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 if (!isLoopInvariant(Step, LoopNest))
835 Loops.set(mapSrcLoop(AddRec->getLoop()));
836 return checkSrcSubscript(Start, LoopNest, Loops);
841 // Examine the scev and return true iff it's linear.
842 // Collect any loops mentioned in the set of "Loops".
843 bool DependenceAnalysis::checkDstSubscript(const SCEV *Dst,
844 const Loop *LoopNest,
845 SmallBitVector &Loops) {
846 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Dst);
848 return isLoopInvariant(Dst, LoopNest);
849 const SCEV *Start = AddRec->getStart();
850 const SCEV *Step = AddRec->getStepRecurrence(*SE);
851 if (!isLoopInvariant(Step, LoopNest))
853 Loops.set(mapDstLoop(AddRec->getLoop()));
854 return checkDstSubscript(Start, LoopNest, Loops);
858 // Examines the subscript pair (the Src and Dst SCEVs)
859 // and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
860 // Collects the associated loops in a set.
861 DependenceAnalysis::Subscript::ClassificationKind
862 DependenceAnalysis::classifyPair(const SCEV *Src, const Loop *SrcLoopNest,
863 const SCEV *Dst, const Loop *DstLoopNest,
864 SmallBitVector &Loops) {
865 SmallBitVector SrcLoops(MaxLevels + 1);
866 SmallBitVector DstLoops(MaxLevels + 1);
867 if (!checkSrcSubscript(Src, SrcLoopNest, SrcLoops))
868 return Subscript::NonLinear;
869 if (!checkDstSubscript(Dst, DstLoopNest, DstLoops))
870 return Subscript::NonLinear;
873 unsigned N = Loops.count();
875 return Subscript::ZIV;
877 return Subscript::SIV;
878 if (N == 2 && (SrcLoops.count() == 0 ||
879 DstLoops.count() == 0 ||
880 (SrcLoops.count() == 1 && DstLoops.count() == 1)))
881 return Subscript::RDIV;
882 return Subscript::MIV;
886 // A wrapper around SCEV::isKnownPredicate.
887 // Looks for cases where we're interested in comparing for equality.
888 // If both X and Y have been identically sign or zero extended,
889 // it strips off the (confusing) extensions before invoking
890 // SCEV::isKnownPredicate. Perhaps, someday, the ScalarEvolution package
891 // will be similarly updated.
893 // If SCEV::isKnownPredicate can't prove the predicate,
894 // we try simple subtraction, which seems to help in some cases
895 // involving symbolics.
896 bool DependenceAnalysis::isKnownPredicate(ICmpInst::Predicate Pred,
898 const SCEV *Y) const {
899 if (Pred == CmpInst::ICMP_EQ ||
900 Pred == CmpInst::ICMP_NE) {
901 if ((isa<SCEVSignExtendExpr>(X) &&
902 isa<SCEVSignExtendExpr>(Y)) ||
903 (isa<SCEVZeroExtendExpr>(X) &&
904 isa<SCEVZeroExtendExpr>(Y))) {
905 const SCEVCastExpr *CX = cast<SCEVCastExpr>(X);
906 const SCEVCastExpr *CY = cast<SCEVCastExpr>(Y);
907 const SCEV *Xop = CX->getOperand();
908 const SCEV *Yop = CY->getOperand();
909 if (Xop->getType() == Yop->getType()) {
915 if (SE->isKnownPredicate(Pred, X, Y))
917 // If SE->isKnownPredicate can't prove the condition,
918 // we try the brute-force approach of subtracting
919 // and testing the difference.
920 // By testing with SE->isKnownPredicate first, we avoid
921 // the possibility of overflow when the arguments are constants.
922 const SCEV *Delta = SE->getMinusSCEV(X, Y);
924 case CmpInst::ICMP_EQ:
925 return Delta->isZero();
926 case CmpInst::ICMP_NE:
927 return SE->isKnownNonZero(Delta);
928 case CmpInst::ICMP_SGE:
929 return SE->isKnownNonNegative(Delta);
930 case CmpInst::ICMP_SLE:
931 return SE->isKnownNonPositive(Delta);
932 case CmpInst::ICMP_SGT:
933 return SE->isKnownPositive(Delta);
934 case CmpInst::ICMP_SLT:
935 return SE->isKnownNegative(Delta);
937 llvm_unreachable("unexpected predicate in isKnownPredicate");
942 // All subscripts are all the same type.
943 // Loop bound may be smaller (e.g., a char).
944 // Should zero extend loop bound, since it's always >= 0.
945 // This routine collects upper bound and extends if needed.
946 // Return null if no bound available.
947 const SCEV *DependenceAnalysis::collectUpperBound(const Loop *L,
949 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
950 const SCEV *UB = SE->getBackedgeTakenCount(L);
951 return SE->getNoopOrZeroExtend(UB, T);
957 // Calls collectUpperBound(), then attempts to cast it to SCEVConstant.
958 // If the cast fails, returns NULL.
959 const SCEVConstant *DependenceAnalysis::collectConstantUpperBound(const Loop *L,
962 if (const SCEV *UB = collectUpperBound(L, T))
963 return dyn_cast<SCEVConstant>(UB);
969 // When we have a pair of subscripts of the form [c1] and [c2],
970 // where c1 and c2 are both loop invariant, we attack it using
971 // the ZIV test. Basically, we test by comparing the two values,
972 // but there are actually three possible results:
973 // 1) the values are equal, so there's a dependence
974 // 2) the values are different, so there's no dependence
975 // 3) the values might be equal, so we have to assume a dependence.
977 // Return true if dependence disproved.
978 bool DependenceAnalysis::testZIV(const SCEV *Src,
980 FullDependence &Result) const {
981 DEBUG(dbgs() << " src = " << *Src << "\n");
982 DEBUG(dbgs() << " dst = " << *Dst << "\n");
984 if (isKnownPredicate(CmpInst::ICMP_EQ, Src, Dst)) {
985 DEBUG(dbgs() << " provably dependent\n");
986 return false; // provably dependent
988 if (isKnownPredicate(CmpInst::ICMP_NE, Src, Dst)) {
989 DEBUG(dbgs() << " provably independent\n");
991 return true; // provably independent
993 DEBUG(dbgs() << " possibly dependent\n");
994 Result.Consistent = false;
995 return false; // possibly dependent
1000 // From the paper, Practical Dependence Testing, Section 4.2.1
1002 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 + a*i],
1003 // where i is an induction variable, c1 and c2 are loop invariant,
1004 // and a is a constant, we can solve it exactly using the Strong SIV test.
1006 // Can prove independence. Failing that, can compute distance (and direction).
1007 // In the presence of symbolic terms, we can sometimes make progress.
1009 // If there's a dependence,
1011 // c1 + a*i = c2 + a*i'
1013 // The dependence distance is
1015 // d = i' - i = (c1 - c2)/a
1017 // A dependence only exists if d is an integer and abs(d) <= U, where U is the
1018 // loop's upper bound. If a dependence exists, the dependence direction is
1022 // direction = { = if d = 0
1025 // Return true if dependence disproved.
1026 bool DependenceAnalysis::strongSIVtest(const SCEV *Coeff,
1027 const SCEV *SrcConst,
1028 const SCEV *DstConst,
1029 const Loop *CurLoop,
1031 FullDependence &Result,
1032 Constraint &NewConstraint) const {
1033 DEBUG(dbgs() << "\tStrong SIV test\n");
1034 DEBUG(dbgs() << "\t Coeff = " << *Coeff);
1035 DEBUG(dbgs() << ", " << *Coeff->getType() << "\n");
1036 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst);
1037 DEBUG(dbgs() << ", " << *SrcConst->getType() << "\n");
1038 DEBUG(dbgs() << "\t DstConst = " << *DstConst);
1039 DEBUG(dbgs() << ", " << *DstConst->getType() << "\n");
1040 ++StrongSIVapplications;
1041 assert(0 < Level && Level <= CommonLevels && "level out of range");
1044 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1045 DEBUG(dbgs() << "\t Delta = " << *Delta);
1046 DEBUG(dbgs() << ", " << *Delta->getType() << "\n");
1048 // check that |Delta| < iteration count
1049 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1050 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound);
1051 DEBUG(dbgs() << ", " << *UpperBound->getType() << "\n");
1052 const SCEV *AbsDelta =
1053 SE->isKnownNonNegative(Delta) ? Delta : SE->getNegativeSCEV(Delta);
1054 const SCEV *AbsCoeff =
1055 SE->isKnownNonNegative(Coeff) ? Coeff : SE->getNegativeSCEV(Coeff);
1056 const SCEV *Product = SE->getMulExpr(UpperBound, AbsCoeff);
1057 if (isKnownPredicate(CmpInst::ICMP_SGT, AbsDelta, Product)) {
1058 // Distance greater than trip count - no dependence
1059 ++StrongSIVindependence;
1060 ++StrongSIVsuccesses;
1065 // Can we compute distance?
1066 if (isa<SCEVConstant>(Delta) && isa<SCEVConstant>(Coeff)) {
1067 APInt ConstDelta = cast<SCEVConstant>(Delta)->getValue()->getValue();
1068 APInt ConstCoeff = cast<SCEVConstant>(Coeff)->getValue()->getValue();
1069 APInt Distance = ConstDelta; // these need to be initialized
1070 APInt Remainder = ConstDelta;
1071 APInt::sdivrem(ConstDelta, ConstCoeff, Distance, Remainder);
1072 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1073 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1074 // Make sure Coeff divides Delta exactly
1075 if (Remainder != 0) {
1076 // Coeff doesn't divide Distance, no dependence
1077 ++StrongSIVindependence;
1078 ++StrongSIVsuccesses;
1081 Result.DV[Level].Distance = SE->getConstant(Distance);
1082 NewConstraint.setDistance(SE->getConstant(Distance), CurLoop);
1083 if (Distance.sgt(0))
1084 Result.DV[Level].Direction &= Dependence::DVEntry::LT;
1085 else if (Distance.slt(0))
1086 Result.DV[Level].Direction &= Dependence::DVEntry::GT;
1088 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1089 ++StrongSIVsuccesses;
1091 else if (Delta->isZero()) {
1093 Result.DV[Level].Distance = Delta;
1094 NewConstraint.setDistance(Delta, CurLoop);
1095 Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
1096 ++StrongSIVsuccesses;
1099 if (Coeff->isOne()) {
1100 DEBUG(dbgs() << "\t Distance = " << *Delta << "\n");
1101 Result.DV[Level].Distance = Delta; // since X/1 == X
1102 NewConstraint.setDistance(Delta, CurLoop);
1105 Result.Consistent = false;
1106 NewConstraint.setLine(Coeff,
1107 SE->getNegativeSCEV(Coeff),
1108 SE->getNegativeSCEV(Delta), CurLoop);
1111 // maybe we can get a useful direction
1112 bool DeltaMaybeZero = !SE->isKnownNonZero(Delta);
1113 bool DeltaMaybePositive = !SE->isKnownNonPositive(Delta);
1114 bool DeltaMaybeNegative = !SE->isKnownNonNegative(Delta);
1115 bool CoeffMaybePositive = !SE->isKnownNonPositive(Coeff);
1116 bool CoeffMaybeNegative = !SE->isKnownNonNegative(Coeff);
1117 // The double negatives above are confusing.
1118 // It helps to read !SE->isKnownNonZero(Delta)
1119 // as "Delta might be Zero"
1120 unsigned NewDirection = Dependence::DVEntry::NONE;
1121 if ((DeltaMaybePositive && CoeffMaybePositive) ||
1122 (DeltaMaybeNegative && CoeffMaybeNegative))
1123 NewDirection = Dependence::DVEntry::LT;
1125 NewDirection |= Dependence::DVEntry::EQ;
1126 if ((DeltaMaybeNegative && CoeffMaybePositive) ||
1127 (DeltaMaybePositive && CoeffMaybeNegative))
1128 NewDirection |= Dependence::DVEntry::GT;
1129 if (NewDirection < Result.DV[Level].Direction)
1130 ++StrongSIVsuccesses;
1131 Result.DV[Level].Direction &= NewDirection;
1137 // weakCrossingSIVtest -
1138 // From the paper, Practical Dependence Testing, Section 4.2.2
1140 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 - a*i],
1141 // where i is an induction variable, c1 and c2 are loop invariant,
1142 // and a is a constant, we can solve it exactly using the
1143 // Weak-Crossing SIV test.
1145 // Given c1 + a*i = c2 - a*i', we can look for the intersection of
1146 // the two lines, where i = i', yielding
1148 // c1 + a*i = c2 - a*i
1152 // If i < 0, there is no dependence.
1153 // If i > upperbound, there is no dependence.
1154 // If i = 0 (i.e., if c1 = c2), there's a dependence with distance = 0.
1155 // If i = upperbound, there's a dependence with distance = 0.
1156 // If i is integral, there's a dependence (all directions).
1157 // If the non-integer part = 1/2, there's a dependence (<> directions).
1158 // Otherwise, there's no dependence.
1160 // Can prove independence. Failing that,
1161 // can sometimes refine the directions.
1162 // Can determine iteration for splitting.
1164 // Return true if dependence disproved.
1165 bool DependenceAnalysis::weakCrossingSIVtest(const SCEV *Coeff,
1166 const SCEV *SrcConst,
1167 const SCEV *DstConst,
1168 const Loop *CurLoop,
1170 FullDependence &Result,
1171 Constraint &NewConstraint,
1172 const SCEV *&SplitIter) const {
1173 DEBUG(dbgs() << "\tWeak-Crossing SIV test\n");
1174 DEBUG(dbgs() << "\t Coeff = " << *Coeff << "\n");
1175 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1176 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1177 ++WeakCrossingSIVapplications;
1178 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1180 Result.Consistent = false;
1181 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1182 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1183 NewConstraint.setLine(Coeff, Coeff, Delta, CurLoop);
1184 if (Delta->isZero()) {
1185 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1186 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1187 ++WeakCrossingSIVsuccesses;
1188 if (!Result.DV[Level].Direction) {
1189 ++WeakCrossingSIVindependence;
1192 Result.DV[Level].Distance = Delta; // = 0
1195 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(Coeff);
1199 Result.DV[Level].Splitable = true;
1200 if (SE->isKnownNegative(ConstCoeff)) {
1201 ConstCoeff = dyn_cast<SCEVConstant>(SE->getNegativeSCEV(ConstCoeff));
1202 assert(ConstCoeff &&
1203 "dynamic cast of negative of ConstCoeff should yield constant");
1204 Delta = SE->getNegativeSCEV(Delta);
1206 assert(SE->isKnownPositive(ConstCoeff) && "ConstCoeff should be positive");
1208 // compute SplitIter for use by DependenceAnalysis::getSplitIteration()
1210 SE->getUDivExpr(SE->getSMaxExpr(SE->getConstant(Delta->getType(), 0),
1212 SE->getMulExpr(SE->getConstant(Delta->getType(), 2),
1214 DEBUG(dbgs() << "\t Split iter = " << *SplitIter << "\n");
1216 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1220 // We're certain that ConstCoeff > 0; therefore,
1221 // if Delta < 0, then no dependence.
1222 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1223 DEBUG(dbgs() << "\t ConstCoeff = " << *ConstCoeff << "\n");
1224 if (SE->isKnownNegative(Delta)) {
1225 // No dependence, Delta < 0
1226 ++WeakCrossingSIVindependence;
1227 ++WeakCrossingSIVsuccesses;
1231 // We're certain that Delta > 0 and ConstCoeff > 0.
1232 // Check Delta/(2*ConstCoeff) against upper loop bound
1233 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1234 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1235 const SCEV *ConstantTwo = SE->getConstant(UpperBound->getType(), 2);
1236 const SCEV *ML = SE->getMulExpr(SE->getMulExpr(ConstCoeff, UpperBound),
1238 DEBUG(dbgs() << "\t ML = " << *ML << "\n");
1239 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, ML)) {
1240 // Delta too big, no dependence
1241 ++WeakCrossingSIVindependence;
1242 ++WeakCrossingSIVsuccesses;
1245 if (isKnownPredicate(CmpInst::ICMP_EQ, Delta, ML)) {
1247 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
1248 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
1249 ++WeakCrossingSIVsuccesses;
1250 if (!Result.DV[Level].Direction) {
1251 ++WeakCrossingSIVindependence;
1254 Result.DV[Level].Splitable = false;
1255 Result.DV[Level].Distance = SE->getConstant(Delta->getType(), 0);
1260 // check that Coeff divides Delta
1261 APInt APDelta = ConstDelta->getValue()->getValue();
1262 APInt APCoeff = ConstCoeff->getValue()->getValue();
1263 APInt Distance = APDelta; // these need to be initialzed
1264 APInt Remainder = APDelta;
1265 APInt::sdivrem(APDelta, APCoeff, Distance, Remainder);
1266 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1267 if (Remainder != 0) {
1268 // Coeff doesn't divide Delta, no dependence
1269 ++WeakCrossingSIVindependence;
1270 ++WeakCrossingSIVsuccesses;
1273 DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
1275 // if 2*Coeff doesn't divide Delta, then the equal direction isn't possible
1276 APInt Two = APInt(Distance.getBitWidth(), 2, true);
1277 Remainder = Distance.srem(Two);
1278 DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
1279 if (Remainder != 0) {
1280 // Equal direction isn't possible
1281 Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::EQ);
1282 ++WeakCrossingSIVsuccesses;
1288 // Kirch's algorithm, from
1290 // Optimizing Supercompilers for Supercomputers
1294 // Program 2.1, page 29.
1295 // Computes the GCD of AM and BM.
1296 // Also finds a solution to the equation ax - by = gcd(a, b).
1297 // Returns true if dependence disproved; i.e., gcd does not divide Delta.
1299 bool findGCD(unsigned Bits, APInt AM, APInt BM, APInt Delta,
1300 APInt &G, APInt &X, APInt &Y) {
1301 APInt A0(Bits, 1, true), A1(Bits, 0, true);
1302 APInt B0(Bits, 0, true), B1(Bits, 1, true);
1303 APInt G0 = AM.abs();
1304 APInt G1 = BM.abs();
1305 APInt Q = G0; // these need to be initialized
1307 APInt::sdivrem(G0, G1, Q, R);
1309 APInt A2 = A0 - Q*A1; A0 = A1; A1 = A2;
1310 APInt B2 = B0 - Q*B1; B0 = B1; B1 = B2;
1312 APInt::sdivrem(G0, G1, Q, R);
1315 DEBUG(dbgs() << "\t GCD = " << G << "\n");
1316 X = AM.slt(0) ? -A1 : A1;
1317 Y = BM.slt(0) ? B1 : -B1;
1319 // make sure gcd divides Delta
1322 return true; // gcd doesn't divide Delta, no dependence
1331 APInt floorOfQuotient(APInt A, APInt B) {
1332 APInt Q = A; // these need to be initialized
1334 APInt::sdivrem(A, B, Q, R);
1337 if ((A.sgt(0) && B.sgt(0)) ||
1338 (A.slt(0) && B.slt(0)))
1346 APInt ceilingOfQuotient(APInt A, APInt B) {
1347 APInt Q = A; // these need to be initialized
1349 APInt::sdivrem(A, B, Q, R);
1352 if ((A.sgt(0) && B.sgt(0)) ||
1353 (A.slt(0) && B.slt(0)))
1361 APInt maxAPInt(APInt A, APInt B) {
1362 return A.sgt(B) ? A : B;
1367 APInt minAPInt(APInt A, APInt B) {
1368 return A.slt(B) ? A : B;
1373 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*i],
1374 // where i is an induction variable, c1 and c2 are loop invariant, and a1
1375 // and a2 are constant, we can solve it exactly using an algorithm developed
1376 // by Banerjee and Wolfe. See Section 2.5.3 in
1378 // Optimizing Supercompilers for Supercomputers
1382 // It's slower than the specialized tests (strong SIV, weak-zero SIV, etc),
1383 // so use them if possible. They're also a bit better with symbolics and,
1384 // in the case of the strong SIV test, can compute Distances.
1386 // Return true if dependence disproved.
1387 bool DependenceAnalysis::exactSIVtest(const SCEV *SrcCoeff,
1388 const SCEV *DstCoeff,
1389 const SCEV *SrcConst,
1390 const SCEV *DstConst,
1391 const Loop *CurLoop,
1393 FullDependence &Result,
1394 Constraint &NewConstraint) const {
1395 DEBUG(dbgs() << "\tExact SIV test\n");
1396 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1397 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1398 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1399 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1400 ++ExactSIVapplications;
1401 assert(0 < Level && Level <= CommonLevels && "Level out of range");
1403 Result.Consistent = false;
1404 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1405 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1406 NewConstraint.setLine(SrcCoeff, SE->getNegativeSCEV(DstCoeff),
1408 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1409 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1410 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1411 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1416 APInt AM = ConstSrcCoeff->getValue()->getValue();
1417 APInt BM = ConstDstCoeff->getValue()->getValue();
1418 unsigned Bits = AM.getBitWidth();
1419 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1420 // gcd doesn't divide Delta, no dependence
1421 ++ExactSIVindependence;
1422 ++ExactSIVsuccesses;
1426 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1428 // since SCEV construction normalizes, LM = 0
1429 APInt UM(Bits, 1, true);
1430 bool UMvalid = false;
1431 // UM is perhaps unavailable, let's check
1432 if (const SCEVConstant *CUB =
1433 collectConstantUpperBound(CurLoop, Delta->getType())) {
1434 UM = CUB->getValue()->getValue();
1435 DEBUG(dbgs() << "\t UM = " << UM << "\n");
1439 APInt TU(APInt::getSignedMaxValue(Bits));
1440 APInt TL(APInt::getSignedMinValue(Bits));
1442 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1443 APInt TMUL = BM.sdiv(G);
1445 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1446 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1448 TU = minAPInt(TU, floorOfQuotient(UM - X, TMUL));
1449 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1453 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1454 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1456 TL = maxAPInt(TL, ceilingOfQuotient(UM - X, TMUL));
1457 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1461 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1464 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1465 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1467 TU = minAPInt(TU, floorOfQuotient(UM - Y, TMUL));
1468 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1472 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1473 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1475 TL = maxAPInt(TL, ceilingOfQuotient(UM - Y, TMUL));
1476 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1480 ++ExactSIVindependence;
1481 ++ExactSIVsuccesses;
1485 // explore directions
1486 unsigned NewDirection = Dependence::DVEntry::NONE;
1489 APInt SaveTU(TU); // save these
1491 DEBUG(dbgs() << "\t exploring LT direction\n");
1494 TL = maxAPInt(TL, ceilingOfQuotient(X - Y + 1, TMUL));
1495 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1498 TU = minAPInt(TU, floorOfQuotient(X - Y + 1, TMUL));
1499 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1502 NewDirection |= Dependence::DVEntry::LT;
1503 ++ExactSIVsuccesses;
1507 TU = SaveTU; // restore
1509 DEBUG(dbgs() << "\t exploring EQ direction\n");
1511 TL = maxAPInt(TL, ceilingOfQuotient(X - Y, TMUL));
1512 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1515 TU = minAPInt(TU, floorOfQuotient(X - Y, TMUL));
1516 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1520 TL = maxAPInt(TL, ceilingOfQuotient(Y - X, TMUL));
1521 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1524 TU = minAPInt(TU, floorOfQuotient(Y - X, TMUL));
1525 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1528 NewDirection |= Dependence::DVEntry::EQ;
1529 ++ExactSIVsuccesses;
1533 TU = SaveTU; // restore
1535 DEBUG(dbgs() << "\t exploring GT direction\n");
1537 TL = maxAPInt(TL, ceilingOfQuotient(Y - X + 1, TMUL));
1538 DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
1541 TU = minAPInt(TU, floorOfQuotient(Y - X + 1, TMUL));
1542 DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
1545 NewDirection |= Dependence::DVEntry::GT;
1546 ++ExactSIVsuccesses;
1550 Result.DV[Level].Direction &= NewDirection;
1551 if (Result.DV[Level].Direction == Dependence::DVEntry::NONE)
1552 ++ExactSIVindependence;
1553 return Result.DV[Level].Direction == Dependence::DVEntry::NONE;
1558 // Return true if the divisor evenly divides the dividend.
1560 bool isRemainderZero(const SCEVConstant *Dividend,
1561 const SCEVConstant *Divisor) {
1562 APInt ConstDividend = Dividend->getValue()->getValue();
1563 APInt ConstDivisor = Divisor->getValue()->getValue();
1564 return ConstDividend.srem(ConstDivisor) == 0;
1568 // weakZeroSrcSIVtest -
1569 // From the paper, Practical Dependence Testing, Section 4.2.2
1571 // When we have a pair of subscripts of the form [c1] and [c2 + a*i],
1572 // where i is an induction variable, c1 and c2 are loop invariant,
1573 // and a is a constant, we can solve it exactly using the
1574 // Weak-Zero SIV test.
1584 // If i is not an integer, there's no dependence.
1585 // If i < 0 or > UB, there's no dependence.
1586 // If i = 0, the direction is <= and peeling the
1587 // 1st iteration will break the dependence.
1588 // If i = UB, the direction is >= and peeling the
1589 // last iteration will break the dependence.
1590 // Otherwise, the direction is *.
1592 // Can prove independence. Failing that, we can sometimes refine
1593 // the directions. Can sometimes show that first or last
1594 // iteration carries all the dependences (so worth peeling).
1596 // (see also weakZeroDstSIVtest)
1598 // Return true if dependence disproved.
1599 bool DependenceAnalysis::weakZeroSrcSIVtest(const SCEV *DstCoeff,
1600 const SCEV *SrcConst,
1601 const SCEV *DstConst,
1602 const Loop *CurLoop,
1604 FullDependence &Result,
1605 Constraint &NewConstraint) const {
1606 // For the WeakSIV test, it's possible the loop isn't common to
1607 // the Src and Dst loops. If it isn't, then there's no need to
1608 // record a direction.
1609 DEBUG(dbgs() << "\tWeak-Zero (src) SIV test\n");
1610 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << "\n");
1611 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1612 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1613 ++WeakZeroSIVapplications;
1614 assert(0 < Level && Level <= MaxLevels && "Level out of range");
1616 Result.Consistent = false;
1617 const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
1618 NewConstraint.setLine(SE->getConstant(Delta->getType(), 0),
1619 DstCoeff, Delta, CurLoop);
1620 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1621 if (isKnownPredicate(CmpInst::ICMP_EQ, SrcConst, DstConst)) {
1622 if (Level < CommonLevels) {
1623 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1624 Result.DV[Level].PeelFirst = true;
1625 ++WeakZeroSIVsuccesses;
1627 return false; // dependences caused by first iteration
1629 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1632 const SCEV *AbsCoeff =
1633 SE->isKnownNegative(ConstCoeff) ?
1634 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1635 const SCEV *NewDelta =
1636 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1638 // check that Delta/SrcCoeff < iteration count
1639 // really check NewDelta < count*AbsCoeff
1640 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1641 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1642 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1643 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1644 ++WeakZeroSIVindependence;
1645 ++WeakZeroSIVsuccesses;
1648 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1649 // dependences caused by last iteration
1650 if (Level < CommonLevels) {
1651 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1652 Result.DV[Level].PeelLast = true;
1653 ++WeakZeroSIVsuccesses;
1659 // check that Delta/SrcCoeff >= 0
1660 // really check that NewDelta >= 0
1661 if (SE->isKnownNegative(NewDelta)) {
1662 // No dependence, newDelta < 0
1663 ++WeakZeroSIVindependence;
1664 ++WeakZeroSIVsuccesses;
1668 // if SrcCoeff doesn't divide Delta, then no dependence
1669 if (isa<SCEVConstant>(Delta) &&
1670 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1671 ++WeakZeroSIVindependence;
1672 ++WeakZeroSIVsuccesses;
1679 // weakZeroDstSIVtest -
1680 // From the paper, Practical Dependence Testing, Section 4.2.2
1682 // When we have a pair of subscripts of the form [c1 + a*i] and [c2],
1683 // where i is an induction variable, c1 and c2 are loop invariant,
1684 // and a is a constant, we can solve it exactly using the
1685 // Weak-Zero SIV test.
1695 // If i is not an integer, there's no dependence.
1696 // If i < 0 or > UB, there's no dependence.
1697 // If i = 0, the direction is <= and peeling the
1698 // 1st iteration will break the dependence.
1699 // If i = UB, the direction is >= and peeling the
1700 // last iteration will break the dependence.
1701 // Otherwise, the direction is *.
1703 // Can prove independence. Failing that, we can sometimes refine
1704 // the directions. Can sometimes show that first or last
1705 // iteration carries all the dependences (so worth peeling).
1707 // (see also weakZeroSrcSIVtest)
1709 // Return true if dependence disproved.
1710 bool DependenceAnalysis::weakZeroDstSIVtest(const SCEV *SrcCoeff,
1711 const SCEV *SrcConst,
1712 const SCEV *DstConst,
1713 const Loop *CurLoop,
1715 FullDependence &Result,
1716 Constraint &NewConstraint) const {
1717 // For the WeakSIV test, it's possible the loop isn't common to the
1718 // Src and Dst loops. If it isn't, then there's no need to record a direction.
1719 DEBUG(dbgs() << "\tWeak-Zero (dst) SIV test\n");
1720 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << "\n");
1721 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1722 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1723 ++WeakZeroSIVapplications;
1724 assert(0 < Level && Level <= SrcLevels && "Level out of range");
1726 Result.Consistent = false;
1727 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1728 NewConstraint.setLine(SrcCoeff, SE->getConstant(Delta->getType(), 0),
1730 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1731 if (isKnownPredicate(CmpInst::ICMP_EQ, DstConst, SrcConst)) {
1732 if (Level < CommonLevels) {
1733 Result.DV[Level].Direction &= Dependence::DVEntry::LE;
1734 Result.DV[Level].PeelFirst = true;
1735 ++WeakZeroSIVsuccesses;
1737 return false; // dependences caused by first iteration
1739 const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1742 const SCEV *AbsCoeff =
1743 SE->isKnownNegative(ConstCoeff) ?
1744 SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
1745 const SCEV *NewDelta =
1746 SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
1748 // check that Delta/SrcCoeff < iteration count
1749 // really check NewDelta < count*AbsCoeff
1750 if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
1751 DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
1752 const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
1753 if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
1754 ++WeakZeroSIVindependence;
1755 ++WeakZeroSIVsuccesses;
1758 if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
1759 // dependences caused by last iteration
1760 if (Level < CommonLevels) {
1761 Result.DV[Level].Direction &= Dependence::DVEntry::GE;
1762 Result.DV[Level].PeelLast = true;
1763 ++WeakZeroSIVsuccesses;
1769 // check that Delta/SrcCoeff >= 0
1770 // really check that NewDelta >= 0
1771 if (SE->isKnownNegative(NewDelta)) {
1772 // No dependence, newDelta < 0
1773 ++WeakZeroSIVindependence;
1774 ++WeakZeroSIVsuccesses;
1778 // if SrcCoeff doesn't divide Delta, then no dependence
1779 if (isa<SCEVConstant>(Delta) &&
1780 !isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
1781 ++WeakZeroSIVindependence;
1782 ++WeakZeroSIVsuccesses;
1789 // exactRDIVtest - Tests the RDIV subscript pair for dependence.
1790 // Things of the form [c1 + a*i] and [c2 + b*j],
1791 // where i and j are induction variable, c1 and c2 are loop invariant,
1792 // and a and b are constants.
1793 // Returns true if any possible dependence is disproved.
1794 // Marks the result as inconsistent.
1795 // Works in some cases that symbolicRDIVtest doesn't, and vice versa.
1796 bool DependenceAnalysis::exactRDIVtest(const SCEV *SrcCoeff,
1797 const SCEV *DstCoeff,
1798 const SCEV *SrcConst,
1799 const SCEV *DstConst,
1800 const Loop *SrcLoop,
1801 const Loop *DstLoop,
1802 FullDependence &Result) const {
1803 DEBUG(dbgs() << "\tExact RDIV test\n");
1804 DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
1805 DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
1806 DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
1807 DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
1808 ++ExactRDIVapplications;
1809 Result.Consistent = false;
1810 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
1811 DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
1812 const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
1813 const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
1814 const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
1815 if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
1820 APInt AM = ConstSrcCoeff->getValue()->getValue();
1821 APInt BM = ConstDstCoeff->getValue()->getValue();
1822 unsigned Bits = AM.getBitWidth();
1823 if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
1824 // gcd doesn't divide Delta, no dependence
1825 ++ExactRDIVindependence;
1829 DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
1831 // since SCEV construction seems to normalize, LM = 0
1832 APInt SrcUM(Bits, 1, true);
1833 bool SrcUMvalid = false;
1834 // SrcUM is perhaps unavailable, let's check
1835 if (const SCEVConstant *UpperBound =
1836 collectConstantUpperBound(SrcLoop, Delta->getType())) {
1837 SrcUM = UpperBound->getValue()->getValue();
1838 DEBUG(dbgs() << "\t SrcUM = " << SrcUM << "\n");
1842 APInt DstUM(Bits, 1, true);
1843 bool DstUMvalid = false;
1844 // UM is perhaps unavailable, let's check
1845 if (const SCEVConstant *UpperBound =
1846 collectConstantUpperBound(DstLoop, Delta->getType())) {
1847 DstUM = UpperBound->getValue()->getValue();
1848 DEBUG(dbgs() << "\t DstUM = " << DstUM << "\n");
1852 APInt TU(APInt::getSignedMaxValue(Bits));
1853 APInt TL(APInt::getSignedMinValue(Bits));
1855 // test(BM/G, LM-X) and test(-BM/G, X-UM)
1856 APInt TMUL = BM.sdiv(G);
1858 TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
1859 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1861 TU = minAPInt(TU, floorOfQuotient(SrcUM - X, TMUL));
1862 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1866 TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
1867 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1869 TL = maxAPInt(TL, ceilingOfQuotient(SrcUM - X, TMUL));
1870 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1874 // test(AM/G, LM-Y) and test(-AM/G, Y-UM)
1877 TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
1878 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1880 TU = minAPInt(TU, floorOfQuotient(DstUM - Y, TMUL));
1881 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1885 TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
1886 DEBUG(dbgs() << "\t TU = " << TU << "\n");
1888 TL = maxAPInt(TL, ceilingOfQuotient(DstUM - Y, TMUL));
1889 DEBUG(dbgs() << "\t TL = " << TL << "\n");
1893 ++ExactRDIVindependence;
1898 // symbolicRDIVtest -
1899 // In Section 4.5 of the Practical Dependence Testing paper,the authors
1900 // introduce a special case of Banerjee's Inequalities (also called the
1901 // Extreme-Value Test) that can handle some of the SIV and RDIV cases,
1902 // particularly cases with symbolics. Since it's only able to disprove
1903 // dependence (not compute distances or directions), we'll use it as a
1904 // fall back for the other tests.
1906 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
1907 // where i and j are induction variables and c1 and c2 are loop invariants,
1908 // we can use the symbolic tests to disprove some dependences, serving as a
1909 // backup for the RDIV test. Note that i and j can be the same variable,
1910 // letting this test serve as a backup for the various SIV tests.
1912 // For a dependence to exist, c1 + a1*i must equal c2 + a2*j for some
1913 // 0 <= i <= N1 and some 0 <= j <= N2, where N1 and N2 are the (normalized)
1914 // loop bounds for the i and j loops, respectively. So, ...
1916 // c1 + a1*i = c2 + a2*j
1917 // a1*i - a2*j = c2 - c1
1919 // To test for a dependence, we compute c2 - c1 and make sure it's in the
1920 // range of the maximum and minimum possible values of a1*i - a2*j.
1921 // Considering the signs of a1 and a2, we have 4 possible cases:
1923 // 1) If a1 >= 0 and a2 >= 0, then
1924 // a1*0 - a2*N2 <= c2 - c1 <= a1*N1 - a2*0
1925 // -a2*N2 <= c2 - c1 <= a1*N1
1927 // 2) If a1 >= 0 and a2 <= 0, then
1928 // a1*0 - a2*0 <= c2 - c1 <= a1*N1 - a2*N2
1929 // 0 <= c2 - c1 <= a1*N1 - a2*N2
1931 // 3) If a1 <= 0 and a2 >= 0, then
1932 // a1*N1 - a2*N2 <= c2 - c1 <= a1*0 - a2*0
1933 // a1*N1 - a2*N2 <= c2 - c1 <= 0
1935 // 4) If a1 <= 0 and a2 <= 0, then
1936 // a1*N1 - a2*0 <= c2 - c1 <= a1*0 - a2*N2
1937 // a1*N1 <= c2 - c1 <= -a2*N2
1939 // return true if dependence disproved
1940 bool DependenceAnalysis::symbolicRDIVtest(const SCEV *A1,
1945 const Loop *Loop2) const {
1946 ++SymbolicRDIVapplications;
1947 DEBUG(dbgs() << "\ttry symbolic RDIV test\n");
1948 DEBUG(dbgs() << "\t A1 = " << *A1);
1949 DEBUG(dbgs() << ", type = " << *A1->getType() << "\n");
1950 DEBUG(dbgs() << "\t A2 = " << *A2 << "\n");
1951 DEBUG(dbgs() << "\t C1 = " << *C1 << "\n");
1952 DEBUG(dbgs() << "\t C2 = " << *C2 << "\n");
1953 const SCEV *N1 = collectUpperBound(Loop1, A1->getType());
1954 const SCEV *N2 = collectUpperBound(Loop2, A1->getType());
1955 DEBUG(if (N1) dbgs() << "\t N1 = " << *N1 << "\n");
1956 DEBUG(if (N2) dbgs() << "\t N2 = " << *N2 << "\n");
1957 const SCEV *C2_C1 = SE->getMinusSCEV(C2, C1);
1958 const SCEV *C1_C2 = SE->getMinusSCEV(C1, C2);
1959 DEBUG(dbgs() << "\t C2 - C1 = " << *C2_C1 << "\n");
1960 DEBUG(dbgs() << "\t C1 - C2 = " << *C1_C2 << "\n");
1961 if (SE->isKnownNonNegative(A1)) {
1962 if (SE->isKnownNonNegative(A2)) {
1963 // A1 >= 0 && A2 >= 0
1965 // make sure that c2 - c1 <= a1*N1
1966 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
1967 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
1968 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1)) {
1969 ++SymbolicRDIVindependence;
1974 // make sure that -a2*N2 <= c2 - c1, or a2*N2 >= c1 - c2
1975 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
1976 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
1977 if (isKnownPredicate(CmpInst::ICMP_SLT, A2N2, C1_C2)) {
1978 ++SymbolicRDIVindependence;
1983 else if (SE->isKnownNonPositive(A2)) {
1984 // a1 >= 0 && a2 <= 0
1986 // make sure that c2 - c1 <= a1*N1 - a2*N2
1987 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
1988 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
1989 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
1990 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
1991 if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1_A2N2)) {
1992 ++SymbolicRDIVindependence;
1996 // make sure that 0 <= c2 - c1
1997 if (SE->isKnownNegative(C2_C1)) {
1998 ++SymbolicRDIVindependence;
2003 else if (SE->isKnownNonPositive(A1)) {
2004 if (SE->isKnownNonNegative(A2)) {
2005 // a1 <= 0 && a2 >= 0
2007 // make sure that a1*N1 - a2*N2 <= c2 - c1
2008 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2009 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2010 const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
2011 DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
2012 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1_A2N2, C2_C1)) {
2013 ++SymbolicRDIVindependence;
2017 // make sure that c2 - c1 <= 0
2018 if (SE->isKnownPositive(C2_C1)) {
2019 ++SymbolicRDIVindependence;
2023 else if (SE->isKnownNonPositive(A2)) {
2024 // a1 <= 0 && a2 <= 0
2026 // make sure that a1*N1 <= c2 - c1
2027 const SCEV *A1N1 = SE->getMulExpr(A1, N1);
2028 DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
2029 if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1, C2_C1)) {
2030 ++SymbolicRDIVindependence;
2035 // make sure that c2 - c1 <= -a2*N2, or c1 - c2 >= a2*N2
2036 const SCEV *A2N2 = SE->getMulExpr(A2, N2);
2037 DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
2038 if (isKnownPredicate(CmpInst::ICMP_SLT, C1_C2, A2N2)) {
2039 ++SymbolicRDIVindependence;
2050 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 - a2*i]
2051 // where i is an induction variable, c1 and c2 are loop invariant, and a1 and
2052 // a2 are constant, we attack it with an SIV test. While they can all be
2053 // solved with the Exact SIV test, it's worthwhile to use simpler tests when
2054 // they apply; they're cheaper and sometimes more precise.
2056 // Return true if dependence disproved.
2057 bool DependenceAnalysis::testSIV(const SCEV *Src,
2060 FullDependence &Result,
2061 Constraint &NewConstraint,
2062 const SCEV *&SplitIter) const {
2063 DEBUG(dbgs() << " src = " << *Src << "\n");
2064 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2065 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2066 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2067 if (SrcAddRec && DstAddRec) {
2068 const SCEV *SrcConst = SrcAddRec->getStart();
2069 const SCEV *DstConst = DstAddRec->getStart();
2070 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2071 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2072 const Loop *CurLoop = SrcAddRec->getLoop();
2073 assert(CurLoop == DstAddRec->getLoop() &&
2074 "both loops in SIV should be same");
2075 Level = mapSrcLoop(CurLoop);
2077 if (SrcCoeff == DstCoeff)
2078 disproven = strongSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2079 Level, Result, NewConstraint);
2080 else if (SrcCoeff == SE->getNegativeSCEV(DstCoeff))
2081 disproven = weakCrossingSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2082 Level, Result, NewConstraint, SplitIter);
2084 disproven = exactSIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop,
2085 Level, Result, NewConstraint);
2087 gcdMIVtest(Src, Dst, Result) ||
2088 symbolicRDIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop, CurLoop);
2091 const SCEV *SrcConst = SrcAddRec->getStart();
2092 const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2093 const SCEV *DstConst = Dst;
2094 const Loop *CurLoop = SrcAddRec->getLoop();
2095 Level = mapSrcLoop(CurLoop);
2096 return weakZeroDstSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
2097 Level, Result, NewConstraint) ||
2098 gcdMIVtest(Src, Dst, Result);
2101 const SCEV *DstConst = DstAddRec->getStart();
2102 const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
2103 const SCEV *SrcConst = Src;
2104 const Loop *CurLoop = DstAddRec->getLoop();
2105 Level = mapDstLoop(CurLoop);
2106 return weakZeroSrcSIVtest(DstCoeff, SrcConst, DstConst,
2107 CurLoop, Level, Result, NewConstraint) ||
2108 gcdMIVtest(Src, Dst, Result);
2110 llvm_unreachable("SIV test expected at least one AddRec");
2116 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
2117 // where i and j are induction variables, c1 and c2 are loop invariant,
2118 // and a1 and a2 are constant, we can solve it exactly with an easy adaptation
2119 // of the Exact SIV test, the Restricted Double Index Variable (RDIV) test.
2120 // It doesn't make sense to talk about distance or direction in this case,
2121 // so there's no point in making special versions of the Strong SIV test or
2122 // the Weak-crossing SIV test.
2124 // With minor algebra, this test can also be used for things like
2125 // [c1 + a1*i + a2*j][c2].
2127 // Return true if dependence disproved.
2128 bool DependenceAnalysis::testRDIV(const SCEV *Src,
2130 FullDependence &Result) const {
2131 // we have 3 possible situations here:
2132 // 1) [a*i + b] and [c*j + d]
2133 // 2) [a*i + c*j + b] and [d]
2134 // 3) [b] and [a*i + c*j + d]
2135 // We need to find what we've got and get organized
2137 const SCEV *SrcConst, *DstConst;
2138 const SCEV *SrcCoeff, *DstCoeff;
2139 const Loop *SrcLoop, *DstLoop;
2141 DEBUG(dbgs() << " src = " << *Src << "\n");
2142 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2143 const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
2144 const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
2145 if (SrcAddRec && DstAddRec) {
2146 SrcConst = SrcAddRec->getStart();
2147 SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
2148 SrcLoop = SrcAddRec->getLoop();
2149 DstConst = DstAddRec->getStart();
2150 DstCoeff = DstAddRec->getStepRecurrence(*SE);
2151 DstLoop = DstAddRec->getLoop();
2153 else if (SrcAddRec) {
2154 if (const SCEVAddRecExpr *tmpAddRec =
2155 dyn_cast<SCEVAddRecExpr>(SrcAddRec->getStart())) {
2156 SrcConst = tmpAddRec->getStart();
2157 SrcCoeff = tmpAddRec->getStepRecurrence(*SE);
2158 SrcLoop = tmpAddRec->getLoop();
2160 DstCoeff = SE->getNegativeSCEV(SrcAddRec->getStepRecurrence(*SE));
2161 DstLoop = SrcAddRec->getLoop();
2164 llvm_unreachable("RDIV reached by surprising SCEVs");
2166 else if (DstAddRec) {
2167 if (const SCEVAddRecExpr *tmpAddRec =
2168 dyn_cast<SCEVAddRecExpr>(DstAddRec->getStart())) {
2169 DstConst = tmpAddRec->getStart();
2170 DstCoeff = tmpAddRec->getStepRecurrence(*SE);
2171 DstLoop = tmpAddRec->getLoop();
2173 SrcCoeff = SE->getNegativeSCEV(DstAddRec->getStepRecurrence(*SE));
2174 SrcLoop = DstAddRec->getLoop();
2177 llvm_unreachable("RDIV reached by surprising SCEVs");
2180 llvm_unreachable("RDIV expected at least one AddRec");
2181 return exactRDIVtest(SrcCoeff, DstCoeff,
2185 gcdMIVtest(Src, Dst, Result) ||
2186 symbolicRDIVtest(SrcCoeff, DstCoeff,
2192 // Tests the single-subscript MIV pair (Src and Dst) for dependence.
2193 // Return true if dependence disproved.
2194 // Can sometimes refine direction vectors.
2195 bool DependenceAnalysis::testMIV(const SCEV *Src,
2197 const SmallBitVector &Loops,
2198 FullDependence &Result) const {
2199 DEBUG(dbgs() << " src = " << *Src << "\n");
2200 DEBUG(dbgs() << " dst = " << *Dst << "\n");
2201 Result.Consistent = false;
2202 return gcdMIVtest(Src, Dst, Result) ||
2203 banerjeeMIVtest(Src, Dst, Loops, Result);
2207 // Given a product, e.g., 10*X*Y, returns the first constant operand,
2208 // in this case 10. If there is no constant part, returns NULL.
2210 const SCEVConstant *getConstantPart(const SCEVMulExpr *Product) {
2211 for (unsigned Op = 0, Ops = Product->getNumOperands(); Op < Ops; Op++) {
2212 if (const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Product->getOperand(Op)))
2219 //===----------------------------------------------------------------------===//
2221 // Tests an MIV subscript pair for dependence.
2222 // Returns true if any possible dependence is disproved.
2223 // Marks the result as inconsistent.
2224 // Can sometimes disprove the equal direction for 1 or more loops,
2225 // as discussed in Michael Wolfe's book,
2226 // High Performance Compilers for Parallel Computing, page 235.
2228 // We spend some effort (code!) to handle cases like
2229 // [10*i + 5*N*j + 15*M + 6], where i and j are induction variables,
2230 // but M and N are just loop-invariant variables.
2231 // This should help us handle linearized subscripts;
2232 // also makes this test a useful backup to the various SIV tests.
2234 // It occurs to me that the presence of loop-invariant variables
2235 // changes the nature of the test from "greatest common divisor"
2236 // to "a common divisor".
2237 bool DependenceAnalysis::gcdMIVtest(const SCEV *Src,
2239 FullDependence &Result) const {
2240 DEBUG(dbgs() << "starting gcd\n");
2242 unsigned BitWidth = SE->getTypeSizeInBits(Src->getType());
2243 APInt RunningGCD = APInt::getNullValue(BitWidth);
2245 // Examine Src coefficients.
2246 // Compute running GCD and record source constant.
2247 // Because we're looking for the constant at the end of the chain,
2248 // we can't quit the loop just because the GCD == 1.
2249 const SCEV *Coefficients = Src;
2250 while (const SCEVAddRecExpr *AddRec =
2251 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2252 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2253 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2254 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2255 // If the coefficient is the product of a constant and other stuff,
2256 // we can use the constant in the GCD computation.
2257 Constant = getConstantPart(Product);
2260 APInt ConstCoeff = Constant->getValue()->getValue();
2261 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2262 Coefficients = AddRec->getStart();
2264 const SCEV *SrcConst = Coefficients;
2266 // Examine Dst coefficients.
2267 // Compute running GCD and record destination constant.
2268 // Because we're looking for the constant at the end of the chain,
2269 // we can't quit the loop just because the GCD == 1.
2271 while (const SCEVAddRecExpr *AddRec =
2272 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2273 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2274 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
2275 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2276 // If the coefficient is the product of a constant and other stuff,
2277 // we can use the constant in the GCD computation.
2278 Constant = getConstantPart(Product);
2281 APInt ConstCoeff = Constant->getValue()->getValue();
2282 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2283 Coefficients = AddRec->getStart();
2285 const SCEV *DstConst = Coefficients;
2287 APInt ExtraGCD = APInt::getNullValue(BitWidth);
2288 const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
2289 DEBUG(dbgs() << " Delta = " << *Delta << "\n");
2290 const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Delta);
2291 if (const SCEVAddExpr *Sum = dyn_cast<SCEVAddExpr>(Delta)) {
2292 // If Delta is a sum of products, we may be able to make further progress.
2293 for (unsigned Op = 0, Ops = Sum->getNumOperands(); Op < Ops; Op++) {
2294 const SCEV *Operand = Sum->getOperand(Op);
2295 if (isa<SCEVConstant>(Operand)) {
2296 assert(!Constant && "Surprised to find multiple constants");
2297 Constant = cast<SCEVConstant>(Operand);
2299 else if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Operand)) {
2300 // Search for constant operand to participate in GCD;
2301 // If none found; return false.
2302 const SCEVConstant *ConstOp = getConstantPart(Product);
2305 APInt ConstOpValue = ConstOp->getValue()->getValue();
2306 ExtraGCD = APIntOps::GreatestCommonDivisor(ExtraGCD,
2307 ConstOpValue.abs());
2315 APInt ConstDelta = cast<SCEVConstant>(Constant)->getValue()->getValue();
2316 DEBUG(dbgs() << " ConstDelta = " << ConstDelta << "\n");
2317 if (ConstDelta == 0)
2319 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ExtraGCD);
2320 DEBUG(dbgs() << " RunningGCD = " << RunningGCD << "\n");
2321 APInt Remainder = ConstDelta.srem(RunningGCD);
2322 if (Remainder != 0) {
2327 // Try to disprove equal directions.
2328 // For example, given a subscript pair [3*i + 2*j] and [i' + 2*j' - 1],
2329 // the code above can't disprove the dependence because the GCD = 1.
2330 // So we consider what happen if i = i' and what happens if j = j'.
2331 // If i = i', we can simplify the subscript to [2*i + 2*j] and [2*j' - 1],
2332 // which is infeasible, so we can disallow the = direction for the i level.
2333 // Setting j = j' doesn't help matters, so we end up with a direction vector
2336 // Given A[5*i + 10*j*M + 9*M*N] and A[15*i + 20*j*M - 21*N*M + 5],
2337 // we need to remember that the constant part is 5 and the RunningGCD should
2338 // be initialized to ExtraGCD = 30.
2339 DEBUG(dbgs() << " ExtraGCD = " << ExtraGCD << '\n');
2341 bool Improved = false;
2343 while (const SCEVAddRecExpr *AddRec =
2344 dyn_cast<SCEVAddRecExpr>(Coefficients)) {
2345 Coefficients = AddRec->getStart();
2346 const Loop *CurLoop = AddRec->getLoop();
2347 RunningGCD = ExtraGCD;
2348 const SCEV *SrcCoeff = AddRec->getStepRecurrence(*SE);
2349 const SCEV *DstCoeff = SE->getMinusSCEV(SrcCoeff, SrcCoeff);
2350 const SCEV *Inner = Src;
2351 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2352 AddRec = cast<SCEVAddRecExpr>(Inner);
2353 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2354 if (CurLoop == AddRec->getLoop())
2355 ; // SrcCoeff == Coeff
2357 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
2358 // If the coefficient is the product of a constant and other stuff,
2359 // we can use the constant in the GCD computation.
2360 Constant = getConstantPart(Product);
2362 Constant = cast<SCEVConstant>(Coeff);
2363 APInt ConstCoeff = Constant->getValue()->getValue();
2364 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2366 Inner = AddRec->getStart();
2369 while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
2370 AddRec = cast<SCEVAddRecExpr>(Inner);
2371 const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
2372 if (CurLoop == AddRec->getLoop())
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();
2386 Delta = SE->getMinusSCEV(SrcCoeff, DstCoeff);
2387 if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Delta))
2388 // If the coefficient is the product of a constant and other stuff,
2389 // we can use the constant in the GCD computation.
2390 Constant = getConstantPart(Product);
2391 else if (isa<SCEVConstant>(Delta))
2392 Constant = cast<SCEVConstant>(Delta);
2394 // The difference of the two coefficients might not be a product
2395 // or constant, in which case we give up on this direction.
2398 APInt ConstCoeff = Constant->getValue()->getValue();
2399 RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
2400 DEBUG(dbgs() << "\tRunningGCD = " << RunningGCD << "\n");
2401 if (RunningGCD != 0) {
2402 Remainder = ConstDelta.srem(RunningGCD);
2403 DEBUG(dbgs() << "\tRemainder = " << Remainder << "\n");
2404 if (Remainder != 0) {
2405 unsigned Level = mapSrcLoop(CurLoop);
2406 Result.DV[Level - 1].Direction &= unsigned(~Dependence::DVEntry::EQ);
2413 DEBUG(dbgs() << "all done\n");
2418 //===----------------------------------------------------------------------===//
2419 // banerjeeMIVtest -
2420 // Use Banerjee's Inequalities to test an MIV subscript pair.
2421 // (Wolfe, in the race-car book, calls this the Extreme Value Test.)
2422 // Generally follows the discussion in Section 2.5.2 of
2424 // Optimizing Supercompilers for Supercomputers
2427 // The inequalities given on page 25 are simplified in that loops are
2428 // normalized so that the lower bound is always 0 and the stride is always 1.
2429 // For example, Wolfe gives
2431 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2433 // where A_k is the coefficient of the kth index in the source subscript,
2434 // B_k is the coefficient of the kth index in the destination subscript,
2435 // U_k is the upper bound of the kth index, L_k is the lower bound of the Kth
2436 // index, and N_k is the stride of the kth index. Since all loops are normalized
2437 // by the SCEV package, N_k = 1 and L_k = 0, allowing us to simplify the
2440 // LB^<_k = (A^-_k - B_k)^- (U_k - 0 - 1) + (A_k - B_k)0 - B_k 1
2441 // = (A^-_k - B_k)^- (U_k - 1) - B_k
2443 // Similar simplifications are possible for the other equations.
2445 // When we can't determine the number of iterations for a loop,
2446 // we use NULL as an indicator for the worst case, infinity.
2447 // When computing the upper bound, NULL denotes +inf;
2448 // for the lower bound, NULL denotes -inf.
2450 // Return true if dependence disproved.
2451 bool DependenceAnalysis::banerjeeMIVtest(const SCEV *Src,
2453 const SmallBitVector &Loops,
2454 FullDependence &Result) const {
2455 DEBUG(dbgs() << "starting Banerjee\n");
2456 ++BanerjeeApplications;
2457 DEBUG(dbgs() << " Src = " << *Src << '\n');
2459 CoefficientInfo *A = collectCoeffInfo(Src, true, A0);
2460 DEBUG(dbgs() << " Dst = " << *Dst << '\n');
2462 CoefficientInfo *B = collectCoeffInfo(Dst, false, B0);
2463 BoundInfo *Bound = new BoundInfo[MaxLevels + 1];
2464 const SCEV *Delta = SE->getMinusSCEV(B0, A0);
2465 DEBUG(dbgs() << "\tDelta = " << *Delta << '\n');
2467 // Compute bounds for all the * directions.
2468 DEBUG(dbgs() << "\tBounds[*]\n");
2469 for (unsigned K = 1; K <= MaxLevels; ++K) {
2470 Bound[K].Iterations = A[K].Iterations ? A[K].Iterations : B[K].Iterations;
2471 Bound[K].Direction = Dependence::DVEntry::ALL;
2472 Bound[K].DirSet = Dependence::DVEntry::NONE;
2473 findBoundsALL(A, B, Bound, K);
2475 DEBUG(dbgs() << "\t " << K << '\t');
2476 if (Bound[K].Lower[Dependence::DVEntry::ALL])
2477 DEBUG(dbgs() << *Bound[K].Lower[Dependence::DVEntry::ALL] << '\t');
2479 DEBUG(dbgs() << "-inf\t");
2480 if (Bound[K].Upper[Dependence::DVEntry::ALL])
2481 DEBUG(dbgs() << *Bound[K].Upper[Dependence::DVEntry::ALL] << '\n');
2483 DEBUG(dbgs() << "+inf\n");
2487 // Test the *, *, *, ... case.
2488 bool Disproved = false;
2489 if (testBounds(Dependence::DVEntry::ALL, 0, Bound, Delta)) {
2490 // Explore the direction vector hierarchy.
2491 unsigned DepthExpanded = 0;
2492 unsigned NewDeps = exploreDirections(1, A, B, Bound,
2493 Loops, DepthExpanded, Delta);
2495 bool Improved = false;
2496 for (unsigned K = 1; K <= CommonLevels; ++K) {
2498 unsigned Old = Result.DV[K - 1].Direction;
2499 Result.DV[K - 1].Direction = Old & Bound[K].DirSet;
2500 Improved |= Old != Result.DV[K - 1].Direction;
2501 if (!Result.DV[K - 1].Direction) {
2509 ++BanerjeeSuccesses;
2512 ++BanerjeeIndependence;
2517 ++BanerjeeIndependence;
2527 // Hierarchically expands the direction vector
2528 // search space, combining the directions of discovered dependences
2529 // in the DirSet field of Bound. Returns the number of distinct
2530 // dependences discovered. If the dependence is disproved,
2531 // it will return 0.
2532 unsigned DependenceAnalysis::exploreDirections(unsigned Level,
2536 const SmallBitVector &Loops,
2537 unsigned &DepthExpanded,
2538 const SCEV *Delta) const {
2539 if (Level > CommonLevels) {
2541 DEBUG(dbgs() << "\t[");
2542 for (unsigned K = 1; K <= CommonLevels; ++K) {
2544 Bound[K].DirSet |= Bound[K].Direction;
2546 switch (Bound[K].Direction) {
2547 case Dependence::DVEntry::LT:
2548 DEBUG(dbgs() << " <");
2550 case Dependence::DVEntry::EQ:
2551 DEBUG(dbgs() << " =");
2553 case Dependence::DVEntry::GT:
2554 DEBUG(dbgs() << " >");
2556 case Dependence::DVEntry::ALL:
2557 DEBUG(dbgs() << " *");
2560 llvm_unreachable("unexpected Bound[K].Direction");
2565 DEBUG(dbgs() << " ]\n");
2569 if (Level > DepthExpanded) {
2570 DepthExpanded = Level;
2571 // compute bounds for <, =, > at current level
2572 findBoundsLT(A, B, Bound, Level);
2573 findBoundsGT(A, B, Bound, Level);
2574 findBoundsEQ(A, B, Bound, Level);
2576 DEBUG(dbgs() << "\tBound for level = " << Level << '\n');
2577 DEBUG(dbgs() << "\t <\t");
2578 if (Bound[Level].Lower[Dependence::DVEntry::LT])
2579 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::LT] << '\t');
2581 DEBUG(dbgs() << "-inf\t");
2582 if (Bound[Level].Upper[Dependence::DVEntry::LT])
2583 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::LT] << '\n');
2585 DEBUG(dbgs() << "+inf\n");
2586 DEBUG(dbgs() << "\t =\t");
2587 if (Bound[Level].Lower[Dependence::DVEntry::EQ])
2588 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::EQ] << '\t');
2590 DEBUG(dbgs() << "-inf\t");
2591 if (Bound[Level].Upper[Dependence::DVEntry::EQ])
2592 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::EQ] << '\n');
2594 DEBUG(dbgs() << "+inf\n");
2595 DEBUG(dbgs() << "\t >\t");
2596 if (Bound[Level].Lower[Dependence::DVEntry::GT])
2597 DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::GT] << '\t');
2599 DEBUG(dbgs() << "-inf\t");
2600 if (Bound[Level].Upper[Dependence::DVEntry::GT])
2601 DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::GT] << '\n');
2603 DEBUG(dbgs() << "+inf\n");
2607 unsigned NewDeps = 0;
2609 // test bounds for <, *, *, ...
2610 if (testBounds(Dependence::DVEntry::LT, Level, Bound, Delta))
2611 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2612 Loops, DepthExpanded, Delta);
2614 // Test bounds for =, *, *, ...
2615 if (testBounds(Dependence::DVEntry::EQ, Level, Bound, Delta))
2616 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2617 Loops, DepthExpanded, Delta);
2619 // test bounds for >, *, *, ...
2620 if (testBounds(Dependence::DVEntry::GT, Level, Bound, Delta))
2621 NewDeps += exploreDirections(Level + 1, A, B, Bound,
2622 Loops, DepthExpanded, Delta);
2624 Bound[Level].Direction = Dependence::DVEntry::ALL;
2628 return exploreDirections(Level + 1, A, B, Bound, Loops, DepthExpanded, Delta);
2632 // Returns true iff the current bounds are plausible.
2633 bool DependenceAnalysis::testBounds(unsigned char DirKind,
2636 const SCEV *Delta) const {
2637 Bound[Level].Direction = DirKind;
2638 if (const SCEV *LowerBound = getLowerBound(Bound))
2639 if (isKnownPredicate(CmpInst::ICMP_SGT, LowerBound, Delta))
2641 if (const SCEV *UpperBound = getUpperBound(Bound))
2642 if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, UpperBound))
2648 // Computes the upper and lower bounds for level K
2649 // using the * direction. Records them in Bound.
2650 // Wolfe gives the equations
2652 // LB^*_k = (A^-_k - B^+_k)(U_k - L_k) + (A_k - B_k)L_k
2653 // UB^*_k = (A^+_k - B^-_k)(U_k - L_k) + (A_k - B_k)L_k
2655 // Since we normalize loops, we can simplify these equations to
2657 // LB^*_k = (A^-_k - B^+_k)U_k
2658 // UB^*_k = (A^+_k - B^-_k)U_k
2660 // We must be careful to handle the case where the upper bound is unknown.
2661 // Note that the lower bound is always <= 0
2662 // and the upper bound is always >= 0.
2663 void DependenceAnalysis::findBoundsALL(CoefficientInfo *A,
2667 Bound[K].Lower[Dependence::DVEntry::ALL] = nullptr; // Default value = -infinity.
2668 Bound[K].Upper[Dependence::DVEntry::ALL] = nullptr; // Default value = +infinity.
2669 if (Bound[K].Iterations) {
2670 Bound[K].Lower[Dependence::DVEntry::ALL] =
2671 SE->getMulExpr(SE->getMinusSCEV(A[K].NegPart, B[K].PosPart),
2672 Bound[K].Iterations);
2673 Bound[K].Upper[Dependence::DVEntry::ALL] =
2674 SE->getMulExpr(SE->getMinusSCEV(A[K].PosPart, B[K].NegPart),
2675 Bound[K].Iterations);
2678 // If the difference is 0, we won't need to know the number of iterations.
2679 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].NegPart, B[K].PosPart))
2680 Bound[K].Lower[Dependence::DVEntry::ALL] =
2681 SE->getConstant(A[K].Coeff->getType(), 0);
2682 if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].PosPart, B[K].NegPart))
2683 Bound[K].Upper[Dependence::DVEntry::ALL] =
2684 SE->getConstant(A[K].Coeff->getType(), 0);
2689 // Computes the upper and lower bounds for level K
2690 // using the = direction. Records them in Bound.
2691 // Wolfe gives the equations
2693 // LB^=_k = (A_k - B_k)^- (U_k - L_k) + (A_k - B_k)L_k
2694 // UB^=_k = (A_k - B_k)^+ (U_k - L_k) + (A_k - B_k)L_k
2696 // Since we normalize loops, we can simplify these equations to
2698 // LB^=_k = (A_k - B_k)^- U_k
2699 // UB^=_k = (A_k - B_k)^+ U_k
2701 // We must be careful to handle the case where the upper bound is unknown.
2702 // Note that the lower bound is always <= 0
2703 // and the upper bound is always >= 0.
2704 void DependenceAnalysis::findBoundsEQ(CoefficientInfo *A,
2708 Bound[K].Lower[Dependence::DVEntry::EQ] = nullptr; // Default value = -infinity.
2709 Bound[K].Upper[Dependence::DVEntry::EQ] = nullptr; // Default value = +infinity.
2710 if (Bound[K].Iterations) {
2711 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2712 const SCEV *NegativePart = getNegativePart(Delta);
2713 Bound[K].Lower[Dependence::DVEntry::EQ] =
2714 SE->getMulExpr(NegativePart, Bound[K].Iterations);
2715 const SCEV *PositivePart = getPositivePart(Delta);
2716 Bound[K].Upper[Dependence::DVEntry::EQ] =
2717 SE->getMulExpr(PositivePart, Bound[K].Iterations);
2720 // If the positive/negative part of the difference is 0,
2721 // we won't need to know the number of iterations.
2722 const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
2723 const SCEV *NegativePart = getNegativePart(Delta);
2724 if (NegativePart->isZero())
2725 Bound[K].Lower[Dependence::DVEntry::EQ] = NegativePart; // Zero
2726 const SCEV *PositivePart = getPositivePart(Delta);
2727 if (PositivePart->isZero())
2728 Bound[K].Upper[Dependence::DVEntry::EQ] = PositivePart; // Zero
2733 // Computes the upper and lower bounds for level K
2734 // using the < direction. Records them in Bound.
2735 // Wolfe gives the equations
2737 // LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2738 // UB^<_k = (A^+_k - B_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
2740 // Since we normalize loops, we can simplify these equations to
2742 // LB^<_k = (A^-_k - B_k)^- (U_k - 1) - B_k
2743 // UB^<_k = (A^+_k - B_k)^+ (U_k - 1) - B_k
2745 // We must be careful to handle the case where the upper bound is unknown.
2746 void DependenceAnalysis::findBoundsLT(CoefficientInfo *A,
2750 Bound[K].Lower[Dependence::DVEntry::LT] = nullptr; // Default value = -infinity.
2751 Bound[K].Upper[Dependence::DVEntry::LT] = nullptr; // Default value = +infinity.
2752 if (Bound[K].Iterations) {
2753 const SCEV *Iter_1 =
2754 SE->getMinusSCEV(Bound[K].Iterations,
2755 SE->getConstant(Bound[K].Iterations->getType(), 1));
2756 const SCEV *NegPart =
2757 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2758 Bound[K].Lower[Dependence::DVEntry::LT] =
2759 SE->getMinusSCEV(SE->getMulExpr(NegPart, Iter_1), B[K].Coeff);
2760 const SCEV *PosPart =
2761 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2762 Bound[K].Upper[Dependence::DVEntry::LT] =
2763 SE->getMinusSCEV(SE->getMulExpr(PosPart, Iter_1), B[K].Coeff);
2766 // If the positive/negative part of the difference is 0,
2767 // we won't need to know the number of iterations.
2768 const SCEV *NegPart =
2769 getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
2770 if (NegPart->isZero())
2771 Bound[K].Lower[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2772 const SCEV *PosPart =
2773 getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
2774 if (PosPart->isZero())
2775 Bound[K].Upper[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
2780 // Computes the upper and lower bounds for level K
2781 // using the > direction. Records them in Bound.
2782 // Wolfe gives the equations
2784 // LB^>_k = (A_k - B^+_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2785 // UB^>_k = (A_k - B^-_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
2787 // Since we normalize loops, we can simplify these equations to
2789 // LB^>_k = (A_k - B^+_k)^- (U_k - 1) + A_k
2790 // UB^>_k = (A_k - B^-_k)^+ (U_k - 1) + A_k
2792 // We must be careful to handle the case where the upper bound is unknown.
2793 void DependenceAnalysis::findBoundsGT(CoefficientInfo *A,
2797 Bound[K].Lower[Dependence::DVEntry::GT] = nullptr; // Default value = -infinity.
2798 Bound[K].Upper[Dependence::DVEntry::GT] = nullptr; // Default value = +infinity.
2799 if (Bound[K].Iterations) {
2800 const SCEV *Iter_1 =
2801 SE->getMinusSCEV(Bound[K].Iterations,
2802 SE->getConstant(Bound[K].Iterations->getType(), 1));
2803 const SCEV *NegPart =
2804 getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2805 Bound[K].Lower[Dependence::DVEntry::GT] =
2806 SE->getAddExpr(SE->getMulExpr(NegPart, Iter_1), A[K].Coeff);
2807 const SCEV *PosPart =
2808 getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2809 Bound[K].Upper[Dependence::DVEntry::GT] =
2810 SE->getAddExpr(SE->getMulExpr(PosPart, Iter_1), A[K].Coeff);
2813 // If the positive/negative part of the difference is 0,
2814 // we won't need to know the number of iterations.
2815 const SCEV *NegPart = getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
2816 if (NegPart->isZero())
2817 Bound[K].Lower[Dependence::DVEntry::GT] = A[K].Coeff;
2818 const SCEV *PosPart = getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
2819 if (PosPart->isZero())
2820 Bound[K].Upper[Dependence::DVEntry::GT] = A[K].Coeff;
2826 const SCEV *DependenceAnalysis::getPositivePart(const SCEV *X) const {
2827 return SE->getSMaxExpr(X, SE->getConstant(X->getType(), 0));
2832 const SCEV *DependenceAnalysis::getNegativePart(const SCEV *X) const {
2833 return SE->getSMinExpr(X, SE->getConstant(X->getType(), 0));
2837 // Walks through the subscript,
2838 // collecting each coefficient, the associated loop bounds,
2839 // and recording its positive and negative parts for later use.
2840 DependenceAnalysis::CoefficientInfo *
2841 DependenceAnalysis::collectCoeffInfo(const SCEV *Subscript,
2843 const SCEV *&Constant) const {
2844 const SCEV *Zero = SE->getConstant(Subscript->getType(), 0);
2845 CoefficientInfo *CI = new CoefficientInfo[MaxLevels + 1];
2846 for (unsigned K = 1; K <= MaxLevels; ++K) {
2848 CI[K].PosPart = Zero;
2849 CI[K].NegPart = Zero;
2850 CI[K].Iterations = nullptr;
2852 while (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Subscript)) {
2853 const Loop *L = AddRec->getLoop();
2854 unsigned K = SrcFlag ? mapSrcLoop(L) : mapDstLoop(L);
2855 CI[K].Coeff = AddRec->getStepRecurrence(*SE);
2856 CI[K].PosPart = getPositivePart(CI[K].Coeff);
2857 CI[K].NegPart = getNegativePart(CI[K].Coeff);
2858 CI[K].Iterations = collectUpperBound(L, Subscript->getType());
2859 Subscript = AddRec->getStart();
2861 Constant = Subscript;
2863 DEBUG(dbgs() << "\tCoefficient Info\n");
2864 for (unsigned K = 1; K <= MaxLevels; ++K) {
2865 DEBUG(dbgs() << "\t " << K << "\t" << *CI[K].Coeff);
2866 DEBUG(dbgs() << "\tPos Part = ");
2867 DEBUG(dbgs() << *CI[K].PosPart);
2868 DEBUG(dbgs() << "\tNeg Part = ");
2869 DEBUG(dbgs() << *CI[K].NegPart);
2870 DEBUG(dbgs() << "\tUpper Bound = ");
2871 if (CI[K].Iterations)
2872 DEBUG(dbgs() << *CI[K].Iterations);
2874 DEBUG(dbgs() << "+inf");
2875 DEBUG(dbgs() << '\n');
2877 DEBUG(dbgs() << "\t Constant = " << *Subscript << '\n');
2883 // Looks through all the bounds info and
2884 // computes the lower bound given the current direction settings
2885 // at each level. If the lower bound for any level is -inf,
2886 // the result is -inf.
2887 const SCEV *DependenceAnalysis::getLowerBound(BoundInfo *Bound) const {
2888 const SCEV *Sum = Bound[1].Lower[Bound[1].Direction];
2889 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2890 if (Bound[K].Lower[Bound[K].Direction])
2891 Sum = SE->getAddExpr(Sum, Bound[K].Lower[Bound[K].Direction]);
2899 // Looks through all the bounds info and
2900 // computes the upper bound given the current direction settings
2901 // at each level. If the upper bound at any level is +inf,
2902 // the result is +inf.
2903 const SCEV *DependenceAnalysis::getUpperBound(BoundInfo *Bound) const {
2904 const SCEV *Sum = Bound[1].Upper[Bound[1].Direction];
2905 for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
2906 if (Bound[K].Upper[Bound[K].Direction])
2907 Sum = SE->getAddExpr(Sum, Bound[K].Upper[Bound[K].Direction]);
2915 //===----------------------------------------------------------------------===//
2916 // Constraint manipulation for Delta test.
2918 // Given a linear SCEV,
2919 // return the coefficient (the step)
2920 // corresponding to the specified loop.
2921 // If there isn't one, return 0.
2922 // For example, given a*i + b*j + c*k, zeroing the coefficient
2923 // corresponding to the j loop would yield b.
2924 const SCEV *DependenceAnalysis::findCoefficient(const SCEV *Expr,
2925 const Loop *TargetLoop) const {
2926 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2928 return SE->getConstant(Expr->getType(), 0);
2929 if (AddRec->getLoop() == TargetLoop)
2930 return AddRec->getStepRecurrence(*SE);
2931 return findCoefficient(AddRec->getStart(), TargetLoop);
2935 // Given a linear SCEV,
2936 // return the SCEV given by zeroing out the coefficient
2937 // corresponding to the specified loop.
2938 // For example, given a*i + b*j + c*k, zeroing the coefficient
2939 // corresponding to the j loop would yield a*i + c*k.
2940 const SCEV *DependenceAnalysis::zeroCoefficient(const SCEV *Expr,
2941 const Loop *TargetLoop) const {
2942 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2944 return Expr; // ignore
2945 if (AddRec->getLoop() == TargetLoop)
2946 return AddRec->getStart();
2947 return SE->getAddRecExpr(zeroCoefficient(AddRec->getStart(), TargetLoop),
2948 AddRec->getStepRecurrence(*SE),
2950 AddRec->getNoWrapFlags());
2954 // Given a linear SCEV Expr,
2955 // return the SCEV given by adding some Value to the
2956 // coefficient corresponding to the specified TargetLoop.
2957 // For example, given a*i + b*j + c*k, adding 1 to the coefficient
2958 // corresponding to the j loop would yield a*i + (b+1)*j + c*k.
2959 const SCEV *DependenceAnalysis::addToCoefficient(const SCEV *Expr,
2960 const Loop *TargetLoop,
2961 const SCEV *Value) const {
2962 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
2963 if (!AddRec) // create a new addRec
2964 return SE->getAddRecExpr(Expr,
2967 SCEV::FlagAnyWrap); // Worst case, with no info.
2968 if (AddRec->getLoop() == TargetLoop) {
2969 const SCEV *Sum = SE->getAddExpr(AddRec->getStepRecurrence(*SE), Value);
2971 return AddRec->getStart();
2972 return SE->getAddRecExpr(AddRec->getStart(),
2975 AddRec->getNoWrapFlags());
2977 if (SE->isLoopInvariant(AddRec, TargetLoop))
2978 return SE->getAddRecExpr(AddRec, Value, TargetLoop, SCEV::FlagAnyWrap);
2979 return SE->getAddRecExpr(
2980 addToCoefficient(AddRec->getStart(), TargetLoop, Value),
2981 AddRec->getStepRecurrence(*SE), AddRec->getLoop(),
2982 AddRec->getNoWrapFlags());
2986 // Review the constraints, looking for opportunities
2987 // to simplify a subscript pair (Src and Dst).
2988 // Return true if some simplification occurs.
2989 // If the simplification isn't exact (that is, if it is conservative
2990 // in terms of dependence), set consistent to false.
2991 // Corresponds to Figure 5 from the paper
2993 // Practical Dependence Testing
2994 // Goff, Kennedy, Tseng
2996 bool DependenceAnalysis::propagate(const SCEV *&Src,
2998 SmallBitVector &Loops,
2999 SmallVectorImpl<Constraint> &Constraints,
3001 bool Result = false;
3002 for (int LI = Loops.find_first(); LI >= 0; LI = Loops.find_next(LI)) {
3003 DEBUG(dbgs() << "\t Constraint[" << LI << "] is");
3004 DEBUG(Constraints[LI].dump(dbgs()));
3005 if (Constraints[LI].isDistance())
3006 Result |= propagateDistance(Src, Dst, Constraints[LI], Consistent);
3007 else if (Constraints[LI].isLine())
3008 Result |= propagateLine(Src, Dst, Constraints[LI], Consistent);
3009 else if (Constraints[LI].isPoint())
3010 Result |= propagatePoint(Src, Dst, Constraints[LI]);
3016 // Attempt to propagate a distance
3017 // constraint into a subscript pair (Src and Dst).
3018 // Return true if some simplification occurs.
3019 // If the simplification isn't exact (that is, if it is conservative
3020 // in terms of dependence), set consistent to false.
3021 bool DependenceAnalysis::propagateDistance(const SCEV *&Src,
3023 Constraint &CurConstraint,
3025 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3026 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3027 const SCEV *A_K = findCoefficient(Src, CurLoop);
3030 const SCEV *DA_K = SE->getMulExpr(A_K, CurConstraint.getD());
3031 Src = SE->getMinusSCEV(Src, DA_K);
3032 Src = zeroCoefficient(Src, CurLoop);
3033 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3034 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3035 Dst = addToCoefficient(Dst, CurLoop, SE->getNegativeSCEV(A_K));
3036 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3037 if (!findCoefficient(Dst, CurLoop)->isZero())
3043 // Attempt to propagate a line
3044 // constraint into a subscript pair (Src and Dst).
3045 // Return true if some simplification occurs.
3046 // If the simplification isn't exact (that is, if it is conservative
3047 // in terms of dependence), set consistent to false.
3048 bool DependenceAnalysis::propagateLine(const SCEV *&Src,
3050 Constraint &CurConstraint,
3052 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3053 const SCEV *A = CurConstraint.getA();
3054 const SCEV *B = CurConstraint.getB();
3055 const SCEV *C = CurConstraint.getC();
3056 DEBUG(dbgs() << "\t\tA = " << *A << ", B = " << *B << ", C = " << *C << "\n");
3057 DEBUG(dbgs() << "\t\tSrc = " << *Src << "\n");
3058 DEBUG(dbgs() << "\t\tDst = " << *Dst << "\n");
3060 const SCEVConstant *Bconst = dyn_cast<SCEVConstant>(B);
3061 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3062 if (!Bconst || !Cconst) return false;
3063 APInt Beta = Bconst->getValue()->getValue();
3064 APInt Charlie = Cconst->getValue()->getValue();
3065 APInt CdivB = Charlie.sdiv(Beta);
3066 assert(Charlie.srem(Beta) == 0 && "C should be evenly divisible by B");
3067 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3068 // Src = SE->getAddExpr(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3069 Src = SE->getMinusSCEV(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
3070 Dst = zeroCoefficient(Dst, CurLoop);
3071 if (!findCoefficient(Src, CurLoop)->isZero())
3074 else if (B->isZero()) {
3075 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3076 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3077 if (!Aconst || !Cconst) return false;
3078 APInt Alpha = Aconst->getValue()->getValue();
3079 APInt Charlie = Cconst->getValue()->getValue();
3080 APInt CdivA = Charlie.sdiv(Alpha);
3081 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3082 const SCEV *A_K = findCoefficient(Src, CurLoop);
3083 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3084 Src = zeroCoefficient(Src, CurLoop);
3085 if (!findCoefficient(Dst, CurLoop)->isZero())
3088 else if (isKnownPredicate(CmpInst::ICMP_EQ, A, B)) {
3089 const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
3090 const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
3091 if (!Aconst || !Cconst) return false;
3092 APInt Alpha = Aconst->getValue()->getValue();
3093 APInt Charlie = Cconst->getValue()->getValue();
3094 APInt CdivA = Charlie.sdiv(Alpha);
3095 assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
3096 const SCEV *A_K = findCoefficient(Src, CurLoop);
3097 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
3098 Src = zeroCoefficient(Src, CurLoop);
3099 Dst = addToCoefficient(Dst, CurLoop, A_K);
3100 if (!findCoefficient(Dst, CurLoop)->isZero())
3104 // paper is incorrect here, or perhaps just misleading
3105 const SCEV *A_K = findCoefficient(Src, CurLoop);
3106 Src = SE->getMulExpr(Src, A);
3107 Dst = SE->getMulExpr(Dst, A);
3108 Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, C));
3109 Src = zeroCoefficient(Src, CurLoop);
3110 Dst = addToCoefficient(Dst, CurLoop, SE->getMulExpr(A_K, B));
3111 if (!findCoefficient(Dst, CurLoop)->isZero())
3114 DEBUG(dbgs() << "\t\tnew Src = " << *Src << "\n");
3115 DEBUG(dbgs() << "\t\tnew Dst = " << *Dst << "\n");
3120 // Attempt to propagate a point
3121 // constraint into a subscript pair (Src and Dst).
3122 // Return true if some simplification occurs.
3123 bool DependenceAnalysis::propagatePoint(const SCEV *&Src,
3125 Constraint &CurConstraint) {
3126 const Loop *CurLoop = CurConstraint.getAssociatedLoop();
3127 const SCEV *A_K = findCoefficient(Src, CurLoop);
3128 const SCEV *AP_K = findCoefficient(Dst, CurLoop);
3129 const SCEV *XA_K = SE->getMulExpr(A_K, CurConstraint.getX());
3130 const SCEV *YAP_K = SE->getMulExpr(AP_K, CurConstraint.getY());
3131 DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
3132 Src = SE->getAddExpr(Src, SE->getMinusSCEV(XA_K, YAP_K));
3133 Src = zeroCoefficient(Src, CurLoop);
3134 DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
3135 DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
3136 Dst = zeroCoefficient(Dst, CurLoop);
3137 DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
3142 // Update direction vector entry based on the current constraint.
3143 void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
3144 const Constraint &CurConstraint
3146 DEBUG(dbgs() << "\tUpdate direction, constraint =");
3147 DEBUG(CurConstraint.dump(dbgs()));
3148 if (CurConstraint.isAny())
3150 else if (CurConstraint.isDistance()) {
3151 // this one is consistent, the others aren't
3152 Level.Scalar = false;
3153 Level.Distance = CurConstraint.getD();
3154 unsigned NewDirection = Dependence::DVEntry::NONE;
3155 if (!SE->isKnownNonZero(Level.Distance)) // if may be zero
3156 NewDirection = Dependence::DVEntry::EQ;
3157 if (!SE->isKnownNonPositive(Level.Distance)) // if may be positive
3158 NewDirection |= Dependence::DVEntry::LT;
3159 if (!SE->isKnownNonNegative(Level.Distance)) // if may be negative
3160 NewDirection |= Dependence::DVEntry::GT;
3161 Level.Direction &= NewDirection;
3163 else if (CurConstraint.isLine()) {
3164 Level.Scalar = false;
3165 Level.Distance = nullptr;
3166 // direction should be accurate
3168 else if (CurConstraint.isPoint()) {
3169 Level.Scalar = false;
3170 Level.Distance = nullptr;
3171 unsigned NewDirection = Dependence::DVEntry::NONE;
3172 if (!isKnownPredicate(CmpInst::ICMP_NE,
3173 CurConstraint.getY(),
3174 CurConstraint.getX()))
3176 NewDirection |= Dependence::DVEntry::EQ;
3177 if (!isKnownPredicate(CmpInst::ICMP_SLE,
3178 CurConstraint.getY(),
3179 CurConstraint.getX()))
3181 NewDirection |= Dependence::DVEntry::LT;
3182 if (!isKnownPredicate(CmpInst::ICMP_SGE,
3183 CurConstraint.getY(),
3184 CurConstraint.getX()))
3186 NewDirection |= Dependence::DVEntry::GT;
3187 Level.Direction &= NewDirection;
3190 llvm_unreachable("constraint has unexpected kind");
3193 /// Check if we can delinearize the subscripts. If the SCEVs representing the
3194 /// source and destination array references are recurrences on a nested loop,
3195 /// this function flattens the nested recurrences into separate recurrences
3196 /// for each loop level.
3197 bool DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV,
3198 const SCEV *DstSCEV,
3199 SmallVectorImpl<Subscript> &Pair,
3200 const SCEV *ElementSize) {
3201 const SCEVUnknown *SrcBase =
3202 dyn_cast<SCEVUnknown>(SE->getPointerBase(SrcSCEV));
3203 const SCEVUnknown *DstBase =
3204 dyn_cast<SCEVUnknown>(SE->getPointerBase(DstSCEV));
3206 if (!SrcBase || !DstBase || SrcBase != DstBase)
3209 SrcSCEV = SE->getMinusSCEV(SrcSCEV, SrcBase);
3210 DstSCEV = SE->getMinusSCEV(DstSCEV, DstBase);
3212 const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
3213 const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
3214 if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
3217 // First step: collect parametric terms in both array references.
3218 SmallVector<const SCEV *, 4> Terms;
3219 SrcAR->collectParametricTerms(*SE, Terms);
3220 DstAR->collectParametricTerms(*SE, Terms);
3222 // Second step: find subscript sizes.
3223 SmallVector<const SCEV *, 4> Sizes;
3224 SE->findArrayDimensions(Terms, Sizes, ElementSize);
3226 // Third step: compute the access functions for each subscript.
3227 SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts;
3228 SrcAR->computeAccessFunctions(*SE, SrcSubscripts, Sizes);
3229 DstAR->computeAccessFunctions(*SE, DstSubscripts, Sizes);
3231 // Fail when there is only a subscript: that's a linearized access function.
3232 if (SrcSubscripts.size() < 2 || DstSubscripts.size() < 2 ||
3233 SrcSubscripts.size() != DstSubscripts.size())
3236 int size = SrcSubscripts.size();
3239 dbgs() << "\nSrcSubscripts: ";
3240 for (int i = 0; i < size; i++)
3241 dbgs() << *SrcSubscripts[i];
3242 dbgs() << "\nDstSubscripts: ";
3243 for (int i = 0; i < size; i++)
3244 dbgs() << *DstSubscripts[i];
3247 // The delinearization transforms a single-subscript MIV dependence test into
3248 // a multi-subscript SIV dependence test that is easier to compute. So we
3249 // resize Pair to contain as many pairs of subscripts as the delinearization
3250 // has found, and then initialize the pairs following the delinearization.
3252 for (int i = 0; i < size; ++i) {
3253 Pair[i].Src = SrcSubscripts[i];
3254 Pair[i].Dst = DstSubscripts[i];
3255 unifySubscriptType(&Pair[i]);
3257 // FIXME: we should record the bounds SrcSizes[i] and DstSizes[i] that the
3258 // delinearization has found, and add these constraints to the dependence
3259 // check to avoid memory accesses overflow from one dimension into another.
3260 // This is related to the problem of determining the existence of data
3261 // dependences in array accesses using a different number of subscripts: in
3262 // C one can access an array A[100][100]; as A[0][9999], *A[9999], etc.
3268 //===----------------------------------------------------------------------===//
3271 // For debugging purposes, dump a small bit vector to dbgs().
3272 static void dumpSmallBitVector(SmallBitVector &BV) {
3274 for (int VI = BV.find_first(); VI >= 0; VI = BV.find_next(VI)) {
3276 if (BV.find_next(VI) >= 0)
3285 // Returns NULL if there is no dependence.
3286 // Otherwise, return a Dependence with as many details as possible.
3287 // Corresponds to Section 3.1 in the paper
3289 // Practical Dependence Testing
3290 // Goff, Kennedy, Tseng
3293 // Care is required to keep the routine below, getSplitIteration(),
3294 // up to date with respect to this routine.
3295 std::unique_ptr<Dependence>
3296 DependenceAnalysis::depends(Instruction *Src, Instruction *Dst,
3297 bool PossiblyLoopIndependent) {
3299 PossiblyLoopIndependent = false;
3301 if ((!Src->mayReadFromMemory() && !Src->mayWriteToMemory()) ||
3302 (!Dst->mayReadFromMemory() && !Dst->mayWriteToMemory()))
3303 // if both instructions don't reference memory, there's no dependence
3306 if (!isLoadOrStore(Src) || !isLoadOrStore(Dst)) {
3307 // can only analyze simple loads and stores, i.e., no calls, invokes, etc.
3308 DEBUG(dbgs() << "can only handle simple loads and stores\n");
3309 return make_unique<Dependence>(Src, Dst);
3312 Value *SrcPtr = getPointerOperand(Src);
3313 Value *DstPtr = getPointerOperand(Dst);
3315 switch (underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3317 case AliasAnalysis::MayAlias:
3318 case AliasAnalysis::PartialAlias:
3319 // cannot analyse objects if we don't understand their aliasing.
3320 DEBUG(dbgs() << "can't analyze may or partial alias\n");
3321 return make_unique<Dependence>(Src, Dst);
3322 case AliasAnalysis::NoAlias:
3323 // If the objects noalias, they are distinct, accesses are independent.
3324 DEBUG(dbgs() << "no alias\n");
3326 case AliasAnalysis::MustAlias:
3327 break; // The underlying objects alias; test accesses for dependence.
3330 // establish loop nesting levels
3331 establishNestingLevels(Src, Dst);
3332 DEBUG(dbgs() << " common nesting levels = " << CommonLevels << "\n");
3333 DEBUG(dbgs() << " maximum nesting levels = " << MaxLevels << "\n");
3335 FullDependence Result(Src, Dst, PossiblyLoopIndependent, CommonLevels);
3338 // See if there are GEPs we can use.
3339 bool UsefulGEP = false;
3340 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3341 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3342 if (SrcGEP && DstGEP &&
3343 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3344 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3345 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3346 DEBUG(dbgs() << " SrcPtrSCEV = " << *SrcPtrSCEV << "\n");
3347 DEBUG(dbgs() << " DstPtrSCEV = " << *DstPtrSCEV << "\n");
3349 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3350 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3351 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3353 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3354 SmallVector<Subscript, 4> Pair(Pairs);
3356 DEBUG(dbgs() << " using GEPs\n");
3358 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3359 SrcEnd = SrcGEP->idx_end(),
3360 DstIdx = DstGEP->idx_begin();
3362 ++SrcIdx, ++DstIdx, ++P) {
3363 Pair[P].Src = SE->getSCEV(*SrcIdx);
3364 Pair[P].Dst = SE->getSCEV(*DstIdx);
3365 unifySubscriptType(&Pair[P]);
3369 DEBUG(dbgs() << " ignoring GEPs\n");
3370 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3371 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3372 DEBUG(dbgs() << " SrcSCEV = " << *SrcSCEV << "\n");
3373 DEBUG(dbgs() << " DstSCEV = " << *DstSCEV << "\n");
3374 Pair[0].Src = SrcSCEV;
3375 Pair[0].Dst = DstSCEV;
3378 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3379 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3380 DEBUG(dbgs() << " delinerized GEP\n");
3381 Pairs = Pair.size();
3384 for (unsigned P = 0; P < Pairs; ++P) {
3385 Pair[P].Loops.resize(MaxLevels + 1);
3386 Pair[P].GroupLoops.resize(MaxLevels + 1);
3387 Pair[P].Group.resize(Pairs);
3388 removeMatchingExtensions(&Pair[P]);
3389 Pair[P].Classification =
3390 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3391 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3393 Pair[P].GroupLoops = Pair[P].Loops;
3394 Pair[P].Group.set(P);
3395 DEBUG(dbgs() << " subscript " << P << "\n");
3396 DEBUG(dbgs() << "\tsrc = " << *Pair[P].Src << "\n");
3397 DEBUG(dbgs() << "\tdst = " << *Pair[P].Dst << "\n");
3398 DEBUG(dbgs() << "\tclass = " << Pair[P].Classification << "\n");
3399 DEBUG(dbgs() << "\tloops = ");
3400 DEBUG(dumpSmallBitVector(Pair[P].Loops));
3403 SmallBitVector Separable(Pairs);
3404 SmallBitVector Coupled(Pairs);
3406 // Partition subscripts into separable and minimally-coupled groups
3407 // Algorithm in paper is algorithmically better;
3408 // this may be faster in practice. Check someday.
3410 // Here's an example of how it works. Consider this code:
3417 // A[i][j][k][m] = ...;
3418 // ... = A[0][j][l][i + j];
3425 // There are 4 subscripts here:
3429 // 3 [m] and [i + j]
3431 // We've already classified each subscript pair as ZIV, SIV, etc.,
3432 // and collected all the loops mentioned by pair P in Pair[P].Loops.
3433 // In addition, we've initialized Pair[P].GroupLoops to Pair[P].Loops
3434 // and set Pair[P].Group = {P}.
3436 // Src Dst Classification Loops GroupLoops Group
3437 // 0 [i] [0] SIV {1} {1} {0}
3438 // 1 [j] [j] SIV {2} {2} {1}
3439 // 2 [k] [l] RDIV {3,4} {3,4} {2}
3440 // 3 [m] [i + j] MIV {1,2,5} {1,2,5} {3}
3442 // For each subscript SI 0 .. 3, we consider each remaining subscript, SJ.
3443 // So, 0 is compared against 1, 2, and 3; 1 is compared against 2 and 3, etc.
3445 // We begin by comparing 0 and 1. The intersection of the GroupLoops is empty.
3446 // Next, 0 and 2. Again, the intersection of their GroupLoops is empty.
3447 // Next 0 and 3. The intersection of their GroupLoop = {1}, not empty,
3448 // so Pair[3].Group = {0,3} and Done = false (that is, 0 will not be added
3449 // to either Separable or Coupled).
3451 // Next, we consider 1 and 2. The intersection of the GroupLoops is empty.
3452 // Next, 1 and 3. The intersectionof their GroupLoops = {2}, not empty,
3453 // so Pair[3].Group = {0, 1, 3} and Done = false.
3455 // Next, we compare 2 against 3. The intersection of the GroupLoops is empty.
3456 // Since Done remains true, we add 2 to the set of Separable pairs.
3458 // Finally, we consider 3. There's nothing to compare it with,
3459 // so Done remains true and we add it to the Coupled set.
3460 // Pair[3].Group = {0, 1, 3} and GroupLoops = {1, 2, 5}.
3462 // In the end, we've got 1 separable subscript and 1 coupled group.
3463 for (unsigned SI = 0; SI < Pairs; ++SI) {
3464 if (Pair[SI].Classification == Subscript::NonLinear) {
3465 // ignore these, but collect loops for later
3466 ++NonlinearSubscriptPairs;
3467 collectCommonLoops(Pair[SI].Src,
3468 LI->getLoopFor(Src->getParent()),
3470 collectCommonLoops(Pair[SI].Dst,
3471 LI->getLoopFor(Dst->getParent()),
3473 Result.Consistent = false;
3474 } else if (Pair[SI].Classification == Subscript::ZIV) {
3479 // SIV, RDIV, or MIV, so check for coupled group
3481 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3482 SmallBitVector Intersection = Pair[SI].GroupLoops;
3483 Intersection &= Pair[SJ].GroupLoops;
3484 if (Intersection.any()) {
3485 // accumulate set of all the loops in group
3486 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3487 // accumulate set of all subscripts in group
3488 Pair[SJ].Group |= Pair[SI].Group;
3493 if (Pair[SI].Group.count() == 1) {
3495 ++SeparableSubscriptPairs;
3499 ++CoupledSubscriptPairs;
3505 DEBUG(dbgs() << " Separable = ");
3506 DEBUG(dumpSmallBitVector(Separable));
3507 DEBUG(dbgs() << " Coupled = ");
3508 DEBUG(dumpSmallBitVector(Coupled));
3510 Constraint NewConstraint;
3511 NewConstraint.setAny(SE);
3513 // test separable subscripts
3514 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3515 DEBUG(dbgs() << "testing subscript " << SI);
3516 switch (Pair[SI].Classification) {
3517 case Subscript::ZIV:
3518 DEBUG(dbgs() << ", ZIV\n");
3519 if (testZIV(Pair[SI].Src, Pair[SI].Dst, Result))
3522 case Subscript::SIV: {
3523 DEBUG(dbgs() << ", SIV\n");
3525 const SCEV *SplitIter = nullptr;
3526 if (testSIV(Pair[SI].Src, Pair[SI].Dst, Level, Result, NewConstraint,
3531 case Subscript::RDIV:
3532 DEBUG(dbgs() << ", RDIV\n");
3533 if (testRDIV(Pair[SI].Src, Pair[SI].Dst, Result))
3536 case Subscript::MIV:
3537 DEBUG(dbgs() << ", MIV\n");
3538 if (testMIV(Pair[SI].Src, Pair[SI].Dst, Pair[SI].Loops, Result))
3542 llvm_unreachable("subscript has unexpected classification");
3546 if (Coupled.count()) {
3547 // test coupled subscript groups
3548 DEBUG(dbgs() << "starting on coupled subscripts\n");
3549 DEBUG(dbgs() << "MaxLevels + 1 = " << MaxLevels + 1 << "\n");
3550 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3551 for (unsigned II = 0; II <= MaxLevels; ++II)
3552 Constraints[II].setAny(SE);
3553 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3554 DEBUG(dbgs() << "testing subscript group " << SI << " { ");
3555 SmallBitVector Group(Pair[SI].Group);
3556 SmallBitVector Sivs(Pairs);
3557 SmallBitVector Mivs(Pairs);
3558 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3559 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3560 DEBUG(dbgs() << SJ << " ");
3561 if (Pair[SJ].Classification == Subscript::SIV)
3566 DEBUG(dbgs() << "}\n");
3567 while (Sivs.any()) {
3568 bool Changed = false;
3569 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3570 DEBUG(dbgs() << "testing subscript " << SJ << ", SIV\n");
3571 // SJ is an SIV subscript that's part of the current coupled group
3573 const SCEV *SplitIter = nullptr;
3574 DEBUG(dbgs() << "SIV\n");
3575 if (testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level, Result, NewConstraint,
3578 ConstrainedLevels.set(Level);
3579 if (intersectConstraints(&Constraints[Level], &NewConstraint)) {
3580 if (Constraints[Level].isEmpty()) {
3581 ++DeltaIndependence;
3589 // propagate, possibly creating new SIVs and ZIVs
3590 DEBUG(dbgs() << " propagating\n");
3591 DEBUG(dbgs() << "\tMivs = ");
3592 DEBUG(dumpSmallBitVector(Mivs));
3593 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3594 // SJ is an MIV subscript that's part of the current coupled group
3595 DEBUG(dbgs() << "\tSJ = " << SJ << "\n");
3596 if (propagate(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops,
3597 Constraints, Result.Consistent)) {
3598 DEBUG(dbgs() << "\t Changed\n");
3599 ++DeltaPropagations;
3600 Pair[SJ].Classification =
3601 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3602 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3604 switch (Pair[SJ].Classification) {
3605 case Subscript::ZIV:
3606 DEBUG(dbgs() << "ZIV\n");
3607 if (testZIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3611 case Subscript::SIV:
3615 case Subscript::RDIV:
3616 case Subscript::MIV:
3619 llvm_unreachable("bad subscript classification");
3626 // test & propagate remaining RDIVs
3627 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3628 if (Pair[SJ].Classification == Subscript::RDIV) {
3629 DEBUG(dbgs() << "RDIV test\n");
3630 if (testRDIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
3632 // I don't yet understand how to propagate RDIV results
3637 // test remaining MIVs
3638 // This code is temporary.
3639 // Better to somehow test all remaining subscripts simultaneously.
3640 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3641 if (Pair[SJ].Classification == Subscript::MIV) {
3642 DEBUG(dbgs() << "MIV test\n");
3643 if (testMIV(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops, Result))
3647 llvm_unreachable("expected only MIV subscripts at this point");
3650 // update Result.DV from constraint vector
3651 DEBUG(dbgs() << " updating\n");
3652 for (int SJ = ConstrainedLevels.find_first(); SJ >= 0;
3653 SJ = ConstrainedLevels.find_next(SJ)) {
3654 updateDirection(Result.DV[SJ - 1], Constraints[SJ]);
3655 if (Result.DV[SJ - 1].Direction == Dependence::DVEntry::NONE)
3661 // Make sure the Scalar flags are set correctly.
3662 SmallBitVector CompleteLoops(MaxLevels + 1);
3663 for (unsigned SI = 0; SI < Pairs; ++SI)
3664 CompleteLoops |= Pair[SI].Loops;
3665 for (unsigned II = 1; II <= CommonLevels; ++II)
3666 if (CompleteLoops[II])
3667 Result.DV[II - 1].Scalar = false;
3669 if (PossiblyLoopIndependent) {
3670 // Make sure the LoopIndependent flag is set correctly.
3671 // All directions must include equal, otherwise no
3672 // loop-independent dependence is possible.
3673 for (unsigned II = 1; II <= CommonLevels; ++II) {
3674 if (!(Result.getDirection(II) & Dependence::DVEntry::EQ)) {
3675 Result.LoopIndependent = false;
3681 // On the other hand, if all directions are equal and there's no
3682 // loop-independent dependence possible, then no dependence exists.
3683 bool AllEqual = true;
3684 for (unsigned II = 1; II <= CommonLevels; ++II) {
3685 if (Result.getDirection(II) != Dependence::DVEntry::EQ) {
3694 auto Final = make_unique<FullDependence>(Result);
3695 Result.DV = nullptr;
3696 return std::move(Final);
3701 //===----------------------------------------------------------------------===//
3702 // getSplitIteration -
3703 // Rather than spend rarely-used space recording the splitting iteration
3704 // during the Weak-Crossing SIV test, we re-compute it on demand.
3705 // The re-computation is basically a repeat of the entire dependence test,
3706 // though simplified since we know that the dependence exists.
3707 // It's tedious, since we must go through all propagations, etc.
3709 // Care is required to keep this code up to date with respect to the routine
3710 // above, depends().
3712 // Generally, the dependence analyzer will be used to build
3713 // a dependence graph for a function (basically a map from instructions
3714 // to dependences). Looking for cycles in the graph shows us loops
3715 // that cannot be trivially vectorized/parallelized.
3717 // We can try to improve the situation by examining all the dependences
3718 // that make up the cycle, looking for ones we can break.
3719 // Sometimes, peeling the first or last iteration of a loop will break
3720 // dependences, and we've got flags for those possibilities.
3721 // Sometimes, splitting a loop at some other iteration will do the trick,
3722 // and we've got a flag for that case. Rather than waste the space to
3723 // record the exact iteration (since we rarely know), we provide
3724 // a method that calculates the iteration. It's a drag that it must work
3725 // from scratch, but wonderful in that it's possible.
3727 // Here's an example:
3729 // for (i = 0; i < 10; i++)
3733 // There's a loop-carried flow dependence from the store to the load,
3734 // found by the weak-crossing SIV test. The dependence will have a flag,
3735 // indicating that the dependence can be broken by splitting the loop.
3736 // Calling getSplitIteration will return 5.
3737 // Splitting the loop breaks the dependence, like so:
3739 // for (i = 0; i <= 5; i++)
3742 // for (i = 6; i < 10; i++)
3746 // breaks the dependence and allows us to vectorize/parallelize
3748 const SCEV *DependenceAnalysis::getSplitIteration(const Dependence &Dep,
3749 unsigned SplitLevel) {
3750 assert(Dep.isSplitable(SplitLevel) &&
3751 "Dep should be splitable at SplitLevel");
3752 Instruction *Src = Dep.getSrc();
3753 Instruction *Dst = Dep.getDst();
3754 assert(Src->mayReadFromMemory() || Src->mayWriteToMemory());
3755 assert(Dst->mayReadFromMemory() || Dst->mayWriteToMemory());
3756 assert(isLoadOrStore(Src));
3757 assert(isLoadOrStore(Dst));
3758 Value *SrcPtr = getPointerOperand(Src);
3759 Value *DstPtr = getPointerOperand(Dst);
3760 assert(underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
3761 SrcPtr) == AliasAnalysis::MustAlias);
3763 // establish loop nesting levels
3764 establishNestingLevels(Src, Dst);
3766 FullDependence Result(Src, Dst, false, CommonLevels);
3768 // See if there are GEPs we can use.
3769 bool UsefulGEP = false;
3770 GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
3771 GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
3772 if (SrcGEP && DstGEP &&
3773 SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
3774 const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
3775 const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
3776 UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
3777 isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
3778 (SrcGEP->getNumOperands() == DstGEP->getNumOperands());
3780 unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
3781 SmallVector<Subscript, 4> Pair(Pairs);
3784 for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
3785 SrcEnd = SrcGEP->idx_end(),
3786 DstIdx = DstGEP->idx_begin();
3788 ++SrcIdx, ++DstIdx, ++P) {
3789 Pair[P].Src = SE->getSCEV(*SrcIdx);
3790 Pair[P].Dst = SE->getSCEV(*DstIdx);
3794 const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
3795 const SCEV *DstSCEV = SE->getSCEV(DstPtr);
3796 Pair[0].Src = SrcSCEV;
3797 Pair[0].Dst = DstSCEV;
3800 if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
3801 tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
3802 DEBUG(dbgs() << " delinerized GEP\n");
3803 Pairs = Pair.size();
3806 for (unsigned P = 0; P < Pairs; ++P) {
3807 Pair[P].Loops.resize(MaxLevels + 1);
3808 Pair[P].GroupLoops.resize(MaxLevels + 1);
3809 Pair[P].Group.resize(Pairs);
3810 removeMatchingExtensions(&Pair[P]);
3811 Pair[P].Classification =
3812 classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
3813 Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
3815 Pair[P].GroupLoops = Pair[P].Loops;
3816 Pair[P].Group.set(P);
3819 SmallBitVector Separable(Pairs);
3820 SmallBitVector Coupled(Pairs);
3822 // partition subscripts into separable and minimally-coupled groups
3823 for (unsigned SI = 0; SI < Pairs; ++SI) {
3824 if (Pair[SI].Classification == Subscript::NonLinear) {
3825 // ignore these, but collect loops for later
3826 collectCommonLoops(Pair[SI].Src,
3827 LI->getLoopFor(Src->getParent()),
3829 collectCommonLoops(Pair[SI].Dst,
3830 LI->getLoopFor(Dst->getParent()),
3832 Result.Consistent = false;
3834 else if (Pair[SI].Classification == Subscript::ZIV)
3837 // SIV, RDIV, or MIV, so check for coupled group
3839 for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
3840 SmallBitVector Intersection = Pair[SI].GroupLoops;
3841 Intersection &= Pair[SJ].GroupLoops;
3842 if (Intersection.any()) {
3843 // accumulate set of all the loops in group
3844 Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
3845 // accumulate set of all subscripts in group
3846 Pair[SJ].Group |= Pair[SI].Group;
3851 if (Pair[SI].Group.count() == 1)
3859 Constraint NewConstraint;
3860 NewConstraint.setAny(SE);
3862 // test separable subscripts
3863 for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
3864 switch (Pair[SI].Classification) {
3865 case Subscript::SIV: {
3867 const SCEV *SplitIter = nullptr;
3868 (void) testSIV(Pair[SI].Src, Pair[SI].Dst, Level,
3869 Result, NewConstraint, SplitIter);
3870 if (Level == SplitLevel) {
3871 assert(SplitIter != nullptr);
3876 case Subscript::ZIV:
3877 case Subscript::RDIV:
3878 case Subscript::MIV:
3881 llvm_unreachable("subscript has unexpected classification");
3885 if (Coupled.count()) {
3886 // test coupled subscript groups
3887 SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
3888 for (unsigned II = 0; II <= MaxLevels; ++II)
3889 Constraints[II].setAny(SE);
3890 for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
3891 SmallBitVector Group(Pair[SI].Group);
3892 SmallBitVector Sivs(Pairs);
3893 SmallBitVector Mivs(Pairs);
3894 SmallBitVector ConstrainedLevels(MaxLevels + 1);
3895 for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
3896 if (Pair[SJ].Classification == Subscript::SIV)
3901 while (Sivs.any()) {
3902 bool Changed = false;
3903 for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
3904 // SJ is an SIV subscript that's part of the current coupled group
3906 const SCEV *SplitIter = nullptr;
3907 (void) testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level,
3908 Result, NewConstraint, SplitIter);
3909 if (Level == SplitLevel && SplitIter)
3911 ConstrainedLevels.set(Level);
3912 if (intersectConstraints(&Constraints[Level], &NewConstraint))
3917 // propagate, possibly creating new SIVs and ZIVs
3918 for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
3919 // SJ is an MIV subscript that's part of the current coupled group
3920 if (propagate(Pair[SJ].Src, Pair[SJ].Dst,
3921 Pair[SJ].Loops, Constraints, Result.Consistent)) {
3922 Pair[SJ].Classification =
3923 classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
3924 Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
3926 switch (Pair[SJ].Classification) {
3927 case Subscript::ZIV:
3930 case Subscript::SIV:
3934 case Subscript::RDIV:
3935 case Subscript::MIV:
3938 llvm_unreachable("bad subscript classification");
3946 llvm_unreachable("somehow reached end of routine");