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llvm/lib/Analysis/DependenceAnalysis.cpp
Karthik Bhat 36b589fd8a Fix a memory corruption in Dependency Analysis. 
This crash occurs due to memory corruption when trying to update dependency
direction based on Constraints.

This crash was observed during lnt regression of Polybench benchmark test case dynprog.

Review: http://reviews.llvm.org/D8059



git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@231788 91177308-0d34-0410-b5e6-96231b3b80d8
2015-03-10 14:32:02 +00:00

3951 lines
145 KiB
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//===-- DependenceAnalysis.cpp - DA Implementation --------------*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// DependenceAnalysis is an LLVM pass that analyses dependences between memory
// accesses. Currently, it is an (incomplete) implementation of the approach
// described in
//
// Practical Dependence Testing
// Goff, Kennedy, Tseng
// PLDI 1991
//
// There's a single entry point that analyzes the dependence between a pair
// of memory references in a function, returning either NULL, for no dependence,
// or a more-or-less detailed description of the dependence between them.
//
// Currently, the implementation cannot propagate constraints between
// coupled RDIV subscripts and lacks a multi-subscript MIV test.
// Both of these are conservative weaknesses;
// that is, not a source of correctness problems.
//
// The implementation depends on the GEP instruction to differentiate
// subscripts. Since Clang linearizes some array subscripts, the dependence
// analysis is using SCEV->delinearize to recover the representation of multiple
// subscripts, and thus avoid the more expensive and less precise MIV tests. The
// delinearization is controlled by the flag -da-delinearize.
//
// We should pay some careful attention to the possibility of integer overflow
// in the implementation of the various tests. This could happen with Add,
// Subtract, or Multiply, with both APInt's and SCEV's.
//
// Some non-linear subscript pairs can be handled by the GCD test
// (and perhaps other tests).
// Should explore how often these things occur.
//
// Finally, it seems like certain test cases expose weaknesses in the SCEV
// simplification, especially in the handling of sign and zero extensions.
// It could be useful to spend time exploring these.
//
// Please note that this is work in progress and the interface is subject to
// change.
//
//===----------------------------------------------------------------------===//
// //
// In memory of Ken Kennedy, 1945 - 2007 //
// //
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/DependenceAnalysis.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/Operator.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/raw_ostream.h"
using namespace llvm;
#define DEBUG_TYPE "da"
//===----------------------------------------------------------------------===//
// statistics
STATISTIC(TotalArrayPairs, "Array pairs tested");
STATISTIC(SeparableSubscriptPairs, "Separable subscript pairs");
STATISTIC(CoupledSubscriptPairs, "Coupled subscript pairs");
STATISTIC(NonlinearSubscriptPairs, "Nonlinear subscript pairs");
STATISTIC(ZIVapplications, "ZIV applications");
STATISTIC(ZIVindependence, "ZIV independence");
STATISTIC(StrongSIVapplications, "Strong SIV applications");
STATISTIC(StrongSIVsuccesses, "Strong SIV successes");
STATISTIC(StrongSIVindependence, "Strong SIV independence");
STATISTIC(WeakCrossingSIVapplications, "Weak-Crossing SIV applications");
STATISTIC(WeakCrossingSIVsuccesses, "Weak-Crossing SIV successes");
STATISTIC(WeakCrossingSIVindependence, "Weak-Crossing SIV independence");
STATISTIC(ExactSIVapplications, "Exact SIV applications");
STATISTIC(ExactSIVsuccesses, "Exact SIV successes");
STATISTIC(ExactSIVindependence, "Exact SIV independence");
STATISTIC(WeakZeroSIVapplications, "Weak-Zero SIV applications");
STATISTIC(WeakZeroSIVsuccesses, "Weak-Zero SIV successes");
STATISTIC(WeakZeroSIVindependence, "Weak-Zero SIV independence");
STATISTIC(ExactRDIVapplications, "Exact RDIV applications");
STATISTIC(ExactRDIVindependence, "Exact RDIV independence");
STATISTIC(SymbolicRDIVapplications, "Symbolic RDIV applications");
STATISTIC(SymbolicRDIVindependence, "Symbolic RDIV independence");
STATISTIC(DeltaApplications, "Delta applications");
STATISTIC(DeltaSuccesses, "Delta successes");
STATISTIC(DeltaIndependence, "Delta independence");
STATISTIC(DeltaPropagations, "Delta propagations");
STATISTIC(GCDapplications, "GCD applications");
STATISTIC(GCDsuccesses, "GCD successes");
STATISTIC(GCDindependence, "GCD independence");
STATISTIC(BanerjeeApplications, "Banerjee applications");
STATISTIC(BanerjeeIndependence, "Banerjee independence");
STATISTIC(BanerjeeSuccesses, "Banerjee successes");
static cl::opt<bool>
Delinearize("da-delinearize", cl::init(false), cl::Hidden, cl::ZeroOrMore,
cl::desc("Try to delinearize array references."));
//===----------------------------------------------------------------------===//
// basics
INITIALIZE_PASS_BEGIN(DependenceAnalysis, "da",
"Dependence Analysis", true, true)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(ScalarEvolution)
INITIALIZE_AG_DEPENDENCY(AliasAnalysis)
INITIALIZE_PASS_END(DependenceAnalysis, "da",
"Dependence Analysis", true, true)
char DependenceAnalysis::ID = 0;
FunctionPass *llvm::createDependenceAnalysisPass() {
return new DependenceAnalysis();
}
bool DependenceAnalysis::runOnFunction(Function &F) {
this->F = &F;
AA = &getAnalysis<AliasAnalysis>();
SE = &getAnalysis<ScalarEvolution>();
LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
return false;
}
void DependenceAnalysis::releaseMemory() {
}
void DependenceAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AliasAnalysis>();
AU.addRequiredTransitive<ScalarEvolution>();
AU.addRequiredTransitive<LoopInfoWrapperPass>();
}
// Used to test the dependence analyzer.
// Looks through the function, noting loads and stores.
// Calls depends() on every possible pair and prints out the result.
// Ignores all other instructions.
static
void dumpExampleDependence(raw_ostream &OS, Function *F,
DependenceAnalysis *DA) {
for (inst_iterator SrcI = inst_begin(F), SrcE = inst_end(F);
SrcI != SrcE; ++SrcI) {
if (isa<StoreInst>(*SrcI) || isa<LoadInst>(*SrcI)) {
for (inst_iterator DstI = SrcI, DstE = inst_end(F);
DstI != DstE; ++DstI) {
if (isa<StoreInst>(*DstI) || isa<LoadInst>(*DstI)) {
OS << "da analyze - ";
if (auto D = DA->depends(&*SrcI, &*DstI, true)) {
D->dump(OS);
for (unsigned Level = 1; Level <= D->getLevels(); Level++) {
if (D->isSplitable(Level)) {
OS << "da analyze - split level = " << Level;
OS << ", iteration = " << *DA->getSplitIteration(*D, Level);
OS << "!\n";
}
}
}
else
OS << "none!\n";
}
}
}
}
}
void DependenceAnalysis::print(raw_ostream &OS, const Module*) const {
dumpExampleDependence(OS, F, const_cast<DependenceAnalysis *>(this));
}
//===----------------------------------------------------------------------===//
// Dependence methods
// Returns true if this is an input dependence.
bool Dependence::isInput() const {
return Src->mayReadFromMemory() && Dst->mayReadFromMemory();
}
// Returns true if this is an output dependence.
bool Dependence::isOutput() const {
return Src->mayWriteToMemory() && Dst->mayWriteToMemory();
}
// Returns true if this is an flow (aka true) dependence.
bool Dependence::isFlow() const {
return Src->mayWriteToMemory() && Dst->mayReadFromMemory();
}
// Returns true if this is an anti dependence.
bool Dependence::isAnti() const {
return Src->mayReadFromMemory() && Dst->mayWriteToMemory();
}
// Returns true if a particular level is scalar; that is,
// if no subscript in the source or destination mention the induction
// variable associated with the loop at this level.
// Leave this out of line, so it will serve as a virtual method anchor
bool Dependence::isScalar(unsigned level) const {
return false;
}
//===----------------------------------------------------------------------===//
// FullDependence methods
FullDependence::FullDependence(Instruction *Source, Instruction *Destination,
bool PossiblyLoopIndependent,
unsigned CommonLevels)
: Dependence(Source, Destination), Levels(CommonLevels),
LoopIndependent(PossiblyLoopIndependent) {
Consistent = true;
DV = CommonLevels ? new DVEntry[CommonLevels] : nullptr;
}
// The rest are simple getters that hide the implementation.
// getDirection - Returns the direction associated with a particular level.
unsigned FullDependence::getDirection(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].Direction;
}
// Returns the distance (or NULL) associated with a particular level.
const SCEV *FullDependence::getDistance(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].Distance;
}
// Returns true if a particular level is scalar; that is,
// if no subscript in the source or destination mention the induction
// variable associated with the loop at this level.
bool FullDependence::isScalar(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].Scalar;
}
// Returns true if peeling the first iteration from this loop
// will break this dependence.
bool FullDependence::isPeelFirst(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].PeelFirst;
}
// Returns true if peeling the last iteration from this loop
// will break this dependence.
bool FullDependence::isPeelLast(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].PeelLast;
}
// Returns true if splitting this loop will break the dependence.
bool FullDependence::isSplitable(unsigned Level) const {
assert(0 < Level && Level <= Levels && "Level out of range");
return DV[Level - 1].Splitable;
}
//===----------------------------------------------------------------------===//
// DependenceAnalysis::Constraint methods
// If constraint is a point <X, Y>, returns X.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getX() const {
assert(Kind == Point && "Kind should be Point");
return A;
}
// If constraint is a point <X, Y>, returns Y.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getY() const {
assert(Kind == Point && "Kind should be Point");
return B;
}
// If constraint is a line AX + BY = C, returns A.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getA() const {
assert((Kind == Line || Kind == Distance) &&
"Kind should be Line (or Distance)");
return A;
}
// If constraint is a line AX + BY = C, returns B.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getB() const {
assert((Kind == Line || Kind == Distance) &&
"Kind should be Line (or Distance)");
return B;
}
// If constraint is a line AX + BY = C, returns C.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getC() const {
assert((Kind == Line || Kind == Distance) &&
"Kind should be Line (or Distance)");
return C;
}
// If constraint is a distance, returns D.
// Otherwise assert.
const SCEV *DependenceAnalysis::Constraint::getD() const {
assert(Kind == Distance && "Kind should be Distance");
return SE->getNegativeSCEV(C);
}
// Returns the loop associated with this constraint.
const Loop *DependenceAnalysis::Constraint::getAssociatedLoop() const {
assert((Kind == Distance || Kind == Line || Kind == Point) &&
"Kind should be Distance, Line, or Point");
return AssociatedLoop;
}
void DependenceAnalysis::Constraint::setPoint(const SCEV *X,
const SCEV *Y,
const Loop *CurLoop) {
Kind = Point;
A = X;
B = Y;
AssociatedLoop = CurLoop;
}
void DependenceAnalysis::Constraint::setLine(const SCEV *AA,
const SCEV *BB,
const SCEV *CC,
const Loop *CurLoop) {
Kind = Line;
A = AA;
B = BB;
C = CC;
AssociatedLoop = CurLoop;
}
void DependenceAnalysis::Constraint::setDistance(const SCEV *D,
const Loop *CurLoop) {
Kind = Distance;
A = SE->getConstant(D->getType(), 1);
B = SE->getNegativeSCEV(A);
C = SE->getNegativeSCEV(D);
AssociatedLoop = CurLoop;
}
void DependenceAnalysis::Constraint::setEmpty() {
Kind = Empty;
}
void DependenceAnalysis::Constraint::setAny(ScalarEvolution *NewSE) {
SE = NewSE;
Kind = Any;
}
// For debugging purposes. Dumps the constraint out to OS.
void DependenceAnalysis::Constraint::dump(raw_ostream &OS) const {
if (isEmpty())
OS << " Empty\n";
else if (isAny())
OS << " Any\n";
else if (isPoint())
OS << " Point is <" << *getX() << ", " << *getY() << ">\n";
else if (isDistance())
OS << " Distance is " << *getD() <<
" (" << *getA() << "*X + " << *getB() << "*Y = " << *getC() << ")\n";
else if (isLine())
OS << " Line is " << *getA() << "*X + " <<
*getB() << "*Y = " << *getC() << "\n";
else
llvm_unreachable("unknown constraint type in Constraint::dump");
}
// Updates X with the intersection
// of the Constraints X and Y. Returns true if X has changed.
// Corresponds to Figure 4 from the paper
//
// Practical Dependence Testing
// Goff, Kennedy, Tseng
// PLDI 1991
bool DependenceAnalysis::intersectConstraints(Constraint *X,
const Constraint *Y) {
++DeltaApplications;
DEBUG(dbgs() << "\tintersect constraints\n");
DEBUG(dbgs() << "\t X ="; X->dump(dbgs()));
DEBUG(dbgs() << "\t Y ="; Y->dump(dbgs()));
assert(!Y->isPoint() && "Y must not be a Point");
if (X->isAny()) {
if (Y->isAny())
return false;
*X = *Y;
return true;
}
if (X->isEmpty())
return false;
if (Y->isEmpty()) {
X->setEmpty();
return true;
}
if (X->isDistance() && Y->isDistance()) {
DEBUG(dbgs() << "\t intersect 2 distances\n");
if (isKnownPredicate(CmpInst::ICMP_EQ, X->getD(), Y->getD()))
return false;
if (isKnownPredicate(CmpInst::ICMP_NE, X->getD(), Y->getD())) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
// Hmmm, interesting situation.
// I guess if either is constant, keep it and ignore the other.
if (isa<SCEVConstant>(Y->getD())) {
*X = *Y;
return true;
}
return false;
}
// At this point, the pseudo-code in Figure 4 of the paper
// checks if (X->isPoint() && Y->isPoint()).
// This case can't occur in our implementation,
// since a Point can only arise as the result of intersecting
// two Line constraints, and the right-hand value, Y, is never
// the result of an intersection.
assert(!(X->isPoint() && Y->isPoint()) &&
"We shouldn't ever see X->isPoint() && Y->isPoint()");
if (X->isLine() && Y->isLine()) {
DEBUG(dbgs() << "\t intersect 2 lines\n");
const SCEV *Prod1 = SE->getMulExpr(X->getA(), Y->getB());
const SCEV *Prod2 = SE->getMulExpr(X->getB(), Y->getA());
if (isKnownPredicate(CmpInst::ICMP_EQ, Prod1, Prod2)) {
// slopes are equal, so lines are parallel
DEBUG(dbgs() << "\t\tsame slope\n");
Prod1 = SE->getMulExpr(X->getC(), Y->getB());
Prod2 = SE->getMulExpr(X->getB(), Y->getC());
if (isKnownPredicate(CmpInst::ICMP_EQ, Prod1, Prod2))
return false;
if (isKnownPredicate(CmpInst::ICMP_NE, Prod1, Prod2)) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
return false;
}
if (isKnownPredicate(CmpInst::ICMP_NE, Prod1, Prod2)) {
// slopes differ, so lines intersect
DEBUG(dbgs() << "\t\tdifferent slopes\n");
const SCEV *C1B2 = SE->getMulExpr(X->getC(), Y->getB());
const SCEV *C1A2 = SE->getMulExpr(X->getC(), Y->getA());
const SCEV *C2B1 = SE->getMulExpr(Y->getC(), X->getB());
const SCEV *C2A1 = SE->getMulExpr(Y->getC(), X->getA());
const SCEV *A1B2 = SE->getMulExpr(X->getA(), Y->getB());
const SCEV *A2B1 = SE->getMulExpr(Y->getA(), X->getB());
const SCEVConstant *C1A2_C2A1 =
dyn_cast<SCEVConstant>(SE->getMinusSCEV(C1A2, C2A1));
const SCEVConstant *C1B2_C2B1 =
dyn_cast<SCEVConstant>(SE->getMinusSCEV(C1B2, C2B1));
const SCEVConstant *A1B2_A2B1 =
dyn_cast<SCEVConstant>(SE->getMinusSCEV(A1B2, A2B1));
const SCEVConstant *A2B1_A1B2 =
dyn_cast<SCEVConstant>(SE->getMinusSCEV(A2B1, A1B2));
if (!C1B2_C2B1 || !C1A2_C2A1 ||
!A1B2_A2B1 || !A2B1_A1B2)
return false;
APInt Xtop = C1B2_C2B1->getValue()->getValue();
APInt Xbot = A1B2_A2B1->getValue()->getValue();
APInt Ytop = C1A2_C2A1->getValue()->getValue();
APInt Ybot = A2B1_A1B2->getValue()->getValue();
DEBUG(dbgs() << "\t\tXtop = " << Xtop << "\n");
DEBUG(dbgs() << "\t\tXbot = " << Xbot << "\n");
DEBUG(dbgs() << "\t\tYtop = " << Ytop << "\n");
DEBUG(dbgs() << "\t\tYbot = " << Ybot << "\n");
APInt Xq = Xtop; // these need to be initialized, even
APInt Xr = Xtop; // though they're just going to be overwritten
APInt::sdivrem(Xtop, Xbot, Xq, Xr);
APInt Yq = Ytop;
APInt Yr = Ytop;
APInt::sdivrem(Ytop, Ybot, Yq, Yr);
if (Xr != 0 || Yr != 0) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
DEBUG(dbgs() << "\t\tX = " << Xq << ", Y = " << Yq << "\n");
if (Xq.slt(0) || Yq.slt(0)) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
if (const SCEVConstant *CUB =
collectConstantUpperBound(X->getAssociatedLoop(), Prod1->getType())) {
APInt UpperBound = CUB->getValue()->getValue();
DEBUG(dbgs() << "\t\tupper bound = " << UpperBound << "\n");
if (Xq.sgt(UpperBound) || Yq.sgt(UpperBound)) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
}
X->setPoint(SE->getConstant(Xq),
SE->getConstant(Yq),
X->getAssociatedLoop());
++DeltaSuccesses;
return true;
}
return false;
}
// if (X->isLine() && Y->isPoint()) This case can't occur.
assert(!(X->isLine() && Y->isPoint()) && "This case should never occur");
if (X->isPoint() && Y->isLine()) {
DEBUG(dbgs() << "\t intersect Point and Line\n");
const SCEV *A1X1 = SE->getMulExpr(Y->getA(), X->getX());
const SCEV *B1Y1 = SE->getMulExpr(Y->getB(), X->getY());
const SCEV *Sum = SE->getAddExpr(A1X1, B1Y1);
if (isKnownPredicate(CmpInst::ICMP_EQ, Sum, Y->getC()))
return false;
if (isKnownPredicate(CmpInst::ICMP_NE, Sum, Y->getC())) {
X->setEmpty();
++DeltaSuccesses;
return true;
}
return false;
}
llvm_unreachable("shouldn't reach the end of Constraint intersection");
return false;
}
//===----------------------------------------------------------------------===//
// DependenceAnalysis methods
// For debugging purposes. Dumps a dependence to OS.
void Dependence::dump(raw_ostream &OS) const {
bool Splitable = false;
if (isConfused())
OS << "confused";
else {
if (isConsistent())
OS << "consistent ";
if (isFlow())
OS << "flow";
else if (isOutput())
OS << "output";
else if (isAnti())
OS << "anti";
else if (isInput())
OS << "input";
unsigned Levels = getLevels();
OS << " [";
for (unsigned II = 1; II <= Levels; ++II) {
if (isSplitable(II))
Splitable = true;
if (isPeelFirst(II))
OS << 'p';
const SCEV *Distance = getDistance(II);
if (Distance)
OS << *Distance;
else if (isScalar(II))
OS << "S";
else {
unsigned Direction = getDirection(II);
if (Direction == DVEntry::ALL)
OS << "*";
else {
if (Direction & DVEntry::LT)
OS << "<";
if (Direction & DVEntry::EQ)
OS << "=";
if (Direction & DVEntry::GT)
OS << ">";
}
}
if (isPeelLast(II))
OS << 'p';
if (II < Levels)
OS << " ";
}
if (isLoopIndependent())
OS << "|<";
OS << "]";
if (Splitable)
OS << " splitable";
}
OS << "!\n";
}
static AliasAnalysis::AliasResult underlyingObjectsAlias(AliasAnalysis *AA,
const DataLayout &DL,
const Value *A,
const Value *B) {
const Value *AObj = GetUnderlyingObject(A, DL);
const Value *BObj = GetUnderlyingObject(B, DL);
return AA->alias(AObj, AA->getTypeStoreSize(AObj->getType()),
BObj, AA->getTypeStoreSize(BObj->getType()));
}
// Returns true if the load or store can be analyzed. Atomic and volatile
// operations have properties which this analysis does not understand.
static
bool isLoadOrStore(const Instruction *I) {
if (const LoadInst *LI = dyn_cast<LoadInst>(I))
return LI->isUnordered();
else if (const StoreInst *SI = dyn_cast<StoreInst>(I))
return SI->isUnordered();
return false;
}
static
Value *getPointerOperand(Instruction *I) {
if (LoadInst *LI = dyn_cast<LoadInst>(I))
return LI->getPointerOperand();
if (StoreInst *SI = dyn_cast<StoreInst>(I))
return SI->getPointerOperand();
llvm_unreachable("Value is not load or store instruction");
return nullptr;
}
// Examines the loop nesting of the Src and Dst
// instructions and establishes their shared loops. Sets the variables
// CommonLevels, SrcLevels, and MaxLevels.
// The source and destination instructions needn't be contained in the same
// loop. The routine establishNestingLevels finds the level of most deeply
// nested loop that contains them both, CommonLevels. An instruction that's
// not contained in a loop is at level = 0. MaxLevels is equal to the level
// of the source plus the level of the destination, minus CommonLevels.
// This lets us allocate vectors MaxLevels in length, with room for every
// distinct loop referenced in both the source and destination subscripts.
// The variable SrcLevels is the nesting depth of the source instruction.
// It's used to help calculate distinct loops referenced by the destination.
// Here's the map from loops to levels:
// 0 - unused
// 1 - outermost common loop
// ... - other common loops
// CommonLevels - innermost common loop
// ... - loops containing Src but not Dst
// SrcLevels - innermost loop containing Src but not Dst
// ... - loops containing Dst but not Src
// MaxLevels - innermost loops containing Dst but not Src
// Consider the follow code fragment:
// for (a = ...) {
// for (b = ...) {
// for (c = ...) {
// for (d = ...) {
// A[] = ...;
// }
// }
// for (e = ...) {
// for (f = ...) {
// for (g = ...) {
// ... = A[];
// }
// }
// }
// }
// }
// If we're looking at the possibility of a dependence between the store
// to A (the Src) and the load from A (the Dst), we'll note that they
// have 2 loops in common, so CommonLevels will equal 2 and the direction
// vector for Result will have 2 entries. SrcLevels = 4 and MaxLevels = 7.
// A map from loop names to loop numbers would look like
// a - 1
// b - 2 = CommonLevels
// c - 3
// d - 4 = SrcLevels
// e - 5
// f - 6
// g - 7 = MaxLevels
void DependenceAnalysis::establishNestingLevels(const Instruction *Src,
const Instruction *Dst) {
const BasicBlock *SrcBlock = Src->getParent();
const BasicBlock *DstBlock = Dst->getParent();
unsigned SrcLevel = LI->getLoopDepth(SrcBlock);
unsigned DstLevel = LI->getLoopDepth(DstBlock);
const Loop *SrcLoop = LI->getLoopFor(SrcBlock);
const Loop *DstLoop = LI->getLoopFor(DstBlock);
SrcLevels = SrcLevel;
MaxLevels = SrcLevel + DstLevel;
while (SrcLevel > DstLevel) {
SrcLoop = SrcLoop->getParentLoop();
SrcLevel--;
}
while (DstLevel > SrcLevel) {
DstLoop = DstLoop->getParentLoop();
DstLevel--;
}
while (SrcLoop != DstLoop) {
SrcLoop = SrcLoop->getParentLoop();
DstLoop = DstLoop->getParentLoop();
SrcLevel--;
}
CommonLevels = SrcLevel;
MaxLevels -= CommonLevels;
}
// Given one of the loops containing the source, return
// its level index in our numbering scheme.
unsigned DependenceAnalysis::mapSrcLoop(const Loop *SrcLoop) const {
return SrcLoop->getLoopDepth();
}
// Given one of the loops containing the destination,
// return its level index in our numbering scheme.
unsigned DependenceAnalysis::mapDstLoop(const Loop *DstLoop) const {
unsigned D = DstLoop->getLoopDepth();
if (D > CommonLevels)
return D - CommonLevels + SrcLevels;
else
return D;
}
// Returns true if Expression is loop invariant in LoopNest.
bool DependenceAnalysis::isLoopInvariant(const SCEV *Expression,
const Loop *LoopNest) const {
if (!LoopNest)
return true;
return SE->isLoopInvariant(Expression, LoopNest) &&
isLoopInvariant(Expression, LoopNest->getParentLoop());
}
// Finds the set of loops from the LoopNest that
// have a level <= CommonLevels and are referred to by the SCEV Expression.
void DependenceAnalysis::collectCommonLoops(const SCEV *Expression,
const Loop *LoopNest,
SmallBitVector &Loops) const {
while (LoopNest) {
unsigned Level = LoopNest->getLoopDepth();
if (Level <= CommonLevels && !SE->isLoopInvariant(Expression, LoopNest))
Loops.set(Level);
LoopNest = LoopNest->getParentLoop();
}
}
void DependenceAnalysis::unifySubscriptType(Subscript *Pair) {
const SCEV *Src = Pair->Src;
const SCEV *Dst = Pair->Dst;
IntegerType *SrcTy = dyn_cast<IntegerType>(Src->getType());
IntegerType *DstTy = dyn_cast<IntegerType>(Dst->getType());
if (SrcTy == nullptr || DstTy == nullptr) {
assert(SrcTy == DstTy && "This function only unify integer types and "
"expect Src and Dst share the same type "
"otherwise.");
return;
}
if (SrcTy->getBitWidth() > DstTy->getBitWidth()) {
// Sign-extend Dst to typeof(Src) if typeof(Src) is wider than typeof(Dst).
Pair->Dst = SE->getSignExtendExpr(Dst, SrcTy);
} else if (SrcTy->getBitWidth() < DstTy->getBitWidth()) {
// Sign-extend Src to typeof(Dst) if typeof(Dst) is wider than typeof(Src).
Pair->Src = SE->getSignExtendExpr(Src, DstTy);
}
}
// removeMatchingExtensions - Examines a subscript pair.
// If the source and destination are identically sign (or zero)
// extended, it strips off the extension in an effect to simplify
// the actual analysis.
void DependenceAnalysis::removeMatchingExtensions(Subscript *Pair) {
const SCEV *Src = Pair->Src;
const SCEV *Dst = Pair->Dst;
if ((isa<SCEVZeroExtendExpr>(Src) && isa<SCEVZeroExtendExpr>(Dst)) ||
(isa<SCEVSignExtendExpr>(Src) && isa<SCEVSignExtendExpr>(Dst))) {
const SCEVCastExpr *SrcCast = cast<SCEVCastExpr>(Src);
const SCEVCastExpr *DstCast = cast<SCEVCastExpr>(Dst);
const SCEV *SrcCastOp = SrcCast->getOperand();
const SCEV *DstCastOp = DstCast->getOperand();
if (SrcCastOp->getType() == DstCastOp->getType()) {
Pair->Src = SrcCastOp;
Pair->Dst = DstCastOp;
}
}
}
// Examine the scev and return true iff it's linear.
// Collect any loops mentioned in the set of "Loops".
bool DependenceAnalysis::checkSrcSubscript(const SCEV *Src,
const Loop *LoopNest,
SmallBitVector &Loops) {
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Src);
if (!AddRec)
return isLoopInvariant(Src, LoopNest);
const SCEV *Start = AddRec->getStart();
const SCEV *Step = AddRec->getStepRecurrence(*SE);
if (!isLoopInvariant(Step, LoopNest))
return false;
Loops.set(mapSrcLoop(AddRec->getLoop()));
return checkSrcSubscript(Start, LoopNest, Loops);
}
// Examine the scev and return true iff it's linear.
// Collect any loops mentioned in the set of "Loops".
bool DependenceAnalysis::checkDstSubscript(const SCEV *Dst,
const Loop *LoopNest,
SmallBitVector &Loops) {
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Dst);
if (!AddRec)
return isLoopInvariant(Dst, LoopNest);
const SCEV *Start = AddRec->getStart();
const SCEV *Step = AddRec->getStepRecurrence(*SE);
if (!isLoopInvariant(Step, LoopNest))
return false;
Loops.set(mapDstLoop(AddRec->getLoop()));
return checkDstSubscript(Start, LoopNest, Loops);
}
// Examines the subscript pair (the Src and Dst SCEVs)
// and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
// Collects the associated loops in a set.
DependenceAnalysis::Subscript::ClassificationKind
DependenceAnalysis::classifyPair(const SCEV *Src, const Loop *SrcLoopNest,
const SCEV *Dst, const Loop *DstLoopNest,
SmallBitVector &Loops) {
SmallBitVector SrcLoops(MaxLevels + 1);
SmallBitVector DstLoops(MaxLevels + 1);
if (!checkSrcSubscript(Src, SrcLoopNest, SrcLoops))
return Subscript::NonLinear;
if (!checkDstSubscript(Dst, DstLoopNest, DstLoops))
return Subscript::NonLinear;
Loops = SrcLoops;
Loops |= DstLoops;
unsigned N = Loops.count();
if (N == 0)
return Subscript::ZIV;
if (N == 1)
return Subscript::SIV;
if (N == 2 && (SrcLoops.count() == 0 ||
DstLoops.count() == 0 ||
(SrcLoops.count() == 1 && DstLoops.count() == 1)))
return Subscript::RDIV;
return Subscript::MIV;
}
// A wrapper around SCEV::isKnownPredicate.
// Looks for cases where we're interested in comparing for equality.
// If both X and Y have been identically sign or zero extended,
// it strips off the (confusing) extensions before invoking
// SCEV::isKnownPredicate. Perhaps, someday, the ScalarEvolution package
// will be similarly updated.
//
// If SCEV::isKnownPredicate can't prove the predicate,
// we try simple subtraction, which seems to help in some cases
// involving symbolics.
bool DependenceAnalysis::isKnownPredicate(ICmpInst::Predicate Pred,
const SCEV *X,
const SCEV *Y) const {
if (Pred == CmpInst::ICMP_EQ ||
Pred == CmpInst::ICMP_NE) {
if ((isa<SCEVSignExtendExpr>(X) &&
isa<SCEVSignExtendExpr>(Y)) ||
(isa<SCEVZeroExtendExpr>(X) &&
isa<SCEVZeroExtendExpr>(Y))) {
const SCEVCastExpr *CX = cast<SCEVCastExpr>(X);
const SCEVCastExpr *CY = cast<SCEVCastExpr>(Y);
const SCEV *Xop = CX->getOperand();
const SCEV *Yop = CY->getOperand();
if (Xop->getType() == Yop->getType()) {
X = Xop;
Y = Yop;
}
}
}
if (SE->isKnownPredicate(Pred, X, Y))
return true;
// If SE->isKnownPredicate can't prove the condition,
// we try the brute-force approach of subtracting
// and testing the difference.
// By testing with SE->isKnownPredicate first, we avoid
// the possibility of overflow when the arguments are constants.
const SCEV *Delta = SE->getMinusSCEV(X, Y);
switch (Pred) {
case CmpInst::ICMP_EQ:
return Delta->isZero();
case CmpInst::ICMP_NE:
return SE->isKnownNonZero(Delta);
case CmpInst::ICMP_SGE:
return SE->isKnownNonNegative(Delta);
case CmpInst::ICMP_SLE:
return SE->isKnownNonPositive(Delta);
case CmpInst::ICMP_SGT:
return SE->isKnownPositive(Delta);
case CmpInst::ICMP_SLT:
return SE->isKnownNegative(Delta);
default:
llvm_unreachable("unexpected predicate in isKnownPredicate");
}
}
// All subscripts are all the same type.
// Loop bound may be smaller (e.g., a char).
// Should zero extend loop bound, since it's always >= 0.
// This routine collects upper bound and extends if needed.
// Return null if no bound available.
const SCEV *DependenceAnalysis::collectUpperBound(const Loop *L,
Type *T) const {
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
const SCEV *UB = SE->getBackedgeTakenCount(L);
return SE->getNoopOrZeroExtend(UB, T);
}
return nullptr;
}
// Calls collectUpperBound(), then attempts to cast it to SCEVConstant.
// If the cast fails, returns NULL.
const SCEVConstant *DependenceAnalysis::collectConstantUpperBound(const Loop *L,
Type *T
) const {
if (const SCEV *UB = collectUpperBound(L, T))
return dyn_cast<SCEVConstant>(UB);
return nullptr;
}
// testZIV -
// When we have a pair of subscripts of the form [c1] and [c2],
// where c1 and c2 are both loop invariant, we attack it using
// the ZIV test. Basically, we test by comparing the two values,
// but there are actually three possible results:
// 1) the values are equal, so there's a dependence
// 2) the values are different, so there's no dependence
// 3) the values might be equal, so we have to assume a dependence.
//
// Return true if dependence disproved.
bool DependenceAnalysis::testZIV(const SCEV *Src,
const SCEV *Dst,
FullDependence &Result) const {
DEBUG(dbgs() << " src = " << *Src << "\n");
DEBUG(dbgs() << " dst = " << *Dst << "\n");
++ZIVapplications;
if (isKnownPredicate(CmpInst::ICMP_EQ, Src, Dst)) {
DEBUG(dbgs() << " provably dependent\n");
return false; // provably dependent
}
if (isKnownPredicate(CmpInst::ICMP_NE, Src, Dst)) {
DEBUG(dbgs() << " provably independent\n");
++ZIVindependence;
return true; // provably independent
}
DEBUG(dbgs() << " possibly dependent\n");
Result.Consistent = false;
return false; // possibly dependent
}
// strongSIVtest -
// From the paper, Practical Dependence Testing, Section 4.2.1
//
// When we have a pair of subscripts of the form [c1 + a*i] and [c2 + a*i],
// where i is an induction variable, c1 and c2 are loop invariant,
// and a is a constant, we can solve it exactly using the Strong SIV test.
//
// Can prove independence. Failing that, can compute distance (and direction).
// In the presence of symbolic terms, we can sometimes make progress.
//
// If there's a dependence,
//
// c1 + a*i = c2 + a*i'
//
// The dependence distance is
//
// d = i' - i = (c1 - c2)/a
//
// A dependence only exists if d is an integer and abs(d) <= U, where U is the
// loop's upper bound. If a dependence exists, the dependence direction is
// defined as
//
// { < if d > 0
// direction = { = if d = 0
// { > if d < 0
//
// Return true if dependence disproved.
bool DependenceAnalysis::strongSIVtest(const SCEV *Coeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *CurLoop,
unsigned Level,
FullDependence &Result,
Constraint &NewConstraint) const {
DEBUG(dbgs() << "\tStrong SIV test\n");
DEBUG(dbgs() << "\t Coeff = " << *Coeff);
DEBUG(dbgs() << ", " << *Coeff->getType() << "\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst);
DEBUG(dbgs() << ", " << *SrcConst->getType() << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst);
DEBUG(dbgs() << ", " << *DstConst->getType() << "\n");
++StrongSIVapplications;
assert(0 < Level && Level <= CommonLevels && "level out of range");
Level--;
const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
DEBUG(dbgs() << "\t Delta = " << *Delta);
DEBUG(dbgs() << ", " << *Delta->getType() << "\n");
// check that |Delta| < iteration count
if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
DEBUG(dbgs() << "\t UpperBound = " << *UpperBound);
DEBUG(dbgs() << ", " << *UpperBound->getType() << "\n");
const SCEV *AbsDelta =
SE->isKnownNonNegative(Delta) ? Delta : SE->getNegativeSCEV(Delta);
const SCEV *AbsCoeff =
SE->isKnownNonNegative(Coeff) ? Coeff : SE->getNegativeSCEV(Coeff);
const SCEV *Product = SE->getMulExpr(UpperBound, AbsCoeff);
if (isKnownPredicate(CmpInst::ICMP_SGT, AbsDelta, Product)) {
// Distance greater than trip count - no dependence
++StrongSIVindependence;
++StrongSIVsuccesses;
return true;
}
}
// Can we compute distance?
if (isa<SCEVConstant>(Delta) && isa<SCEVConstant>(Coeff)) {
APInt ConstDelta = cast<SCEVConstant>(Delta)->getValue()->getValue();
APInt ConstCoeff = cast<SCEVConstant>(Coeff)->getValue()->getValue();
APInt Distance = ConstDelta; // these need to be initialized
APInt Remainder = ConstDelta;
APInt::sdivrem(ConstDelta, ConstCoeff, Distance, Remainder);
DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
// Make sure Coeff divides Delta exactly
if (Remainder != 0) {
// Coeff doesn't divide Distance, no dependence
++StrongSIVindependence;
++StrongSIVsuccesses;
return true;
}
Result.DV[Level].Distance = SE->getConstant(Distance);
NewConstraint.setDistance(SE->getConstant(Distance), CurLoop);
if (Distance.sgt(0))
Result.DV[Level].Direction &= Dependence::DVEntry::LT;
else if (Distance.slt(0))
Result.DV[Level].Direction &= Dependence::DVEntry::GT;
else
Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
++StrongSIVsuccesses;
}
else if (Delta->isZero()) {
// since 0/X == 0
Result.DV[Level].Distance = Delta;
NewConstraint.setDistance(Delta, CurLoop);
Result.DV[Level].Direction &= Dependence::DVEntry::EQ;
++StrongSIVsuccesses;
}
else {
if (Coeff->isOne()) {
DEBUG(dbgs() << "\t Distance = " << *Delta << "\n");
Result.DV[Level].Distance = Delta; // since X/1 == X
NewConstraint.setDistance(Delta, CurLoop);
}
else {
Result.Consistent = false;
NewConstraint.setLine(Coeff,
SE->getNegativeSCEV(Coeff),
SE->getNegativeSCEV(Delta), CurLoop);
}
// maybe we can get a useful direction
bool DeltaMaybeZero = !SE->isKnownNonZero(Delta);
bool DeltaMaybePositive = !SE->isKnownNonPositive(Delta);
bool DeltaMaybeNegative = !SE->isKnownNonNegative(Delta);
bool CoeffMaybePositive = !SE->isKnownNonPositive(Coeff);
bool CoeffMaybeNegative = !SE->isKnownNonNegative(Coeff);
// The double negatives above are confusing.
// It helps to read !SE->isKnownNonZero(Delta)
// as "Delta might be Zero"
unsigned NewDirection = Dependence::DVEntry::NONE;
if ((DeltaMaybePositive && CoeffMaybePositive) ||
(DeltaMaybeNegative && CoeffMaybeNegative))
NewDirection = Dependence::DVEntry::LT;
if (DeltaMaybeZero)
NewDirection |= Dependence::DVEntry::EQ;
if ((DeltaMaybeNegative && CoeffMaybePositive) ||
(DeltaMaybePositive && CoeffMaybeNegative))
NewDirection |= Dependence::DVEntry::GT;
if (NewDirection < Result.DV[Level].Direction)
++StrongSIVsuccesses;
Result.DV[Level].Direction &= NewDirection;
}
return false;
}
// weakCrossingSIVtest -
// From the paper, Practical Dependence Testing, Section 4.2.2
//
// When we have a pair of subscripts of the form [c1 + a*i] and [c2 - a*i],
// where i is an induction variable, c1 and c2 are loop invariant,
// and a is a constant, we can solve it exactly using the
// Weak-Crossing SIV test.
//
// Given c1 + a*i = c2 - a*i', we can look for the intersection of
// the two lines, where i = i', yielding
//
// c1 + a*i = c2 - a*i
// 2a*i = c2 - c1
// i = (c2 - c1)/2a
//
// If i < 0, there is no dependence.
// If i > upperbound, there is no dependence.
// If i = 0 (i.e., if c1 = c2), there's a dependence with distance = 0.
// If i = upperbound, there's a dependence with distance = 0.
// If i is integral, there's a dependence (all directions).
// If the non-integer part = 1/2, there's a dependence (<> directions).
// Otherwise, there's no dependence.
//
// Can prove independence. Failing that,
// can sometimes refine the directions.
// Can determine iteration for splitting.
//
// Return true if dependence disproved.
bool DependenceAnalysis::weakCrossingSIVtest(const SCEV *Coeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *CurLoop,
unsigned Level,
FullDependence &Result,
Constraint &NewConstraint,
const SCEV *&SplitIter) const {
DEBUG(dbgs() << "\tWeak-Crossing SIV test\n");
DEBUG(dbgs() << "\t Coeff = " << *Coeff << "\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
++WeakCrossingSIVapplications;
assert(0 < Level && Level <= CommonLevels && "Level out of range");
Level--;
Result.Consistent = false;
const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
NewConstraint.setLine(Coeff, Coeff, Delta, CurLoop);
if (Delta->isZero()) {
Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
++WeakCrossingSIVsuccesses;
if (!Result.DV[Level].Direction) {
++WeakCrossingSIVindependence;
return true;
}
Result.DV[Level].Distance = Delta; // = 0
return false;
}
const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(Coeff);
if (!ConstCoeff)
return false;
Result.DV[Level].Splitable = true;
if (SE->isKnownNegative(ConstCoeff)) {
ConstCoeff = dyn_cast<SCEVConstant>(SE->getNegativeSCEV(ConstCoeff));
assert(ConstCoeff &&
"dynamic cast of negative of ConstCoeff should yield constant");
Delta = SE->getNegativeSCEV(Delta);
}
assert(SE->isKnownPositive(ConstCoeff) && "ConstCoeff should be positive");
// compute SplitIter for use by DependenceAnalysis::getSplitIteration()
SplitIter =
SE->getUDivExpr(SE->getSMaxExpr(SE->getConstant(Delta->getType(), 0),
Delta),
SE->getMulExpr(SE->getConstant(Delta->getType(), 2),
ConstCoeff));
DEBUG(dbgs() << "\t Split iter = " << *SplitIter << "\n");
const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
if (!ConstDelta)
return false;
// We're certain that ConstCoeff > 0; therefore,
// if Delta < 0, then no dependence.
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
DEBUG(dbgs() << "\t ConstCoeff = " << *ConstCoeff << "\n");
if (SE->isKnownNegative(Delta)) {
// No dependence, Delta < 0
++WeakCrossingSIVindependence;
++WeakCrossingSIVsuccesses;
return true;
}
// We're certain that Delta > 0 and ConstCoeff > 0.
// Check Delta/(2*ConstCoeff) against upper loop bound
if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
const SCEV *ConstantTwo = SE->getConstant(UpperBound->getType(), 2);
const SCEV *ML = SE->getMulExpr(SE->getMulExpr(ConstCoeff, UpperBound),
ConstantTwo);
DEBUG(dbgs() << "\t ML = " << *ML << "\n");
if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, ML)) {
// Delta too big, no dependence
++WeakCrossingSIVindependence;
++WeakCrossingSIVsuccesses;
return true;
}
if (isKnownPredicate(CmpInst::ICMP_EQ, Delta, ML)) {
// i = i' = UB
Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::LT);
Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::GT);
++WeakCrossingSIVsuccesses;
if (!Result.DV[Level].Direction) {
++WeakCrossingSIVindependence;
return true;
}
Result.DV[Level].Splitable = false;
Result.DV[Level].Distance = SE->getConstant(Delta->getType(), 0);
return false;
}
}
// check that Coeff divides Delta
APInt APDelta = ConstDelta->getValue()->getValue();
APInt APCoeff = ConstCoeff->getValue()->getValue();
APInt Distance = APDelta; // these need to be initialzed
APInt Remainder = APDelta;
APInt::sdivrem(APDelta, APCoeff, Distance, Remainder);
DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
if (Remainder != 0) {
// Coeff doesn't divide Delta, no dependence
++WeakCrossingSIVindependence;
++WeakCrossingSIVsuccesses;
return true;
}
DEBUG(dbgs() << "\t Distance = " << Distance << "\n");
// if 2*Coeff doesn't divide Delta, then the equal direction isn't possible
APInt Two = APInt(Distance.getBitWidth(), 2, true);
Remainder = Distance.srem(Two);
DEBUG(dbgs() << "\t Remainder = " << Remainder << "\n");
if (Remainder != 0) {
// Equal direction isn't possible
Result.DV[Level].Direction &= unsigned(~Dependence::DVEntry::EQ);
++WeakCrossingSIVsuccesses;
}
return false;
}
// Kirch's algorithm, from
//
// Optimizing Supercompilers for Supercomputers
// Michael Wolfe
// MIT Press, 1989
//
// Program 2.1, page 29.
// Computes the GCD of AM and BM.
// Also finds a solution to the equation ax - by = gcd(a, b).
// Returns true if dependence disproved; i.e., gcd does not divide Delta.
static
bool findGCD(unsigned Bits, APInt AM, APInt BM, APInt Delta,
APInt &G, APInt &X, APInt &Y) {
APInt A0(Bits, 1, true), A1(Bits, 0, true);
APInt B0(Bits, 0, true), B1(Bits, 1, true);
APInt G0 = AM.abs();
APInt G1 = BM.abs();
APInt Q = G0; // these need to be initialized
APInt R = G0;
APInt::sdivrem(G0, G1, Q, R);
while (R != 0) {
APInt A2 = A0 - Q*A1; A0 = A1; A1 = A2;
APInt B2 = B0 - Q*B1; B0 = B1; B1 = B2;
G0 = G1; G1 = R;
APInt::sdivrem(G0, G1, Q, R);
}
G = G1;
DEBUG(dbgs() << "\t GCD = " << G << "\n");
X = AM.slt(0) ? -A1 : A1;
Y = BM.slt(0) ? B1 : -B1;
// make sure gcd divides Delta
R = Delta.srem(G);
if (R != 0)
return true; // gcd doesn't divide Delta, no dependence
Q = Delta.sdiv(G);
X *= Q;
Y *= Q;
return false;
}
static
APInt floorOfQuotient(APInt A, APInt B) {
APInt Q = A; // these need to be initialized
APInt R = A;
APInt::sdivrem(A, B, Q, R);
if (R == 0)
return Q;
if ((A.sgt(0) && B.sgt(0)) ||
(A.slt(0) && B.slt(0)))
return Q;
else
return Q - 1;
}
static
APInt ceilingOfQuotient(APInt A, APInt B) {
APInt Q = A; // these need to be initialized
APInt R = A;
APInt::sdivrem(A, B, Q, R);
if (R == 0)
return Q;
if ((A.sgt(0) && B.sgt(0)) ||
(A.slt(0) && B.slt(0)))
return Q + 1;
else
return Q;
}
static
APInt maxAPInt(APInt A, APInt B) {
return A.sgt(B) ? A : B;
}
static
APInt minAPInt(APInt A, APInt B) {
return A.slt(B) ? A : B;
}
// exactSIVtest -
// When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*i],
// where i is an induction variable, c1 and c2 are loop invariant, and a1
// and a2 are constant, we can solve it exactly using an algorithm developed
// by Banerjee and Wolfe. See Section 2.5.3 in
//
// Optimizing Supercompilers for Supercomputers
// Michael Wolfe
// MIT Press, 1989
//
// It's slower than the specialized tests (strong SIV, weak-zero SIV, etc),
// so use them if possible. They're also a bit better with symbolics and,
// in the case of the strong SIV test, can compute Distances.
//
// Return true if dependence disproved.
bool DependenceAnalysis::exactSIVtest(const SCEV *SrcCoeff,
const SCEV *DstCoeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *CurLoop,
unsigned Level,
FullDependence &Result,
Constraint &NewConstraint) const {
DEBUG(dbgs() << "\tExact SIV test\n");
DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
++ExactSIVapplications;
assert(0 < Level && Level <= CommonLevels && "Level out of range");
Level--;
Result.Consistent = false;
const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
NewConstraint.setLine(SrcCoeff, SE->getNegativeSCEV(DstCoeff),
Delta, CurLoop);
const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
return false;
// find gcd
APInt G, X, Y;
APInt AM = ConstSrcCoeff->getValue()->getValue();
APInt BM = ConstDstCoeff->getValue()->getValue();
unsigned Bits = AM.getBitWidth();
if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
// gcd doesn't divide Delta, no dependence
++ExactSIVindependence;
++ExactSIVsuccesses;
return true;
}
DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
// since SCEV construction normalizes, LM = 0
APInt UM(Bits, 1, true);
bool UMvalid = false;
// UM is perhaps unavailable, let's check
if (const SCEVConstant *CUB =
collectConstantUpperBound(CurLoop, Delta->getType())) {
UM = CUB->getValue()->getValue();
DEBUG(dbgs() << "\t UM = " << UM << "\n");
UMvalid = true;
}
APInt TU(APInt::getSignedMaxValue(Bits));
APInt TL(APInt::getSignedMinValue(Bits));
// test(BM/G, LM-X) and test(-BM/G, X-UM)
APInt TMUL = BM.sdiv(G);
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
if (UMvalid) {
TU = minAPInt(TU, floorOfQuotient(UM - X, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
}
}
else {
TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
if (UMvalid) {
TL = maxAPInt(TL, ceilingOfQuotient(UM - X, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
}
}
// test(AM/G, LM-Y) and test(-AM/G, Y-UM)
TMUL = AM.sdiv(G);
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
if (UMvalid) {
TU = minAPInt(TU, floorOfQuotient(UM - Y, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
}
}
else {
TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
if (UMvalid) {
TL = maxAPInt(TL, ceilingOfQuotient(UM - Y, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
}
}
if (TL.sgt(TU)) {
++ExactSIVindependence;
++ExactSIVsuccesses;
return true;
}
// explore directions
unsigned NewDirection = Dependence::DVEntry::NONE;
// less than
APInt SaveTU(TU); // save these
APInt SaveTL(TL);
DEBUG(dbgs() << "\t exploring LT direction\n");
TMUL = AM - BM;
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(X - Y + 1, TMUL));
DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
}
else {
TU = minAPInt(TU, floorOfQuotient(X - Y + 1, TMUL));
DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
}
if (TL.sle(TU)) {
NewDirection |= Dependence::DVEntry::LT;
++ExactSIVsuccesses;
}
// equal
TU = SaveTU; // restore
TL = SaveTL;
DEBUG(dbgs() << "\t exploring EQ direction\n");
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(X - Y, TMUL));
DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
}
else {
TU = minAPInt(TU, floorOfQuotient(X - Y, TMUL));
DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
}
TMUL = BM - AM;
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(Y - X, TMUL));
DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
}
else {
TU = minAPInt(TU, floorOfQuotient(Y - X, TMUL));
DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
}
if (TL.sle(TU)) {
NewDirection |= Dependence::DVEntry::EQ;
++ExactSIVsuccesses;
}
// greater than
TU = SaveTU; // restore
TL = SaveTL;
DEBUG(dbgs() << "\t exploring GT direction\n");
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(Y - X + 1, TMUL));
DEBUG(dbgs() << "\t\t TL = " << TL << "\n");
}
else {
TU = minAPInt(TU, floorOfQuotient(Y - X + 1, TMUL));
DEBUG(dbgs() << "\t\t TU = " << TU << "\n");
}
if (TL.sle(TU)) {
NewDirection |= Dependence::DVEntry::GT;
++ExactSIVsuccesses;
}
// finished
Result.DV[Level].Direction &= NewDirection;
if (Result.DV[Level].Direction == Dependence::DVEntry::NONE)
++ExactSIVindependence;
return Result.DV[Level].Direction == Dependence::DVEntry::NONE;
}
// Return true if the divisor evenly divides the dividend.
static
bool isRemainderZero(const SCEVConstant *Dividend,
const SCEVConstant *Divisor) {
APInt ConstDividend = Dividend->getValue()->getValue();
APInt ConstDivisor = Divisor->getValue()->getValue();
return ConstDividend.srem(ConstDivisor) == 0;
}
// weakZeroSrcSIVtest -
// From the paper, Practical Dependence Testing, Section 4.2.2
//
// When we have a pair of subscripts of the form [c1] and [c2 + a*i],
// where i is an induction variable, c1 and c2 are loop invariant,
// and a is a constant, we can solve it exactly using the
// Weak-Zero SIV test.
//
// Given
//
// c1 = c2 + a*i
//
// we get
//
// (c1 - c2)/a = i
//
// If i is not an integer, there's no dependence.
// If i < 0 or > UB, there's no dependence.
// If i = 0, the direction is <= and peeling the
// 1st iteration will break the dependence.
// If i = UB, the direction is >= and peeling the
// last iteration will break the dependence.
// Otherwise, the direction is *.
//
// Can prove independence. Failing that, we can sometimes refine
// the directions. Can sometimes show that first or last
// iteration carries all the dependences (so worth peeling).
//
// (see also weakZeroDstSIVtest)
//
// Return true if dependence disproved.
bool DependenceAnalysis::weakZeroSrcSIVtest(const SCEV *DstCoeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *CurLoop,
unsigned Level,
FullDependence &Result,
Constraint &NewConstraint) const {
// For the WeakSIV test, it's possible the loop isn't common to
// the Src and Dst loops. If it isn't, then there's no need to
// record a direction.
DEBUG(dbgs() << "\tWeak-Zero (src) SIV test\n");
DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << "\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
++WeakZeroSIVapplications;
assert(0 < Level && Level <= MaxLevels && "Level out of range");
Level--;
Result.Consistent = false;
const SCEV *Delta = SE->getMinusSCEV(SrcConst, DstConst);
NewConstraint.setLine(SE->getConstant(Delta->getType(), 0),
DstCoeff, Delta, CurLoop);
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
if (isKnownPredicate(CmpInst::ICMP_EQ, SrcConst, DstConst)) {
if (Level < CommonLevels) {
Result.DV[Level].Direction &= Dependence::DVEntry::LE;
Result.DV[Level].PeelFirst = true;
++WeakZeroSIVsuccesses;
}
return false; // dependences caused by first iteration
}
const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
if (!ConstCoeff)
return false;
const SCEV *AbsCoeff =
SE->isKnownNegative(ConstCoeff) ?
SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
const SCEV *NewDelta =
SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
// check that Delta/SrcCoeff < iteration count
// really check NewDelta < count*AbsCoeff
if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
// dependences caused by last iteration
if (Level < CommonLevels) {
Result.DV[Level].Direction &= Dependence::DVEntry::GE;
Result.DV[Level].PeelLast = true;
++WeakZeroSIVsuccesses;
}
return false;
}
}
// check that Delta/SrcCoeff >= 0
// really check that NewDelta >= 0
if (SE->isKnownNegative(NewDelta)) {
// No dependence, newDelta < 0
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
// if SrcCoeff doesn't divide Delta, then no dependence
if (isa<SCEVConstant>(Delta) &&
!isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
return false;
}
// weakZeroDstSIVtest -
// From the paper, Practical Dependence Testing, Section 4.2.2
//
// When we have a pair of subscripts of the form [c1 + a*i] and [c2],
// where i is an induction variable, c1 and c2 are loop invariant,
// and a is a constant, we can solve it exactly using the
// Weak-Zero SIV test.
//
// Given
//
// c1 + a*i = c2
//
// we get
//
// i = (c2 - c1)/a
//
// If i is not an integer, there's no dependence.
// If i < 0 or > UB, there's no dependence.
// If i = 0, the direction is <= and peeling the
// 1st iteration will break the dependence.
// If i = UB, the direction is >= and peeling the
// last iteration will break the dependence.
// Otherwise, the direction is *.
//
// Can prove independence. Failing that, we can sometimes refine
// the directions. Can sometimes show that first or last
// iteration carries all the dependences (so worth peeling).
//
// (see also weakZeroSrcSIVtest)
//
// Return true if dependence disproved.
bool DependenceAnalysis::weakZeroDstSIVtest(const SCEV *SrcCoeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *CurLoop,
unsigned Level,
FullDependence &Result,
Constraint &NewConstraint) const {
// For the WeakSIV test, it's possible the loop isn't common to the
// Src and Dst loops. If it isn't, then there's no need to record a direction.
DEBUG(dbgs() << "\tWeak-Zero (dst) SIV test\n");
DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << "\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
++WeakZeroSIVapplications;
assert(0 < Level && Level <= SrcLevels && "Level out of range");
Level--;
Result.Consistent = false;
const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
NewConstraint.setLine(SrcCoeff, SE->getConstant(Delta->getType(), 0),
Delta, CurLoop);
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
if (isKnownPredicate(CmpInst::ICMP_EQ, DstConst, SrcConst)) {
if (Level < CommonLevels) {
Result.DV[Level].Direction &= Dependence::DVEntry::LE;
Result.DV[Level].PeelFirst = true;
++WeakZeroSIVsuccesses;
}
return false; // dependences caused by first iteration
}
const SCEVConstant *ConstCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
if (!ConstCoeff)
return false;
const SCEV *AbsCoeff =
SE->isKnownNegative(ConstCoeff) ?
SE->getNegativeSCEV(ConstCoeff) : ConstCoeff;
const SCEV *NewDelta =
SE->isKnownNegative(ConstCoeff) ? SE->getNegativeSCEV(Delta) : Delta;
// check that Delta/SrcCoeff < iteration count
// really check NewDelta < count*AbsCoeff
if (const SCEV *UpperBound = collectUpperBound(CurLoop, Delta->getType())) {
DEBUG(dbgs() << "\t UpperBound = " << *UpperBound << "\n");
const SCEV *Product = SE->getMulExpr(AbsCoeff, UpperBound);
if (isKnownPredicate(CmpInst::ICMP_SGT, NewDelta, Product)) {
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
if (isKnownPredicate(CmpInst::ICMP_EQ, NewDelta, Product)) {
// dependences caused by last iteration
if (Level < CommonLevels) {
Result.DV[Level].Direction &= Dependence::DVEntry::GE;
Result.DV[Level].PeelLast = true;
++WeakZeroSIVsuccesses;
}
return false;
}
}
// check that Delta/SrcCoeff >= 0
// really check that NewDelta >= 0
if (SE->isKnownNegative(NewDelta)) {
// No dependence, newDelta < 0
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
// if SrcCoeff doesn't divide Delta, then no dependence
if (isa<SCEVConstant>(Delta) &&
!isRemainderZero(cast<SCEVConstant>(Delta), ConstCoeff)) {
++WeakZeroSIVindependence;
++WeakZeroSIVsuccesses;
return true;
}
return false;
}
// exactRDIVtest - Tests the RDIV subscript pair for dependence.
// Things of the form [c1 + a*i] and [c2 + b*j],
// where i and j are induction variable, c1 and c2 are loop invariant,
// and a and b are constants.
// Returns true if any possible dependence is disproved.
// Marks the result as inconsistent.
// Works in some cases that symbolicRDIVtest doesn't, and vice versa.
bool DependenceAnalysis::exactRDIVtest(const SCEV *SrcCoeff,
const SCEV *DstCoeff,
const SCEV *SrcConst,
const SCEV *DstConst,
const Loop *SrcLoop,
const Loop *DstLoop,
FullDependence &Result) const {
DEBUG(dbgs() << "\tExact RDIV test\n");
DEBUG(dbgs() << "\t SrcCoeff = " << *SrcCoeff << " = AM\n");
DEBUG(dbgs() << "\t DstCoeff = " << *DstCoeff << " = BM\n");
DEBUG(dbgs() << "\t SrcConst = " << *SrcConst << "\n");
DEBUG(dbgs() << "\t DstConst = " << *DstConst << "\n");
++ExactRDIVapplications;
Result.Consistent = false;
const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
DEBUG(dbgs() << "\t Delta = " << *Delta << "\n");
const SCEVConstant *ConstDelta = dyn_cast<SCEVConstant>(Delta);
const SCEVConstant *ConstSrcCoeff = dyn_cast<SCEVConstant>(SrcCoeff);
const SCEVConstant *ConstDstCoeff = dyn_cast<SCEVConstant>(DstCoeff);
if (!ConstDelta || !ConstSrcCoeff || !ConstDstCoeff)
return false;
// find gcd
APInt G, X, Y;
APInt AM = ConstSrcCoeff->getValue()->getValue();
APInt BM = ConstDstCoeff->getValue()->getValue();
unsigned Bits = AM.getBitWidth();
if (findGCD(Bits, AM, BM, ConstDelta->getValue()->getValue(), G, X, Y)) {
// gcd doesn't divide Delta, no dependence
++ExactRDIVindependence;
return true;
}
DEBUG(dbgs() << "\t X = " << X << ", Y = " << Y << "\n");
// since SCEV construction seems to normalize, LM = 0
APInt SrcUM(Bits, 1, true);
bool SrcUMvalid = false;
// SrcUM is perhaps unavailable, let's check
if (const SCEVConstant *UpperBound =
collectConstantUpperBound(SrcLoop, Delta->getType())) {
SrcUM = UpperBound->getValue()->getValue();
DEBUG(dbgs() << "\t SrcUM = " << SrcUM << "\n");
SrcUMvalid = true;
}
APInt DstUM(Bits, 1, true);
bool DstUMvalid = false;
// UM is perhaps unavailable, let's check
if (const SCEVConstant *UpperBound =
collectConstantUpperBound(DstLoop, Delta->getType())) {
DstUM = UpperBound->getValue()->getValue();
DEBUG(dbgs() << "\t DstUM = " << DstUM << "\n");
DstUMvalid = true;
}
APInt TU(APInt::getSignedMaxValue(Bits));
APInt TL(APInt::getSignedMinValue(Bits));
// test(BM/G, LM-X) and test(-BM/G, X-UM)
APInt TMUL = BM.sdiv(G);
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(-X, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
if (SrcUMvalid) {
TU = minAPInt(TU, floorOfQuotient(SrcUM - X, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
}
}
else {
TU = minAPInt(TU, floorOfQuotient(-X, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
if (SrcUMvalid) {
TL = maxAPInt(TL, ceilingOfQuotient(SrcUM - X, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
}
}
// test(AM/G, LM-Y) and test(-AM/G, Y-UM)
TMUL = AM.sdiv(G);
if (TMUL.sgt(0)) {
TL = maxAPInt(TL, ceilingOfQuotient(-Y, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
if (DstUMvalid) {
TU = minAPInt(TU, floorOfQuotient(DstUM - Y, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
}
}
else {
TU = minAPInt(TU, floorOfQuotient(-Y, TMUL));
DEBUG(dbgs() << "\t TU = " << TU << "\n");
if (DstUMvalid) {
TL = maxAPInt(TL, ceilingOfQuotient(DstUM - Y, TMUL));
DEBUG(dbgs() << "\t TL = " << TL << "\n");
}
}
if (TL.sgt(TU))
++ExactRDIVindependence;
return TL.sgt(TU);
}
// symbolicRDIVtest -
// In Section 4.5 of the Practical Dependence Testing paper,the authors
// introduce a special case of Banerjee's Inequalities (also called the
// Extreme-Value Test) that can handle some of the SIV and RDIV cases,
// particularly cases with symbolics. Since it's only able to disprove
// dependence (not compute distances or directions), we'll use it as a
// fall back for the other tests.
//
// When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
// where i and j are induction variables and c1 and c2 are loop invariants,
// we can use the symbolic tests to disprove some dependences, serving as a
// backup for the RDIV test. Note that i and j can be the same variable,
// letting this test serve as a backup for the various SIV tests.
//
// For a dependence to exist, c1 + a1*i must equal c2 + a2*j for some
// 0 <= i <= N1 and some 0 <= j <= N2, where N1 and N2 are the (normalized)
// loop bounds for the i and j loops, respectively. So, ...
//
// c1 + a1*i = c2 + a2*j
// a1*i - a2*j = c2 - c1
//
// To test for a dependence, we compute c2 - c1 and make sure it's in the
// range of the maximum and minimum possible values of a1*i - a2*j.
// Considering the signs of a1 and a2, we have 4 possible cases:
//
// 1) If a1 >= 0 and a2 >= 0, then
// a1*0 - a2*N2 <= c2 - c1 <= a1*N1 - a2*0
// -a2*N2 <= c2 - c1 <= a1*N1
//
// 2) If a1 >= 0 and a2 <= 0, then
// a1*0 - a2*0 <= c2 - c1 <= a1*N1 - a2*N2
// 0 <= c2 - c1 <= a1*N1 - a2*N2
//
// 3) If a1 <= 0 and a2 >= 0, then
// a1*N1 - a2*N2 <= c2 - c1 <= a1*0 - a2*0
// a1*N1 - a2*N2 <= c2 - c1 <= 0
//
// 4) If a1 <= 0 and a2 <= 0, then
// a1*N1 - a2*0 <= c2 - c1 <= a1*0 - a2*N2
// a1*N1 <= c2 - c1 <= -a2*N2
//
// return true if dependence disproved
bool DependenceAnalysis::symbolicRDIVtest(const SCEV *A1,
const SCEV *A2,
const SCEV *C1,
const SCEV *C2,
const Loop *Loop1,
const Loop *Loop2) const {
++SymbolicRDIVapplications;
DEBUG(dbgs() << "\ttry symbolic RDIV test\n");
DEBUG(dbgs() << "\t A1 = " << *A1);
DEBUG(dbgs() << ", type = " << *A1->getType() << "\n");
DEBUG(dbgs() << "\t A2 = " << *A2 << "\n");
DEBUG(dbgs() << "\t C1 = " << *C1 << "\n");
DEBUG(dbgs() << "\t C2 = " << *C2 << "\n");
const SCEV *N1 = collectUpperBound(Loop1, A1->getType());
const SCEV *N2 = collectUpperBound(Loop2, A1->getType());
DEBUG(if (N1) dbgs() << "\t N1 = " << *N1 << "\n");
DEBUG(if (N2) dbgs() << "\t N2 = " << *N2 << "\n");
const SCEV *C2_C1 = SE->getMinusSCEV(C2, C1);
const SCEV *C1_C2 = SE->getMinusSCEV(C1, C2);
DEBUG(dbgs() << "\t C2 - C1 = " << *C2_C1 << "\n");
DEBUG(dbgs() << "\t C1 - C2 = " << *C1_C2 << "\n");
if (SE->isKnownNonNegative(A1)) {
if (SE->isKnownNonNegative(A2)) {
// A1 >= 0 && A2 >= 0
if (N1) {
// make sure that c2 - c1 <= a1*N1
const SCEV *A1N1 = SE->getMulExpr(A1, N1);
DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1)) {
++SymbolicRDIVindependence;
return true;
}
}
if (N2) {
// make sure that -a2*N2 <= c2 - c1, or a2*N2 >= c1 - c2
const SCEV *A2N2 = SE->getMulExpr(A2, N2);
DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SLT, A2N2, C1_C2)) {
++SymbolicRDIVindependence;
return true;
}
}
}
else if (SE->isKnownNonPositive(A2)) {
// a1 >= 0 && a2 <= 0
if (N1 && N2) {
// make sure that c2 - c1 <= a1*N1 - a2*N2
const SCEV *A1N1 = SE->getMulExpr(A1, N1);
const SCEV *A2N2 = SE->getMulExpr(A2, N2);
const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SGT, C2_C1, A1N1_A2N2)) {
++SymbolicRDIVindependence;
return true;
}
}
// make sure that 0 <= c2 - c1
if (SE->isKnownNegative(C2_C1)) {
++SymbolicRDIVindependence;
return true;
}
}
}
else if (SE->isKnownNonPositive(A1)) {
if (SE->isKnownNonNegative(A2)) {
// a1 <= 0 && a2 >= 0
if (N1 && N2) {
// make sure that a1*N1 - a2*N2 <= c2 - c1
const SCEV *A1N1 = SE->getMulExpr(A1, N1);
const SCEV *A2N2 = SE->getMulExpr(A2, N2);
const SCEV *A1N1_A2N2 = SE->getMinusSCEV(A1N1, A2N2);
DEBUG(dbgs() << "\t A1*N1 - A2*N2 = " << *A1N1_A2N2 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1_A2N2, C2_C1)) {
++SymbolicRDIVindependence;
return true;
}
}
// make sure that c2 - c1 <= 0
if (SE->isKnownPositive(C2_C1)) {
++SymbolicRDIVindependence;
return true;
}
}
else if (SE->isKnownNonPositive(A2)) {
// a1 <= 0 && a2 <= 0
if (N1) {
// make sure that a1*N1 <= c2 - c1
const SCEV *A1N1 = SE->getMulExpr(A1, N1);
DEBUG(dbgs() << "\t A1*N1 = " << *A1N1 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SGT, A1N1, C2_C1)) {
++SymbolicRDIVindependence;
return true;
}
}
if (N2) {
// make sure that c2 - c1 <= -a2*N2, or c1 - c2 >= a2*N2
const SCEV *A2N2 = SE->getMulExpr(A2, N2);
DEBUG(dbgs() << "\t A2*N2 = " << *A2N2 << "\n");
if (isKnownPredicate(CmpInst::ICMP_SLT, C1_C2, A2N2)) {
++SymbolicRDIVindependence;
return true;
}
}
}
}
return false;
}
// testSIV -
// When we have a pair of subscripts of the form [c1 + a1*i] and [c2 - a2*i]
// where i is an induction variable, c1 and c2 are loop invariant, and a1 and
// a2 are constant, we attack it with an SIV test. While they can all be
// solved with the Exact SIV test, it's worthwhile to use simpler tests when
// they apply; they're cheaper and sometimes more precise.
//
// Return true if dependence disproved.
bool DependenceAnalysis::testSIV(const SCEV *Src,
const SCEV *Dst,
unsigned &Level,
FullDependence &Result,
Constraint &NewConstraint,
const SCEV *&SplitIter) const {
DEBUG(dbgs() << " src = " << *Src << "\n");
DEBUG(dbgs() << " dst = " << *Dst << "\n");
const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
if (SrcAddRec && DstAddRec) {
const SCEV *SrcConst = SrcAddRec->getStart();
const SCEV *DstConst = DstAddRec->getStart();
const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
const Loop *CurLoop = SrcAddRec->getLoop();
assert(CurLoop == DstAddRec->getLoop() &&
"both loops in SIV should be same");
Level = mapSrcLoop(CurLoop);
bool disproven;
if (SrcCoeff == DstCoeff)
disproven = strongSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
Level, Result, NewConstraint);
else if (SrcCoeff == SE->getNegativeSCEV(DstCoeff))
disproven = weakCrossingSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
Level, Result, NewConstraint, SplitIter);
else
disproven = exactSIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop,
Level, Result, NewConstraint);
return disproven ||
gcdMIVtest(Src, Dst, Result) ||
symbolicRDIVtest(SrcCoeff, DstCoeff, SrcConst, DstConst, CurLoop, CurLoop);
}
if (SrcAddRec) {
const SCEV *SrcConst = SrcAddRec->getStart();
const SCEV *SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
const SCEV *DstConst = Dst;
const Loop *CurLoop = SrcAddRec->getLoop();
Level = mapSrcLoop(CurLoop);
return weakZeroDstSIVtest(SrcCoeff, SrcConst, DstConst, CurLoop,
Level, Result, NewConstraint) ||
gcdMIVtest(Src, Dst, Result);
}
if (DstAddRec) {
const SCEV *DstConst = DstAddRec->getStart();
const SCEV *DstCoeff = DstAddRec->getStepRecurrence(*SE);
const SCEV *SrcConst = Src;
const Loop *CurLoop = DstAddRec->getLoop();
Level = mapDstLoop(CurLoop);
return weakZeroSrcSIVtest(DstCoeff, SrcConst, DstConst,
CurLoop, Level, Result, NewConstraint) ||
gcdMIVtest(Src, Dst, Result);
}
llvm_unreachable("SIV test expected at least one AddRec");
return false;
}
// testRDIV -
// When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
// where i and j are induction variables, c1 and c2 are loop invariant,
// and a1 and a2 are constant, we can solve it exactly with an easy adaptation
// of the Exact SIV test, the Restricted Double Index Variable (RDIV) test.
// It doesn't make sense to talk about distance or direction in this case,
// so there's no point in making special versions of the Strong SIV test or
// the Weak-crossing SIV test.
//
// With minor algebra, this test can also be used for things like
// [c1 + a1*i + a2*j][c2].
//
// Return true if dependence disproved.
bool DependenceAnalysis::testRDIV(const SCEV *Src,
const SCEV *Dst,
FullDependence &Result) const {
// we have 3 possible situations here:
// 1) [a*i + b] and [c*j + d]
// 2) [a*i + c*j + b] and [d]
// 3) [b] and [a*i + c*j + d]
// We need to find what we've got and get organized
const SCEV *SrcConst, *DstConst;
const SCEV *SrcCoeff, *DstCoeff;
const Loop *SrcLoop, *DstLoop;
DEBUG(dbgs() << " src = " << *Src << "\n");
DEBUG(dbgs() << " dst = " << *Dst << "\n");
const SCEVAddRecExpr *SrcAddRec = dyn_cast<SCEVAddRecExpr>(Src);
const SCEVAddRecExpr *DstAddRec = dyn_cast<SCEVAddRecExpr>(Dst);
if (SrcAddRec && DstAddRec) {
SrcConst = SrcAddRec->getStart();
SrcCoeff = SrcAddRec->getStepRecurrence(*SE);
SrcLoop = SrcAddRec->getLoop();
DstConst = DstAddRec->getStart();
DstCoeff = DstAddRec->getStepRecurrence(*SE);
DstLoop = DstAddRec->getLoop();
}
else if (SrcAddRec) {
if (const SCEVAddRecExpr *tmpAddRec =
dyn_cast<SCEVAddRecExpr>(SrcAddRec->getStart())) {
SrcConst = tmpAddRec->getStart();
SrcCoeff = tmpAddRec->getStepRecurrence(*SE);
SrcLoop = tmpAddRec->getLoop();
DstConst = Dst;
DstCoeff = SE->getNegativeSCEV(SrcAddRec->getStepRecurrence(*SE));
DstLoop = SrcAddRec->getLoop();
}
else
llvm_unreachable("RDIV reached by surprising SCEVs");
}
else if (DstAddRec) {
if (const SCEVAddRecExpr *tmpAddRec =
dyn_cast<SCEVAddRecExpr>(DstAddRec->getStart())) {
DstConst = tmpAddRec->getStart();
DstCoeff = tmpAddRec->getStepRecurrence(*SE);
DstLoop = tmpAddRec->getLoop();
SrcConst = Src;
SrcCoeff = SE->getNegativeSCEV(DstAddRec->getStepRecurrence(*SE));
SrcLoop = DstAddRec->getLoop();
}
else
llvm_unreachable("RDIV reached by surprising SCEVs");
}
else
llvm_unreachable("RDIV expected at least one AddRec");
return exactRDIVtest(SrcCoeff, DstCoeff,
SrcConst, DstConst,
SrcLoop, DstLoop,
Result) ||
gcdMIVtest(Src, Dst, Result) ||
symbolicRDIVtest(SrcCoeff, DstCoeff,
SrcConst, DstConst,
SrcLoop, DstLoop);
}
// Tests the single-subscript MIV pair (Src and Dst) for dependence.
// Return true if dependence disproved.
// Can sometimes refine direction vectors.
bool DependenceAnalysis::testMIV(const SCEV *Src,
const SCEV *Dst,
const SmallBitVector &Loops,
FullDependence &Result) const {
DEBUG(dbgs() << " src = " << *Src << "\n");
DEBUG(dbgs() << " dst = " << *Dst << "\n");
Result.Consistent = false;
return gcdMIVtest(Src, Dst, Result) ||
banerjeeMIVtest(Src, Dst, Loops, Result);
}
// Given a product, e.g., 10*X*Y, returns the first constant operand,
// in this case 10. If there is no constant part, returns NULL.
static
const SCEVConstant *getConstantPart(const SCEVMulExpr *Product) {
for (unsigned Op = 0, Ops = Product->getNumOperands(); Op < Ops; Op++) {
if (const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Product->getOperand(Op)))
return Constant;
}
return nullptr;
}
//===----------------------------------------------------------------------===//
// gcdMIVtest -
// Tests an MIV subscript pair for dependence.
// Returns true if any possible dependence is disproved.
// Marks the result as inconsistent.
// Can sometimes disprove the equal direction for 1 or more loops,
// as discussed in Michael Wolfe's book,
// High Performance Compilers for Parallel Computing, page 235.
//
// We spend some effort (code!) to handle cases like
// [10*i + 5*N*j + 15*M + 6], where i and j are induction variables,
// but M and N are just loop-invariant variables.
// This should help us handle linearized subscripts;
// also makes this test a useful backup to the various SIV tests.
//
// It occurs to me that the presence of loop-invariant variables
// changes the nature of the test from "greatest common divisor"
// to "a common divisor".
bool DependenceAnalysis::gcdMIVtest(const SCEV *Src,
const SCEV *Dst,
FullDependence &Result) const {
DEBUG(dbgs() << "starting gcd\n");
++GCDapplications;
unsigned BitWidth = SE->getTypeSizeInBits(Src->getType());
APInt RunningGCD = APInt::getNullValue(BitWidth);
// Examine Src coefficients.
// Compute running GCD and record source constant.
// Because we're looking for the constant at the end of the chain,
// we can't quit the loop just because the GCD == 1.
const SCEV *Coefficients = Src;
while (const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(Coefficients)) {
const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
// If the coefficient is the product of a constant and other stuff,
// we can use the constant in the GCD computation.
Constant = getConstantPart(Product);
if (!Constant)
return false;
APInt ConstCoeff = Constant->getValue()->getValue();
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
Coefficients = AddRec->getStart();
}
const SCEV *SrcConst = Coefficients;
// Examine Dst coefficients.
// Compute running GCD and record destination constant.
// Because we're looking for the constant at the end of the chain,
// we can't quit the loop just because the GCD == 1.
Coefficients = Dst;
while (const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(Coefficients)) {
const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Coeff);
if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
// If the coefficient is the product of a constant and other stuff,
// we can use the constant in the GCD computation.
Constant = getConstantPart(Product);
if (!Constant)
return false;
APInt ConstCoeff = Constant->getValue()->getValue();
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
Coefficients = AddRec->getStart();
}
const SCEV *DstConst = Coefficients;
APInt ExtraGCD = APInt::getNullValue(BitWidth);
const SCEV *Delta = SE->getMinusSCEV(DstConst, SrcConst);
DEBUG(dbgs() << " Delta = " << *Delta << "\n");
const SCEVConstant *Constant = dyn_cast<SCEVConstant>(Delta);
if (const SCEVAddExpr *Sum = dyn_cast<SCEVAddExpr>(Delta)) {
// If Delta is a sum of products, we may be able to make further progress.
for (unsigned Op = 0, Ops = Sum->getNumOperands(); Op < Ops; Op++) {
const SCEV *Operand = Sum->getOperand(Op);
if (isa<SCEVConstant>(Operand)) {
assert(!Constant && "Surprised to find multiple constants");
Constant = cast<SCEVConstant>(Operand);
}
else if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Operand)) {
// Search for constant operand to participate in GCD;
// If none found; return false.
const SCEVConstant *ConstOp = getConstantPart(Product);
if (!ConstOp)
return false;
APInt ConstOpValue = ConstOp->getValue()->getValue();
ExtraGCD = APIntOps::GreatestCommonDivisor(ExtraGCD,
ConstOpValue.abs());
}
else
return false;
}
}
if (!Constant)
return false;
APInt ConstDelta = cast<SCEVConstant>(Constant)->getValue()->getValue();
DEBUG(dbgs() << " ConstDelta = " << ConstDelta << "\n");
if (ConstDelta == 0)
return false;
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ExtraGCD);
DEBUG(dbgs() << " RunningGCD = " << RunningGCD << "\n");
APInt Remainder = ConstDelta.srem(RunningGCD);
if (Remainder != 0) {
++GCDindependence;
return true;
}
// Try to disprove equal directions.
// For example, given a subscript pair [3*i + 2*j] and [i' + 2*j' - 1],
// the code above can't disprove the dependence because the GCD = 1.
// So we consider what happen if i = i' and what happens if j = j'.
// If i = i', we can simplify the subscript to [2*i + 2*j] and [2*j' - 1],
// which is infeasible, so we can disallow the = direction for the i level.
// Setting j = j' doesn't help matters, so we end up with a direction vector
// of [<>, *]
//
// Given A[5*i + 10*j*M + 9*M*N] and A[15*i + 20*j*M - 21*N*M + 5],
// we need to remember that the constant part is 5 and the RunningGCD should
// be initialized to ExtraGCD = 30.
DEBUG(dbgs() << " ExtraGCD = " << ExtraGCD << '\n');
bool Improved = false;
Coefficients = Src;
while (const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(Coefficients)) {
Coefficients = AddRec->getStart();
const Loop *CurLoop = AddRec->getLoop();
RunningGCD = ExtraGCD;
const SCEV *SrcCoeff = AddRec->getStepRecurrence(*SE);
const SCEV *DstCoeff = SE->getMinusSCEV(SrcCoeff, SrcCoeff);
const SCEV *Inner = Src;
while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
AddRec = cast<SCEVAddRecExpr>(Inner);
const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
if (CurLoop == AddRec->getLoop())
; // SrcCoeff == Coeff
else {
if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
// If the coefficient is the product of a constant and other stuff,
// we can use the constant in the GCD computation.
Constant = getConstantPart(Product);
else
Constant = cast<SCEVConstant>(Coeff);
APInt ConstCoeff = Constant->getValue()->getValue();
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
}
Inner = AddRec->getStart();
}
Inner = Dst;
while (RunningGCD != 1 && isa<SCEVAddRecExpr>(Inner)) {
AddRec = cast<SCEVAddRecExpr>(Inner);
const SCEV *Coeff = AddRec->getStepRecurrence(*SE);
if (CurLoop == AddRec->getLoop())
DstCoeff = Coeff;
else {
if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Coeff))
// If the coefficient is the product of a constant and other stuff,
// we can use the constant in the GCD computation.
Constant = getConstantPart(Product);
else
Constant = cast<SCEVConstant>(Coeff);
APInt ConstCoeff = Constant->getValue()->getValue();
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
}
Inner = AddRec->getStart();
}
Delta = SE->getMinusSCEV(SrcCoeff, DstCoeff);
if (const SCEVMulExpr *Product = dyn_cast<SCEVMulExpr>(Delta))
// If the coefficient is the product of a constant and other stuff,
// we can use the constant in the GCD computation.
Constant = getConstantPart(Product);
else if (isa<SCEVConstant>(Delta))
Constant = cast<SCEVConstant>(Delta);
else {
// The difference of the two coefficients might not be a product
// or constant, in which case we give up on this direction.
continue;
}
APInt ConstCoeff = Constant->getValue()->getValue();
RunningGCD = APIntOps::GreatestCommonDivisor(RunningGCD, ConstCoeff.abs());
DEBUG(dbgs() << "\tRunningGCD = " << RunningGCD << "\n");
if (RunningGCD != 0) {
Remainder = ConstDelta.srem(RunningGCD);
DEBUG(dbgs() << "\tRemainder = " << Remainder << "\n");
if (Remainder != 0) {
unsigned Level = mapSrcLoop(CurLoop);
Result.DV[Level - 1].Direction &= unsigned(~Dependence::DVEntry::EQ);
Improved = true;
}
}
}
if (Improved)
++GCDsuccesses;
DEBUG(dbgs() << "all done\n");
return false;
}
//===----------------------------------------------------------------------===//
// banerjeeMIVtest -
// Use Banerjee's Inequalities to test an MIV subscript pair.
// (Wolfe, in the race-car book, calls this the Extreme Value Test.)
// Generally follows the discussion in Section 2.5.2 of
//
// Optimizing Supercompilers for Supercomputers
// Michael Wolfe
//
// The inequalities given on page 25 are simplified in that loops are
// normalized so that the lower bound is always 0 and the stride is always 1.
// For example, Wolfe gives
//
// LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
//
// where A_k is the coefficient of the kth index in the source subscript,
// B_k is the coefficient of the kth index in the destination subscript,
// U_k is the upper bound of the kth index, L_k is the lower bound of the Kth
// index, and N_k is the stride of the kth index. Since all loops are normalized
// by the SCEV package, N_k = 1 and L_k = 0, allowing us to simplify the
// equation to
//
// LB^<_k = (A^-_k - B_k)^- (U_k - 0 - 1) + (A_k - B_k)0 - B_k 1
// = (A^-_k - B_k)^- (U_k - 1) - B_k
//
// Similar simplifications are possible for the other equations.
//
// When we can't determine the number of iterations for a loop,
// we use NULL as an indicator for the worst case, infinity.
// When computing the upper bound, NULL denotes +inf;
// for the lower bound, NULL denotes -inf.
//
// Return true if dependence disproved.
bool DependenceAnalysis::banerjeeMIVtest(const SCEV *Src,
const SCEV *Dst,
const SmallBitVector &Loops,
FullDependence &Result) const {
DEBUG(dbgs() << "starting Banerjee\n");
++BanerjeeApplications;
DEBUG(dbgs() << " Src = " << *Src << '\n');
const SCEV *A0;
CoefficientInfo *A = collectCoeffInfo(Src, true, A0);
DEBUG(dbgs() << " Dst = " << *Dst << '\n');
const SCEV *B0;
CoefficientInfo *B = collectCoeffInfo(Dst, false, B0);
BoundInfo *Bound = new BoundInfo[MaxLevels + 1];
const SCEV *Delta = SE->getMinusSCEV(B0, A0);
DEBUG(dbgs() << "\tDelta = " << *Delta << '\n');
// Compute bounds for all the * directions.
DEBUG(dbgs() << "\tBounds[*]\n");
for (unsigned K = 1; K <= MaxLevels; ++K) {
Bound[K].Iterations = A[K].Iterations ? A[K].Iterations : B[K].Iterations;
Bound[K].Direction = Dependence::DVEntry::ALL;
Bound[K].DirSet = Dependence::DVEntry::NONE;
findBoundsALL(A, B, Bound, K);
#ifndef NDEBUG
DEBUG(dbgs() << "\t " << K << '\t');
if (Bound[K].Lower[Dependence::DVEntry::ALL])
DEBUG(dbgs() << *Bound[K].Lower[Dependence::DVEntry::ALL] << '\t');
else
DEBUG(dbgs() << "-inf\t");
if (Bound[K].Upper[Dependence::DVEntry::ALL])
DEBUG(dbgs() << *Bound[K].Upper[Dependence::DVEntry::ALL] << '\n');
else
DEBUG(dbgs() << "+inf\n");
#endif
}
// Test the *, *, *, ... case.
bool Disproved = false;
if (testBounds(Dependence::DVEntry::ALL, 0, Bound, Delta)) {
// Explore the direction vector hierarchy.
unsigned DepthExpanded = 0;
unsigned NewDeps = exploreDirections(1, A, B, Bound,
Loops, DepthExpanded, Delta);
if (NewDeps > 0) {
bool Improved = false;
for (unsigned K = 1; K <= CommonLevels; ++K) {
if (Loops[K]) {
unsigned Old = Result.DV[K - 1].Direction;
Result.DV[K - 1].Direction = Old & Bound[K].DirSet;
Improved |= Old != Result.DV[K - 1].Direction;
if (!Result.DV[K - 1].Direction) {
Improved = false;
Disproved = true;
break;
}
}
}
if (Improved)
++BanerjeeSuccesses;
}
else {
++BanerjeeIndependence;
Disproved = true;
}
}
else {
++BanerjeeIndependence;
Disproved = true;
}
delete [] Bound;
delete [] A;
delete [] B;
return Disproved;
}
// Hierarchically expands the direction vector
// search space, combining the directions of discovered dependences
// in the DirSet field of Bound. Returns the number of distinct
// dependences discovered. If the dependence is disproved,
// it will return 0.
unsigned DependenceAnalysis::exploreDirections(unsigned Level,
CoefficientInfo *A,
CoefficientInfo *B,
BoundInfo *Bound,
const SmallBitVector &Loops,
unsigned &DepthExpanded,
const SCEV *Delta) const {
if (Level > CommonLevels) {
// record result
DEBUG(dbgs() << "\t[");
for (unsigned K = 1; K <= CommonLevels; ++K) {
if (Loops[K]) {
Bound[K].DirSet |= Bound[K].Direction;
#ifndef NDEBUG
switch (Bound[K].Direction) {
case Dependence::DVEntry::LT:
DEBUG(dbgs() << " <");
break;
case Dependence::DVEntry::EQ:
DEBUG(dbgs() << " =");
break;
case Dependence::DVEntry::GT:
DEBUG(dbgs() << " >");
break;
case Dependence::DVEntry::ALL:
DEBUG(dbgs() << " *");
break;
default:
llvm_unreachable("unexpected Bound[K].Direction");
}
#endif
}
}
DEBUG(dbgs() << " ]\n");
return 1;
}
if (Loops[Level]) {
if (Level > DepthExpanded) {
DepthExpanded = Level;
// compute bounds for <, =, > at current level
findBoundsLT(A, B, Bound, Level);
findBoundsGT(A, B, Bound, Level);
findBoundsEQ(A, B, Bound, Level);
#ifndef NDEBUG
DEBUG(dbgs() << "\tBound for level = " << Level << '\n');
DEBUG(dbgs() << "\t <\t");
if (Bound[Level].Lower[Dependence::DVEntry::LT])
DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::LT] << '\t');
else
DEBUG(dbgs() << "-inf\t");
if (Bound[Level].Upper[Dependence::DVEntry::LT])
DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::LT] << '\n');
else
DEBUG(dbgs() << "+inf\n");
DEBUG(dbgs() << "\t =\t");
if (Bound[Level].Lower[Dependence::DVEntry::EQ])
DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::EQ] << '\t');
else
DEBUG(dbgs() << "-inf\t");
if (Bound[Level].Upper[Dependence::DVEntry::EQ])
DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::EQ] << '\n');
else
DEBUG(dbgs() << "+inf\n");
DEBUG(dbgs() << "\t >\t");
if (Bound[Level].Lower[Dependence::DVEntry::GT])
DEBUG(dbgs() << *Bound[Level].Lower[Dependence::DVEntry::GT] << '\t');
else
DEBUG(dbgs() << "-inf\t");
if (Bound[Level].Upper[Dependence::DVEntry::GT])
DEBUG(dbgs() << *Bound[Level].Upper[Dependence::DVEntry::GT] << '\n');
else
DEBUG(dbgs() << "+inf\n");
#endif
}
unsigned NewDeps = 0;
// test bounds for <, *, *, ...
if (testBounds(Dependence::DVEntry::LT, Level, Bound, Delta))
NewDeps += exploreDirections(Level + 1, A, B, Bound,
Loops, DepthExpanded, Delta);
// Test bounds for =, *, *, ...
if (testBounds(Dependence::DVEntry::EQ, Level, Bound, Delta))
NewDeps += exploreDirections(Level + 1, A, B, Bound,
Loops, DepthExpanded, Delta);
// test bounds for >, *, *, ...
if (testBounds(Dependence::DVEntry::GT, Level, Bound, Delta))
NewDeps += exploreDirections(Level + 1, A, B, Bound,
Loops, DepthExpanded, Delta);
Bound[Level].Direction = Dependence::DVEntry::ALL;
return NewDeps;
}
else
return exploreDirections(Level + 1, A, B, Bound, Loops, DepthExpanded, Delta);
}
// Returns true iff the current bounds are plausible.
bool DependenceAnalysis::testBounds(unsigned char DirKind,
unsigned Level,
BoundInfo *Bound,
const SCEV *Delta) const {
Bound[Level].Direction = DirKind;
if (const SCEV *LowerBound = getLowerBound(Bound))
if (isKnownPredicate(CmpInst::ICMP_SGT, LowerBound, Delta))
return false;
if (const SCEV *UpperBound = getUpperBound(Bound))
if (isKnownPredicate(CmpInst::ICMP_SGT, Delta, UpperBound))
return false;
return true;
}
// Computes the upper and lower bounds for level K
// using the * direction. Records them in Bound.
// Wolfe gives the equations
//
// LB^*_k = (A^-_k - B^+_k)(U_k - L_k) + (A_k - B_k)L_k
// UB^*_k = (A^+_k - B^-_k)(U_k - L_k) + (A_k - B_k)L_k
//
// Since we normalize loops, we can simplify these equations to
//
// LB^*_k = (A^-_k - B^+_k)U_k
// UB^*_k = (A^+_k - B^-_k)U_k
//
// We must be careful to handle the case where the upper bound is unknown.
// Note that the lower bound is always <= 0
// and the upper bound is always >= 0.
void DependenceAnalysis::findBoundsALL(CoefficientInfo *A,
CoefficientInfo *B,
BoundInfo *Bound,
unsigned K) const {
Bound[K].Lower[Dependence::DVEntry::ALL] = nullptr; // Default value = -infinity.
Bound[K].Upper[Dependence::DVEntry::ALL] = nullptr; // Default value = +infinity.
if (Bound[K].Iterations) {
Bound[K].Lower[Dependence::DVEntry::ALL] =
SE->getMulExpr(SE->getMinusSCEV(A[K].NegPart, B[K].PosPart),
Bound[K].Iterations);
Bound[K].Upper[Dependence::DVEntry::ALL] =
SE->getMulExpr(SE->getMinusSCEV(A[K].PosPart, B[K].NegPart),
Bound[K].Iterations);
}
else {
// If the difference is 0, we won't need to know the number of iterations.
if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].NegPart, B[K].PosPart))
Bound[K].Lower[Dependence::DVEntry::ALL] =
SE->getConstant(A[K].Coeff->getType(), 0);
if (isKnownPredicate(CmpInst::ICMP_EQ, A[K].PosPart, B[K].NegPart))
Bound[K].Upper[Dependence::DVEntry::ALL] =
SE->getConstant(A[K].Coeff->getType(), 0);
}
}
// Computes the upper and lower bounds for level K
// using the = direction. Records them in Bound.
// Wolfe gives the equations
//
// LB^=_k = (A_k - B_k)^- (U_k - L_k) + (A_k - B_k)L_k
// UB^=_k = (A_k - B_k)^+ (U_k - L_k) + (A_k - B_k)L_k
//
// Since we normalize loops, we can simplify these equations to
//
// LB^=_k = (A_k - B_k)^- U_k
// UB^=_k = (A_k - B_k)^+ U_k
//
// We must be careful to handle the case where the upper bound is unknown.
// Note that the lower bound is always <= 0
// and the upper bound is always >= 0.
void DependenceAnalysis::findBoundsEQ(CoefficientInfo *A,
CoefficientInfo *B,
BoundInfo *Bound,
unsigned K) const {
Bound[K].Lower[Dependence::DVEntry::EQ] = nullptr; // Default value = -infinity.
Bound[K].Upper[Dependence::DVEntry::EQ] = nullptr; // Default value = +infinity.
if (Bound[K].Iterations) {
const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
const SCEV *NegativePart = getNegativePart(Delta);
Bound[K].Lower[Dependence::DVEntry::EQ] =
SE->getMulExpr(NegativePart, Bound[K].Iterations);
const SCEV *PositivePart = getPositivePart(Delta);
Bound[K].Upper[Dependence::DVEntry::EQ] =
SE->getMulExpr(PositivePart, Bound[K].Iterations);
}
else {
// If the positive/negative part of the difference is 0,
// we won't need to know the number of iterations.
const SCEV *Delta = SE->getMinusSCEV(A[K].Coeff, B[K].Coeff);
const SCEV *NegativePart = getNegativePart(Delta);
if (NegativePart->isZero())
Bound[K].Lower[Dependence::DVEntry::EQ] = NegativePart; // Zero
const SCEV *PositivePart = getPositivePart(Delta);
if (PositivePart->isZero())
Bound[K].Upper[Dependence::DVEntry::EQ] = PositivePart; // Zero
}
}
// Computes the upper and lower bounds for level K
// using the < direction. Records them in Bound.
// Wolfe gives the equations
//
// LB^<_k = (A^-_k - B_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
// UB^<_k = (A^+_k - B_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k - B_k N_k
//
// Since we normalize loops, we can simplify these equations to
//
// LB^<_k = (A^-_k - B_k)^- (U_k - 1) - B_k
// UB^<_k = (A^+_k - B_k)^+ (U_k - 1) - B_k
//
// We must be careful to handle the case where the upper bound is unknown.
void DependenceAnalysis::findBoundsLT(CoefficientInfo *A,
CoefficientInfo *B,
BoundInfo *Bound,
unsigned K) const {
Bound[K].Lower[Dependence::DVEntry::LT] = nullptr; // Default value = -infinity.
Bound[K].Upper[Dependence::DVEntry::LT] = nullptr; // Default value = +infinity.
if (Bound[K].Iterations) {
const SCEV *Iter_1 =
SE->getMinusSCEV(Bound[K].Iterations,
SE->getConstant(Bound[K].Iterations->getType(), 1));
const SCEV *NegPart =
getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
Bound[K].Lower[Dependence::DVEntry::LT] =
SE->getMinusSCEV(SE->getMulExpr(NegPart, Iter_1), B[K].Coeff);
const SCEV *PosPart =
getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
Bound[K].Upper[Dependence::DVEntry::LT] =
SE->getMinusSCEV(SE->getMulExpr(PosPart, Iter_1), B[K].Coeff);
}
else {
// If the positive/negative part of the difference is 0,
// we won't need to know the number of iterations.
const SCEV *NegPart =
getNegativePart(SE->getMinusSCEV(A[K].NegPart, B[K].Coeff));
if (NegPart->isZero())
Bound[K].Lower[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
const SCEV *PosPart =
getPositivePart(SE->getMinusSCEV(A[K].PosPart, B[K].Coeff));
if (PosPart->isZero())
Bound[K].Upper[Dependence::DVEntry::LT] = SE->getNegativeSCEV(B[K].Coeff);
}
}
// Computes the upper and lower bounds for level K
// using the > direction. Records them in Bound.
// Wolfe gives the equations
//
// LB^>_k = (A_k - B^+_k)^- (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
// UB^>_k = (A_k - B^-_k)^+ (U_k - L_k - N_k) + (A_k - B_k)L_k + A_k N_k
//
// Since we normalize loops, we can simplify these equations to
//
// LB^>_k = (A_k - B^+_k)^- (U_k - 1) + A_k
// UB^>_k = (A_k - B^-_k)^+ (U_k - 1) + A_k
//
// We must be careful to handle the case where the upper bound is unknown.
void DependenceAnalysis::findBoundsGT(CoefficientInfo *A,
CoefficientInfo *B,
BoundInfo *Bound,
unsigned K) const {
Bound[K].Lower[Dependence::DVEntry::GT] = nullptr; // Default value = -infinity.
Bound[K].Upper[Dependence::DVEntry::GT] = nullptr; // Default value = +infinity.
if (Bound[K].Iterations) {
const SCEV *Iter_1 =
SE->getMinusSCEV(Bound[K].Iterations,
SE->getConstant(Bound[K].Iterations->getType(), 1));
const SCEV *NegPart =
getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
Bound[K].Lower[Dependence::DVEntry::GT] =
SE->getAddExpr(SE->getMulExpr(NegPart, Iter_1), A[K].Coeff);
const SCEV *PosPart =
getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
Bound[K].Upper[Dependence::DVEntry::GT] =
SE->getAddExpr(SE->getMulExpr(PosPart, Iter_1), A[K].Coeff);
}
else {
// If the positive/negative part of the difference is 0,
// we won't need to know the number of iterations.
const SCEV *NegPart = getNegativePart(SE->getMinusSCEV(A[K].Coeff, B[K].PosPart));
if (NegPart->isZero())
Bound[K].Lower[Dependence::DVEntry::GT] = A[K].Coeff;
const SCEV *PosPart = getPositivePart(SE->getMinusSCEV(A[K].Coeff, B[K].NegPart));
if (PosPart->isZero())
Bound[K].Upper[Dependence::DVEntry::GT] = A[K].Coeff;
}
}
// X^+ = max(X, 0)
const SCEV *DependenceAnalysis::getPositivePart(const SCEV *X) const {
return SE->getSMaxExpr(X, SE->getConstant(X->getType(), 0));
}
// X^- = min(X, 0)
const SCEV *DependenceAnalysis::getNegativePart(const SCEV *X) const {
return SE->getSMinExpr(X, SE->getConstant(X->getType(), 0));
}
// Walks through the subscript,
// collecting each coefficient, the associated loop bounds,
// and recording its positive and negative parts for later use.
DependenceAnalysis::CoefficientInfo *
DependenceAnalysis::collectCoeffInfo(const SCEV *Subscript,
bool SrcFlag,
const SCEV *&Constant) const {
const SCEV *Zero = SE->getConstant(Subscript->getType(), 0);
CoefficientInfo *CI = new CoefficientInfo[MaxLevels + 1];
for (unsigned K = 1; K <= MaxLevels; ++K) {
CI[K].Coeff = Zero;
CI[K].PosPart = Zero;
CI[K].NegPart = Zero;
CI[K].Iterations = nullptr;
}
while (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Subscript)) {
const Loop *L = AddRec->getLoop();
unsigned K = SrcFlag ? mapSrcLoop(L) : mapDstLoop(L);
CI[K].Coeff = AddRec->getStepRecurrence(*SE);
CI[K].PosPart = getPositivePart(CI[K].Coeff);
CI[K].NegPart = getNegativePart(CI[K].Coeff);
CI[K].Iterations = collectUpperBound(L, Subscript->getType());
Subscript = AddRec->getStart();
}
Constant = Subscript;
#ifndef NDEBUG
DEBUG(dbgs() << "\tCoefficient Info\n");
for (unsigned K = 1; K <= MaxLevels; ++K) {
DEBUG(dbgs() << "\t " << K << "\t" << *CI[K].Coeff);
DEBUG(dbgs() << "\tPos Part = ");
DEBUG(dbgs() << *CI[K].PosPart);
DEBUG(dbgs() << "\tNeg Part = ");
DEBUG(dbgs() << *CI[K].NegPart);
DEBUG(dbgs() << "\tUpper Bound = ");
if (CI[K].Iterations)
DEBUG(dbgs() << *CI[K].Iterations);
else
DEBUG(dbgs() << "+inf");
DEBUG(dbgs() << '\n');
}
DEBUG(dbgs() << "\t Constant = " << *Subscript << '\n');
#endif
return CI;
}
// Looks through all the bounds info and
// computes the lower bound given the current direction settings
// at each level. If the lower bound for any level is -inf,
// the result is -inf.
const SCEV *DependenceAnalysis::getLowerBound(BoundInfo *Bound) const {
const SCEV *Sum = Bound[1].Lower[Bound[1].Direction];
for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
if (Bound[K].Lower[Bound[K].Direction])
Sum = SE->getAddExpr(Sum, Bound[K].Lower[Bound[K].Direction]);
else
Sum = nullptr;
}
return Sum;
}
// Looks through all the bounds info and
// computes the upper bound given the current direction settings
// at each level. If the upper bound at any level is +inf,
// the result is +inf.
const SCEV *DependenceAnalysis::getUpperBound(BoundInfo *Bound) const {
const SCEV *Sum = Bound[1].Upper[Bound[1].Direction];
for (unsigned K = 2; Sum && K <= MaxLevels; ++K) {
if (Bound[K].Upper[Bound[K].Direction])
Sum = SE->getAddExpr(Sum, Bound[K].Upper[Bound[K].Direction]);
else
Sum = nullptr;
}
return Sum;
}
//===----------------------------------------------------------------------===//
// Constraint manipulation for Delta test.
// Given a linear SCEV,
// return the coefficient (the step)
// corresponding to the specified loop.
// If there isn't one, return 0.
// For example, given a*i + b*j + c*k, zeroing the coefficient
// corresponding to the j loop would yield b.
const SCEV *DependenceAnalysis::findCoefficient(const SCEV *Expr,
const Loop *TargetLoop) const {
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
if (!AddRec)
return SE->getConstant(Expr->getType(), 0);
if (AddRec->getLoop() == TargetLoop)
return AddRec->getStepRecurrence(*SE);
return findCoefficient(AddRec->getStart(), TargetLoop);
}
// Given a linear SCEV,
// return the SCEV given by zeroing out the coefficient
// corresponding to the specified loop.
// For example, given a*i + b*j + c*k, zeroing the coefficient
// corresponding to the j loop would yield a*i + c*k.
const SCEV *DependenceAnalysis::zeroCoefficient(const SCEV *Expr,
const Loop *TargetLoop) const {
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
if (!AddRec)
return Expr; // ignore
if (AddRec->getLoop() == TargetLoop)
return AddRec->getStart();
return SE->getAddRecExpr(zeroCoefficient(AddRec->getStart(), TargetLoop),
AddRec->getStepRecurrence(*SE),
AddRec->getLoop(),
AddRec->getNoWrapFlags());
}
// Given a linear SCEV Expr,
// return the SCEV given by adding some Value to the
// coefficient corresponding to the specified TargetLoop.
// For example, given a*i + b*j + c*k, adding 1 to the coefficient
// corresponding to the j loop would yield a*i + (b+1)*j + c*k.
const SCEV *DependenceAnalysis::addToCoefficient(const SCEV *Expr,
const Loop *TargetLoop,
const SCEV *Value) const {
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Expr);
if (!AddRec) // create a new addRec
return SE->getAddRecExpr(Expr,
Value,
TargetLoop,
SCEV::FlagAnyWrap); // Worst case, with no info.
if (AddRec->getLoop() == TargetLoop) {
const SCEV *Sum = SE->getAddExpr(AddRec->getStepRecurrence(*SE), Value);
if (Sum->isZero())
return AddRec->getStart();
return SE->getAddRecExpr(AddRec->getStart(),
Sum,
AddRec->getLoop(),
AddRec->getNoWrapFlags());
}
if (SE->isLoopInvariant(AddRec, TargetLoop))
return SE->getAddRecExpr(AddRec, Value, TargetLoop, SCEV::FlagAnyWrap);
return SE->getAddRecExpr(
addToCoefficient(AddRec->getStart(), TargetLoop, Value),
AddRec->getStepRecurrence(*SE), AddRec->getLoop(),
AddRec->getNoWrapFlags());
}
// Review the constraints, looking for opportunities
// to simplify a subscript pair (Src and Dst).
// Return true if some simplification occurs.
// If the simplification isn't exact (that is, if it is conservative
// in terms of dependence), set consistent to false.
// Corresponds to Figure 5 from the paper
//
// Practical Dependence Testing
// Goff, Kennedy, Tseng
// PLDI 1991
bool DependenceAnalysis::propagate(const SCEV *&Src,
const SCEV *&Dst,
SmallBitVector &Loops,
SmallVectorImpl<Constraint> &Constraints,
bool &Consistent) {
bool Result = false;
for (int LI = Loops.find_first(); LI >= 0; LI = Loops.find_next(LI)) {
DEBUG(dbgs() << "\t Constraint[" << LI << "] is");
DEBUG(Constraints[LI].dump(dbgs()));
if (Constraints[LI].isDistance())
Result |= propagateDistance(Src, Dst, Constraints[LI], Consistent);
else if (Constraints[LI].isLine())
Result |= propagateLine(Src, Dst, Constraints[LI], Consistent);
else if (Constraints[LI].isPoint())
Result |= propagatePoint(Src, Dst, Constraints[LI]);
}
return Result;
}
// Attempt to propagate a distance
// constraint into a subscript pair (Src and Dst).
// Return true if some simplification occurs.
// If the simplification isn't exact (that is, if it is conservative
// in terms of dependence), set consistent to false.
bool DependenceAnalysis::propagateDistance(const SCEV *&Src,
const SCEV *&Dst,
Constraint &CurConstraint,
bool &Consistent) {
const Loop *CurLoop = CurConstraint.getAssociatedLoop();
DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
const SCEV *A_K = findCoefficient(Src, CurLoop);
if (A_K->isZero())
return false;
const SCEV *DA_K = SE->getMulExpr(A_K, CurConstraint.getD());
Src = SE->getMinusSCEV(Src, DA_K);
Src = zeroCoefficient(Src, CurLoop);
DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
Dst = addToCoefficient(Dst, CurLoop, SE->getNegativeSCEV(A_K));
DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
if (!findCoefficient(Dst, CurLoop)->isZero())
Consistent = false;
return true;
}
// Attempt to propagate a line
// constraint into a subscript pair (Src and Dst).
// Return true if some simplification occurs.
// If the simplification isn't exact (that is, if it is conservative
// in terms of dependence), set consistent to false.
bool DependenceAnalysis::propagateLine(const SCEV *&Src,
const SCEV *&Dst,
Constraint &CurConstraint,
bool &Consistent) {
const Loop *CurLoop = CurConstraint.getAssociatedLoop();
const SCEV *A = CurConstraint.getA();
const SCEV *B = CurConstraint.getB();
const SCEV *C = CurConstraint.getC();
DEBUG(dbgs() << "\t\tA = " << *A << ", B = " << *B << ", C = " << *C << "\n");
DEBUG(dbgs() << "\t\tSrc = " << *Src << "\n");
DEBUG(dbgs() << "\t\tDst = " << *Dst << "\n");
if (A->isZero()) {
const SCEVConstant *Bconst = dyn_cast<SCEVConstant>(B);
const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
if (!Bconst || !Cconst) return false;
APInt Beta = Bconst->getValue()->getValue();
APInt Charlie = Cconst->getValue()->getValue();
APInt CdivB = Charlie.sdiv(Beta);
assert(Charlie.srem(Beta) == 0 && "C should be evenly divisible by B");
const SCEV *AP_K = findCoefficient(Dst, CurLoop);
// Src = SE->getAddExpr(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
Src = SE->getMinusSCEV(Src, SE->getMulExpr(AP_K, SE->getConstant(CdivB)));
Dst = zeroCoefficient(Dst, CurLoop);
if (!findCoefficient(Src, CurLoop)->isZero())
Consistent = false;
}
else if (B->isZero()) {
const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
if (!Aconst || !Cconst) return false;
APInt Alpha = Aconst->getValue()->getValue();
APInt Charlie = Cconst->getValue()->getValue();
APInt CdivA = Charlie.sdiv(Alpha);
assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
const SCEV *A_K = findCoefficient(Src, CurLoop);
Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
Src = zeroCoefficient(Src, CurLoop);
if (!findCoefficient(Dst, CurLoop)->isZero())
Consistent = false;
}
else if (isKnownPredicate(CmpInst::ICMP_EQ, A, B)) {
const SCEVConstant *Aconst = dyn_cast<SCEVConstant>(A);
const SCEVConstant *Cconst = dyn_cast<SCEVConstant>(C);
if (!Aconst || !Cconst) return false;
APInt Alpha = Aconst->getValue()->getValue();
APInt Charlie = Cconst->getValue()->getValue();
APInt CdivA = Charlie.sdiv(Alpha);
assert(Charlie.srem(Alpha) == 0 && "C should be evenly divisible by A");
const SCEV *A_K = findCoefficient(Src, CurLoop);
Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, SE->getConstant(CdivA)));
Src = zeroCoefficient(Src, CurLoop);
Dst = addToCoefficient(Dst, CurLoop, A_K);
if (!findCoefficient(Dst, CurLoop)->isZero())
Consistent = false;
}
else {
// paper is incorrect here, or perhaps just misleading
const SCEV *A_K = findCoefficient(Src, CurLoop);
Src = SE->getMulExpr(Src, A);
Dst = SE->getMulExpr(Dst, A);
Src = SE->getAddExpr(Src, SE->getMulExpr(A_K, C));
Src = zeroCoefficient(Src, CurLoop);
Dst = addToCoefficient(Dst, CurLoop, SE->getMulExpr(A_K, B));
if (!findCoefficient(Dst, CurLoop)->isZero())
Consistent = false;
}
DEBUG(dbgs() << "\t\tnew Src = " << *Src << "\n");
DEBUG(dbgs() << "\t\tnew Dst = " << *Dst << "\n");
return true;
}
// Attempt to propagate a point
// constraint into a subscript pair (Src and Dst).
// Return true if some simplification occurs.
bool DependenceAnalysis::propagatePoint(const SCEV *&Src,
const SCEV *&Dst,
Constraint &CurConstraint) {
const Loop *CurLoop = CurConstraint.getAssociatedLoop();
const SCEV *A_K = findCoefficient(Src, CurLoop);
const SCEV *AP_K = findCoefficient(Dst, CurLoop);
const SCEV *XA_K = SE->getMulExpr(A_K, CurConstraint.getX());
const SCEV *YAP_K = SE->getMulExpr(AP_K, CurConstraint.getY());
DEBUG(dbgs() << "\t\tSrc is " << *Src << "\n");
Src = SE->getAddExpr(Src, SE->getMinusSCEV(XA_K, YAP_K));
Src = zeroCoefficient(Src, CurLoop);
DEBUG(dbgs() << "\t\tnew Src is " << *Src << "\n");
DEBUG(dbgs() << "\t\tDst is " << *Dst << "\n");
Dst = zeroCoefficient(Dst, CurLoop);
DEBUG(dbgs() << "\t\tnew Dst is " << *Dst << "\n");
return true;
}
// Update direction vector entry based on the current constraint.
void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
const Constraint &CurConstraint
) const {
DEBUG(dbgs() << "\tUpdate direction, constraint =");
DEBUG(CurConstraint.dump(dbgs()));
if (CurConstraint.isAny())
; // use defaults
else if (CurConstraint.isDistance()) {
// this one is consistent, the others aren't
Level.Scalar = false;
Level.Distance = CurConstraint.getD();
unsigned NewDirection = Dependence::DVEntry::NONE;
if (!SE->isKnownNonZero(Level.Distance)) // if may be zero
NewDirection = Dependence::DVEntry::EQ;
if (!SE->isKnownNonPositive(Level.Distance)) // if may be positive
NewDirection |= Dependence::DVEntry::LT;
if (!SE->isKnownNonNegative(Level.Distance)) // if may be negative
NewDirection |= Dependence::DVEntry::GT;
Level.Direction &= NewDirection;
}
else if (CurConstraint.isLine()) {
Level.Scalar = false;
Level.Distance = nullptr;
// direction should be accurate
}
else if (CurConstraint.isPoint()) {
Level.Scalar = false;
Level.Distance = nullptr;
unsigned NewDirection = Dependence::DVEntry::NONE;
if (!isKnownPredicate(CmpInst::ICMP_NE,
CurConstraint.getY(),
CurConstraint.getX()))
// if X may be = Y
NewDirection |= Dependence::DVEntry::EQ;
if (!isKnownPredicate(CmpInst::ICMP_SLE,
CurConstraint.getY(),
CurConstraint.getX()))
// if Y may be > X
NewDirection |= Dependence::DVEntry::LT;
if (!isKnownPredicate(CmpInst::ICMP_SGE,
CurConstraint.getY(),
CurConstraint.getX()))
// if Y may be < X
NewDirection |= Dependence::DVEntry::GT;
Level.Direction &= NewDirection;
}
else
llvm_unreachable("constraint has unexpected kind");
}
/// Check if we can delinearize the subscripts. If the SCEVs representing the
/// source and destination array references are recurrences on a nested loop,
/// this function flattens the nested recurrences into separate recurrences
/// for each loop level.
bool DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV,
const SCEV *DstSCEV,
SmallVectorImpl<Subscript> &Pair,
const SCEV *ElementSize) {
const SCEVUnknown *SrcBase =
dyn_cast<SCEVUnknown>(SE->getPointerBase(SrcSCEV));
const SCEVUnknown *DstBase =
dyn_cast<SCEVUnknown>(SE->getPointerBase(DstSCEV));
if (!SrcBase || !DstBase || SrcBase != DstBase)
return false;
SrcSCEV = SE->getMinusSCEV(SrcSCEV, SrcBase);
DstSCEV = SE->getMinusSCEV(DstSCEV, DstBase);
const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
return false;
// First step: collect parametric terms in both array references.
SmallVector<const SCEV *, 4> Terms;
SrcAR->collectParametricTerms(*SE, Terms);
DstAR->collectParametricTerms(*SE, Terms);
// Second step: find subscript sizes.
SmallVector<const SCEV *, 4> Sizes;
SE->findArrayDimensions(Terms, Sizes, ElementSize);
// Third step: compute the access functions for each subscript.
SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts;
SrcAR->computeAccessFunctions(*SE, SrcSubscripts, Sizes);
DstAR->computeAccessFunctions(*SE, DstSubscripts, Sizes);
// Fail when there is only a subscript: that's a linearized access function.
if (SrcSubscripts.size() < 2 || DstSubscripts.size() < 2 ||
SrcSubscripts.size() != DstSubscripts.size())
return false;
int size = SrcSubscripts.size();
DEBUG({
dbgs() << "\nSrcSubscripts: ";
for (int i = 0; i < size; i++)
dbgs() << *SrcSubscripts[i];
dbgs() << "\nDstSubscripts: ";
for (int i = 0; i < size; i++)
dbgs() << *DstSubscripts[i];
});
// The delinearization transforms a single-subscript MIV dependence test into
// a multi-subscript SIV dependence test that is easier to compute. So we
// resize Pair to contain as many pairs of subscripts as the delinearization
// has found, and then initialize the pairs following the delinearization.
Pair.resize(size);
for (int i = 0; i < size; ++i) {
Pair[i].Src = SrcSubscripts[i];
Pair[i].Dst = DstSubscripts[i];
unifySubscriptType(&Pair[i]);
// FIXME: we should record the bounds SrcSizes[i] and DstSizes[i] that the
// delinearization has found, and add these constraints to the dependence
// check to avoid memory accesses overflow from one dimension into another.
// This is related to the problem of determining the existence of data
// dependences in array accesses using a different number of subscripts: in
// C one can access an array A[100][100]; as A[0][9999], *A[9999], etc.
}
return true;
}
//===----------------------------------------------------------------------===//
#ifndef NDEBUG
// For debugging purposes, dump a small bit vector to dbgs().
static void dumpSmallBitVector(SmallBitVector &BV) {
dbgs() << "{";
for (int VI = BV.find_first(); VI >= 0; VI = BV.find_next(VI)) {
dbgs() << VI;
if (BV.find_next(VI) >= 0)
dbgs() << ' ';
}
dbgs() << "}\n";
}
#endif
// depends -
// Returns NULL if there is no dependence.
// Otherwise, return a Dependence with as many details as possible.
// Corresponds to Section 3.1 in the paper
//
// Practical Dependence Testing
// Goff, Kennedy, Tseng
// PLDI 1991
//
// Care is required to keep the routine below, getSplitIteration(),
// up to date with respect to this routine.
std::unique_ptr<Dependence>
DependenceAnalysis::depends(Instruction *Src, Instruction *Dst,
bool PossiblyLoopIndependent) {
if (Src == Dst)
PossiblyLoopIndependent = false;
if ((!Src->mayReadFromMemory() && !Src->mayWriteToMemory()) ||
(!Dst->mayReadFromMemory() && !Dst->mayWriteToMemory()))
// if both instructions don't reference memory, there's no dependence
return nullptr;
if (!isLoadOrStore(Src) || !isLoadOrStore(Dst)) {
// can only analyze simple loads and stores, i.e., no calls, invokes, etc.
DEBUG(dbgs() << "can only handle simple loads and stores\n");
return make_unique<Dependence>(Src, Dst);
}
Value *SrcPtr = getPointerOperand(Src);
Value *DstPtr = getPointerOperand(Dst);
switch (underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
SrcPtr)) {
case AliasAnalysis::MayAlias:
case AliasAnalysis::PartialAlias:
// cannot analyse objects if we don't understand their aliasing.
DEBUG(dbgs() << "can't analyze may or partial alias\n");
return make_unique<Dependence>(Src, Dst);
case AliasAnalysis::NoAlias:
// If the objects noalias, they are distinct, accesses are independent.
DEBUG(dbgs() << "no alias\n");
return nullptr;
case AliasAnalysis::MustAlias:
break; // The underlying objects alias; test accesses for dependence.
}
// establish loop nesting levels
establishNestingLevels(Src, Dst);
DEBUG(dbgs() << " common nesting levels = " << CommonLevels << "\n");
DEBUG(dbgs() << " maximum nesting levels = " << MaxLevels << "\n");
FullDependence Result(Src, Dst, PossiblyLoopIndependent, CommonLevels);
++TotalArrayPairs;
// See if there are GEPs we can use.
bool UsefulGEP = false;
GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
if (SrcGEP && DstGEP &&
SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
DEBUG(dbgs() << " SrcPtrSCEV = " << *SrcPtrSCEV << "\n");
DEBUG(dbgs() << " DstPtrSCEV = " << *DstPtrSCEV << "\n");
UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
(SrcGEP->getNumOperands() == DstGEP->getNumOperands());
}
unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
SmallVector<Subscript, 4> Pair(Pairs);
if (UsefulGEP) {
DEBUG(dbgs() << " using GEPs\n");
unsigned P = 0;
for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
SrcEnd = SrcGEP->idx_end(),
DstIdx = DstGEP->idx_begin();
SrcIdx != SrcEnd;
++SrcIdx, ++DstIdx, ++P) {
Pair[P].Src = SE->getSCEV(*SrcIdx);
Pair[P].Dst = SE->getSCEV(*DstIdx);
unifySubscriptType(&Pair[P]);
}
}
else {
DEBUG(dbgs() << " ignoring GEPs\n");
const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
const SCEV *DstSCEV = SE->getSCEV(DstPtr);
DEBUG(dbgs() << " SrcSCEV = " << *SrcSCEV << "\n");
DEBUG(dbgs() << " DstSCEV = " << *DstSCEV << "\n");
Pair[0].Src = SrcSCEV;
Pair[0].Dst = DstSCEV;
}
if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
DEBUG(dbgs() << " delinerized GEP\n");
Pairs = Pair.size();
}
for (unsigned P = 0; P < Pairs; ++P) {
Pair[P].Loops.resize(MaxLevels + 1);
Pair[P].GroupLoops.resize(MaxLevels + 1);
Pair[P].Group.resize(Pairs);
removeMatchingExtensions(&Pair[P]);
Pair[P].Classification =
classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
Pair[P].Loops);
Pair[P].GroupLoops = Pair[P].Loops;
Pair[P].Group.set(P);
DEBUG(dbgs() << " subscript " << P << "\n");
DEBUG(dbgs() << "\tsrc = " << *Pair[P].Src << "\n");
DEBUG(dbgs() << "\tdst = " << *Pair[P].Dst << "\n");
DEBUG(dbgs() << "\tclass = " << Pair[P].Classification << "\n");
DEBUG(dbgs() << "\tloops = ");
DEBUG(dumpSmallBitVector(Pair[P].Loops));
}
SmallBitVector Separable(Pairs);
SmallBitVector Coupled(Pairs);
// Partition subscripts into separable and minimally-coupled groups
// Algorithm in paper is algorithmically better;
// this may be faster in practice. Check someday.
//
// Here's an example of how it works. Consider this code:
//
// for (i = ...) {
// for (j = ...) {
// for (k = ...) {
// for (l = ...) {
// for (m = ...) {
// A[i][j][k][m] = ...;
// ... = A[0][j][l][i + j];
// }
// }
// }
// }
// }
//
// There are 4 subscripts here:
// 0 [i] and [0]
// 1 [j] and [j]
// 2 [k] and [l]
// 3 [m] and [i + j]
//
// We've already classified each subscript pair as ZIV, SIV, etc.,
// and collected all the loops mentioned by pair P in Pair[P].Loops.
// In addition, we've initialized Pair[P].GroupLoops to Pair[P].Loops
// and set Pair[P].Group = {P}.
//
// Src Dst Classification Loops GroupLoops Group
// 0 [i] [0] SIV {1} {1} {0}
// 1 [j] [j] SIV {2} {2} {1}
// 2 [k] [l] RDIV {3,4} {3,4} {2}
// 3 [m] [i + j] MIV {1,2,5} {1,2,5} {3}
//
// For each subscript SI 0 .. 3, we consider each remaining subscript, SJ.
// So, 0 is compared against 1, 2, and 3; 1 is compared against 2 and 3, etc.
//
// We begin by comparing 0 and 1. The intersection of the GroupLoops is empty.
// Next, 0 and 2. Again, the intersection of their GroupLoops is empty.
// Next 0 and 3. The intersection of their GroupLoop = {1}, not empty,
// so Pair[3].Group = {0,3} and Done = false (that is, 0 will not be added
// to either Separable or Coupled).
//
// Next, we consider 1 and 2. The intersection of the GroupLoops is empty.
// Next, 1 and 3. The intersectionof their GroupLoops = {2}, not empty,
// so Pair[3].Group = {0, 1, 3} and Done = false.
//
// Next, we compare 2 against 3. The intersection of the GroupLoops is empty.
// Since Done remains true, we add 2 to the set of Separable pairs.
//
// Finally, we consider 3. There's nothing to compare it with,
// so Done remains true and we add it to the Coupled set.
// Pair[3].Group = {0, 1, 3} and GroupLoops = {1, 2, 5}.
//
// In the end, we've got 1 separable subscript and 1 coupled group.
for (unsigned SI = 0; SI < Pairs; ++SI) {
if (Pair[SI].Classification == Subscript::NonLinear) {
// ignore these, but collect loops for later
++NonlinearSubscriptPairs;
collectCommonLoops(Pair[SI].Src,
LI->getLoopFor(Src->getParent()),
Pair[SI].Loops);
collectCommonLoops(Pair[SI].Dst,
LI->getLoopFor(Dst->getParent()),
Pair[SI].Loops);
Result.Consistent = false;
} else if (Pair[SI].Classification == Subscript::ZIV) {
// always separable
Separable.set(SI);
}
else {
// SIV, RDIV, or MIV, so check for coupled group
bool Done = true;
for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
SmallBitVector Intersection = Pair[SI].GroupLoops;
Intersection &= Pair[SJ].GroupLoops;
if (Intersection.any()) {
// accumulate set of all the loops in group
Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
// accumulate set of all subscripts in group
Pair[SJ].Group |= Pair[SI].Group;
Done = false;
}
}
if (Done) {
if (Pair[SI].Group.count() == 1) {
Separable.set(SI);
++SeparableSubscriptPairs;
}
else {
Coupled.set(SI);
++CoupledSubscriptPairs;
}
}
}
}
DEBUG(dbgs() << " Separable = ");
DEBUG(dumpSmallBitVector(Separable));
DEBUG(dbgs() << " Coupled = ");
DEBUG(dumpSmallBitVector(Coupled));
Constraint NewConstraint;
NewConstraint.setAny(SE);
// test separable subscripts
for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
DEBUG(dbgs() << "testing subscript " << SI);
switch (Pair[SI].Classification) {
case Subscript::ZIV:
DEBUG(dbgs() << ", ZIV\n");
if (testZIV(Pair[SI].Src, Pair[SI].Dst, Result))
return nullptr;
break;
case Subscript::SIV: {
DEBUG(dbgs() << ", SIV\n");
unsigned Level;
const SCEV *SplitIter = nullptr;
if (testSIV(Pair[SI].Src, Pair[SI].Dst, Level, Result, NewConstraint,
SplitIter))
return nullptr;
break;
}
case Subscript::RDIV:
DEBUG(dbgs() << ", RDIV\n");
if (testRDIV(Pair[SI].Src, Pair[SI].Dst, Result))
return nullptr;
break;
case Subscript::MIV:
DEBUG(dbgs() << ", MIV\n");
if (testMIV(Pair[SI].Src, Pair[SI].Dst, Pair[SI].Loops, Result))
return nullptr;
break;
default:
llvm_unreachable("subscript has unexpected classification");
}
}
if (Coupled.count()) {
// test coupled subscript groups
DEBUG(dbgs() << "starting on coupled subscripts\n");
DEBUG(dbgs() << "MaxLevels + 1 = " << MaxLevels + 1 << "\n");
SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
for (unsigned II = 0; II <= MaxLevels; ++II)
Constraints[II].setAny(SE);
for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
DEBUG(dbgs() << "testing subscript group " << SI << " { ");
SmallBitVector Group(Pair[SI].Group);
SmallBitVector Sivs(Pairs);
SmallBitVector Mivs(Pairs);
SmallBitVector ConstrainedLevels(MaxLevels + 1);
for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
DEBUG(dbgs() << SJ << " ");
if (Pair[SJ].Classification == Subscript::SIV)
Sivs.set(SJ);
else
Mivs.set(SJ);
}
DEBUG(dbgs() << "}\n");
while (Sivs.any()) {
bool Changed = false;
for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
DEBUG(dbgs() << "testing subscript " << SJ << ", SIV\n");
// SJ is an SIV subscript that's part of the current coupled group
unsigned Level;
const SCEV *SplitIter = nullptr;
DEBUG(dbgs() << "SIV\n");
if (testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level, Result, NewConstraint,
SplitIter))
return nullptr;
ConstrainedLevels.set(Level);
if (intersectConstraints(&Constraints[Level], &NewConstraint)) {
if (Constraints[Level].isEmpty()) {
++DeltaIndependence;
return nullptr;
}
Changed = true;
}
Sivs.reset(SJ);
}
if (Changed) {
// propagate, possibly creating new SIVs and ZIVs
DEBUG(dbgs() << " propagating\n");
DEBUG(dbgs() << "\tMivs = ");
DEBUG(dumpSmallBitVector(Mivs));
for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
// SJ is an MIV subscript that's part of the current coupled group
DEBUG(dbgs() << "\tSJ = " << SJ << "\n");
if (propagate(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops,
Constraints, Result.Consistent)) {
DEBUG(dbgs() << "\t Changed\n");
++DeltaPropagations;
Pair[SJ].Classification =
classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
Pair[SJ].Loops);
switch (Pair[SJ].Classification) {
case Subscript::ZIV:
DEBUG(dbgs() << "ZIV\n");
if (testZIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
return nullptr;
Mivs.reset(SJ);
break;
case Subscript::SIV:
Sivs.set(SJ);
Mivs.reset(SJ);
break;
case Subscript::RDIV:
case Subscript::MIV:
break;
default:
llvm_unreachable("bad subscript classification");
}
}
}
}
}
// test & propagate remaining RDIVs
for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
if (Pair[SJ].Classification == Subscript::RDIV) {
DEBUG(dbgs() << "RDIV test\n");
if (testRDIV(Pair[SJ].Src, Pair[SJ].Dst, Result))
return nullptr;
// I don't yet understand how to propagate RDIV results
Mivs.reset(SJ);
}
}
// test remaining MIVs
// This code is temporary.
// Better to somehow test all remaining subscripts simultaneously.
for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
if (Pair[SJ].Classification == Subscript::MIV) {
DEBUG(dbgs() << "MIV test\n");
if (testMIV(Pair[SJ].Src, Pair[SJ].Dst, Pair[SJ].Loops, Result))
return nullptr;
}
else
llvm_unreachable("expected only MIV subscripts at this point");
}
// update Result.DV from constraint vector
DEBUG(dbgs() << " updating\n");
for (int SJ = ConstrainedLevels.find_first(); SJ >= 0;
SJ = ConstrainedLevels.find_next(SJ)) {
if (SJ > (int)CommonLevels)
break;
updateDirection(Result.DV[SJ - 1], Constraints[SJ]);
if (Result.DV[SJ - 1].Direction == Dependence::DVEntry::NONE)
return nullptr;
}
}
}
// Make sure the Scalar flags are set correctly.
SmallBitVector CompleteLoops(MaxLevels + 1);
for (unsigned SI = 0; SI < Pairs; ++SI)
CompleteLoops |= Pair[SI].Loops;
for (unsigned II = 1; II <= CommonLevels; ++II)
if (CompleteLoops[II])
Result.DV[II - 1].Scalar = false;
if (PossiblyLoopIndependent) {
// Make sure the LoopIndependent flag is set correctly.
// All directions must include equal, otherwise no
// loop-independent dependence is possible.
for (unsigned II = 1; II <= CommonLevels; ++II) {
if (!(Result.getDirection(II) & Dependence::DVEntry::EQ)) {
Result.LoopIndependent = false;
break;
}
}
}
else {
// On the other hand, if all directions are equal and there's no
// loop-independent dependence possible, then no dependence exists.
bool AllEqual = true;
for (unsigned II = 1; II <= CommonLevels; ++II) {
if (Result.getDirection(II) != Dependence::DVEntry::EQ) {
AllEqual = false;
break;
}
}
if (AllEqual)
return nullptr;
}
auto Final = make_unique<FullDependence>(Result);
Result.DV = nullptr;
return std::move(Final);
}
//===----------------------------------------------------------------------===//
// getSplitIteration -
// Rather than spend rarely-used space recording the splitting iteration
// during the Weak-Crossing SIV test, we re-compute it on demand.
// The re-computation is basically a repeat of the entire dependence test,
// though simplified since we know that the dependence exists.
// It's tedious, since we must go through all propagations, etc.
//
// Care is required to keep this code up to date with respect to the routine
// above, depends().
//
// Generally, the dependence analyzer will be used to build
// a dependence graph for a function (basically a map from instructions
// to dependences). Looking for cycles in the graph shows us loops
// that cannot be trivially vectorized/parallelized.
//
// We can try to improve the situation by examining all the dependences
// that make up the cycle, looking for ones we can break.
// Sometimes, peeling the first or last iteration of a loop will break
// dependences, and we've got flags for those possibilities.
// Sometimes, splitting a loop at some other iteration will do the trick,
// and we've got a flag for that case. Rather than waste the space to
// record the exact iteration (since we rarely know), we provide
// a method that calculates the iteration. It's a drag that it must work
// from scratch, but wonderful in that it's possible.
//
// Here's an example:
//
// for (i = 0; i < 10; i++)
// A[i] = ...
// ... = A[11 - i]
//
// There's a loop-carried flow dependence from the store to the load,
// found by the weak-crossing SIV test. The dependence will have a flag,
// indicating that the dependence can be broken by splitting the loop.
// Calling getSplitIteration will return 5.
// Splitting the loop breaks the dependence, like so:
//
// for (i = 0; i <= 5; i++)
// A[i] = ...
// ... = A[11 - i]
// for (i = 6; i < 10; i++)
// A[i] = ...
// ... = A[11 - i]
//
// breaks the dependence and allows us to vectorize/parallelize
// both loops.
const SCEV *DependenceAnalysis::getSplitIteration(const Dependence &Dep,
unsigned SplitLevel) {
assert(Dep.isSplitable(SplitLevel) &&
"Dep should be splitable at SplitLevel");
Instruction *Src = Dep.getSrc();
Instruction *Dst = Dep.getDst();
assert(Src->mayReadFromMemory() || Src->mayWriteToMemory());
assert(Dst->mayReadFromMemory() || Dst->mayWriteToMemory());
assert(isLoadOrStore(Src));
assert(isLoadOrStore(Dst));
Value *SrcPtr = getPointerOperand(Src);
Value *DstPtr = getPointerOperand(Dst);
assert(underlyingObjectsAlias(AA, F->getParent()->getDataLayout(), DstPtr,
SrcPtr) == AliasAnalysis::MustAlias);
// establish loop nesting levels
establishNestingLevels(Src, Dst);
FullDependence Result(Src, Dst, false, CommonLevels);
// See if there are GEPs we can use.
bool UsefulGEP = false;
GEPOperator *SrcGEP = dyn_cast<GEPOperator>(SrcPtr);
GEPOperator *DstGEP = dyn_cast<GEPOperator>(DstPtr);
if (SrcGEP && DstGEP &&
SrcGEP->getPointerOperandType() == DstGEP->getPointerOperandType()) {
const SCEV *SrcPtrSCEV = SE->getSCEV(SrcGEP->getPointerOperand());
const SCEV *DstPtrSCEV = SE->getSCEV(DstGEP->getPointerOperand());
UsefulGEP = isLoopInvariant(SrcPtrSCEV, LI->getLoopFor(Src->getParent())) &&
isLoopInvariant(DstPtrSCEV, LI->getLoopFor(Dst->getParent())) &&
(SrcGEP->getNumOperands() == DstGEP->getNumOperands());
}
unsigned Pairs = UsefulGEP ? SrcGEP->idx_end() - SrcGEP->idx_begin() : 1;
SmallVector<Subscript, 4> Pair(Pairs);
if (UsefulGEP) {
unsigned P = 0;
for (GEPOperator::const_op_iterator SrcIdx = SrcGEP->idx_begin(),
SrcEnd = SrcGEP->idx_end(),
DstIdx = DstGEP->idx_begin();
SrcIdx != SrcEnd;
++SrcIdx, ++DstIdx, ++P) {
Pair[P].Src = SE->getSCEV(*SrcIdx);
Pair[P].Dst = SE->getSCEV(*DstIdx);
}
}
else {
const SCEV *SrcSCEV = SE->getSCEV(SrcPtr);
const SCEV *DstSCEV = SE->getSCEV(DstPtr);
Pair[0].Src = SrcSCEV;
Pair[0].Dst = DstSCEV;
}
if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
DEBUG(dbgs() << " delinerized GEP\n");
Pairs = Pair.size();
}
for (unsigned P = 0; P < Pairs; ++P) {
Pair[P].Loops.resize(MaxLevels + 1);
Pair[P].GroupLoops.resize(MaxLevels + 1);
Pair[P].Group.resize(Pairs);
removeMatchingExtensions(&Pair[P]);
Pair[P].Classification =
classifyPair(Pair[P].Src, LI->getLoopFor(Src->getParent()),
Pair[P].Dst, LI->getLoopFor(Dst->getParent()),
Pair[P].Loops);
Pair[P].GroupLoops = Pair[P].Loops;
Pair[P].Group.set(P);
}
SmallBitVector Separable(Pairs);
SmallBitVector Coupled(Pairs);
// partition subscripts into separable and minimally-coupled groups
for (unsigned SI = 0; SI < Pairs; ++SI) {
if (Pair[SI].Classification == Subscript::NonLinear) {
// ignore these, but collect loops for later
collectCommonLoops(Pair[SI].Src,
LI->getLoopFor(Src->getParent()),
Pair[SI].Loops);
collectCommonLoops(Pair[SI].Dst,
LI->getLoopFor(Dst->getParent()),
Pair[SI].Loops);
Result.Consistent = false;
}
else if (Pair[SI].Classification == Subscript::ZIV)
Separable.set(SI);
else {
// SIV, RDIV, or MIV, so check for coupled group
bool Done = true;
for (unsigned SJ = SI + 1; SJ < Pairs; ++SJ) {
SmallBitVector Intersection = Pair[SI].GroupLoops;
Intersection &= Pair[SJ].GroupLoops;
if (Intersection.any()) {
// accumulate set of all the loops in group
Pair[SJ].GroupLoops |= Pair[SI].GroupLoops;
// accumulate set of all subscripts in group
Pair[SJ].Group |= Pair[SI].Group;
Done = false;
}
}
if (Done) {
if (Pair[SI].Group.count() == 1)
Separable.set(SI);
else
Coupled.set(SI);
}
}
}
Constraint NewConstraint;
NewConstraint.setAny(SE);
// test separable subscripts
for (int SI = Separable.find_first(); SI >= 0; SI = Separable.find_next(SI)) {
switch (Pair[SI].Classification) {
case Subscript::SIV: {
unsigned Level;
const SCEV *SplitIter = nullptr;
(void) testSIV(Pair[SI].Src, Pair[SI].Dst, Level,
Result, NewConstraint, SplitIter);
if (Level == SplitLevel) {
assert(SplitIter != nullptr);
return SplitIter;
}
break;
}
case Subscript::ZIV:
case Subscript::RDIV:
case Subscript::MIV:
break;
default:
llvm_unreachable("subscript has unexpected classification");
}
}
if (Coupled.count()) {
// test coupled subscript groups
SmallVector<Constraint, 4> Constraints(MaxLevels + 1);
for (unsigned II = 0; II <= MaxLevels; ++II)
Constraints[II].setAny(SE);
for (int SI = Coupled.find_first(); SI >= 0; SI = Coupled.find_next(SI)) {
SmallBitVector Group(Pair[SI].Group);
SmallBitVector Sivs(Pairs);
SmallBitVector Mivs(Pairs);
SmallBitVector ConstrainedLevels(MaxLevels + 1);
for (int SJ = Group.find_first(); SJ >= 0; SJ = Group.find_next(SJ)) {
if (Pair[SJ].Classification == Subscript::SIV)
Sivs.set(SJ);
else
Mivs.set(SJ);
}
while (Sivs.any()) {
bool Changed = false;
for (int SJ = Sivs.find_first(); SJ >= 0; SJ = Sivs.find_next(SJ)) {
// SJ is an SIV subscript that's part of the current coupled group
unsigned Level;
const SCEV *SplitIter = nullptr;
(void) testSIV(Pair[SJ].Src, Pair[SJ].Dst, Level,
Result, NewConstraint, SplitIter);
if (Level == SplitLevel && SplitIter)
return SplitIter;
ConstrainedLevels.set(Level);
if (intersectConstraints(&Constraints[Level], &NewConstraint))
Changed = true;
Sivs.reset(SJ);
}
if (Changed) {
// propagate, possibly creating new SIVs and ZIVs
for (int SJ = Mivs.find_first(); SJ >= 0; SJ = Mivs.find_next(SJ)) {
// SJ is an MIV subscript that's part of the current coupled group
if (propagate(Pair[SJ].Src, Pair[SJ].Dst,
Pair[SJ].Loops, Constraints, Result.Consistent)) {
Pair[SJ].Classification =
classifyPair(Pair[SJ].Src, LI->getLoopFor(Src->getParent()),
Pair[SJ].Dst, LI->getLoopFor(Dst->getParent()),
Pair[SJ].Loops);
switch (Pair[SJ].Classification) {
case Subscript::ZIV:
Mivs.reset(SJ);
break;
case Subscript::SIV:
Sivs.set(SJ);
Mivs.reset(SJ);
break;
case Subscript::RDIV:
case Subscript::MIV:
break;
default:
llvm_unreachable("bad subscript classification");
}
}
}
}
}
}
}
llvm_unreachable("somehow reached end of routine");
return nullptr;
}
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