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llvm-mirror/lib/Analysis/DependenceAnalysis.cpp
Jingyue Wu 230717d66d [DependenceAnalysis] Allow subscripts of different types 
Summary:
Several places in DependenceAnalysis assumes both SCEVs in a subscript pair
share the same integer type. For instance, isKnownPredicate calls
SE->getMinusSCEV(X, Y) which asserts X and Y share the same type. However,
DependenceAnalysis fails to ensure this assumption when producing a subscript
pair, causing tests such as NonCanonicalizedSubscript to crash. With this
patch, DependenceAnalysis runs unifySubscriptType before producing any
subscript pair, ensuring the assumption.

Test Plan:
Added NonCanonicalizedSubscript.ll on which DependenceAnalysis before the fix
crashed because subscripts have different types.

Reviewers: spop, sebpop, jingyue

Reviewed By: jingyue

Subscribers: eliben, meheff, llvm-commits

Differential Revision: http://reviews.llvm.org/D6289

llvm-svn: 222100
2014-11-16 16:52:44 +00:00

3951 lines
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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/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/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(LoopInfo)
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<LoopInfo>();
return false;
}
void DependenceAnalysis::releaseMemory() {
}
void DependenceAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<AliasAnalysis>();
AU.addRequiredTransitive<ScalarEvolution>();
AU.addRequiredTransitive<LoopInfo>();
}
// 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 Value *A,
const Value *B) {
const Value *AObj = GetUnderlyingObject(A);
const Value *BObj = GetUnderlyingObject(B);
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, 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()));
}
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)) {
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, 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()));
}
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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