {
                    expressions.push_back(storm::expressions::iff(manager.boolean(false), newNodeVariable));
                }
            } else {
                // In the non-terminal case, we recursively translate the children nodes and then construct and appropriate ite-expression.
                BDD t = sylvan_high(dd);
                BDD e = sylvan_low(dd);
                BDD T = bdd_regular(t);
                BDD E = bdd_regular(e);
                storm::expressions::Variable thenVariable = toExpressionRec(T, manager, expressions, indexToVariableMap, countIndexToVariablePair, nodeToCounterMap, nextCounterForIndex);
                storm::expressions::Variable elseVariable = toExpressionRec(E, manager, expressions, indexToVariableMap, countIndexToVariablePair, nodeToCounterMap, nextCounterForIndex);
                
                // Create the appropriate expression.
                // Create the appropriate expression.
                auto indexVariable = indexToVariableMap.find(sylvan_var(dd));
                storm::expressions::Variable levelVariable;
                if (indexVariable == indexToVariableMap.end()) {
                    levelVariable = manager.declareFreshBooleanVariable();
                    indexToVariableMap[sylvan_var(dd)] = levelVariable;
                } else {
                    levelVariable = indexVariable->second;
                }
                expressions.push_back(storm::expressions::iff(newNodeVariable, storm::expressions::ite(levelVariable, t == T ? thenVariable : !thenVariable, e == E ? elseVariable : !elseVariable)));
            }
            
            // Return the variable for this node.
            return newNodeVariable;
        }
        
        template InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::fromVector(InternalDdManager<DdType::Sylvan> const* ddManager, std::vector<double> const& values, Odd const& odd, std::vector<uint_fast64_t> const& sortedDdVariableIndices, std::function<bool (double const&)> const& filter);
        template InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::fromVector(InternalDdManager<DdType::Sylvan> const* ddManager, std::vector<uint_fast64_t> const& values, Odd const& odd, std::vector<uint_fast64_t> const& sortedDdVariableIndices, std::function<bool (uint_fast64_t const&)> const& filter);
		template InternalBdd<DdType::Sylvan> InternalBdd<DdType::Sylvan>::fromVector(InternalDdManager<DdType::Sylvan> const* ddManager, std::vector<storm::RationalFunction> const& values, Odd const& odd, std::vector<uint_fast64_t> const& sortedDdVariableIndices, std::function<bool(storm::RationalFunction const&)> const& filter);
        
        template InternalAdd<DdType::Sylvan, double> InternalBdd<DdType::Sylvan>::toAdd() const;
        template InternalAdd<DdType::Sylvan, uint_fast64_t> InternalBdd<DdType::Sylvan>::toAdd() const;
		template InternalAdd<DdType::Sylvan, storm::RationalFunction> InternalBdd<DdType::Sylvan>::toAdd() const;
                
        template void InternalBdd<DdType::Sylvan>::filterExplicitVector(Odd const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<double> const& sourceValues, std::vector<double>& targetValues) const;
        template void InternalBdd<DdType::Sylvan>::filterExplicitVector(Odd const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<uint_fast64_t> const& sourceValues, std::vector<uint_fast64_t>& targetValues) const;
		template void InternalBdd<DdType::Sylvan>::filterExplicitVector(Odd const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<storm::RationalFunction> const& sourceValues, std::vector<storm::RationalFunction>& targetValues) const;
        
        template InternalAdd<DdType::Sylvan, double> InternalBdd<DdType::Sylvan>::ite(InternalAdd<DdType::Sylvan, double> const& thenAdd, InternalAdd<DdType::Sylvan, double> const& elseAdd) const;
        template InternalAdd<DdType::Sylvan, uint_fast64_t> InternalBdd<DdType::Sylvan>::ite(InternalAdd<DdType::Sylvan, uint_fast64_t> const& thenAdd, InternalAdd<DdType::Sylvan, uint_fast64_t> const& elseAdd) const;
		template InternalAdd<DdType::Sylvan, storm::RationalFunction> InternalBdd<DdType::Sylvan>::ite(InternalAdd<DdType::Sylvan, storm::RationalFunction> const& thenAdd, InternalAdd<DdType::Sylvan, storm::RationalFunction> const& elseAdd) const;
    }
}