1 //===------- ABCD.cpp - Removes redundant conditional branches ------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This pass removes redundant branch instructions. This algorithm was
11 // described by Rastislav Bodik, Rajiv Gupta and Vivek Sarkar in their paper
12 // "ABCD: Eliminating Array Bounds Checks on Demand (2000)". The original
13 // Algorithm was created to remove array bound checks for strongly typed
14 // languages. This implementation expands the idea and removes any conditional
15 // branches that can be proved redundant, not only those used in array bound
16 // checks. With the SSI representation, each variable has a
17 // constraint. By analyzing these constraints we can prove that a branch is
18 // redundant. When a branch is proved redundant it means that
19 // one direction will always be taken; thus, we can change this branch into an
20 // unconditional jump.
21 // It is advisable to run SimplifyCFG and Aggressive Dead Code Elimination
22 // after ABCD to clean up the code.
23 // This implementation was created based on the implementation of the ABCD
24 // algorithm implemented for the compiler Jitrino.
26 //===----------------------------------------------------------------------===//
28 #define DEBUG_TYPE "abcd"
29 #include "llvm/ADT/DenseMap.h"
30 #include "llvm/ADT/OwningPtr.h"
31 #include "llvm/ADT/SmallPtrSet.h"
32 #include "llvm/ADT/Statistic.h"
33 #include "llvm/Constants.h"
34 #include "llvm/Function.h"
35 #include "llvm/Instructions.h"
36 #include "llvm/Pass.h"
37 #include "llvm/Support/raw_ostream.h"
38 #include "llvm/Support/Debug.h"
39 #include "llvm/Transforms/Scalar.h"
40 #include "llvm/Transforms/Utils/SSI.h"
44 STATISTIC(NumBranchTested, "Number of conditional branches analyzed");
45 STATISTIC(NumBranchRemoved, "Number of conditional branches removed");
49 class ABCD : public FunctionPass {
51 static char ID; // Pass identification, replacement for typeid.
52 ABCD() : FunctionPass(&ID) {}
54 void getAnalysisUsage(AnalysisUsage &AU) const {
55 AU.addRequired<SSI>();
58 bool runOnFunction(Function &F);
61 /// Keep track of whether we've modified the program yet.
70 typedef ProveResult (*meet_function)(ProveResult, ProveResult);
71 static ProveResult max(ProveResult res1, ProveResult res2) {
72 return (ProveResult) std::max(res1, res2);
74 static ProveResult min(ProveResult res1, ProveResult res2) {
75 return (ProveResult) std::min(res1, res2);
80 Bound(APInt v, bool upper) : value(v), upper_bound(upper) {}
81 Bound(const Bound &b, int cnst)
82 : value(b.value - cnst), upper_bound(b.upper_bound) {}
83 Bound(const Bound &b, const APInt &cnst)
84 : value(b.value - cnst), upper_bound(b.upper_bound) {}
86 /// Test if Bound is an upper bound
87 bool isUpperBound() const { return upper_bound; }
89 /// Get the bitwidth of this bound
90 int32_t getBitWidth() const { return value.getBitWidth(); }
92 /// Creates a Bound incrementing the one received
93 static Bound createIncrement(const Bound &b) {
94 return Bound(b.isUpperBound() ? b.value+1 : b.value-1,
98 /// Creates a Bound decrementing the one received
99 static Bound createDecrement(const Bound &b) {
100 return Bound(b.isUpperBound() ? b.value-1 : b.value+1,
104 /// Test if two bounds are equal
105 static bool eq(const Bound *a, const Bound *b) {
106 if (!a || !b) return false;
108 assert(a->isUpperBound() == b->isUpperBound());
109 return a->value == b->value;
112 /// Test if val is less than or equal to Bound b
113 static bool leq(APInt val, const Bound &b) {
114 return b.isUpperBound() ? val.sle(b.value) : val.sge(b.value);
117 /// Test if Bound a is less then or equal to Bound
118 static bool leq(const Bound &a, const Bound &b) {
119 assert(a.isUpperBound() == b.isUpperBound());
120 return a.isUpperBound() ? a.value.sle(b.value) :
121 a.value.sge(b.value);
124 /// Test if Bound a is less then Bound b
125 static bool lt(const Bound &a, const Bound &b) {
126 assert(a.isUpperBound() == b.isUpperBound());
127 return a.isUpperBound() ? a.value.slt(b.value) :
128 a.value.sgt(b.value);
131 /// Test if Bound b is greater then or equal val
132 static bool geq(const Bound &b, APInt val) {
136 /// Test if Bound a is greater then or equal Bound b
137 static bool geq(const Bound &a, const Bound &b) {
146 /// This class is used to store results some parts of the graph,
147 /// so information does not need to be recalculated. The maximum false,
148 /// minimum true and minimum reduced results are stored
149 class MemoizedResultChart {
151 MemoizedResultChart() {}
152 MemoizedResultChart(const MemoizedResultChart &other) {
154 max_false.reset(new Bound(*other.max_false));
156 min_true.reset(new Bound(*other.min_true));
157 if (other.min_reduced)
158 min_reduced.reset(new Bound(*other.min_reduced));
161 /// Returns the max false
162 const Bound *getFalse() const { return max_false.get(); }
164 /// Returns the min true
165 const Bound *getTrue() const { return min_true.get(); }
167 /// Returns the min reduced
168 const Bound *getReduced() const { return min_reduced.get(); }
170 /// Return the stored result for this bound
171 ProveResult getResult(const Bound &bound) const;
173 /// Stores a false found
174 void addFalse(const Bound &bound);
176 /// Stores a true found
177 void addTrue(const Bound &bound);
179 /// Stores a Reduced found
180 void addReduced(const Bound &bound);
182 /// Clears redundant reduced
183 /// If a min_true is smaller than a min_reduced then the min_reduced
184 /// is unnecessary and then removed. It also works for min_reduced
185 /// begin smaller than max_false.
186 void clearRedundantReduced();
195 OwningPtr<Bound> max_false, min_true, min_reduced;
198 /// This class stores the result found for a node of the graph,
199 /// so these results do not need to be recalculated, only searched for.
200 class MemoizedResult {
202 /// Test if there is true result stored from b to a
203 /// that is less then the bound
204 bool hasTrue(Value *b, const Bound &bound) const {
205 const Bound *trueBound = map.lookup(b).getTrue();
206 return trueBound && Bound::leq(*trueBound, bound);
209 /// Test if there is false result stored from b to a
210 /// that is less then the bound
211 bool hasFalse(Value *b, const Bound &bound) const {
212 const Bound *falseBound = map.lookup(b).getFalse();
213 return falseBound && Bound::leq(*falseBound, bound);
216 /// Test if there is reduced result stored from b to a
217 /// that is less then the bound
218 bool hasReduced(Value *b, const Bound &bound) const {
219 const Bound *reducedBound = map.lookup(b).getReduced();
220 return reducedBound && Bound::leq(*reducedBound, bound);
223 /// Returns the stored bound for b
224 ProveResult getBoundResult(Value *b, const Bound &bound) {
225 return map[b].getResult(bound);
230 DenseMapIterator<Value*, MemoizedResultChart> begin = map.begin();
231 DenseMapIterator<Value*, MemoizedResultChart> end = map.end();
232 for (; begin != end; ++begin) {
233 begin->second.clear();
238 /// Stores the bound found
239 void updateBound(Value *b, const Bound &bound, const ProveResult res);
242 // Maps a nod in the graph with its results found.
243 DenseMap<Value*, MemoizedResultChart> map;
246 /// This class represents an edge in the inequality graph used by the
247 /// ABCD algorithm. An edge connects node v to node u with a value c if
248 /// we could infer a constraint v <= u + c in the source program.
251 Edge(Value *V, APInt val, bool upper)
252 : vertex(V), value(val), upper_bound(upper) {}
254 Value *getVertex() const { return vertex; }
255 const APInt &getValue() const { return value; }
256 bool isUpperBound() const { return upper_bound; }
264 /// Weighted and Directed graph to represent constraints.
265 /// There is one type of constraint, a <= b + X, which will generate an
266 /// edge from b to a with weight X.
267 class InequalityGraph {
270 /// Adds an edge from V_from to V_to with weight value
271 void addEdge(Value *V_from, Value *V_to, APInt value, bool upper);
273 /// Test if there is a node V
274 bool hasNode(Value *V) const { return graph.count(V); }
276 /// Test if there is any edge from V in the upper direction
277 bool hasEdge(Value *V, bool upper) const;
279 /// Returns all edges pointed by vertex V
280 SmallVector<Edge, 16> getEdges(Value *V) const {
281 return graph.lookup(V);
284 /// Prints the graph in dot format.
285 /// Blue edges represent upper bound and Red lower bound.
286 void printGraph(raw_ostream &OS, Function &F) const {
298 DenseMap<Value *, SmallVector<Edge, 16> > graph;
300 /// Prints the header of the dot file
301 void printHeader(raw_ostream &OS, Function &F) const;
303 /// Prints the footer of the dot file
304 void printFooter(raw_ostream &OS) const {
308 /// Prints the body of the dot file
309 void printBody(raw_ostream &OS) const;
311 /// Prints vertex source to the dot file
312 void printVertex(raw_ostream &OS, Value *source) const;
314 /// Prints the edge to the dot file
315 void printEdge(raw_ostream &OS, Value *source, const Edge &edge) const;
317 void printName(raw_ostream &OS, Value *info) const;
320 /// Iterates through all BasicBlocks, if the Terminator Instruction
321 /// uses an Comparator Instruction, all operands of this comparator
322 /// are sent to be transformed to SSI. Only Instruction operands are
324 void createSSI(Function &F);
326 /// Creates the graphs for this function.
327 /// It will look for all comparators used in branches, and create them.
328 /// These comparators will create constraints for any instruction as an
330 void executeABCD(Function &F);
332 /// Seeks redundancies in the comparator instruction CI.
333 /// If the ABCD algorithm can prove that the comparator CI always
334 /// takes one way, then the Terminator Instruction TI is substituted from
335 /// a conditional branch to a unconditional one.
336 /// This code basically receives a comparator, and verifies which kind of
337 /// instruction it is. Depending on the kind of instruction, we use different
338 /// strategies to prove its redundancy.
339 void seekRedundancy(ICmpInst *ICI, TerminatorInst *TI);
341 /// Substitutes Terminator Instruction TI, that is a conditional branch,
342 /// with one unconditional branch. Succ_edge determines if the new
343 /// unconditional edge will be the first or second edge of the former TI
345 void removeRedundancy(TerminatorInst *TI, bool Succ_edge);
347 /// When an conditional branch is removed, the BasicBlock that is no longer
348 /// reachable will have problems in phi functions. This method fixes these
349 /// phis removing the former BasicBlock from the list of incoming BasicBlocks
350 /// of all phis. In case the phi remains with no predecessor it will be
351 /// marked to be removed later.
352 void fixPhi(BasicBlock *BB, BasicBlock *Succ);
354 /// Removes phis that have no predecessor
357 /// Creates constraints for Instructions.
358 /// If the constraint for this instruction has already been created
360 void createConstraintInstruction(Instruction *I);
362 /// Creates constraints for Binary Operators.
363 /// It will create constraints only for addition and subtraction,
364 /// the other binary operations are not treated by ABCD.
365 /// For additions in the form a = b + X and a = X + b, where X is a constant,
366 /// the constraint a <= b + X can be obtained. For this constraint, an edge
367 /// a->b with weight X is added to the lower bound graph, and an edge
368 /// b->a with weight -X is added to the upper bound graph.
369 /// Only subtractions in the format a = b - X is used by ABCD.
370 /// Edges are created using the same semantic as addition.
371 void createConstraintBinaryOperator(BinaryOperator *BO);
373 /// Creates constraints for Comparator Instructions.
374 /// Only comparators that have any of the following operators
375 /// are used to create constraints: >=, >, <=, <. And only if
376 /// at least one operand is an Instruction. In a Comparator Instruction
377 /// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
378 /// t and f represent sigma for operands in true and false branches. The
379 /// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
380 /// b_f <= b. There are two more constraints that depend on the operator.
381 /// For the operator <= : a_t <= b_t and b_f <= a_f-1
382 /// For the operator < : a_t <= b_t-1 and b_f <= a_f
383 /// For the operator >= : b_t <= a_t and a_f <= b_f-1
384 /// For the operator > : b_t <= a_t-1 and a_f <= b_f
385 void createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI);
387 /// Creates constraints for PHI nodes.
388 /// In a PHI node a = phi(b,c) we can create the constraint
389 /// a<= max(b,c). With this constraint there will be the edges,
390 /// b->a and c->a with weight 0 in the lower bound graph, and the edges
391 /// a->b and a->c with weight 0 in the upper bound graph.
392 void createConstraintPHINode(PHINode *PN);
394 /// Given a binary operator, we are only interest in the case
395 /// that one operand is an Instruction and the other is a ConstantInt. In
396 /// this case the method returns true, otherwise false. It also obtains the
397 /// Instruction and ConstantInt from the BinaryOperator and returns it.
398 bool createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
399 Instruction **I2, ConstantInt **C1,
402 /// This method creates a constraint between a Sigma and an Instruction.
403 /// These constraints are created as soon as we find a comparator that uses a
405 void createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
406 BasicBlock *BB_succ_f, PHINode **SIG_op_t,
409 /// If PN_op1 and PN_o2 are different from NULL, create a constraint
410 /// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
411 /// with the respective V_op#, if V_op# is a ConstantInt.
412 void createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2,
413 ConstantInt *V_op1, ConstantInt *V_op2,
416 /// Returns the sigma representing the Instruction I in BasicBlock BB.
417 /// Returns NULL in case there is no sigma for this Instruction in this
418 /// Basic Block. This methods assume that sigmas are the first instructions
419 /// in a block, and that there can be only two sigmas in a block. So it will
420 /// only look on the first two instructions of BasicBlock BB.
421 PHINode *findSigma(BasicBlock *BB, Instruction *I);
423 /// Original ABCD algorithm to prove redundant checks.
424 /// This implementation works on any kind of inequality branch.
425 bool demandProve(Value *a, Value *b, int c, bool upper_bound);
427 /// Prove that distance between b and a is <= bound
428 ProveResult prove(Value *a, Value *b, const Bound &bound, unsigned level);
430 /// Updates the distance value for a and b
431 void updateMemDistance(Value *a, Value *b, const Bound &bound, unsigned level,
434 InequalityGraph inequality_graph;
435 MemoizedResult mem_result;
436 DenseMap<Value*, const Bound*> active;
437 SmallPtrSet<Value*, 16> created;
438 SmallVector<PHINode *, 16> phis_to_remove;
441 } // end anonymous namespace.
444 static RegisterPass<ABCD> X("abcd", "ABCD: Eliminating Array Bounds Checks on Demand");
447 bool ABCD::runOnFunction(Function &F) {
451 DEBUG(inequality_graph.printGraph(dbgs(), F));
454 inequality_graph.clear();
458 phis_to_remove.clear();
462 /// Iterates through all BasicBlocks, if the Terminator Instruction
463 /// uses an Comparator Instruction, all operands of this comparator
464 /// are sent to be transformed to SSI. Only Instruction operands are
466 void ABCD::createSSI(Function &F) {
467 SSI *ssi = &getAnalysis<SSI>();
469 SmallVector<Instruction *, 16> Insts;
471 for (Function::iterator begin = F.begin(), end = F.end();
472 begin != end; ++begin) {
473 BasicBlock *BB = begin;
474 TerminatorInst *TI = BB->getTerminator();
475 if (TI->getNumOperands() == 0)
478 if (ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0))) {
479 if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(0))) {
480 modified = true; // XXX: but yet createSSI might do nothing
483 if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(1))) {
489 ssi->createSSI(Insts);
492 /// Creates the graphs for this function.
493 /// It will look for all comparators used in branches, and create them.
494 /// These comparators will create constraints for any instruction as an
496 void ABCD::executeABCD(Function &F) {
497 for (Function::iterator begin = F.begin(), end = F.end();
498 begin != end; ++begin) {
499 BasicBlock *BB = begin;
500 TerminatorInst *TI = BB->getTerminator();
501 if (TI->getNumOperands() == 0)
504 ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0));
505 if (!ICI || !ICI->getOperand(0)->getType()->isIntegerTy())
508 createConstraintCmpInst(ICI, TI);
509 seekRedundancy(ICI, TI);
513 /// Seeks redundancies in the comparator instruction CI.
514 /// If the ABCD algorithm can prove that the comparator CI always
515 /// takes one way, then the Terminator Instruction TI is substituted from
516 /// a conditional branch to a unconditional one.
517 /// This code basically receives a comparator, and verifies which kind of
518 /// instruction it is. Depending on the kind of instruction, we use different
519 /// strategies to prove its redundancy.
520 void ABCD::seekRedundancy(ICmpInst *ICI, TerminatorInst *TI) {
521 CmpInst::Predicate Pred = ICI->getPredicate();
523 Value *source, *dest;
524 int distance1, distance2;
528 case CmpInst::ICMP_SGT: // signed greater than
534 case CmpInst::ICMP_SGE: // signed greater or equal
540 case CmpInst::ICMP_SLT: // signed less than
546 case CmpInst::ICMP_SLE: // signed less or equal
557 source = ICI->getOperand(0);
558 dest = ICI->getOperand(1);
559 if (demandProve(dest, source, distance1, upper)) {
560 removeRedundancy(TI, true);
561 } else if (demandProve(dest, source, distance2, !upper)) {
562 removeRedundancy(TI, false);
566 /// Substitutes Terminator Instruction TI, that is a conditional branch,
567 /// with one unconditional branch. Succ_edge determines if the new
568 /// unconditional edge will be the first or second edge of the former TI
570 void ABCD::removeRedundancy(TerminatorInst *TI, bool Succ_edge) {
573 Succ = TI->getSuccessor(0);
574 fixPhi(TI->getParent(), TI->getSuccessor(1));
576 Succ = TI->getSuccessor(1);
577 fixPhi(TI->getParent(), TI->getSuccessor(0));
580 BranchInst::Create(Succ, TI);
581 TI->eraseFromParent(); // XXX: invoke
586 /// When an conditional branch is removed, the BasicBlock that is no longer
587 /// reachable will have problems in phi functions. This method fixes these
588 /// phis removing the former BasicBlock from the list of incoming BasicBlocks
589 /// of all phis. In case the phi remains with no predecessor it will be
590 /// marked to be removed later.
591 void ABCD::fixPhi(BasicBlock *BB, BasicBlock *Succ) {
592 BasicBlock::iterator begin = Succ->begin();
593 while (PHINode *PN = dyn_cast<PHINode>(begin++)) {
594 PN->removeIncomingValue(BB, false);
595 if (PN->getNumIncomingValues() == 0)
596 phis_to_remove.push_back(PN);
600 /// Removes phis that have no predecessor
601 void ABCD::removePhis() {
602 for (unsigned i = 0, e = phis_to_remove.size(); i != e; ++i) {
603 PHINode *PN = phis_to_remove[i];
604 PN->replaceAllUsesWith(UndefValue::get(PN->getType()));
605 PN->eraseFromParent();
609 /// Creates constraints for Instructions.
610 /// If the constraint for this instruction has already been created
612 void ABCD::createConstraintInstruction(Instruction *I) {
613 // Test if this instruction has not been created before
614 if (created.insert(I)) {
615 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(I)) {
616 createConstraintBinaryOperator(BO);
617 } else if (PHINode *PN = dyn_cast<PHINode>(I)) {
618 createConstraintPHINode(PN);
623 /// Creates constraints for Binary Operators.
624 /// It will create constraints only for addition and subtraction,
625 /// the other binary operations are not treated by ABCD.
626 /// For additions in the form a = b + X and a = X + b, where X is a constant,
627 /// the constraint a <= b + X can be obtained. For this constraint, an edge
628 /// a->b with weight X is added to the lower bound graph, and an edge
629 /// b->a with weight -X is added to the upper bound graph.
630 /// Only subtractions in the format a = b - X is used by ABCD.
631 /// Edges are created using the same semantic as addition.
632 void ABCD::createConstraintBinaryOperator(BinaryOperator *BO) {
633 Instruction *I1 = NULL, *I2 = NULL;
634 ConstantInt *CI1 = NULL, *CI2 = NULL;
636 // Test if an operand is an Instruction and the other is a Constant
637 if (!createBinaryOperatorInfo(BO, &I1, &I2, &CI1, &CI2))
643 switch (BO->getOpcode()) {
644 case Instruction::Add:
647 value = CI2->getValue();
650 value = CI1->getValue();
654 case Instruction::Sub:
655 // Instructions like a = X-b, where X is a constant are not represented
661 value = -CI2->getValue();
668 inequality_graph.addEdge(I, BO, value, true);
669 inequality_graph.addEdge(BO, I, -value, false);
670 createConstraintInstruction(I);
673 /// Given a binary operator, we are only interest in the case
674 /// that one operand is an Instruction and the other is a ConstantInt. In
675 /// this case the method returns true, otherwise false. It also obtains the
676 /// Instruction and ConstantInt from the BinaryOperator and returns it.
677 bool ABCD::createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
678 Instruction **I2, ConstantInt **C1,
680 Value *op1 = BO->getOperand(0);
681 Value *op2 = BO->getOperand(1);
683 if ((*I1 = dyn_cast<Instruction>(op1))) {
684 if ((*C2 = dyn_cast<ConstantInt>(op2)))
685 return true; // First is Instruction and second ConstantInt
687 return false; // Both are Instruction
689 if ((*C1 = dyn_cast<ConstantInt>(op1)) &&
690 (*I2 = dyn_cast<Instruction>(op2)))
691 return true; // First is ConstantInt and second Instruction
693 return false; // Both are not Instruction
697 /// Creates constraints for Comparator Instructions.
698 /// Only comparators that have any of the following operators
699 /// are used to create constraints: >=, >, <=, <. And only if
700 /// at least one operand is an Instruction. In a Comparator Instruction
701 /// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
702 /// t and f represent sigma for operands in true and false branches. The
703 /// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
704 /// b_f <= b. There are two more constraints that depend on the operator.
705 /// For the operator <= : a_t <= b_t and b_f <= a_f-1
706 /// For the operator < : a_t <= b_t-1 and b_f <= a_f
707 /// For the operator >= : b_t <= a_t and a_f <= b_f-1
708 /// For the operator > : b_t <= a_t-1 and a_f <= b_f
709 void ABCD::createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI) {
710 Value *V_op1 = ICI->getOperand(0);
711 Value *V_op2 = ICI->getOperand(1);
713 if (!V_op1->getType()->isIntegerTy())
716 Instruction *I_op1 = dyn_cast<Instruction>(V_op1);
717 Instruction *I_op2 = dyn_cast<Instruction>(V_op2);
719 // Test if at least one operand is an Instruction
720 if (!I_op1 && !I_op2)
723 BasicBlock *BB_succ_t = TI->getSuccessor(0);
724 BasicBlock *BB_succ_f = TI->getSuccessor(1);
726 PHINode *SIG_op1_t = NULL, *SIG_op1_f = NULL,
727 *SIG_op2_t = NULL, *SIG_op2_f = NULL;
729 createConstraintSigInst(I_op1, BB_succ_t, BB_succ_f, &SIG_op1_t, &SIG_op1_f);
730 createConstraintSigInst(I_op2, BB_succ_t, BB_succ_f, &SIG_op2_t, &SIG_op2_f);
732 int32_t width = cast<IntegerType>(V_op1->getType())->getBitWidth();
733 APInt MinusOne = APInt::getAllOnesValue(width);
734 APInt Zero = APInt::getNullValue(width);
736 CmpInst::Predicate Pred = ICI->getPredicate();
737 ConstantInt *CI1 = dyn_cast<ConstantInt>(V_op1);
738 ConstantInt *CI2 = dyn_cast<ConstantInt>(V_op2);
740 case CmpInst::ICMP_SGT: // signed greater than
741 createConstraintSigSig(SIG_op2_t, SIG_op1_t, CI2, CI1, MinusOne);
742 createConstraintSigSig(SIG_op1_f, SIG_op2_f, CI1, CI2, Zero);
745 case CmpInst::ICMP_SGE: // signed greater or equal
746 createConstraintSigSig(SIG_op2_t, SIG_op1_t, CI2, CI1, Zero);
747 createConstraintSigSig(SIG_op1_f, SIG_op2_f, CI1, CI2, MinusOne);
750 case CmpInst::ICMP_SLT: // signed less than
751 createConstraintSigSig(SIG_op1_t, SIG_op2_t, CI1, CI2, MinusOne);
752 createConstraintSigSig(SIG_op2_f, SIG_op1_f, CI2, CI1, Zero);
755 case CmpInst::ICMP_SLE: // signed less or equal
756 createConstraintSigSig(SIG_op1_t, SIG_op2_t, CI1, CI2, Zero);
757 createConstraintSigSig(SIG_op2_f, SIG_op1_f, CI2, CI1, MinusOne);
765 createConstraintInstruction(I_op1);
767 createConstraintInstruction(I_op2);
770 /// Creates constraints for PHI nodes.
771 /// In a PHI node a = phi(b,c) we can create the constraint
772 /// a<= max(b,c). With this constraint there will be the edges,
773 /// b->a and c->a with weight 0 in the lower bound graph, and the edges
774 /// a->b and a->c with weight 0 in the upper bound graph.
775 void ABCD::createConstraintPHINode(PHINode *PN) {
776 // FIXME: We really want to disallow sigma nodes, but I don't know the best
777 // way to detect the other than this.
778 if (PN->getNumOperands() == 2) return;
780 int32_t width = cast<IntegerType>(PN->getType())->getBitWidth();
781 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
782 Value *V = PN->getIncomingValue(i);
783 if (Instruction *I = dyn_cast<Instruction>(V)) {
784 createConstraintInstruction(I);
786 inequality_graph.addEdge(V, PN, APInt(width, 0), true);
787 inequality_graph.addEdge(V, PN, APInt(width, 0), false);
791 /// This method creates a constraint between a Sigma and an Instruction.
792 /// These constraints are created as soon as we find a comparator that uses a
794 void ABCD::createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
795 BasicBlock *BB_succ_f, PHINode **SIG_op_t,
796 PHINode **SIG_op_f) {
797 *SIG_op_t = findSigma(BB_succ_t, I_op);
798 *SIG_op_f = findSigma(BB_succ_f, I_op);
801 int32_t width = cast<IntegerType>((*SIG_op_t)->getType())->getBitWidth();
802 inequality_graph.addEdge(I_op, *SIG_op_t, APInt(width, 0), true);
803 inequality_graph.addEdge(*SIG_op_t, I_op, APInt(width, 0), false);
806 int32_t width = cast<IntegerType>((*SIG_op_f)->getType())->getBitWidth();
807 inequality_graph.addEdge(I_op, *SIG_op_f, APInt(width, 0), true);
808 inequality_graph.addEdge(*SIG_op_f, I_op, APInt(width, 0), false);
812 /// If PN_op1 and PN_o2 are different from NULL, create a constraint
813 /// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
814 /// with the respective V_op#, if V_op# is a ConstantInt.
815 void ABCD::createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2,
816 ConstantInt *V_op1, ConstantInt *V_op2,
818 if (SIG_op1 && SIG_op2) {
819 inequality_graph.addEdge(SIG_op2, SIG_op1, value, true);
820 inequality_graph.addEdge(SIG_op1, SIG_op2, -value, false);
821 } else if (SIG_op1 && V_op2) {
822 inequality_graph.addEdge(V_op2, SIG_op1, value, true);
823 inequality_graph.addEdge(SIG_op1, V_op2, -value, false);
824 } else if (SIG_op2 && V_op1) {
825 inequality_graph.addEdge(SIG_op2, V_op1, value, true);
826 inequality_graph.addEdge(V_op1, SIG_op2, -value, false);
830 /// Returns the sigma representing the Instruction I in BasicBlock BB.
831 /// Returns NULL in case there is no sigma for this Instruction in this
832 /// Basic Block. This methods assume that sigmas are the first instructions
833 /// in a block, and that there can be only two sigmas in a block. So it will
834 /// only look on the first two instructions of BasicBlock BB.
835 PHINode *ABCD::findSigma(BasicBlock *BB, Instruction *I) {
836 // BB has more than one predecessor, BB cannot have sigmas.
837 if (I == NULL || BB->getSinglePredecessor() == NULL)
840 BasicBlock::iterator begin = BB->begin();
841 BasicBlock::iterator end = BB->end();
843 for (unsigned i = 0; i < 2 && begin != end; ++i, ++begin) {
844 Instruction *I_succ = begin;
845 if (PHINode *PN = dyn_cast<PHINode>(I_succ))
846 if (PN->getIncomingValue(0) == I)
853 /// Original ABCD algorithm to prove redundant checks.
854 /// This implementation works on any kind of inequality branch.
855 bool ABCD::demandProve(Value *a, Value *b, int c, bool upper_bound) {
856 int32_t width = cast<IntegerType>(a->getType())->getBitWidth();
857 Bound bound(APInt(width, c), upper_bound);
862 ProveResult res = prove(a, b, bound, 0);
866 /// Prove that distance between b and a is <= bound
867 ABCD::ProveResult ABCD::prove(Value *a, Value *b, const Bound &bound,
869 // if (C[b-a<=e] == True for some e <= bound
870 // Same or stronger difference was already proven
871 if (mem_result.hasTrue(b, bound))
874 // if (C[b-a<=e] == False for some e >= bound
875 // Same or weaker difference was already disproved
876 if (mem_result.hasFalse(b, bound))
879 // if (C[b-a<=e] == Reduced for some e <= bound
880 // b is on a cycle that was reduced for same or stronger difference
881 if (mem_result.hasReduced(b, bound))
884 // traversal reached the source vertex
885 if (a == b && Bound::geq(bound, APInt(bound.getBitWidth(), 0, true)))
888 // if b has no predecessor then fail
889 if (!inequality_graph.hasEdge(b, bound.isUpperBound()))
892 // a cycle was encountered
893 if (active.count(b)) {
894 if (Bound::leq(*active.lookup(b), bound))
895 return Reduced; // a "harmless" cycle
897 return False; // an amplifying cycle
901 PHINode *PN = dyn_cast<PHINode>(b);
903 // Test if a Value is a Phi. If it is a PHINode with more than 1 incoming
904 // value, then it is a phi, if it has 1 incoming value it is a sigma.
905 if (PN && PN->getNumIncomingValues() > 1)
906 updateMemDistance(a, b, bound, level, min);
908 updateMemDistance(a, b, bound, level, max);
912 ABCD::ProveResult res = mem_result.getBoundResult(b, bound);
916 /// Updates the distance value for a and b
917 void ABCD::updateMemDistance(Value *a, Value *b, const Bound &bound,
918 unsigned level, meet_function meet) {
919 ABCD::ProveResult res = (meet == max) ? False : True;
921 SmallVector<Edge, 16> Edges = inequality_graph.getEdges(b);
922 SmallVector<Edge, 16>::iterator begin = Edges.begin(), end = Edges.end();
924 for (; begin != end ; ++begin) {
925 if (((res >= Reduced) && (meet == max)) ||
926 ((res == False) && (meet == min))) {
929 const Edge &in = *begin;
930 if (in.isUpperBound() == bound.isUpperBound()) {
931 Value *succ = in.getVertex();
932 res = meet(res, prove(a, succ, Bound(bound, in.getValue()),
937 mem_result.updateBound(b, bound, res);
940 /// Return the stored result for this bound
941 ABCD::ProveResult ABCD::MemoizedResultChart::getResult(const Bound &bound)const{
942 if (max_false && Bound::leq(bound, *max_false))
944 if (min_true && Bound::leq(*min_true, bound))
946 if (min_reduced && Bound::leq(*min_reduced, bound))
951 /// Stores a false found
952 void ABCD::MemoizedResultChart::addFalse(const Bound &bound) {
953 if (!max_false || Bound::leq(*max_false, bound))
954 max_false.reset(new Bound(bound));
956 if (Bound::eq(max_false.get(), min_reduced.get()))
957 min_reduced.reset(new Bound(Bound::createIncrement(*min_reduced)));
958 if (Bound::eq(max_false.get(), min_true.get()))
959 min_true.reset(new Bound(Bound::createIncrement(*min_true)));
960 if (Bound::eq(min_reduced.get(), min_true.get()))
962 clearRedundantReduced();
965 /// Stores a true found
966 void ABCD::MemoizedResultChart::addTrue(const Bound &bound) {
967 if (!min_true || Bound::leq(bound, *min_true))
968 min_true.reset(new Bound(bound));
970 if (Bound::eq(min_true.get(), min_reduced.get()))
971 min_reduced.reset(new Bound(Bound::createDecrement(*min_reduced)));
972 if (Bound::eq(min_true.get(), max_false.get()))
973 max_false.reset(new Bound(Bound::createDecrement(*max_false)));
974 if (Bound::eq(max_false.get(), min_reduced.get()))
976 clearRedundantReduced();
979 /// Stores a Reduced found
980 void ABCD::MemoizedResultChart::addReduced(const Bound &bound) {
981 if (!min_reduced || Bound::leq(bound, *min_reduced))
982 min_reduced.reset(new Bound(bound));
984 if (Bound::eq(min_reduced.get(), min_true.get()))
985 min_true.reset(new Bound(Bound::createIncrement(*min_true)));
986 if (Bound::eq(min_reduced.get(), max_false.get()))
987 max_false.reset(new Bound(Bound::createDecrement(*max_false)));
990 /// Clears redundant reduced
991 /// If a min_true is smaller than a min_reduced then the min_reduced
992 /// is unnecessary and then removed. It also works for min_reduced
993 /// begin smaller than max_false.
994 void ABCD::MemoizedResultChart::clearRedundantReduced() {
995 if (min_true && min_reduced && Bound::lt(*min_true, *min_reduced))
997 if (max_false && min_reduced && Bound::lt(*min_reduced, *max_false))
1001 /// Stores the bound found
1002 void ABCD::MemoizedResult::updateBound(Value *b, const Bound &bound,
1003 const ProveResult res) {
1005 map[b].addFalse(bound);
1006 } else if (res == True) {
1007 map[b].addTrue(bound);
1009 map[b].addReduced(bound);
1013 /// Adds an edge from V_from to V_to with weight value
1014 void ABCD::InequalityGraph::addEdge(Value *V_to, Value *V_from,
1015 APInt value, bool upper) {
1016 assert(V_from->getType() == V_to->getType());
1017 assert(cast<IntegerType>(V_from->getType())->getBitWidth() ==
1018 value.getBitWidth());
1020 graph[V_from].push_back(Edge(V_to, value, upper));
1023 /// Test if there is any edge from V in the upper direction
1024 bool ABCD::InequalityGraph::hasEdge(Value *V, bool upper) const {
1025 SmallVector<Edge, 16> it = graph.lookup(V);
1027 SmallVector<Edge, 16>::iterator begin = it.begin();
1028 SmallVector<Edge, 16>::iterator end = it.end();
1029 for (; begin != end; ++begin) {
1030 if (begin->isUpperBound() == upper) {
1037 /// Prints the header of the dot file
1038 void ABCD::InequalityGraph::printHeader(raw_ostream &OS, Function &F) const {
1039 OS << "digraph dotgraph {\n";
1040 OS << "label=\"Inequality Graph for \'";
1041 OS << F.getNameStr() << "\' function\";\n";
1042 OS << "node [shape=record,fontname=\"Times-Roman\",fontsize=14];\n";
1045 /// Prints the body of the dot file
1046 void ABCD::InequalityGraph::printBody(raw_ostream &OS) const {
1047 DenseMap<Value *, SmallVector<Edge, 16> >::const_iterator begin =
1048 graph.begin(), end = graph.end();
1050 for (; begin != end ; ++begin) {
1051 SmallVector<Edge, 16>::const_iterator begin_par =
1052 begin->second.begin(), end_par = begin->second.end();
1053 Value *source = begin->first;
1055 printVertex(OS, source);
1057 for (; begin_par != end_par ; ++begin_par) {
1058 const Edge &edge = *begin_par;
1059 printEdge(OS, source, edge);
1064 /// Prints vertex source to the dot file
1066 void ABCD::InequalityGraph::printVertex(raw_ostream &OS, Value *source) const {
1068 printName(OS, source);
1070 OS << " [label=\"{";
1071 printName(OS, source);
1075 /// Prints the edge to the dot file
1076 void ABCD::InequalityGraph::printEdge(raw_ostream &OS, Value *source,
1077 const Edge &edge) const {
1078 Value *dest = edge.getVertex();
1079 APInt value = edge.getValue();
1080 bool upper = edge.isUpperBound();
1083 printName(OS, source);
1087 printName(OS, dest);
1089 OS << " [label=\"" << value << "\"";
1091 OS << "color=\"blue\"";
1093 OS << "color=\"red\"";
1098 void ABCD::InequalityGraph::printName(raw_ostream &OS, Value *info) const {
1099 if (ConstantInt *CI = dyn_cast<ConstantInt>(info)) {
1102 if (!info->hasName()) {
1105 OS << info->getNameStr();
1109 /// createABCDPass - The public interface to this file...
1110 FunctionPass *llvm::createABCDPass() {