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 AliasAnalysis::AliasResult underlyingObjectsAlias(AliasAnalysis *AA,
629 const DataLayout &DL,
632 const Value *AObj = GetUnderlyingObject(A, DL);
633 const Value *BObj = GetUnderlyingObject(B, DL);
634 return AA->alias(AObj, AA->getTypeStoreSize(AObj->getType()),
635 BObj, AA->getTypeStoreSize(BObj->getType()));
639 // Returns true if the load or store can be analyzed. Atomic and volatile
640 // operations have properties which this analysis does not understand.
642 bool isLoadOrStore(const Instruction *I) {
643 if (const LoadInst *LI = dyn_cast<LoadInst>(I))
644 return LI->isUnordered();
645 else if (const StoreInst *SI = dyn_cast<StoreInst>(I))
646 return SI->isUnordered();
652 Value *getPointerOperand(Instruction *I) {
653 if (LoadInst *LI = dyn_cast<LoadInst>(I))
654 return LI->getPointerOperand();
655 if (StoreInst *SI = dyn_cast<StoreInst>(I))
656 return SI->getPointerOperand();
657 llvm_unreachable("Value is not load or store instruction");
662 // Examines the loop nesting of the Src and Dst
663 // instructions and establishes their shared loops. Sets the variables
664 // CommonLevels, SrcLevels, and MaxLevels.
665 // The source and destination instructions needn't be contained in the same
666 // loop. The routine establishNestingLevels finds the level of most deeply
667 // nested loop that contains them both, CommonLevels. An instruction that's
668 // not contained in a loop is at level = 0. MaxLevels is equal to the level
669 // of the source plus the level of the destination, minus CommonLevels.
670 // This lets us allocate vectors MaxLevels in length, with room for every
671 // distinct loop referenced in both the source and destination subscripts.
672 // The variable SrcLevels is the nesting depth of the source instruction.
673 // It's used to help calculate distinct loops referenced by the destination.
674 // Here's the map from loops to levels:
676 // 1 - outermost common loop
677 // ... - other common loops
678 // CommonLevels - innermost common loop
679 // ... - loops containing Src but not Dst
680 // SrcLevels - innermost loop containing Src but not Dst
681 // ... - loops containing Dst but not Src
682 // MaxLevels - innermost loops containing Dst but not Src
683 // Consider the follow code fragment:
700 // If we're looking at the possibility of a dependence between the store
701 // to A (the Src) and the load from A (the Dst), we'll note that they
702 // have 2 loops in common, so CommonLevels will equal 2 and the direction
703 // vector for Result will have 2 entries. SrcLevels = 4 and MaxLevels = 7.
704 // A map from loop names to loop numbers would look like
706 // b - 2 = CommonLevels
712 void DependenceAnalysis::establishNestingLevels(const Instruction *Src,
713 const Instruction *Dst) {
714 const BasicBlock *SrcBlock = Src->getParent();
715 const BasicBlock *DstBlock = Dst->getParent();
716 unsigned SrcLevel = LI->getLoopDepth(SrcBlock);
717 unsigned DstLevel = LI->getLoopDepth(DstBlock);
718 const Loop *SrcLoop = LI->getLoopFor(SrcBlock);
719 const Loop *DstLoop = LI->getLoopFor(DstBlock);
720 SrcLevels = SrcLevel;
721 MaxLevels = SrcLevel + DstLevel;
722 while (SrcLevel > DstLevel) {
723 SrcLoop = SrcLoop->getParentLoop();
726 while (DstLevel > SrcLevel) {
727 DstLoop = DstLoop->getParentLoop();
730 while (SrcLoop != DstLoop) {
731 SrcLoop = SrcLoop->getParentLoop();
732 DstLoop = DstLoop->getParentLoop();
735 CommonLevels = SrcLevel;
736 MaxLevels -= CommonLevels;
740 // Given one of the loops containing the source, return
741 // its level index in our numbering scheme.
742 unsigned DependenceAnalysis::mapSrcLoop(const Loop *SrcLoop) const {
743 return SrcLoop->getLoopDepth();
747 // Given one of the loops containing the destination,
748 // return its level index in our numbering scheme.
749 unsigned DependenceAnalysis::mapDstLoop(const Loop *DstLoop) const {
750 unsigned D = DstLoop->getLoopDepth();
751 if (D > CommonLevels)
752 return D - CommonLevels + SrcLevels;
758 // Returns true if Expression is loop invariant in LoopNest.
759 bool DependenceAnalysis::isLoopInvariant(const SCEV *Expression,
760 const Loop *LoopNest) const {
763 return SE->isLoopInvariant(Expression, LoopNest) &&
764 isLoopInvariant(Expression, LoopNest->getParentLoop());
769 // Finds the set of loops from the LoopNest that
770 // have a level <= CommonLevels and are referred to by the SCEV Expression.
771 void DependenceAnalysis::collectCommonLoops(const SCEV *Expression,
772 const Loop *LoopNest,
773 SmallBitVector &Loops) const {
775 unsigned Level = LoopNest->getLoopDepth();
776 if (Level <= CommonLevels && !SE->isLoopInvariant(Expression, LoopNest))
778 LoopNest = LoopNest->getParentLoop();
782 void DependenceAnalysis::unifySubscriptType(Subscript *Pair) {
783 const SCEV *Src = Pair->Src;
784 const SCEV *Dst = Pair->Dst;
785 IntegerType *SrcTy = dyn_cast<IntegerType>(Src->getType());
786 IntegerType *DstTy = dyn_cast<IntegerType>(Dst->getType());
787 if (SrcTy == nullptr || DstTy == nullptr) {
788 assert(SrcTy == DstTy && "This function only unify integer types and "
789 "expect Src and Dst share the same type "
793 if (SrcTy->getBitWidth() > DstTy->getBitWidth()) {
794 // Sign-extend Dst to typeof(Src) if typeof(Src) is wider than typeof(Dst).
795 Pair->Dst = SE->getSignExtendExpr(Dst, SrcTy);
796 } else if (SrcTy->getBitWidth() < DstTy->getBitWidth()) {
797 // Sign-extend Src to typeof(Dst) if typeof(Dst) is wider than typeof(Src).
798 Pair->Src = SE->getSignExtendExpr(Src, DstTy);
802 // removeMatchingExtensions - Examines a subscript pair.
803 // If the source and destination are identically sign (or zero)
804 // extended, it strips off the extension in an effect to simplify
805 // the actual analysis.
806 void DependenceAnalysis::removeMatchingExtensions(Subscript *Pair) {
807 const SCEV *Src = Pair->Src;
808 const SCEV *Dst = Pair->Dst;
809 if ((isa<SCEVZeroExtendExpr>(Src) && isa<SCEVZeroExtendExpr>(Dst)) ||
810 (isa<SCEVSignExtendExpr>(Src) && isa<SCEVSignExtendExpr>(Dst))) {
811 const SCEVCastExpr *SrcCast = cast<SCEVCastExpr>(Src);
812 const SCEVCastExpr *DstCast = cast<SCEVCastExpr>(Dst);
813 const SCEV *SrcCastOp = SrcCast->getOperand();
814 const SCEV *DstCastOp = DstCast->getOperand();
815 if (SrcCastOp->getType() == DstCastOp->getType()) {
816 Pair->Src = SrcCastOp;
817 Pair->Dst = DstCastOp;
823 // Examine the scev and return true iff it's linear.
824 // Collect any loops mentioned in the set of "Loops".
825 bool DependenceAnalysis::checkSrcSubscript(const SCEV *Src,
826 const Loop *LoopNest,
827 SmallBitVector &Loops) {
828 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Src);
830 return isLoopInvariant(Src, LoopNest);
831 const SCEV *Start = AddRec->getStart();
832 const SCEV *Step = AddRec->getStepRecurrence(*SE);
833 const SCEV *UB = SE->getBackedgeTakenCount(AddRec->getLoop());
834 if (!isa<SCEVCouldNotCompute>(UB)) {
835 if (SE->getTypeSizeInBits(Start->getType()) <
836 SE->getTypeSizeInBits(UB->getType())) {
837 if (!AddRec->getNoWrapFlags())
841 if (!isLoopInvariant(Step, LoopNest))
843 Loops.set(mapSrcLoop(AddRec->getLoop()));
844 return checkSrcSubscript(Start, LoopNest, Loops);
849 // Examine the scev and return true iff it's linear.
850 // Collect any loops mentioned in the set of "Loops".
851 bool DependenceAnalysis::checkDstSubscript(const SCEV *Dst,
852 const Loop *LoopNest,
853 SmallBitVector &Loops) {
854 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Dst);
856 return isLoopInvariant(Dst, LoopNest);
857 const SCEV *Start = AddRec->getStart();
858 const SCEV *Step = AddRec->getStepRecurrence(*SE);
859 const SCEV *UB = SE->getBackedgeTakenCount(AddRec->getLoop());
860 if (!isa<SCEVCouldNotCompute>(UB)) {
861 if (SE->getTypeSizeInBits(Start->getType()) <
862 SE->getTypeSizeInBits(UB->getType())) {
863 if (!AddRec->getNoWrapFlags())
867 if (!isLoopInvariant(Step, LoopNest))
869 Loops.set(mapDstLoop(AddRec->getLoop()));
870 return checkDstSubscript(Start, LoopNest, Loops);
874 // Examines the subscript pair (the Src and Dst SCEVs)
875 // and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
876 // Collects the associated loops in a set.
877 DependenceAnalysis::Subscript::ClassificationKind
878 DependenceAnalysis::classifyPair(const SCEV *Src, const Loop *SrcLoopNest,
879 const SCEV *Dst, const Loop *DstLoopNest,
880 SmallBitVector &Loops) {
881 SmallBitVector SrcLoops(MaxLevels + 1);
882 SmallBitVector DstLoops(MaxLevels + 1);
883 if (!checkSrcSubscript(Src, SrcLoopNest, SrcLoops))
884 return Subscript::NonLinear;
885 if (!checkDstSubscript(Dst, DstLoopNest, DstLoops))
886 return Subscript::NonLinear;
889 unsigned N = Loops.count();
891 return Subscript::ZIV;
893 return Subscript::SIV;
894 if (N == 2 && (SrcLoops.count() == 0 ||
895 DstLoops.count() == 0 ||
896 (SrcLoops.count() == 1 && DstLoops.count() == 1)))
897 return Subscript::RDIV;
898 return Subscript::MIV;
902 // A wrapper around SCEV::isKnownPredicate.
903 // Looks for cases where we're interested in comparing for equality.
904 // If both X and Y have been identically sign or zero extended,
905 // it strips off the (confusing) extensions before invoking
906 // SCEV::isKnownPredicate. Perhaps, someday, the ScalarEvolution package
907 // will be similarly updated.
909 // If SCEV::isKnownPredicate can't prove the predicate,
910 // we try simple subtraction, which seems to help in some cases
911 // involving symbolics.
912 bool DependenceAnalysis::isKnownPredicate(ICmpInst::Predicate Pred,
914 const SCEV *Y) const {
915 if (Pred == CmpInst::ICMP_EQ ||
916 Pred == CmpInst::ICMP_NE) {
917 if ((isa<SCEVSignExtendExpr>(X) &&
918 isa<SCEVSignExtendExpr>(Y)) ||
919 (isa<SCEVZeroExtendExpr>(X) &&
920 isa<SCEVZeroExtendExpr>(Y))) {
921 const SCEVCastExpr *CX = cast<SCEVCastExpr>(X);
922 const SCEVCastExpr *CY = cast<SCEVCastExpr>(Y);
923 const SCEV *Xop = CX->getOperand();
924 const SCEV *Yop = CY->getOperand();
925 if (Xop->getType() == Yop->getType()) {
931 if (SE->isKnownPredicate(Pred, X, Y))
933 // If SE->isKnownPredicate can't prove the condition,
934 // we try the brute-force approach of subtracting
935 // and testing the difference.
936 // By testing with SE->isKnownPredicate first, we avoid
937 // the possibility of overflow when the arguments are constants.
938 const SCEV *Delta = SE->getMinusSCEV(X, Y);
940 case CmpInst::ICMP_EQ:
941 return Delta->isZero();
942 case CmpInst::ICMP_NE:
943 return SE->isKnownNonZero(Delta);
944 case CmpInst::ICMP_SGE:
945 return SE->isKnownNonNegative(Delta);
946 case CmpInst::ICMP_SLE:
947 return SE->isKnownNonPositive(Delta);
948 case CmpInst::ICMP_SGT:
949 return SE->isKnownPositive(Delta);
950 case CmpInst::ICMP_SLT:
951 return SE->isKnownNegative(Delta);
953 llvm_unreachable("unexpected predicate in isKnownPredicate");
958 // All subscripts are all the same type.
959 // Loop bound may be smaller (e.g., a char).
960 // Should zero extend loop bound, since it's always >= 0.
961 // This routine collects upper bound and extends or truncates if needed.
962 // Truncating is safe when subscripts are known not to wrap. Cases without
963 // nowrap flags should have been rejected earlier.
964 // Return null if no bound available.
965 const SCEV *DependenceAnalysis::collectUpperBound(const Loop *L,
967 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
968 const SCEV *UB = SE->getBackedgeTakenCount(L);
969 return SE->getTruncateOrZeroExtend(UB, T);
975 // Calls collectUpperBound(), then attempts to cast it to SCEVConstant.
976 // If the cast fails, returns NULL.
977 const SCEVConstant *DependenceAnalysis::collectConstantUpperBound(const Loop *L,
980 if (const SCEV *UB = collectUpperBound(L, T))
981 return dyn_cast<SCEVConstant>(UB);
987 // When we have a pair of subscripts of the form [c1] and [c2],
988 // where c1 and c2 are both loop invariant, we attack it using
989 // the ZIV test. Basically, we test by comparing the two values,
990 // but there are actually three possible results:
991 // 1) the values are equal, so there's a dependence
992 // 2) the values are different, so there's no dependence
993 // 3) the values might be equal, so we have to assume a dependence.
995 // Return true if dependence disproved.
996 bool DependenceAnalysis::testZIV(const SCEV *Src,
998 FullDependence &Result) const {
999 DEBUG(dbgs() << " src = " << *Src << "\n");
1000 DEBUG(dbgs() << " dst = " << *Dst << "\n");
1002 if (isKnownPredicate(CmpInst::ICMP_EQ, Src, Dst)) {
1003 DEBUG(dbgs() << " provably dependent\n");
1004 return false; // provably dependent
1006 if (isKnownPredicate(CmpInst::ICMP_NE, Src, Dst)) {
1007 DEBUG(dbgs() << " provably independent\n");
1009 return true; // provably independent
1011 DEBUG(dbgs() << " possibly dependent\n");
1012 Result.Consistent = false;
1013 return false; // possibly dependent
1018 // From the paper, Practical Dependence Testing, Section 4.2.1
1020 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 + a*i],
1021 // where i is an induction variable, c1 and c2 are loop invariant,
1022 // and a is a constant, we can solve it exactly using the Strong SIV test.
1024 // Can prove independence. Failing that, can compute distance (and direction).
1025 // In the presence of symbolic terms, we can sometimes make progress.
1027 // If there's a dependence,
1029 // c1 + a*i = c2 + a*i'
1031 // The dependence distance is
1033 // d = i' - i = (c1 - c2)/a
1035 // A dependence only exists if d is an integer and abs(d) <= U, where U is the
1036 // loop's upper bound. If a dependence exists, the dependence direction is
1040 // direction = { = if d = 0
1043 // Return true if dependence disproved.
1044 bool DependenceAnalysis::strongSIVtest(const SCEV *Coeff,
1045 const SCEV *SrcConst,
1046 const SCEV *DstConst,
1047 const Loop *CurLoop,
1049 FullDependence &Result,
1050 Constraint &NewConstraint) const {
1051 DEBUG(dbgs() << "\tStrong SIV test\n");
1052 DEBUG(dbgs() << "\t Coeff = " << *Coeff);
1053 DEBUG(dbgs() << ", " << *Coeff->getType() << "\n");
1054 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst);
1055 DEBUG(dbgs() << ", " << *SrcConst->getType() << "\n");
1056 DEBUG(dbgs() << "\t DstConst = " << *DstConst);
1057 DEBUG(dbgs() << ", " << *DstConst->getType() << "\n");
1058 ++StrongSIVapplications;
1059 assert(0 < Level && Level <= CommonLevels && "level out of range");
1062 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1063 DEBUG(dbgs() << "\t Delta = " << *Delta);
1064 DEBUG(dbgs() << ", " << *Delta->getType() << "\n");
1066 // check that |Delta| < iteration count
1067 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1068 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound);
1069 DEBUG(dbgs() << ", " << *UpperBound->getType() << "\n");
1070 const SCEV *AbsDelta =
1071 SE->isKnownNonNegative(Delta) ? Delta : SE->getNegativeSCEV(Delta);
1072 const SCEV *AbsCoeff =
1073 SE->isKnownNonNegative(Coeff) ? Coeff : SE->getNegativeSCEV(Coeff);
1074 const SCEV *Product = SE->getMulExpr(UpperBound, AbsCoeff);
1075 if (isKnownPredicate(CmpInst::ICMP_SGT, AbsDelta, Product)) {
1076 // Distance greater than trip count - no dependence
1077 ++StrongSIVindependence;
1078 ++StrongSIVsuccesses;
1083 // Can we compute distance?
1084 if (isa<SCEVConstant>(Delta) && isa<SCEVConstant>(Coeff)) {
1085 APInt ConstDelta = cast<SCEVConstant>(Delta)->getValue()->getValue();
1086 APInt ConstCoeff = cast<SCEVConstant>(Coeff)->getValue()->getValue();
1087 APInt Distance = ConstDelta; // these need to be initialized
1088 APInt Remainder = ConstDelta;
1089 APInt::sdivrem(ConstDelta, ConstCoeff, Distance, Remainder);
1090 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1091 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1092 // Make sure Coeff divides Delta exactly
1093 if (Remainder != 0) {
1094 // Coeff doesn't divide Distance, no dependence
1095 ++StrongSIVindependence;
1096 ++StrongSIVsuccesses;
1099 Result.DV[Level].Distance = SE->getConstant(Distance);
1100 NewConstraint.setDistance(SE->getConstant(Distance), CurLoop);
1101 if (Distance.sgt(0))
1102 Result.DV[Level].Direction &= Dependence::DVEntry::LT;
1103 else if (Distance.slt(0))
1104 Result.DV[Level].Direction &= Dependence::DVEntry::GT;
1106 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1107 ++StrongSIVsuccesses;
1109 else if (Delta->isZero()) {
1111 Result.DV[Level].Distance = Delta;
1112 NewConstraint.setDistance(Delta, CurLoop);
1113 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1114 ++StrongSIVsuccesses;
1117 if (Coeff->isOne()) {
1118 DEBUG(dbgs() << "\t Distance = " << *Delta << "\n");
1119 Result.DV[Level].Distance = Delta; // since X/1 == X
1120 NewConstraint.setDistance(Delta, CurLoop);
1123 Result.Consistent = false;
1124 NewConstraint.setLine(Coeff,
1125 SE->getNegativeSCEV(Coeff),
1126 SE->getNegativeSCEV(Delta), CurLoop);
1129 // maybe we can get a useful direction
1130 bool DeltaMaybeZero = !SE->isKnownNonZero(Delta);
1131 bool DeltaMaybePositive = !SE->isKnownNonPositive(Delta);
1132 bool DeltaMaybeNegative = !SE->isKnownNonNegative(Delta);
1133 bool CoeffMaybePositive = !SE->isKnownNonPositive(Coeff);
1134 bool CoeffMaybeNegative = !SE->isKnownNonNegative(Coeff);
1135 // The double negatives above are confusing.
1136 // It helps to read !SE->isKnownNonZero(Delta)
1137 // as "Delta might be Zero"
1138 unsigned NewDirection = Dependence::DVEntry::NONE;
1139 if ((DeltaMaybePositive && CoeffMaybePositive) ||
1140 (DeltaMaybeNegative && CoeffMaybeNegative))
1141 NewDirection = Dependence::DVEntry::LT;
1143 NewDirection |= Dependence::DVEntry::EQ;
1144 if ((DeltaMaybeNegative && CoeffMaybePositive) ||
1145 (DeltaMaybePositive && CoeffMaybeNegative))
1146 NewDirection |= Dependence::DVEntry::GT;
1147 if (NewDirection < Result.DV[Level].Direction)
1148 ++StrongSIVsuccesses;
1149 Result.DV[Level].Direction &= NewDirection;
1155 // weakCrossingSIVtest -
1156 // From the paper, Practical Dependence Testing, Section 4.2.2
1158 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 - a*i],
1159 // where i is an induction variable, c1 and c2 are loop invariant,
1160 // and a is a constant, we can solve it exactly using the
1161 // Weak-Crossing SIV test.
1163 // Given c1 + a*i = c2 - a*i', we can look for the intersection of
1164 // the two lines, where i = i', yielding
1166 // c1 + a*i = c2 - a*i
1170 // If i < 0, there is no dependence.
1171 // If i > upperbound, there is no dependence.
1172 // If i = 0 (i.e., if c1 = c2), there's a dependence with distance = 0.
1173 // If i = upperbound, there's a dependence with distance = 0.
1174 // If i is integral, there's a dependence (all directions).
1175 // If the non-integer part = 1/2, there's a dependence (<> directions).
1176 // Otherwise, there's no dependence.
1178 // Can prove independence. Failing that,
1179 // can sometimes refine the directions.
1180 // Can determine iteration for splitting.
1182 // Return true if dependence disproved.
1183 bool DependenceAnalysis::weakCrossingSIVtest(const SCEV *Coeff,
1184 const SCEV *SrcConst,
1185 const SCEV *DstConst,
1186 const Loop *CurLoop,
1188 FullDependence &Result,
1189 Constraint &NewConstraint,
1190 const SCEV *&SplitIter) const {
1191 DEBUG(dbgs() << "\tWeak-Crossing SIV test\n");
1192 DEBUG(dbgs() << "\t Coeff = " << *Coeff << "\n");
1193 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1194 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1195 ++WeakCrossingSIVapplications;
1196 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1198 Result.Consistent = false;
1199 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1200 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1201 NewConstraint.setLine(Coeff, Coeff, Delta, CurLoop);
1202 if (Delta->isZero()) {
1203 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1204 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1205 ++WeakCrossingSIVsuccesses;
1206 if (!Result.DV[Level].Direction) {
1207 ++WeakCrossingSIVindependence;
1210 Result.DV[Level].Distance = Delta; // = 0
1213 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(Coeff);
1217 Result.DV[Level].Splitable = true;
1218 if (SE->isKnownNegative(ConstCoeff)) {
1219 ConstCoeff = dyn_cast<SCEVConstant>(SE->getNegativeSCEV(ConstCoeff));
1220 assert(ConstCoeff &&
1221 "dynamic cast of negative of ConstCoeff should yield constant");
1222 Delta = SE->getNegativeSCEV(Delta);
1224 assert(SE->isKnownPositive(ConstCoeff) && "ConstCoeff should be positive");
1226 // compute SplitIter for use by DependenceAnalysis::getSplitIteration()
1228 SE->getUDivExpr(SE->getSMaxExpr(SE->getConstant(Delta->getType(), 0),
1230 SE->getMulExpr(SE->getConstant(Delta->getType(), 2),
1232 DEBUG(dbgs() << "\t Split iter = " << *SplitIter << "\n");
1234 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1238 // We're certain that ConstCoeff > 0; therefore,
1239 // if Delta < 0, then no dependence.
1240 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1241 DEBUG(dbgs() << "\t ConstCoeff = " << *ConstCoeff << "\n");
1242 if (SE->isKnownNegative(Delta)) {
1243 // No dependence, Delta < 0
1244 ++WeakCrossingSIVindependence;
1245 ++WeakCrossingSIVsuccesses;
1249 // We're certain that Delta > 0 and ConstCoeff > 0.
1250 // Check Delta/(2*ConstCoeff) against upper loop bound
1251 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1252 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1253 const SCEV *ConstantTwo = SE->getConstant(UpperBound->getType(), 2);
1254 const SCEV *ML = SE->getMulExpr(SE->getMulExpr(ConstCoeff, UpperBound),
1256 DEBUG(dbgs() << "\t ML = " << *ML << "\n");
1257 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, ML)) {
1258 // Delta too big, no dependence
1259 ++WeakCrossingSIVindependence;
1260 ++WeakCrossingSIVsuccesses;
1263 if (isKnownPredicate(CmpInst::ICMP_EQ, Delta, ML)) {
1265 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1266 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1267 ++WeakCrossingSIVsuccesses;
1268 if (!Result.DV[Level].Direction) {
1269 ++WeakCrossingSIVindependence;
1272 Result.DV[Level].Splitable = false;
1273 Result.DV[Level].Distance = SE->getConstant(Delta->getType(), 0);
1278 // check that Coeff divides Delta
1279 APInt APDelta = ConstDelta->getValue()->getValue();
1280 APInt APCoeff = ConstCoeff->getValue()->getValue();
1281 APInt Distance = APDelta; // these need to be initialzed
1282 APInt Remainder = APDelta;
1283 APInt::sdivrem(APDelta, APCoeff, Distance, Remainder);
1284 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1285 if (Remainder != 0) {
1286 // Coeff doesn't divide Delta, no dependence
1287 ++WeakCrossingSIVindependence;
1288 ++WeakCrossingSIVsuccesses;
1291 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1293 // if 2*Coeff doesn't divide Delta, then the equal direction isn't possible
1294 APInt Two = APInt(Distance.getBitWidth(), 2, true);
1295 Remainder = Distance.srem(Two);
1296 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1297 if (Remainder != 0) {
1298 // Equal direction isn't possible
1299 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::EQ);
1300 ++WeakCrossingSIVsuccesses;
1306 // Kirch's algorithm, from
1308 // Optimizing Supercompilers for Supercomputers
1312 // Program 2.1, page 29.
1313 // Computes the GCD of AM and BM.
1314 // Also finds a solution to the equation ax - by = gcd(a, b).
1315 // Returns true if dependence disproved; i.e., gcd does not divide Delta.
1317 bool findGCD(unsigned Bits, APInt AM, APInt BM, APInt Delta,
1318 APInt &G, APInt &X, APInt &Y) {
1319 APInt A0(Bits, 1, true), A1(Bits, 0, true);
1320 APInt B0(Bits, 0, true), B1(Bits, 1, true);
1321 APInt G0 = AM.abs();
1322 APInt G1 = BM.abs();
1323 APInt Q = G0; // these need to be initialized
1325 APInt::sdivrem(G0, G1, Q, R);
1327 APInt A2 = A0 - Q*A1; A0 = A1; A1 = A2;
1328 APInt B2 = B0 - Q*B1; B0 = B1; B1 = B2;
1330 APInt::sdivrem(G0, G1, Q, R);
1333 DEBUG(dbgs() << "\t GCD = " << G << "\n");
1334 X = AM.slt(0) ? -A1 : A1;
1335 Y = BM.slt(0) ? B1 : -B1;
1337 // make sure gcd divides Delta
1340 return true; // gcd doesn't divide Delta, no dependence
1349 APInt floorOfQuotient(APInt A, APInt B) {
1350 APInt Q = A; // these need to be initialized
1352 APInt::sdivrem(A, B, Q, R);
1355 if ((A.sgt(0) && B.sgt(0)) ||
1356 (A.slt(0) && B.slt(0)))
1364 APInt ceilingOfQuotient(APInt A, APInt B) {
1365 APInt Q = A; // these need to be initialized
1367 APInt::sdivrem(A, B, Q, R);
1370 if ((A.sgt(0) && B.sgt(0)) ||
1371 (A.slt(0) && B.slt(0)))
1379 APInt maxAPInt(APInt A, APInt B) {
1380 return A.sgt(B) ? A : B;
1385 APInt minAPInt(APInt A, APInt B) {
1386 return A.slt(B) ? A : B;
1391 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*i],
1392 // where i is an induction variable, c1 and c2 are loop invariant, and a1
1393 // and a2 are constant, we can solve it exactly using an algorithm developed
1394 // by Banerjee and Wolfe. See Section 2.5.3 in
1396 // Optimizing Supercompilers for Supercomputers
1400 // It's slower than the specialized tests (strong SIV, weak-zero SIV, etc),
1401 // so use them if possible. They're also a bit better with symbolics and,
1402 // in the case of the strong SIV test, can compute Distances.
1404 // Return true if dependence disproved.
1405 bool DependenceAnalysis::exactSIVtest(const SCEV *SrcCoeff,
1406 const SCEV *DstCoeff,
1407 const SCEV *SrcConst,
1408 const SCEV *DstConst,
1409 const Loop *CurLoop,
1411 FullDependence &Result,
1412 Constraint &NewConstraint) const {
1413 DEBUG(dbgs() << "\tExact SIV test\n");
1414 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1415 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1416 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1417 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1418 ++ExactSIVapplications;
1419 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1421 Result.Consistent = false;
1422 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1423 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1424 NewConstraint.setLine(SrcCoeff, SE->getNegativeSCEV(DstCoeff),
1426 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1427 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1428 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1429 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1434 APInt AM = ConstSrcCoeff->getValue()->getValue();
1435 APInt BM = ConstDstCoeff->getValue()->getValue();
1436 unsigned Bits = AM.getBitWidth();
1437 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1438 // gcd doesn't divide Delta, no dependence
1439 ++ExactSIVindependence;
1440 ++ExactSIVsuccesses;
1444 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1446 // since SCEV construction normalizes, LM = 0
1447 APInt UM(Bits, 1, true);
1448 bool UMvalid = false;
1449 // UM is perhaps unavailable, let's check
1450 if (const SCEVConstant *CUB =
1451 collectConstantUpperBound(CurLoop, Delta->getType())) {
1452 UM = CUB->getValue()->getValue();
1453 DEBUG(dbgs() << "\t UM = " << UM << "\n");
1457 APInt TU(APInt::getSignedMaxValue(Bits));
1458 APInt TL(APInt::getSignedMinValue(Bits));
1460 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1461 APInt TMUL = BM.sdiv(G);
1463 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1464 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1466 TU = minAPInt(TU, floorOfQuotient(UM - X, TMUL));
1467 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1471 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1472 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1474 TL = maxAPInt(TL, ceilingOfQuotient(UM - X, TMUL));
1475 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1479 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1482 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1483 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1485 TU = minAPInt(TU, floorOfQuotient(UM - Y, TMUL));
1486 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1490 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1491 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1493 TL = maxAPInt(TL, ceilingOfQuotient(UM - Y, TMUL));
1494 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1498 ++ExactSIVindependence;
1499 ++ExactSIVsuccesses;
1503 // explore directions
1504 unsigned NewDirection = Dependence::DVEntry::NONE;
1507 APInt SaveTU(TU); // save these
1509 DEBUG(dbgs() << "\t exploring LT direction\n");
1512 TL = maxAPInt(TL, ceilingOfQuotient(X - Y + 1, TMUL));
1513 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1516 TU = minAPInt(TU, floorOfQuotient(X - Y + 1, TMUL));
1517 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1520 NewDirection |= Dependence::DVEntry::LT;
1521 ++ExactSIVsuccesses;
1525 TU = SaveTU; // restore
1527 DEBUG(dbgs() << "\t exploring EQ direction\n");
1529 TL = maxAPInt(TL, ceilingOfQuotient(X - Y, TMUL));
1530 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1533 TU = minAPInt(TU, floorOfQuotient(X - Y, TMUL));
1534 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1538 TL = maxAPInt(TL, ceilingOfQuotient(Y - X, TMUL));
1539 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1542 TU = minAPInt(TU, floorOfQuotient(Y - X, TMUL));
1543 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1546 NewDirection |= Dependence::DVEntry::EQ;
1547 ++ExactSIVsuccesses;
1551 TU = SaveTU; // restore
1553 DEBUG(dbgs() << "\t exploring GT direction\n");
1555 TL = maxAPInt(TL, ceilingOfQuotient(Y - X + 1, TMUL));
1556 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1559 TU = minAPInt(TU, floorOfQuotient(Y - X + 1, TMUL));
1560 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1563 NewDirection |= Dependence::DVEntry::GT;
1564 ++ExactSIVsuccesses;
1568 Result.DV[Level].Direction &= NewDirection;
1569 if (Result.DV[Level].Direction == Dependence::DVEntry::NONE)
1570 ++ExactSIVindependence;
1571 return Result.DV[Level].Direction == Dependence::DVEntry::NONE;
1576 // Return true if the divisor evenly divides the dividend.
1578 bool isRemainderZero(const SCEVConstant *Dividend,
1579 const SCEVConstant *Divisor) {
1580 APInt ConstDividend = Dividend->getValue()->getValue();
1581 APInt ConstDivisor = Divisor->getValue()->getValue();
1582 return ConstDividend.srem(ConstDivisor) == 0;
1586 // weakZeroSrcSIVtest -
1587 // From the paper, Practical Dependence Testing, Section 4.2.2
1589 // When we have a pair of subscripts of the form [c1] and [c2 + a*i],
1590 // where i is an induction variable, c1 and c2 are loop invariant,
1591 // and a is a constant, we can solve it exactly using the
1592 // Weak-Zero SIV test.
1602 // If i is not an integer, there's no dependence.
1603 // If i < 0 or > UB, there's no dependence.
1604 // If i = 0, the direction is <= and peeling the
1605 // 1st iteration will break the dependence.
1606 // If i = UB, the direction is >= and peeling the
1607 // last iteration will break the dependence.
1608 // Otherwise, the direction is *.
1610 // Can prove independence. Failing that, we can sometimes refine
1611 // the directions. Can sometimes show that first or last
1612 // iteration carries all the dependences (so worth peeling).
1614 // (see also weakZeroDstSIVtest)
1616 // Return true if dependence disproved.
1617 bool DependenceAnalysis::weakZeroSrcSIVtest(const SCEV *DstCoeff,
1618 const SCEV *SrcConst,
1619 const SCEV *DstConst,
1620 const Loop *CurLoop,
1622 FullDependence &Result,
1623 Constraint &NewConstraint) const {
1624 // For the WeakSIV test, it's possible the loop isn't common to
1625 // the Src and Dst loops. If it isn't, then there's no need to
1626 // record a direction.
1627 DEBUG(dbgs() << "\tWeak-Zero (src) SIV test\n");
1628 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << "\n");
1629 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1630 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1631 ++WeakZeroSIVapplications;
1632 assert(0 < Level && Level <= MaxLevels && "Level out of range");
1634 Result.Consistent = false;
1635 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1636 NewConstraint.setLine(SE->getConstant(Delta->getType(), 0),
1637 DstCoeff, Delta, CurLoop);
1638 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1639 if (isKnownPredicate(CmpInst::ICMP_EQ, SrcConst, DstConst)) {
1640 if (Level < CommonLevels) {
1641 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1642 Result.DV[Level].PeelFirst = true;
1643 ++WeakZeroSIVsuccesses;
1645 return false; // dependences caused by first iteration
1647 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1650 const SCEV *AbsCoeff =
1651 SE->isKnownNegative(ConstCoeff) ?
1652 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1653 const SCEV *NewDelta =
1654 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1656 // check that Delta/SrcCoeff < iteration count
1657 // really check NewDelta < count*AbsCoeff
1658 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1659 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1660 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1661 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1662 ++WeakZeroSIVindependence;
1663 ++WeakZeroSIVsuccesses;
1666 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1667 // dependences caused by last iteration
1668 if (Level < CommonLevels) {
1669 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1670 Result.DV[Level].PeelLast = true;
1671 ++WeakZeroSIVsuccesses;
1677 // check that Delta/SrcCoeff >= 0
1678 // really check that NewDelta >= 0
1679 if (SE->isKnownNegative(NewDelta)) {
1680 // No dependence, newDelta < 0
1681 ++WeakZeroSIVindependence;
1682 ++WeakZeroSIVsuccesses;
1686 // if SrcCoeff doesn't divide Delta, then no dependence
1687 if (isa<SCEVConstant>(Delta) &&
1688 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1689 ++WeakZeroSIVindependence;
1690 ++WeakZeroSIVsuccesses;
1697 // weakZeroDstSIVtest -
1698 // From the paper, Practical Dependence Testing, Section 4.2.2
1700 // When we have a pair of subscripts of the form [c1 + a*i] and [c2],
1701 // where i is an induction variable, c1 and c2 are loop invariant,
1702 // and a is a constant, we can solve it exactly using the
1703 // Weak-Zero SIV test.
1713 // If i is not an integer, there's no dependence.
1714 // If i < 0 or > UB, there's no dependence.
1715 // If i = 0, the direction is <= and peeling the
1716 // 1st iteration will break the dependence.
1717 // If i = UB, the direction is >= and peeling the
1718 // last iteration will break the dependence.
1719 // Otherwise, the direction is *.
1721 // Can prove independence. Failing that, we can sometimes refine
1722 // the directions. Can sometimes show that first or last
1723 // iteration carries all the dependences (so worth peeling).
1725 // (see also weakZeroSrcSIVtest)
1727 // Return true if dependence disproved.
1728 bool DependenceAnalysis::weakZeroDstSIVtest(const SCEV *SrcCoeff,
1729 const SCEV *SrcConst,
1730 const SCEV *DstConst,
1731 const Loop *CurLoop,
1733 FullDependence &Result,
1734 Constraint &NewConstraint) const {
1735 // For the WeakSIV test, it's possible the loop isn't common to the
1736 // Src and Dst loops. If it isn't, then there's no need to record a direction.
1737 DEBUG(dbgs() << "\tWeak-Zero (dst) SIV test\n");
1738 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << "\n");
1739 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1740 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1741 ++WeakZeroSIVapplications;
1742 assert(0 < Level && Level <= SrcLevels && "Level out of range");
1744 Result.Consistent = false;
1745 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1746 NewConstraint.setLine(SrcCoeff, SE->getConstant(Delta->getType(), 0),
1748 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1749 if (isKnownPredicate(CmpInst::ICMP_EQ, DstConst, SrcConst)) {
1750 if (Level < CommonLevels) {
1751 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1752 Result.DV[Level].PeelFirst = true;
1753 ++WeakZeroSIVsuccesses;
1755 return false; // dependences caused by first iteration
1757 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1760 const SCEV *AbsCoeff =
1761 SE->isKnownNegative(ConstCoeff) ?
1762 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1763 const SCEV *NewDelta =
1764 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1766 // check that Delta/SrcCoeff < iteration count
1767 // really check NewDelta < count*AbsCoeff
1768 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1769 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1770 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1771 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1772 ++WeakZeroSIVindependence;
1773 ++WeakZeroSIVsuccesses;
1776 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1777 // dependences caused by last iteration
1778 if (Level < CommonLevels) {
1779 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1780 Result.DV[Level].PeelLast = true;
1781 ++WeakZeroSIVsuccesses;
1787 // check that Delta/SrcCoeff >= 0
1788 // really check that NewDelta >= 0
1789 if (SE->isKnownNegative(NewDelta)) {
1790 // No dependence, newDelta < 0
1791 ++WeakZeroSIVindependence;
1792 ++WeakZeroSIVsuccesses;
1796 // if SrcCoeff doesn't divide Delta, then no dependence
1797 if (isa<SCEVConstant>(Delta) &&
1798 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1799 ++WeakZeroSIVindependence;
1800 ++WeakZeroSIVsuccesses;
1807 // exactRDIVtest - Tests the RDIV subscript pair for dependence.
1808 // Things of the form [c1 + a*i] and [c2 + b*j],
1809 // where i and j are induction variable, c1 and c2 are loop invariant,
1810 // and a and b are constants.
1811 // Returns true if any possible dependence is disproved.
1812 // Marks the result as inconsistent.
1813 // Works in some cases that symbolicRDIVtest doesn't, and vice versa.
1814 bool DependenceAnalysis::exactRDIVtest(const SCEV *SrcCoeff,
1815 const SCEV *DstCoeff,
1816 const SCEV *SrcConst,
1817 const SCEV *DstConst,
1818 const Loop *SrcLoop,
1819 const Loop *DstLoop,
1820 FullDependence &Result) const {
1821 DEBUG(dbgs() << "\tExact RDIV test\n");
1822 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1823 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1824 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1825 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1826 ++ExactRDIVapplications;
1827 Result.Consistent = false;
1828 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1829 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1830 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1831 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1832 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1833 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1838 APInt AM = ConstSrcCoeff->getValue()->getValue();
1839 APInt BM = ConstDstCoeff->getValue()->getValue();
1840 unsigned Bits = AM.getBitWidth();
1841 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1842 // gcd doesn't divide Delta, no dependence
1843 ++ExactRDIVindependence;
1847 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1849 // since SCEV construction seems to normalize, LM = 0
1850 APInt SrcUM(Bits, 1, true);
1851 bool SrcUMvalid = false;
1852 // SrcUM is perhaps unavailable, let's check
1853 if (const SCEVConstant *UpperBound =
1854 collectConstantUpperBound(SrcLoop, Delta->getType())) {
1855 SrcUM = UpperBound->getValue()->getValue();
1856 DEBUG(dbgs() << "\t SrcUM = " << SrcUM << "\n");
1860 APInt DstUM(Bits, 1, true);
1861 bool DstUMvalid = false;
1862 // UM is perhaps unavailable, let's check
1863 if (const SCEVConstant *UpperBound =
1864 collectConstantUpperBound(DstLoop, Delta->getType())) {
1865 DstUM = UpperBound->getValue()->getValue();
1866 DEBUG(dbgs() << "\t DstUM = " << DstUM << "\n");
1870 APInt TU(APInt::getSignedMaxValue(Bits));
1871 APInt TL(APInt::getSignedMinValue(Bits));
1873 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1874 APInt TMUL = BM.sdiv(G);
1876 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1877 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1879 TU = minAPInt(TU, floorOfQuotient(SrcUM - X, TMUL));
1880 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1884 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1885 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1887 TL = maxAPInt(TL, ceilingOfQuotient(SrcUM - X, TMUL));
1888 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1892 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1895 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1896 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1898 TU = minAPInt(TU, floorOfQuotient(DstUM - Y, TMUL));
1899 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1903 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1904 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1906 TL = maxAPInt(TL, ceilingOfQuotient(DstUM - Y, TMUL));
1907 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1911 ++ExactRDIVindependence;
1916 // symbolicRDIVtest -
1917 // In Section 4.5 of the Practical Dependence Testing paper,the authors
1918 // introduce a special case of Banerjee's Inequalities (also called the
1919 // Extreme-Value Test) that can handle some of the SIV and RDIV cases,
1920 // particularly cases with symbolics. Since it's only able to disprove
1921 // dependence (not compute distances or directions), we'll use it as a
1922 // fall back for the other tests.
1924 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
1925 // where i and j are induction variables and c1 and c2 are loop invariants,
1926 // we can use the symbolic tests to disprove some dependences, serving as a
1927 // backup for the RDIV test. Note that i and j can be the same variable,
1928 // letting this test serve as a backup for the various SIV tests.
1930 // For a dependence to exist, c1 + a1*i must equal c2 + a2*j for some
1931 // 0 <= i <= N1 and some 0 <= j <= N2, where N1 and N2 are the (normalized)
1932 // loop bounds for the i and j loops, respectively. So, ...
1934 // c1 + a1*i = c2 + a2*j
1935 // a1*i - a2*j = c2 - c1
1937 // To test for a dependence, we compute c2 - c1 and make sure it's in the
1938 // range of the maximum and minimum possible values of a1*i - a2*j.
1939 // Considering the signs of a1 and a2, we have 4 possible cases:
1941 // 1) If a1 >= 0 and a2 >= 0, then
1942 // a1*0 - a2*N2 <= c2 - c1 <= a1*N1 - a2*0
1943 // -a2*N2 <= c2 - c1 <= a1*N1
1945 // 2) If a1 >= 0 and a2 <= 0, then
1946 // a1*0 - a2*0 <= c2 - c1 <= a1*N1 - a2*N2
1947 // 0 <= c2 - c1 <= a1*N1 - a2*N2
1949 // 3) If a1 <= 0 and a2 >= 0, then
1950 // a1*N1 - a2*N2 <= c2 - c1 <= a1*0 - a2*0
1951 // a1*N1 - a2*N2 <= c2 - c1 <= 0
1953 // 4) If a1 <= 0 and a2 <= 0, then
1954 // a1*N1 - a2*0 <= c2 - c1 <= a1*0 - a2*N2
1955 // a1*N1 <= c2 - c1 <= -a2*N2
1957 // return true if dependence disproved
1958 bool DependenceAnalysis::symbolicRDIVtest(const SCEV *A1,
1963 const Loop *Loop2) const {
1964 ++SymbolicRDIVapplications;
1965 DEBUG(dbgs() << "\ttry symbolic RDIV test\n");
1966 DEBUG(dbgs() << "\t A1 = " << *A1);
1967 DEBUG(dbgs() << ", type = " << *A1->getType() << "\n");
1968 DEBUG(dbgs() << "\t A2 = " << *A2 << "\n");
1969 DEBUG(dbgs() << "\t C1 = " << *C1 << "\n");
1970 DEBUG(dbgs() << "\t C2 = " << *C2 << "\n");
1971 const SCEV *N1 = collectUpperBound(Loop1, A1->getType());
1972 const SCEV *N2 = collectUpperBound(Loop2, A1->getType());
1973 DEBUG(if (N1) dbgs() << "\t N1 = " << *N1 << "\n");
1974 DEBUG(if (N2) dbgs() << "\t N2 = " << *N2 << "\n");
1975 const SCEV *C2_C1 = SE->getMinusSCEV(C2, C1);
1976 const SCEV *C1_C2 = SE->getMinusSCEV(C1, C2);
1977 DEBUG(dbgs() << "\t C2 - C1 = " << *C2_C1 << "\n");
1978 DEBUG(dbgs() << "\t C1 - C2 = " << *C1_C2 << "\n");
1979 if (SE->isKnownNonNegative(A1)) {
1980 if (SE->isKnownNonNegative(A2)) {
1981 // A1 >= 0 && A2 >= 0
1983 // make sure that c2 - c1 <= a1*N1
1984 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
1985 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
1986 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1)) {
1987 ++SymbolicRDIVindependence;
1992 // make sure that -a2*N2 <= c2 - c1, or a2*N2 >= c1 - c2
1993 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
1994 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
1995 if (isKnownPredicate(CmpInst::ICMP_SLT, A2N2, C1_C2)) {
1996 ++SymbolicRDIVindependence;
2001 else if (SE->isKnownNonPositive(A2)) {
2002 // a1 >= 0 && a2 <= 0
2004 // make sure that c2 - c1 <= a1*N1 - a2*N2
2005 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2006 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2007 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
2008 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
2009 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1_A2N2)) {
2010 ++SymbolicRDIVindependence;
2014 // make sure that 0 <= c2 - c1
2015 if (SE->isKnownNegative(C2_C1)) {
2016 ++SymbolicRDIVindependence;
2021 else if (SE->isKnownNonPositive(A1)) {
2022 if (SE->isKnownNonNegative(A2)) {
2023 // a1 <= 0 && a2 >= 0
2025 // make sure that a1*N1 - a2*N2 <= c2 - c1
2026 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2027 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2028 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
2029 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
2030 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1_A2N2, C2_C1)) {
2031 ++SymbolicRDIVindependence;
2035 // make sure that c2 - c1 <= 0
2036 if (SE->isKnownPositive(C2_C1)) {
2037 ++SymbolicRDIVindependence;
2041 else if (SE->isKnownNonPositive(A2)) {
2042 // a1 <= 0 && a2 <= 0
2044 // make sure that a1*N1 <= c2 - c1
2045 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2046 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
2047 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1, C2_C1)) {
2048 ++SymbolicRDIVindependence;
2053 // make sure that c2 - c1 <= -a2*N2, or c1 - c2 >= a2*N2
2054 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2055 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
2056 if (isKnownPredicate(CmpInst::ICMP_SLT, C1_C2, A2N2)) {
2057 ++SymbolicRDIVindependence;
2068 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 - a2*i]
2069 // where i is an induction variable, c1 and c2 are loop invariant, and a1 and
2070 // a2 are constant, we attack it with an SIV test. While they can all be
2071 // solved with the Exact SIV test, it's worthwhile to use simpler tests when
2072 // they apply; they're cheaper and sometimes more precise.
2074 // Return true if dependence disproved.
2075 bool DependenceAnalysis::testSIV(const SCEV *Src,
2078 FullDependence &Result,
2079 Constraint &NewConstraint,
2080 const SCEV *&SplitIter) const {
2081 DEBUG(dbgs() << " src = " << *Src << "\n");
2082 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2083 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2084 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2085 if (SrcAddRec && DstAddRec) {
2086 const SCEV *SrcConst = SrcAddRec->getStart();
2087 const SCEV *DstConst = DstAddRec->getStart();
2088 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2089 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2090 const Loop *CurLoop = SrcAddRec->getLoop();
2091 assert(CurLoop == DstAddRec->getLoop() &&
2092 "both loops in SIV should be same");
2093 Level = mapSrcLoop(CurLoop);
2095 if (SrcCoeff == DstCoeff)
2096 disproven = strongSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2097 Level, Result, NewConstraint);
2098 else if (SrcCoeff == SE->getNegativeSCEV(DstCoeff))
2099 disproven = weakCrossingSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2100 Level, Result, NewConstraint, SplitIter);
2102 disproven = exactSIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop,
2103 Level, Result, NewConstraint);
2105 gcdMIVtest(Src, Dst, Result) ||
2106 symbolicRDIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop, CurLoop);
2109 const SCEV *SrcConst = SrcAddRec->getStart();
2110 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2111 const SCEV *DstConst = Dst;
2112 const Loop *CurLoop = SrcAddRec->getLoop();
2113 Level = mapSrcLoop(CurLoop);
2114 return weakZeroDstSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2115 Level, Result, NewConstraint) ||
2116 gcdMIVtest(Src, Dst, Result);
2119 const SCEV *DstConst = DstAddRec->getStart();
2120 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2121 const SCEV *SrcConst = Src;
2122 const Loop *CurLoop = DstAddRec->getLoop();
2123 Level = mapDstLoop(CurLoop);
2124 return weakZeroSrcSIVtest(DstCoeff, SrcConst, DstConst,
2125 CurLoop, Level, Result, NewConstraint) ||
2126 gcdMIVtest(Src, Dst, Result);
2128 llvm_unreachable("SIV test expected at least one AddRec");
2134 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
2135 // where i and j are induction variables, c1 and c2 are loop invariant,
2136 // and a1 and a2 are constant, we can solve it exactly with an easy adaptation
2137 // of the Exact SIV test, the Restricted Double Index Variable (RDIV) test.
2138 // It doesn't make sense to talk about distance or direction in this case,
2139 // so there's no point in making special versions of the Strong SIV test or
2140 // the Weak-crossing SIV test.
2142 // With minor algebra, this test can also be used for things like
2143 // [c1 + a1*i + a2*j][c2].
2145 // Return true if dependence disproved.
2146 bool DependenceAnalysis::testRDIV(const SCEV *Src,
2148 FullDependence &Result) const {
2149 // we have 3 possible situations here:
2150 // 1) [a*i + b] and [c*j + d]
2151 // 2) [a*i + c*j + b] and [d]
2152 // 3) [b] and [a*i + c*j + d]
2153 // We need to find what we've got and get organized
2155 const SCEV *SrcConst, *DstConst;
2156 const SCEV *SrcCoeff, *DstCoeff;
2157 const Loop *SrcLoop, *DstLoop;
2159 DEBUG(dbgs() << " src = " << *Src << "\n");
2160 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2161 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2162 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2163 if (SrcAddRec && DstAddRec) {
2164 SrcConst = SrcAddRec->getStart();
2165 SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2166 SrcLoop = SrcAddRec->getLoop();
2167 DstConst = DstAddRec->getStart();
2168 DstCoeff = DstAddRec->getStepRecurrence(*SE);
2169 DstLoop = DstAddRec->getLoop();
2171 else if (SrcAddRec) {
2172 if (const SCEVAddRecExpr *tmpAddRec =
2173 dyn_cast<SCEVAddRecExpr>(SrcAddRec->getStart())) {
2174 SrcConst = tmpAddRec->getStart();
2175 SrcCoeff = tmpAddRec->getStepRecurrence(*SE);
2176 SrcLoop = tmpAddRec->getLoop();
2178 DstCoeff = SE->getNegativeSCEV(SrcAddRec->getStepRecurrence(*SE));
2179 DstLoop = SrcAddRec->getLoop();
2182 llvm_unreachable("RDIV reached by surprising SCEVs");
2184 else if (DstAddRec) {
2185 if (const SCEVAddRecExpr *tmpAddRec =
2186 dyn_cast<SCEVAddRecExpr>(DstAddRec->getStart())) {
2187 DstConst = tmpAddRec->getStart();
2188 DstCoeff = tmpAddRec->getStepRecurrence(*SE);
2189 DstLoop = tmpAddRec->getLoop();
2191 SrcCoeff = SE->getNegativeSCEV(DstAddRec->getStepRecurrence(*SE));
2192 SrcLoop = DstAddRec->getLoop();
2195 llvm_unreachable("RDIV reached by surprising SCEVs");
2198 llvm_unreachable("RDIV expected at least one AddRec");
2199 return exactRDIVtest(SrcCoeff, DstCoeff,
2203 gcdMIVtest(Src, Dst, Result) ||
2204 symbolicRDIVtest(SrcCoeff, DstCoeff,
2210 // Tests the single-subscript MIV pair (Src and Dst) for dependence.
2211 // Return true if dependence disproved.
2212 // Can sometimes refine direction vectors.
2213 bool DependenceAnalysis::testMIV(const SCEV *Src,
2215 const SmallBitVector &Loops,
2216 FullDependence &Result) const {
2217 DEBUG(dbgs() << " src = " << *Src << "\n");
2218 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2219 Result.Consistent = false;
2220 return gcdMIVtest(Src, Dst, Result) ||
2221 banerjeeMIVtest(Src, Dst, Loops, Result);
2225 // Given a product, e.g., 10*X*Y, returns the first constant operand,
2226 // in this case 10. If there is no constant part, returns NULL.
2228 const SCEVConstant *getConstantPart(const SCEVMulExpr *Product) {
2229 for (unsigned Op = 0, Ops = Product->getNumOperands(); Op < Ops; Op++) {
2230 if (const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Product->getOperand(Op)))
2237 //===----------------------------------------------------------------------===//
2239 // Tests an MIV subscript pair for dependence.
2240 // Returns true if any possible dependence is disproved.
2241 // Marks the result as inconsistent.
2242 // Can sometimes disprove the equal direction for 1 or more loops,
2243 // as discussed in Michael Wolfe's book,
2244 // High Performance Compilers for Parallel Computing, page 235.
2246 // We spend some effort (code!) to handle cases like
2247 // [10*i + 5*N*j + 15*M + 6], where i and j are induction variables,
2248 // but M and N are just loop-invariant variables.
2249 // This should help us handle linearized subscripts;
2250 // also makes this test a useful backup to the various SIV tests.
2252 // It occurs to me that the presence of loop-invariant variables
2253 // changes the nature of the test from "greatest common divisor"
2254 // to "a common divisor".
2255 bool DependenceAnalysis::gcdMIVtest(const SCEV *Src,
2257 FullDependence &Result) const {
2258 DEBUG(dbgs() << "starting gcd\n");
2260 unsigned BitWidth = SE->getTypeSizeInBits(Src->getType());
2261 APInt RunningGCD = APInt::getNullValue(BitWidth);
2263 // Examine Src coefficients.
2264 // Compute running GCD and record source constant.
2265 // Because we're looking for the constant at the end of the chain,
2266 // we can't quit the loop just because the GCD == 1.
2267 const SCEV *Coefficients = Src;
2268 while (const SCEVAddRecExpr *AddRec =
2269 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2270 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2271 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2272 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2273 // If the coefficient is the product of a constant and other stuff,
2274 // we can use the constant in the GCD computation.
2275 Constant = getConstantPart(Product);
2278 APInt ConstCoeff = Constant->getValue()->getValue();
2279 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2280 Coefficients = AddRec->getStart();
2282 const SCEV *SrcConst = Coefficients;
2284 // Examine Dst coefficients.
2285 // Compute running GCD and record destination constant.
2286 // Because we're looking for the constant at the end of the chain,
2287 // we can't quit the loop just because the GCD == 1.
2289 while (const SCEVAddRecExpr *AddRec =
2290 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2291 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2292 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2293 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2294 // If the coefficient is the product of a constant and other stuff,
2295 // we can use the constant in the GCD computation.
2296 Constant = getConstantPart(Product);
2299 APInt ConstCoeff = Constant->getValue()->getValue();
2300 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2301 Coefficients = AddRec->getStart();
2303 const SCEV *DstConst = Coefficients;
2305 APInt ExtraGCD = APInt::getNullValue(BitWidth);
2306 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
2307 DEBUG(dbgs() << " Delta = " << *Delta << "\n");
2308 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Delta);
2309 if (const SCEVAddExpr *Sum = dyn_cast<SCEVAddExpr>(Delta)) {
2310 // If Delta is a sum of products, we may be able to make further progress.
2311 for (unsigned Op = 0, Ops = Sum->getNumOperands(); Op < Ops; Op++) {
2312 const SCEV *Operand = Sum->getOperand(Op);
2313 if (isa<SCEVConstant>(Operand)) {
2314 assert(!Constant && "Surprised to find multiple constants");
2315 Constant = cast<SCEVConstant>(Operand);
2317 else if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Operand)) {
2318 // Search for constant operand to participate in GCD;
2319 // If none found; return false.
2320 const SCEVConstant *ConstOp = getConstantPart(Product);
2323 APInt ConstOpValue = ConstOp->getValue()->getValue();
2324 ExtraGCD = APIntOps::GreatestCommonDivisor(ExtraGCD,
2325 ConstOpValue.abs());
2333 APInt ConstDelta = cast<SCEVConstant>(Constant)->getValue()->getValue();
2334 DEBUG(dbgs() << " ConstDelta = " << ConstDelta << "\n");
2335 if (ConstDelta == 0)
2337 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ExtraGCD);
2338 DEBUG(dbgs() << " RunningGCD = " << RunningGCD << "\n");
2339 APInt Remainder = ConstDelta.srem(RunningGCD);
2340 if (Remainder != 0) {
2345 // Try to disprove equal directions.
2346 // For example, given a subscript pair [3*i + 2*j] and [i' + 2*j' - 1],
2347 // the code above can't disprove the dependence because the GCD = 1.
2348 // So we consider what happen if i = i' and what happens if j = j'.
2349 // If i = i', we can simplify the subscript to [2*i + 2*j] and [2*j' - 1],
2350 // which is infeasible, so we can disallow the = direction for the i level.
2351 // Setting j = j' doesn't help matters, so we end up with a direction vector
2354 // Given A[5*i + 10*j*M + 9*M*N] and A[15*i + 20*j*M - 21*N*M + 5],
2355 // we need to remember that the constant part is 5 and the RunningGCD should
2356 // be initialized to ExtraGCD = 30.
2357 DEBUG(dbgs() << " ExtraGCD = " << ExtraGCD << '\n');
2359 bool Improved = false;
2361 while (const SCEVAddRecExpr *AddRec =
2362 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2363 Coefficients = AddRec->getStart();
2364 const Loop *CurLoop = AddRec->getLoop();
2365 RunningGCD = ExtraGCD;
2366 const SCEV *SrcCoeff = AddRec->getStepRecurrence(*SE);
2367 const SCEV *DstCoeff = SE->getMinusSCEV(SrcCoeff, SrcCoeff);
2368 const SCEV *Inner = Src;
2369 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2370 AddRec = cast<SCEVAddRecExpr>(Inner);
2371 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2372 if (CurLoop == AddRec->getLoop())
2373 ; // SrcCoeff == Coeff
2375 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2376 // If the coefficient is the product of a constant and other stuff,
2377 // we can use the constant in the GCD computation.
2378 Constant = getConstantPart(Product);
2380 Constant = cast<SCEVConstant>(Coeff);
2381 APInt ConstCoeff = Constant->getValue()->getValue();
2382 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2384 Inner = AddRec->getStart();
2387 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2388 AddRec = cast<SCEVAddRecExpr>(Inner);
2389 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2390 if (CurLoop == AddRec->getLoop())
2393 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2394 // If the coefficient is the product of a constant and other stuff,
2395 // we can use the constant in the GCD computation.
2396 Constant = getConstantPart(Product);
2398 Constant = cast<SCEVConstant>(Coeff);
2399 APInt ConstCoeff = Constant->getValue()->getValue();
2400 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2402 Inner = AddRec->getStart();
2404 Delta = SE->getMinusSCEV(SrcCoeff, DstCoeff);
2405 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Delta))
2406 // If the coefficient is the product of a constant and other stuff,
2407 // we can use the constant in the GCD computation.
2408 Constant = getConstantPart(Product);
2409 else if (isa<SCEVConstant>(Delta))
2410 Constant = cast<SCEVConstant>(Delta);
2412 // The difference of the two coefficients might not be a product
2413 // or constant, in which case we give up on this direction.
2416 APInt ConstCoeff = Constant->getValue()->getValue();
2417 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2418 DEBUG(dbgs() << "\tRunningGCD = " << RunningGCD << "\n");
2419 if (RunningGCD != 0) {
2420 Remainder = ConstDelta.srem(RunningGCD);
2421 DEBUG(dbgs() << "\tRemainder = " << Remainder << "\n");
2422 if (Remainder != 0) {
2423 unsigned Level = mapSrcLoop(CurLoop);
2424 Result.DV[Level - 1].Direction &= unsigned(~Dependence::DVEntry::EQ);
2431 DEBUG(dbgs() << "all done\n");
2436 //===----------------------------------------------------------------------===//
2437 // banerjeeMIVtest -
2438 // Use Banerjee's Inequalities to test an MIV subscript pair.
2439 // (Wolfe, in the race-car book, calls this the Extreme Value Test.)
2440 // Generally follows the discussion in Section 2.5.2 of
2442 // Optimizing Supercompilers for Supercomputers
2445 // The inequalities given on page 25 are simplified in that loops are
2446 // normalized so that the lower bound is always 0 and the stride is always 1.
2447 // For example, Wolfe gives
2449 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2451 // where A_k is the coefficient of the kth index in the source subscript,
2452 // B_k is the coefficient of the kth index in the destination subscript,
2453 // U_k is the upper bound of the kth index, L_k is the lower bound of the Kth
2454 // index, and N_k is the stride of the kth index. Since all loops are normalized
2455 // by the SCEV package, N_k = 1 and L_k = 0, allowing us to simplify the
2458 // LB^<_k = (A^-_k - B_k)^- (U_k - 0 - 1) + (A_k - B_k)0 - B_k 1
2459 // = (A^-_k - B_k)^- (U_k - 1) - B_k
2461 // Similar simplifications are possible for the other equations.
2463 // When we can't determine the number of iterations for a loop,
2464 // we use NULL as an indicator for the worst case, infinity.
2465 // When computing the upper bound, NULL denotes +inf;
2466 // for the lower bound, NULL denotes -inf.
2468 // Return true if dependence disproved.
2469 bool DependenceAnalysis::banerjeeMIVtest(const SCEV *Src,
2471 const SmallBitVector &Loops,
2472 FullDependence &Result) const {
2473 DEBUG(dbgs() << "starting Banerjee\n");
2474 ++BanerjeeApplications;
2475 DEBUG(dbgs() << " Src = " << *Src << '\n');
2477 CoefficientInfo *A = collectCoeffInfo(Src, true, A0);
2478 DEBUG(dbgs() << " Dst = " << *Dst << '\n');
2480 CoefficientInfo *B = collectCoeffInfo(Dst, false, B0);
2481 BoundInfo *Bound = new BoundInfo[MaxLevels + 1];
2482 const SCEV *Delta = SE->getMinusSCEV(B0, A0);
2483 DEBUG(dbgs() << "\tDelta = " << *Delta << '\n');
2485 // Compute bounds for all the * directions.
2486 DEBUG(dbgs() << "\tBounds[*]\n");
2487 for (unsigned K = 1; K <= MaxLevels; ++K) {
2488 Bound[K].Iterations = A[K].Iterations ? A[K].Iterations : B[K].Iterations;
2489 Bound[K].Direction = Dependence::DVEntry::ALL;
2490 Bound[K].DirSet = Dependence::DVEntry::NONE;
2491 findBoundsALL(A, B, Bound, K);
2493 DEBUG(dbgs() << "\t " << K << '\t');
2494 if (Bound[K].Lower[Dependence::DVEntry::ALL])
2495 DEBUG(dbgs() << *Bound[K].Lower[Dependence::DVEntry::ALL] << '\t');
2497 DEBUG(dbgs() << "-inf\t");
2498 if (Bound[K].Upper[Dependence::DVEntry::ALL])
2499 DEBUG(dbgs() << *Bound[K].Upper[Dependence::DVEntry::ALL] << '\n');
2501 DEBUG(dbgs() << "+inf\n");
2505 // Test the *, *, *, ... case.
2506 bool Disproved = false;
2507 if (testBounds(Dependence::DVEntry::ALL, 0, Bound, Delta)) {
2508 // Explore the direction vector hierarchy.
2509 unsigned DepthExpanded = 0;
2510 unsigned NewDeps = exploreDirections(1, A, B, Bound,
2511 Loops, DepthExpanded, Delta);
2513 bool Improved = false;
2514 for (unsigned K = 1; K <= CommonLevels; ++K) {
2516 unsigned Old = Result.DV[K - 1].Direction;
2517 Result.DV[K - 1].Direction = Old & Bound[K].DirSet;
2518 Improved |= Old != Result.DV[K - 1].Direction;
2519 if (!Result.DV[K - 1].Direction) {
2527 ++BanerjeeSuccesses;
2530 ++BanerjeeIndependence;
2535 ++BanerjeeIndependence;
2545 // Hierarchically expands the direction vector
2546 // search space, combining the directions of discovered dependences
2547 // in the DirSet field of Bound. Returns the number of distinct
2548 // dependences discovered. If the dependence is disproved,
2549 // it will return 0.
2550 unsigned DependenceAnalysis::exploreDirections(unsigned Level,
2554 const SmallBitVector &Loops,
2555 unsigned &DepthExpanded,
2556 const SCEV *Delta) const {
2557 if (Level > CommonLevels) {
2559 DEBUG(dbgs() << "\t[");
2560 for (unsigned K = 1; K <= CommonLevels; ++K) {
2562 Bound[K].DirSet |= Bound[K].Direction;
2564 switch (Bound[K].Direction) {
2565 case Dependence::DVEntry::LT:
2566 DEBUG(dbgs() << " <");
2568 case Dependence::DVEntry::EQ:
2569 DEBUG(dbgs() << " =");
2571 case Dependence::DVEntry::GT:
2572 DEBUG(dbgs() << " >");
2574 case Dependence::DVEntry::ALL:
2575 DEBUG(dbgs() << " *");
2578 llvm_unreachable("unexpected Bound[K].Direction");
2583 DEBUG(dbgs() << " ]\n");
2587 if (Level > DepthExpanded) {
2588 DepthExpanded = Level;
2589 // compute bounds for <, =, > at current level
2590 findBoundsLT(A, B, Bound, Level);
2591 findBoundsGT(A, B, Bound, Level);
2592 findBoundsEQ(A, B, Bound, Level);
2594 DEBUG(dbgs() << "\tBound for level = " << Level << '\n');
2595 DEBUG(dbgs() << "\t <\t");
2596 if (Bound[Level].Lower[Dependence::DVEntry::LT])
2597 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::LT] << '\t');
2599 DEBUG(dbgs() << "-inf\t");
2600 if (Bound[Level].Upper[Dependence::DVEntry::LT])
2601 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::LT] << '\n');
2603 DEBUG(dbgs() << "+inf\n");
2604 DEBUG(dbgs() << "\t =\t");
2605 if (Bound[Level].Lower[Dependence::DVEntry::EQ])
2606 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::EQ] << '\t');
2608 DEBUG(dbgs() << "-inf\t");
2609 if (Bound[Level].Upper[Dependence::DVEntry::EQ])
2610 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::EQ] << '\n');
2612 DEBUG(dbgs() << "+inf\n");
2613 DEBUG(dbgs() << "\t >\t");
2614 if (Bound[Level].Lower[Dependence::DVEntry::GT])
2615 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::GT] << '\t');
2617 DEBUG(dbgs() << "-inf\t");
2618 if (Bound[Level].Upper[Dependence::DVEntry::GT])
2619 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::GT] << '\n');
2621 DEBUG(dbgs() << "+inf\n");
2625 unsigned NewDeps = 0;
2627 // test bounds for <, *, *, ...
2628 if (testBounds(Dependence::DVEntry::LT, Level, Bound, Delta))
2629 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2630 Loops, DepthExpanded, Delta);
2632 // Test bounds for =, *, *, ...
2633 if (testBounds(Dependence::DVEntry::EQ, Level, Bound, Delta))
2634 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2635 Loops, DepthExpanded, Delta);
2637 // test bounds for >, *, *, ...
2638 if (testBounds(Dependence::DVEntry::GT, Level, Bound, Delta))
2639 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2640 Loops, DepthExpanded, Delta);
2642 Bound[Level].Direction = Dependence::DVEntry::ALL;
2646 return exploreDirections(Level + 1, A, B, Bound, Loops, DepthExpanded, Delta);
2650 // Returns true iff the current bounds are plausible.
2651 bool DependenceAnalysis::testBounds(unsigned char DirKind,
2654 const SCEV *Delta) const {
2655 Bound[Level].Direction = DirKind;
2656 if (const SCEV *LowerBound = getLowerBound(Bound))
2657 if (isKnownPredicate(CmpInst::ICMP_SGT, LowerBound, Delta))
2659 if (const SCEV *UpperBound = getUpperBound(Bound))
2660 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, UpperBound))
2666 // Computes the upper and lower bounds for level K
2667 // using the * direction. Records them in Bound.
2668 // Wolfe gives the equations
2670 // LB^*_k = (A^-_k - B^+_k)(U_k - L_k) + (A_k - B_k)L_k
2671 // UB^*_k = (A^+_k - B^-_k)(U_k - L_k) + (A_k - B_k)L_k
2673 // Since we normalize loops, we can simplify these equations to
2675 // LB^*_k = (A^-_k - B^+_k)U_k
2676 // UB^*_k = (A^+_k - B^-_k)U_k
2678 // We must be careful to handle the case where the upper bound is unknown.
2679 // Note that the lower bound is always <= 0
2680 // and the upper bound is always >= 0.
2681 void DependenceAnalysis::findBoundsALL(CoefficientInfo *A,
2685 Bound[K].Lower[Dependence::DVEntry::ALL] = nullptr; // Default value = -infinity.
2686 Bound[K].Upper[Dependence::DVEntry::ALL] = nullptr; // Default value = +infinity.
2687 if (Bound[K].Iterations) {
2688 Bound[K].Lower[Dependence::DVEntry::ALL] =
2689 SE->getMulExpr(SE->getMinusSCEV(A[K].NegPart, B[K].PosPart),
2690 Bound[K].Iterations);
2691 Bound[K].Upper[Dependence::DVEntry::ALL] =
2692 SE->getMulExpr(SE->getMinusSCEV(A[K].PosPart, B[K].NegPart),
2693 Bound[K].Iterations);
2696 // If the difference is 0, we won't need to know the number of iterations.
2697 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].NegPart, B[K].PosPart))
2698 Bound[K].Lower[Dependence::DVEntry::ALL] =
2699 SE->getConstant(A[K].Coeff->getType(), 0);
2700 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].PosPart, B[K].NegPart))
2701 Bound[K].Upper[Dependence::DVEntry::ALL] =
2702 SE->getConstant(A[K].Coeff->getType(), 0);
2707 // Computes the upper and lower bounds for level K
2708 // using the = direction. Records them in Bound.
2709 // Wolfe gives the equations
2711 // LB^=_k = (A_k - B_k)^- (U_k - L_k) + (A_k - B_k)L_k
2712 // UB^=_k = (A_k - B_k)^+ (U_k - L_k) + (A_k - B_k)L_k
2714 // Since we normalize loops, we can simplify these equations to
2716 // LB^=_k = (A_k - B_k)^- U_k
2717 // UB^=_k = (A_k - B_k)^+ U_k
2719 // We must be careful to handle the case where the upper bound is unknown.
2720 // Note that the lower bound is always <= 0
2721 // and the upper bound is always >= 0.
2722 void DependenceAnalysis::findBoundsEQ(CoefficientInfo *A,
2726 Bound[K].Lower[Dependence::DVEntry::EQ] = nullptr; // Default value = -infinity.
2727 Bound[K].Upper[Dependence::DVEntry::EQ] = nullptr; // Default value = +infinity.
2728 if (Bound[K].Iterations) {
2729 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2730 const SCEV *NegativePart = getNegativePart(Delta);
2731 Bound[K].Lower[Dependence::DVEntry::EQ] =
2732 SE->getMulExpr(NegativePart, Bound[K].Iterations);
2733 const SCEV *PositivePart = getPositivePart(Delta);
2734 Bound[K].Upper[Dependence::DVEntry::EQ] =
2735 SE->getMulExpr(PositivePart, Bound[K].Iterations);
2738 // If the positive/negative part of the difference is 0,
2739 // we won't need to know the number of iterations.
2740 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2741 const SCEV *NegativePart = getNegativePart(Delta);
2742 if (NegativePart->isZero())
2743 Bound[K].Lower[Dependence::DVEntry::EQ] = NegativePart; // Zero
2744 const SCEV *PositivePart = getPositivePart(Delta);
2745 if (PositivePart->isZero())
2746 Bound[K].Upper[Dependence::DVEntry::EQ] = PositivePart; // Zero
2751 // Computes the upper and lower bounds for level K
2752 // using the < direction. Records them in Bound.
2753 // Wolfe gives the equations
2755 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2756 // UB^<_k = (A^+_k - B_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2758 // Since we normalize loops, we can simplify these equations to
2760 // LB^<_k = (A^-_k - B_k)^- (U_k - 1) - B_k
2761 // UB^<_k = (A^+_k - B_k)^+ (U_k - 1) - B_k
2763 // We must be careful to handle the case where the upper bound is unknown.
2764 void DependenceAnalysis::findBoundsLT(CoefficientInfo *A,
2768 Bound[K].Lower[Dependence::DVEntry::LT] = nullptr; // Default value = -infinity.
2769 Bound[K].Upper[Dependence::DVEntry::LT] = nullptr; // Default value = +infinity.
2770 if (Bound[K].Iterations) {
2771 const SCEV *Iter_1 =
2772 SE->getMinusSCEV(Bound[K].Iterations,
2773 SE->getConstant(Bound[K].Iterations->getType(), 1));
2774 const SCEV *NegPart =
2775 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2776 Bound[K].Lower[Dependence::DVEntry::LT] =
2777 SE->getMinusSCEV(SE->getMulExpr(NegPart, Iter_1), B[K].Coeff);
2778 const SCEV *PosPart =
2779 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2780 Bound[K].Upper[Dependence::DVEntry::LT] =
2781 SE->getMinusSCEV(SE->getMulExpr(PosPart, Iter_1), B[K].Coeff);
2784 // If the positive/negative part of the difference is 0,
2785 // we won't need to know the number of iterations.
2786 const SCEV *NegPart =
2787 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2788 if (NegPart->isZero())
2789 Bound[K].Lower[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2790 const SCEV *PosPart =
2791 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2792 if (PosPart->isZero())
2793 Bound[K].Upper[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2798 // Computes the upper and lower bounds for level K
2799 // using the > direction. Records them in Bound.
2800 // Wolfe gives the equations
2802 // LB^>_k = (A_k - B^+_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2803 // UB^>_k = (A_k - B^-_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2805 // Since we normalize loops, we can simplify these equations to
2807 // LB^>_k = (A_k - B^+_k)^- (U_k - 1) + A_k
2808 // UB^>_k = (A_k - B^-_k)^+ (U_k - 1) + A_k
2810 // We must be careful to handle the case where the upper bound is unknown.
2811 void DependenceAnalysis::findBoundsGT(CoefficientInfo *A,
2815 Bound[K].Lower[Dependence::DVEntry::GT] = nullptr; // Default value = -infinity.
2816 Bound[K].Upper[Dependence::DVEntry::GT] = nullptr; // Default value = +infinity.
2817 if (Bound[K].Iterations) {
2818 const SCEV *Iter_1 =
2819 SE->getMinusSCEV(Bound[K].Iterations,
2820 SE->getConstant(Bound[K].Iterations->getType(), 1));
2821 const SCEV *NegPart =
2822 getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2823 Bound[K].Lower[Dependence::DVEntry::GT] =
2824 SE->getAddExpr(SE->getMulExpr(NegPart, Iter_1), A[K].Coeff);
2825 const SCEV *PosPart =
2826 getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2827 Bound[K].Upper[Dependence::DVEntry::GT] =
2828 SE->getAddExpr(SE->getMulExpr(PosPart, Iter_1), A[K].Coeff);
2831 // If the positive/negative part of the difference is 0,
2832 // we won't need to know the number of iterations.
2833 const SCEV *NegPart = getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2834 if (NegPart->isZero())
2835 Bound[K].Lower[Dependence::DVEntry::GT] = A[K].Coeff;
2836 const SCEV *PosPart = getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2837 if (PosPart->isZero())
2838 Bound[K].Upper[Dependence::DVEntry::GT] = A[K].Coeff;
2844 const SCEV *DependenceAnalysis::getPositivePart(const SCEV *X) const {
2845 return SE->getSMaxExpr(X, SE->getConstant(X->getType(), 0));
2850 const SCEV *DependenceAnalysis::getNegativePart(const SCEV *X) const {
2851 return SE->getSMinExpr(X, SE->getConstant(X->getType(), 0));
2855 // Walks through the subscript,
2856 // collecting each coefficient, the associated loop bounds,
2857 // and recording its positive and negative parts for later use.
2858 DependenceAnalysis::CoefficientInfo *
2859 DependenceAnalysis::collectCoeffInfo(const SCEV *Subscript,
2861 const SCEV *&Constant) const {
2862 const SCEV *Zero = SE->getConstant(Subscript->getType(), 0);
2863 CoefficientInfo *CI = new CoefficientInfo[MaxLevels + 1];
2864 for (unsigned K = 1; K <= MaxLevels; ++K) {
2866 CI[K].PosPart = Zero;
2867 CI[K].NegPart = Zero;
2868 CI[K].Iterations = nullptr;
2870 while (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Subscript)) {
2871 const Loop *L = AddRec->getLoop();
2872 unsigned K = SrcFlag ? mapSrcLoop(L) : mapDstLoop(L);
2873 CI[K].Coeff = AddRec->getStepRecurrence(*SE);
2874 CI[K].PosPart = getPositivePart(CI[K].Coeff);
2875 CI[K].NegPart = getNegativePart(CI[K].Coeff);
2876 CI[K].Iterations = collectUpperBound(L, Subscript->getType());
2877 Subscript = AddRec->getStart();
2879 Constant = Subscript;
2881 DEBUG(dbgs() << "\tCoefficient Info\n");
2882 for (unsigned K = 1; K <= MaxLevels; ++K) {
2883 DEBUG(dbgs() << "\t " << K << "\t" << *CI[K].Coeff);
2884 DEBUG(dbgs() << "\tPos Part = ");
2885 DEBUG(dbgs() << *CI[K].PosPart);
2886 DEBUG(dbgs() << "\tNeg Part = ");
2887 DEBUG(dbgs() << *CI[K].NegPart);
2888 DEBUG(dbgs() << "\tUpper Bound = ");
2889 if (CI[K].Iterations)
2890 DEBUG(dbgs() << *CI[K].Iterations);
2892 DEBUG(dbgs() << "+inf");
2893 DEBUG(dbgs() << '\n');
2895 DEBUG(dbgs() << "\t Constant = " << *Subscript << '\n');
2901 // Looks through all the bounds info and
2902 // computes the lower bound given the current direction settings
2903 // at each level. If the lower bound for any level is -inf,
2904 // the result is -inf.
2905 const SCEV *DependenceAnalysis::getLowerBound(BoundInfo *Bound) const {
2906 const SCEV *Sum = Bound[1].Lower[Bound[1].Direction];
2907 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2908 if (Bound[K].Lower[Bound[K].Direction])
2909 Sum = SE->getAddExpr(Sum, Bound[K].Lower[Bound[K].Direction]);
2917 // Looks through all the bounds info and
2918 // computes the upper bound given the current direction settings
2919 // at each level. If the upper bound at any level is +inf,
2920 // the result is +inf.
2921 const SCEV *DependenceAnalysis::getUpperBound(BoundInfo *Bound) const {
2922 const SCEV *Sum = Bound[1].Upper[Bound[1].Direction];
2923 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2924 if (Bound[K].Upper[Bound[K].Direction])
2925 Sum = SE->getAddExpr(Sum, Bound[K].Upper[Bound[K].Direction]);
2933 //===----------------------------------------------------------------------===//
2934 // Constraint manipulation for Delta test.
2936 // Given a linear SCEV,
2937 // return the coefficient (the step)
2938 // corresponding to the specified loop.
2939 // If there isn't one, return 0.
2940 // For example, given a*i + b*j + c*k, zeroing the coefficient
2941 // corresponding to the j loop would yield b.
2942 const SCEV *DependenceAnalysis::findCoefficient(const SCEV *Expr,
2943 const Loop *TargetLoop) const {
2944 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2946 return SE->getConstant(Expr->getType(), 0);
2947 if (AddRec->getLoop() == TargetLoop)
2948 return AddRec->getStepRecurrence(*SE);
2949 return findCoefficient(AddRec->getStart(), TargetLoop);
2953 // Given a linear SCEV,
2954 // return the SCEV given by zeroing out the coefficient
2955 // corresponding to the specified loop.
2956 // For example, given a*i + b*j + c*k, zeroing the coefficient
2957 // corresponding to the j loop would yield a*i + c*k.
2958 const SCEV *DependenceAnalysis::zeroCoefficient(const SCEV *Expr,
2959 const Loop *TargetLoop) const {
2960 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2962 return Expr; // ignore
2963 if (AddRec->getLoop() == TargetLoop)
2964 return AddRec->getStart();
2965 return SE->getAddRecExpr(zeroCoefficient(AddRec->getStart(), TargetLoop),
2966 AddRec->getStepRecurrence(*SE),
2968 AddRec->getNoWrapFlags());
2972 // Given a linear SCEV Expr,
2973 // return the SCEV given by adding some Value to the
2974 // coefficient corresponding to the specified TargetLoop.
2975 // For example, given a*i + b*j + c*k, adding 1 to the coefficient
2976 // corresponding to the j loop would yield a*i + (b+1)*j + c*k.
2977 const SCEV *DependenceAnalysis::addToCoefficient(const SCEV *Expr,
2978 const Loop *TargetLoop,
2979 const SCEV *Value) const {
2980 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2981 if (!AddRec) // create a new addRec
2982 return SE->getAddRecExpr(Expr,
2985 SCEV::FlagAnyWrap); // Worst case, with no info.
2986 if (AddRec->getLoop() == TargetLoop) {
2987 const SCEV *Sum = SE->getAddExpr(AddRec->getStepRecurrence(*SE), Value);
2989 return AddRec->getStart();
2990 return SE->getAddRecExpr(AddRec->getStart(),
2993 AddRec->getNoWrapFlags());
2995 if (SE->isLoopInvariant(AddRec, TargetLoop))
2996 return SE->getAddRecExpr(AddRec, Value, TargetLoop, SCEV::FlagAnyWrap);
2997 return SE->getAddRecExpr(
2998 addToCoefficient(AddRec->getStart(), TargetLoop, Value),
2999 AddRec->getStepRecurrence(*SE), AddRec->getLoop(),
3000 AddRec->getNoWrapFlags());
3004 // Review the constraints, looking for opportunities
3005 // to simplify a subscript pair (Src and Dst).
3006 // Return true if some simplification occurs.
3007 // If the simplification isn't exact (that is, if it is conservative
3008 // in terms of dependence), set consistent to false.
3009 // Corresponds to Figure 5 from the paper
3011 // Practical Dependence Testing
3012 // Goff, Kennedy, Tseng
3014 bool DependenceAnalysis::propagate(const SCEV *&Src,
3016 SmallBitVector &Loops,
3017 SmallVectorImpl<Constraint> &Constraints,
3019 bool Result = false;
3020 for (int LI = Loops.find_first(); LI >= 0; LI = Loops.find_next(LI)) {
3021 DEBUG(dbgs() << "\t Constraint[" << LI << "] is");
3022 DEBUG(Constraints[LI].dump(dbgs()));
3023 if (Constraints[LI].isDistance())
3024 Result |= propagateDistance(Src, Dst, Constraints[LI], Consistent);
3025 else if (Constraints[LI].isLine())
3026 Result |= propagateLine(Src, Dst, Constraints[LI], Consistent);
3027 else if (Constraints[LI].isPoint())
3028 Result |= propagatePoint(Src, Dst, Constraints[LI]);
3034 // Attempt to propagate a distance
3035 // constraint into a subscript pair (Src and Dst).
3036 // Return true if some simplification occurs.
3037 // If the simplification isn't exact (that is, if it is conservative
3038 // in terms of dependence), set consistent to false.
3039 bool DependenceAnalysis::propagateDistance(const SCEV *&Src,
3041 Constraint &CurConstraint,
3043 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3044 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3045 const SCEV *A_K = findCoefficient(Src, CurLoop);
3048 const SCEV *DA_K = SE->getMulExpr(A_K, CurConstraint.getD());
3049 Src = SE->getMinusSCEV(Src, DA_K);
3050 Src = zeroCoefficient(Src, CurLoop);
3051 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3052 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3053 Dst = addToCoefficient(Dst, CurLoop, SE->getNegativeSCEV(A_K));
3054 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3055 if (!findCoefficient(Dst, CurLoop)->isZero())
3061 // Attempt to propagate a line
3062 // constraint into a subscript pair (Src and Dst).
3063 // Return true if some simplification occurs.
3064 // If the simplification isn't exact (that is, if it is conservative
3065 // in terms of dependence), set consistent to false.
3066 bool DependenceAnalysis::propagateLine(const SCEV *&Src,
3068 Constraint &CurConstraint,
3070 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3071 const SCEV *A = CurConstraint.getA();
3072 const SCEV *B = CurConstraint.getB();
3073 const SCEV *C = CurConstraint.getC();
3074 DEBUG(dbgs() << "\t\tA = " << *A << ", B = " << *B << ", C = " << *C << "\n");
3075 DEBUG(dbgs() << "\t\tSrc = " << *Src << "\n");
3076 DEBUG(dbgs() << "\t\tDst = " << *Dst << "\n");
3078 const SCEVConstant *Bconst = dyn_cast<SCEVConstant>(B);
3079 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3080 if (!Bconst || !Cconst) return false;
3081 APInt Beta = Bconst->getValue()->getValue();
3082 APInt Charlie = Cconst->getValue()->getValue();
3083 APInt CdivB = Charlie.sdiv(Beta);
3084 assert(Charlie.srem(Beta) == 0 && "C should be evenly divisible by B");
3085 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3086 // Src = SE->getAddExpr(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3087 Src = SE->getMinusSCEV(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3088 Dst = zeroCoefficient(Dst, CurLoop);
3089 if (!findCoefficient(Src, CurLoop)->isZero())
3092 else if (B->isZero()) {
3093 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3094 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3095 if (!Aconst || !Cconst) return false;
3096 APInt Alpha = Aconst->getValue()->getValue();
3097 APInt Charlie = Cconst->getValue()->getValue();
3098 APInt CdivA = Charlie.sdiv(Alpha);
3099 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3100 const SCEV *A_K = findCoefficient(Src, CurLoop);
3101 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3102 Src = zeroCoefficient(Src, CurLoop);
3103 if (!findCoefficient(Dst, CurLoop)->isZero())
3106 else if (isKnownPredicate(CmpInst::ICMP_EQ, A, B)) {
3107 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3108 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3109 if (!Aconst || !Cconst) return false;
3110 APInt Alpha = Aconst->getValue()->getValue();
3111 APInt Charlie = Cconst->getValue()->getValue();
3112 APInt CdivA = Charlie.sdiv(Alpha);
3113 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3114 const SCEV *A_K = findCoefficient(Src, CurLoop);
3115 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3116 Src = zeroCoefficient(Src, CurLoop);
3117 Dst = addToCoefficient(Dst, CurLoop, A_K);
3118 if (!findCoefficient(Dst, CurLoop)->isZero())
3122 // paper is incorrect here, or perhaps just misleading
3123 const SCEV *A_K = findCoefficient(Src, CurLoop);
3124 Src = SE->getMulExpr(Src, A);
3125 Dst = SE->getMulExpr(Dst, A);
3126 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, C));
3127 Src = zeroCoefficient(Src, CurLoop);
3128 Dst = addToCoefficient(Dst, CurLoop, SE->getMulExpr(A_K, B));
3129 if (!findCoefficient(Dst, CurLoop)->isZero())
3132 DEBUG(dbgs() << "\t\tnew Src = " << *Src << "\n");
3133 DEBUG(dbgs() << "\t\tnew Dst = " << *Dst << "\n");
3138 // Attempt to propagate a point
3139 // constraint into a subscript pair (Src and Dst).
3140 // Return true if some simplification occurs.
3141 bool DependenceAnalysis::propagatePoint(const SCEV *&Src,
3143 Constraint &CurConstraint) {
3144 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3145 const SCEV *A_K = findCoefficient(Src, CurLoop);
3146 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3147 const SCEV *XA_K = SE->getMulExpr(A_K, CurConstraint.getX());
3148 const SCEV *YAP_K = SE->getMulExpr(AP_K, CurConstraint.getY());
3149 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3150 Src = SE->getAddExpr(Src, SE->getMinusSCEV(XA_K, YAP_K));
3151 Src = zeroCoefficient(Src, CurLoop);
3152 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3153 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3154 Dst = zeroCoefficient(Dst, CurLoop);
3155 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3160 // Update direction vector entry based on the current constraint.
3161 void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
3162 const Constraint &CurConstraint
3164 DEBUG(dbgs() << "\tUpdate direction, constraint =");
3165 DEBUG(CurConstraint.dump(dbgs()));
3166 if (CurConstraint.isAny())
3168 else if (CurConstraint.isDistance()) {
3169 // this one is consistent, the others aren't
3170 Level.Scalar = false;
3171 Level.Distance = CurConstraint.getD();
3172 unsigned NewDirection = Dependence::DVEntry::NONE;
3173 if (!SE->isKnownNonZero(Level.Distance)) // if may be zero
3174 NewDirection = Dependence::DVEntry::EQ;
3175 if (!SE->isKnownNonPositive(Level.Distance)) // if may be positive
3176 NewDirection |= Dependence::DVEntry::LT;
3177 if (!SE->isKnownNonNegative(Level.Distance)) // if may be negative
3178 NewDirection |= Dependence::DVEntry::GT;
3179 Level.Direction &= NewDirection;
3181 else if (CurConstraint.isLine()) {
3182 Level.Scalar = false;
3183 Level.Distance = nullptr;
3184 // direction should be accurate
3186 else if (CurConstraint.isPoint()) {
3187 Level.Scalar = false;
3188 Level.Distance = nullptr;
3189 unsigned NewDirection = Dependence::DVEntry::NONE;
3190 if (!isKnownPredicate(CmpInst::ICMP_NE,
3191 CurConstraint.getY(),
3192 CurConstraint.getX()))
3194 NewDirection |= Dependence::DVEntry::EQ;
3195 if (!isKnownPredicate(CmpInst::ICMP_SLE,
3196 CurConstraint.getY(),
3197 CurConstraint.getX()))
3199 NewDirection |= Dependence::DVEntry::LT;
3200 if (!isKnownPredicate(CmpInst::ICMP_SGE,
3201 CurConstraint.getY(),
3202 CurConstraint.getX()))
3204 NewDirection |= Dependence::DVEntry::GT;
3205 Level.Direction &= NewDirection;
3208 llvm_unreachable("constraint has unexpected kind");
3211 /// Check if we can delinearize the subscripts. If the SCEVs representing the
3212 /// source and destination array references are recurrences on a nested loop,
3213 /// this function flattens the nested recurrences into separate recurrences
3214 /// for each loop level.
3215 bool DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV,
3216 const SCEV *DstSCEV,
3217 SmallVectorImpl<Subscript> &Pair,
3218 const SCEV *ElementSize) {
3219 const SCEVUnknown *SrcBase =
3220 dyn_cast<SCEVUnknown>(SE->getPointerBase(SrcSCEV));
3221 const SCEVUnknown *DstBase =
3222 dyn_cast<SCEVUnknown>(SE->getPointerBase(DstSCEV));
3224 if (!SrcBase || !DstBase || SrcBase != DstBase)
3227 SrcSCEV = SE->getMinusSCEV(SrcSCEV, SrcBase);
3228 DstSCEV = SE->getMinusSCEV(DstSCEV, DstBase);
3230 const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
3231 const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
3232 if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
3235 // First step: collect parametric terms in both array references.
3236 SmallVector<const SCEV *, 4> Terms;
3237 SrcAR->collectParametricTerms(*SE, Terms);
3238 DstAR->collectParametricTerms(*SE, Terms);
3240 // Second step: find subscript sizes.
3241 SmallVector<const SCEV *, 4> Sizes;
3242 SE->findArrayDimensions(Terms, Sizes, ElementSize);
3244 // Third step: compute the access functions for each subscript.
3245 SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts;
3246 SrcAR->computeAccessFunctions(*SE, SrcSubscripts, Sizes);
3247 DstAR->computeAccessFunctions(*SE, DstSubscripts, Sizes);
3249 // Fail when there is only a subscript: that's a linearized access function.
3250 if (SrcSubscripts.size() < 2 || DstSubscripts.size() < 2 ||
3251 SrcSubscripts.size() != DstSubscripts.size())
3254 int size = SrcSubscripts.size();
3257 dbgs() << "\nSrcSubscripts: ";
3258 for (int i = 0; i < size; i++)
3259 dbgs() << *SrcSubscripts[i];
3260 dbgs() << "\nDstSubscripts: ";
3261 for (int i = 0; i < size; i++)
3262 dbgs() << *DstSubscripts[i];
3265 // The delinearization transforms a single-subscript MIV dependence test into
3266 // a multi-subscript SIV dependence test that is easier to compute. So we
3267 // resize Pair to contain as many pairs of subscripts as the delinearization
3268 // has found, and then initialize the pairs following the delinearization.
3270 for (int i = 0; i < size; ++i) {
3271 Pair[i].Src = SrcSubscripts[i];
3272 Pair[i].Dst = DstSubscripts[i];
3273 unifySubscriptType(&Pair[i]);
3275 // FIXME: we should record the bounds SrcSizes[i] and DstSizes[i] that the
3276 // delinearization has found, and add these constraints to the dependence
3277 // check to avoid memory accesses overflow from one dimension into another.
3278 // This is related to the problem of determining the existence of data
3279 // dependences in array accesses using a different number of subscripts: in
3280 // C one can access an array A[100][100]; as A[0][9999], *A[9999], etc.
3286 //===----------------------------------------------------------------------===//
3289 // For debugging purposes, dump a small bit vector to dbgs().
3290 static void dumpSmallBitVector(SmallBitVector &BV) {
3292 for (int VI = BV.find_first(); VI >= 0; VI = BV.find_next(VI)) {
3294 if (BV.find_next(VI) >= 0)
3303 // Returns NULL if there is no dependence.
3304 // Otherwise, return a Dependence with as many details as possible.
3305 // Corresponds to Section 3.1 in the paper
3307 // Practical Dependence Testing
3308 // Goff, Kennedy, Tseng
3311 // Care is required to keep the routine below, getSplitIteration(),
3312 // up to date with respect to this routine.
3313 std::unique_ptr<Dependence>
3314 DependenceAnalysis::depends(Instruction *Src, Instruction *Dst,
3315 bool PossiblyLoopIndependent) {
3317 PossiblyLoopIndependent = false;
3319 if ((!Src->mayReadFromMemory() && !Src->mayWriteToMemory()) ||
3320 (!Dst->mayReadFromMemory() && !Dst->mayWriteToMemory()))
3321 // if both instructions don't reference memory, there's no dependence
3324 if (!isLoadOrStore(Src) || !isLoadOrStore(Dst)) {
3325 // can only analyze simple loads and stores, i.e., no calls, invokes, etc.
3326 DEBUG(dbgs() << "can only handle simple loads and stores\n");
3327 return make_unique<Dependence>(Src, Dst);
3330 Value *SrcPtr = getPointerOperand(Src);
3331 Value *DstPtr = getPointerOperand(Dst);
3333 switch (underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3335 case AliasAnalysis::MayAlias:
3336 case AliasAnalysis::PartialAlias:
3337 // cannot analyse objects if we don't understand their aliasing.
3338 DEBUG(dbgs() << "can't analyze may or partial alias\n");
3339 return make_unique<Dependence>(Src, Dst);
3340 case AliasAnalysis::NoAlias:
3341 // If the objects noalias, they are distinct, accesses are independent.
3342 DEBUG(dbgs() << "no alias\n");
3344 case AliasAnalysis::MustAlias:
3345 break; // The underlying objects alias; test accesses for dependence.
3348 // establish loop nesting levels
3349 establishNestingLevels(Src, Dst);
3350 DEBUG(dbgs() << " common nesting levels = " << CommonLevels << "\n");
3351 DEBUG(dbgs() << " maximum nesting levels = " << MaxLevels << "\n");
3353 FullDependence Result(Src, Dst, PossiblyLoopIndependent, CommonLevels);
3356 // See if there are GEPs we can use.
3357 bool UsefulGEP = false;
3358 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3359 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3360 if (SrcGEP && DstGEP &&
3361 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3362 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3363 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3364 DEBUG(dbgs() << " SrcPtrSCEV = " << *SrcPtrSCEV << "\n");
3365 DEBUG(dbgs() << " DstPtrSCEV = " << *DstPtrSCEV << "\n");
3367 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3368 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3369 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3371 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3372 SmallVector<Subscript, 4> Pair(Pairs);
3374 DEBUG(dbgs() << " using GEPs\n");
3376 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3377 SrcEnd = SrcGEP->idx_end(),
3378 DstIdx = DstGEP->idx_begin();
3380 ++SrcIdx, ++DstIdx, ++P) {
3381 Pair[P].Src = SE->getSCEV(*SrcIdx);
3382 Pair[P].Dst = SE->getSCEV(*DstIdx);
3383 unifySubscriptType(&Pair[P]);
3387 DEBUG(dbgs() << " ignoring GEPs\n");
3388 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3389 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3390 DEBUG(dbgs() << " SrcSCEV = " << *SrcSCEV << "\n");
3391 DEBUG(dbgs() << " DstSCEV = " << *DstSCEV << "\n");
3392 Pair[0].Src = SrcSCEV;
3393 Pair[0].Dst = DstSCEV;
3396 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3397 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3398 DEBUG(dbgs() << " delinerized GEP\n");
3399 Pairs = Pair.size();
3402 for (unsigned P = 0; P < Pairs; ++P) {
3403 Pair[P].Loops.resize(MaxLevels + 1);
3404 Pair[P].GroupLoops.resize(MaxLevels + 1);
3405 Pair[P].Group.resize(Pairs);
3406 removeMatchingExtensions(&Pair[P]);
3407 Pair[P].Classification =
3408 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3409 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3411 Pair[P].GroupLoops = Pair[P].Loops;
3412 Pair[P].Group.set(P);
3413 DEBUG(dbgs() << " subscript " << P << "\n");
3414 DEBUG(dbgs() << "\tsrc = " << *Pair[P].Src << "\n");
3415 DEBUG(dbgs() << "\tdst = " << *Pair[P].Dst << "\n");
3416 DEBUG(dbgs() << "\tclass = " << Pair[P].Classification << "\n");
3417 DEBUG(dbgs() << "\tloops = ");
3418 DEBUG(dumpSmallBitVector(Pair[P].Loops));
3421 SmallBitVector Separable(Pairs);
3422 SmallBitVector Coupled(Pairs);
3424 // Partition subscripts into separable and minimally-coupled groups
3425 // Algorithm in paper is algorithmically better;
3426 // this may be faster in practice. Check someday.
3428 // Here's an example of how it works. Consider this code:
3435 // A[i][j][k][m] = ...;
3436 // ... = A[0][j][l][i + j];
3443 // There are 4 subscripts here:
3447 // 3 [m] and [i + j]
3449 // We've already classified each subscript pair as ZIV, SIV, etc.,
3450 // and collected all the loops mentioned by pair P in Pair[P].Loops.
3451 // In addition, we've initialized Pair[P].GroupLoops to Pair[P].Loops
3452 // and set Pair[P].Group = {P}.
3454 // Src Dst Classification Loops GroupLoops Group
3455 // 0 [i] [0] SIV {1} {1} {0}
3456 // 1 [j] [j] SIV {2} {2} {1}
3457 // 2 [k] [l] RDIV {3,4} {3,4} {2}
3458 // 3 [m] [i + j] MIV {1,2,5} {1,2,5} {3}
3460 // For each subscript SI 0 .. 3, we consider each remaining subscript, SJ.
3461 // So, 0 is compared against 1, 2, and 3; 1 is compared against 2 and 3, etc.
3463 // We begin by comparing 0 and 1. The intersection of the GroupLoops is empty.
3464 // Next, 0 and 2. Again, the intersection of their GroupLoops is empty.
3465 // Next 0 and 3. The intersection of their GroupLoop = {1}, not empty,
3466 // so Pair[3].Group = {0,3} and Done = false (that is, 0 will not be added
3467 // to either Separable or Coupled).
3469 // Next, we consider 1 and 2. The intersection of the GroupLoops is empty.
3470 // Next, 1 and 3. The intersectionof their GroupLoops = {2}, not empty,
3471 // so Pair[3].Group = {0, 1, 3} and Done = false.
3473 // Next, we compare 2 against 3. The intersection of the GroupLoops is empty.
3474 // Since Done remains true, we add 2 to the set of Separable pairs.
3476 // Finally, we consider 3. There's nothing to compare it with,
3477 // so Done remains true and we add it to the Coupled set.
3478 // Pair[3].Group = {0, 1, 3} and GroupLoops = {1, 2, 5}.
3480 // In the end, we've got 1 separable subscript and 1 coupled group.
3481 for (unsigned SI = 0; SI < Pairs; ++SI) {
3482 if (Pair[SI].Classification == Subscript::NonLinear) {
3483 // ignore these, but collect loops for later
3484 ++NonlinearSubscriptPairs;
3485 collectCommonLoops(Pair[SI].Src,
3486 LI->getLoopFor(Src->getParent()),
3488 collectCommonLoops(Pair[SI].Dst,
3489 LI->getLoopFor(Dst->getParent()),
3491 Result.Consistent = false;
3492 } else if (Pair[SI].Classification == Subscript::ZIV) {
3497 // SIV, RDIV, or MIV, so check for coupled group
3499 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3500 SmallBitVector Intersection = Pair[SI].GroupLoops;
3501 Intersection &= Pair[SJ].GroupLoops;
3502 if (Intersection.any()) {
3503 // accumulate set of all the loops in group
3504 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3505 // accumulate set of all subscripts in group
3506 Pair[SJ].Group |= Pair[SI].Group;
3511 if (Pair[SI].Group.count() == 1) {
3513 ++SeparableSubscriptPairs;
3517 ++CoupledSubscriptPairs;
3523 DEBUG(dbgs() << " Separable = ");
3524 DEBUG(dumpSmallBitVector(Separable));
3525 DEBUG(dbgs() << " Coupled = ");
3526 DEBUG(dumpSmallBitVector(Coupled));
3528 Constraint NewConstraint;
3529 NewConstraint.setAny(SE);
3531 // test separable subscripts
3532 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3533 DEBUG(dbgs() << "testing subscript " << SI);
3534 switch (Pair[SI].Classification) {
3535 case Subscript::ZIV:
3536 DEBUG(dbgs() << ", ZIV\n");
3537 if (testZIV(Pair[SI].Src, Pair[SI].Dst, Result))
3540 case Subscript::SIV: {
3541 DEBUG(dbgs() << ", SIV\n");
3543 const SCEV *SplitIter = nullptr;
3544 if (testSIV(Pair[SI].Src, Pair[SI].Dst, Level, Result, NewConstraint,
3549 case Subscript::RDIV:
3550 DEBUG(dbgs() << ", RDIV\n");
3551 if (testRDIV(Pair[SI].Src, Pair[SI].Dst, Result))
3554 case Subscript::MIV:
3555 DEBUG(dbgs() << ", MIV\n");
3556 if (testMIV(Pair[SI].Src, Pair[SI].Dst, Pair[SI].Loops, Result))
3560 llvm_unreachable("subscript has unexpected classification");
3564 if (Coupled.count()) {
3565 // test coupled subscript groups
3566 DEBUG(dbgs() << "starting on coupled subscripts\n");
3567 DEBUG(dbgs() << "MaxLevels + 1 = " << MaxLevels + 1 << "\n");
3568 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3569 for (unsigned II = 0; II <= MaxLevels; ++II)
3570 Constraints[II].setAny(SE);
3571 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3572 DEBUG(dbgs() << "testing subscript group " << SI << " { ");
3573 SmallBitVector Group(Pair[SI].Group);
3574 SmallBitVector Sivs(Pairs);
3575 SmallBitVector Mivs(Pairs);
3576 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3577 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3578 DEBUG(dbgs() << SJ << " ");
3579 if (Pair[SJ].Classification == Subscript::SIV)
3584 DEBUG(dbgs() << "}\n");
3585 while (Sivs.any()) {
3586 bool Changed = false;
3587 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3588 DEBUG(dbgs() << "testing subscript " << SJ << ", SIV\n");
3589 // SJ is an SIV subscript that's part of the current coupled group
3591 const SCEV *SplitIter = nullptr;
3592 DEBUG(dbgs() << "SIV\n");
3593 if (testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level, Result, NewConstraint,
3596 ConstrainedLevels.set(Level);
3597 if (intersectConstraints(&Constraints[Level], &NewConstraint)) {
3598 if (Constraints[Level].isEmpty()) {
3599 ++DeltaIndependence;
3607 // propagate, possibly creating new SIVs and ZIVs
3608 DEBUG(dbgs() << " propagating\n");
3609 DEBUG(dbgs() << "\tMivs = ");
3610 DEBUG(dumpSmallBitVector(Mivs));
3611 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3612 // SJ is an MIV subscript that's part of the current coupled group
3613 DEBUG(dbgs() << "\tSJ = " << SJ << "\n");
3614 if (propagate(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops,
3615 Constraints, Result.Consistent)) {
3616 DEBUG(dbgs() << "\t Changed\n");
3617 ++DeltaPropagations;
3618 Pair[SJ].Classification =
3619 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3620 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3622 switch (Pair[SJ].Classification) {
3623 case Subscript::ZIV:
3624 DEBUG(dbgs() << "ZIV\n");
3625 if (testZIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3629 case Subscript::SIV:
3633 case Subscript::RDIV:
3634 case Subscript::MIV:
3637 llvm_unreachable("bad subscript classification");
3644 // test & propagate remaining RDIVs
3645 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3646 if (Pair[SJ].Classification == Subscript::RDIV) {
3647 DEBUG(dbgs() << "RDIV test\n");
3648 if (testRDIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3650 // I don't yet understand how to propagate RDIV results
3655 // test remaining MIVs
3656 // This code is temporary.
3657 // Better to somehow test all remaining subscripts simultaneously.
3658 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3659 if (Pair[SJ].Classification == Subscript::MIV) {
3660 DEBUG(dbgs() << "MIV test\n");
3661 if (testMIV(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops, Result))
3665 llvm_unreachable("expected only MIV subscripts at this point");
3668 // update Result.DV from constraint vector
3669 DEBUG(dbgs() << " updating\n");
3670 for (int SJ = ConstrainedLevels.find_first(); SJ >= 0;
3671 SJ = ConstrainedLevels.find_next(SJ)) {
3672 if (SJ > (int)CommonLevels)
3674 updateDirection(Result.DV[SJ - 1], Constraints[SJ]);
3675 if (Result.DV[SJ - 1].Direction == Dependence::DVEntry::NONE)
3681 // Make sure the Scalar flags are set correctly.
3682 SmallBitVector CompleteLoops(MaxLevels + 1);
3683 for (unsigned SI = 0; SI < Pairs; ++SI)
3684 CompleteLoops |= Pair[SI].Loops;
3685 for (unsigned II = 1; II <= CommonLevels; ++II)
3686 if (CompleteLoops[II])
3687 Result.DV[II - 1].Scalar = false;
3689 if (PossiblyLoopIndependent) {
3690 // Make sure the LoopIndependent flag is set correctly.
3691 // All directions must include equal, otherwise no
3692 // loop-independent dependence is possible.
3693 for (unsigned II = 1; II <= CommonLevels; ++II) {
3694 if (!(Result.getDirection(II) & Dependence::DVEntry::EQ)) {
3695 Result.LoopIndependent = false;
3701 // On the other hand, if all directions are equal and there's no
3702 // loop-independent dependence possible, then no dependence exists.
3703 bool AllEqual = true;
3704 for (unsigned II = 1; II <= CommonLevels; ++II) {
3705 if (Result.getDirection(II) != Dependence::DVEntry::EQ) {
3714 auto Final = make_unique<FullDependence>(Result);
3715 Result.DV = nullptr;
3716 return std::move(Final);
3721 //===----------------------------------------------------------------------===//
3722 // getSplitIteration -
3723 // Rather than spend rarely-used space recording the splitting iteration
3724 // during the Weak-Crossing SIV test, we re-compute it on demand.
3725 // The re-computation is basically a repeat of the entire dependence test,
3726 // though simplified since we know that the dependence exists.
3727 // It's tedious, since we must go through all propagations, etc.
3729 // Care is required to keep this code up to date with respect to the routine
3730 // above, depends().
3732 // Generally, the dependence analyzer will be used to build
3733 // a dependence graph for a function (basically a map from instructions
3734 // to dependences). Looking for cycles in the graph shows us loops
3735 // that cannot be trivially vectorized/parallelized.
3737 // We can try to improve the situation by examining all the dependences
3738 // that make up the cycle, looking for ones we can break.
3739 // Sometimes, peeling the first or last iteration of a loop will break
3740 // dependences, and we've got flags for those possibilities.
3741 // Sometimes, splitting a loop at some other iteration will do the trick,
3742 // and we've got a flag for that case. Rather than waste the space to
3743 // record the exact iteration (since we rarely know), we provide
3744 // a method that calculates the iteration. It's a drag that it must work
3745 // from scratch, but wonderful in that it's possible.
3747 // Here's an example:
3749 // for (i = 0; i < 10; i++)
3753 // There's a loop-carried flow dependence from the store to the load,
3754 // found by the weak-crossing SIV test. The dependence will have a flag,
3755 // indicating that the dependence can be broken by splitting the loop.
3756 // Calling getSplitIteration will return 5.
3757 // Splitting the loop breaks the dependence, like so:
3759 // for (i = 0; i <= 5; i++)
3762 // for (i = 6; i < 10; i++)
3766 // breaks the dependence and allows us to vectorize/parallelize
3768 const SCEV *DependenceAnalysis::getSplitIteration(const Dependence &Dep,
3769 unsigned SplitLevel) {
3770 assert(Dep.isSplitable(SplitLevel) &&
3771 "Dep should be splitable at SplitLevel");
3772 Instruction *Src = Dep.getSrc();
3773 Instruction *Dst = Dep.getDst();
3774 assert(Src->mayReadFromMemory() || Src->mayWriteToMemory());
3775 assert(Dst->mayReadFromMemory() || Dst->mayWriteToMemory());
3776 assert(isLoadOrStore(Src));
3777 assert(isLoadOrStore(Dst));
3778 Value *SrcPtr = getPointerOperand(Src);
3779 Value *DstPtr = getPointerOperand(Dst);
3780 assert(underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3781 SrcPtr) == AliasAnalysis::MustAlias);
3783 // establish loop nesting levels
3784 establishNestingLevels(Src, Dst);
3786 FullDependence Result(Src, Dst, false, CommonLevels);
3788 // See if there are GEPs we can use.
3789 bool UsefulGEP = false;
3790 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3791 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3792 if (SrcGEP && DstGEP &&
3793 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3794 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3795 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3796 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3797 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3798 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3800 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3801 SmallVector<Subscript, 4> Pair(Pairs);
3804 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3805 SrcEnd = SrcGEP->idx_end(),
3806 DstIdx = DstGEP->idx_begin();
3808 ++SrcIdx, ++DstIdx, ++P) {
3809 Pair[P].Src = SE->getSCEV(*SrcIdx);
3810 Pair[P].Dst = SE->getSCEV(*DstIdx);
3814 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3815 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3816 Pair[0].Src = SrcSCEV;
3817 Pair[0].Dst = DstSCEV;
3820 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3821 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3822 DEBUG(dbgs() << " delinerized GEP\n");
3823 Pairs = Pair.size();
3826 for (unsigned P = 0; P < Pairs; ++P) {
3827 Pair[P].Loops.resize(MaxLevels + 1);
3828 Pair[P].GroupLoops.resize(MaxLevels + 1);
3829 Pair[P].Group.resize(Pairs);
3830 removeMatchingExtensions(&Pair[P]);
3831 Pair[P].Classification =
3832 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3833 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3835 Pair[P].GroupLoops = Pair[P].Loops;
3836 Pair[P].Group.set(P);
3839 SmallBitVector Separable(Pairs);
3840 SmallBitVector Coupled(Pairs);
3842 // partition subscripts into separable and minimally-coupled groups
3843 for (unsigned SI = 0; SI < Pairs; ++SI) {
3844 if (Pair[SI].Classification == Subscript::NonLinear) {
3845 // ignore these, but collect loops for later
3846 collectCommonLoops(Pair[SI].Src,
3847 LI->getLoopFor(Src->getParent()),
3849 collectCommonLoops(Pair[SI].Dst,
3850 LI->getLoopFor(Dst->getParent()),
3852 Result.Consistent = false;
3854 else if (Pair[SI].Classification == Subscript::ZIV)
3857 // SIV, RDIV, or MIV, so check for coupled group
3859 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3860 SmallBitVector Intersection = Pair[SI].GroupLoops;
3861 Intersection &= Pair[SJ].GroupLoops;
3862 if (Intersection.any()) {
3863 // accumulate set of all the loops in group
3864 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3865 // accumulate set of all subscripts in group
3866 Pair[SJ].Group |= Pair[SI].Group;
3871 if (Pair[SI].Group.count() == 1)
3879 Constraint NewConstraint;
3880 NewConstraint.setAny(SE);
3882 // test separable subscripts
3883 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3884 switch (Pair[SI].Classification) {
3885 case Subscript::SIV: {
3887 const SCEV *SplitIter = nullptr;
3888 (void) testSIV(Pair[SI].Src, Pair[SI].Dst, Level,
3889 Result, NewConstraint, SplitIter);
3890 if (Level == SplitLevel) {
3891 assert(SplitIter != nullptr);
3896 case Subscript::ZIV:
3897 case Subscript::RDIV:
3898 case Subscript::MIV:
3901 llvm_unreachable("subscript has unexpected classification");
3905 if (Coupled.count()) {
3906 // test coupled subscript groups
3907 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3908 for (unsigned II = 0; II <= MaxLevels; ++II)
3909 Constraints[II].setAny(SE);
3910 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3911 SmallBitVector Group(Pair[SI].Group);
3912 SmallBitVector Sivs(Pairs);
3913 SmallBitVector Mivs(Pairs);
3914 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3915 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3916 if (Pair[SJ].Classification == Subscript::SIV)
3921 while (Sivs.any()) {
3922 bool Changed = false;
3923 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3924 // SJ is an SIV subscript that's part of the current coupled group
3926 const SCEV *SplitIter = nullptr;
3927 (void) testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level,
3928 Result, NewConstraint, SplitIter);
3929 if (Level == SplitLevel && SplitIter)
3931 ConstrainedLevels.set(Level);
3932 if (intersectConstraints(&Constraints[Level], &NewConstraint))
3937 // propagate, possibly creating new SIVs and ZIVs
3938 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3939 // SJ is an MIV subscript that's part of the current coupled group
3940 if (propagate(Pair[SJ].Src, Pair[SJ].Dst,
3941 Pair[SJ].Loops, Constraints, Result.Consistent)) {
3942 Pair[SJ].Classification =
3943 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3944 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3946 switch (Pair[SJ].Classification) {
3947 case Subscript::ZIV:
3950 case Subscript::SIV:
3954 case Subscript::RDIV:
3955 case Subscript::MIV:
3958 llvm_unreachable("bad subscript classification");
3966 llvm_unreachable("somehow reached end of routine");