--- /dev/null
+//===------- ABCD.cpp - Removes redundant conditional branches ------------===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// This pass removes redundant branch instructions. This algorithm was
+// described by Rastislav Bodik, Rajiv Gupta and Vivek Sarkar in their paper
+// "ABCD: Eliminating Array Bounds Checks on Demand (2000)". The original
+// Algorithm was created to remove array bound checks for strongly typed
+// languages. This implementation expands the idea and removes any conditional
+// branches that can be proved redundant, not only those used in array bound
+// checks. With the SSI representation, each variable has a
+// constraint. By analyzing these constraints we can proof that a branch is
+// redundant. When a branch is proved redundant it means that
+// one direction will always be taken; thus, we can change this branch into an
+// unconditional jump.
+// It is advisable to run SimplifyCFG and Aggressive Dead Code Elimination
+// after ABCD to clean up the code.
+// This implementation was created based on the implementation of the ABCD
+// algorithm implemented for the compiler Jitrino.
+//
+//===----------------------------------------------------------------------===//
+
+#define DEBUG_TYPE "abcd"
+#include "llvm/ADT/DenseMap.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "llvm/ADT/Statistic.h"
+#include "llvm/Constants.h"
+#include "llvm/Function.h"
+#include "llvm/Instructions.h"
+#include "llvm/Pass.h"
+#include "llvm/Support/raw_ostream.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Transforms/Scalar.h"
+#include "llvm/Transforms/Utils/SSI.h"
+
+using namespace llvm;
+
+STATISTIC(NumBranchTested, "Number of conditional branches analyzed");
+STATISTIC(NumBranchRemoved, "Number of conditional branches removed");
+
+//namespace {
+
+class ABCD : public FunctionPass {
+ public:
+ static char ID; // Pass identification, replacement for typeid.
+ ABCD() : FunctionPass(&ID) {}
+
+ void getAnalysisUsage(AnalysisUsage &AU) const {
+ AU.addRequired<SSI>();
+ }
+
+ bool runOnFunction(Function &F);
+
+ private:
+ bool modified;
+
+ enum ProveResult {
+ False = 0,
+ Reduced = 1,
+ True = 2
+ };
+
+ typedef ProveResult (*meet_function)(ProveResult, ProveResult);
+ static ProveResult max(ProveResult res1, ProveResult res2) {
+ return (ProveResult) std::max(res1, res2);
+ }
+ static ProveResult min(ProveResult res1, ProveResult res2) {
+ return (ProveResult) std::min(res1, res2);
+ }
+
+ class Bound {
+ public:
+ Bound(APInt v, bool upper) : value(v), upper_bound(upper) {}
+ Bound(const Bound *b, int cnst)
+ : value(b->value - cnst), upper_bound(b->upper_bound) {}
+ Bound(const Bound *b, const APInt &cnst)
+ : value(b->value - cnst), upper_bound(b->upper_bound) {}
+
+ /// Test if Bound is an upper bound
+ bool isUpperBound() const { return upper_bound; }
+
+ /// Get the bitwidth of this bound
+ int32_t getBitWidth() const { return value.getBitWidth(); }
+
+ /// Creates a Bound incrementing the one received
+ static Bound *createIncrement(const Bound *b) {
+ return new Bound(b->isUpperBound() ? b->value+1 : b->value-1,
+ b->upper_bound);
+ }
+
+ /// Creates a Bound decrementing the one received
+ static Bound *createDecrement(const Bound *b) {
+ return new Bound(b->isUpperBound() ? b->value-1 : b->value+1,
+ b->upper_bound);
+ }
+
+ /// Test if two bounds are equal
+ static bool eq(const Bound *a, const Bound *b) {
+ if (!a || !b) return false;
+
+ assert(a->isUpperBound() == b->isUpperBound());
+ return a->value == b->value;
+ }
+
+ /// Test if val is less than or equal to Bound b
+ static bool leq(APInt val, const Bound *b) {
+ if (!b) return false;
+ return b->isUpperBound() ? val.sle(b->value) : val.sge(b->value);
+ }
+
+ /// Test if Bound a is less then or equal to Bound
+ static bool leq(const Bound *a, const Bound *b) {
+ if (!a || !b) return false;
+
+ assert(a->isUpperBound() == b->isUpperBound());
+ return a->isUpperBound() ? a->value.sle(b->value) :
+ a->value.sge(b->value);
+ }
+
+ /// Test if Bound a is less then Bound b
+ static bool lt(const Bound *a, const Bound *b) {
+ if (!a || !b) return false;
+
+ assert(a->isUpperBound() == b->isUpperBound());
+ return a->isUpperBound() ? a->value.slt(b->value) :
+ a->value.sgt(b->value);
+ }
+
+ /// Test if Bound b is greater then or equal val
+ static bool geq(const Bound *b, APInt val) {
+ return leq(val, b);
+ }
+
+ /// Test if Bound a is greater then or equal Bound b
+ static bool geq(const Bound *a, const Bound *b) {
+ return leq(b, a);
+ }
+
+ private:
+ APInt value;
+ bool upper_bound;
+ };
+
+ /// This class is used to store results some parts of the graph,
+ /// so information does not need to be recalculated. The maximum false,
+ /// minimum true and minimum reduced results are stored
+ class MemoizedResultChart {
+ public:
+ MemoizedResultChart() : max_false(NULL), min_true(NULL),
+ min_reduced(NULL) {}
+
+ /// Returns the max false
+ Bound *getFalse() const { return max_false; }
+
+ /// Returns the min true
+ Bound *getTrue() const { return min_true; }
+
+ /// Returns the min reduced
+ Bound *getReduced() const { return min_reduced; }
+
+ /// Return the stored result for this bound
+ ProveResult getResult(const Bound *bound) const;
+
+ /// Stores a false found
+ void addFalse(Bound *bound);
+
+ /// Stores a true found
+ void addTrue(Bound *bound);
+
+ /// Stores a Reduced found
+ void addReduced(Bound *bound);
+
+ /// Clears redundant reduced
+ /// If a min_true is smaller than a min_reduced then the min_reduced
+ /// is unnecessary and then removed. It also works for min_reduced
+ /// begin smaller than max_false.
+ void clearRedundantReduced();
+
+ void clear() {
+ delete max_false;
+ delete min_true;
+ delete min_reduced;
+ }
+
+ private:
+ Bound *max_false, *min_true, *min_reduced;
+ };
+
+ /// This class stores the result found for a node of the graph,
+ /// so these results do not need to be recalculate and only searched for.
+ class MemoizedResult {
+ public:
+ /// Test if there is true result stored from b to a
+ /// that is less then the bound
+ bool hasTrue(Value *b, const Bound *bound) const {
+ Bound *trueBound = map.lookup(b).getTrue();
+ return trueBound && Bound::leq(trueBound, bound);
+ }
+
+ /// Test if there is false result stored from b to a
+ /// that is less then the bound
+ bool hasFalse(Value *b, const Bound *bound) const {
+ Bound *falseBound = map.lookup(b).getFalse();
+ return falseBound && Bound::leq(falseBound, bound);
+ }
+
+ /// Test if there is reduced result stored from b to a
+ /// that is less then the bound
+ bool hasReduced(Value *b, const Bound *bound) const {
+ Bound *reducedBound = map.lookup(b).getReduced();
+ return reducedBound && Bound::leq(reducedBound, bound);
+ }
+
+ /// Returns the stored bound for b
+ ProveResult getBoundResult(Value *b, Bound *bound) {
+ return map[b].getResult(bound);
+ }
+
+ /// Clears the map
+ void clear() {
+ DenseMapIterator<Value*, MemoizedResultChart> begin = map.begin();
+ DenseMapIterator<Value*, MemoizedResultChart> end = map.end();
+ for (; begin != end; ++begin) {
+ begin->second.clear();
+ }
+ map.clear();
+ }
+
+ /// Stores the bound found
+ void updateBound(Value *b, Bound *bound, const ProveResult res);
+
+ private:
+ // Maps a nod in the graph with its results found.
+ DenseMap<Value*, MemoizedResultChart> map;
+ };
+
+ /// This class represents an edge in the inequality graph used by the
+ /// ABCD algorithm. An edge connects node v to node u with a value c if
+ /// we could infer a constraint v <= u + c in the source program.
+ class Edge {
+ public:
+ Edge(Value *V, APInt val, bool upper) : vertex(V), value(val),
+ upper_bound(upper)
+ {}
+
+ Value *getVertex() const { return vertex; }
+ const APInt &getValue() const { return value; }
+ bool isUpperBound() const { return upper_bound; }
+
+ private:
+ Value *vertex;
+ APInt value;
+ bool upper_bound;
+ };
+
+ /// Weighted and Directed graph to represent constraints.
+ /// There is one type of constraint, a <= b + X, which will generate an
+ /// edge from b to a with weight X.
+ class InequalityGraph {
+ public:
+
+ /// Adds an edge from V_from to V_to with weight value
+ void addEdge(Value *V_from, Value *V_to, APInt value, bool upper);
+
+ /// Test if there is a node V
+ bool hasNode(Value *V) const { return graph.count(V); }
+
+ /// Test if there is any edge from V in the upper direction
+ bool hasEdge(Value *V, bool upper) const;
+
+ /// Returns all edges pointed by vertex V
+ SmallPtrSet<Edge *, 16> getEdges(Value *V) const {
+ return graph.lookup(V);
+ }
+
+ /// Prints the graph in dot format.
+ /// Blue edges represent upper bound and Red lower bound.
+ void printGraph(raw_ostream &OS, Function &F) const {
+ printHeader(OS, F);
+ printBody(OS);
+ printFooter(OS);
+ }
+
+ /// Clear the graph
+ void clear() {
+ graph.clear();
+ }
+
+ private:
+ DenseMap<Value *, SmallPtrSet<Edge *, 16> > graph;
+
+ /// Adds a Node to the graph.
+ DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator addNode(Value *V) {
+ SmallPtrSet<Edge *, 16> p;
+ return graph.insert(std::make_pair(V, p)).first;
+ }
+
+ /// Prints the header of the dot file
+ void printHeader(raw_ostream &OS, Function &F) const;
+
+ /// Prints the footer of the dot file
+ void printFooter(raw_ostream &OS) const {
+ OS << "}\n";
+ }
+
+ /// Prints the body of the dot file
+ void printBody(raw_ostream &OS) const;
+
+ /// Prints vertex source to the dot file
+ void printVertex(raw_ostream &OS, Value *source) const;
+
+ /// Prints the edge to the dot file
+ void printEdge(raw_ostream &OS, Value *source, Edge *edge) const;
+
+ void printName(raw_ostream &OS, Value *info) const;
+ };
+
+ /// Iterates through all BasicBlocks, if the Terminator Instruction
+ /// uses an Comparator Instruction, all operands of this comparator
+ /// are sent to be transformed to SSI. Only Instruction operands are
+ /// transformed.
+ void createSSI(Function &F);
+
+ /// Creates the graphs for this function.
+ /// It will look for all comparators used in branches, and create them.
+ /// These comparators will create constraints for any instruction as an
+ /// operand.
+ void executeABCD(Function &F);
+
+ /// Seeks redundancies in the comparator instruction CI.
+ /// If the ABCD algorithm can prove that the comparator CI always
+ /// takes one way, then the Terminator Instruction TI is substituted from
+ /// a conditional branch to a unconditional one.
+ /// This code basically receives a comparator, and verifies which kind of
+ /// instruction it is. Depending on the kind of instruction, we use different
+ /// strategies to prove its redundancy.
+ void seekRedundancy(ICmpInst *ICI, TerminatorInst *TI);
+
+ /// Substitutes Terminator Instruction TI, that is a conditional branch,
+ /// with one unconditional branch. Succ_edge determines if the new
+ /// unconditional edge will be the first or second edge of the former TI
+ /// instruction.
+ void removeRedundancy(TerminatorInst *TI, bool Succ_edge);
+
+ /// When an conditional branch is removed, the BasicBlock that is no longer
+ /// reachable will have problems in phi functions. This method fixes these
+ /// phis removing the former BasicBlock from the list of incoming BasicBlocks
+ /// of all phis. In case the phi remains with no predecessor it will be
+ /// marked to be removed later.
+ void fixPhi(BasicBlock *BB, BasicBlock *Succ);
+
+ /// Removes phis that have no predecessor
+ void removePhis();
+
+ /// Creates constraints for Instructions.
+ /// If the constraint for this instruction has already been created
+ /// nothing is done.
+ void createConstraintInstruction(Instruction *I);
+
+ /// Creates constraints for Binary Operators.
+ /// It will create constraints only for addition and subtraction,
+ /// the other binary operations are not treated by ABCD.
+ /// For additions in the form a = b + X and a = X + b, where X is a constant,
+ /// the constraint a <= b + X can be obtained. For this constraint, an edge
+ /// a->b with weight X is added to the lower bound graph, and an edge
+ /// b->a with weight -X is added to the upper bound graph.
+ /// Only subtractions in the format a = b - X is used by ABCD.
+ /// Edges are created using the same semantic as addition.
+ void createConstraintBinaryOperator(BinaryOperator *BO);
+
+ /// Creates constraints for Comparator Instructions.
+ /// Only comparators that have any of the following operators
+ /// are used to create constraints: >=, >, <=, <. And only if
+ /// at least one operand is an Instruction. In a Comparator Instruction
+ /// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
+ /// t and f represent sigma for operands in true and false branches. The
+ /// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
+ /// b_f <= b. There are two more constraints that depend on the operator.
+ /// For the operator <= : a_t <= b_t and b_f <= a_f-1
+ /// For the operator < : a_t <= b_t-1 and b_f <= a_f
+ /// For the operator >= : b_t <= a_t and a_f <= b_f-1
+ /// For the operator > : b_t <= a_t-1 and a_f <= b_f
+ void createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI);
+
+ /// Creates constraints for PHI nodes.
+ /// In a PHI node a = phi(b,c) we can create the constraint
+ /// a<= max(b,c). With this constraint there will be the edges,
+ /// b->a and c->a with weight 0 in the lower bound graph, and the edges
+ /// a->b and a->c with weight 0 in the upper bound graph.
+ void createConstraintPHINode(PHINode *PN);
+
+ /// Given a binary operator, we are only interest in the case
+ /// that one operand is an Instruction and the other is a ConstantInt. In
+ /// this case the method returns true, otherwise false. It also obtains the
+ /// Instruction and ConstantInt from the BinaryOperator and returns it.
+ bool createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
+ Instruction **I2, ConstantInt **C1,
+ ConstantInt **C2);
+
+ /// This method creates a constraint between a Sigma and an Instruction.
+ /// These constraints are created as soon as we find a comparator that uses a
+ /// SSI variable.
+ void createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
+ BasicBlock *BB_succ_f, PHINode **SIG_op_t,
+ PHINode **SIG_op_f);
+
+ /// If PN_op1 and PN_o2 are different from NULL, create a constraint
+ /// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
+ /// with the respective V_op#, if V_op# is a ConstantInt.
+ void createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2, APInt value);
+
+ /// Returns the sigma representing the Instruction I in BasicBlock BB.
+ /// Returns NULL in case there is no sigma for this Instruction in this
+ /// Basic Block. This methods assume that sigmas are the first instructions
+ /// in a block, and that there can be only two sigmas in a block. So it will
+ /// only look on the first two instructions of BasicBlock BB.
+ PHINode *findSigma(BasicBlock *BB, Instruction *I);
+
+ /// Original ABCD algorithm to prove redundant checks.
+ /// This implementation works on any kind of inequality branch.
+ bool demandProve(Value *a, Value *b, int c, bool upper_bound);
+
+ /// Prove that distance between b and a is <= bound
+ ProveResult prove(Value *a, Value *b, Bound *bound, unsigned level);
+
+ /// Updates the distance value for a and b
+ void updateMemDistance(Value *a, Value *b, Bound *bound, unsigned level,
+ meet_function meet);
+
+ InequalityGraph inequality_graph;
+ MemoizedResult mem_result;
+ DenseMap<Value*, Bound*> active;
+ SmallPtrSet<Value*, 16> created;
+ SmallVector<PHINode *, 16> phis_to_remove;
+};
+
+//} // end anonymous namespace.
+
+char ABCD::ID = 0;
+static RegisterPass<ABCD> X("abcd", "ABCD: Eliminating Array Bounds Checks on Demand");
+
+
+bool ABCD::runOnFunction(Function &F) {
+ modified = false;
+ createSSI(F);
+ executeABCD(F);
+ DEBUG(inequality_graph.printGraph(errs(), F));
+ removePhis();
+
+ inequality_graph.clear();
+ mem_result.clear();
+ active.clear();
+ created.clear();
+ phis_to_remove.clear();
+ return modified;
+}
+
+/// Iterates through all BasicBlocks, if the Terminator Instruction
+/// uses an Comparator Instruction, all operands of this comparator
+/// are sent to be transformed to SSI. Only Instruction operands are
+/// transformed.
+void ABCD::createSSI(Function &F) {
+ SSI *ssi = &getAnalysis<SSI>();
+
+ SmallVector<Instruction *, 16> Insts;
+
+ for (Function::iterator begin = F.begin(), end = F.end();
+ begin != end; ++begin) {
+ BasicBlock *BB = begin;
+ TerminatorInst *TI = BB->getTerminator();
+ if (TI->getNumOperands() == 0)
+ continue;
+
+ if (ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0))) {
+ if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(0))) {
+ modified = true; // XXX: but yet createSSI might do nothing
+ Insts.push_back(I);
+ }
+ if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(1))) {
+ modified = true;
+ Insts.push_back(I);
+ }
+ }
+ }
+ ssi->createSSI(Insts);
+}
+
+/// Creates the graphs for this function.
+/// It will look for all comparators used in branches, and create them.
+/// These comparators will create constraints for any instruction as an
+/// operand.
+void ABCD::executeABCD(Function &F) {
+ for (Function::iterator begin = F.begin(), end = F.end();
+ begin != end; ++begin) {
+ BasicBlock *BB = begin;
+ TerminatorInst *TI = BB->getTerminator();
+ if (TI->getNumOperands() == 0)
+ continue;
+
+ ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0));
+ if (!ICI || !isa<IntegerType>(ICI->getOperand(0)->getType()))
+ continue;
+
+ createConstraintCmpInst(ICI, TI);
+ seekRedundancy(ICI, TI);
+ }
+}
+
+/// Seeks redundancies in the comparator instruction CI.
+/// If the ABCD algorithm can prove that the comparator CI always
+/// takes one way, then the Terminator Instruction TI is substituted from
+/// a conditional branch to a unconditional one.
+/// This code basically receives a comparator, and verifies which kind of
+/// instruction it is. Depending on the kind of instruction, we use different
+/// strategies to prove its redundancy.
+void ABCD::seekRedundancy(ICmpInst *ICI, TerminatorInst *TI) {
+ CmpInst::Predicate Pred = ICI->getPredicate();
+
+ Value *source, *dest;
+ int distance1, distance2;
+ bool upper;
+
+ switch(Pred) {
+ case CmpInst::ICMP_SGT: // signed greater than
+ upper = false;
+ distance1 = 1;
+ distance2 = 0;
+ break;
+
+ case CmpInst::ICMP_SGE: // signed greater or equal
+ upper = false;
+ distance1 = 0;
+ distance2 = -1;
+ break;
+
+ case CmpInst::ICMP_SLT: // signed less than
+ upper = true;
+ distance1 = -1;
+ distance2 = 0;
+ break;
+
+ case CmpInst::ICMP_SLE: // signed less or equal
+ upper = true;
+ distance1 = 0;
+ distance2 = 1;
+ break;
+
+ default:
+ return;
+ }
+
+ ++NumBranchTested;
+ source = ICI->getOperand(0);
+ dest = ICI->getOperand(1);
+ if (demandProve(dest, source, distance1, upper)) {
+ removeRedundancy(TI, true);
+ } else if (demandProve(dest, source, distance2, !upper)) {
+ removeRedundancy(TI, false);
+ }
+}
+
+/// Substitutes Terminator Instruction TI, that is a conditional branch,
+/// with one unconditional branch. Succ_edge determines if the new
+/// unconditional edge will be the first or second edge of the former TI
+/// instruction.
+void ABCD::removeRedundancy(TerminatorInst *TI, bool Succ_edge) {
+ BasicBlock *Succ;
+ if (Succ_edge) {
+ Succ = TI->getSuccessor(0);
+ fixPhi(TI->getParent(), TI->getSuccessor(1));
+ } else {
+ Succ = TI->getSuccessor(1);
+ fixPhi(TI->getParent(), TI->getSuccessor(0));
+ }
+
+ BranchInst::Create(Succ, TI);
+ TI->eraseFromParent(); // XXX: invoke
+ ++NumBranchRemoved;
+ modified = true;
+}
+
+/// When an conditional branch is removed, the BasicBlock that is no longer
+/// reachable will have problems in phi functions. This method fixes these
+/// phis removing the former BasicBlock from the list of incoming BasicBlocks
+/// of all phis. In case the phi remains with no predecessor it will be
+/// marked to be removed later.
+void ABCD::fixPhi(BasicBlock *BB, BasicBlock *Succ) {
+ BasicBlock::iterator begin = Succ->begin();
+ while (PHINode *PN = dyn_cast<PHINode>(begin++)) {
+ PN->removeIncomingValue(BB, false);
+ if (PN->getNumIncomingValues() == 0)
+ phis_to_remove.push_back(PN);
+ }
+}
+
+/// Removes phis that have no predecessor
+void ABCD::removePhis() {
+ for (unsigned i = 0, end = phis_to_remove.size(); i < end; ++i) {
+ PHINode *PN = phis_to_remove[i];
+ PN->replaceAllUsesWith(UndefValue::get(PN->getType()));
+ PN->eraseFromParent();
+ }
+}
+
+/// Creates constraints for Instructions.
+/// If the constraint for this instruction has already been created
+/// nothing is done.
+void ABCD::createConstraintInstruction(Instruction *I) {
+ // Test if this instruction has not been created before
+ if (created.insert(I)) {
+ if (BinaryOperator *BO = dyn_cast<BinaryOperator>(I)) {
+ createConstraintBinaryOperator(BO);
+ } else if (PHINode *PN = dyn_cast<PHINode>(I)) {
+ createConstraintPHINode(PN);
+ }
+ }
+}
+
+/// Creates constraints for Binary Operators.
+/// It will create constraints only for addition and subtraction,
+/// the other binary operations are not treated by ABCD.
+/// For additions in the form a = b + X and a = X + b, where X is a constant,
+/// the constraint a <= b + X can be obtained. For this constraint, an edge
+/// a->b with weight X is added to the lower bound graph, and an edge
+/// b->a with weight -X is added to the upper bound graph.
+/// Only subtractions in the format a = b - X is used by ABCD.
+/// Edges are created using the same semantic as addition.
+void ABCD::createConstraintBinaryOperator(BinaryOperator *BO) {
+ Instruction *I1 = NULL, *I2 = NULL;
+ ConstantInt *CI1 = NULL, *CI2 = NULL;
+
+ // Test if an operand is an Instruction and the other is a Constant
+ if (!createBinaryOperatorInfo(BO, &I1, &I2, &CI1, &CI2))
+ return;
+
+ Instruction *I = 0;
+ APInt value;
+
+ switch (BO->getOpcode()) {
+ case Instruction::Add:
+ if (I1) {
+ I = I1;
+ value = CI2->getValue();
+ } else if (I2) {
+ I = I2;
+ value = CI1->getValue();
+ }
+ break;
+
+ case Instruction::Sub:
+ // Instructions like a = X-b, where X is a constant are not represented
+ // in the graph.
+ if (!I1)
+ return;
+
+ I = I1;
+ value = -CI2->getValue();
+ break;
+
+ default:
+ return;
+ }
+
+ APInt MinusOne = APInt::getAllOnesValue(value.getBitWidth());
+ inequality_graph.addEdge(I, BO, value, true);
+ inequality_graph.addEdge(BO, I, value * MinusOne, false);
+ createConstraintInstruction(I);
+}
+
+/// Given a binary operator, we are only interest in the case
+/// that one operand is an Instruction and the other is a ConstantInt. In
+/// this case the method returns true, otherwise false. It also obtains the
+/// Instruction and ConstantInt from the BinaryOperator and returns it.
+bool ABCD::createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
+ Instruction **I2, ConstantInt **C1,
+ ConstantInt **C2) {
+ Value *op1 = BO->getOperand(0);
+ Value *op2 = BO->getOperand(1);
+
+ if ((*I1 = dyn_cast<Instruction>(op1))) {
+ if ((*C2 = dyn_cast<ConstantInt>(op2)))
+ return true; // First is Instruction and second ConstantInt
+
+ return false; // Both are Instruction
+ } else {
+ if ((*C1 = dyn_cast<ConstantInt>(op1)) &&
+ (*I2 = dyn_cast<Instruction>(op2)))
+ return true; // First is ConstantInt and second Instruction
+
+ return false; // Both are not Instruction
+ }
+}
+
+/// Creates constraints for Comparator Instructions.
+/// Only comparators that have any of the following operators
+/// are used to create constraints: >=, >, <=, <. And only if
+/// at least one operand is an Instruction. In a Comparator Instruction
+/// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
+/// t and f represent sigma for operands in true and false branches. The
+/// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
+/// b_f <= b. There are two more constraints that depend on the operator.
+/// For the operator <= : a_t <= b_t and b_f <= a_f-1
+/// For the operator < : a_t <= b_t-1 and b_f <= a_f
+/// For the operator >= : b_t <= a_t and a_f <= b_f-1
+/// For the operator > : b_t <= a_t-1 and a_f <= b_f
+void ABCD::createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI) {
+ Value *V_op1 = ICI->getOperand(0);
+ Value *V_op2 = ICI->getOperand(1);
+
+ if (!isa<IntegerType>(V_op1->getType()))
+ return;
+
+ Instruction *I_op1 = dyn_cast<Instruction>(V_op1);
+ Instruction *I_op2 = dyn_cast<Instruction>(V_op2);
+
+ // Test if at least one operand is an Instruction
+ if (!I_op1 && !I_op2)
+ return;
+
+ BasicBlock *BB_succ_t = TI->getSuccessor(0);
+ BasicBlock *BB_succ_f = TI->getSuccessor(1);
+
+ PHINode *SIG_op1_t = NULL, *SIG_op1_f = NULL,
+ *SIG_op2_t = NULL, *SIG_op2_f = NULL;
+
+ createConstraintSigInst(I_op1, BB_succ_t, BB_succ_f,
+ &SIG_op1_t, &SIG_op1_f);
+ createConstraintSigInst(I_op2, BB_succ_t, BB_succ_f,
+ &SIG_op2_t, &SIG_op2_f);
+
+ int32_t width = cast<IntegerType>(V_op1->getType())->getBitWidth();
+ APInt MinusOne = APInt::getAllOnesValue(width);
+ APInt Zero = APInt::getNullValue(width);
+
+ CmpInst::Predicate Pred = ICI->getPredicate();
+ switch (Pred) {
+ case CmpInst::ICMP_SGT: // signed greater than
+ createConstraintSigSig(SIG_op2_t, SIG_op1_t, MinusOne);
+ createConstraintSigSig(SIG_op1_f, SIG_op2_f, Zero);
+ break;
+
+ case CmpInst::ICMP_SGE: // signed greater or equal
+ createConstraintSigSig(SIG_op2_t, SIG_op1_t, Zero);
+ createConstraintSigSig(SIG_op1_f, SIG_op2_f, MinusOne);
+ break;
+
+ case CmpInst::ICMP_SLT: // signed less than
+ createConstraintSigSig(SIG_op1_t, SIG_op2_t, MinusOne);
+ createConstraintSigSig(SIG_op2_f, SIG_op1_f, Zero);
+ break;
+
+ case CmpInst::ICMP_SLE: // signed less or equal
+ createConstraintSigSig(SIG_op1_t, SIG_op2_t, Zero);
+ createConstraintSigSig(SIG_op2_f, SIG_op1_f, MinusOne);
+ break;
+
+ default:
+ break;
+ }
+
+ if (I_op1)
+ createConstraintInstruction(I_op1);
+ if (I_op2)
+ createConstraintInstruction(I_op2);
+}
+
+/// Creates constraints for PHI nodes.
+/// In a PHI node a = phi(b,c) we can create the constraint
+/// a<= max(b,c). With this constraint there will be the edges,
+/// b->a and c->a with weight 0 in the lower bound graph, and the edges
+/// a->b and a->c with weight 0 in the upper bound graph.
+void ABCD::createConstraintPHINode(PHINode *PN) {
+ int32_t width = cast<IntegerType>(PN->getType())->getBitWidth();
+ for (unsigned i = 0, end = PN->getNumIncomingValues(); i < end; ++i) {
+ Value *V = PN->getIncomingValue(i);
+ if (Instruction *I = dyn_cast<Instruction>(V)) {
+ createConstraintInstruction(I);
+ }
+ inequality_graph.addEdge(V, PN, APInt(width, 0), true);
+ inequality_graph.addEdge(V, PN, APInt(width, 0), false);
+ }
+}
+
+/// This method creates a constraint between a Sigma and an Instruction.
+/// These constraints are created as soon as we find a comparator that uses a
+/// SSI variable.
+void ABCD::createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
+ BasicBlock *BB_succ_f, PHINode **SIG_op_t,
+ PHINode **SIG_op_f) {
+ *SIG_op_t = findSigma(BB_succ_t, I_op);
+ *SIG_op_f = findSigma(BB_succ_f, I_op);
+
+ if (*SIG_op_t) {
+ int32_t width = cast<IntegerType>((*SIG_op_t)->getType())->getBitWidth();
+ inequality_graph.addEdge(I_op, *SIG_op_t, APInt(width, 0), true);
+ inequality_graph.addEdge(*SIG_op_t, I_op, APInt(width, 0), false);
+ created.insert(*SIG_op_t);
+ }
+ if (*SIG_op_f) {
+ int32_t width = cast<IntegerType>((*SIG_op_f)->getType())->getBitWidth();
+ inequality_graph.addEdge(I_op, *SIG_op_f, APInt(width, 0), true);
+ inequality_graph.addEdge(*SIG_op_f, I_op, APInt(width, 0), false);
+ created.insert(*SIG_op_f);
+ }
+}
+
+/// If PN_op1 and PN_o2 are different from NULL, create a constraint
+/// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
+/// with the respective V_op#, if V_op# is a ConstantInt.
+void ABCD::createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2,
+ APInt value) {
+ if (SIG_op1 && SIG_op2) {
+ APInt MinusOne = APInt::getAllOnesValue(value.getBitWidth());
+ inequality_graph.addEdge(SIG_op2, SIG_op1, value, true);
+ inequality_graph.addEdge(SIG_op1, SIG_op2, value * MinusOne, false);
+ }
+}
+
+/// Returns the sigma representing the Instruction I in BasicBlock BB.
+/// Returns NULL in case there is no sigma for this Instruction in this
+/// Basic Block. This methods assume that sigmas are the first instructions
+/// in a block, and that there can be only two sigmas in a block. So it will
+/// only look on the first two instructions of BasicBlock BB.
+PHINode *ABCD::findSigma(BasicBlock *BB, Instruction *I) {
+ // BB has more than one predecessor, BB cannot have sigmas.
+ if (I == NULL || BB->getSinglePredecessor() == NULL)
+ return NULL;
+
+ BasicBlock::iterator begin = BB->begin();
+ BasicBlock::iterator end = BB->end();
+
+ for (unsigned i = 0; i < 2 && begin != end; ++i, ++begin) {
+ Instruction *I_succ = begin;
+ if (PHINode *PN = dyn_cast<PHINode>(I_succ))
+ if (PN->getIncomingValue(0) == I)
+ return PN;
+ }
+
+ return NULL;
+}
+
+/// Original ABCD algorithm to prove redundant checks.
+/// This implementation works on any kind of inequality branch.
+bool ABCD::demandProve(Value *a, Value *b, int c, bool upper_bound) {
+ int32_t width = cast<IntegerType>(a->getType())->getBitWidth();
+ Bound *bound = new Bound(APInt(width, c), upper_bound);
+
+ mem_result.clear();
+ active.clear();
+
+ ProveResult res = prove(a, b, bound, 0);
+ return res != False;
+}
+
+/// Prove that distance between b and a is <= bound
+ABCD::ProveResult ABCD::prove(Value *a, Value *b, Bound *bound,
+ unsigned level) {
+ // if (C[b-a<=e] == True for some e <= bound
+ // Same or stronger difference was already proven
+ if (mem_result.hasTrue(b, bound))
+ return True;
+
+ // if (C[b-a<=e] == False for some e >= bound
+ // Same or weaker difference was already disproved
+ if (mem_result.hasFalse(b, bound))
+ return False;
+
+ // if (C[b-a<=e] == Reduced for some e <= bound
+ // b is on a cycle that was reduced for same or stronger difference
+ if (mem_result.hasReduced(b, bound))
+ return Reduced;
+
+ // traversal reached the source vertex
+ if (a == b && Bound::geq(bound, APInt(bound->getBitWidth(), 0, true)))
+ return True;
+
+ // if b has no predecessor then fail
+ if (!inequality_graph.hasEdge(b, bound->isUpperBound()))
+ return False;
+
+ // a cycle was encountered
+ if (active.count(b)) {
+ if (Bound::leq(active.lookup(b), bound))
+ return Reduced; // a "harmless" cycle
+
+ return False; // an amplifying cycle
+ }
+
+ active[b] = bound;
+ PHINode *PN = dyn_cast<PHINode>(b);
+
+ // Test if a Value is a Phi. If it is a PHINode with more than 1 incoming
+ // value, then it is a phi, if it has 1 incoming value it is a sigma.
+ if (PN && PN->getNumIncomingValues() > 1)
+ updateMemDistance(a, b, bound, level, min);
+ else
+ updateMemDistance(a, b, bound, level, max);
+
+ active.erase(b);
+
+ ABCD::ProveResult res = mem_result.getBoundResult(b, bound);
+ return res;
+}
+
+/// Updates the distance value for a and b
+void ABCD::updateMemDistance(Value *a, Value *b, Bound *bound, unsigned level,
+ meet_function meet) {
+ ABCD::ProveResult res = (meet == max) ? False : True;
+
+ SmallPtrSet<Edge *, 16> Edges = inequality_graph.getEdges(b);
+ SmallPtrSet<Edge *, 16>::iterator begin = Edges.begin(), end = Edges.end();
+
+ for (; begin != end ; ++begin) {
+ if (((res >= Reduced) && (meet == max)) ||
+ ((res == False) && (meet == min))) {
+ break;
+ }
+ Edge *in = *begin;
+ if (in->isUpperBound() == bound->isUpperBound()) {
+ Value *succ = in->getVertex();
+ res = meet(res, prove(a, succ, new Bound(bound, in->getValue()),
+ level+1));
+ }
+ }
+
+ mem_result.updateBound(b, bound, res);
+}
+
+/// Return the stored result for this bound
+ABCD::ProveResult ABCD::MemoizedResultChart::getResult(const Bound *bound)const{
+ if (max_false && Bound::leq(bound, max_false))
+ return False;
+ if (min_true && Bound::leq(min_true, bound))
+ return True;
+ if (min_reduced && Bound::leq(min_reduced, bound))
+ return Reduced;
+ return False;
+}
+
+/// Stores a false found
+void ABCD::MemoizedResultChart::addFalse(Bound *bound) {
+ if (!max_false || Bound::leq(max_false, bound))
+ max_false = bound;
+
+ if (Bound::eq(max_false, min_reduced))
+ min_reduced = Bound::createIncrement(min_reduced);
+ if (Bound::eq(max_false, min_true))
+ min_true = Bound::createIncrement(min_true);
+ if (Bound::eq(min_reduced, min_true))
+ min_reduced = NULL;
+ clearRedundantReduced();
+}
+
+/// Stores a true found
+void ABCD::MemoizedResultChart::addTrue(Bound *bound) {
+ if (!min_true || Bound::leq(bound, min_true))
+ min_true = bound;
+
+ if (Bound::eq(min_true, min_reduced))
+ min_reduced = Bound::createDecrement(min_reduced);
+ if (Bound::eq(min_true, max_false))
+ max_false = Bound::createDecrement(max_false);
+ if (Bound::eq(max_false, min_reduced))
+ min_reduced = NULL;
+ clearRedundantReduced();
+}
+
+/// Stores a Reduced found
+void ABCD::MemoizedResultChart::addReduced(Bound *bound) {
+ if (!min_reduced || Bound::leq(bound, min_reduced))
+ min_reduced = bound;
+
+ if (Bound::eq(min_reduced, min_true))
+ min_true = Bound::createIncrement(min_true);
+ if (Bound::eq(min_reduced, max_false))
+ max_false = Bound::createDecrement(max_false);
+}
+
+/// Clears redundant reduced
+/// If a min_true is smaller than a min_reduced then the min_reduced
+/// is unnecessary and then removed. It also works for min_reduced
+/// begin smaller than max_false.
+void ABCD::MemoizedResultChart::clearRedundantReduced() {
+ if (min_true && min_reduced && Bound::lt(min_true, min_reduced))
+ min_reduced = NULL;
+ if (max_false && min_reduced && Bound::lt(min_reduced, max_false))
+ min_reduced = NULL;
+}
+
+/// Stores the bound found
+void ABCD::MemoizedResult::updateBound(Value *b, Bound *bound,
+ const ProveResult res) {
+ if (res == False) {
+ map[b].addFalse(bound);
+ } else if (res == True) {
+ map[b].addTrue(bound);
+ } else {
+ map[b].addReduced(bound);
+ }
+}
+
+/// Adds an edge from V_from to V_to with weight value
+void ABCD::InequalityGraph::addEdge(Value *V_to, Value *V_from,
+ APInt value, bool upper) {
+ assert(V_from->getType() == V_to->getType());
+ assert(cast<IntegerType>(V_from->getType())->getBitWidth() ==
+ value.getBitWidth());
+
+ DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator from;
+ from = addNode(V_from);
+ from->second.insert(new Edge(V_to, value, upper));
+}
+
+/// Test if there is any edge from V in the upper direction
+bool ABCD::InequalityGraph::hasEdge(Value *V, bool upper) const {
+ SmallPtrSet<Edge *, 16> it = graph.lookup(V);
+
+ SmallPtrSet<Edge *, 16>::iterator begin = it.begin();
+ SmallPtrSet<Edge *, 16>::iterator end = it.end();
+ for (; begin != end; ++begin) {
+ if ((*begin)->isUpperBound() == upper) {
+ return true;
+ }
+ }
+ return false;
+}
+
+/// Prints the header of the dot file
+void ABCD::InequalityGraph::printHeader(raw_ostream &OS, Function &F) const {
+ OS << "digraph dotgraph {\n";
+ OS << "label=\"Inequality Graph for \'";
+ OS << F.getNameStr() << "\' function\";\n";
+ OS << "node [shape=record,fontname=\"Times-Roman\",fontsize=14];\n";
+}
+
+/// Prints the body of the dot file
+void ABCD::InequalityGraph::printBody(raw_ostream &OS) const {
+ DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator begin =
+ graph.begin(), end = graph.end();
+
+ for (; begin != end ; ++begin) {
+ SmallPtrSet<Edge *, 16>::iterator begin_par =
+ begin->second.begin(), end_par = begin->second.end();
+ Value *source = begin->first;
+
+ printVertex(OS, source);
+
+ for (; begin_par != end_par ; ++begin_par) {
+ Edge *edge = *begin_par;
+ printEdge(OS, source, edge);
+ }
+ }
+}
+
+/// Prints vertex source to the dot file
+///
+void ABCD::InequalityGraph::printVertex(raw_ostream &OS, Value *source) const {
+ OS << "\"";
+ printName(OS, source);
+ OS << "\"";
+ OS << " [label=\"{";
+ printName(OS, source);
+ OS << "}\"];\n";
+}
+
+/// Prints the edge to the dot file
+void ABCD::InequalityGraph::printEdge(raw_ostream &OS, Value *source,
+ Edge *edge) const {
+ Value *dest = edge->getVertex();
+ APInt value = edge->getValue();
+ bool upper = edge->isUpperBound();
+
+ OS << "\"";
+ printName(OS, source);
+ OS << "\"";
+ OS << " -> ";
+ OS << "\"";
+ printName(OS, dest);
+ OS << "\"";
+ OS << " [label=\"" << value << "\"";
+ if (upper) {
+ OS << "color=\"blue\"";
+ } else {
+ OS << "color=\"red\"";
+ }
+ OS << "];\n";
+}
+
+void ABCD::InequalityGraph::printName(raw_ostream &OS, Value *info) const {
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(info)) {
+ OS << *CI->getValue().getRawData();
+ } else {
+ if (info->getName() == "") {
+ info->setName("V");
+ }
+ OS << info->getNameStr();
+ }
+}
+
+/// createABCDPass - The public interface to this file...
+FunctionPass *llvm::createABCDPass() {
+ return new ABCD();
+}
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