+namespace {
+struct FindUndefs {
+ bool Found;
+ FindUndefs() : Found(false) {}
+
+ bool follow(const SCEV *S) {
+ if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
+ if (isa<UndefValue>(C->getValue()))
+ Found = true;
+ } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
+ if (isa<UndefValue>(C->getValue()))
+ Found = true;
+ }
+
+ // Keep looking if we haven't found it yet.
+ return !Found;
+ }
+ bool isDone() const {
+ // Stop recursion if we have found an undef.
+ return Found;
+ }
+};
+}
+
+// Return true when S contains at least an undef value.
+static inline bool
+containsUndefs(const SCEV *S) {
+ FindUndefs F;
+ SCEVTraversal<FindUndefs> ST(F);
+ ST.visitAll(S);
+
+ return F.Found;
+}
+
+namespace {
+// Collect all steps of SCEV expressions.
+struct SCEVCollectStrides {
+ ScalarEvolution &SE;
+ SmallVectorImpl<const SCEV *> &Strides;
+
+ SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
+ : SE(SE), Strides(S) {}
+
+ bool follow(const SCEV *S) {
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
+ Strides.push_back(AR->getStepRecurrence(SE));
+ return true;
+ }
+ bool isDone() const { return false; }
+};
+
+// Collect all SCEVUnknown and SCEVMulExpr expressions.
+struct SCEVCollectTerms {
+ SmallVectorImpl<const SCEV *> &Terms;
+
+ SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
+ : Terms(T) {}
+
+ bool follow(const SCEV *S) {
+ if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
+ if (!containsUndefs(S))
+ Terms.push_back(S);
+
+ // Stop recursion: once we collected a term, do not walk its operands.
+ return false;
+ }
+
+ // Keep looking.
+ return true;
+ }
+ bool isDone() const { return false; }
+};
+}
+
+/// Find parametric terms in this SCEVAddRecExpr.
+void SCEVAddRecExpr::collectParametricTerms(
+ ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
+ SmallVector<const SCEV *, 4> Strides;
+ SCEVCollectStrides StrideCollector(SE, Strides);
+ visitAll(this, StrideCollector);
+
+ DEBUG({
+ dbgs() << "Strides:\n";
+ for (const SCEV *S : Strides)
+ dbgs() << *S << "\n";
+ });
+
+ for (const SCEV *S : Strides) {
+ SCEVCollectTerms TermCollector(Terms);
+ visitAll(S, TermCollector);
+ }
+
+ DEBUG({
+ dbgs() << "Terms:\n";
+ for (const SCEV *T : Terms)
+ dbgs() << *T << "\n";
+ });
+}
+
+static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
+ APInt A = C1->getValue()->getValue();
+ APInt B = C2->getValue()->getValue();
+ uint32_t ABW = A.getBitWidth();
+ uint32_t BBW = B.getBitWidth();
+
+ if (ABW > BBW)
+ B = B.sext(ABW);
+ else if (ABW < BBW)
+ A = A.sext(BBW);
+
+ return APIntOps::srem(A, B);
+}
+
+static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
+ APInt A = C1->getValue()->getValue();
+ APInt B = C2->getValue()->getValue();
+ uint32_t ABW = A.getBitWidth();
+ uint32_t BBW = B.getBitWidth();
+
+ if (ABW > BBW)
+ B = B.sext(ABW);
+ else if (ABW < BBW)
+ A = A.sext(BBW);
+
+ return APIntOps::sdiv(A, B);
+}
+
+namespace {
+struct FindSCEVSize {
+ int Size;
+ FindSCEVSize() : Size(0) {}
+
+ bool follow(const SCEV *S) {
+ ++Size;
+ // Keep looking at all operands of S.
+ return true;
+ }
+ bool isDone() const {
+ return false;
+ }
+};
+}
+
+// Returns the size of the SCEV S.
+static inline int sizeOfSCEV(const SCEV *S) {
+ FindSCEVSize F;
+ SCEVTraversal<FindSCEVSize> ST(F);
+ ST.visitAll(S);
+ return F.Size;
+}
+
+namespace {
+
+struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
+public:
+ // Computes the Quotient and Remainder of the division of Numerator by
+ // Denominator.
+ static void divide(ScalarEvolution &SE, const SCEV *Numerator,
+ const SCEV *Denominator, const SCEV **Quotient,
+ const SCEV **Remainder) {
+ assert(Numerator && Denominator && "Uninitialized SCEV");
+
+ SCEVDivision D(SE, Numerator, Denominator);
+
+ // Check for the trivial case here to avoid having to check for it in the
+ // rest of the code.
+ if (Numerator == Denominator) {
+ *Quotient = D.One;
+ *Remainder = D.Zero;
+ return;
+ }
+
+ if (Numerator->isZero()) {
+ *Quotient = D.Zero;
+ *Remainder = D.Zero;
+ return;
+ }
+
+ // Split the Denominator when it is a product.
+ if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
+ const SCEV *Q, *R;
+ *Quotient = Numerator;
+ for (const SCEV *Op : T->operands()) {
+ divide(SE, *Quotient, Op, &Q, &R);
+ *Quotient = Q;
+
+ // Bail out when the Numerator is not divisible by one of the terms of
+ // the Denominator.
+ if (!R->isZero()) {
+ *Quotient = D.Zero;
+ *Remainder = Numerator;
+ return;
+ }
+ }
+ *Remainder = D.Zero;
+ return;
+ }
+
+ D.visit(Numerator);
+ *Quotient = D.Quotient;
+ *Remainder = D.Remainder;
+ }
+
+ SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator)
+ : SE(S), Denominator(Denominator) {
+ Zero = SE.getConstant(Denominator->getType(), 0);
+ One = SE.getConstant(Denominator->getType(), 1);
+
+ // By default, we don't know how to divide Expr by Denominator.
+ // Providing the default here simplifies the rest of the code.
+ Quotient = Zero;
+ Remainder = Numerator;
+ }
+
+ // Except in the trivial case described above, we do not know how to divide
+ // Expr by Denominator for the following functions with empty implementation.
+ void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
+ void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
+ void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
+ void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
+ void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
+ void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
+ void visitUnknown(const SCEVUnknown *Numerator) {}
+ void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
+
+ void visitConstant(const SCEVConstant *Numerator) {
+ if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
+ Quotient = SE.getConstant(sdiv(Numerator, D));
+ Remainder = SE.getConstant(srem(Numerator, D));
+ return;
+ }
+ }
+
+ void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
+ const SCEV *StartQ, *StartR, *StepQ, *StepR;
+ assert(Numerator->isAffine() && "Numerator should be affine");
+ divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
+ divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
+ Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
+ Numerator->getNoWrapFlags());
+ Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
+ Numerator->getNoWrapFlags());
+ }
+
+ void visitAddExpr(const SCEVAddExpr *Numerator) {
+ SmallVector<const SCEV *, 2> Qs, Rs;
+ Type *Ty = Denominator->getType();
+
+ for (const SCEV *Op : Numerator->operands()) {
+ const SCEV *Q, *R;
+ divide(SE, Op, Denominator, &Q, &R);
+
+ // Bail out if types do not match.
+ if (Ty != Q->getType() || Ty != R->getType()) {
+ Quotient = Zero;
+ Remainder = Numerator;
+ return;
+ }
+
+ Qs.push_back(Q);
+ Rs.push_back(R);
+ }
+
+ if (Qs.size() == 1) {
+ Quotient = Qs[0];
+ Remainder = Rs[0];
+ return;
+ }
+
+ Quotient = SE.getAddExpr(Qs);
+ Remainder = SE.getAddExpr(Rs);
+ }
+
+ void visitMulExpr(const SCEVMulExpr *Numerator) {
+ SmallVector<const SCEV *, 2> Qs;
+ Type *Ty = Denominator->getType();
+
+ bool FoundDenominatorTerm = false;
+ for (const SCEV *Op : Numerator->operands()) {
+ // Bail out if types do not match.
+ if (Ty != Op->getType()) {
+ Quotient = Zero;
+ Remainder = Numerator;
+ return;
+ }
+
+ if (FoundDenominatorTerm) {
+ Qs.push_back(Op);
+ continue;
+ }
+
+ // Check whether Denominator divides one of the product operands.
+ const SCEV *Q, *R;
+ divide(SE, Op, Denominator, &Q, &R);
+ if (!R->isZero()) {
+ Qs.push_back(Op);
+ continue;
+ }
+
+ // Bail out if types do not match.
+ if (Ty != Q->getType()) {
+ Quotient = Zero;
+ Remainder = Numerator;
+ return;
+ }
+
+ FoundDenominatorTerm = true;
+ Qs.push_back(Q);
+ }
+
+ if (FoundDenominatorTerm) {
+ Remainder = Zero;
+ if (Qs.size() == 1)
+ Quotient = Qs[0];
+ else
+ Quotient = SE.getMulExpr(Qs);
+ return;
+ }
+
+ if (!isa<SCEVUnknown>(Denominator)) {
+ Quotient = Zero;
+ Remainder = Numerator;
+ return;
+ }
+
+ // The Remainder is obtained by replacing Denominator by 0 in Numerator.
+ ValueToValueMap RewriteMap;
+ RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
+ cast<SCEVConstant>(Zero)->getValue();
+ Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
+
+ if (Remainder->isZero()) {
+ // The Quotient is obtained by replacing Denominator by 1 in Numerator.
+ RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
+ cast<SCEVConstant>(One)->getValue();
+ Quotient =
+ SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
+ return;
+ }
+
+ // Quotient is (Numerator - Remainder) divided by Denominator.
+ const SCEV *Q, *R;
+ const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
+ if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
+ // This SCEV does not seem to simplify: fail the division here.
+ Quotient = Zero;
+ Remainder = Numerator;
+ return;
+ }
+ divide(SE, Diff, Denominator, &Q, &R);
+ assert(R == Zero &&
+ "(Numerator - Remainder) should evenly divide Denominator");
+ Quotient = Q;
+ }
+
+private:
+ ScalarEvolution &SE;
+ const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
+};
+}
+
+static bool findArrayDimensionsRec(ScalarEvolution &SE,
+ SmallVectorImpl<const SCEV *> &Terms,
+ SmallVectorImpl<const SCEV *> &Sizes) {
+ int Last = Terms.size() - 1;
+ const SCEV *Step = Terms[Last];
+
+ // End of recursion.
+ if (Last == 0) {
+ if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
+ SmallVector<const SCEV *, 2> Qs;
+ for (const SCEV *Op : M->operands())
+ if (!isa<SCEVConstant>(Op))
+ Qs.push_back(Op);
+
+ Step = SE.getMulExpr(Qs);
+ }
+
+ Sizes.push_back(Step);
+ return true;
+ }
+
+ for (const SCEV *&Term : Terms) {
+ // Normalize the terms before the next call to findArrayDimensionsRec.
+ const SCEV *Q, *R;
+ SCEVDivision::divide(SE, Term, Step, &Q, &R);