1 //===-- DependenceAnalysis.cpp - DA Implementation --------------*- C++ -*-===//
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 // DependenceAnalysis is an LLVM pass that analyses dependences between memory
11 // accesses. Currently, it is an (incomplete) implementation of the approach
14 // Practical Dependence Testing
15 // Goff, Kennedy, Tseng
18 // There's a single entry point that analyzes the dependence between a pair
19 // of memory references in a function, returning either NULL, for no dependence,
20 // or a more-or-less detailed description of the dependence between them.
22 // Currently, the implementation cannot propagate constraints between
23 // coupled RDIV subscripts and lacks a multi-subscript MIV test.
24 // Both of these are conservative weaknesses;
25 // that is, not a source of correctness problems.
27 // The implementation depends on the GEP instruction to differentiate
28 // subscripts. Since Clang linearizes some array subscripts, the dependence
29 // analysis is using SCEV->delinearize to recover the representation of multiple
30 // subscripts, and thus avoid the more expensive and less precise MIV tests. The
31 // delinearization is controlled by the flag -da-delinearize.
33 // We should pay some careful attention to the possibility of integer overflow
34 // in the implementation of the various tests. This could happen with Add,
35 // Subtract, or Multiply, with both APInt's and SCEV's.
37 // Some non-linear subscript pairs can be handled by the GCD test
38 // (and perhaps other tests).
39 // Should explore how often these things occur.
41 // Finally, it seems like certain test cases expose weaknesses in the SCEV
42 // simplification, especially in the handling of sign and zero extensions.
43 // It could be useful to spend time exploring these.
45 // Please note that this is work in progress and the interface is subject to
48 //===----------------------------------------------------------------------===//
50 // In memory of Ken Kennedy, 1945 - 2007 //
52 //===----------------------------------------------------------------------===//
54 #include "llvm/Analysis/DependenceAnalysis.h"
55 #include "llvm/ADT/STLExtras.h"
56 #include "llvm/ADT/Statistic.h"
57 #include "llvm/Analysis/AliasAnalysis.h"
58 #include "llvm/Analysis/LoopInfo.h"
59 #include "llvm/Analysis/ScalarEvolution.h"
60 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
61 #include "llvm/Analysis/ValueTracking.h"
62 #include "llvm/IR/InstIterator.h"
63 #include "llvm/IR/Module.h"
64 #include "llvm/IR/Operator.h"
65 #include "llvm/Support/CommandLine.h"
66 #include "llvm/Support/Debug.h"
67 #include "llvm/Support/ErrorHandling.h"
68 #include "llvm/Support/raw_ostream.h"
72 #define DEBUG_TYPE "da"
74 //===----------------------------------------------------------------------===//
77 STATISTIC(TotalArrayPairs, "Array pairs tested");
78 STATISTIC(SeparableSubscriptPairs, "Separable subscript pairs");
79 STATISTIC(CoupledSubscriptPairs, "Coupled subscript pairs");
80 STATISTIC(NonlinearSubscriptPairs, "Nonlinear subscript pairs");
81 STATISTIC(ZIVapplications, "ZIV applications");
82 STATISTIC(ZIVindependence, "ZIV independence");
83 STATISTIC(StrongSIVapplications, "Strong SIV applications");
84 STATISTIC(StrongSIVsuccesses, "Strong SIV successes");
85 STATISTIC(StrongSIVindependence, "Strong SIV independence");
86 STATISTIC(WeakCrossingSIVapplications, "Weak-Crossing SIV applications");
87 STATISTIC(WeakCrossingSIVsuccesses, "Weak-Crossing SIV successes");
88 STATISTIC(WeakCrossingSIVindependence, "Weak-Crossing SIV independence");
89 STATISTIC(ExactSIVapplications, "Exact SIV applications");
90 STATISTIC(ExactSIVsuccesses, "Exact SIV successes");
91 STATISTIC(ExactSIVindependence, "Exact SIV independence");
92 STATISTIC(WeakZeroSIVapplications, "Weak-Zero SIV applications");
93 STATISTIC(WeakZeroSIVsuccesses, "Weak-Zero SIV successes");
94 STATISTIC(WeakZeroSIVindependence, "Weak-Zero SIV independence");
95 STATISTIC(ExactRDIVapplications, "Exact RDIV applications");
96 STATISTIC(ExactRDIVindependence, "Exact RDIV independence");
97 STATISTIC(SymbolicRDIVapplications, "Symbolic RDIV applications");
98 STATISTIC(SymbolicRDIVindependence, "Symbolic RDIV independence");
99 STATISTIC(DeltaApplications, "Delta applications");
100 STATISTIC(DeltaSuccesses, "Delta successes");
101 STATISTIC(DeltaIndependence, "Delta independence");
102 STATISTIC(DeltaPropagations, "Delta propagations");
103 STATISTIC(GCDapplications, "GCD applications");
104 STATISTIC(GCDsuccesses, "GCD successes");
105 STATISTIC(GCDindependence, "GCD independence");
106 STATISTIC(BanerjeeApplications, "Banerjee applications");
107 STATISTIC(BanerjeeIndependence, "Banerjee independence");
108 STATISTIC(BanerjeeSuccesses, "Banerjee successes");
111 Delinearize("da-delinearize", cl::init(false), cl::Hidden, cl::ZeroOrMore,
112 cl::desc("Try to delinearize array references."));
114 //===----------------------------------------------------------------------===//
117 INITIALIZE_PASS_BEGIN(DependenceAnalysis, "da",
118 "Dependence Analysis", true, true)
119 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
120 INITIALIZE_PASS_DEPENDENCY(ScalarEvolution)
121 INITIALIZE_AG_DEPENDENCY(AliasAnalysis)
122 INITIALIZE_PASS_END(DependenceAnalysis, "da",
123 "Dependence Analysis", true, true)
125 char DependenceAnalysis::ID = 0;
128 FunctionPass *llvm::createDependenceAnalysisPass() {
129 return new DependenceAnalysis();
133 bool DependenceAnalysis::runOnFunction(Function &F) {
135 AA = &getAnalysis<AliasAnalysis>();
136 SE = &getAnalysis<ScalarEvolution>();
137 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
142 void DependenceAnalysis::releaseMemory() {
146 void DependenceAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
147 AU.setPreservesAll();
148 AU.addRequiredTransitive<AliasAnalysis>();
149 AU.addRequiredTransitive<ScalarEvolution>();
150 AU.addRequiredTransitive<LoopInfoWrapperPass>();
154 // Used to test the dependence analyzer.
155 // Looks through the function, noting loads and stores.
156 // Calls depends() on every possible pair and prints out the result.
157 // Ignores all other instructions.
159 void dumpExampleDependence(raw_ostream &OS, Function *F,
160 DependenceAnalysis *DA) {
161 for (inst_iterator SrcI = inst_begin(F), SrcE = inst_end(F);
162 SrcI != SrcE; ++SrcI) {
163 if (isa<StoreInst>(*SrcI) || isa<LoadInst>(*SrcI)) {
164 for (inst_iterator DstI = SrcI, DstE = inst_end(F);
165 DstI != DstE; ++DstI) {
166 if (isa<StoreInst>(*DstI) || isa<LoadInst>(*DstI)) {
167 OS << "da analyze - ";
168 if (auto D = DA->depends(&*SrcI, &*DstI, true)) {
170 for (unsigned Level = 1; Level <= D->getLevels(); Level++) {
171 if (D->isSplitable(Level)) {
172 OS << "da analyze - split level = " << Level;
173 OS << ", iteration = " << *DA->getSplitIteration(*D, Level);
187 void DependenceAnalysis::print(raw_ostream &OS, const Module*) const {
188 dumpExampleDependence(OS, F, const_cast<DependenceAnalysis *>(this));
191 //===----------------------------------------------------------------------===//
192 // Dependence methods
194 // Returns true if this is an input dependence.
195 bool Dependence::isInput() const {
196 return Src->mayReadFromMemory() && Dst->mayReadFromMemory();
200 // Returns true if this is an output dependence.
201 bool Dependence::isOutput() const {
202 return Src->mayWriteToMemory() && Dst->mayWriteToMemory();
206 // Returns true if this is an flow (aka true) dependence.
207 bool Dependence::isFlow() const {
208 return Src->mayWriteToMemory() && Dst->mayReadFromMemory();
212 // Returns true if this is an anti dependence.
213 bool Dependence::isAnti() const {
214 return Src->mayReadFromMemory() && Dst->mayWriteToMemory();
218 // Returns true if a particular level is scalar; that is,
219 // if no subscript in the source or destination mention the induction
220 // variable associated with the loop at this level.
221 // Leave this out of line, so it will serve as a virtual method anchor
222 bool Dependence::isScalar(unsigned level) const {
227 //===----------------------------------------------------------------------===//
228 // FullDependence methods
230 FullDependence::FullDependence(Instruction *Source, Instruction *Destination,
231 bool PossiblyLoopIndependent,
232 unsigned CommonLevels)
233 : Dependence(Source, Destination), Levels(CommonLevels),
234 LoopIndependent(PossiblyLoopIndependent) {
236 DV = CommonLevels ? new DVEntry[CommonLevels] : nullptr;
239 // The rest are simple getters that hide the implementation.
241 // getDirection - Returns the direction associated with a particular level.
242 unsigned FullDependence::getDirection(unsigned Level) const {
243 assert(0 < Level && Level <= Levels && "Level out of range");
244 return DV[Level - 1].Direction;
248 // Returns the distance (or NULL) associated with a particular level.
249 const SCEV *FullDependence::getDistance(unsigned Level) const {
250 assert(0 < Level && Level <= Levels && "Level out of range");
251 return DV[Level - 1].Distance;
255 // Returns true if a particular level is scalar; that is,
256 // if no subscript in the source or destination mention the induction
257 // variable associated with the loop at this level.
258 bool FullDependence::isScalar(unsigned Level) const {
259 assert(0 < Level && Level <= Levels && "Level out of range");
260 return DV[Level - 1].Scalar;
264 // Returns true if peeling the first iteration from this loop
265 // will break this dependence.
266 bool FullDependence::isPeelFirst(unsigned Level) const {
267 assert(0 < Level && Level <= Levels && "Level out of range");
268 return DV[Level - 1].PeelFirst;
272 // Returns true if peeling the last iteration from this loop
273 // will break this dependence.
274 bool FullDependence::isPeelLast(unsigned Level) const {
275 assert(0 < Level && Level <= Levels && "Level out of range");
276 return DV[Level - 1].PeelLast;
280 // Returns true if splitting this loop will break the dependence.
281 bool FullDependence::isSplitable(unsigned Level) const {
282 assert(0 < Level && Level <= Levels && "Level out of range");
283 return DV[Level - 1].Splitable;
287 //===----------------------------------------------------------------------===//
288 // DependenceAnalysis::Constraint methods
290 // If constraint is a point <X, Y>, returns X.
292 const SCEV *DependenceAnalysis::Constraint::getX() const {
293 assert(Kind == Point && "Kind should be Point");
298 // If constraint is a point <X, Y>, returns Y.
300 const SCEV *DependenceAnalysis::Constraint::getY() const {
301 assert(Kind == Point && "Kind should be Point");
306 // If constraint is a line AX + BY = C, returns A.
308 const SCEV *DependenceAnalysis::Constraint::getA() const {
309 assert((Kind == Line || Kind == Distance) &&
310 "Kind should be Line (or Distance)");
315 // If constraint is a line AX + BY = C, returns B.
317 const SCEV *DependenceAnalysis::Constraint::getB() const {
318 assert((Kind == Line || Kind == Distance) &&
319 "Kind should be Line (or Distance)");
324 // If constraint is a line AX + BY = C, returns C.
326 const SCEV *DependenceAnalysis::Constraint::getC() const {
327 assert((Kind == Line || Kind == Distance) &&
328 "Kind should be Line (or Distance)");
333 // If constraint is a distance, returns D.
335 const SCEV *DependenceAnalysis::Constraint::getD() const {
336 assert(Kind == Distance && "Kind should be Distance");
337 return SE->getNegativeSCEV(C);
341 // Returns the loop associated with this constraint.
342 const Loop *DependenceAnalysis::Constraint::getAssociatedLoop() const {
343 assert((Kind == Distance || Kind == Line || Kind == Point) &&
344 "Kind should be Distance, Line, or Point");
345 return AssociatedLoop;
349 void DependenceAnalysis::Constraint::setPoint(const SCEV *X,
351 const Loop *CurLoop) {
355 AssociatedLoop = CurLoop;
359 void DependenceAnalysis::Constraint::setLine(const SCEV *AA,
362 const Loop *CurLoop) {
367 AssociatedLoop = CurLoop;
371 void DependenceAnalysis::Constraint::setDistance(const SCEV *D,
372 const Loop *CurLoop) {
374 A = SE->getConstant(D->getType(), 1);
375 B = SE->getNegativeSCEV(A);
376 C = SE->getNegativeSCEV(D);
377 AssociatedLoop = CurLoop;
381 void DependenceAnalysis::Constraint::setEmpty() {
386 void DependenceAnalysis::Constraint::setAny(ScalarEvolution *NewSE) {
392 // For debugging purposes. Dumps the constraint out to OS.
393 void DependenceAnalysis::Constraint::dump(raw_ostream &OS) const {
399 OS << " Point is <" << *getX() << ", " << *getY() << ">\n";
400 else if (isDistance())
401 OS << " Distance is " << *getD() <<
402 " (" << *getA() << "*X + " << *getB() << "*Y = " << *getC() << ")\n";
404 OS << " Line is " << *getA() << "*X + " <<
405 *getB() << "*Y = " << *getC() << "\n";
407 llvm_unreachable("unknown constraint type in Constraint::dump");
411 // Updates X with the intersection
412 // of the Constraints X and Y. Returns true if X has changed.
413 // Corresponds to Figure 4 from the paper
415 // Practical Dependence Testing
416 // Goff, Kennedy, Tseng
418 bool DependenceAnalysis::intersectConstraints(Constraint *X,
419 const Constraint *Y) {
421 DEBUG(dbgs() << "\tintersect constraints\n");
422 DEBUG(dbgs() << "\t X ="; X->dump(dbgs()));
423 DEBUG(dbgs() << "\t Y ="; Y->dump(dbgs()));
424 assert(!Y->isPoint() && "Y must not be a Point");
438 if (X->isDistance() && Y->isDistance()) {
439 DEBUG(dbgs() << "\t intersect 2 distances\n");
440 if (isKnownPredicate(CmpInst::ICMP_EQ, X->getD(), Y->getD()))
442 if (isKnownPredicate(CmpInst::ICMP_NE, X->getD(), Y->getD())) {
447 // Hmmm, interesting situation.
448 // I guess if either is constant, keep it and ignore the other.
449 if (isa<SCEVConstant>(Y->getD())) {
456 // At this point, the pseudo-code in Figure 4 of the paper
457 // checks if (X->isPoint() && Y->isPoint()).
458 // This case can't occur in our implementation,
459 // since a Point can only arise as the result of intersecting
460 // two Line constraints, and the right-hand value, Y, is never
461 // the result of an intersection.
462 assert(!(X->isPoint() && Y->isPoint()) &&
463 "We shouldn't ever see X->isPoint() && Y->isPoint()");
465 if (X->isLine() && Y->isLine()) {
466 DEBUG(dbgs() << "\t intersect 2 lines\n");
467 const SCEV *Prod1 = SE->getMulExpr(X->getA(), Y->getB());
468 const SCEV *Prod2 = SE->getMulExpr(X->getB(), Y->getA());
469 if (isKnownPredicate(CmpInst::ICMP_EQ, Prod1, Prod2)) {
470 // slopes are equal, so lines are parallel
471 DEBUG(dbgs() << "\t\tsame slope\n");
472 Prod1 = SE->getMulExpr(X->getC(), Y->getB());
473 Prod2 = SE->getMulExpr(X->getB(), Y->getC());
474 if (isKnownPredicate(CmpInst::ICMP_EQ, Prod1, Prod2))
476 if (isKnownPredicate(CmpInst::ICMP_NE, Prod1, Prod2)) {
483 if (isKnownPredicate(CmpInst::ICMP_NE, Prod1, Prod2)) {
484 // slopes differ, so lines intersect
485 DEBUG(dbgs() << "\t\tdifferent slopes\n");
486 const SCEV *C1B2 = SE->getMulExpr(X->getC(), Y->getB());
487 const SCEV *C1A2 = SE->getMulExpr(X->getC(), Y->getA());
488 const SCEV *C2B1 = SE->getMulExpr(Y->getC(), X->getB());
489 const SCEV *C2A1 = SE->getMulExpr(Y->getC(), X->getA());
490 const SCEV *A1B2 = SE->getMulExpr(X->getA(), Y->getB());
491 const SCEV *A2B1 = SE->getMulExpr(Y->getA(), X->getB());
492 const SCEVConstant *C1A2_C2A1 =
493 dyn_cast<SCEVConstant>(SE->getMinusSCEV(C1A2, C2A1));
494 const SCEVConstant *C1B2_C2B1 =
495 dyn_cast<SCEVConstant>(SE->getMinusSCEV(C1B2, C2B1));
496 const SCEVConstant *A1B2_A2B1 =
497 dyn_cast<SCEVConstant>(SE->getMinusSCEV(A1B2, A2B1));
498 const SCEVConstant *A2B1_A1B2 =
499 dyn_cast<SCEVConstant>(SE->getMinusSCEV(A2B1, A1B2));
500 if (!C1B2_C2B1 || !C1A2_C2A1 ||
501 !A1B2_A2B1 || !A2B1_A1B2)
503 APInt Xtop = C1B2_C2B1->getValue()->getValue();
504 APInt Xbot = A1B2_A2B1->getValue()->getValue();
505 APInt Ytop = C1A2_C2A1->getValue()->getValue();
506 APInt Ybot = A2B1_A1B2->getValue()->getValue();
507 DEBUG(dbgs() << "\t\tXtop = " << Xtop << "\n");
508 DEBUG(dbgs() << "\t\tXbot = " << Xbot << "\n");
509 DEBUG(dbgs() << "\t\tYtop = " << Ytop << "\n");
510 DEBUG(dbgs() << "\t\tYbot = " << Ybot << "\n");
511 APInt Xq = Xtop; // these need to be initialized, even
512 APInt Xr = Xtop; // though they're just going to be overwritten
513 APInt::sdivrem(Xtop, Xbot, Xq, Xr);
516 APInt::sdivrem(Ytop, Ybot, Yq, Yr);
517 if (Xr != 0 || Yr != 0) {
522 DEBUG(dbgs() << "\t\tX = " << Xq << ", Y = " << Yq << "\n");
523 if (Xq.slt(0) || Yq.slt(0)) {
528 if (const SCEVConstant *CUB =
529 collectConstantUpperBound(X->getAssociatedLoop(), Prod1->getType())) {
530 APInt UpperBound = CUB->getValue()->getValue();
531 DEBUG(dbgs() << "\t\tupper bound = " << UpperBound << "\n");
532 if (Xq.sgt(UpperBound) || Yq.sgt(UpperBound)) {
538 X->setPoint(SE->getConstant(Xq),
540 X->getAssociatedLoop());
547 // if (X->isLine() && Y->isPoint()) This case can't occur.
548 assert(!(X->isLine() && Y->isPoint()) && "This case should never occur");
550 if (X->isPoint() && Y->isLine()) {
551 DEBUG(dbgs() << "\t intersect Point and Line\n");
552 const SCEV *A1X1 = SE->getMulExpr(Y->getA(), X->getX());
553 const SCEV *B1Y1 = SE->getMulExpr(Y->getB(), X->getY());
554 const SCEV *Sum = SE->getAddExpr(A1X1, B1Y1);
555 if (isKnownPredicate(CmpInst::ICMP_EQ, Sum, Y->getC()))
557 if (isKnownPredicate(CmpInst::ICMP_NE, Sum, Y->getC())) {
565 llvm_unreachable("shouldn't reach the end of Constraint intersection");
570 //===----------------------------------------------------------------------===//
571 // DependenceAnalysis methods
573 // For debugging purposes. Dumps a dependence to OS.
574 void Dependence::dump(raw_ostream &OS) const {
575 bool Splitable = false;
589 unsigned Levels = getLevels();
591 for (unsigned II = 1; II <= Levels; ++II) {
596 const SCEV *Distance = getDistance(II);
599 else if (isScalar(II))
602 unsigned Direction = getDirection(II);
603 if (Direction == DVEntry::ALL)
606 if (Direction & DVEntry::LT)
608 if (Direction & DVEntry::EQ)
610 if (Direction & DVEntry::GT)
619 if (isLoopIndependent())
628 static AliasResult underlyingObjectsAlias(AliasAnalysis *AA,
629 const DataLayout &DL, const Value *A,
631 const Value *AObj = GetUnderlyingObject(A, DL);
632 const Value *BObj = GetUnderlyingObject(B, DL);
633 return AA->alias(AObj, AA->getTypeStoreSize(AObj->getType()),
634 BObj, AA->getTypeStoreSize(BObj->getType()));
638 // Returns true if the load or store can be analyzed. Atomic and volatile
639 // operations have properties which this analysis does not understand.
641 bool isLoadOrStore(const Instruction *I) {
642 if (const LoadInst *LI = dyn_cast<LoadInst>(I))
643 return LI->isUnordered();
644 else if (const StoreInst *SI = dyn_cast<StoreInst>(I))
645 return SI->isUnordered();
651 Value *getPointerOperand(Instruction *I) {
652 if (LoadInst *LI = dyn_cast<LoadInst>(I))
653 return LI->getPointerOperand();
654 if (StoreInst *SI = dyn_cast<StoreInst>(I))
655 return SI->getPointerOperand();
656 llvm_unreachable("Value is not load or store instruction");
661 // Examines the loop nesting of the Src and Dst
662 // instructions and establishes their shared loops. Sets the variables
663 // CommonLevels, SrcLevels, and MaxLevels.
664 // The source and destination instructions needn't be contained in the same
665 // loop. The routine establishNestingLevels finds the level of most deeply
666 // nested loop that contains them both, CommonLevels. An instruction that's
667 // not contained in a loop is at level = 0. MaxLevels is equal to the level
668 // of the source plus the level of the destination, minus CommonLevels.
669 // This lets us allocate vectors MaxLevels in length, with room for every
670 // distinct loop referenced in both the source and destination subscripts.
671 // The variable SrcLevels is the nesting depth of the source instruction.
672 // It's used to help calculate distinct loops referenced by the destination.
673 // Here's the map from loops to levels:
675 // 1 - outermost common loop
676 // ... - other common loops
677 // CommonLevels - innermost common loop
678 // ... - loops containing Src but not Dst
679 // SrcLevels - innermost loop containing Src but not Dst
680 // ... - loops containing Dst but not Src
681 // MaxLevels - innermost loops containing Dst but not Src
682 // Consider the follow code fragment:
699 // If we're looking at the possibility of a dependence between the store
700 // to A (the Src) and the load from A (the Dst), we'll note that they
701 // have 2 loops in common, so CommonLevels will equal 2 and the direction
702 // vector for Result will have 2 entries. SrcLevels = 4 and MaxLevels = 7.
703 // A map from loop names to loop numbers would look like
705 // b - 2 = CommonLevels
711 void DependenceAnalysis::establishNestingLevels(const Instruction *Src,
712 const Instruction *Dst) {
713 const BasicBlock *SrcBlock = Src->getParent();
714 const BasicBlock *DstBlock = Dst->getParent();
715 unsigned SrcLevel = LI->getLoopDepth(SrcBlock);
716 unsigned DstLevel = LI->getLoopDepth(DstBlock);
717 const Loop *SrcLoop = LI->getLoopFor(SrcBlock);
718 const Loop *DstLoop = LI->getLoopFor(DstBlock);
719 SrcLevels = SrcLevel;
720 MaxLevels = SrcLevel + DstLevel;
721 while (SrcLevel > DstLevel) {
722 SrcLoop = SrcLoop->getParentLoop();
725 while (DstLevel > SrcLevel) {
726 DstLoop = DstLoop->getParentLoop();
729 while (SrcLoop != DstLoop) {
730 SrcLoop = SrcLoop->getParentLoop();
731 DstLoop = DstLoop->getParentLoop();
734 CommonLevels = SrcLevel;
735 MaxLevels -= CommonLevels;
739 // Given one of the loops containing the source, return
740 // its level index in our numbering scheme.
741 unsigned DependenceAnalysis::mapSrcLoop(const Loop *SrcLoop) const {
742 return SrcLoop->getLoopDepth();
746 // Given one of the loops containing the destination,
747 // return its level index in our numbering scheme.
748 unsigned DependenceAnalysis::mapDstLoop(const Loop *DstLoop) const {
749 unsigned D = DstLoop->getLoopDepth();
750 if (D > CommonLevels)
751 return D - CommonLevels + SrcLevels;
757 // Returns true if Expression is loop invariant in LoopNest.
758 bool DependenceAnalysis::isLoopInvariant(const SCEV *Expression,
759 const Loop *LoopNest) const {
762 return SE->isLoopInvariant(Expression, LoopNest) &&
763 isLoopInvariant(Expression, LoopNest->getParentLoop());
768 // Finds the set of loops from the LoopNest that
769 // have a level <= CommonLevels and are referred to by the SCEV Expression.
770 void DependenceAnalysis::collectCommonLoops(const SCEV *Expression,
771 const Loop *LoopNest,
772 SmallBitVector &Loops) const {
774 unsigned Level = LoopNest->getLoopDepth();
775 if (Level <= CommonLevels && !SE->isLoopInvariant(Expression, LoopNest))
777 LoopNest = LoopNest->getParentLoop();
781 void DependenceAnalysis::unifySubscriptType(ArrayRef<Subscript *> Pairs) {
783 unsigned widestWidthSeen = 0;
786 // Go through each pair and find the widest bit to which we need
787 // to extend all of them.
788 for (unsigned i = 0; i < Pairs.size(); i++) {
789 const SCEV *Src = Pairs[i]->Src;
790 const SCEV *Dst = Pairs[i]->Dst;
791 IntegerType *SrcTy = dyn_cast<IntegerType>(Src->getType());
792 IntegerType *DstTy = dyn_cast<IntegerType>(Dst->getType());
793 if (SrcTy == nullptr || DstTy == nullptr) {
794 assert(SrcTy == DstTy && "This function only unify integer types and "
795 "expect Src and Dst share the same type "
799 if (SrcTy->getBitWidth() > widestWidthSeen) {
800 widestWidthSeen = SrcTy->getBitWidth();
803 if (DstTy->getBitWidth() > widestWidthSeen) {
804 widestWidthSeen = DstTy->getBitWidth();
810 assert(widestWidthSeen > 0);
812 // Now extend each pair to the widest seen.
813 for (unsigned i = 0; i < Pairs.size(); i++) {
814 const SCEV *Src = Pairs[i]->Src;
815 const SCEV *Dst = Pairs[i]->Dst;
816 IntegerType *SrcTy = dyn_cast<IntegerType>(Src->getType());
817 IntegerType *DstTy = dyn_cast<IntegerType>(Dst->getType());
818 if (SrcTy == nullptr || DstTy == nullptr) {
819 assert(SrcTy == DstTy && "This function only unify integer types and "
820 "expect Src and Dst share the same type "
824 if (SrcTy->getBitWidth() < widestWidthSeen)
825 // Sign-extend Src to widestType
826 Pairs[i]->Src = SE->getSignExtendExpr(Src, widestType);
827 if (DstTy->getBitWidth() < widestWidthSeen) {
828 // Sign-extend Dst to widestType
829 Pairs[i]->Dst = SE->getSignExtendExpr(Dst, widestType);
834 // removeMatchingExtensions - Examines a subscript pair.
835 // If the source and destination are identically sign (or zero)
836 // extended, it strips off the extension in an effect to simplify
837 // the actual analysis.
838 void DependenceAnalysis::removeMatchingExtensions(Subscript *Pair) {
839 const SCEV *Src = Pair->Src;
840 const SCEV *Dst = Pair->Dst;
841 if ((isa<SCEVZeroExtendExpr>(Src) && isa<SCEVZeroExtendExpr>(Dst)) ||
842 (isa<SCEVSignExtendExpr>(Src) && isa<SCEVSignExtendExpr>(Dst))) {
843 const SCEVCastExpr *SrcCast = cast<SCEVCastExpr>(Src);
844 const SCEVCastExpr *DstCast = cast<SCEVCastExpr>(Dst);
845 const SCEV *SrcCastOp = SrcCast->getOperand();
846 const SCEV *DstCastOp = DstCast->getOperand();
847 if (SrcCastOp->getType() == DstCastOp->getType()) {
848 Pair->Src = SrcCastOp;
849 Pair->Dst = DstCastOp;
855 // Examine the scev and return true iff it's linear.
856 // Collect any loops mentioned in the set of "Loops".
857 bool DependenceAnalysis::checkSrcSubscript(const SCEV *Src,
858 const Loop *LoopNest,
859 SmallBitVector &Loops) {
860 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Src);
862 return isLoopInvariant(Src, LoopNest);
863 const SCEV *Start = AddRec->getStart();
864 const SCEV *Step = AddRec->getStepRecurrence(*SE);
865 const SCEV *UB = SE->getBackedgeTakenCount(AddRec->getLoop());
866 if (!isa<SCEVCouldNotCompute>(UB)) {
867 if (SE->getTypeSizeInBits(Start->getType()) <
868 SE->getTypeSizeInBits(UB->getType())) {
869 if (!AddRec->getNoWrapFlags())
873 if (!isLoopInvariant(Step, LoopNest))
875 Loops.set(mapSrcLoop(AddRec->getLoop()));
876 return checkSrcSubscript(Start, LoopNest, Loops);
881 // Examine the scev and return true iff it's linear.
882 // Collect any loops mentioned in the set of "Loops".
883 bool DependenceAnalysis::checkDstSubscript(const SCEV *Dst,
884 const Loop *LoopNest,
885 SmallBitVector &Loops) {
886 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Dst);
888 return isLoopInvariant(Dst, LoopNest);
889 const SCEV *Start = AddRec->getStart();
890 const SCEV *Step = AddRec->getStepRecurrence(*SE);
891 const SCEV *UB = SE->getBackedgeTakenCount(AddRec->getLoop());
892 if (!isa<SCEVCouldNotCompute>(UB)) {
893 if (SE->getTypeSizeInBits(Start->getType()) <
894 SE->getTypeSizeInBits(UB->getType())) {
895 if (!AddRec->getNoWrapFlags())
899 if (!isLoopInvariant(Step, LoopNest))
901 Loops.set(mapDstLoop(AddRec->getLoop()));
902 return checkDstSubscript(Start, LoopNest, Loops);
906 // Examines the subscript pair (the Src and Dst SCEVs)
907 // and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
908 // Collects the associated loops in a set.
909 DependenceAnalysis::Subscript::ClassificationKind
910 DependenceAnalysis::classifyPair(const SCEV *Src, const Loop *SrcLoopNest,
911 const SCEV *Dst, const Loop *DstLoopNest,
912 SmallBitVector &Loops) {
913 SmallBitVector SrcLoops(MaxLevels + 1);
914 SmallBitVector DstLoops(MaxLevels + 1);
915 if (!checkSrcSubscript(Src, SrcLoopNest, SrcLoops))
916 return Subscript::NonLinear;
917 if (!checkDstSubscript(Dst, DstLoopNest, DstLoops))
918 return Subscript::NonLinear;
921 unsigned N = Loops.count();
923 return Subscript::ZIV;
925 return Subscript::SIV;
926 if (N == 2 && (SrcLoops.count() == 0 ||
927 DstLoops.count() == 0 ||
928 (SrcLoops.count() == 1 && DstLoops.count() == 1)))
929 return Subscript::RDIV;
930 return Subscript::MIV;
934 // A wrapper around SCEV::isKnownPredicate.
935 // Looks for cases where we're interested in comparing for equality.
936 // If both X and Y have been identically sign or zero extended,
937 // it strips off the (confusing) extensions before invoking
938 // SCEV::isKnownPredicate. Perhaps, someday, the ScalarEvolution package
939 // will be similarly updated.
941 // If SCEV::isKnownPredicate can't prove the predicate,
942 // we try simple subtraction, which seems to help in some cases
943 // involving symbolics.
944 bool DependenceAnalysis::isKnownPredicate(ICmpInst::Predicate Pred,
946 const SCEV *Y) const {
947 if (Pred == CmpInst::ICMP_EQ ||
948 Pred == CmpInst::ICMP_NE) {
949 if ((isa<SCEVSignExtendExpr>(X) &&
950 isa<SCEVSignExtendExpr>(Y)) ||
951 (isa<SCEVZeroExtendExpr>(X) &&
952 isa<SCEVZeroExtendExpr>(Y))) {
953 const SCEVCastExpr *CX = cast<SCEVCastExpr>(X);
954 const SCEVCastExpr *CY = cast<SCEVCastExpr>(Y);
955 const SCEV *Xop = CX->getOperand();
956 const SCEV *Yop = CY->getOperand();
957 if (Xop->getType() == Yop->getType()) {
963 if (SE->isKnownPredicate(Pred, X, Y))
965 // If SE->isKnownPredicate can't prove the condition,
966 // we try the brute-force approach of subtracting
967 // and testing the difference.
968 // By testing with SE->isKnownPredicate first, we avoid
969 // the possibility of overflow when the arguments are constants.
970 const SCEV *Delta = SE->getMinusSCEV(X, Y);
972 case CmpInst::ICMP_EQ:
973 return Delta->isZero();
974 case CmpInst::ICMP_NE:
975 return SE->isKnownNonZero(Delta);
976 case CmpInst::ICMP_SGE:
977 return SE->isKnownNonNegative(Delta);
978 case CmpInst::ICMP_SLE:
979 return SE->isKnownNonPositive(Delta);
980 case CmpInst::ICMP_SGT:
981 return SE->isKnownPositive(Delta);
982 case CmpInst::ICMP_SLT:
983 return SE->isKnownNegative(Delta);
985 llvm_unreachable("unexpected predicate in isKnownPredicate");
990 // All subscripts are all the same type.
991 // Loop bound may be smaller (e.g., a char).
992 // Should zero extend loop bound, since it's always >= 0.
993 // This routine collects upper bound and extends or truncates if needed.
994 // Truncating is safe when subscripts are known not to wrap. Cases without
995 // nowrap flags should have been rejected earlier.
996 // Return null if no bound available.
997 const SCEV *DependenceAnalysis::collectUpperBound(const Loop *L,
999 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
1000 const SCEV *UB = SE->getBackedgeTakenCount(L);
1001 return SE->getTruncateOrZeroExtend(UB, T);
1007 // Calls collectUpperBound(), then attempts to cast it to SCEVConstant.
1008 // If the cast fails, returns NULL.
1009 const SCEVConstant *DependenceAnalysis::collectConstantUpperBound(const Loop *L,
1012 if (const SCEV *UB = collectUpperBound(L, T))
1013 return dyn_cast<SCEVConstant>(UB);
1019 // When we have a pair of subscripts of the form [c1] and [c2],
1020 // where c1 and c2 are both loop invariant, we attack it using
1021 // the ZIV test. Basically, we test by comparing the two values,
1022 // but there are actually three possible results:
1023 // 1) the values are equal, so there's a dependence
1024 // 2) the values are different, so there's no dependence
1025 // 3) the values might be equal, so we have to assume a dependence.
1027 // Return true if dependence disproved.
1028 bool DependenceAnalysis::testZIV(const SCEV *Src,
1030 FullDependence &Result) const {
1031 DEBUG(dbgs() << " src = " << *Src << "\n");
1032 DEBUG(dbgs() << " dst = " << *Dst << "\n");
1034 if (isKnownPredicate(CmpInst::ICMP_EQ, Src, Dst)) {
1035 DEBUG(dbgs() << " provably dependent\n");
1036 return false; // provably dependent
1038 if (isKnownPredicate(CmpInst::ICMP_NE, Src, Dst)) {
1039 DEBUG(dbgs() << " provably independent\n");
1041 return true; // provably independent
1043 DEBUG(dbgs() << " possibly dependent\n");
1044 Result.Consistent = false;
1045 return false; // possibly dependent
1050 // From the paper, Practical Dependence Testing, Section 4.2.1
1052 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 + a*i],
1053 // where i is an induction variable, c1 and c2 are loop invariant,
1054 // and a is a constant, we can solve it exactly using the Strong SIV test.
1056 // Can prove independence. Failing that, can compute distance (and direction).
1057 // In the presence of symbolic terms, we can sometimes make progress.
1059 // If there's a dependence,
1061 // c1 + a*i = c2 + a*i'
1063 // The dependence distance is
1065 // d = i' - i = (c1 - c2)/a
1067 // A dependence only exists if d is an integer and abs(d) <= U, where U is the
1068 // loop's upper bound. If a dependence exists, the dependence direction is
1072 // direction = { = if d = 0
1075 // Return true if dependence disproved.
1076 bool DependenceAnalysis::strongSIVtest(const SCEV *Coeff,
1077 const SCEV *SrcConst,
1078 const SCEV *DstConst,
1079 const Loop *CurLoop,
1081 FullDependence &Result,
1082 Constraint &NewConstraint) const {
1083 DEBUG(dbgs() << "\tStrong SIV test\n");
1084 DEBUG(dbgs() << "\t Coeff = " << *Coeff);
1085 DEBUG(dbgs() << ", " << *Coeff->getType() << "\n");
1086 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst);
1087 DEBUG(dbgs() << ", " << *SrcConst->getType() << "\n");
1088 DEBUG(dbgs() << "\t DstConst = " << *DstConst);
1089 DEBUG(dbgs() << ", " << *DstConst->getType() << "\n");
1090 ++StrongSIVapplications;
1091 assert(0 < Level && Level <= CommonLevels && "level out of range");
1094 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1095 DEBUG(dbgs() << "\t Delta = " << *Delta);
1096 DEBUG(dbgs() << ", " << *Delta->getType() << "\n");
1098 // check that |Delta| < iteration count
1099 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1100 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound);
1101 DEBUG(dbgs() << ", " << *UpperBound->getType() << "\n");
1102 const SCEV *AbsDelta =
1103 SE->isKnownNonNegative(Delta) ? Delta : SE->getNegativeSCEV(Delta);
1104 const SCEV *AbsCoeff =
1105 SE->isKnownNonNegative(Coeff) ? Coeff : SE->getNegativeSCEV(Coeff);
1106 const SCEV *Product = SE->getMulExpr(UpperBound, AbsCoeff);
1107 if (isKnownPredicate(CmpInst::ICMP_SGT, AbsDelta, Product)) {
1108 // Distance greater than trip count - no dependence
1109 ++StrongSIVindependence;
1110 ++StrongSIVsuccesses;
1115 // Can we compute distance?
1116 if (isa<SCEVConstant>(Delta) && isa<SCEVConstant>(Coeff)) {
1117 APInt ConstDelta = cast<SCEVConstant>(Delta)->getValue()->getValue();
1118 APInt ConstCoeff = cast<SCEVConstant>(Coeff)->getValue()->getValue();
1119 APInt Distance = ConstDelta; // these need to be initialized
1120 APInt Remainder = ConstDelta;
1121 APInt::sdivrem(ConstDelta, ConstCoeff, Distance, Remainder);
1122 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1123 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1124 // Make sure Coeff divides Delta exactly
1125 if (Remainder != 0) {
1126 // Coeff doesn't divide Distance, no dependence
1127 ++StrongSIVindependence;
1128 ++StrongSIVsuccesses;
1131 Result.DV[Level].Distance = SE->getConstant(Distance);
1132 NewConstraint.setDistance(SE->getConstant(Distance), CurLoop);
1133 if (Distance.sgt(0))
1134 Result.DV[Level].Direction &= Dependence::DVEntry::LT;
1135 else if (Distance.slt(0))
1136 Result.DV[Level].Direction &= Dependence::DVEntry::GT;
1138 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1139 ++StrongSIVsuccesses;
1141 else if (Delta->isZero()) {
1143 Result.DV[Level].Distance = Delta;
1144 NewConstraint.setDistance(Delta, CurLoop);
1145 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1146 ++StrongSIVsuccesses;
1149 if (Coeff->isOne()) {
1150 DEBUG(dbgs() << "\t Distance = " << *Delta << "\n");
1151 Result.DV[Level].Distance = Delta; // since X/1 == X
1152 NewConstraint.setDistance(Delta, CurLoop);
1155 Result.Consistent = false;
1156 NewConstraint.setLine(Coeff,
1157 SE->getNegativeSCEV(Coeff),
1158 SE->getNegativeSCEV(Delta), CurLoop);
1161 // maybe we can get a useful direction
1162 bool DeltaMaybeZero = !SE->isKnownNonZero(Delta);
1163 bool DeltaMaybePositive = !SE->isKnownNonPositive(Delta);
1164 bool DeltaMaybeNegative = !SE->isKnownNonNegative(Delta);
1165 bool CoeffMaybePositive = !SE->isKnownNonPositive(Coeff);
1166 bool CoeffMaybeNegative = !SE->isKnownNonNegative(Coeff);
1167 // The double negatives above are confusing.
1168 // It helps to read !SE->isKnownNonZero(Delta)
1169 // as "Delta might be Zero"
1170 unsigned NewDirection = Dependence::DVEntry::NONE;
1171 if ((DeltaMaybePositive && CoeffMaybePositive) ||
1172 (DeltaMaybeNegative && CoeffMaybeNegative))
1173 NewDirection = Dependence::DVEntry::LT;
1175 NewDirection |= Dependence::DVEntry::EQ;
1176 if ((DeltaMaybeNegative && CoeffMaybePositive) ||
1177 (DeltaMaybePositive && CoeffMaybeNegative))
1178 NewDirection |= Dependence::DVEntry::GT;
1179 if (NewDirection < Result.DV[Level].Direction)
1180 ++StrongSIVsuccesses;
1181 Result.DV[Level].Direction &= NewDirection;
1187 // weakCrossingSIVtest -
1188 // From the paper, Practical Dependence Testing, Section 4.2.2
1190 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 - a*i],
1191 // where i is an induction variable, c1 and c2 are loop invariant,
1192 // and a is a constant, we can solve it exactly using the
1193 // Weak-Crossing SIV test.
1195 // Given c1 + a*i = c2 - a*i', we can look for the intersection of
1196 // the two lines, where i = i', yielding
1198 // c1 + a*i = c2 - a*i
1202 // If i < 0, there is no dependence.
1203 // If i > upperbound, there is no dependence.
1204 // If i = 0 (i.e., if c1 = c2), there's a dependence with distance = 0.
1205 // If i = upperbound, there's a dependence with distance = 0.
1206 // If i is integral, there's a dependence (all directions).
1207 // If the non-integer part = 1/2, there's a dependence (<> directions).
1208 // Otherwise, there's no dependence.
1210 // Can prove independence. Failing that,
1211 // can sometimes refine the directions.
1212 // Can determine iteration for splitting.
1214 // Return true if dependence disproved.
1215 bool DependenceAnalysis::weakCrossingSIVtest(const SCEV *Coeff,
1216 const SCEV *SrcConst,
1217 const SCEV *DstConst,
1218 const Loop *CurLoop,
1220 FullDependence &Result,
1221 Constraint &NewConstraint,
1222 const SCEV *&SplitIter) const {
1223 DEBUG(dbgs() << "\tWeak-Crossing SIV test\n");
1224 DEBUG(dbgs() << "\t Coeff = " << *Coeff << "\n");
1225 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1226 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1227 ++WeakCrossingSIVapplications;
1228 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1230 Result.Consistent = false;
1231 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1232 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1233 NewConstraint.setLine(Coeff, Coeff, Delta, CurLoop);
1234 if (Delta->isZero()) {
1235 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1236 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1237 ++WeakCrossingSIVsuccesses;
1238 if (!Result.DV[Level].Direction) {
1239 ++WeakCrossingSIVindependence;
1242 Result.DV[Level].Distance = Delta; // = 0
1245 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(Coeff);
1249 Result.DV[Level].Splitable = true;
1250 if (SE->isKnownNegative(ConstCoeff)) {
1251 ConstCoeff = dyn_cast<SCEVConstant>(SE->getNegativeSCEV(ConstCoeff));
1252 assert(ConstCoeff &&
1253 "dynamic cast of negative of ConstCoeff should yield constant");
1254 Delta = SE->getNegativeSCEV(Delta);
1256 assert(SE->isKnownPositive(ConstCoeff) && "ConstCoeff should be positive");
1258 // compute SplitIter for use by DependenceAnalysis::getSplitIteration()
1260 SE->getUDivExpr(SE->getSMaxExpr(SE->getConstant(Delta->getType(), 0),
1262 SE->getMulExpr(SE->getConstant(Delta->getType(), 2),
1264 DEBUG(dbgs() << "\t Split iter = " << *SplitIter << "\n");
1266 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1270 // We're certain that ConstCoeff > 0; therefore,
1271 // if Delta < 0, then no dependence.
1272 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1273 DEBUG(dbgs() << "\t ConstCoeff = " << *ConstCoeff << "\n");
1274 if (SE->isKnownNegative(Delta)) {
1275 // No dependence, Delta < 0
1276 ++WeakCrossingSIVindependence;
1277 ++WeakCrossingSIVsuccesses;
1281 // We're certain that Delta > 0 and ConstCoeff > 0.
1282 // Check Delta/(2*ConstCoeff) against upper loop bound
1283 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1284 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1285 const SCEV *ConstantTwo = SE->getConstant(UpperBound->getType(), 2);
1286 const SCEV *ML = SE->getMulExpr(SE->getMulExpr(ConstCoeff, UpperBound),
1288 DEBUG(dbgs() << "\t ML = " << *ML << "\n");
1289 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, ML)) {
1290 // Delta too big, no dependence
1291 ++WeakCrossingSIVindependence;
1292 ++WeakCrossingSIVsuccesses;
1295 if (isKnownPredicate(CmpInst::ICMP_EQ, Delta, ML)) {
1297 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1298 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1299 ++WeakCrossingSIVsuccesses;
1300 if (!Result.DV[Level].Direction) {
1301 ++WeakCrossingSIVindependence;
1304 Result.DV[Level].Splitable = false;
1305 Result.DV[Level].Distance = SE->getConstant(Delta->getType(), 0);
1310 // check that Coeff divides Delta
1311 APInt APDelta = ConstDelta->getValue()->getValue();
1312 APInt APCoeff = ConstCoeff->getValue()->getValue();
1313 APInt Distance = APDelta; // these need to be initialzed
1314 APInt Remainder = APDelta;
1315 APInt::sdivrem(APDelta, APCoeff, Distance, Remainder);
1316 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1317 if (Remainder != 0) {
1318 // Coeff doesn't divide Delta, no dependence
1319 ++WeakCrossingSIVindependence;
1320 ++WeakCrossingSIVsuccesses;
1323 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1325 // if 2*Coeff doesn't divide Delta, then the equal direction isn't possible
1326 APInt Two = APInt(Distance.getBitWidth(), 2, true);
1327 Remainder = Distance.srem(Two);
1328 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1329 if (Remainder != 0) {
1330 // Equal direction isn't possible
1331 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::EQ);
1332 ++WeakCrossingSIVsuccesses;
1338 // Kirch's algorithm, from
1340 // Optimizing Supercompilers for Supercomputers
1344 // Program 2.1, page 29.
1345 // Computes the GCD of AM and BM.
1346 // Also finds a solution to the equation ax - by = gcd(a, b).
1347 // Returns true if dependence disproved; i.e., gcd does not divide Delta.
1349 bool findGCD(unsigned Bits, APInt AM, APInt BM, APInt Delta,
1350 APInt &G, APInt &X, APInt &Y) {
1351 APInt A0(Bits, 1, true), A1(Bits, 0, true);
1352 APInt B0(Bits, 0, true), B1(Bits, 1, true);
1353 APInt G0 = AM.abs();
1354 APInt G1 = BM.abs();
1355 APInt Q = G0; // these need to be initialized
1357 APInt::sdivrem(G0, G1, Q, R);
1359 APInt A2 = A0 - Q*A1; A0 = A1; A1 = A2;
1360 APInt B2 = B0 - Q*B1; B0 = B1; B1 = B2;
1362 APInt::sdivrem(G0, G1, Q, R);
1365 DEBUG(dbgs() << "\t GCD = " << G << "\n");
1366 X = AM.slt(0) ? -A1 : A1;
1367 Y = BM.slt(0) ? B1 : -B1;
1369 // make sure gcd divides Delta
1372 return true; // gcd doesn't divide Delta, no dependence
1381 APInt floorOfQuotient(APInt A, APInt B) {
1382 APInt Q = A; // these need to be initialized
1384 APInt::sdivrem(A, B, Q, R);
1387 if ((A.sgt(0) && B.sgt(0)) ||
1388 (A.slt(0) && B.slt(0)))
1396 APInt ceilingOfQuotient(APInt A, APInt B) {
1397 APInt Q = A; // these need to be initialized
1399 APInt::sdivrem(A, B, Q, R);
1402 if ((A.sgt(0) && B.sgt(0)) ||
1403 (A.slt(0) && B.slt(0)))
1411 APInt maxAPInt(APInt A, APInt B) {
1412 return A.sgt(B) ? A : B;
1417 APInt minAPInt(APInt A, APInt B) {
1418 return A.slt(B) ? A : B;
1423 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*i],
1424 // where i is an induction variable, c1 and c2 are loop invariant, and a1
1425 // and a2 are constant, we can solve it exactly using an algorithm developed
1426 // by Banerjee and Wolfe. See Section 2.5.3 in
1428 // Optimizing Supercompilers for Supercomputers
1432 // It's slower than the specialized tests (strong SIV, weak-zero SIV, etc),
1433 // so use them if possible. They're also a bit better with symbolics and,
1434 // in the case of the strong SIV test, can compute Distances.
1436 // Return true if dependence disproved.
1437 bool DependenceAnalysis::exactSIVtest(const SCEV *SrcCoeff,
1438 const SCEV *DstCoeff,
1439 const SCEV *SrcConst,
1440 const SCEV *DstConst,
1441 const Loop *CurLoop,
1443 FullDependence &Result,
1444 Constraint &NewConstraint) const {
1445 DEBUG(dbgs() << "\tExact SIV test\n");
1446 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1447 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1448 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1449 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1450 ++ExactSIVapplications;
1451 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1453 Result.Consistent = false;
1454 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1455 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1456 NewConstraint.setLine(SrcCoeff, SE->getNegativeSCEV(DstCoeff),
1458 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1459 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1460 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1461 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1466 APInt AM = ConstSrcCoeff->getValue()->getValue();
1467 APInt BM = ConstDstCoeff->getValue()->getValue();
1468 unsigned Bits = AM.getBitWidth();
1469 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1470 // gcd doesn't divide Delta, no dependence
1471 ++ExactSIVindependence;
1472 ++ExactSIVsuccesses;
1476 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1478 // since SCEV construction normalizes, LM = 0
1479 APInt UM(Bits, 1, true);
1480 bool UMvalid = false;
1481 // UM is perhaps unavailable, let's check
1482 if (const SCEVConstant *CUB =
1483 collectConstantUpperBound(CurLoop, Delta->getType())) {
1484 UM = CUB->getValue()->getValue();
1485 DEBUG(dbgs() << "\t UM = " << UM << "\n");
1489 APInt TU(APInt::getSignedMaxValue(Bits));
1490 APInt TL(APInt::getSignedMinValue(Bits));
1492 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1493 APInt TMUL = BM.sdiv(G);
1495 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1496 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1498 TU = minAPInt(TU, floorOfQuotient(UM - X, TMUL));
1499 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1503 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1504 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1506 TL = maxAPInt(TL, ceilingOfQuotient(UM - X, TMUL));
1507 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1511 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1514 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1515 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1517 TU = minAPInt(TU, floorOfQuotient(UM - Y, TMUL));
1518 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1522 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1523 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1525 TL = maxAPInt(TL, ceilingOfQuotient(UM - Y, TMUL));
1526 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1530 ++ExactSIVindependence;
1531 ++ExactSIVsuccesses;
1535 // explore directions
1536 unsigned NewDirection = Dependence::DVEntry::NONE;
1539 APInt SaveTU(TU); // save these
1541 DEBUG(dbgs() << "\t exploring LT direction\n");
1544 TL = maxAPInt(TL, ceilingOfQuotient(X - Y + 1, TMUL));
1545 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1548 TU = minAPInt(TU, floorOfQuotient(X - Y + 1, TMUL));
1549 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1552 NewDirection |= Dependence::DVEntry::LT;
1553 ++ExactSIVsuccesses;
1557 TU = SaveTU; // restore
1559 DEBUG(dbgs() << "\t exploring EQ direction\n");
1561 TL = maxAPInt(TL, ceilingOfQuotient(X - Y, TMUL));
1562 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1565 TU = minAPInt(TU, floorOfQuotient(X - Y, TMUL));
1566 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1570 TL = maxAPInt(TL, ceilingOfQuotient(Y - X, TMUL));
1571 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1574 TU = minAPInt(TU, floorOfQuotient(Y - X, TMUL));
1575 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1578 NewDirection |= Dependence::DVEntry::EQ;
1579 ++ExactSIVsuccesses;
1583 TU = SaveTU; // restore
1585 DEBUG(dbgs() << "\t exploring GT direction\n");
1587 TL = maxAPInt(TL, ceilingOfQuotient(Y - X + 1, TMUL));
1588 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1591 TU = minAPInt(TU, floorOfQuotient(Y - X + 1, TMUL));
1592 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1595 NewDirection |= Dependence::DVEntry::GT;
1596 ++ExactSIVsuccesses;
1600 Result.DV[Level].Direction &= NewDirection;
1601 if (Result.DV[Level].Direction == Dependence::DVEntry::NONE)
1602 ++ExactSIVindependence;
1603 return Result.DV[Level].Direction == Dependence::DVEntry::NONE;
1608 // Return true if the divisor evenly divides the dividend.
1610 bool isRemainderZero(const SCEVConstant *Dividend,
1611 const SCEVConstant *Divisor) {
1612 APInt ConstDividend = Dividend->getValue()->getValue();
1613 APInt ConstDivisor = Divisor->getValue()->getValue();
1614 return ConstDividend.srem(ConstDivisor) == 0;
1618 // weakZeroSrcSIVtest -
1619 // From the paper, Practical Dependence Testing, Section 4.2.2
1621 // When we have a pair of subscripts of the form [c1] and [c2 + a*i],
1622 // where i is an induction variable, c1 and c2 are loop invariant,
1623 // and a is a constant, we can solve it exactly using the
1624 // Weak-Zero SIV test.
1634 // If i is not an integer, there's no dependence.
1635 // If i < 0 or > UB, there's no dependence.
1636 // If i = 0, the direction is <= and peeling the
1637 // 1st iteration will break the dependence.
1638 // If i = UB, the direction is >= and peeling the
1639 // last iteration will break the dependence.
1640 // Otherwise, the direction is *.
1642 // Can prove independence. Failing that, we can sometimes refine
1643 // the directions. Can sometimes show that first or last
1644 // iteration carries all the dependences (so worth peeling).
1646 // (see also weakZeroDstSIVtest)
1648 // Return true if dependence disproved.
1649 bool DependenceAnalysis::weakZeroSrcSIVtest(const SCEV *DstCoeff,
1650 const SCEV *SrcConst,
1651 const SCEV *DstConst,
1652 const Loop *CurLoop,
1654 FullDependence &Result,
1655 Constraint &NewConstraint) const {
1656 // For the WeakSIV test, it's possible the loop isn't common to
1657 // the Src and Dst loops. If it isn't, then there's no need to
1658 // record a direction.
1659 DEBUG(dbgs() << "\tWeak-Zero (src) SIV test\n");
1660 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << "\n");
1661 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1662 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1663 ++WeakZeroSIVapplications;
1664 assert(0 < Level && Level <= MaxLevels && "Level out of range");
1666 Result.Consistent = false;
1667 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1668 NewConstraint.setLine(SE->getConstant(Delta->getType(), 0),
1669 DstCoeff, Delta, CurLoop);
1670 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1671 if (isKnownPredicate(CmpInst::ICMP_EQ, SrcConst, DstConst)) {
1672 if (Level < CommonLevels) {
1673 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1674 Result.DV[Level].PeelFirst = true;
1675 ++WeakZeroSIVsuccesses;
1677 return false; // dependences caused by first iteration
1679 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1682 const SCEV *AbsCoeff =
1683 SE->isKnownNegative(ConstCoeff) ?
1684 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1685 const SCEV *NewDelta =
1686 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1688 // check that Delta/SrcCoeff < iteration count
1689 // really check NewDelta < count*AbsCoeff
1690 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1691 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1692 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1693 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1694 ++WeakZeroSIVindependence;
1695 ++WeakZeroSIVsuccesses;
1698 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1699 // dependences caused by last iteration
1700 if (Level < CommonLevels) {
1701 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1702 Result.DV[Level].PeelLast = true;
1703 ++WeakZeroSIVsuccesses;
1709 // check that Delta/SrcCoeff >= 0
1710 // really check that NewDelta >= 0
1711 if (SE->isKnownNegative(NewDelta)) {
1712 // No dependence, newDelta < 0
1713 ++WeakZeroSIVindependence;
1714 ++WeakZeroSIVsuccesses;
1718 // if SrcCoeff doesn't divide Delta, then no dependence
1719 if (isa<SCEVConstant>(Delta) &&
1720 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1721 ++WeakZeroSIVindependence;
1722 ++WeakZeroSIVsuccesses;
1729 // weakZeroDstSIVtest -
1730 // From the paper, Practical Dependence Testing, Section 4.2.2
1732 // When we have a pair of subscripts of the form [c1 + a*i] and [c2],
1733 // where i is an induction variable, c1 and c2 are loop invariant,
1734 // and a is a constant, we can solve it exactly using the
1735 // Weak-Zero SIV test.
1745 // If i is not an integer, there's no dependence.
1746 // If i < 0 or > UB, there's no dependence.
1747 // If i = 0, the direction is <= and peeling the
1748 // 1st iteration will break the dependence.
1749 // If i = UB, the direction is >= and peeling the
1750 // last iteration will break the dependence.
1751 // Otherwise, the direction is *.
1753 // Can prove independence. Failing that, we can sometimes refine
1754 // the directions. Can sometimes show that first or last
1755 // iteration carries all the dependences (so worth peeling).
1757 // (see also weakZeroSrcSIVtest)
1759 // Return true if dependence disproved.
1760 bool DependenceAnalysis::weakZeroDstSIVtest(const SCEV *SrcCoeff,
1761 const SCEV *SrcConst,
1762 const SCEV *DstConst,
1763 const Loop *CurLoop,
1765 FullDependence &Result,
1766 Constraint &NewConstraint) const {
1767 // For the WeakSIV test, it's possible the loop isn't common to the
1768 // Src and Dst loops. If it isn't, then there's no need to record a direction.
1769 DEBUG(dbgs() << "\tWeak-Zero (dst) SIV test\n");
1770 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << "\n");
1771 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1772 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1773 ++WeakZeroSIVapplications;
1774 assert(0 < Level && Level <= SrcLevels && "Level out of range");
1776 Result.Consistent = false;
1777 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1778 NewConstraint.setLine(SrcCoeff, SE->getConstant(Delta->getType(), 0),
1780 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1781 if (isKnownPredicate(CmpInst::ICMP_EQ, DstConst, SrcConst)) {
1782 if (Level < CommonLevels) {
1783 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1784 Result.DV[Level].PeelFirst = true;
1785 ++WeakZeroSIVsuccesses;
1787 return false; // dependences caused by first iteration
1789 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1792 const SCEV *AbsCoeff =
1793 SE->isKnownNegative(ConstCoeff) ?
1794 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1795 const SCEV *NewDelta =
1796 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1798 // check that Delta/SrcCoeff < iteration count
1799 // really check NewDelta < count*AbsCoeff
1800 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1801 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1802 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1803 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1804 ++WeakZeroSIVindependence;
1805 ++WeakZeroSIVsuccesses;
1808 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1809 // dependences caused by last iteration
1810 if (Level < CommonLevels) {
1811 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1812 Result.DV[Level].PeelLast = true;
1813 ++WeakZeroSIVsuccesses;
1819 // check that Delta/SrcCoeff >= 0
1820 // really check that NewDelta >= 0
1821 if (SE->isKnownNegative(NewDelta)) {
1822 // No dependence, newDelta < 0
1823 ++WeakZeroSIVindependence;
1824 ++WeakZeroSIVsuccesses;
1828 // if SrcCoeff doesn't divide Delta, then no dependence
1829 if (isa<SCEVConstant>(Delta) &&
1830 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1831 ++WeakZeroSIVindependence;
1832 ++WeakZeroSIVsuccesses;
1839 // exactRDIVtest - Tests the RDIV subscript pair for dependence.
1840 // Things of the form [c1 + a*i] and [c2 + b*j],
1841 // where i and j are induction variable, c1 and c2 are loop invariant,
1842 // and a and b are constants.
1843 // Returns true if any possible dependence is disproved.
1844 // Marks the result as inconsistent.
1845 // Works in some cases that symbolicRDIVtest doesn't, and vice versa.
1846 bool DependenceAnalysis::exactRDIVtest(const SCEV *SrcCoeff,
1847 const SCEV *DstCoeff,
1848 const SCEV *SrcConst,
1849 const SCEV *DstConst,
1850 const Loop *SrcLoop,
1851 const Loop *DstLoop,
1852 FullDependence &Result) const {
1853 DEBUG(dbgs() << "\tExact RDIV test\n");
1854 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1855 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1856 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1857 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1858 ++ExactRDIVapplications;
1859 Result.Consistent = false;
1860 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1861 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1862 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1863 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1864 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1865 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1870 APInt AM = ConstSrcCoeff->getValue()->getValue();
1871 APInt BM = ConstDstCoeff->getValue()->getValue();
1872 unsigned Bits = AM.getBitWidth();
1873 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1874 // gcd doesn't divide Delta, no dependence
1875 ++ExactRDIVindependence;
1879 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1881 // since SCEV construction seems to normalize, LM = 0
1882 APInt SrcUM(Bits, 1, true);
1883 bool SrcUMvalid = false;
1884 // SrcUM is perhaps unavailable, let's check
1885 if (const SCEVConstant *UpperBound =
1886 collectConstantUpperBound(SrcLoop, Delta->getType())) {
1887 SrcUM = UpperBound->getValue()->getValue();
1888 DEBUG(dbgs() << "\t SrcUM = " << SrcUM << "\n");
1892 APInt DstUM(Bits, 1, true);
1893 bool DstUMvalid = false;
1894 // UM is perhaps unavailable, let's check
1895 if (const SCEVConstant *UpperBound =
1896 collectConstantUpperBound(DstLoop, Delta->getType())) {
1897 DstUM = UpperBound->getValue()->getValue();
1898 DEBUG(dbgs() << "\t DstUM = " << DstUM << "\n");
1902 APInt TU(APInt::getSignedMaxValue(Bits));
1903 APInt TL(APInt::getSignedMinValue(Bits));
1905 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1906 APInt TMUL = BM.sdiv(G);
1908 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1909 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1911 TU = minAPInt(TU, floorOfQuotient(SrcUM - X, TMUL));
1912 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1916 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1917 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1919 TL = maxAPInt(TL, ceilingOfQuotient(SrcUM - X, TMUL));
1920 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1924 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1927 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1928 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1930 TU = minAPInt(TU, floorOfQuotient(DstUM - Y, TMUL));
1931 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1935 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1936 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1938 TL = maxAPInt(TL, ceilingOfQuotient(DstUM - Y, TMUL));
1939 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1943 ++ExactRDIVindependence;
1948 // symbolicRDIVtest -
1949 // In Section 4.5 of the Practical Dependence Testing paper,the authors
1950 // introduce a special case of Banerjee's Inequalities (also called the
1951 // Extreme-Value Test) that can handle some of the SIV and RDIV cases,
1952 // particularly cases with symbolics. Since it's only able to disprove
1953 // dependence (not compute distances or directions), we'll use it as a
1954 // fall back for the other tests.
1956 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
1957 // where i and j are induction variables and c1 and c2 are loop invariants,
1958 // we can use the symbolic tests to disprove some dependences, serving as a
1959 // backup for the RDIV test. Note that i and j can be the same variable,
1960 // letting this test serve as a backup for the various SIV tests.
1962 // For a dependence to exist, c1 + a1*i must equal c2 + a2*j for some
1963 // 0 <= i <= N1 and some 0 <= j <= N2, where N1 and N2 are the (normalized)
1964 // loop bounds for the i and j loops, respectively. So, ...
1966 // c1 + a1*i = c2 + a2*j
1967 // a1*i - a2*j = c2 - c1
1969 // To test for a dependence, we compute c2 - c1 and make sure it's in the
1970 // range of the maximum and minimum possible values of a1*i - a2*j.
1971 // Considering the signs of a1 and a2, we have 4 possible cases:
1973 // 1) If a1 >= 0 and a2 >= 0, then
1974 // a1*0 - a2*N2 <= c2 - c1 <= a1*N1 - a2*0
1975 // -a2*N2 <= c2 - c1 <= a1*N1
1977 // 2) If a1 >= 0 and a2 <= 0, then
1978 // a1*0 - a2*0 <= c2 - c1 <= a1*N1 - a2*N2
1979 // 0 <= c2 - c1 <= a1*N1 - a2*N2
1981 // 3) If a1 <= 0 and a2 >= 0, then
1982 // a1*N1 - a2*N2 <= c2 - c1 <= a1*0 - a2*0
1983 // a1*N1 - a2*N2 <= c2 - c1 <= 0
1985 // 4) If a1 <= 0 and a2 <= 0, then
1986 // a1*N1 - a2*0 <= c2 - c1 <= a1*0 - a2*N2
1987 // a1*N1 <= c2 - c1 <= -a2*N2
1989 // return true if dependence disproved
1990 bool DependenceAnalysis::symbolicRDIVtest(const SCEV *A1,
1995 const Loop *Loop2) const {
1996 ++SymbolicRDIVapplications;
1997 DEBUG(dbgs() << "\ttry symbolic RDIV test\n");
1998 DEBUG(dbgs() << "\t A1 = " << *A1);
1999 DEBUG(dbgs() << ", type = " << *A1->getType() << "\n");
2000 DEBUG(dbgs() << "\t A2 = " << *A2 << "\n");
2001 DEBUG(dbgs() << "\t C1 = " << *C1 << "\n");
2002 DEBUG(dbgs() << "\t C2 = " << *C2 << "\n");
2003 const SCEV *N1 = collectUpperBound(Loop1, A1->getType());
2004 const SCEV *N2 = collectUpperBound(Loop2, A1->getType());
2005 DEBUG(if (N1) dbgs() << "\t N1 = " << *N1 << "\n");
2006 DEBUG(if (N2) dbgs() << "\t N2 = " << *N2 << "\n");
2007 const SCEV *C2_C1 = SE->getMinusSCEV(C2, C1);
2008 const SCEV *C1_C2 = SE->getMinusSCEV(C1, C2);
2009 DEBUG(dbgs() << "\t C2 - C1 = " << *C2_C1 << "\n");
2010 DEBUG(dbgs() << "\t C1 - C2 = " << *C1_C2 << "\n");
2011 if (SE->isKnownNonNegative(A1)) {
2012 if (SE->isKnownNonNegative(A2)) {
2013 // A1 >= 0 && A2 >= 0
2015 // make sure that c2 - c1 <= a1*N1
2016 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2017 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
2018 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1)) {
2019 ++SymbolicRDIVindependence;
2024 // make sure that -a2*N2 <= c2 - c1, or a2*N2 >= c1 - c2
2025 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2026 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
2027 if (isKnownPredicate(CmpInst::ICMP_SLT, A2N2, C1_C2)) {
2028 ++SymbolicRDIVindependence;
2033 else if (SE->isKnownNonPositive(A2)) {
2034 // a1 >= 0 && a2 <= 0
2036 // make sure that c2 - c1 <= a1*N1 - a2*N2
2037 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2038 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2039 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
2040 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
2041 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1_A2N2)) {
2042 ++SymbolicRDIVindependence;
2046 // make sure that 0 <= c2 - c1
2047 if (SE->isKnownNegative(C2_C1)) {
2048 ++SymbolicRDIVindependence;
2053 else if (SE->isKnownNonPositive(A1)) {
2054 if (SE->isKnownNonNegative(A2)) {
2055 // a1 <= 0 && a2 >= 0
2057 // make sure that a1*N1 - a2*N2 <= c2 - c1
2058 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2059 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2060 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
2061 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
2062 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1_A2N2, C2_C1)) {
2063 ++SymbolicRDIVindependence;
2067 // make sure that c2 - c1 <= 0
2068 if (SE->isKnownPositive(C2_C1)) {
2069 ++SymbolicRDIVindependence;
2073 else if (SE->isKnownNonPositive(A2)) {
2074 // a1 <= 0 && a2 <= 0
2076 // make sure that a1*N1 <= c2 - c1
2077 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2078 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
2079 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1, C2_C1)) {
2080 ++SymbolicRDIVindependence;
2085 // make sure that c2 - c1 <= -a2*N2, or c1 - c2 >= a2*N2
2086 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2087 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
2088 if (isKnownPredicate(CmpInst::ICMP_SLT, C1_C2, A2N2)) {
2089 ++SymbolicRDIVindependence;
2100 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 - a2*i]
2101 // where i is an induction variable, c1 and c2 are loop invariant, and a1 and
2102 // a2 are constant, we attack it with an SIV test. While they can all be
2103 // solved with the Exact SIV test, it's worthwhile to use simpler tests when
2104 // they apply; they're cheaper and sometimes more precise.
2106 // Return true if dependence disproved.
2107 bool DependenceAnalysis::testSIV(const SCEV *Src,
2110 FullDependence &Result,
2111 Constraint &NewConstraint,
2112 const SCEV *&SplitIter) const {
2113 DEBUG(dbgs() << " src = " << *Src << "\n");
2114 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2115 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2116 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2117 if (SrcAddRec && DstAddRec) {
2118 const SCEV *SrcConst = SrcAddRec->getStart();
2119 const SCEV *DstConst = DstAddRec->getStart();
2120 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2121 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2122 const Loop *CurLoop = SrcAddRec->getLoop();
2123 assert(CurLoop == DstAddRec->getLoop() &&
2124 "both loops in SIV should be same");
2125 Level = mapSrcLoop(CurLoop);
2127 if (SrcCoeff == DstCoeff)
2128 disproven = strongSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2129 Level, Result, NewConstraint);
2130 else if (SrcCoeff == SE->getNegativeSCEV(DstCoeff))
2131 disproven = weakCrossingSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2132 Level, Result, NewConstraint, SplitIter);
2134 disproven = exactSIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop,
2135 Level, Result, NewConstraint);
2137 gcdMIVtest(Src, Dst, Result) ||
2138 symbolicRDIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop, CurLoop);
2141 const SCEV *SrcConst = SrcAddRec->getStart();
2142 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2143 const SCEV *DstConst = Dst;
2144 const Loop *CurLoop = SrcAddRec->getLoop();
2145 Level = mapSrcLoop(CurLoop);
2146 return weakZeroDstSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2147 Level, Result, NewConstraint) ||
2148 gcdMIVtest(Src, Dst, Result);
2151 const SCEV *DstConst = DstAddRec->getStart();
2152 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2153 const SCEV *SrcConst = Src;
2154 const Loop *CurLoop = DstAddRec->getLoop();
2155 Level = mapDstLoop(CurLoop);
2156 return weakZeroSrcSIVtest(DstCoeff, SrcConst, DstConst,
2157 CurLoop, Level, Result, NewConstraint) ||
2158 gcdMIVtest(Src, Dst, Result);
2160 llvm_unreachable("SIV test expected at least one AddRec");
2166 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
2167 // where i and j are induction variables, c1 and c2 are loop invariant,
2168 // and a1 and a2 are constant, we can solve it exactly with an easy adaptation
2169 // of the Exact SIV test, the Restricted Double Index Variable (RDIV) test.
2170 // It doesn't make sense to talk about distance or direction in this case,
2171 // so there's no point in making special versions of the Strong SIV test or
2172 // the Weak-crossing SIV test.
2174 // With minor algebra, this test can also be used for things like
2175 // [c1 + a1*i + a2*j][c2].
2177 // Return true if dependence disproved.
2178 bool DependenceAnalysis::testRDIV(const SCEV *Src,
2180 FullDependence &Result) const {
2181 // we have 3 possible situations here:
2182 // 1) [a*i + b] and [c*j + d]
2183 // 2) [a*i + c*j + b] and [d]
2184 // 3) [b] and [a*i + c*j + d]
2185 // We need to find what we've got and get organized
2187 const SCEV *SrcConst, *DstConst;
2188 const SCEV *SrcCoeff, *DstCoeff;
2189 const Loop *SrcLoop, *DstLoop;
2191 DEBUG(dbgs() << " src = " << *Src << "\n");
2192 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2193 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2194 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2195 if (SrcAddRec && DstAddRec) {
2196 SrcConst = SrcAddRec->getStart();
2197 SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2198 SrcLoop = SrcAddRec->getLoop();
2199 DstConst = DstAddRec->getStart();
2200 DstCoeff = DstAddRec->getStepRecurrence(*SE);
2201 DstLoop = DstAddRec->getLoop();
2203 else if (SrcAddRec) {
2204 if (const SCEVAddRecExpr *tmpAddRec =
2205 dyn_cast<SCEVAddRecExpr>(SrcAddRec->getStart())) {
2206 SrcConst = tmpAddRec->getStart();
2207 SrcCoeff = tmpAddRec->getStepRecurrence(*SE);
2208 SrcLoop = tmpAddRec->getLoop();
2210 DstCoeff = SE->getNegativeSCEV(SrcAddRec->getStepRecurrence(*SE));
2211 DstLoop = SrcAddRec->getLoop();
2214 llvm_unreachable("RDIV reached by surprising SCEVs");
2216 else if (DstAddRec) {
2217 if (const SCEVAddRecExpr *tmpAddRec =
2218 dyn_cast<SCEVAddRecExpr>(DstAddRec->getStart())) {
2219 DstConst = tmpAddRec->getStart();
2220 DstCoeff = tmpAddRec->getStepRecurrence(*SE);
2221 DstLoop = tmpAddRec->getLoop();
2223 SrcCoeff = SE->getNegativeSCEV(DstAddRec->getStepRecurrence(*SE));
2224 SrcLoop = DstAddRec->getLoop();
2227 llvm_unreachable("RDIV reached by surprising SCEVs");
2230 llvm_unreachable("RDIV expected at least one AddRec");
2231 return exactRDIVtest(SrcCoeff, DstCoeff,
2235 gcdMIVtest(Src, Dst, Result) ||
2236 symbolicRDIVtest(SrcCoeff, DstCoeff,
2242 // Tests the single-subscript MIV pair (Src and Dst) for dependence.
2243 // Return true if dependence disproved.
2244 // Can sometimes refine direction vectors.
2245 bool DependenceAnalysis::testMIV(const SCEV *Src,
2247 const SmallBitVector &Loops,
2248 FullDependence &Result) const {
2249 DEBUG(dbgs() << " src = " << *Src << "\n");
2250 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2251 Result.Consistent = false;
2252 return gcdMIVtest(Src, Dst, Result) ||
2253 banerjeeMIVtest(Src, Dst, Loops, Result);
2257 // Given a product, e.g., 10*X*Y, returns the first constant operand,
2258 // in this case 10. If there is no constant part, returns NULL.
2260 const SCEVConstant *getConstantPart(const SCEVMulExpr *Product) {
2261 for (unsigned Op = 0, Ops = Product->getNumOperands(); Op < Ops; Op++) {
2262 if (const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Product->getOperand(Op)))
2269 //===----------------------------------------------------------------------===//
2271 // Tests an MIV subscript pair for dependence.
2272 // Returns true if any possible dependence is disproved.
2273 // Marks the result as inconsistent.
2274 // Can sometimes disprove the equal direction for 1 or more loops,
2275 // as discussed in Michael Wolfe's book,
2276 // High Performance Compilers for Parallel Computing, page 235.
2278 // We spend some effort (code!) to handle cases like
2279 // [10*i + 5*N*j + 15*M + 6], where i and j are induction variables,
2280 // but M and N are just loop-invariant variables.
2281 // This should help us handle linearized subscripts;
2282 // also makes this test a useful backup to the various SIV tests.
2284 // It occurs to me that the presence of loop-invariant variables
2285 // changes the nature of the test from "greatest common divisor"
2286 // to "a common divisor".
2287 bool DependenceAnalysis::gcdMIVtest(const SCEV *Src,
2289 FullDependence &Result) const {
2290 DEBUG(dbgs() << "starting gcd\n");
2292 unsigned BitWidth = SE->getTypeSizeInBits(Src->getType());
2293 APInt RunningGCD = APInt::getNullValue(BitWidth);
2295 // Examine Src coefficients.
2296 // Compute running GCD and record source constant.
2297 // Because we're looking for the constant at the end of the chain,
2298 // we can't quit the loop just because the GCD == 1.
2299 const SCEV *Coefficients = Src;
2300 while (const SCEVAddRecExpr *AddRec =
2301 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2302 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2303 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2304 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2305 // If the coefficient is the product of a constant and other stuff,
2306 // we can use the constant in the GCD computation.
2307 Constant = getConstantPart(Product);
2310 APInt ConstCoeff = Constant->getValue()->getValue();
2311 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2312 Coefficients = AddRec->getStart();
2314 const SCEV *SrcConst = Coefficients;
2316 // Examine Dst coefficients.
2317 // Compute running GCD and record destination constant.
2318 // Because we're looking for the constant at the end of the chain,
2319 // we can't quit the loop just because the GCD == 1.
2321 while (const SCEVAddRecExpr *AddRec =
2322 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2323 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2324 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2325 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2326 // If the coefficient is the product of a constant and other stuff,
2327 // we can use the constant in the GCD computation.
2328 Constant = getConstantPart(Product);
2331 APInt ConstCoeff = Constant->getValue()->getValue();
2332 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2333 Coefficients = AddRec->getStart();
2335 const SCEV *DstConst = Coefficients;
2337 APInt ExtraGCD = APInt::getNullValue(BitWidth);
2338 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
2339 DEBUG(dbgs() << " Delta = " << *Delta << "\n");
2340 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Delta);
2341 if (const SCEVAddExpr *Sum = dyn_cast<SCEVAddExpr>(Delta)) {
2342 // If Delta is a sum of products, we may be able to make further progress.
2343 for (unsigned Op = 0, Ops = Sum->getNumOperands(); Op < Ops; Op++) {
2344 const SCEV *Operand = Sum->getOperand(Op);
2345 if (isa<SCEVConstant>(Operand)) {
2346 assert(!Constant && "Surprised to find multiple constants");
2347 Constant = cast<SCEVConstant>(Operand);
2349 else if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Operand)) {
2350 // Search for constant operand to participate in GCD;
2351 // If none found; return false.
2352 const SCEVConstant *ConstOp = getConstantPart(Product);
2355 APInt ConstOpValue = ConstOp->getValue()->getValue();
2356 ExtraGCD = APIntOps::GreatestCommonDivisor(ExtraGCD,
2357 ConstOpValue.abs());
2365 APInt ConstDelta = cast<SCEVConstant>(Constant)->getValue()->getValue();
2366 DEBUG(dbgs() << " ConstDelta = " << ConstDelta << "\n");
2367 if (ConstDelta == 0)
2369 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ExtraGCD);
2370 DEBUG(dbgs() << " RunningGCD = " << RunningGCD << "\n");
2371 APInt Remainder = ConstDelta.srem(RunningGCD);
2372 if (Remainder != 0) {
2377 // Try to disprove equal directions.
2378 // For example, given a subscript pair [3*i + 2*j] and [i' + 2*j' - 1],
2379 // the code above can't disprove the dependence because the GCD = 1.
2380 // So we consider what happen if i = i' and what happens if j = j'.
2381 // If i = i', we can simplify the subscript to [2*i + 2*j] and [2*j' - 1],
2382 // which is infeasible, so we can disallow the = direction for the i level.
2383 // Setting j = j' doesn't help matters, so we end up with a direction vector
2386 // Given A[5*i + 10*j*M + 9*M*N] and A[15*i + 20*j*M - 21*N*M + 5],
2387 // we need to remember that the constant part is 5 and the RunningGCD should
2388 // be initialized to ExtraGCD = 30.
2389 DEBUG(dbgs() << " ExtraGCD = " << ExtraGCD << '\n');
2391 bool Improved = false;
2393 while (const SCEVAddRecExpr *AddRec =
2394 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2395 Coefficients = AddRec->getStart();
2396 const Loop *CurLoop = AddRec->getLoop();
2397 RunningGCD = ExtraGCD;
2398 const SCEV *SrcCoeff = AddRec->getStepRecurrence(*SE);
2399 const SCEV *DstCoeff = SE->getMinusSCEV(SrcCoeff, SrcCoeff);
2400 const SCEV *Inner = Src;
2401 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2402 AddRec = cast<SCEVAddRecExpr>(Inner);
2403 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2404 if (CurLoop == AddRec->getLoop())
2405 ; // SrcCoeff == Coeff
2407 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2408 // If the coefficient is the product of a constant and other stuff,
2409 // we can use the constant in the GCD computation.
2410 Constant = getConstantPart(Product);
2412 Constant = cast<SCEVConstant>(Coeff);
2413 APInt ConstCoeff = Constant->getValue()->getValue();
2414 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2416 Inner = AddRec->getStart();
2419 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2420 AddRec = cast<SCEVAddRecExpr>(Inner);
2421 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2422 if (CurLoop == AddRec->getLoop())
2425 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2426 // If the coefficient is the product of a constant and other stuff,
2427 // we can use the constant in the GCD computation.
2428 Constant = getConstantPart(Product);
2430 Constant = cast<SCEVConstant>(Coeff);
2431 APInt ConstCoeff = Constant->getValue()->getValue();
2432 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2434 Inner = AddRec->getStart();
2436 Delta = SE->getMinusSCEV(SrcCoeff, DstCoeff);
2437 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Delta))
2438 // If the coefficient is the product of a constant and other stuff,
2439 // we can use the constant in the GCD computation.
2440 Constant = getConstantPart(Product);
2441 else if (isa<SCEVConstant>(Delta))
2442 Constant = cast<SCEVConstant>(Delta);
2444 // The difference of the two coefficients might not be a product
2445 // or constant, in which case we give up on this direction.
2448 APInt ConstCoeff = Constant->getValue()->getValue();
2449 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2450 DEBUG(dbgs() << "\tRunningGCD = " << RunningGCD << "\n");
2451 if (RunningGCD != 0) {
2452 Remainder = ConstDelta.srem(RunningGCD);
2453 DEBUG(dbgs() << "\tRemainder = " << Remainder << "\n");
2454 if (Remainder != 0) {
2455 unsigned Level = mapSrcLoop(CurLoop);
2456 Result.DV[Level - 1].Direction &= unsigned(~Dependence::DVEntry::EQ);
2463 DEBUG(dbgs() << "all done\n");
2468 //===----------------------------------------------------------------------===//
2469 // banerjeeMIVtest -
2470 // Use Banerjee's Inequalities to test an MIV subscript pair.
2471 // (Wolfe, in the race-car book, calls this the Extreme Value Test.)
2472 // Generally follows the discussion in Section 2.5.2 of
2474 // Optimizing Supercompilers for Supercomputers
2477 // The inequalities given on page 25 are simplified in that loops are
2478 // normalized so that the lower bound is always 0 and the stride is always 1.
2479 // For example, Wolfe gives
2481 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2483 // where A_k is the coefficient of the kth index in the source subscript,
2484 // B_k is the coefficient of the kth index in the destination subscript,
2485 // U_k is the upper bound of the kth index, L_k is the lower bound of the Kth
2486 // index, and N_k is the stride of the kth index. Since all loops are normalized
2487 // by the SCEV package, N_k = 1 and L_k = 0, allowing us to simplify the
2490 // LB^<_k = (A^-_k - B_k)^- (U_k - 0 - 1) + (A_k - B_k)0 - B_k 1
2491 // = (A^-_k - B_k)^- (U_k - 1) - B_k
2493 // Similar simplifications are possible for the other equations.
2495 // When we can't determine the number of iterations for a loop,
2496 // we use NULL as an indicator for the worst case, infinity.
2497 // When computing the upper bound, NULL denotes +inf;
2498 // for the lower bound, NULL denotes -inf.
2500 // Return true if dependence disproved.
2501 bool DependenceAnalysis::banerjeeMIVtest(const SCEV *Src,
2503 const SmallBitVector &Loops,
2504 FullDependence &Result) const {
2505 DEBUG(dbgs() << "starting Banerjee\n");
2506 ++BanerjeeApplications;
2507 DEBUG(dbgs() << " Src = " << *Src << '\n');
2509 CoefficientInfo *A = collectCoeffInfo(Src, true, A0);
2510 DEBUG(dbgs() << " Dst = " << *Dst << '\n');
2512 CoefficientInfo *B = collectCoeffInfo(Dst, false, B0);
2513 BoundInfo *Bound = new BoundInfo[MaxLevels + 1];
2514 const SCEV *Delta = SE->getMinusSCEV(B0, A0);
2515 DEBUG(dbgs() << "\tDelta = " << *Delta << '\n');
2517 // Compute bounds for all the * directions.
2518 DEBUG(dbgs() << "\tBounds[*]\n");
2519 for (unsigned K = 1; K <= MaxLevels; ++K) {
2520 Bound[K].Iterations = A[K].Iterations ? A[K].Iterations : B[K].Iterations;
2521 Bound[K].Direction = Dependence::DVEntry::ALL;
2522 Bound[K].DirSet = Dependence::DVEntry::NONE;
2523 findBoundsALL(A, B, Bound, K);
2525 DEBUG(dbgs() << "\t " << K << '\t');
2526 if (Bound[K].Lower[Dependence::DVEntry::ALL])
2527 DEBUG(dbgs() << *Bound[K].Lower[Dependence::DVEntry::ALL] << '\t');
2529 DEBUG(dbgs() << "-inf\t");
2530 if (Bound[K].Upper[Dependence::DVEntry::ALL])
2531 DEBUG(dbgs() << *Bound[K].Upper[Dependence::DVEntry::ALL] << '\n');
2533 DEBUG(dbgs() << "+inf\n");
2537 // Test the *, *, *, ... case.
2538 bool Disproved = false;
2539 if (testBounds(Dependence::DVEntry::ALL, 0, Bound, Delta)) {
2540 // Explore the direction vector hierarchy.
2541 unsigned DepthExpanded = 0;
2542 unsigned NewDeps = exploreDirections(1, A, B, Bound,
2543 Loops, DepthExpanded, Delta);
2545 bool Improved = false;
2546 for (unsigned K = 1; K <= CommonLevels; ++K) {
2548 unsigned Old = Result.DV[K - 1].Direction;
2549 Result.DV[K - 1].Direction = Old & Bound[K].DirSet;
2550 Improved |= Old != Result.DV[K - 1].Direction;
2551 if (!Result.DV[K - 1].Direction) {
2559 ++BanerjeeSuccesses;
2562 ++BanerjeeIndependence;
2567 ++BanerjeeIndependence;
2577 // Hierarchically expands the direction vector
2578 // search space, combining the directions of discovered dependences
2579 // in the DirSet field of Bound. Returns the number of distinct
2580 // dependences discovered. If the dependence is disproved,
2581 // it will return 0.
2582 unsigned DependenceAnalysis::exploreDirections(unsigned Level,
2586 const SmallBitVector &Loops,
2587 unsigned &DepthExpanded,
2588 const SCEV *Delta) const {
2589 if (Level > CommonLevels) {
2591 DEBUG(dbgs() << "\t[");
2592 for (unsigned K = 1; K <= CommonLevels; ++K) {
2594 Bound[K].DirSet |= Bound[K].Direction;
2596 switch (Bound[K].Direction) {
2597 case Dependence::DVEntry::LT:
2598 DEBUG(dbgs() << " <");
2600 case Dependence::DVEntry::EQ:
2601 DEBUG(dbgs() << " =");
2603 case Dependence::DVEntry::GT:
2604 DEBUG(dbgs() << " >");
2606 case Dependence::DVEntry::ALL:
2607 DEBUG(dbgs() << " *");
2610 llvm_unreachable("unexpected Bound[K].Direction");
2615 DEBUG(dbgs() << " ]\n");
2619 if (Level > DepthExpanded) {
2620 DepthExpanded = Level;
2621 // compute bounds for <, =, > at current level
2622 findBoundsLT(A, B, Bound, Level);
2623 findBoundsGT(A, B, Bound, Level);
2624 findBoundsEQ(A, B, Bound, Level);
2626 DEBUG(dbgs() << "\tBound for level = " << Level << '\n');
2627 DEBUG(dbgs() << "\t <\t");
2628 if (Bound[Level].Lower[Dependence::DVEntry::LT])
2629 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::LT] << '\t');
2631 DEBUG(dbgs() << "-inf\t");
2632 if (Bound[Level].Upper[Dependence::DVEntry::LT])
2633 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::LT] << '\n');
2635 DEBUG(dbgs() << "+inf\n");
2636 DEBUG(dbgs() << "\t =\t");
2637 if (Bound[Level].Lower[Dependence::DVEntry::EQ])
2638 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::EQ] << '\t');
2640 DEBUG(dbgs() << "-inf\t");
2641 if (Bound[Level].Upper[Dependence::DVEntry::EQ])
2642 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::EQ] << '\n');
2644 DEBUG(dbgs() << "+inf\n");
2645 DEBUG(dbgs() << "\t >\t");
2646 if (Bound[Level].Lower[Dependence::DVEntry::GT])
2647 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::GT] << '\t');
2649 DEBUG(dbgs() << "-inf\t");
2650 if (Bound[Level].Upper[Dependence::DVEntry::GT])
2651 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::GT] << '\n');
2653 DEBUG(dbgs() << "+inf\n");
2657 unsigned NewDeps = 0;
2659 // test bounds for <, *, *, ...
2660 if (testBounds(Dependence::DVEntry::LT, Level, Bound, Delta))
2661 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2662 Loops, DepthExpanded, Delta);
2664 // Test bounds for =, *, *, ...
2665 if (testBounds(Dependence::DVEntry::EQ, Level, Bound, Delta))
2666 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2667 Loops, DepthExpanded, Delta);
2669 // test bounds for >, *, *, ...
2670 if (testBounds(Dependence::DVEntry::GT, Level, Bound, Delta))
2671 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2672 Loops, DepthExpanded, Delta);
2674 Bound[Level].Direction = Dependence::DVEntry::ALL;
2678 return exploreDirections(Level + 1, A, B, Bound, Loops, DepthExpanded, Delta);
2682 // Returns true iff the current bounds are plausible.
2683 bool DependenceAnalysis::testBounds(unsigned char DirKind,
2686 const SCEV *Delta) const {
2687 Bound[Level].Direction = DirKind;
2688 if (const SCEV *LowerBound = getLowerBound(Bound))
2689 if (isKnownPredicate(CmpInst::ICMP_SGT, LowerBound, Delta))
2691 if (const SCEV *UpperBound = getUpperBound(Bound))
2692 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, UpperBound))
2698 // Computes the upper and lower bounds for level K
2699 // using the * direction. Records them in Bound.
2700 // Wolfe gives the equations
2702 // LB^*_k = (A^-_k - B^+_k)(U_k - L_k) + (A_k - B_k)L_k
2703 // UB^*_k = (A^+_k - B^-_k)(U_k - L_k) + (A_k - B_k)L_k
2705 // Since we normalize loops, we can simplify these equations to
2707 // LB^*_k = (A^-_k - B^+_k)U_k
2708 // UB^*_k = (A^+_k - B^-_k)U_k
2710 // We must be careful to handle the case where the upper bound is unknown.
2711 // Note that the lower bound is always <= 0
2712 // and the upper bound is always >= 0.
2713 void DependenceAnalysis::findBoundsALL(CoefficientInfo *A,
2717 Bound[K].Lower[Dependence::DVEntry::ALL] = nullptr; // Default value = -infinity.
2718 Bound[K].Upper[Dependence::DVEntry::ALL] = nullptr; // Default value = +infinity.
2719 if (Bound[K].Iterations) {
2720 Bound[K].Lower[Dependence::DVEntry::ALL] =
2721 SE->getMulExpr(SE->getMinusSCEV(A[K].NegPart, B[K].PosPart),
2722 Bound[K].Iterations);
2723 Bound[K].Upper[Dependence::DVEntry::ALL] =
2724 SE->getMulExpr(SE->getMinusSCEV(A[K].PosPart, B[K].NegPart),
2725 Bound[K].Iterations);
2728 // If the difference is 0, we won't need to know the number of iterations.
2729 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].NegPart, B[K].PosPart))
2730 Bound[K].Lower[Dependence::DVEntry::ALL] =
2731 SE->getConstant(A[K].Coeff->getType(), 0);
2732 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].PosPart, B[K].NegPart))
2733 Bound[K].Upper[Dependence::DVEntry::ALL] =
2734 SE->getConstant(A[K].Coeff->getType(), 0);
2739 // Computes the upper and lower bounds for level K
2740 // using the = direction. Records them in Bound.
2741 // Wolfe gives the equations
2743 // LB^=_k = (A_k - B_k)^- (U_k - L_k) + (A_k - B_k)L_k
2744 // UB^=_k = (A_k - B_k)^+ (U_k - L_k) + (A_k - B_k)L_k
2746 // Since we normalize loops, we can simplify these equations to
2748 // LB^=_k = (A_k - B_k)^- U_k
2749 // UB^=_k = (A_k - B_k)^+ U_k
2751 // We must be careful to handle the case where the upper bound is unknown.
2752 // Note that the lower bound is always <= 0
2753 // and the upper bound is always >= 0.
2754 void DependenceAnalysis::findBoundsEQ(CoefficientInfo *A,
2758 Bound[K].Lower[Dependence::DVEntry::EQ] = nullptr; // Default value = -infinity.
2759 Bound[K].Upper[Dependence::DVEntry::EQ] = nullptr; // Default value = +infinity.
2760 if (Bound[K].Iterations) {
2761 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2762 const SCEV *NegativePart = getNegativePart(Delta);
2763 Bound[K].Lower[Dependence::DVEntry::EQ] =
2764 SE->getMulExpr(NegativePart, Bound[K].Iterations);
2765 const SCEV *PositivePart = getPositivePart(Delta);
2766 Bound[K].Upper[Dependence::DVEntry::EQ] =
2767 SE->getMulExpr(PositivePart, Bound[K].Iterations);
2770 // If the positive/negative part of the difference is 0,
2771 // we won't need to know the number of iterations.
2772 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2773 const SCEV *NegativePart = getNegativePart(Delta);
2774 if (NegativePart->isZero())
2775 Bound[K].Lower[Dependence::DVEntry::EQ] = NegativePart; // Zero
2776 const SCEV *PositivePart = getPositivePart(Delta);
2777 if (PositivePart->isZero())
2778 Bound[K].Upper[Dependence::DVEntry::EQ] = PositivePart; // Zero
2783 // Computes the upper and lower bounds for level K
2784 // using the < direction. Records them in Bound.
2785 // Wolfe gives the equations
2787 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2788 // UB^<_k = (A^+_k - B_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2790 // Since we normalize loops, we can simplify these equations to
2792 // LB^<_k = (A^-_k - B_k)^- (U_k - 1) - B_k
2793 // UB^<_k = (A^+_k - B_k)^+ (U_k - 1) - B_k
2795 // We must be careful to handle the case where the upper bound is unknown.
2796 void DependenceAnalysis::findBoundsLT(CoefficientInfo *A,
2800 Bound[K].Lower[Dependence::DVEntry::LT] = nullptr; // Default value = -infinity.
2801 Bound[K].Upper[Dependence::DVEntry::LT] = nullptr; // Default value = +infinity.
2802 if (Bound[K].Iterations) {
2803 const SCEV *Iter_1 =
2804 SE->getMinusSCEV(Bound[K].Iterations,
2805 SE->getConstant(Bound[K].Iterations->getType(), 1));
2806 const SCEV *NegPart =
2807 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2808 Bound[K].Lower[Dependence::DVEntry::LT] =
2809 SE->getMinusSCEV(SE->getMulExpr(NegPart, Iter_1), B[K].Coeff);
2810 const SCEV *PosPart =
2811 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2812 Bound[K].Upper[Dependence::DVEntry::LT] =
2813 SE->getMinusSCEV(SE->getMulExpr(PosPart, Iter_1), B[K].Coeff);
2816 // If the positive/negative part of the difference is 0,
2817 // we won't need to know the number of iterations.
2818 const SCEV *NegPart =
2819 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2820 if (NegPart->isZero())
2821 Bound[K].Lower[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2822 const SCEV *PosPart =
2823 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2824 if (PosPart->isZero())
2825 Bound[K].Upper[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2830 // Computes the upper and lower bounds for level K
2831 // using the > direction. Records them in Bound.
2832 // Wolfe gives the equations
2834 // LB^>_k = (A_k - B^+_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2835 // UB^>_k = (A_k - B^-_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2837 // Since we normalize loops, we can simplify these equations to
2839 // LB^>_k = (A_k - B^+_k)^- (U_k - 1) + A_k
2840 // UB^>_k = (A_k - B^-_k)^+ (U_k - 1) + A_k
2842 // We must be careful to handle the case where the upper bound is unknown.
2843 void DependenceAnalysis::findBoundsGT(CoefficientInfo *A,
2847 Bound[K].Lower[Dependence::DVEntry::GT] = nullptr; // Default value = -infinity.
2848 Bound[K].Upper[Dependence::DVEntry::GT] = nullptr; // Default value = +infinity.
2849 if (Bound[K].Iterations) {
2850 const SCEV *Iter_1 =
2851 SE->getMinusSCEV(Bound[K].Iterations,
2852 SE->getConstant(Bound[K].Iterations->getType(), 1));
2853 const SCEV *NegPart =
2854 getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2855 Bound[K].Lower[Dependence::DVEntry::GT] =
2856 SE->getAddExpr(SE->getMulExpr(NegPart, Iter_1), A[K].Coeff);
2857 const SCEV *PosPart =
2858 getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2859 Bound[K].Upper[Dependence::DVEntry::GT] =
2860 SE->getAddExpr(SE->getMulExpr(PosPart, Iter_1), A[K].Coeff);
2863 // If the positive/negative part of the difference is 0,
2864 // we won't need to know the number of iterations.
2865 const SCEV *NegPart = getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2866 if (NegPart->isZero())
2867 Bound[K].Lower[Dependence::DVEntry::GT] = A[K].Coeff;
2868 const SCEV *PosPart = getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2869 if (PosPart->isZero())
2870 Bound[K].Upper[Dependence::DVEntry::GT] = A[K].Coeff;
2876 const SCEV *DependenceAnalysis::getPositivePart(const SCEV *X) const {
2877 return SE->getSMaxExpr(X, SE->getConstant(X->getType(), 0));
2882 const SCEV *DependenceAnalysis::getNegativePart(const SCEV *X) const {
2883 return SE->getSMinExpr(X, SE->getConstant(X->getType(), 0));
2887 // Walks through the subscript,
2888 // collecting each coefficient, the associated loop bounds,
2889 // and recording its positive and negative parts for later use.
2890 DependenceAnalysis::CoefficientInfo *
2891 DependenceAnalysis::collectCoeffInfo(const SCEV *Subscript,
2893 const SCEV *&Constant) const {
2894 const SCEV *Zero = SE->getConstant(Subscript->getType(), 0);
2895 CoefficientInfo *CI = new CoefficientInfo[MaxLevels + 1];
2896 for (unsigned K = 1; K <= MaxLevels; ++K) {
2898 CI[K].PosPart = Zero;
2899 CI[K].NegPart = Zero;
2900 CI[K].Iterations = nullptr;
2902 while (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Subscript)) {
2903 const Loop *L = AddRec->getLoop();
2904 unsigned K = SrcFlag ? mapSrcLoop(L) : mapDstLoop(L);
2905 CI[K].Coeff = AddRec->getStepRecurrence(*SE);
2906 CI[K].PosPart = getPositivePart(CI[K].Coeff);
2907 CI[K].NegPart = getNegativePart(CI[K].Coeff);
2908 CI[K].Iterations = collectUpperBound(L, Subscript->getType());
2909 Subscript = AddRec->getStart();
2911 Constant = Subscript;
2913 DEBUG(dbgs() << "\tCoefficient Info\n");
2914 for (unsigned K = 1; K <= MaxLevels; ++K) {
2915 DEBUG(dbgs() << "\t " << K << "\t" << *CI[K].Coeff);
2916 DEBUG(dbgs() << "\tPos Part = ");
2917 DEBUG(dbgs() << *CI[K].PosPart);
2918 DEBUG(dbgs() << "\tNeg Part = ");
2919 DEBUG(dbgs() << *CI[K].NegPart);
2920 DEBUG(dbgs() << "\tUpper Bound = ");
2921 if (CI[K].Iterations)
2922 DEBUG(dbgs() << *CI[K].Iterations);
2924 DEBUG(dbgs() << "+inf");
2925 DEBUG(dbgs() << '\n');
2927 DEBUG(dbgs() << "\t Constant = " << *Subscript << '\n');
2933 // Looks through all the bounds info and
2934 // computes the lower bound given the current direction settings
2935 // at each level. If the lower bound for any level is -inf,
2936 // the result is -inf.
2937 const SCEV *DependenceAnalysis::getLowerBound(BoundInfo *Bound) const {
2938 const SCEV *Sum = Bound[1].Lower[Bound[1].Direction];
2939 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2940 if (Bound[K].Lower[Bound[K].Direction])
2941 Sum = SE->getAddExpr(Sum, Bound[K].Lower[Bound[K].Direction]);
2949 // Looks through all the bounds info and
2950 // computes the upper bound given the current direction settings
2951 // at each level. If the upper bound at any level is +inf,
2952 // the result is +inf.
2953 const SCEV *DependenceAnalysis::getUpperBound(BoundInfo *Bound) const {
2954 const SCEV *Sum = Bound[1].Upper[Bound[1].Direction];
2955 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2956 if (Bound[K].Upper[Bound[K].Direction])
2957 Sum = SE->getAddExpr(Sum, Bound[K].Upper[Bound[K].Direction]);
2965 //===----------------------------------------------------------------------===//
2966 // Constraint manipulation for Delta test.
2968 // Given a linear SCEV,
2969 // return the coefficient (the step)
2970 // corresponding to the specified loop.
2971 // If there isn't one, return 0.
2972 // For example, given a*i + b*j + c*k, finding the coefficient
2973 // corresponding to the j loop would yield b.
2974 const SCEV *DependenceAnalysis::findCoefficient(const SCEV *Expr,
2975 const Loop *TargetLoop) const {
2976 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2978 return SE->getConstant(Expr->getType(), 0);
2979 if (AddRec->getLoop() == TargetLoop)
2980 return AddRec->getStepRecurrence(*SE);
2981 return findCoefficient(AddRec->getStart(), TargetLoop);
2985 // Given a linear SCEV,
2986 // return the SCEV given by zeroing out the coefficient
2987 // corresponding to the specified loop.
2988 // For example, given a*i + b*j + c*k, zeroing the coefficient
2989 // corresponding to the j loop would yield a*i + c*k.
2990 const SCEV *DependenceAnalysis::zeroCoefficient(const SCEV *Expr,
2991 const Loop *TargetLoop) const {
2992 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2994 return Expr; // ignore
2995 if (AddRec->getLoop() == TargetLoop)
2996 return AddRec->getStart();
2997 return SE->getAddRecExpr(zeroCoefficient(AddRec->getStart(), TargetLoop),
2998 AddRec->getStepRecurrence(*SE),
3000 AddRec->getNoWrapFlags());
3004 // Given a linear SCEV Expr,
3005 // return the SCEV given by adding some Value to the
3006 // coefficient corresponding to the specified TargetLoop.
3007 // For example, given a*i + b*j + c*k, adding 1 to the coefficient
3008 // corresponding to the j loop would yield a*i + (b+1)*j + c*k.
3009 const SCEV *DependenceAnalysis::addToCoefficient(const SCEV *Expr,
3010 const Loop *TargetLoop,
3011 const SCEV *Value) const {
3012 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
3013 if (!AddRec) // create a new addRec
3014 return SE->getAddRecExpr(Expr,
3017 SCEV::FlagAnyWrap); // Worst case, with no info.
3018 if (AddRec->getLoop() == TargetLoop) {
3019 const SCEV *Sum = SE->getAddExpr(AddRec->getStepRecurrence(*SE), Value);
3021 return AddRec->getStart();
3022 return SE->getAddRecExpr(AddRec->getStart(),
3025 AddRec->getNoWrapFlags());
3027 if (SE->isLoopInvariant(AddRec, TargetLoop))
3028 return SE->getAddRecExpr(AddRec, Value, TargetLoop, SCEV::FlagAnyWrap);
3029 return SE->getAddRecExpr(
3030 addToCoefficient(AddRec->getStart(), TargetLoop, Value),
3031 AddRec->getStepRecurrence(*SE), AddRec->getLoop(),
3032 AddRec->getNoWrapFlags());
3036 // Review the constraints, looking for opportunities
3037 // to simplify a subscript pair (Src and Dst).
3038 // Return true if some simplification occurs.
3039 // If the simplification isn't exact (that is, if it is conservative
3040 // in terms of dependence), set consistent to false.
3041 // Corresponds to Figure 5 from the paper
3043 // Practical Dependence Testing
3044 // Goff, Kennedy, Tseng
3046 bool DependenceAnalysis::propagate(const SCEV *&Src,
3048 SmallBitVector &Loops,
3049 SmallVectorImpl<Constraint> &Constraints,
3051 bool Result = false;
3052 for (int LI = Loops.find_first(); LI >= 0; LI = Loops.find_next(LI)) {
3053 DEBUG(dbgs() << "\t Constraint[" << LI << "] is");
3054 DEBUG(Constraints[LI].dump(dbgs()));
3055 if (Constraints[LI].isDistance())
3056 Result |= propagateDistance(Src, Dst, Constraints[LI], Consistent);
3057 else if (Constraints[LI].isLine())
3058 Result |= propagateLine(Src, Dst, Constraints[LI], Consistent);
3059 else if (Constraints[LI].isPoint())
3060 Result |= propagatePoint(Src, Dst, Constraints[LI]);
3066 // Attempt to propagate a distance
3067 // constraint into a subscript pair (Src and Dst).
3068 // Return true if some simplification occurs.
3069 // If the simplification isn't exact (that is, if it is conservative
3070 // in terms of dependence), set consistent to false.
3071 bool DependenceAnalysis::propagateDistance(const SCEV *&Src,
3073 Constraint &CurConstraint,
3075 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3076 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3077 const SCEV *A_K = findCoefficient(Src, CurLoop);
3080 const SCEV *DA_K = SE->getMulExpr(A_K, CurConstraint.getD());
3081 Src = SE->getMinusSCEV(Src, DA_K);
3082 Src = zeroCoefficient(Src, CurLoop);
3083 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3084 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3085 Dst = addToCoefficient(Dst, CurLoop, SE->getNegativeSCEV(A_K));
3086 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3087 if (!findCoefficient(Dst, CurLoop)->isZero())
3093 // Attempt to propagate a line
3094 // constraint into a subscript pair (Src and Dst).
3095 // Return true if some simplification occurs.
3096 // If the simplification isn't exact (that is, if it is conservative
3097 // in terms of dependence), set consistent to false.
3098 bool DependenceAnalysis::propagateLine(const SCEV *&Src,
3100 Constraint &CurConstraint,
3102 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3103 const SCEV *A = CurConstraint.getA();
3104 const SCEV *B = CurConstraint.getB();
3105 const SCEV *C = CurConstraint.getC();
3106 DEBUG(dbgs() << "\t\tA = " << *A << ", B = " << *B << ", C = " << *C << "\n");
3107 DEBUG(dbgs() << "\t\tSrc = " << *Src << "\n");
3108 DEBUG(dbgs() << "\t\tDst = " << *Dst << "\n");
3110 const SCEVConstant *Bconst = dyn_cast<SCEVConstant>(B);
3111 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3112 if (!Bconst || !Cconst) return false;
3113 APInt Beta = Bconst->getValue()->getValue();
3114 APInt Charlie = Cconst->getValue()->getValue();
3115 APInt CdivB = Charlie.sdiv(Beta);
3116 assert(Charlie.srem(Beta) == 0 && "C should be evenly divisible by B");
3117 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3118 // Src = SE->getAddExpr(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3119 Src = SE->getMinusSCEV(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3120 Dst = zeroCoefficient(Dst, CurLoop);
3121 if (!findCoefficient(Src, CurLoop)->isZero())
3124 else if (B->isZero()) {
3125 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3126 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3127 if (!Aconst || !Cconst) return false;
3128 APInt Alpha = Aconst->getValue()->getValue();
3129 APInt Charlie = Cconst->getValue()->getValue();
3130 APInt CdivA = Charlie.sdiv(Alpha);
3131 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3132 const SCEV *A_K = findCoefficient(Src, CurLoop);
3133 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3134 Src = zeroCoefficient(Src, CurLoop);
3135 if (!findCoefficient(Dst, CurLoop)->isZero())
3138 else if (isKnownPredicate(CmpInst::ICMP_EQ, A, B)) {
3139 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3140 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3141 if (!Aconst || !Cconst) return false;
3142 APInt Alpha = Aconst->getValue()->getValue();
3143 APInt Charlie = Cconst->getValue()->getValue();
3144 APInt CdivA = Charlie.sdiv(Alpha);
3145 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3146 const SCEV *A_K = findCoefficient(Src, CurLoop);
3147 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3148 Src = zeroCoefficient(Src, CurLoop);
3149 Dst = addToCoefficient(Dst, CurLoop, A_K);
3150 if (!findCoefficient(Dst, CurLoop)->isZero())
3154 // paper is incorrect here, or perhaps just misleading
3155 const SCEV *A_K = findCoefficient(Src, CurLoop);
3156 Src = SE->getMulExpr(Src, A);
3157 Dst = SE->getMulExpr(Dst, A);
3158 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, C));
3159 Src = zeroCoefficient(Src, CurLoop);
3160 Dst = addToCoefficient(Dst, CurLoop, SE->getMulExpr(A_K, B));
3161 if (!findCoefficient(Dst, CurLoop)->isZero())
3164 DEBUG(dbgs() << "\t\tnew Src = " << *Src << "\n");
3165 DEBUG(dbgs() << "\t\tnew Dst = " << *Dst << "\n");
3170 // Attempt to propagate a point
3171 // constraint into a subscript pair (Src and Dst).
3172 // Return true if some simplification occurs.
3173 bool DependenceAnalysis::propagatePoint(const SCEV *&Src,
3175 Constraint &CurConstraint) {
3176 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3177 const SCEV *A_K = findCoefficient(Src, CurLoop);
3178 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3179 const SCEV *XA_K = SE->getMulExpr(A_K, CurConstraint.getX());
3180 const SCEV *YAP_K = SE->getMulExpr(AP_K, CurConstraint.getY());
3181 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3182 Src = SE->getAddExpr(Src, SE->getMinusSCEV(XA_K, YAP_K));
3183 Src = zeroCoefficient(Src, CurLoop);
3184 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3185 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3186 Dst = zeroCoefficient(Dst, CurLoop);
3187 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3192 // Update direction vector entry based on the current constraint.
3193 void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
3194 const Constraint &CurConstraint
3196 DEBUG(dbgs() << "\tUpdate direction, constraint =");
3197 DEBUG(CurConstraint.dump(dbgs()));
3198 if (CurConstraint.isAny())
3200 else if (CurConstraint.isDistance()) {
3201 // this one is consistent, the others aren't
3202 Level.Scalar = false;
3203 Level.Distance = CurConstraint.getD();
3204 unsigned NewDirection = Dependence::DVEntry::NONE;
3205 if (!SE->isKnownNonZero(Level.Distance)) // if may be zero
3206 NewDirection = Dependence::DVEntry::EQ;
3207 if (!SE->isKnownNonPositive(Level.Distance)) // if may be positive
3208 NewDirection |= Dependence::DVEntry::LT;
3209 if (!SE->isKnownNonNegative(Level.Distance)) // if may be negative
3210 NewDirection |= Dependence::DVEntry::GT;
3211 Level.Direction &= NewDirection;
3213 else if (CurConstraint.isLine()) {
3214 Level.Scalar = false;
3215 Level.Distance = nullptr;
3216 // direction should be accurate
3218 else if (CurConstraint.isPoint()) {
3219 Level.Scalar = false;
3220 Level.Distance = nullptr;
3221 unsigned NewDirection = Dependence::DVEntry::NONE;
3222 if (!isKnownPredicate(CmpInst::ICMP_NE,
3223 CurConstraint.getY(),
3224 CurConstraint.getX()))
3226 NewDirection |= Dependence::DVEntry::EQ;
3227 if (!isKnownPredicate(CmpInst::ICMP_SLE,
3228 CurConstraint.getY(),
3229 CurConstraint.getX()))
3231 NewDirection |= Dependence::DVEntry::LT;
3232 if (!isKnownPredicate(CmpInst::ICMP_SGE,
3233 CurConstraint.getY(),
3234 CurConstraint.getX()))
3236 NewDirection |= Dependence::DVEntry::GT;
3237 Level.Direction &= NewDirection;
3240 llvm_unreachable("constraint has unexpected kind");
3243 /// Check if we can delinearize the subscripts. If the SCEVs representing the
3244 /// source and destination array references are recurrences on a nested loop,
3245 /// this function flattens the nested recurrences into separate recurrences
3246 /// for each loop level.
3247 bool DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV,
3248 const SCEV *DstSCEV,
3249 SmallVectorImpl<Subscript> &Pair,
3250 const SCEV *ElementSize) {
3251 const SCEVUnknown *SrcBase =
3252 dyn_cast<SCEVUnknown>(SE->getPointerBase(SrcSCEV));
3253 const SCEVUnknown *DstBase =
3254 dyn_cast<SCEVUnknown>(SE->getPointerBase(DstSCEV));
3256 if (!SrcBase || !DstBase || SrcBase != DstBase)
3259 SrcSCEV = SE->getMinusSCEV(SrcSCEV, SrcBase);
3260 DstSCEV = SE->getMinusSCEV(DstSCEV, DstBase);
3262 const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
3263 const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
3264 if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
3267 // First step: collect parametric terms in both array references.
3268 SmallVector<const SCEV *, 4> Terms;
3269 SE->collectParametricTerms(SrcAR, Terms);
3270 SE->collectParametricTerms(DstAR, Terms);
3272 // Second step: find subscript sizes.
3273 SmallVector<const SCEV *, 4> Sizes;
3274 SE->findArrayDimensions(Terms, Sizes, ElementSize);
3276 // Third step: compute the access functions for each subscript.
3277 SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts;
3278 SE->computeAccessFunctions(SrcAR, SrcSubscripts, Sizes);
3279 SE->computeAccessFunctions(DstAR, DstSubscripts, Sizes);
3281 // Fail when there is only a subscript: that's a linearized access function.
3282 if (SrcSubscripts.size() < 2 || DstSubscripts.size() < 2 ||
3283 SrcSubscripts.size() != DstSubscripts.size())
3286 int size = SrcSubscripts.size();
3289 dbgs() << "\nSrcSubscripts: ";
3290 for (int i = 0; i < size; i++)
3291 dbgs() << *SrcSubscripts[i];
3292 dbgs() << "\nDstSubscripts: ";
3293 for (int i = 0; i < size; i++)
3294 dbgs() << *DstSubscripts[i];
3297 // The delinearization transforms a single-subscript MIV dependence test into
3298 // a multi-subscript SIV dependence test that is easier to compute. So we
3299 // resize Pair to contain as many pairs of subscripts as the delinearization
3300 // has found, and then initialize the pairs following the delinearization.
3302 for (int i = 0; i < size; ++i) {
3303 Pair[i].Src = SrcSubscripts[i];
3304 Pair[i].Dst = DstSubscripts[i];
3305 unifySubscriptType(&Pair[i]);
3307 // FIXME: we should record the bounds SrcSizes[i] and DstSizes[i] that the
3308 // delinearization has found, and add these constraints to the dependence
3309 // check to avoid memory accesses overflow from one dimension into another.
3310 // This is related to the problem of determining the existence of data
3311 // dependences in array accesses using a different number of subscripts: in
3312 // C one can access an array A[100][100]; as A[0][9999], *A[9999], etc.
3318 //===----------------------------------------------------------------------===//
3321 // For debugging purposes, dump a small bit vector to dbgs().
3322 static void dumpSmallBitVector(SmallBitVector &BV) {
3324 for (int VI = BV.find_first(); VI >= 0; VI = BV.find_next(VI)) {
3326 if (BV.find_next(VI) >= 0)
3335 // Returns NULL if there is no dependence.
3336 // Otherwise, return a Dependence with as many details as possible.
3337 // Corresponds to Section 3.1 in the paper
3339 // Practical Dependence Testing
3340 // Goff, Kennedy, Tseng
3343 // Care is required to keep the routine below, getSplitIteration(),
3344 // up to date with respect to this routine.
3345 std::unique_ptr<Dependence>
3346 DependenceAnalysis::depends(Instruction *Src, Instruction *Dst,
3347 bool PossiblyLoopIndependent) {
3349 PossiblyLoopIndependent = false;
3351 if ((!Src->mayReadFromMemory() && !Src->mayWriteToMemory()) ||
3352 (!Dst->mayReadFromMemory() && !Dst->mayWriteToMemory()))
3353 // if both instructions don't reference memory, there's no dependence
3356 if (!isLoadOrStore(Src) || !isLoadOrStore(Dst)) {
3357 // can only analyze simple loads and stores, i.e., no calls, invokes, etc.
3358 DEBUG(dbgs() << "can only handle simple loads and stores\n");
3359 return make_unique<Dependence>(Src, Dst);
3362 Value *SrcPtr = getPointerOperand(Src);
3363 Value *DstPtr = getPointerOperand(Dst);
3365 switch (underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3369 // cannot analyse objects if we don't understand their aliasing.
3370 DEBUG(dbgs() << "can't analyze may or partial alias\n");
3371 return make_unique<Dependence>(Src, Dst);
3373 // If the objects noalias, they are distinct, accesses are independent.
3374 DEBUG(dbgs() << "no alias\n");
3377 break; // The underlying objects alias; test accesses for dependence.
3380 // establish loop nesting levels
3381 establishNestingLevels(Src, Dst);
3382 DEBUG(dbgs() << " common nesting levels = " << CommonLevels << "\n");
3383 DEBUG(dbgs() << " maximum nesting levels = " << MaxLevels << "\n");
3385 FullDependence Result(Src, Dst, PossiblyLoopIndependent, CommonLevels);
3388 // See if there are GEPs we can use.
3389 bool UsefulGEP = false;
3390 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3391 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3392 if (SrcGEP && DstGEP &&
3393 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3394 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3395 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3396 DEBUG(dbgs() << " SrcPtrSCEV = " << *SrcPtrSCEV << "\n");
3397 DEBUG(dbgs() << " DstPtrSCEV = " << *DstPtrSCEV << "\n");
3399 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3400 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3401 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3403 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3404 SmallVector<Subscript, 4> Pair(Pairs);
3406 DEBUG(dbgs() << " using GEPs\n");
3408 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3409 SrcEnd = SrcGEP->idx_end(),
3410 DstIdx = DstGEP->idx_begin();
3412 ++SrcIdx, ++DstIdx, ++P) {
3413 Pair[P].Src = SE->getSCEV(*SrcIdx);
3414 Pair[P].Dst = SE->getSCEV(*DstIdx);
3415 unifySubscriptType(&Pair[P]);
3419 DEBUG(dbgs() << " ignoring GEPs\n");
3420 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3421 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3422 DEBUG(dbgs() << " SrcSCEV = " << *SrcSCEV << "\n");
3423 DEBUG(dbgs() << " DstSCEV = " << *DstSCEV << "\n");
3424 Pair[0].Src = SrcSCEV;
3425 Pair[0].Dst = DstSCEV;
3428 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3429 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3430 DEBUG(dbgs() << " delinerized GEP\n");
3431 Pairs = Pair.size();
3434 for (unsigned P = 0; P < Pairs; ++P) {
3435 Pair[P].Loops.resize(MaxLevels + 1);
3436 Pair[P].GroupLoops.resize(MaxLevels + 1);
3437 Pair[P].Group.resize(Pairs);
3438 removeMatchingExtensions(&Pair[P]);
3439 Pair[P].Classification =
3440 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3441 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3443 Pair[P].GroupLoops = Pair[P].Loops;
3444 Pair[P].Group.set(P);
3445 DEBUG(dbgs() << " subscript " << P << "\n");
3446 DEBUG(dbgs() << "\tsrc = " << *Pair[P].Src << "\n");
3447 DEBUG(dbgs() << "\tdst = " << *Pair[P].Dst << "\n");
3448 DEBUG(dbgs() << "\tclass = " << Pair[P].Classification << "\n");
3449 DEBUG(dbgs() << "\tloops = ");
3450 DEBUG(dumpSmallBitVector(Pair[P].Loops));
3453 SmallBitVector Separable(Pairs);
3454 SmallBitVector Coupled(Pairs);
3456 // Partition subscripts into separable and minimally-coupled groups
3457 // Algorithm in paper is algorithmically better;
3458 // this may be faster in practice. Check someday.
3460 // Here's an example of how it works. Consider this code:
3467 // A[i][j][k][m] = ...;
3468 // ... = A[0][j][l][i + j];
3475 // There are 4 subscripts here:
3479 // 3 [m] and [i + j]
3481 // We've already classified each subscript pair as ZIV, SIV, etc.,
3482 // and collected all the loops mentioned by pair P in Pair[P].Loops.
3483 // In addition, we've initialized Pair[P].GroupLoops to Pair[P].Loops
3484 // and set Pair[P].Group = {P}.
3486 // Src Dst Classification Loops GroupLoops Group
3487 // 0 [i] [0] SIV {1} {1} {0}
3488 // 1 [j] [j] SIV {2} {2} {1}
3489 // 2 [k] [l] RDIV {3,4} {3,4} {2}
3490 // 3 [m] [i + j] MIV {1,2,5} {1,2,5} {3}
3492 // For each subscript SI 0 .. 3, we consider each remaining subscript, SJ.
3493 // So, 0 is compared against 1, 2, and 3; 1 is compared against 2 and 3, etc.
3495 // We begin by comparing 0 and 1. The intersection of the GroupLoops is empty.
3496 // Next, 0 and 2. Again, the intersection of their GroupLoops is empty.
3497 // Next 0 and 3. The intersection of their GroupLoop = {1}, not empty,
3498 // so Pair[3].Group = {0,3} and Done = false (that is, 0 will not be added
3499 // to either Separable or Coupled).
3501 // Next, we consider 1 and 2. The intersection of the GroupLoops is empty.
3502 // Next, 1 and 3. The intersectionof their GroupLoops = {2}, not empty,
3503 // so Pair[3].Group = {0, 1, 3} and Done = false.
3505 // Next, we compare 2 against 3. The intersection of the GroupLoops is empty.
3506 // Since Done remains true, we add 2 to the set of Separable pairs.
3508 // Finally, we consider 3. There's nothing to compare it with,
3509 // so Done remains true and we add it to the Coupled set.
3510 // Pair[3].Group = {0, 1, 3} and GroupLoops = {1, 2, 5}.
3512 // In the end, we've got 1 separable subscript and 1 coupled group.
3513 for (unsigned SI = 0; SI < Pairs; ++SI) {
3514 if (Pair[SI].Classification == Subscript::NonLinear) {
3515 // ignore these, but collect loops for later
3516 ++NonlinearSubscriptPairs;
3517 collectCommonLoops(Pair[SI].Src,
3518 LI->getLoopFor(Src->getParent()),
3520 collectCommonLoops(Pair[SI].Dst,
3521 LI->getLoopFor(Dst->getParent()),
3523 Result.Consistent = false;
3524 } else if (Pair[SI].Classification == Subscript::ZIV) {
3529 // SIV, RDIV, or MIV, so check for coupled group
3531 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3532 SmallBitVector Intersection = Pair[SI].GroupLoops;
3533 Intersection &= Pair[SJ].GroupLoops;
3534 if (Intersection.any()) {
3535 // accumulate set of all the loops in group
3536 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3537 // accumulate set of all subscripts in group
3538 Pair[SJ].Group |= Pair[SI].Group;
3543 if (Pair[SI].Group.count() == 1) {
3545 ++SeparableSubscriptPairs;
3549 ++CoupledSubscriptPairs;
3555 DEBUG(dbgs() << " Separable = ");
3556 DEBUG(dumpSmallBitVector(Separable));
3557 DEBUG(dbgs() << " Coupled = ");
3558 DEBUG(dumpSmallBitVector(Coupled));
3560 Constraint NewConstraint;
3561 NewConstraint.setAny(SE);
3563 // test separable subscripts
3564 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3565 DEBUG(dbgs() << "testing subscript " << SI);
3566 switch (Pair[SI].Classification) {
3567 case Subscript::ZIV:
3568 DEBUG(dbgs() << ", ZIV\n");
3569 if (testZIV(Pair[SI].Src, Pair[SI].Dst, Result))
3572 case Subscript::SIV: {
3573 DEBUG(dbgs() << ", SIV\n");
3575 const SCEV *SplitIter = nullptr;
3576 if (testSIV(Pair[SI].Src, Pair[SI].Dst, Level, Result, NewConstraint,
3581 case Subscript::RDIV:
3582 DEBUG(dbgs() << ", RDIV\n");
3583 if (testRDIV(Pair[SI].Src, Pair[SI].Dst, Result))
3586 case Subscript::MIV:
3587 DEBUG(dbgs() << ", MIV\n");
3588 if (testMIV(Pair[SI].Src, Pair[SI].Dst, Pair[SI].Loops, Result))
3592 llvm_unreachable("subscript has unexpected classification");
3596 if (Coupled.count()) {
3597 // test coupled subscript groups
3598 DEBUG(dbgs() << "starting on coupled subscripts\n");
3599 DEBUG(dbgs() << "MaxLevels + 1 = " << MaxLevels + 1 << "\n");
3600 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3601 for (unsigned II = 0; II <= MaxLevels; ++II)
3602 Constraints[II].setAny(SE);
3603 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3604 DEBUG(dbgs() << "testing subscript group " << SI << " { ");
3605 SmallBitVector Group(Pair[SI].Group);
3606 SmallBitVector Sivs(Pairs);
3607 SmallBitVector Mivs(Pairs);
3608 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3609 SmallVector<Subscript *, 4> PairsInGroup;
3610 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3611 DEBUG(dbgs() << SJ << " ");
3612 if (Pair[SJ].Classification == Subscript::SIV)
3616 PairsInGroup.push_back(&Pair[SJ]);
3618 unifySubscriptType(PairsInGroup);
3619 DEBUG(dbgs() << "}\n");
3620 while (Sivs.any()) {
3621 bool Changed = false;
3622 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3623 DEBUG(dbgs() << "testing subscript " << SJ << ", SIV\n");
3624 // SJ is an SIV subscript that's part of the current coupled group
3626 const SCEV *SplitIter = nullptr;
3627 DEBUG(dbgs() << "SIV\n");
3628 if (testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level, Result, NewConstraint,
3631 ConstrainedLevels.set(Level);
3632 if (intersectConstraints(&Constraints[Level], &NewConstraint)) {
3633 if (Constraints[Level].isEmpty()) {
3634 ++DeltaIndependence;
3642 // propagate, possibly creating new SIVs and ZIVs
3643 DEBUG(dbgs() << " propagating\n");
3644 DEBUG(dbgs() << "\tMivs = ");
3645 DEBUG(dumpSmallBitVector(Mivs));
3646 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3647 // SJ is an MIV subscript that's part of the current coupled group
3648 DEBUG(dbgs() << "\tSJ = " << SJ << "\n");
3649 if (propagate(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops,
3650 Constraints, Result.Consistent)) {
3651 DEBUG(dbgs() << "\t Changed\n");
3652 ++DeltaPropagations;
3653 Pair[SJ].Classification =
3654 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3655 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3657 switch (Pair[SJ].Classification) {
3658 case Subscript::ZIV:
3659 DEBUG(dbgs() << "ZIV\n");
3660 if (testZIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3664 case Subscript::SIV:
3668 case Subscript::RDIV:
3669 case Subscript::MIV:
3672 llvm_unreachable("bad subscript classification");
3679 // test & propagate remaining RDIVs
3680 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3681 if (Pair[SJ].Classification == Subscript::RDIV) {
3682 DEBUG(dbgs() << "RDIV test\n");
3683 if (testRDIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3685 // I don't yet understand how to propagate RDIV results
3690 // test remaining MIVs
3691 // This code is temporary.
3692 // Better to somehow test all remaining subscripts simultaneously.
3693 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3694 if (Pair[SJ].Classification == Subscript::MIV) {
3695 DEBUG(dbgs() << "MIV test\n");
3696 if (testMIV(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops, Result))
3700 llvm_unreachable("expected only MIV subscripts at this point");
3703 // update Result.DV from constraint vector
3704 DEBUG(dbgs() << " updating\n");
3705 for (int SJ = ConstrainedLevels.find_first(); SJ >= 0;
3706 SJ = ConstrainedLevels.find_next(SJ)) {
3707 if (SJ > (int)CommonLevels)
3709 updateDirection(Result.DV[SJ - 1], Constraints[SJ]);
3710 if (Result.DV[SJ - 1].Direction == Dependence::DVEntry::NONE)
3716 // Make sure the Scalar flags are set correctly.
3717 SmallBitVector CompleteLoops(MaxLevels + 1);
3718 for (unsigned SI = 0; SI < Pairs; ++SI)
3719 CompleteLoops |= Pair[SI].Loops;
3720 for (unsigned II = 1; II <= CommonLevels; ++II)
3721 if (CompleteLoops[II])
3722 Result.DV[II - 1].Scalar = false;
3724 if (PossiblyLoopIndependent) {
3725 // Make sure the LoopIndependent flag is set correctly.
3726 // All directions must include equal, otherwise no
3727 // loop-independent dependence is possible.
3728 for (unsigned II = 1; II <= CommonLevels; ++II) {
3729 if (!(Result.getDirection(II) & Dependence::DVEntry::EQ)) {
3730 Result.LoopIndependent = false;
3736 // On the other hand, if all directions are equal and there's no
3737 // loop-independent dependence possible, then no dependence exists.
3738 bool AllEqual = true;
3739 for (unsigned II = 1; II <= CommonLevels; ++II) {
3740 if (Result.getDirection(II) != Dependence::DVEntry::EQ) {
3749 auto Final = make_unique<FullDependence>(Result);
3750 Result.DV = nullptr;
3751 return std::move(Final);
3756 //===----------------------------------------------------------------------===//
3757 // getSplitIteration -
3758 // Rather than spend rarely-used space recording the splitting iteration
3759 // during the Weak-Crossing SIV test, we re-compute it on demand.
3760 // The re-computation is basically a repeat of the entire dependence test,
3761 // though simplified since we know that the dependence exists.
3762 // It's tedious, since we must go through all propagations, etc.
3764 // Care is required to keep this code up to date with respect to the routine
3765 // above, depends().
3767 // Generally, the dependence analyzer will be used to build
3768 // a dependence graph for a function (basically a map from instructions
3769 // to dependences). Looking for cycles in the graph shows us loops
3770 // that cannot be trivially vectorized/parallelized.
3772 // We can try to improve the situation by examining all the dependences
3773 // that make up the cycle, looking for ones we can break.
3774 // Sometimes, peeling the first or last iteration of a loop will break
3775 // dependences, and we've got flags for those possibilities.
3776 // Sometimes, splitting a loop at some other iteration will do the trick,
3777 // and we've got a flag for that case. Rather than waste the space to
3778 // record the exact iteration (since we rarely know), we provide
3779 // a method that calculates the iteration. It's a drag that it must work
3780 // from scratch, but wonderful in that it's possible.
3782 // Here's an example:
3784 // for (i = 0; i < 10; i++)
3788 // There's a loop-carried flow dependence from the store to the load,
3789 // found by the weak-crossing SIV test. The dependence will have a flag,
3790 // indicating that the dependence can be broken by splitting the loop.
3791 // Calling getSplitIteration will return 5.
3792 // Splitting the loop breaks the dependence, like so:
3794 // for (i = 0; i <= 5; i++)
3797 // for (i = 6; i < 10; i++)
3801 // breaks the dependence and allows us to vectorize/parallelize
3803 const SCEV *DependenceAnalysis::getSplitIteration(const Dependence &Dep,
3804 unsigned SplitLevel) {
3805 assert(Dep.isSplitable(SplitLevel) &&
3806 "Dep should be splitable at SplitLevel");
3807 Instruction *Src = Dep.getSrc();
3808 Instruction *Dst = Dep.getDst();
3809 assert(Src->mayReadFromMemory() || Src->mayWriteToMemory());
3810 assert(Dst->mayReadFromMemory() || Dst->mayWriteToMemory());
3811 assert(isLoadOrStore(Src));
3812 assert(isLoadOrStore(Dst));
3813 Value *SrcPtr = getPointerOperand(Src);
3814 Value *DstPtr = getPointerOperand(Dst);
3815 assert(underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3816 SrcPtr) == MustAlias);
3818 // establish loop nesting levels
3819 establishNestingLevels(Src, Dst);
3821 FullDependence Result(Src, Dst, false, CommonLevels);
3823 // See if there are GEPs we can use.
3824 bool UsefulGEP = false;
3825 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3826 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3827 if (SrcGEP && DstGEP &&
3828 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3829 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3830 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3831 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3832 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3833 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3835 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3836 SmallVector<Subscript, 4> Pair(Pairs);
3839 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3840 SrcEnd = SrcGEP->idx_end(),
3841 DstIdx = DstGEP->idx_begin();
3843 ++SrcIdx, ++DstIdx, ++P) {
3844 Pair[P].Src = SE->getSCEV(*SrcIdx);
3845 Pair[P].Dst = SE->getSCEV(*DstIdx);
3849 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3850 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3851 Pair[0].Src = SrcSCEV;
3852 Pair[0].Dst = DstSCEV;
3855 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3856 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3857 DEBUG(dbgs() << " delinerized GEP\n");
3858 Pairs = Pair.size();
3861 for (unsigned P = 0; P < Pairs; ++P) {
3862 Pair[P].Loops.resize(MaxLevels + 1);
3863 Pair[P].GroupLoops.resize(MaxLevels + 1);
3864 Pair[P].Group.resize(Pairs);
3865 removeMatchingExtensions(&Pair[P]);
3866 Pair[P].Classification =
3867 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3868 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3870 Pair[P].GroupLoops = Pair[P].Loops;
3871 Pair[P].Group.set(P);
3874 SmallBitVector Separable(Pairs);
3875 SmallBitVector Coupled(Pairs);
3877 // partition subscripts into separable and minimally-coupled groups
3878 for (unsigned SI = 0; SI < Pairs; ++SI) {
3879 if (Pair[SI].Classification == Subscript::NonLinear) {
3880 // ignore these, but collect loops for later
3881 collectCommonLoops(Pair[SI].Src,
3882 LI->getLoopFor(Src->getParent()),
3884 collectCommonLoops(Pair[SI].Dst,
3885 LI->getLoopFor(Dst->getParent()),
3887 Result.Consistent = false;
3889 else if (Pair[SI].Classification == Subscript::ZIV)
3892 // SIV, RDIV, or MIV, so check for coupled group
3894 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3895 SmallBitVector Intersection = Pair[SI].GroupLoops;
3896 Intersection &= Pair[SJ].GroupLoops;
3897 if (Intersection.any()) {
3898 // accumulate set of all the loops in group
3899 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3900 // accumulate set of all subscripts in group
3901 Pair[SJ].Group |= Pair[SI].Group;
3906 if (Pair[SI].Group.count() == 1)
3914 Constraint NewConstraint;
3915 NewConstraint.setAny(SE);
3917 // test separable subscripts
3918 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3919 switch (Pair[SI].Classification) {
3920 case Subscript::SIV: {
3922 const SCEV *SplitIter = nullptr;
3923 (void) testSIV(Pair[SI].Src, Pair[SI].Dst, Level,
3924 Result, NewConstraint, SplitIter);
3925 if (Level == SplitLevel) {
3926 assert(SplitIter != nullptr);
3931 case Subscript::ZIV:
3932 case Subscript::RDIV:
3933 case Subscript::MIV:
3936 llvm_unreachable("subscript has unexpected classification");
3940 if (Coupled.count()) {
3941 // test coupled subscript groups
3942 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3943 for (unsigned II = 0; II <= MaxLevels; ++II)
3944 Constraints[II].setAny(SE);
3945 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3946 SmallBitVector Group(Pair[SI].Group);
3947 SmallBitVector Sivs(Pairs);
3948 SmallBitVector Mivs(Pairs);
3949 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3950 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3951 if (Pair[SJ].Classification == Subscript::SIV)
3956 while (Sivs.any()) {
3957 bool Changed = false;
3958 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3959 // SJ is an SIV subscript that's part of the current coupled group
3961 const SCEV *SplitIter = nullptr;
3962 (void) testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level,
3963 Result, NewConstraint, SplitIter);
3964 if (Level == SplitLevel && SplitIter)
3966 ConstrainedLevels.set(Level);
3967 if (intersectConstraints(&Constraints[Level], &NewConstraint))
3972 // propagate, possibly creating new SIVs and ZIVs
3973 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3974 // SJ is an MIV subscript that's part of the current coupled group
3975 if (propagate(Pair[SJ].Src, Pair[SJ].Dst,
3976 Pair[SJ].Loops, Constraints, Result.Consistent)) {
3977 Pair[SJ].Classification =
3978 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3979 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3981 switch (Pair[SJ].Classification) {
3982 case Subscript::ZIV:
3985 case Subscript::SIV:
3989 case Subscript::RDIV:
3990 case Subscript::MIV:
3993 llvm_unreachable("bad subscript classification");
4001 llvm_unreachable("somehow reached end of routine");