1 //===- CorrelatedExprs.cpp - Pass to detect and eliminated c.e.'s ---------===//
3 // Correlated Expression Elimination propogates information from conditional
4 // branches to blocks dominated by destinations of the branch. It propogates
5 // information from the condition check itself into the body of the branch,
6 // allowing transformations like these for example:
9 // ... 4*i; // constant propogation
13 // X = M-N; // = M-M == 0;
15 // This is called Correlated Expression Elimination because we eliminate or
16 // simplify expressions that are correlated with the direction of a branch. In
17 // this way we use static information to give us some information about the
18 // dynamic value of a variable.
20 //===----------------------------------------------------------------------===//
22 #include "llvm/Transforms/Scalar.h"
23 #include "llvm/Pass.h"
24 #include "llvm/Function.h"
25 #include "llvm/iTerminators.h"
26 #include "llvm/iPHINode.h"
27 #include "llvm/iOperators.h"
28 #include "llvm/ConstantHandling.h"
29 #include "llvm/Assembly/Writer.h"
30 #include "llvm/Analysis/Dominators.h"
31 #include "llvm/Transforms/Utils/Local.h"
32 #include "llvm/Support/ConstantRange.h"
33 #include "llvm/Support/CFG.h"
34 #include "Support/PostOrderIterator.h"
35 #include "Support/Statistic.h"
39 Statistic<> NumSetCCRemoved("cee", "Number of setcc instruction eliminated");
40 Statistic<> NumOperandsCann("cee", "Number of operands cannonicalized");
41 Statistic<> BranchRevectors("cee", "Number of branches revectored");
45 Value *Val; // Relation to what value?
46 Instruction::BinaryOps Rel; // SetCC relation, or Add if no information
48 Relation(Value *V) : Val(V), Rel(Instruction::Add) {}
49 bool operator<(const Relation &R) const { return Val < R.Val; }
50 Value *getValue() const { return Val; }
51 Instruction::BinaryOps getRelation() const { return Rel; }
53 // contradicts - Return true if the relationship specified by the operand
54 // contradicts already known information.
56 bool contradicts(Instruction::BinaryOps Rel, const ValueInfo &VI) const;
58 // incorporate - Incorporate information in the argument into this relation
59 // entry. This assumes that the information doesn't contradict itself. If
60 // any new information is gained, true is returned, otherwise false is
61 // returned to indicate that nothing was updated.
63 bool incorporate(Instruction::BinaryOps Rel, ValueInfo &VI);
65 // KnownResult - Whether or not this condition determines the result of a
66 // setcc in the program. False & True are intentionally 0 & 1 so we can
67 // convert to bool by casting after checking for unknown.
69 enum KnownResult { KnownFalse = 0, KnownTrue = 1, Unknown = 2 };
71 // getImpliedResult - If this relationship between two values implies that
72 // the specified relationship is true or false, return that. If we cannot
73 // determine the result required, return Unknown.
75 KnownResult getImpliedResult(Instruction::BinaryOps Rel) const;
77 // print - Output this relation to the specified stream
78 void print(std::ostream &OS) const;
83 // ValueInfo - One instance of this record exists for every value with
84 // relationships between other values. It keeps track of all of the
85 // relationships to other values in the program (specified with Relation) that
86 // are known to be valid in a region.
89 // RelationShips - this value is know to have the specified relationships to
90 // other values. There can only be one entry per value, and this list is
91 // kept sorted by the Val field.
92 std::vector<Relation> Relationships;
94 // If information about this value is known or propogated from constant
95 // expressions, this range contains the possible values this value may hold.
98 // If we find that this value is equal to another value that has a lower
99 // rank, this value is used as it's replacement.
103 ValueInfo(const Type *Ty)
104 : Bounds(Ty->isIntegral() ? Ty : Type::IntTy), Replacement(0) {}
106 // getBounds() - Return the constant bounds of the value...
107 const ConstantRange &getBounds() const { return Bounds; }
108 ConstantRange &getBounds() { return Bounds; }
110 const std::vector<Relation> &getRelationships() { return Relationships; }
112 // getReplacement - Return the value this value is to be replaced with if it
113 // exists, otherwise return null.
115 Value *getReplacement() const { return Replacement; }
117 // setReplacement - Used by the replacement calculation pass to figure out
118 // what to replace this value with, if anything.
120 void setReplacement(Value *Repl) { Replacement = Repl; }
122 // getRelation - return the relationship entry for the specified value.
123 // This can invalidate references to other Relation's, so use it carefully.
125 Relation &getRelation(Value *V) {
126 // Binary search for V's entry...
127 std::vector<Relation>::iterator I =
128 std::lower_bound(Relationships.begin(), Relationships.end(), V);
130 // If we found the entry, return it...
131 if (I != Relationships.end() && I->getValue() == V)
134 // Insert and return the new relationship...
135 return *Relationships.insert(I, V);
138 const Relation *requestRelation(Value *V) const {
139 // Binary search for V's entry...
140 std::vector<Relation>::const_iterator I =
141 std::lower_bound(Relationships.begin(), Relationships.end(), V);
142 if (I != Relationships.end() && I->getValue() == V)
147 // print - Output information about this value relation...
148 void print(std::ostream &OS, Value *V) const;
152 // RegionInfo - Keeps track of all of the value relationships for a region. A
153 // region is the are dominated by a basic block. RegionInfo's keep track of
154 // the RegionInfo for their dominator, because anything known in a dominator
155 // is known to be true in a dominated block as well.
160 // ValueMap - Tracks the ValueInformation known for this region
161 typedef std::map<Value*, ValueInfo> ValueMapTy;
164 RegionInfo(BasicBlock *bb) : BB(bb) {}
166 // getEntryBlock - Return the block that dominates all of the members of
168 BasicBlock *getEntryBlock() const { return BB; }
170 // empty - return true if this region has no information known about it.
171 bool empty() const { return ValueMap.empty(); }
173 const RegionInfo &operator=(const RegionInfo &RI) {
174 ValueMap = RI.ValueMap;
178 // print - Output information about this region...
179 void print(std::ostream &OS) const;
182 // Allow external access.
183 typedef ValueMapTy::iterator iterator;
184 iterator begin() { return ValueMap.begin(); }
185 iterator end() { return ValueMap.end(); }
187 ValueInfo &getValueInfo(Value *V) {
188 ValueMapTy::iterator I = ValueMap.lower_bound(V);
189 if (I != ValueMap.end() && I->first == V) return I->second;
190 return ValueMap.insert(I, std::make_pair(V, V->getType()))->second;
193 const ValueInfo *requestValueInfo(Value *V) const {
194 ValueMapTy::const_iterator I = ValueMap.find(V);
195 if (I != ValueMap.end()) return &I->second;
199 /// removeValueInfo - Remove anything known about V from our records. This
200 /// works whether or not we know anything about V.
202 void removeValueInfo(Value *V) {
207 /// CEE - Correlated Expression Elimination
208 class CEE : public FunctionPass {
209 std::map<Value*, unsigned> RankMap;
210 std::map<BasicBlock*, RegionInfo> RegionInfoMap;
214 virtual bool runOnFunction(Function &F);
216 // We don't modify the program, so we preserve all analyses
217 virtual void getAnalysisUsage(AnalysisUsage &AU) const {
218 AU.addRequired<DominatorSet>();
219 AU.addRequired<DominatorTree>();
220 AU.addRequiredID(BreakCriticalEdgesID);
223 // print - Implement the standard print form to print out analysis
225 virtual void print(std::ostream &O, const Module *M) const;
228 RegionInfo &getRegionInfo(BasicBlock *BB) {
229 std::map<BasicBlock*, RegionInfo>::iterator I
230 = RegionInfoMap.lower_bound(BB);
231 if (I != RegionInfoMap.end() && I->first == BB) return I->second;
232 return RegionInfoMap.insert(I, std::make_pair(BB, BB))->second;
235 void BuildRankMap(Function &F);
236 unsigned getRank(Value *V) const {
237 if (isa<Constant>(V) || isa<GlobalValue>(V)) return 0;
238 std::map<Value*, unsigned>::const_iterator I = RankMap.find(V);
239 if (I != RankMap.end()) return I->second;
240 return 0; // Must be some other global thing
243 bool TransformRegion(BasicBlock *BB, std::set<BasicBlock*> &VisitedBlocks);
245 bool ForwardCorrelatedEdgeDestination(TerminatorInst *TI, unsigned SuccNo,
248 void ForwardSuccessorTo(TerminatorInst *TI, unsigned Succ, BasicBlock *D,
250 void ReplaceUsesOfValueInRegion(Value *Orig, Value *New,
251 BasicBlock *RegionDominator);
252 void CalculateRegionExitBlocks(BasicBlock *BB, BasicBlock *OldSucc,
253 std::vector<BasicBlock*> &RegionExitBlocks);
254 void InsertRegionExitMerges(PHINode *NewPHI, Instruction *OldVal,
255 const std::vector<BasicBlock*> &RegionExitBlocks);
257 void PropogateBranchInfo(BranchInst *BI);
258 void PropogateEquality(Value *Op0, Value *Op1, RegionInfo &RI);
259 void PropogateRelation(Instruction::BinaryOps Opcode, Value *Op0,
260 Value *Op1, RegionInfo &RI);
261 void UpdateUsersOfValue(Value *V, RegionInfo &RI);
262 void IncorporateInstruction(Instruction *Inst, RegionInfo &RI);
263 void ComputeReplacements(RegionInfo &RI);
266 // getSetCCResult - Given a setcc instruction, determine if the result is
267 // determined by facts we already know about the region under analysis.
268 // Return KnownTrue, KnownFalse, or Unknown based on what we can determine.
270 Relation::KnownResult getSetCCResult(SetCondInst *SC, const RegionInfo &RI);
273 bool SimplifyBasicBlock(BasicBlock &BB, const RegionInfo &RI);
274 bool SimplifyInstruction(Instruction *Inst, const RegionInfo &RI);
276 RegisterOpt<CEE> X("cee", "Correlated Expression Elimination");
279 Pass *createCorrelatedExpressionEliminationPass() { return new CEE(); }
282 bool CEE::runOnFunction(Function &F) {
283 // Build a rank map for the function...
286 // Traverse the dominator tree, computing information for each node in the
287 // tree. Note that our traversal will not even touch unreachable basic
289 DS = &getAnalysis<DominatorSet>();
290 DT = &getAnalysis<DominatorTree>();
292 std::set<BasicBlock*> VisitedBlocks;
293 bool Changed = TransformRegion(&F.getEntryNode(), VisitedBlocks);
295 RegionInfoMap.clear();
300 // TransformRegion - Transform the region starting with BB according to the
301 // calculated region information for the block. Transforming the region
302 // involves analyzing any information this block provides to successors,
303 // propogating the information to successors, and finally transforming
306 // This method processes the function in depth first order, which guarantees
307 // that we process the immediate dominator of a block before the block itself.
308 // Because we are passing information from immediate dominators down to
309 // dominatees, we obviously have to process the information source before the
310 // information consumer.
312 bool CEE::TransformRegion(BasicBlock *BB, std::set<BasicBlock*> &VisitedBlocks){
313 // Prevent infinite recursion...
314 if (VisitedBlocks.count(BB)) return false;
315 VisitedBlocks.insert(BB);
317 // Get the computed region information for this block...
318 RegionInfo &RI = getRegionInfo(BB);
320 // Compute the replacement information for this block...
321 ComputeReplacements(RI);
323 // If debugging, print computed region information...
324 DEBUG(RI.print(std::cerr));
326 // Simplify the contents of this block...
327 bool Changed = SimplifyBasicBlock(*BB, RI);
329 // Get the terminator of this basic block...
330 TerminatorInst *TI = BB->getTerminator();
332 // Loop over all of the blocks that this block is the immediate dominator for.
333 // Because all information known in this region is also known in all of the
334 // blocks that are dominated by this one, we can safely propogate the
335 // information down now.
337 DominatorTree::Node *BBN = (*DT)[BB];
338 if (!RI.empty()) // Time opt: only propogate if we can change something
339 for (unsigned i = 0, e = BBN->getChildren().size(); i != e; ++i) {
340 BasicBlock *Dominated = BBN->getChildren()[i]->getNode();
341 assert(RegionInfoMap.find(Dominated) == RegionInfoMap.end() &&
342 "RegionInfo should be calculated in dominanace order!");
343 getRegionInfo(Dominated) = RI;
346 // Now that all of our successors have information if they deserve it,
347 // propogate any information our terminator instruction finds to our
349 if (BranchInst *BI = dyn_cast<BranchInst>(TI))
350 if (BI->isConditional())
351 PropogateBranchInfo(BI);
353 // If this is a branch to a block outside our region that simply performs
354 // another conditional branch, one whose outcome is known inside of this
355 // region, then vector this outgoing edge directly to the known destination.
357 for (unsigned i = 0, e = TI->getNumSuccessors(); i != e; ++i)
358 while (ForwardCorrelatedEdgeDestination(TI, i, RI)) {
363 // Now that all of our successors have information, recursively process them.
364 for (unsigned i = 0, e = BBN->getChildren().size(); i != e; ++i)
365 Changed |= TransformRegion(BBN->getChildren()[i]->getNode(), VisitedBlocks);
370 // isBlockSimpleEnoughForCheck to see if the block is simple enough for us to
371 // revector the conditional branch in the bottom of the block, do so now.
373 static bool isBlockSimpleEnough(BasicBlock *BB) {
374 assert(isa<BranchInst>(BB->getTerminator()));
375 BranchInst *BI = cast<BranchInst>(BB->getTerminator());
376 assert(BI->isConditional());
378 // Check the common case first: empty block, or block with just a setcc.
379 if (BB->size() == 1 ||
380 (BB->size() == 2 && &BB->front() == BI->getCondition() &&
381 BI->getCondition()->use_size() == 1))
384 // Check the more complex case now...
385 BasicBlock::iterator I = BB->begin();
387 // FIXME: This should be reenabled once the regression with SIM is fixed!
389 // PHI Nodes are ok, just skip over them...
390 while (isa<PHINode>(*I)) ++I;
393 // Accept the setcc instruction...
394 if (&*I == BI->getCondition())
397 // Nothing else is acceptable here yet. We must not revector... unless we are
398 // at the terminator instruction.
406 bool CEE::ForwardCorrelatedEdgeDestination(TerminatorInst *TI, unsigned SuccNo,
408 // If this successor is a simple block not in the current region, which
409 // contains only a conditional branch, we decide if the outcome of the branch
410 // can be determined from information inside of the region. Instead of going
411 // to this block, we can instead go to the destination we know is the right
415 // Check to see if we dominate the block. If so, this block will get the
416 // condition turned to a constant anyway.
418 //if (DS->dominates(RI.getEntryBlock(), BB))
421 BasicBlock *BB = TI->getParent();
423 // Get the destination block of this edge...
424 BasicBlock *OldSucc = TI->getSuccessor(SuccNo);
426 // Make sure that the block ends with a conditional branch and is simple
427 // enough for use to be able to revector over.
428 BranchInst *BI = dyn_cast<BranchInst>(OldSucc->getTerminator());
429 if (BI == 0 || !BI->isConditional() || !isBlockSimpleEnough(OldSucc))
432 // We can only forward the branch over the block if the block ends with a
433 // setcc we can determine the outcome for.
435 // FIXME: we can make this more generic. Code below already handles more
437 SetCondInst *SCI = dyn_cast<SetCondInst>(BI->getCondition());
438 if (SCI == 0) return false;
440 // Make a new RegionInfo structure so that we can simulate the effect of the
441 // PHI nodes in the block we are skipping over...
443 RegionInfo NewRI(RI);
445 // Remove value information for all of the values we are simulating... to make
446 // sure we don't have any stale information.
447 for (BasicBlock::iterator I = OldSucc->begin(), E = OldSucc->end(); I!=E; ++I)
448 if (I->getType() != Type::VoidTy)
449 NewRI.removeValueInfo(I);
451 // Put the newly discovered information into the RegionInfo...
452 for (BasicBlock::iterator I = OldSucc->begin(), E = OldSucc->end(); I!=E; ++I)
453 if (PHINode *PN = dyn_cast<PHINode>(&*I)) {
454 int OpNum = PN->getBasicBlockIndex(BB);
455 assert(OpNum != -1 && "PHI doesn't have incoming edge for predecessor!?");
456 PropogateEquality(PN, PN->getIncomingValue(OpNum), NewRI);
457 } else if (SetCondInst *SCI = dyn_cast<SetCondInst>(&*I)) {
458 Relation::KnownResult Res = getSetCCResult(SCI, NewRI);
459 if (Res == Relation::Unknown) return false;
460 PropogateEquality(SCI, ConstantBool::get(Res), NewRI);
462 assert(isa<BranchInst>(*I) && "Unexpected instruction type!");
465 // Compute the facts implied by what we have discovered...
466 ComputeReplacements(NewRI);
468 ValueInfo &PredicateVI = NewRI.getValueInfo(BI->getCondition());
469 if (PredicateVI.getReplacement() &&
470 isa<Constant>(PredicateVI.getReplacement())) {
471 ConstantBool *CB = cast<ConstantBool>(PredicateVI.getReplacement());
473 // Forward to the successor that corresponds to the branch we will take.
474 ForwardSuccessorTo(TI, SuccNo, BI->getSuccessor(!CB->getValue()), NewRI);
481 static Value *getReplacementOrValue(Value *V, RegionInfo &RI) {
482 if (const ValueInfo *VI = RI.requestValueInfo(V))
483 if (Value *Repl = VI->getReplacement())
488 /// ForwardSuccessorTo - We have found that we can forward successor # 'SuccNo'
489 /// of Terminator 'TI' to the 'Dest' BasicBlock. This method performs the
490 /// mechanics of updating SSA information and revectoring the branch.
492 void CEE::ForwardSuccessorTo(TerminatorInst *TI, unsigned SuccNo,
493 BasicBlock *Dest, RegionInfo &RI) {
494 // If there are any PHI nodes in the Dest BB, we must duplicate the entry
495 // in the PHI node for the old successor to now include an entry from the
496 // current basic block.
498 BasicBlock *OldSucc = TI->getSuccessor(SuccNo);
499 BasicBlock *BB = TI->getParent();
501 DEBUG(std::cerr << "Forwarding branch in basic block %" << BB->getName()
502 << " from block %" << OldSucc->getName() << " to block %"
503 << Dest->getName() << "\n");
505 DEBUG(std::cerr << "Before forwarding: " << *BB->getParent());
507 // Because we know that there cannot be critical edges in the flow graph, and
508 // that OldSucc has multiple outgoing edges, this means that Dest cannot have
509 // multiple incoming edges.
512 pred_iterator DPI = pred_begin(Dest); ++DPI;
513 assert(DPI == pred_end(Dest) && "Critical edge found!!");
516 // Loop over any PHI nodes in the destination, eliminating them, because they
517 // may only have one input.
519 while (PHINode *PN = dyn_cast<PHINode>(&Dest->front())) {
520 assert(PN->getNumIncomingValues() == 1 && "Crit edge found!");
521 // Eliminate the PHI node
522 PN->replaceAllUsesWith(PN->getIncomingValue(0));
523 Dest->getInstList().erase(PN);
526 // If there are values defined in the "OldSucc" basic block, we need to insert
527 // PHI nodes in the regions we are dealing with to emulate them. This can
528 // insert dead phi nodes, but it is more trouble to see if they are used than
529 // to just blindly insert them.
531 if (DS->dominates(OldSucc, Dest)) {
532 // RegionExitBlocks - Find all of the blocks that are not dominated by Dest,
533 // but have predecessors that are. Additionally, prune down the set to only
534 // include blocks that are dominated by OldSucc as well.
536 std::vector<BasicBlock*> RegionExitBlocks;
537 CalculateRegionExitBlocks(Dest, OldSucc, RegionExitBlocks);
539 for (BasicBlock::iterator I = OldSucc->begin(), E = OldSucc->end();
541 if (I->getType() != Type::VoidTy) {
542 // Create and insert the PHI node into the top of Dest.
543 PHINode *NewPN = new PHINode(I->getType(), I->getName()+".fw_merge",
545 // There is definately an edge from OldSucc... add the edge now
546 NewPN->addIncoming(I, OldSucc);
548 // There is also an edge from BB now, add the edge with the calculated
549 // value from the RI.
550 NewPN->addIncoming(getReplacementOrValue(I, RI), BB);
552 // Make everything in the Dest region use the new PHI node now...
553 ReplaceUsesOfValueInRegion(I, NewPN, Dest);
555 // Make sure that exits out of the region dominated by NewPN get PHI
556 // nodes that merge the values as appropriate.
557 InsertRegionExitMerges(NewPN, I, RegionExitBlocks);
561 // If there were PHI nodes in OldSucc, we need to remove the entry for this
562 // edge from the PHI node, and we need to replace any references to the PHI
563 // node with a new value.
565 for (BasicBlock::iterator I = OldSucc->begin();
566 PHINode *PN = dyn_cast<PHINode>(&*I); ) {
568 // Get the value flowing across the old edge and remove the PHI node entry
569 // for this edge: we are about to remove the edge! Don't remove the PHI
570 // node yet though if this is the last edge into it.
571 Value *EdgeValue = PN->removeIncomingValue(BB, false);
573 // Make sure that anything that used to use PN now refers to EdgeValue
574 ReplaceUsesOfValueInRegion(PN, EdgeValue, Dest);
576 // If there is only one value left coming into the PHI node, replace the PHI
577 // node itself with the one incoming value left.
579 if (PN->getNumIncomingValues() == 1) {
580 assert(PN->getNumIncomingValues() == 1);
581 PN->replaceAllUsesWith(PN->getIncomingValue(0));
582 PN->getParent()->getInstList().erase(PN);
583 I = OldSucc->begin();
584 } else if (PN->getNumIncomingValues() == 0) { // Nuke the PHI
585 // If we removed the last incoming value to this PHI, nuke the PHI node
587 PN->replaceAllUsesWith(Constant::getNullValue(PN->getType()));
588 PN->getParent()->getInstList().erase(PN);
589 I = OldSucc->begin();
591 ++I; // Otherwise, move on to the next PHI node
595 // Actually revector the branch now...
596 TI->setSuccessor(SuccNo, Dest);
598 // If we just introduced a critical edge in the flow graph, make sure to break
600 if (isCriticalEdge(TI, SuccNo))
601 SplitCriticalEdge(TI, SuccNo, this);
603 // Make sure that we don't introduce critical edges from oldsucc now!
604 for (unsigned i = 0, e = OldSucc->getTerminator()->getNumSuccessors();
606 if (isCriticalEdge(OldSucc->getTerminator(), i))
607 SplitCriticalEdge(OldSucc->getTerminator(), i, this);
609 // Since we invalidated the CFG, recalculate the dominator set so that it is
610 // useful for later processing!
611 // FIXME: This is much worse than it really should be!
614 DEBUG(std::cerr << "After forwarding: " << *BB->getParent());
617 /// ReplaceUsesOfValueInRegion - This method replaces all uses of Orig with uses
618 /// of New. It only affects instructions that are defined in basic blocks that
619 /// are dominated by Head.
621 void CEE::ReplaceUsesOfValueInRegion(Value *Orig, Value *New,
622 BasicBlock *RegionDominator) {
623 assert(Orig != New && "Cannot replace value with itself");
624 std::vector<Instruction*> InstsToChange;
625 std::vector<PHINode*> PHIsToChange;
626 InstsToChange.reserve(Orig->use_size());
628 // Loop over instructions adding them to InstsToChange vector, this allows us
629 // an easy way to avoid invalidating the use_iterator at a bad time.
630 for (Value::use_iterator I = Orig->use_begin(), E = Orig->use_end();
632 if (Instruction *User = dyn_cast<Instruction>(*I))
633 if (DS->dominates(RegionDominator, User->getParent()))
634 InstsToChange.push_back(User);
635 else if (PHINode *PN = dyn_cast<PHINode>(User)) {
636 PHIsToChange.push_back(PN);
639 // PHIsToChange contains PHI nodes that use Orig that do not live in blocks
640 // dominated by orig. If the block the value flows in from is dominated by
641 // RegionDominator, then we rewrite the PHI
642 for (unsigned i = 0, e = PHIsToChange.size(); i != e; ++i) {
643 PHINode *PN = PHIsToChange[i];
644 for (unsigned j = 0, e = PN->getNumIncomingValues(); j != e; ++j)
645 if (PN->getIncomingValue(j) == Orig &&
646 DS->dominates(RegionDominator, PN->getIncomingBlock(j)))
647 PN->setIncomingValue(j, New);
650 // Loop over the InstsToChange list, replacing all uses of Orig with uses of
651 // New. This list contains all of the instructions in our region that use
653 for (unsigned i = 0, e = InstsToChange.size(); i != e; ++i)
654 if (PHINode *PN = dyn_cast<PHINode>(InstsToChange[i])) {
655 // PHINodes must be handled carefully. If the PHI node itself is in the
656 // region, we have to make sure to only do the replacement for incoming
657 // values that correspond to basic blocks in the region.
658 for (unsigned j = 0, e = PN->getNumIncomingValues(); j != e; ++j)
659 if (PN->getIncomingValue(j) == Orig &&
660 DS->dominates(RegionDominator, PN->getIncomingBlock(j)))
661 PN->setIncomingValue(j, New);
664 InstsToChange[i]->replaceUsesOfWith(Orig, New);
668 static void CalcRegionExitBlocks(BasicBlock *Header, BasicBlock *BB,
669 std::set<BasicBlock*> &Visited,
671 std::vector<BasicBlock*> &RegionExitBlocks) {
672 if (Visited.count(BB)) return;
675 if (DS.dominates(Header, BB)) { // Block in the region, recursively traverse
676 for (succ_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I)
677 CalcRegionExitBlocks(Header, *I, Visited, DS, RegionExitBlocks);
679 // Header does not dominate this block, but we have a predecessor that does
680 // dominate us. Add ourself to the list.
681 RegionExitBlocks.push_back(BB);
685 /// CalculateRegionExitBlocks - Find all of the blocks that are not dominated by
686 /// BB, but have predecessors that are. Additionally, prune down the set to
687 /// only include blocks that are dominated by OldSucc as well.
689 void CEE::CalculateRegionExitBlocks(BasicBlock *BB, BasicBlock *OldSucc,
690 std::vector<BasicBlock*> &RegionExitBlocks){
691 std::set<BasicBlock*> Visited; // Don't infinite loop
693 // Recursively calculate blocks we are interested in...
694 CalcRegionExitBlocks(BB, BB, Visited, *DS, RegionExitBlocks);
696 // Filter out blocks that are not dominated by OldSucc...
697 for (unsigned i = 0; i != RegionExitBlocks.size(); ) {
698 if (DS->dominates(OldSucc, RegionExitBlocks[i]))
699 ++i; // Block is ok, keep it.
701 // Move to end of list...
702 std::swap(RegionExitBlocks[i], RegionExitBlocks.back());
703 RegionExitBlocks.pop_back(); // Nuke the end
708 void CEE::InsertRegionExitMerges(PHINode *BBVal, Instruction *OldVal,
709 const std::vector<BasicBlock*> &RegionExitBlocks) {
710 assert(BBVal->getType() == OldVal->getType() && "Should be derived values!");
711 BasicBlock *BB = BBVal->getParent();
712 BasicBlock *OldSucc = OldVal->getParent();
714 // Loop over all of the blocks we have to place PHIs in, doing it.
715 for (unsigned i = 0, e = RegionExitBlocks.size(); i != e; ++i) {
716 BasicBlock *FBlock = RegionExitBlocks[i]; // Block on the frontier
718 // Create the new PHI node
719 PHINode *NewPN = new PHINode(BBVal->getType(),
720 OldVal->getName()+".fw_frontier",
723 // Add an incoming value for every predecessor of the block...
724 for (pred_iterator PI = pred_begin(FBlock), PE = pred_end(FBlock);
726 // If the incoming edge is from the region dominated by BB, use BBVal,
727 // otherwise use OldVal.
728 NewPN->addIncoming(DS->dominates(BB, *PI) ? BBVal : OldVal, *PI);
731 // Now make everyone dominated by this block use this new value!
732 ReplaceUsesOfValueInRegion(OldVal, NewPN, FBlock);
738 // BuildRankMap - This method builds the rank map data structure which gives
739 // each instruction/value in the function a value based on how early it appears
740 // in the function. We give constants and globals rank 0, arguments are
741 // numbered starting at one, and instructions are numbered in reverse post-order
742 // from where the arguments leave off. This gives instructions in loops higher
743 // values than instructions not in loops.
745 void CEE::BuildRankMap(Function &F) {
746 unsigned Rank = 1; // Skip rank zero.
748 // Number the arguments...
749 for (Function::aiterator I = F.abegin(), E = F.aend(); I != E; ++I)
752 // Number the instructions in reverse post order...
753 ReversePostOrderTraversal<Function*> RPOT(&F);
754 for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(),
755 E = RPOT.end(); I != E; ++I)
756 for (BasicBlock::iterator BBI = (*I)->begin(), E = (*I)->end();
758 if (BBI->getType() != Type::VoidTy)
759 RankMap[BBI] = Rank++;
763 // PropogateBranchInfo - When this method is invoked, we need to propogate
764 // information derived from the branch condition into the true and false
765 // branches of BI. Since we know that there aren't any critical edges in the
766 // flow graph, this can proceed unconditionally.
768 void CEE::PropogateBranchInfo(BranchInst *BI) {
769 assert(BI->isConditional() && "Must be a conditional branch!");
771 // Propogate information into the true block...
773 PropogateEquality(BI->getCondition(), ConstantBool::True,
774 getRegionInfo(BI->getSuccessor(0)));
776 // Propogate information into the false block...
778 PropogateEquality(BI->getCondition(), ConstantBool::False,
779 getRegionInfo(BI->getSuccessor(1)));
783 // PropogateEquality - If we discover that two values are equal to each other in
784 // a specified region, propogate this knowledge recursively.
786 void CEE::PropogateEquality(Value *Op0, Value *Op1, RegionInfo &RI) {
787 if (Op0 == Op1) return; // Gee whiz. Are these really equal each other?
789 if (isa<Constant>(Op0)) // Make sure the constant is always Op1
792 // Make sure we don't already know these are equal, to avoid infinite loops...
793 ValueInfo &VI = RI.getValueInfo(Op0);
795 // Get information about the known relationship between Op0 & Op1
796 Relation &KnownRelation = VI.getRelation(Op1);
798 // If we already know they're equal, don't reprocess...
799 if (KnownRelation.getRelation() == Instruction::SetEQ)
802 // If this is boolean, check to see if one of the operands is a constant. If
803 // it's a constant, then see if the other one is one of a setcc instruction,
804 // an AND, OR, or XOR instruction.
806 if (ConstantBool *CB = dyn_cast<ConstantBool>(Op1)) {
808 if (Instruction *Inst = dyn_cast<Instruction>(Op0)) {
809 // If we know that this instruction is an AND instruction, and the result
810 // is true, this means that both operands to the OR are known to be true
813 if (CB->getValue() && Inst->getOpcode() == Instruction::And) {
814 PropogateEquality(Inst->getOperand(0), CB, RI);
815 PropogateEquality(Inst->getOperand(1), CB, RI);
818 // If we know that this instruction is an OR instruction, and the result
819 // is false, this means that both operands to the OR are know to be false
822 if (!CB->getValue() && Inst->getOpcode() == Instruction::Or) {
823 PropogateEquality(Inst->getOperand(0), CB, RI);
824 PropogateEquality(Inst->getOperand(1), CB, RI);
827 // If we know that this instruction is a NOT instruction, we know that the
828 // operand is known to be the inverse of whatever the current value is.
830 if (BinaryOperator *BOp = dyn_cast<BinaryOperator>(Inst))
831 if (BinaryOperator::isNot(BOp))
832 PropogateEquality(BinaryOperator::getNotArgument(BOp),
833 ConstantBool::get(!CB->getValue()), RI);
835 // If we know the value of a SetCC instruction, propogate the information
836 // about the relation into this region as well.
838 if (SetCondInst *SCI = dyn_cast<SetCondInst>(Inst)) {
839 if (CB->getValue()) { // If we know the condition is true...
840 // Propogate info about the LHS to the RHS & RHS to LHS
841 PropogateRelation(SCI->getOpcode(), SCI->getOperand(0),
842 SCI->getOperand(1), RI);
843 PropogateRelation(SCI->getSwappedCondition(),
844 SCI->getOperand(1), SCI->getOperand(0), RI);
846 } else { // If we know the condition is false...
847 // We know the opposite of the condition is true...
848 Instruction::BinaryOps C = SCI->getInverseCondition();
850 PropogateRelation(C, SCI->getOperand(0), SCI->getOperand(1), RI);
851 PropogateRelation(SetCondInst::getSwappedCondition(C),
852 SCI->getOperand(1), SCI->getOperand(0), RI);
858 // Propogate information about Op0 to Op1 & visa versa
859 PropogateRelation(Instruction::SetEQ, Op0, Op1, RI);
860 PropogateRelation(Instruction::SetEQ, Op1, Op0, RI);
864 // PropogateRelation - We know that the specified relation is true in all of the
865 // blocks in the specified region. Propogate the information about Op0 and
866 // anything derived from it into this region.
868 void CEE::PropogateRelation(Instruction::BinaryOps Opcode, Value *Op0,
869 Value *Op1, RegionInfo &RI) {
870 assert(Op0->getType() == Op1->getType() && "Equal types expected!");
872 // Constants are already pretty well understood. We will apply information
873 // about the constant to Op1 in another call to PropogateRelation.
875 if (isa<Constant>(Op0)) return;
877 // Get the region information for this block to update...
878 ValueInfo &VI = RI.getValueInfo(Op0);
880 // Get information about the known relationship between Op0 & Op1
881 Relation &Op1R = VI.getRelation(Op1);
883 // Quick bailout for common case if we are reprocessing an instruction...
884 if (Op1R.getRelation() == Opcode)
887 // If we already have information that contradicts the current information we
888 // are propogating, ignore this info. Something bad must have happened!
890 if (Op1R.contradicts(Opcode, VI)) {
891 Op1R.contradicts(Opcode, VI);
892 std::cerr << "Contradiction found for opcode: "
893 << Instruction::getOpcodeName(Opcode) << "\n";
894 Op1R.print(std::cerr);
898 // If the information propogted is new, then we want process the uses of this
899 // instruction to propogate the information down to them.
901 if (Op1R.incorporate(Opcode, VI))
902 UpdateUsersOfValue(Op0, RI);
906 // UpdateUsersOfValue - The information about V in this region has been updated.
907 // Propogate this to all consumers of the value.
909 void CEE::UpdateUsersOfValue(Value *V, RegionInfo &RI) {
910 for (Value::use_iterator I = V->use_begin(), E = V->use_end();
912 if (Instruction *Inst = dyn_cast<Instruction>(*I)) {
913 // If this is an instruction using a value that we know something about,
914 // try to propogate information to the value produced by the
915 // instruction. We can only do this if it is an instruction we can
916 // propogate information for (a setcc for example), and we only WANT to
917 // do this if the instruction dominates this region.
919 // If the instruction doesn't dominate this region, then it cannot be
920 // used in this region and we don't care about it. If the instruction
921 // is IN this region, then we will simplify the instruction before we
922 // get to uses of it anyway, so there is no reason to bother with it
923 // here. This check is also effectively checking to make sure that Inst
924 // is in the same function as our region (in case V is a global f.e.).
926 if (DS->properlyDominates(Inst->getParent(), RI.getEntryBlock()))
927 IncorporateInstruction(Inst, RI);
931 // IncorporateInstruction - We just updated the information about one of the
932 // operands to the specified instruction. Update the information about the
933 // value produced by this instruction
935 void CEE::IncorporateInstruction(Instruction *Inst, RegionInfo &RI) {
936 if (SetCondInst *SCI = dyn_cast<SetCondInst>(Inst)) {
937 // See if we can figure out a result for this instruction...
938 Relation::KnownResult Result = getSetCCResult(SCI, RI);
939 if (Result != Relation::Unknown) {
940 PropogateEquality(SCI, Result ? ConstantBool::True : ConstantBool::False,
947 // ComputeReplacements - Some values are known to be equal to other values in a
948 // region. For example if there is a comparison of equality between a variable
949 // X and a constant C, we can replace all uses of X with C in the region we are
950 // interested in. We generalize this replacement to replace variables with
951 // other variables if they are equal and there is a variable with lower rank
952 // than the current one. This offers a cannonicalizing property that exposes
953 // more redundancies for later transformations to take advantage of.
955 void CEE::ComputeReplacements(RegionInfo &RI) {
956 // Loop over all of the values in the region info map...
957 for (RegionInfo::iterator I = RI.begin(), E = RI.end(); I != E; ++I) {
958 ValueInfo &VI = I->second;
960 // If we know that this value is a particular constant, set Replacement to
962 Value *Replacement = VI.getBounds().getSingleElement();
964 // If this value is not known to be some constant, figure out the lowest
965 // rank value that it is known to be equal to (if anything).
967 if (Replacement == 0) {
968 // Find out if there are any equality relationships with values of lower
969 // rank than VI itself...
970 unsigned MinRank = getRank(I->first);
972 // Loop over the relationships known about Op0.
973 const std::vector<Relation> &Relationships = VI.getRelationships();
974 for (unsigned i = 0, e = Relationships.size(); i != e; ++i)
975 if (Relationships[i].getRelation() == Instruction::SetEQ) {
976 unsigned R = getRank(Relationships[i].getValue());
979 Replacement = Relationships[i].getValue();
984 // If we found something to replace this value with, keep track of it.
986 VI.setReplacement(Replacement);
990 // SimplifyBasicBlock - Given information about values in region RI, simplify
991 // the instructions in the specified basic block.
993 bool CEE::SimplifyBasicBlock(BasicBlock &BB, const RegionInfo &RI) {
994 bool Changed = false;
995 for (BasicBlock::iterator I = BB.begin(), E = BB.end(); I != E; ) {
996 Instruction *Inst = &*I++;
998 // Convert instruction arguments to canonical forms...
999 Changed |= SimplifyInstruction(Inst, RI);
1001 if (SetCondInst *SCI = dyn_cast<SetCondInst>(Inst)) {
1002 // Try to simplify a setcc instruction based on inherited information
1003 Relation::KnownResult Result = getSetCCResult(SCI, RI);
1004 if (Result != Relation::Unknown) {
1005 DEBUG(std::cerr << "Replacing setcc with " << Result
1006 << " constant: " << SCI);
1008 SCI->replaceAllUsesWith(ConstantBool::get((bool)Result));
1009 // The instruction is now dead, remove it from the program.
1010 SCI->getParent()->getInstList().erase(SCI);
1020 // SimplifyInstruction - Inspect the operands of the instruction, converting
1021 // them to their cannonical form if possible. This takes care of, for example,
1022 // replacing a value 'X' with a constant 'C' if the instruction in question is
1023 // dominated by a true seteq 'X', 'C'.
1025 bool CEE::SimplifyInstruction(Instruction *I, const RegionInfo &RI) {
1026 bool Changed = false;
1028 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i)
1029 if (const ValueInfo *VI = RI.requestValueInfo(I->getOperand(i)))
1030 if (Value *Repl = VI->getReplacement()) {
1031 // If we know if a replacement with lower rank than Op0, make the
1033 DEBUG(std::cerr << "In Inst: " << I << " Replacing operand #" << i
1034 << " with " << Repl << "\n");
1035 I->setOperand(i, Repl);
1044 // getSetCCResult - Try to simplify a setcc instruction based on information
1045 // inherited from a dominating setcc instruction. V is one of the operands to
1046 // the setcc instruction, and VI is the set of information known about it. We
1047 // take two cases into consideration here. If the comparison is against a
1048 // constant value, we can use the constant range to see if the comparison is
1049 // possible to succeed. If it is not a comparison against a constant, we check
1050 // to see if there is a known relationship between the two values. If so, we
1051 // may be able to eliminate the check.
1053 Relation::KnownResult CEE::getSetCCResult(SetCondInst *SCI,
1054 const RegionInfo &RI) {
1055 Value *Op0 = SCI->getOperand(0), *Op1 = SCI->getOperand(1);
1056 Instruction::BinaryOps Opcode = SCI->getOpcode();
1058 if (isa<Constant>(Op0)) {
1059 if (isa<Constant>(Op1)) {
1060 if (Constant *Result = ConstantFoldInstruction(SCI)) {
1061 // Wow, this is easy, directly eliminate the SetCondInst.
1062 DEBUG(std::cerr << "Replacing setcc with constant fold: " << SCI);
1063 return cast<ConstantBool>(Result)->getValue()
1064 ? Relation::KnownTrue : Relation::KnownFalse;
1067 // We want to swap this instruction so that operand #0 is the constant.
1068 std::swap(Op0, Op1);
1069 Opcode = SCI->getSwappedCondition();
1073 // Try to figure out what the result of this comparison will be...
1074 Relation::KnownResult Result = Relation::Unknown;
1076 // We have to know something about the relationship to prove anything...
1077 if (const ValueInfo *Op0VI = RI.requestValueInfo(Op0)) {
1079 // At this point, we know that if we have a constant argument that it is in
1080 // Op1. Check to see if we know anything about comparing value with a
1081 // constant, and if we can use this info to fold the setcc.
1083 if (ConstantIntegral *C = dyn_cast<ConstantIntegral>(Op1)) {
1084 // Check to see if we already know the result of this comparison...
1085 ConstantRange R = ConstantRange(Opcode, C);
1086 ConstantRange Int = R.intersectWith(Op0VI->getBounds());
1088 // If the intersection of the two ranges is empty, then the condition
1089 // could never be true!
1091 if (Int.isEmptySet()) {
1092 Result = Relation::KnownFalse;
1094 // Otherwise, if VI.getBounds() (the possible values) is a subset of R
1095 // (the allowed values) then we know that the condition must always be
1098 } else if (Int == Op0VI->getBounds()) {
1099 Result = Relation::KnownTrue;
1102 // If we are here, we know that the second argument is not a constant
1103 // integral. See if we know anything about Op0 & Op1 that allows us to
1104 // fold this anyway.
1106 // Do we have value information about Op0 and a relation to Op1?
1107 if (const Relation *Op2R = Op0VI->requestRelation(Op1))
1108 Result = Op2R->getImpliedResult(Opcode);
1114 //===----------------------------------------------------------------------===//
1115 // Relation Implementation
1116 //===----------------------------------------------------------------------===//
1118 // CheckCondition - Return true if the specified condition is false. Bound may
1120 static bool CheckCondition(Constant *Bound, Constant *C,
1121 Instruction::BinaryOps BO) {
1122 assert(C != 0 && "C is not specified!");
1123 if (Bound == 0) return false;
1127 default: assert(0 && "Unknown Condition code!");
1128 case Instruction::SetEQ: Val = *Bound == *C; break;
1129 case Instruction::SetNE: Val = *Bound != *C; break;
1130 case Instruction::SetLT: Val = *Bound < *C; break;
1131 case Instruction::SetGT: Val = *Bound > *C; break;
1132 case Instruction::SetLE: Val = *Bound <= *C; break;
1133 case Instruction::SetGE: Val = *Bound >= *C; break;
1136 // ConstantHandling code may not succeed in the comparison...
1137 if (Val == 0) return false;
1138 return !Val->getValue(); // Return true if the condition is false...
1141 // contradicts - Return true if the relationship specified by the operand
1142 // contradicts already known information.
1144 bool Relation::contradicts(Instruction::BinaryOps Op,
1145 const ValueInfo &VI) const {
1146 assert (Op != Instruction::Add && "Invalid relation argument!");
1148 // If this is a relationship with a constant, make sure that this relationship
1149 // does not contradict properties known about the bounds of the constant.
1151 if (ConstantIntegral *C = dyn_cast<ConstantIntegral>(Val))
1152 if (ConstantRange(Op, C).intersectWith(VI.getBounds()).isEmptySet())
1156 default: assert(0 && "Unknown Relationship code!");
1157 case Instruction::Add: return false; // Nothing known, nothing contradicts
1158 case Instruction::SetEQ:
1159 return Op == Instruction::SetLT || Op == Instruction::SetGT ||
1160 Op == Instruction::SetNE;
1161 case Instruction::SetNE: return Op == Instruction::SetEQ;
1162 case Instruction::SetLE: return Op == Instruction::SetGT;
1163 case Instruction::SetGE: return Op == Instruction::SetLT;
1164 case Instruction::SetLT:
1165 return Op == Instruction::SetEQ || Op == Instruction::SetGT ||
1166 Op == Instruction::SetGE;
1167 case Instruction::SetGT:
1168 return Op == Instruction::SetEQ || Op == Instruction::SetLT ||
1169 Op == Instruction::SetLE;
1173 // incorporate - Incorporate information in the argument into this relation
1174 // entry. This assumes that the information doesn't contradict itself. If any
1175 // new information is gained, true is returned, otherwise false is returned to
1176 // indicate that nothing was updated.
1178 bool Relation::incorporate(Instruction::BinaryOps Op, ValueInfo &VI) {
1179 assert(!contradicts(Op, VI) &&
1180 "Cannot incorporate contradictory information!");
1182 // If this is a relationship with a constant, make sure that we update the
1183 // range that is possible for the value to have...
1185 if (ConstantIntegral *C = dyn_cast<ConstantIntegral>(Val))
1186 VI.getBounds() = ConstantRange(Op, C).intersectWith(VI.getBounds());
1189 default: assert(0 && "Unknown prior value!");
1190 case Instruction::Add: Rel = Op; return true;
1191 case Instruction::SetEQ: return false; // Nothing is more precise
1192 case Instruction::SetNE: return false; // Nothing is more precise
1193 case Instruction::SetLT: return false; // Nothing is more precise
1194 case Instruction::SetGT: return false; // Nothing is more precise
1195 case Instruction::SetLE:
1196 if (Op == Instruction::SetEQ || Op == Instruction::SetLT) {
1199 } else if (Op == Instruction::SetNE) {
1200 Rel = Instruction::SetLT;
1204 case Instruction::SetGE: return Op == Instruction::SetLT;
1205 if (Op == Instruction::SetEQ || Op == Instruction::SetGT) {
1208 } else if (Op == Instruction::SetNE) {
1209 Rel = Instruction::SetGT;
1216 // getImpliedResult - If this relationship between two values implies that
1217 // the specified relationship is true or false, return that. If we cannot
1218 // determine the result required, return Unknown.
1220 Relation::KnownResult
1221 Relation::getImpliedResult(Instruction::BinaryOps Op) const {
1222 if (Rel == Op) return KnownTrue;
1223 if (Rel == SetCondInst::getInverseCondition(Op)) return KnownFalse;
1226 default: assert(0 && "Unknown prior value!");
1227 case Instruction::SetEQ:
1228 if (Op == Instruction::SetLE || Op == Instruction::SetGE) return KnownTrue;
1229 if (Op == Instruction::SetLT || Op == Instruction::SetGT) return KnownFalse;
1231 case Instruction::SetLT:
1232 if (Op == Instruction::SetNE || Op == Instruction::SetLE) return KnownTrue;
1233 if (Op == Instruction::SetEQ) return KnownFalse;
1235 case Instruction::SetGT:
1236 if (Op == Instruction::SetNE || Op == Instruction::SetGE) return KnownTrue;
1237 if (Op == Instruction::SetEQ) return KnownFalse;
1239 case Instruction::SetNE:
1240 case Instruction::SetLE:
1241 case Instruction::SetGE:
1242 case Instruction::Add:
1249 //===----------------------------------------------------------------------===//
1250 // Printing Support...
1251 //===----------------------------------------------------------------------===//
1253 // print - Implement the standard print form to print out analysis information.
1254 void CEE::print(std::ostream &O, const Module *M) const {
1255 O << "\nPrinting Correlated Expression Info:\n";
1256 for (std::map<BasicBlock*, RegionInfo>::const_iterator I =
1257 RegionInfoMap.begin(), E = RegionInfoMap.end(); I != E; ++I)
1261 // print - Output information about this region...
1262 void RegionInfo::print(std::ostream &OS) const {
1263 if (ValueMap.empty()) return;
1265 OS << " RegionInfo for basic block: " << BB->getName() << "\n";
1266 for (std::map<Value*, ValueInfo>::const_iterator
1267 I = ValueMap.begin(), E = ValueMap.end(); I != E; ++I)
1268 I->second.print(OS, I->first);
1272 // print - Output information about this value relation...
1273 void ValueInfo::print(std::ostream &OS, Value *V) const {
1274 if (Relationships.empty()) return;
1277 OS << " ValueInfo for: ";
1278 WriteAsOperand(OS, V);
1280 OS << "\n Bounds = " << Bounds << "\n";
1282 OS << " Replacement = ";
1283 WriteAsOperand(OS, Replacement);
1286 for (unsigned i = 0, e = Relationships.size(); i != e; ++i)
1287 Relationships[i].print(OS);
1290 // print - Output this relation to the specified stream
1291 void Relation::print(std::ostream &OS) const {
1294 default: OS << "*UNKNOWN*"; break;
1295 case Instruction::SetEQ: OS << "== "; break;
1296 case Instruction::SetNE: OS << "!= "; break;
1297 case Instruction::SetLT: OS << "< "; break;
1298 case Instruction::SetGT: OS << "> "; break;
1299 case Instruction::SetLE: OS << "<= "; break;
1300 case Instruction::SetGE: OS << ">= "; break;
1303 WriteAsOperand(OS, Val);
1307 // Don't inline these methods or else we won't be able to call them from GDB!
1308 void Relation::dump() const { print(std::cerr); }
1309 void ValueInfo::dump() const { print(std::cerr, 0); }
1310 void RegionInfo::dump() const { print(std::cerr); }