Check in LLVM r95781.
diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
new file mode 100644
index 0000000..82be9cd
--- /dev/null
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -0,0 +1,5412 @@
+//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// This file contains the implementation of the scalar evolution analysis
+// engine, which is used primarily to analyze expressions involving induction
+// variables in loops.
+//
+// There are several aspects to this library. First is the representation of
+// scalar expressions, which are represented as subclasses of the SCEV class.
+// These classes are used to represent certain types of subexpressions that we
+// can handle. We only create one SCEV of a particular shape, so
+// pointer-comparisons for equality are legal.
+//
+// One important aspect of the SCEV objects is that they are never cyclic, even
+// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
+// the PHI node is one of the idioms that we can represent (e.g., a polynomial
+// recurrence) then we represent it directly as a recurrence node, otherwise we
+// represent it as a SCEVUnknown node.
+//
+// In addition to being able to represent expressions of various types, we also
+// have folders that are used to build the *canonical* representation for a
+// particular expression. These folders are capable of using a variety of
+// rewrite rules to simplify the expressions.
+//
+// Once the folders are defined, we can implement the more interesting
+// higher-level code, such as the code that recognizes PHI nodes of various
+// types, computes the execution count of a loop, etc.
+//
+// TODO: We should use these routines and value representations to implement
+// dependence analysis!
+//
+//===----------------------------------------------------------------------===//
+//
+// There are several good references for the techniques used in this analysis.
+//
+// Chains of recurrences -- a method to expedite the evaluation
+// of closed-form functions
+// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
+//
+// On computational properties of chains of recurrences
+// Eugene V. Zima
+//
+// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
+// Robert A. van Engelen
+//
+// Efficient Symbolic Analysis for Optimizing Compilers
+// Robert A. van Engelen
+//
+// Using the chains of recurrences algebra for data dependence testing and
+// induction variable substitution
+// MS Thesis, Johnie Birch
+//
+//===----------------------------------------------------------------------===//
+
+#define DEBUG_TYPE "scalar-evolution"
+#include "llvm/Analysis/ScalarEvolutionExpressions.h"
+#include "llvm/Constants.h"
+#include "llvm/DerivedTypes.h"
+#include "llvm/GlobalVariable.h"
+#include "llvm/GlobalAlias.h"
+#include "llvm/Instructions.h"
+#include "llvm/LLVMContext.h"
+#include "llvm/Operator.h"
+#include "llvm/Analysis/ConstantFolding.h"
+#include "llvm/Analysis/Dominators.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/ValueTracking.h"
+#include "llvm/Assembly/Writer.h"
+#include "llvm/Target/TargetData.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/ConstantRange.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/ErrorHandling.h"
+#include "llvm/Support/GetElementPtrTypeIterator.h"
+#include "llvm/Support/InstIterator.h"
+#include "llvm/Support/MathExtras.h"
+#include "llvm/Support/raw_ostream.h"
+#include "llvm/ADT/Statistic.h"
+#include "llvm/ADT/STLExtras.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include <algorithm>
+using namespace llvm;
+
+STATISTIC(NumArrayLenItCounts,
+ "Number of trip counts computed with array length");
+STATISTIC(NumTripCountsComputed,
+ "Number of loops with predictable loop counts");
+STATISTIC(NumTripCountsNotComputed,
+ "Number of loops without predictable loop counts");
+STATISTIC(NumBruteForceTripCountsComputed,
+ "Number of loops with trip counts computed by force");
+
+static cl::opt<unsigned>
+MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
+ cl::desc("Maximum number of iterations SCEV will "
+ "symbolically execute a constant "
+ "derived loop"),
+ cl::init(100));
+
+static RegisterPass<ScalarEvolution>
+R("scalar-evolution", "Scalar Evolution Analysis", false, true);
+char ScalarEvolution::ID = 0;
+
+//===----------------------------------------------------------------------===//
+// SCEV class definitions
+//===----------------------------------------------------------------------===//
+
+//===----------------------------------------------------------------------===//
+// Implementation of the SCEV class.
+//
+
+SCEV::~SCEV() {}
+
+void SCEV::dump() const {
+ print(dbgs());
+ dbgs() << '\n';
+}
+
+bool SCEV::isZero() const {
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
+ return SC->getValue()->isZero();
+ return false;
+}
+
+bool SCEV::isOne() const {
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
+ return SC->getValue()->isOne();
+ return false;
+}
+
+bool SCEV::isAllOnesValue() const {
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
+ return SC->getValue()->isAllOnesValue();
+ return false;
+}
+
+SCEVCouldNotCompute::SCEVCouldNotCompute() :
+ SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
+
+bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ return false;
+}
+
+const Type *SCEVCouldNotCompute::getType() const {
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ return 0;
+}
+
+bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ return false;
+}
+
+bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
+ llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
+ return false;
+}
+
+void SCEVCouldNotCompute::print(raw_ostream &OS) const {
+ OS << "***COULDNOTCOMPUTE***";
+}
+
+bool SCEVCouldNotCompute::classof(const SCEV *S) {
+ return S->getSCEVType() == scCouldNotCompute;
+}
+
+const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
+ FoldingSetNodeID ID;
+ ID.AddInteger(scConstant);
+ ID.AddPointer(V);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
+ new (S) SCEVConstant(ID, V);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
+ return getConstant(ConstantInt::get(getContext(), Val));
+}
+
+const SCEV *
+ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
+ return getConstant(
+ ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
+}
+
+const Type *SCEVConstant::getType() const { return V->getType(); }
+
+void SCEVConstant::print(raw_ostream &OS) const {
+ WriteAsOperand(OS, V, false);
+}
+
+SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
+ unsigned SCEVTy, const SCEV *op, const Type *ty)
+ : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
+
+bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ return Op->dominates(BB, DT);
+}
+
+bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
+ return Op->properlyDominates(BB, DT);
+}
+
+SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
+ const SCEV *op, const Type *ty)
+ : SCEVCastExpr(ID, scTruncate, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot truncate non-integer value!");
+}
+
+void SCEVTruncateExpr::print(raw_ostream &OS) const {
+ OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
+ const SCEV *op, const Type *ty)
+ : SCEVCastExpr(ID, scZeroExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot zero extend non-integer value!");
+}
+
+void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
+ OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
+ const SCEV *op, const Type *ty)
+ : SCEVCastExpr(ID, scSignExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot sign extend non-integer value!");
+}
+
+void SCEVSignExtendExpr::print(raw_ostream &OS) const {
+ OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+void SCEVCommutativeExpr::print(raw_ostream &OS) const {
+ assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
+ const char *OpStr = getOperationStr();
+ OS << "(" << *Operands[0];
+ for (unsigned i = 1, e = Operands.size(); i != e; ++i)
+ OS << OpStr << *Operands[i];
+ OS << ")";
+}
+
+bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ if (!getOperand(i)->dominates(BB, DT))
+ return false;
+ }
+ return true;
+}
+
+bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ if (!getOperand(i)->properlyDominates(BB, DT))
+ return false;
+ }
+ return true;
+}
+
+bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
+}
+
+bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
+ return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
+}
+
+void SCEVUDivExpr::print(raw_ostream &OS) const {
+ OS << "(" << *LHS << " /u " << *RHS << ")";
+}
+
+const Type *SCEVUDivExpr::getType() const {
+ // In most cases the types of LHS and RHS will be the same, but in some
+ // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
+ // depend on the type for correctness, but handling types carefully can
+ // avoid extra casts in the SCEVExpander. The LHS is more likely to be
+ // a pointer type than the RHS, so use the RHS' type here.
+ return RHS->getType();
+}
+
+bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
+ // Add recurrences are never invariant in the function-body (null loop).
+ if (!QueryLoop)
+ return false;
+
+ // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
+ if (QueryLoop->contains(L))
+ return false;
+
+ // This recurrence is variant w.r.t. QueryLoop if any of its operands
+ // are variant.
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
+ if (!getOperand(i)->isLoopInvariant(QueryLoop))
+ return false;
+
+ // Otherwise it's loop-invariant.
+ return true;
+}
+
+void SCEVAddRecExpr::print(raw_ostream &OS) const {
+ OS << "{" << *Operands[0];
+ for (unsigned i = 1, e = Operands.size(); i != e; ++i)
+ OS << ",+," << *Operands[i];
+ OS << "}<";
+ WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
+ OS << ">";
+}
+
+bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
+ // All non-instruction values are loop invariant. All instructions are loop
+ // invariant if they are not contained in the specified loop.
+ // Instructions are never considered invariant in the function body
+ // (null loop) because they are defined within the "loop".
+ if (Instruction *I = dyn_cast<Instruction>(V))
+ return L && !L->contains(I);
+ return true;
+}
+
+bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ if (Instruction *I = dyn_cast<Instruction>(getValue()))
+ return DT->dominates(I->getParent(), BB);
+ return true;
+}
+
+bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
+ if (Instruction *I = dyn_cast<Instruction>(getValue()))
+ return DT->properlyDominates(I->getParent(), BB);
+ return true;
+}
+
+const Type *SCEVUnknown::getType() const {
+ return V->getType();
+}
+
+bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
+ if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
+ if (VCE->getOpcode() == Instruction::PtrToInt)
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
+ if (CE->getOpcode() == Instruction::GetElementPtr &&
+ CE->getOperand(0)->isNullValue() &&
+ CE->getNumOperands() == 2)
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
+ if (CI->isOne()) {
+ AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
+ ->getElementType();
+ return true;
+ }
+
+ return false;
+}
+
+bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
+ if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
+ if (VCE->getOpcode() == Instruction::PtrToInt)
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
+ if (CE->getOpcode() == Instruction::GetElementPtr &&
+ CE->getOperand(0)->isNullValue()) {
+ const Type *Ty =
+ cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
+ if (const StructType *STy = dyn_cast<StructType>(Ty))
+ if (!STy->isPacked() &&
+ CE->getNumOperands() == 3 &&
+ CE->getOperand(1)->isNullValue()) {
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
+ if (CI->isOne() &&
+ STy->getNumElements() == 2 &&
+ STy->getElementType(0)->isInteger(1)) {
+ AllocTy = STy->getElementType(1);
+ return true;
+ }
+ }
+ }
+
+ return false;
+}
+
+bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
+ if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
+ if (VCE->getOpcode() == Instruction::PtrToInt)
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
+ if (CE->getOpcode() == Instruction::GetElementPtr &&
+ CE->getNumOperands() == 3 &&
+ CE->getOperand(0)->isNullValue() &&
+ CE->getOperand(1)->isNullValue()) {
+ const Type *Ty =
+ cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
+ // Ignore vector types here so that ScalarEvolutionExpander doesn't
+ // emit getelementptrs that index into vectors.
+ if (isa<StructType>(Ty) || isa<ArrayType>(Ty)) {
+ CTy = Ty;
+ FieldNo = CE->getOperand(2);
+ return true;
+ }
+ }
+
+ return false;
+}
+
+void SCEVUnknown::print(raw_ostream &OS) const {
+ const Type *AllocTy;
+ if (isSizeOf(AllocTy)) {
+ OS << "sizeof(" << *AllocTy << ")";
+ return;
+ }
+ if (isAlignOf(AllocTy)) {
+ OS << "alignof(" << *AllocTy << ")";
+ return;
+ }
+
+ const Type *CTy;
+ Constant *FieldNo;
+ if (isOffsetOf(CTy, FieldNo)) {
+ OS << "offsetof(" << *CTy << ", ";
+ WriteAsOperand(OS, FieldNo, false);
+ OS << ")";
+ return;
+ }
+
+ // Otherwise just print it normally.
+ WriteAsOperand(OS, V, false);
+}
+
+//===----------------------------------------------------------------------===//
+// SCEV Utilities
+//===----------------------------------------------------------------------===//
+
+static bool CompareTypes(const Type *A, const Type *B) {
+ if (A->getTypeID() != B->getTypeID())
+ return A->getTypeID() < B->getTypeID();
+ if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
+ const IntegerType *BI = cast<IntegerType>(B);
+ return AI->getBitWidth() < BI->getBitWidth();
+ }
+ if (const PointerType *AI = dyn_cast<PointerType>(A)) {
+ const PointerType *BI = cast<PointerType>(B);
+ return CompareTypes(AI->getElementType(), BI->getElementType());
+ }
+ if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
+ const ArrayType *BI = cast<ArrayType>(B);
+ if (AI->getNumElements() != BI->getNumElements())
+ return AI->getNumElements() < BI->getNumElements();
+ return CompareTypes(AI->getElementType(), BI->getElementType());
+ }
+ if (const VectorType *AI = dyn_cast<VectorType>(A)) {
+ const VectorType *BI = cast<VectorType>(B);
+ if (AI->getNumElements() != BI->getNumElements())
+ return AI->getNumElements() < BI->getNumElements();
+ return CompareTypes(AI->getElementType(), BI->getElementType());
+ }
+ if (const StructType *AI = dyn_cast<StructType>(A)) {
+ const StructType *BI = cast<StructType>(B);
+ if (AI->getNumElements() != BI->getNumElements())
+ return AI->getNumElements() < BI->getNumElements();
+ for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
+ if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
+ CompareTypes(BI->getElementType(i), AI->getElementType(i)))
+ return CompareTypes(AI->getElementType(i), BI->getElementType(i));
+ }
+ return false;
+}
+
+namespace {
+ /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
+ /// than the complexity of the RHS. This comparator is used to canonicalize
+ /// expressions.
+ class SCEVComplexityCompare {
+ LoopInfo *LI;
+ public:
+ explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
+
+ bool operator()(const SCEV *LHS, const SCEV *RHS) const {
+ // Fast-path: SCEVs are uniqued so we can do a quick equality check.
+ if (LHS == RHS)
+ return false;
+
+ // Primarily, sort the SCEVs by their getSCEVType().
+ if (LHS->getSCEVType() != RHS->getSCEVType())
+ return LHS->getSCEVType() < RHS->getSCEVType();
+
+ // Aside from the getSCEVType() ordering, the particular ordering
+ // isn't very important except that it's beneficial to be consistent,
+ // so that (a + b) and (b + a) don't end up as different expressions.
+
+ // Sort SCEVUnknown values with some loose heuristics. TODO: This is
+ // not as complete as it could be.
+ if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
+ const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
+
+ // Order pointer values after integer values. This helps SCEVExpander
+ // form GEPs.
+ if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
+ return false;
+ if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
+ return true;
+
+ // Compare getValueID values.
+ if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
+ return LU->getValue()->getValueID() < RU->getValue()->getValueID();
+
+ // Sort arguments by their position.
+ if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
+ const Argument *RA = cast<Argument>(RU->getValue());
+ return LA->getArgNo() < RA->getArgNo();
+ }
+
+ // For instructions, compare their loop depth, and their opcode.
+ // This is pretty loose.
+ if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
+ Instruction *RV = cast<Instruction>(RU->getValue());
+
+ // Compare loop depths.
+ if (LI->getLoopDepth(LV->getParent()) !=
+ LI->getLoopDepth(RV->getParent()))
+ return LI->getLoopDepth(LV->getParent()) <
+ LI->getLoopDepth(RV->getParent());
+
+ // Compare opcodes.
+ if (LV->getOpcode() != RV->getOpcode())
+ return LV->getOpcode() < RV->getOpcode();
+
+ // Compare the number of operands.
+ if (LV->getNumOperands() != RV->getNumOperands())
+ return LV->getNumOperands() < RV->getNumOperands();
+ }
+
+ return false;
+ }
+
+ // Compare constant values.
+ if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
+ const SCEVConstant *RC = cast<SCEVConstant>(RHS);
+ if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
+ return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
+ return LC->getValue()->getValue().ult(RC->getValue()->getValue());
+ }
+
+ // Compare addrec loop depths.
+ if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
+ const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
+ if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
+ return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
+ }
+
+ // Lexicographically compare n-ary expressions.
+ if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
+ const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
+ for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
+ if (i >= RC->getNumOperands())
+ return false;
+ if (operator()(LC->getOperand(i), RC->getOperand(i)))
+ return true;
+ if (operator()(RC->getOperand(i), LC->getOperand(i)))
+ return false;
+ }
+ return LC->getNumOperands() < RC->getNumOperands();
+ }
+
+ // Lexicographically compare udiv expressions.
+ if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
+ const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
+ if (operator()(LC->getLHS(), RC->getLHS()))
+ return true;
+ if (operator()(RC->getLHS(), LC->getLHS()))
+ return false;
+ if (operator()(LC->getRHS(), RC->getRHS()))
+ return true;
+ if (operator()(RC->getRHS(), LC->getRHS()))
+ return false;
+ return false;
+ }
+
+ // Compare cast expressions by operand.
+ if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
+ const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
+ return operator()(LC->getOperand(), RC->getOperand());
+ }
+
+ llvm_unreachable("Unknown SCEV kind!");
+ return false;
+ }
+ };
+}
+
+/// GroupByComplexity - Given a list of SCEV objects, order them by their
+/// complexity, and group objects of the same complexity together by value.
+/// When this routine is finished, we know that any duplicates in the vector are
+/// consecutive and that complexity is monotonically increasing.
+///
+/// Note that we go take special precautions to ensure that we get determinstic
+/// results from this routine. In other words, we don't want the results of
+/// this to depend on where the addresses of various SCEV objects happened to
+/// land in memory.
+///
+static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
+ LoopInfo *LI) {
+ if (Ops.size() < 2) return; // Noop
+ if (Ops.size() == 2) {
+ // This is the common case, which also happens to be trivially simple.
+ // Special case it.
+ if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
+ std::swap(Ops[0], Ops[1]);
+ return;
+ }
+
+ // Do the rough sort by complexity.
+ std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
+
+ // Now that we are sorted by complexity, group elements of the same
+ // complexity. Note that this is, at worst, N^2, but the vector is likely to
+ // be extremely short in practice. Note that we take this approach because we
+ // do not want to depend on the addresses of the objects we are grouping.
+ for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
+ const SCEV *S = Ops[i];
+ unsigned Complexity = S->getSCEVType();
+
+ // If there are any objects of the same complexity and same value as this
+ // one, group them.
+ for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
+ if (Ops[j] == S) { // Found a duplicate.
+ // Move it to immediately after i'th element.
+ std::swap(Ops[i+1], Ops[j]);
+ ++i; // no need to rescan it.
+ if (i == e-2) return; // Done!
+ }
+ }
+ }
+}
+
+
+
+//===----------------------------------------------------------------------===//
+// Simple SCEV method implementations
+//===----------------------------------------------------------------------===//
+
+/// BinomialCoefficient - Compute BC(It, K). The result has width W.
+/// Assume, K > 0.
+static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
+ ScalarEvolution &SE,
+ const Type* ResultTy) {
+ // Handle the simplest case efficiently.
+ if (K == 1)
+ return SE.getTruncateOrZeroExtend(It, ResultTy);
+
+ // We are using the following formula for BC(It, K):
+ //
+ // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
+ //
+ // Suppose, W is the bitwidth of the return value. We must be prepared for
+ // overflow. Hence, we must assure that the result of our computation is
+ // equal to the accurate one modulo 2^W. Unfortunately, division isn't
+ // safe in modular arithmetic.
+ //
+ // However, this code doesn't use exactly that formula; the formula it uses
+ // is something like the following, where T is the number of factors of 2 in
+ // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
+ // exponentiation:
+ //
+ // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
+ //
+ // This formula is trivially equivalent to the previous formula. However,
+ // this formula can be implemented much more efficiently. The trick is that
+ // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
+ // arithmetic. To do exact division in modular arithmetic, all we have
+ // to do is multiply by the inverse. Therefore, this step can be done at
+ // width W.
+ //
+ // The next issue is how to safely do the division by 2^T. The way this
+ // is done is by doing the multiplication step at a width of at least W + T
+ // bits. This way, the bottom W+T bits of the product are accurate. Then,
+ // when we perform the division by 2^T (which is equivalent to a right shift
+ // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
+ // truncated out after the division by 2^T.
+ //
+ // In comparison to just directly using the first formula, this technique
+ // is much more efficient; using the first formula requires W * K bits,
+ // but this formula less than W + K bits. Also, the first formula requires
+ // a division step, whereas this formula only requires multiplies and shifts.
+ //
+ // It doesn't matter whether the subtraction step is done in the calculation
+ // width or the input iteration count's width; if the subtraction overflows,
+ // the result must be zero anyway. We prefer here to do it in the width of
+ // the induction variable because it helps a lot for certain cases; CodeGen
+ // isn't smart enough to ignore the overflow, which leads to much less
+ // efficient code if the width of the subtraction is wider than the native
+ // register width.
+ //
+ // (It's possible to not widen at all by pulling out factors of 2 before
+ // the multiplication; for example, K=2 can be calculated as
+ // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
+ // extra arithmetic, so it's not an obvious win, and it gets
+ // much more complicated for K > 3.)
+
+ // Protection from insane SCEVs; this bound is conservative,
+ // but it probably doesn't matter.
+ if (K > 1000)
+ return SE.getCouldNotCompute();
+
+ unsigned W = SE.getTypeSizeInBits(ResultTy);
+
+ // Calculate K! / 2^T and T; we divide out the factors of two before
+ // multiplying for calculating K! / 2^T to avoid overflow.
+ // Other overflow doesn't matter because we only care about the bottom
+ // W bits of the result.
+ APInt OddFactorial(W, 1);
+ unsigned T = 1;
+ for (unsigned i = 3; i <= K; ++i) {
+ APInt Mult(W, i);
+ unsigned TwoFactors = Mult.countTrailingZeros();
+ T += TwoFactors;
+ Mult = Mult.lshr(TwoFactors);
+ OddFactorial *= Mult;
+ }
+
+ // We need at least W + T bits for the multiplication step
+ unsigned CalculationBits = W + T;
+
+ // Calcuate 2^T, at width T+W.
+ APInt DivFactor = APInt(CalculationBits, 1).shl(T);
+
+ // Calculate the multiplicative inverse of K! / 2^T;
+ // this multiplication factor will perform the exact division by
+ // K! / 2^T.
+ APInt Mod = APInt::getSignedMinValue(W+1);
+ APInt MultiplyFactor = OddFactorial.zext(W+1);
+ MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
+ MultiplyFactor = MultiplyFactor.trunc(W);
+
+ // Calculate the product, at width T+W
+ const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
+ CalculationBits);
+ const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
+ for (unsigned i = 1; i != K; ++i) {
+ const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
+ Dividend = SE.getMulExpr(Dividend,
+ SE.getTruncateOrZeroExtend(S, CalculationTy));
+ }
+
+ // Divide by 2^T
+ const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
+
+ // Truncate the result, and divide by K! / 2^T.
+
+ return SE.getMulExpr(SE.getConstant(MultiplyFactor),
+ SE.getTruncateOrZeroExtend(DivResult, ResultTy));
+}
+
+/// evaluateAtIteration - Return the value of this chain of recurrences at
+/// the specified iteration number. We can evaluate this recurrence by
+/// multiplying each element in the chain by the binomial coefficient
+/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
+///
+/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
+///
+/// where BC(It, k) stands for binomial coefficient.
+///
+const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
+ ScalarEvolution &SE) const {
+ const SCEV *Result = getStart();
+ for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
+ // The computation is correct in the face of overflow provided that the
+ // multiplication is performed _after_ the evaluation of the binomial
+ // coefficient.
+ const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
+ if (isa<SCEVCouldNotCompute>(Coeff))
+ return Coeff;
+
+ Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
+ }
+ return Result;
+}
+
+//===----------------------------------------------------------------------===//
+// SCEV Expression folder implementations
+//===----------------------------------------------------------------------===//
+
+const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
+ const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
+ "This is not a truncating conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scTruncate);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
+
+ // trunc(trunc(x)) --> trunc(x)
+ if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
+ return getTruncateExpr(ST->getOperand(), Ty);
+
+ // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
+ if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
+ return getTruncateOrSignExtend(SS->getOperand(), Ty);
+
+ // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
+
+ // If the input value is a chrec scev, truncate the chrec's operands.
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
+ SmallVector<const SCEV *, 4> Operands;
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
+ Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
+ return getAddRecExpr(Operands, AddRec->getLoop());
+ }
+
+ // The cast wasn't folded; create an explicit cast node.
+ // Recompute the insert position, as it may have been invalidated.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
+ new (S) SCEVTruncateExpr(ID, Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
+ const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
+ const Type *IntTy = getEffectiveSCEVType(Ty);
+ Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
+ if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
+ return getConstant(cast<ConstantInt>(C));
+ }
+
+ // zext(zext(x)) --> zext(x)
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getZeroExtendExpr(SZ->getOperand(), Ty);
+
+ // Before doing any expensive analysis, check to see if we've already
+ // computed a SCEV for this Op and Ty.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scZeroExtend);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+
+ // If the input value is a chrec scev, and we can prove that the value
+ // did not overflow the old, smaller, value, we can zero extend all of the
+ // operands (often constants). This allows analysis of something like
+ // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
+ if (AR->isAffine()) {
+ const SCEV *Start = AR->getStart();
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ unsigned BitWidth = getTypeSizeInBits(AR->getType());
+ const Loop *L = AR->getLoop();
+
+ // If we have special knowledge that this addrec won't overflow,
+ // we don't need to do any further analysis.
+ if (AR->hasNoUnsignedWrap())
+ return getAddRecExpr(getZeroExtendExpr(Start, Ty),
+ getZeroExtendExpr(Step, Ty),
+ L);
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for
+ // overflow.
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ const SCEV *CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType());
+ const SCEV *RecastedMaxBECount =
+ getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
+ if (MaxBECount == RecastedMaxBECount) {
+ const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
+ // Check whether Start+Step*MaxBECount has no unsigned overflow.
+ const SCEV *ZMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrZeroExtend(Step, Start->getType()));
+ const SCEV *Add = getAddExpr(Start, ZMul);
+ const SCEV *OperandExtendedAdd =
+ getAddExpr(getZeroExtendExpr(Start, WideTy),
+ getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
+ getZeroExtendExpr(Step, WideTy)));
+ if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getZeroExtendExpr(Start, Ty),
+ getZeroExtendExpr(Step, Ty),
+ L);
+
+ // Similar to above, only this time treat the step value as signed.
+ // This covers loops that count down.
+ const SCEV *SMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrSignExtend(Step, Start->getType()));
+ Add = getAddExpr(Start, SMul);
+ OperandExtendedAdd =
+ getAddExpr(getZeroExtendExpr(Start, WideTy),
+ getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
+ getSignExtendExpr(Step, WideTy)));
+ if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getZeroExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+ }
+
+ // If the backedge is guarded by a comparison with the pre-inc value
+ // the addrec is safe. Also, if the entry is guarded by a comparison
+ // with the start value and the backedge is guarded by a comparison
+ // with the post-inc value, the addrec is safe.
+ if (isKnownPositive(Step)) {
+ const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
+ getUnsignedRange(Step).getUnsignedMax());
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
+ (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
+ isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
+ AR->getPostIncExpr(*this), N)))
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getZeroExtendExpr(Start, Ty),
+ getZeroExtendExpr(Step, Ty),
+ L);
+ } else if (isKnownNegative(Step)) {
+ const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
+ getSignedRange(Step).getSignedMin());
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
+ (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
+ isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
+ AR->getPostIncExpr(*this), N)))
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getZeroExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+ }
+ }
+ }
+
+ // The cast wasn't folded; create an explicit cast node.
+ // Recompute the insert position, as it may have been invalidated.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
+ new (S) SCEVZeroExtendExpr(ID, Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
+ const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ // Fold if the operand is constant.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
+ const Type *IntTy = getEffectiveSCEVType(Ty);
+ Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
+ if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
+ return getConstant(cast<ConstantInt>(C));
+ }
+
+ // sext(sext(x)) --> sext(x)
+ if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
+ return getSignExtendExpr(SS->getOperand(), Ty);
+
+ // Before doing any expensive analysis, check to see if we've already
+ // computed a SCEV for this Op and Ty.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scSignExtend);
+ ID.AddPointer(Op);
+ ID.AddPointer(Ty);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+
+ // If the input value is a chrec scev, and we can prove that the value
+ // did not overflow the old, smaller, value, we can sign extend all of the
+ // operands (often constants). This allows analysis of something like
+ // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
+ if (AR->isAffine()) {
+ const SCEV *Start = AR->getStart();
+ const SCEV *Step = AR->getStepRecurrence(*this);
+ unsigned BitWidth = getTypeSizeInBits(AR->getType());
+ const Loop *L = AR->getLoop();
+
+ // If we have special knowledge that this addrec won't overflow,
+ // we don't need to do any further analysis.
+ if (AR->hasNoSignedWrap())
+ return getAddRecExpr(getSignExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+
+ // Check whether the backedge-taken count is SCEVCouldNotCompute.
+ // Note that this serves two purposes: It filters out loops that are
+ // simply not analyzable, and it covers the case where this code is
+ // being called from within backedge-taken count analysis, such that
+ // attempting to ask for the backedge-taken count would likely result
+ // in infinite recursion. In the later case, the analysis code will
+ // cope with a conservative value, and it will take care to purge
+ // that value once it has finished.
+ const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for
+ // overflow.
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ const SCEV *CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType());
+ const SCEV *RecastedMaxBECount =
+ getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
+ if (MaxBECount == RecastedMaxBECount) {
+ const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
+ // Check whether Start+Step*MaxBECount has no signed overflow.
+ const SCEV *SMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrSignExtend(Step, Start->getType()));
+ const SCEV *Add = getAddExpr(Start, SMul);
+ const SCEV *OperandExtendedAdd =
+ getAddExpr(getSignExtendExpr(Start, WideTy),
+ getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
+ getSignExtendExpr(Step, WideTy)));
+ if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getSignExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+
+ // Similar to above, only this time treat the step value as unsigned.
+ // This covers loops that count up with an unsigned step.
+ const SCEV *UMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrZeroExtend(Step, Start->getType()));
+ Add = getAddExpr(Start, UMul);
+ OperandExtendedAdd =
+ getAddExpr(getSignExtendExpr(Start, WideTy),
+ getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
+ getZeroExtendExpr(Step, WideTy)));
+ if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getSignExtendExpr(Start, Ty),
+ getZeroExtendExpr(Step, Ty),
+ L);
+ }
+
+ // If the backedge is guarded by a comparison with the pre-inc value
+ // the addrec is safe. Also, if the entry is guarded by a comparison
+ // with the start value and the backedge is guarded by a comparison
+ // with the post-inc value, the addrec is safe.
+ if (isKnownPositive(Step)) {
+ const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
+ getSignedRange(Step).getSignedMax());
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
+ (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
+ isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
+ AR->getPostIncExpr(*this), N)))
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getSignExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+ } else if (isKnownNegative(Step)) {
+ const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
+ getSignedRange(Step).getSignedMin());
+ if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
+ (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
+ isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
+ AR->getPostIncExpr(*this), N)))
+ // Return the expression with the addrec on the outside.
+ return getAddRecExpr(getSignExtendExpr(Start, Ty),
+ getSignExtendExpr(Step, Ty),
+ L);
+ }
+ }
+ }
+
+ // The cast wasn't folded; create an explicit cast node.
+ // Recompute the insert position, as it may have been invalidated.
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
+ new (S) SCEVSignExtendExpr(ID, Op, Ty);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+/// getAnyExtendExpr - Return a SCEV for the given operand extended with
+/// unspecified bits out to the given type.
+///
+const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
+ const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+ assert(isSCEVable(Ty) &&
+ "This is not a conversion to a SCEVable type!");
+ Ty = getEffectiveSCEVType(Ty);
+
+ // Sign-extend negative constants.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ if (SC->getValue()->getValue().isNegative())
+ return getSignExtendExpr(Op, Ty);
+
+ // Peel off a truncate cast.
+ if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
+ const SCEV *NewOp = T->getOperand();
+ if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
+ return getAnyExtendExpr(NewOp, Ty);
+ return getTruncateOrNoop(NewOp, Ty);
+ }
+
+ // Next try a zext cast. If the cast is folded, use it.
+ const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
+ if (!isa<SCEVZeroExtendExpr>(ZExt))
+ return ZExt;
+
+ // Next try a sext cast. If the cast is folded, use it.
+ const SCEV *SExt = getSignExtendExpr(Op, Ty);
+ if (!isa<SCEVSignExtendExpr>(SExt))
+ return SExt;
+
+ // Force the cast to be folded into the operands of an addrec.
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
+ SmallVector<const SCEV *, 4> Ops;
+ for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
+ I != E; ++I)
+ Ops.push_back(getAnyExtendExpr(*I, Ty));
+ return getAddRecExpr(Ops, AR->getLoop());
+ }
+
+ // If the expression is obviously signed, use the sext cast value.
+ if (isa<SCEVSMaxExpr>(Op))
+ return SExt;
+
+ // Absent any other information, use the zext cast value.
+ return ZExt;
+}
+
+/// CollectAddOperandsWithScales - Process the given Ops list, which is
+/// a list of operands to be added under the given scale, update the given
+/// map. This is a helper function for getAddRecExpr. As an example of
+/// what it does, given a sequence of operands that would form an add
+/// expression like this:
+///
+/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
+///
+/// where A and B are constants, update the map with these values:
+///
+/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
+///
+/// and add 13 + A*B*29 to AccumulatedConstant.
+/// This will allow getAddRecExpr to produce this:
+///
+/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
+///
+/// This form often exposes folding opportunities that are hidden in
+/// the original operand list.
+///
+/// Return true iff it appears that any interesting folding opportunities
+/// may be exposed. This helps getAddRecExpr short-circuit extra work in
+/// the common case where no interesting opportunities are present, and
+/// is also used as a check to avoid infinite recursion.
+///
+static bool
+CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
+ SmallVector<const SCEV *, 8> &NewOps,
+ APInt &AccumulatedConstant,
+ const SmallVectorImpl<const SCEV *> &Ops,
+ const APInt &Scale,
+ ScalarEvolution &SE) {
+ bool Interesting = false;
+
+ // Iterate over the add operands.
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
+ const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
+ if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
+ APInt NewScale =
+ Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
+ if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
+ // A multiplication of a constant with another add; recurse.
+ Interesting |=
+ CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
+ cast<SCEVAddExpr>(Mul->getOperand(1))
+ ->getOperands(),
+ NewScale, SE);
+ } else {
+ // A multiplication of a constant with some other value. Update
+ // the map.
+ SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
+ const SCEV *Key = SE.getMulExpr(MulOps);
+ std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
+ M.insert(std::make_pair(Key, NewScale));
+ if (Pair.second) {
+ NewOps.push_back(Pair.first->first);
+ } else {
+ Pair.first->second += NewScale;
+ // The map already had an entry for this value, which may indicate
+ // a folding opportunity.
+ Interesting = true;
+ }
+ }
+ } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
+ // Pull a buried constant out to the outside.
+ if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
+ Interesting = true;
+ AccumulatedConstant += Scale * C->getValue()->getValue();
+ } else {
+ // An ordinary operand. Update the map.
+ std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
+ M.insert(std::make_pair(Ops[i], Scale));
+ if (Pair.second) {
+ NewOps.push_back(Pair.first->first);
+ } else {
+ Pair.first->second += Scale;
+ // The map already had an entry for this value, which may indicate
+ // a folding opportunity.
+ Interesting = true;
+ }
+ }
+ }
+
+ return Interesting;
+}
+
+namespace {
+ struct APIntCompare {
+ bool operator()(const APInt &LHS, const APInt &RHS) const {
+ return LHS.ult(RHS);
+ }
+ };
+}
+
+/// getAddExpr - Get a canonical add expression, or something simpler if
+/// possible.
+const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
+ bool HasNUW, bool HasNSW) {
+ assert(!Ops.empty() && "Cannot get empty add!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Ops[i]->getType()) ==
+ getEffectiveSCEVType(Ops[0]->getType()) &&
+ "SCEVAddExpr operand types don't match!");
+#endif
+
+ // If HasNSW is true and all the operands are non-negative, infer HasNUW.
+ if (!HasNUW && HasNSW) {
+ bool All = true;
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (!isKnownNonNegative(Ops[i])) {
+ All = false;
+ break;
+ }
+ if (All) HasNUW = true;
+ }
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops, LI);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ Ops[0] = getConstant(LHSC->getValue()->getValue() +
+ RHSC->getValue()->getValue());
+ if (Ops.size() == 2) return Ops[0];
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ }
+
+ // If we are left with a constant zero being added, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ }
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ // Okay, check to see if the same value occurs in the operand list twice. If
+ // so, merge them together into an multiply expression. Since we sorted the
+ // list, these values are required to be adjacent.
+ const Type *Ty = Ops[0]->getType();
+ for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
+ if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
+ // Found a match, merge the two values into a multiply, and add any
+ // remaining values to the result.
+ const SCEV *Two = getIntegerSCEV(2, Ty);
+ const SCEV *Mul = getMulExpr(Ops[i], Two);
+ if (Ops.size() == 2)
+ return Mul;
+ Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
+ Ops.push_back(Mul);
+ return getAddExpr(Ops, HasNUW, HasNSW);
+ }
+
+ // Check for truncates. If all the operands are truncated from the same
+ // type, see if factoring out the truncate would permit the result to be
+ // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
+ // if the contents of the resulting outer trunc fold to something simple.
+ for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
+ const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
+ const Type *DstType = Trunc->getType();
+ const Type *SrcType = Trunc->getOperand()->getType();
+ SmallVector<const SCEV *, 8> LargeOps;
+ bool Ok = true;
+ // Check all the operands to see if they can be represented in the
+ // source type of the truncate.
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
+ if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
+ if (T->getOperand()->getType() != SrcType) {
+ Ok = false;
+ break;
+ }
+ LargeOps.push_back(T->getOperand());
+ } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
+ // This could be either sign or zero extension, but sign extension
+ // is much more likely to be foldable here.
+ LargeOps.push_back(getSignExtendExpr(C, SrcType));
+ } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
+ SmallVector<const SCEV *, 8> LargeMulOps;
+ for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
+ if (const SCEVTruncateExpr *T =
+ dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
+ if (T->getOperand()->getType() != SrcType) {
+ Ok = false;
+ break;
+ }
+ LargeMulOps.push_back(T->getOperand());
+ } else if (const SCEVConstant *C =
+ dyn_cast<SCEVConstant>(M->getOperand(j))) {
+ // This could be either sign or zero extension, but sign extension
+ // is much more likely to be foldable here.
+ LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
+ } else {
+ Ok = false;
+ break;
+ }
+ }
+ if (Ok)
+ LargeOps.push_back(getMulExpr(LargeMulOps));
+ } else {
+ Ok = false;
+ break;
+ }
+ }
+ if (Ok) {
+ // Evaluate the expression in the larger type.
+ const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
+ // If it folds to something simple, use it. Otherwise, don't.
+ if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
+ return getTruncateExpr(Fold, DstType);
+ }
+ }
+
+ // Skip past any other cast SCEVs.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
+ ++Idx;
+
+ // If there are add operands they would be next.
+ if (Idx < Ops.size()) {
+ bool DeletedAdd = false;
+ while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
+ // If we have an add, expand the add operands onto the end of the operands
+ // list.
+ Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
+ Ops.erase(Ops.begin()+Idx);
+ DeletedAdd = true;
+ }
+
+ // If we deleted at least one add, we added operands to the end of the list,
+ // and they are not necessarily sorted. Recurse to resort and resimplify
+ // any operands we just aquired.
+ if (DeletedAdd)
+ return getAddExpr(Ops);
+ }
+
+ // Skip over the add expression until we get to a multiply.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
+ ++Idx;
+
+ // Check to see if there are any folding opportunities present with
+ // operands multiplied by constant values.
+ if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
+ uint64_t BitWidth = getTypeSizeInBits(Ty);
+ DenseMap<const SCEV *, APInt> M;
+ SmallVector<const SCEV *, 8> NewOps;
+ APInt AccumulatedConstant(BitWidth, 0);
+ if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
+ Ops, APInt(BitWidth, 1), *this)) {
+ // Some interesting folding opportunity is present, so its worthwhile to
+ // re-generate the operands list. Group the operands by constant scale,
+ // to avoid multiplying by the same constant scale multiple times.
+ std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
+ for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
+ E = NewOps.end(); I != E; ++I)
+ MulOpLists[M.find(*I)->second].push_back(*I);
+ // Re-generate the operands list.
+ Ops.clear();
+ if (AccumulatedConstant != 0)
+ Ops.push_back(getConstant(AccumulatedConstant));
+ for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
+ I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
+ if (I->first != 0)
+ Ops.push_back(getMulExpr(getConstant(I->first),
+ getAddExpr(I->second)));
+ if (Ops.empty())
+ return getIntegerSCEV(0, Ty);
+ if (Ops.size() == 1)
+ return Ops[0];
+ return getAddExpr(Ops);
+ }
+ }
+
+ // If we are adding something to a multiply expression, make sure the
+ // something is not already an operand of the multiply. If so, merge it into
+ // the multiply.
+ for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
+ const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
+ for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
+ const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
+ for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
+ if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
+ // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
+ const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
+ if (Mul->getNumOperands() != 2) {
+ // If the multiply has more than two operands, we must get the
+ // Y*Z term.
+ SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
+ MulOps.erase(MulOps.begin()+MulOp);
+ InnerMul = getMulExpr(MulOps);
+ }
+ const SCEV *One = getIntegerSCEV(1, Ty);
+ const SCEV *AddOne = getAddExpr(InnerMul, One);
+ const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
+ if (Ops.size() == 2) return OuterMul;
+ if (AddOp < Idx) {
+ Ops.erase(Ops.begin()+AddOp);
+ Ops.erase(Ops.begin()+Idx-1);
+ } else {
+ Ops.erase(Ops.begin()+Idx);
+ Ops.erase(Ops.begin()+AddOp-1);
+ }
+ Ops.push_back(OuterMul);
+ return getAddExpr(Ops);
+ }
+
+ // Check this multiply against other multiplies being added together.
+ for (unsigned OtherMulIdx = Idx+1;
+ OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
+ ++OtherMulIdx) {
+ const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
+ // If MulOp occurs in OtherMul, we can fold the two multiplies
+ // together.
+ for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
+ OMulOp != e; ++OMulOp)
+ if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
+ // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
+ const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
+ if (Mul->getNumOperands() != 2) {
+ SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
+ Mul->op_end());
+ MulOps.erase(MulOps.begin()+MulOp);
+ InnerMul1 = getMulExpr(MulOps);
+ }
+ const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
+ if (OtherMul->getNumOperands() != 2) {
+ SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
+ OtherMul->op_end());
+ MulOps.erase(MulOps.begin()+OMulOp);
+ InnerMul2 = getMulExpr(MulOps);
+ }
+ const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
+ const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
+ if (Ops.size() == 2) return OuterMul;
+ Ops.erase(Ops.begin()+Idx);
+ Ops.erase(Ops.begin()+OtherMulIdx-1);
+ Ops.push_back(OuterMul);
+ return getAddExpr(Ops);
+ }
+ }
+ }
+ }
+
+ // If there are any add recurrences in the operands list, see if any other
+ // added values are loop invariant. If so, we can fold them into the
+ // recurrence.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
+ ++Idx;
+
+ // Scan over all recurrences, trying to fold loop invariants into them.
+ for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
+ // Scan all of the other operands to this add and add them to the vector if
+ // they are loop invariant w.r.t. the recurrence.
+ SmallVector<const SCEV *, 8> LIOps;
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
+ LIOps.push_back(Ops[i]);
+ Ops.erase(Ops.begin()+i);
+ --i; --e;
+ }
+
+ // If we found some loop invariants, fold them into the recurrence.
+ if (!LIOps.empty()) {
+ // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
+ LIOps.push_back(AddRec->getStart());
+
+ SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
+ AddRec->op_end());
+ AddRecOps[0] = getAddExpr(LIOps);
+
+ // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
+ // is not associative so this isn't necessarily safe.
+ const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
+
+ // If all of the other operands were loop invariant, we are done.
+ if (Ops.size() == 1) return NewRec;
+
+ // Otherwise, add the folded AddRec by the non-liv parts.
+ for (unsigned i = 0;; ++i)
+ if (Ops[i] == AddRec) {
+ Ops[i] = NewRec;
+ break;
+ }
+ return getAddExpr(Ops);
+ }
+
+ // Okay, if there weren't any loop invariants to be folded, check to see if
+ // there are multiple AddRec's with the same loop induction variable being
+ // added together. If so, we can fold them.
+ for (unsigned OtherIdx = Idx+1;
+ OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
+ if (OtherIdx != Idx) {
+ const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
+ if (AddRec->getLoop() == OtherAddRec->getLoop()) {
+ // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
+ SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
+ AddRec->op_end());
+ for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
+ if (i >= NewOps.size()) {
+ NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
+ OtherAddRec->op_end());
+ break;
+ }
+ NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
+ }
+ const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
+
+ if (Ops.size() == 2) return NewAddRec;
+
+ Ops.erase(Ops.begin()+Idx);
+ Ops.erase(Ops.begin()+OtherIdx-1);
+ Ops.push_back(NewAddRec);
+ return getAddExpr(Ops);
+ }
+ }
+
+ // Otherwise couldn't fold anything into this recurrence. Move onto the
+ // next one.
+ }
+
+ // Okay, it looks like we really DO need an add expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scAddExpr);
+ ID.AddInteger(Ops.size());
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ ID.AddPointer(Ops[i]);
+ void *IP = 0;
+ SCEVAddExpr *S =
+ static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ S = SCEVAllocator.Allocate<SCEVAddExpr>();
+ new (S) SCEVAddExpr(ID, Ops);
+ UniqueSCEVs.InsertNode(S, IP);
+ }
+ if (HasNUW) S->setHasNoUnsignedWrap(true);
+ if (HasNSW) S->setHasNoSignedWrap(true);
+ return S;
+}
+
+/// getMulExpr - Get a canonical multiply expression, or something simpler if
+/// possible.
+const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
+ bool HasNUW, bool HasNSW) {
+ assert(!Ops.empty() && "Cannot get empty mul!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Ops[i]->getType()) ==
+ getEffectiveSCEVType(Ops[0]->getType()) &&
+ "SCEVMulExpr operand types don't match!");
+#endif
+
+ // If HasNSW is true and all the operands are non-negative, infer HasNUW.
+ if (!HasNUW && HasNSW) {
+ bool All = true;
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (!isKnownNonNegative(Ops[i])) {
+ All = false;
+ break;
+ }
+ if (All) HasNUW = true;
+ }
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops, LI);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+
+ // C1*(C2+V) -> C1*C2 + C1*V
+ if (Ops.size() == 2)
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
+ if (Add->getNumOperands() == 2 &&
+ isa<SCEVConstant>(Add->getOperand(0)))
+ return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
+ getMulExpr(LHSC, Add->getOperand(1)));
+
+ ++Idx;
+ while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ ConstantInt *Fold = ConstantInt::get(getContext(),
+ LHSC->getValue()->getValue() *
+ RHSC->getValue()->getValue());
+ Ops[0] = getConstant(Fold);
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ if (Ops.size() == 1) return Ops[0];
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ }
+
+ // If we are left with a constant one being multiplied, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
+ // If we have a multiply of zero, it will always be zero.
+ return Ops[0];
+ } else if (Ops[0]->isAllOnesValue()) {
+ // If we have a mul by -1 of an add, try distributing the -1 among the
+ // add operands.
+ if (Ops.size() == 2)
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
+ SmallVector<const SCEV *, 4> NewOps;
+ bool AnyFolded = false;
+ for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
+ I != E; ++I) {
+ const SCEV *Mul = getMulExpr(Ops[0], *I);
+ if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
+ NewOps.push_back(Mul);
+ }
+ if (AnyFolded)
+ return getAddExpr(NewOps);
+ }
+ }
+ }
+
+ // Skip over the add expression until we get to a multiply.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
+ ++Idx;
+
+ if (Ops.size() == 1)
+ return Ops[0];
+
+ // If there are mul operands inline them all into this expression.
+ if (Idx < Ops.size()) {
+ bool DeletedMul = false;
+ while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
+ // If we have an mul, expand the mul operands onto the end of the operands
+ // list.
+ Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
+ Ops.erase(Ops.begin()+Idx);
+ DeletedMul = true;
+ }
+
+ // If we deleted at least one mul, we added operands to the end of the list,
+ // and they are not necessarily sorted. Recurse to resort and resimplify
+ // any operands we just aquired.
+ if (DeletedMul)
+ return getMulExpr(Ops);
+ }
+
+ // If there are any add recurrences in the operands list, see if any other
+ // added values are loop invariant. If so, we can fold them into the
+ // recurrence.
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
+ ++Idx;
+
+ // Scan over all recurrences, trying to fold loop invariants into them.
+ for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
+ // Scan all of the other operands to this mul and add them to the vector if
+ // they are loop invariant w.r.t. the recurrence.
+ SmallVector<const SCEV *, 8> LIOps;
+ const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
+ LIOps.push_back(Ops[i]);
+ Ops.erase(Ops.begin()+i);
+ --i; --e;
+ }
+
+ // If we found some loop invariants, fold them into the recurrence.
+ if (!LIOps.empty()) {
+ // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
+ SmallVector<const SCEV *, 4> NewOps;
+ NewOps.reserve(AddRec->getNumOperands());
+ if (LIOps.size() == 1) {
+ const SCEV *Scale = LIOps[0];
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
+ NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
+ } else {
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
+ SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
+ MulOps.push_back(AddRec->getOperand(i));
+ NewOps.push_back(getMulExpr(MulOps));
+ }
+ }
+
+ // It's tempting to propagate the NSW flag here, but nsw multiplication
+ // is not associative so this isn't necessarily safe.
+ const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
+ HasNUW && AddRec->hasNoUnsignedWrap(),
+ /*HasNSW=*/false);
+
+ // If all of the other operands were loop invariant, we are done.
+ if (Ops.size() == 1) return NewRec;
+
+ // Otherwise, multiply the folded AddRec by the non-liv parts.
+ for (unsigned i = 0;; ++i)
+ if (Ops[i] == AddRec) {
+ Ops[i] = NewRec;
+ break;
+ }
+ return getMulExpr(Ops);
+ }
+
+ // Okay, if there weren't any loop invariants to be folded, check to see if
+ // there are multiple AddRec's with the same loop induction variable being
+ // multiplied together. If so, we can fold them.
+ for (unsigned OtherIdx = Idx+1;
+ OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
+ if (OtherIdx != Idx) {
+ const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
+ if (AddRec->getLoop() == OtherAddRec->getLoop()) {
+ // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
+ const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
+ const SCEV *NewStart = getMulExpr(F->getStart(),
+ G->getStart());
+ const SCEV *B = F->getStepRecurrence(*this);
+ const SCEV *D = G->getStepRecurrence(*this);
+ const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
+ getMulExpr(G, B),
+ getMulExpr(B, D));
+ const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
+ F->getLoop());
+ if (Ops.size() == 2) return NewAddRec;
+
+ Ops.erase(Ops.begin()+Idx);
+ Ops.erase(Ops.begin()+OtherIdx-1);
+ Ops.push_back(NewAddRec);
+ return getMulExpr(Ops);
+ }
+ }
+
+ // Otherwise couldn't fold anything into this recurrence. Move onto the
+ // next one.
+ }
+
+ // Okay, it looks like we really DO need an mul expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scMulExpr);
+ ID.AddInteger(Ops.size());
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ ID.AddPointer(Ops[i]);
+ void *IP = 0;
+ SCEVMulExpr *S =
+ static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ S = SCEVAllocator.Allocate<SCEVMulExpr>();
+ new (S) SCEVMulExpr(ID, Ops);
+ UniqueSCEVs.InsertNode(S, IP);
+ }
+ if (HasNUW) S->setHasNoUnsignedWrap(true);
+ if (HasNSW) S->setHasNoSignedWrap(true);
+ return S;
+}
+
+/// getUDivExpr - Get a canonical unsigned division expression, or something
+/// simpler if possible.
+const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
+ const SCEV *RHS) {
+ assert(getEffectiveSCEVType(LHS->getType()) ==
+ getEffectiveSCEVType(RHS->getType()) &&
+ "SCEVUDivExpr operand types don't match!");
+
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+ if (RHSC->getValue()->equalsInt(1))
+ return LHS; // X udiv 1 --> x
+ if (RHSC->isZero())
+ return getIntegerSCEV(0, LHS->getType()); // value is undefined
+
+ // Determine if the division can be folded into the operands of
+ // its operands.
+ // TODO: Generalize this to non-constants by using known-bits information.
+ const Type *Ty = LHS->getType();
+ unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
+ unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
+ // For non-power-of-two values, effectively round the value up to the
+ // nearest power of two.
+ if (!RHSC->getValue()->getValue().isPowerOf2())
+ ++MaxShiftAmt;
+ const IntegerType *ExtTy =
+ IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
+ // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
+ if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
+ if (const SCEVConstant *Step =
+ dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
+ if (!Step->getValue()->getValue()
+ .urem(RHSC->getValue()->getValue()) &&
+ getZeroExtendExpr(AR, ExtTy) ==
+ getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
+ getZeroExtendExpr(Step, ExtTy),
+ AR->getLoop())) {
+ SmallVector<const SCEV *, 4> Operands;
+ for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
+ Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
+ return getAddRecExpr(Operands, AR->getLoop());
+ }
+ // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
+ if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
+ SmallVector<const SCEV *, 4> Operands;
+ for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
+ Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
+ if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
+ // Find an operand that's safely divisible.
+ for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
+ const SCEV *Op = M->getOperand(i);
+ const SCEV *Div = getUDivExpr(Op, RHSC);
+ if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
+ const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
+ Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
+ MOperands.end());
+ Operands[i] = Div;
+ return getMulExpr(Operands);
+ }
+ }
+ }
+ // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
+ if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
+ SmallVector<const SCEV *, 4> Operands;
+ for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
+ Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
+ if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
+ Operands.clear();
+ for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
+ const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
+ if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
+ break;
+ Operands.push_back(Op);
+ }
+ if (Operands.size() == A->getNumOperands())
+ return getAddExpr(Operands);
+ }
+ }
+
+ // Fold if both operands are constant.
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
+ Constant *LHSCV = LHSC->getValue();
+ Constant *RHSCV = RHSC->getValue();
+ return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
+ RHSCV)));
+ }
+ }
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scUDivExpr);
+ ID.AddPointer(LHS);
+ ID.AddPointer(RHS);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
+ new (S) SCEVUDivExpr(ID, LHS, RHS);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+
+/// getAddRecExpr - Get an add recurrence expression for the specified loop.
+/// Simplify the expression as much as possible.
+const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
+ const SCEV *Step, const Loop *L,
+ bool HasNUW, bool HasNSW) {
+ SmallVector<const SCEV *, 4> Operands;
+ Operands.push_back(Start);
+ if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
+ if (StepChrec->getLoop() == L) {
+ Operands.insert(Operands.end(), StepChrec->op_begin(),
+ StepChrec->op_end());
+ return getAddRecExpr(Operands, L);
+ }
+
+ Operands.push_back(Step);
+ return getAddRecExpr(Operands, L, HasNUW, HasNSW);
+}
+
+/// getAddRecExpr - Get an add recurrence expression for the specified loop.
+/// Simplify the expression as much as possible.
+const SCEV *
+ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
+ const Loop *L,
+ bool HasNUW, bool HasNSW) {
+ if (Operands.size() == 1) return Operands[0];
+#ifndef NDEBUG
+ for (unsigned i = 1, e = Operands.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Operands[i]->getType()) ==
+ getEffectiveSCEVType(Operands[0]->getType()) &&
+ "SCEVAddRecExpr operand types don't match!");
+#endif
+
+ if (Operands.back()->isZero()) {
+ Operands.pop_back();
+ return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
+ }
+
+ // If HasNSW is true and all the operands are non-negative, infer HasNUW.
+ if (!HasNUW && HasNSW) {
+ bool All = true;
+ for (unsigned i = 0, e = Operands.size(); i != e; ++i)
+ if (!isKnownNonNegative(Operands[i])) {
+ All = false;
+ break;
+ }
+ if (All) HasNUW = true;
+ }
+
+ // Canonicalize nested AddRecs in by nesting them in order of loop depth.
+ if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
+ const Loop *NestedLoop = NestedAR->getLoop();
+ if (L->contains(NestedLoop->getHeader()) ?
+ (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
+ (!NestedLoop->contains(L->getHeader()) &&
+ DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
+ SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
+ NestedAR->op_end());
+ Operands[0] = NestedAR->getStart();
+ // AddRecs require their operands be loop-invariant with respect to their
+ // loops. Don't perform this transformation if it would break this
+ // requirement.
+ bool AllInvariant = true;
+ for (unsigned i = 0, e = Operands.size(); i != e; ++i)
+ if (!Operands[i]->isLoopInvariant(L)) {
+ AllInvariant = false;
+ break;
+ }
+ if (AllInvariant) {
+ NestedOperands[0] = getAddRecExpr(Operands, L);
+ AllInvariant = true;
+ for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
+ if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
+ AllInvariant = false;
+ break;
+ }
+ if (AllInvariant)
+ // Ok, both add recurrences are valid after the transformation.
+ return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
+ }
+ // Reset Operands to its original state.
+ Operands[0] = NestedAR;
+ }
+ }
+
+ // Okay, it looks like we really DO need an addrec expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scAddRecExpr);
+ ID.AddInteger(Operands.size());
+ for (unsigned i = 0, e = Operands.size(); i != e; ++i)
+ ID.AddPointer(Operands[i]);
+ ID.AddPointer(L);
+ void *IP = 0;
+ SCEVAddRecExpr *S =
+ static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
+ if (!S) {
+ S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
+ new (S) SCEVAddRecExpr(ID, Operands, L);
+ UniqueSCEVs.InsertNode(S, IP);
+ }
+ if (HasNUW) S->setHasNoUnsignedWrap(true);
+ if (HasNSW) S->setHasNoSignedWrap(true);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
+ const SCEV *RHS) {
+ SmallVector<const SCEV *, 2> Ops;
+ Ops.push_back(LHS);
+ Ops.push_back(RHS);
+ return getSMaxExpr(Ops);
+}
+
+const SCEV *
+ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
+ assert(!Ops.empty() && "Cannot get empty smax!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Ops[i]->getType()) ==
+ getEffectiveSCEVType(Ops[0]->getType()) &&
+ "SCEVSMaxExpr operand types don't match!");
+#endif
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops, LI);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ ConstantInt *Fold = ConstantInt::get(getContext(),
+ APIntOps::smax(LHSC->getValue()->getValue(),
+ RHSC->getValue()->getValue()));
+ Ops[0] = getConstant(Fold);
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ if (Ops.size() == 1) return Ops[0];
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ }
+
+ // If we are left with a constant minimum-int, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
+ // If we have an smax with a constant maximum-int, it will always be
+ // maximum-int.
+ return Ops[0];
+ }
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ // Find the first SMax
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
+ ++Idx;
+
+ // Check to see if one of the operands is an SMax. If so, expand its operands
+ // onto our operand list, and recurse to simplify.
+ if (Idx < Ops.size()) {
+ bool DeletedSMax = false;
+ while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
+ Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
+ Ops.erase(Ops.begin()+Idx);
+ DeletedSMax = true;
+ }
+
+ if (DeletedSMax)
+ return getSMaxExpr(Ops);
+ }
+
+ // Okay, check to see if the same value occurs in the operand list twice. If
+ // so, delete one. Since we sorted the list, these values are required to
+ // be adjacent.
+ for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
+ if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
+ Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
+ --i; --e;
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ assert(!Ops.empty() && "Reduced smax down to nothing!");
+
+ // Okay, it looks like we really DO need an smax expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scSMaxExpr);
+ ID.AddInteger(Ops.size());
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ ID.AddPointer(Ops[i]);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
+ new (S) SCEVSMaxExpr(ID, Ops);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
+ const SCEV *RHS) {
+ SmallVector<const SCEV *, 2> Ops;
+ Ops.push_back(LHS);
+ Ops.push_back(RHS);
+ return getUMaxExpr(Ops);
+}
+
+const SCEV *
+ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
+ assert(!Ops.empty() && "Cannot get empty umax!");
+ if (Ops.size() == 1) return Ops[0];
+#ifndef NDEBUG
+ for (unsigned i = 1, e = Ops.size(); i != e; ++i)
+ assert(getEffectiveSCEVType(Ops[i]->getType()) ==
+ getEffectiveSCEVType(Ops[0]->getType()) &&
+ "SCEVUMaxExpr operand types don't match!");
+#endif
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops, LI);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ ConstantInt *Fold = ConstantInt::get(getContext(),
+ APIntOps::umax(LHSC->getValue()->getValue(),
+ RHSC->getValue()->getValue()));
+ Ops[0] = getConstant(Fold);
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ if (Ops.size() == 1) return Ops[0];
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ }
+
+ // If we are left with a constant minimum-int, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
+ // If we have an umax with a constant maximum-int, it will always be
+ // maximum-int.
+ return Ops[0];
+ }
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ // Find the first UMax
+ while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
+ ++Idx;
+
+ // Check to see if one of the operands is a UMax. If so, expand its operands
+ // onto our operand list, and recurse to simplify.
+ if (Idx < Ops.size()) {
+ bool DeletedUMax = false;
+ while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
+ Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
+ Ops.erase(Ops.begin()+Idx);
+ DeletedUMax = true;
+ }
+
+ if (DeletedUMax)
+ return getUMaxExpr(Ops);
+ }
+
+ // Okay, check to see if the same value occurs in the operand list twice. If
+ // so, delete one. Since we sorted the list, these values are required to
+ // be adjacent.
+ for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
+ if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
+ Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
+ --i; --e;
+ }
+
+ if (Ops.size() == 1) return Ops[0];
+
+ assert(!Ops.empty() && "Reduced umax down to nothing!");
+
+ // Okay, it looks like we really DO need a umax expr. Check to see if we
+ // already have one, otherwise create a new one.
+ FoldingSetNodeID ID;
+ ID.AddInteger(scUMaxExpr);
+ ID.AddInteger(Ops.size());
+ for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+ ID.AddPointer(Ops[i]);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
+ new (S) SCEVUMaxExpr(ID, Ops);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
+ const SCEV *RHS) {
+ // ~smax(~x, ~y) == smin(x, y).
+ return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
+}
+
+const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
+ const SCEV *RHS) {
+ // ~umax(~x, ~y) == umin(x, y)
+ return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
+}
+
+const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
+ Constant *C = ConstantExpr::getSizeOf(AllocTy);
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
+ C = ConstantFoldConstantExpression(CE, TD);
+ const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
+ return getTruncateOrZeroExtend(getSCEV(C), Ty);
+}
+
+const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
+ Constant *C = ConstantExpr::getAlignOf(AllocTy);
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
+ C = ConstantFoldConstantExpression(CE, TD);
+ const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
+ return getTruncateOrZeroExtend(getSCEV(C), Ty);
+}
+
+const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
+ unsigned FieldNo) {
+ Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
+ C = ConstantFoldConstantExpression(CE, TD);
+ const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
+ return getTruncateOrZeroExtend(getSCEV(C), Ty);
+}
+
+const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
+ Constant *FieldNo) {
+ Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
+ if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
+ C = ConstantFoldConstantExpression(CE, TD);
+ const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
+ return getTruncateOrZeroExtend(getSCEV(C), Ty);
+}
+
+const SCEV *ScalarEvolution::getUnknown(Value *V) {
+ // Don't attempt to do anything other than create a SCEVUnknown object
+ // here. createSCEV only calls getUnknown after checking for all other
+ // interesting possibilities, and any other code that calls getUnknown
+ // is doing so in order to hide a value from SCEV canonicalization.
+
+ FoldingSetNodeID ID;
+ ID.AddInteger(scUnknown);
+ ID.AddPointer(V);
+ void *IP = 0;
+ if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
+ SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
+ new (S) SCEVUnknown(ID, V);
+ UniqueSCEVs.InsertNode(S, IP);
+ return S;
+}
+
+//===----------------------------------------------------------------------===//
+// Basic SCEV Analysis and PHI Idiom Recognition Code
+//
+
+/// isSCEVable - Test if values of the given type are analyzable within
+/// the SCEV framework. This primarily includes integer types, and it
+/// can optionally include pointer types if the ScalarEvolution class
+/// has access to target-specific information.
+bool ScalarEvolution::isSCEVable(const Type *Ty) const {
+ // Integers and pointers are always SCEVable.
+ return Ty->isInteger() || isa<PointerType>(Ty);
+}
+
+/// getTypeSizeInBits - Return the size in bits of the specified type,
+/// for which isSCEVable must return true.
+uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
+ assert(isSCEVable(Ty) && "Type is not SCEVable!");
+
+ // If we have a TargetData, use it!
+ if (TD)
+ return TD->getTypeSizeInBits(Ty);
+
+ // Integer types have fixed sizes.
+ if (Ty->isInteger())
+ return Ty->getPrimitiveSizeInBits();
+
+ // The only other support type is pointer. Without TargetData, conservatively
+ // assume pointers are 64-bit.
+ assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!");
+ return 64;
+}
+
+/// getEffectiveSCEVType - Return a type with the same bitwidth as
+/// the given type and which represents how SCEV will treat the given
+/// type, for which isSCEVable must return true. For pointer types,
+/// this is the pointer-sized integer type.
+const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
+ assert(isSCEVable(Ty) && "Type is not SCEVable!");
+
+ if (Ty->isInteger())
+ return Ty;
+
+ // The only other support type is pointer.
+ assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
+ if (TD) return TD->getIntPtrType(getContext());
+
+ // Without TargetData, conservatively assume pointers are 64-bit.
+ return Type::getInt64Ty(getContext());
+}
+
+const SCEV *ScalarEvolution::getCouldNotCompute() {
+ return &CouldNotCompute;
+}
+
+/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
+/// expression and create a new one.
+const SCEV *ScalarEvolution::getSCEV(Value *V) {
+ assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
+
+ std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
+ if (I != Scalars.end()) return I->second;
+ const SCEV *S = createSCEV(V);
+ Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
+ return S;
+}
+
+/// getIntegerSCEV - Given a SCEVable type, create a constant for the
+/// specified signed integer value and return a SCEV for the constant.
+const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
+ const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
+ return getConstant(ConstantInt::get(ITy, Val));
+}
+
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
+
+ const Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ return getMulExpr(V,
+ getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
+}
+
+/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getConstant(
+ cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
+
+ const Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ const SCEV *AllOnes =
+ getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
+ return getMinusSCEV(AllOnes, V);
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
+ const SCEV *RHS) {
+ // X - Y --> X + -Y
+ return getAddExpr(LHS, getNegativeSCEV(RHS));
+}
+
+/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. If the type must be extended, it is zero
+/// extended.
+const SCEV *
+ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
+ const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot truncate or zero extend with non-integer arguments!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
+ return getTruncateExpr(V, Ty);
+ return getZeroExtendExpr(V, Ty);
+}
+
+/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. If the type must be extended, it is sign
+/// extended.
+const SCEV *
+ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
+ const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot truncate or zero extend with non-integer arguments!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
+ return getTruncateExpr(V, Ty);
+ return getSignExtendExpr(V, Ty);
+}
+
+/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. If the type must be extended, it is zero
+/// extended. The conversion must not be narrowing.
+const SCEV *
+ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot noop or zero extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrZeroExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getZeroExtendExpr(V, Ty);
+}
+
+/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. If the type must be extended, it is sign
+/// extended. The conversion must not be narrowing.
+const SCEV *
+ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot noop or sign extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrSignExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getSignExtendExpr(V, Ty);
+}
+
+/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
+/// the input value to the specified type. If the type must be extended,
+/// it is extended with unspecified bits. The conversion must not be
+/// narrowing.
+const SCEV *
+ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot noop or any extend with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
+ "getNoopOrAnyExtend cannot truncate!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getAnyExtendExpr(V, Ty);
+}
+
+/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. The conversion must not be widening.
+const SCEV *
+ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot truncate or noop with non-integer arguments!");
+ assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
+ "getTruncateOrNoop cannot extend!");
+ if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
+ return V; // No conversion
+ return getTruncateExpr(V, Ty);
+}
+
+/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
+/// the types using zero-extension, and then perform a umax operation
+/// with them.
+const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
+ const SCEV *RHS) {
+ const SCEV *PromotedLHS = LHS;
+ const SCEV *PromotedRHS = RHS;
+
+ if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
+ PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
+ else
+ PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
+
+ return getUMaxExpr(PromotedLHS, PromotedRHS);
+}
+
+/// getUMinFromMismatchedTypes - Promote the operands to the wider of
+/// the types using zero-extension, and then perform a umin operation
+/// with them.
+const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
+ const SCEV *RHS) {
+ const SCEV *PromotedLHS = LHS;
+ const SCEV *PromotedRHS = RHS;
+
+ if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
+ PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
+ else
+ PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
+
+ return getUMinExpr(PromotedLHS, PromotedRHS);
+}
+
+/// PushDefUseChildren - Push users of the given Instruction
+/// onto the given Worklist.
+static void
+PushDefUseChildren(Instruction *I,
+ SmallVectorImpl<Instruction *> &Worklist) {
+ // Push the def-use children onto the Worklist stack.
+ for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
+ UI != UE; ++UI)
+ Worklist.push_back(cast<Instruction>(UI));
+}
+
+/// ForgetSymbolicValue - This looks up computed SCEV values for all
+/// instructions that depend on the given instruction and removes them from
+/// the Scalars map if they reference SymName. This is used during PHI
+/// resolution.
+void
+ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
+ SmallVector<Instruction *, 16> Worklist;
+ PushDefUseChildren(I, Worklist);
+
+ SmallPtrSet<Instruction *, 8> Visited;
+ Visited.insert(I);
+ while (!Worklist.empty()) {
+ Instruction *I = Worklist.pop_back_val();
+ if (!Visited.insert(I)) continue;
+
+ std::map<SCEVCallbackVH, const SCEV *>::iterator It =
+ Scalars.find(static_cast<Value *>(I));
+ if (It != Scalars.end()) {
+ // Short-circuit the def-use traversal if the symbolic name
+ // ceases to appear in expressions.
+ if (!It->second->hasOperand(SymName))
+ continue;
+
+ // SCEVUnknown for a PHI either means that it has an unrecognized
+ // structure, or it's a PHI that's in the progress of being computed
+ // by createNodeForPHI. In the former case, additional loop trip
+ // count information isn't going to change anything. In the later
+ // case, createNodeForPHI will perform the necessary updates on its
+ // own when it gets to that point.
+ if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
+ ValuesAtScopes.erase(It->second);
+ Scalars.erase(It);
+ }
+ }
+
+ PushDefUseChildren(I, Worklist);
+ }
+}
+
+/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
+/// a loop header, making it a potential recurrence, or it doesn't.
+///
+const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
+ if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
+ if (const Loop *L = LI->getLoopFor(PN->getParent()))
+ if (L->getHeader() == PN->getParent()) {
+ // If it lives in the loop header, it has two incoming values, one
+ // from outside the loop, and one from inside.
+ unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
+ unsigned BackEdge = IncomingEdge^1;
+
+ // While we are analyzing this PHI node, handle its value symbolically.
+ const SCEV *SymbolicName = getUnknown(PN);
+ assert(Scalars.find(PN) == Scalars.end() &&
+ "PHI node already processed?");
+ Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
+
+ // Using this symbolic name for the PHI, analyze the value coming around
+ // the back-edge.
+ Value *BEValueV = PN->getIncomingValue(BackEdge);
+ const SCEV *BEValue = getSCEV(BEValueV);
+
+ // NOTE: If BEValue is loop invariant, we know that the PHI node just
+ // has a special value for the first iteration of the loop.
+
+ // If the value coming around the backedge is an add with the symbolic
+ // value we just inserted, then we found a simple induction variable!
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
+ // If there is a single occurrence of the symbolic value, replace it
+ // with a recurrence.
+ unsigned FoundIndex = Add->getNumOperands();
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (Add->getOperand(i) == SymbolicName)
+ if (FoundIndex == e) {
+ FoundIndex = i;
+ break;
+ }
+
+ if (FoundIndex != Add->getNumOperands()) {
+ // Create an add with everything but the specified operand.
+ SmallVector<const SCEV *, 8> Ops;
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (i != FoundIndex)
+ Ops.push_back(Add->getOperand(i));
+ const SCEV *Accum = getAddExpr(Ops);
+
+ // This is not a valid addrec if the step amount is varying each
+ // loop iteration, but is not itself an addrec in this loop.
+ if (Accum->isLoopInvariant(L) ||
+ (isa<SCEVAddRecExpr>(Accum) &&
+ cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
+ bool HasNUW = false;
+ bool HasNSW = false;
+
+ // If the increment doesn't overflow, then neither the addrec nor
+ // the post-increment will overflow.
+ if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
+ if (OBO->hasNoUnsignedWrap())
+ HasNUW = true;
+ if (OBO->hasNoSignedWrap())
+ HasNSW = true;
+ }
+
+ const SCEV *StartVal =
+ getSCEV(PN->getIncomingValue(IncomingEdge));
+ const SCEV *PHISCEV =
+ getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
+
+ // Since the no-wrap flags are on the increment, they apply to the
+ // post-incremented value as well.
+ if (Accum->isLoopInvariant(L))
+ (void)getAddRecExpr(getAddExpr(StartVal, Accum),
+ Accum, L, HasNUW, HasNSW);
+
+ // Okay, for the entire analysis of this edge we assumed the PHI
+ // to be symbolic. We now need to go back and purge all of the
+ // entries for the scalars that use the symbolic expression.
+ ForgetSymbolicName(PN, SymbolicName);
+ Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
+ return PHISCEV;
+ }
+ }
+ } else if (const SCEVAddRecExpr *AddRec =
+ dyn_cast<SCEVAddRecExpr>(BEValue)) {
+ // Otherwise, this could be a loop like this:
+ // i = 0; for (j = 1; ..; ++j) { .... i = j; }
+ // In this case, j = {1,+,1} and BEValue is j.
+ // Because the other in-value of i (0) fits the evolution of BEValue
+ // i really is an addrec evolution.
+ if (AddRec->getLoop() == L && AddRec->isAffine()) {
+ const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
+
+ // If StartVal = j.start - j.stride, we can use StartVal as the
+ // initial step of the addrec evolution.
+ if (StartVal == getMinusSCEV(AddRec->getOperand(0),
+ AddRec->getOperand(1))) {
+ const SCEV *PHISCEV =
+ getAddRecExpr(StartVal, AddRec->getOperand(1), L);
+
+ // Okay, for the entire analysis of this edge we assumed the PHI
+ // to be symbolic. We now need to go back and purge all of the
+ // entries for the scalars that use the symbolic expression.
+ ForgetSymbolicName(PN, SymbolicName);
+ Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
+ return PHISCEV;
+ }
+ }
+ }
+
+ return SymbolicName;
+ }
+
+ // It's tempting to recognize PHIs with a unique incoming value, however
+ // this leads passes like indvars to break LCSSA form. Fortunately, such
+ // PHIs are rare, as instcombine zaps them.
+
+ // If it's not a loop phi, we can't handle it yet.
+ return getUnknown(PN);
+}
+
+/// createNodeForGEP - Expand GEP instructions into add and multiply
+/// operations. This allows them to be analyzed by regular SCEV code.
+///
+const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
+
+ bool InBounds = GEP->isInBounds();
+ const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
+ Value *Base = GEP->getOperand(0);
+ // Don't attempt to analyze GEPs over unsized objects.
+ if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
+ return getUnknown(GEP);
+ const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
+ gep_type_iterator GTI = gep_type_begin(GEP);
+ for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
+ E = GEP->op_end();
+ I != E; ++I) {
+ Value *Index = *I;
+ // Compute the (potentially symbolic) offset in bytes for this index.
+ if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
+ // For a struct, add the member offset.
+ unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
+ TotalOffset = getAddExpr(TotalOffset,
+ getOffsetOfExpr(STy, FieldNo),
+ /*HasNUW=*/false, /*HasNSW=*/InBounds);
+ } else {
+ // For an array, add the element offset, explicitly scaled.
+ const SCEV *LocalOffset = getSCEV(Index);
+ // Getelementptr indicies are signed.
+ LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
+ // Lower "inbounds" GEPs to NSW arithmetic.
+ LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
+ /*HasNUW=*/false, /*HasNSW=*/InBounds);
+ TotalOffset = getAddExpr(TotalOffset, LocalOffset,
+ /*HasNUW=*/false, /*HasNSW=*/InBounds);
+ }
+ }
+ return getAddExpr(getSCEV(Base), TotalOffset,
+ /*HasNUW=*/false, /*HasNSW=*/InBounds);
+}
+
+/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
+/// guaranteed to end in (at every loop iteration). It is, at the same time,
+/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
+/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
+uint32_t
+ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return C->getValue()->getValue().countTrailingZeros();
+
+ if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
+ return std::min(GetMinTrailingZeros(T->getOperand()),
+ (uint32_t)getTypeSizeInBits(T->getType()));
+
+ if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
+ return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
+ getTypeSizeInBits(E->getType()) : OpRes;
+ }
+
+ if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
+ return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
+ getTypeSizeInBits(E->getType()) : OpRes;
+ }
+
+ if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
+ return MinOpRes;
+ }
+
+ if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
+ // The result is the sum of all operands results.
+ uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
+ uint32_t BitWidth = getTypeSizeInBits(M->getType());
+ for (unsigned i = 1, e = M->getNumOperands();
+ SumOpRes != BitWidth && i != e; ++i)
+ SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
+ BitWidth);
+ return SumOpRes;
+ }
+
+ if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
+ return MinOpRes;
+ }
+
+ if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
+ return MinOpRes;
+ }
+
+ if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
+ return MinOpRes;
+ }
+
+ if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
+ // For a SCEVUnknown, ask ValueTracking.
+ unsigned BitWidth = getTypeSizeInBits(U->getType());
+ APInt Mask = APInt::getAllOnesValue(BitWidth);
+ APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
+ ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
+ return Zeros.countTrailingOnes();
+ }
+
+ // SCEVUDivExpr
+ return 0;
+}
+
+/// getUnsignedRange - Determine the unsigned range for a particular SCEV.
+///
+ConstantRange
+ScalarEvolution::getUnsignedRange(const SCEV *S) {
+
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return ConstantRange(C->getValue()->getValue());
+
+ unsigned BitWidth = getTypeSizeInBits(S->getType());
+ ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
+
+ // If the value has known zeros, the maximum unsigned value will have those
+ // known zeros as well.
+ uint32_t TZ = GetMinTrailingZeros(S);
+ if (TZ != 0)
+ ConservativeResult =
+ ConstantRange(APInt::getMinValue(BitWidth),
+ APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
+
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
+ ConstantRange X = getUnsignedRange(Add->getOperand(0));
+ for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
+ X = X.add(getUnsignedRange(Add->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
+ ConstantRange X = getUnsignedRange(Mul->getOperand(0));
+ for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
+ X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
+ ConstantRange X = getUnsignedRange(SMax->getOperand(0));
+ for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
+ X = X.smax(getUnsignedRange(SMax->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
+ ConstantRange X = getUnsignedRange(UMax->getOperand(0));
+ for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
+ X = X.umax(getUnsignedRange(UMax->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
+ ConstantRange X = getUnsignedRange(UDiv->getLHS());
+ ConstantRange Y = getUnsignedRange(UDiv->getRHS());
+ return ConservativeResult.intersectWith(X.udiv(Y));
+ }
+
+ if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
+ ConstantRange X = getUnsignedRange(ZExt->getOperand());
+ return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
+ }
+
+ if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
+ ConstantRange X = getUnsignedRange(SExt->getOperand());
+ return ConservativeResult.intersectWith(X.signExtend(BitWidth));
+ }
+
+ if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
+ ConstantRange X = getUnsignedRange(Trunc->getOperand());
+ return ConservativeResult.intersectWith(X.truncate(BitWidth));
+ }
+
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
+ // If there's no unsigned wrap, the value will never be less than its
+ // initial value.
+ if (AddRec->hasNoUnsignedWrap())
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
+ ConservativeResult =
+ ConstantRange(C->getValue()->getValue(),
+ APInt(getTypeSizeInBits(C->getType()), 0));
+
+ // TODO: non-affine addrec
+ if (AddRec->isAffine()) {
+ const Type *Ty = AddRec->getType();
+ const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
+ if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
+ getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
+ MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
+
+ const SCEV *Start = AddRec->getStart();
+ const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
+
+ // Check for overflow.
+ if (!AddRec->hasNoUnsignedWrap())
+ return ConservativeResult;
+
+ ConstantRange StartRange = getUnsignedRange(Start);
+ ConstantRange EndRange = getUnsignedRange(End);
+ APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
+ EndRange.getUnsignedMin());
+ APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
+ EndRange.getUnsignedMax());
+ if (Min.isMinValue() && Max.isMaxValue())
+ return ConservativeResult;
+ return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
+ }
+ }
+
+ return ConservativeResult;
+ }
+
+ if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
+ // For a SCEVUnknown, ask ValueTracking.
+ unsigned BitWidth = getTypeSizeInBits(U->getType());
+ APInt Mask = APInt::getAllOnesValue(BitWidth);
+ APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
+ ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
+ if (Ones == ~Zeros + 1)
+ return ConservativeResult;
+ return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
+ }
+
+ return ConservativeResult;
+}
+
+/// getSignedRange - Determine the signed range for a particular SCEV.
+///
+ConstantRange
+ScalarEvolution::getSignedRange(const SCEV *S) {
+
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return ConstantRange(C->getValue()->getValue());
+
+ unsigned BitWidth = getTypeSizeInBits(S->getType());
+ ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
+
+ // If the value has known zeros, the maximum signed value will have those
+ // known zeros as well.
+ uint32_t TZ = GetMinTrailingZeros(S);
+ if (TZ != 0)
+ ConservativeResult =
+ ConstantRange(APInt::getSignedMinValue(BitWidth),
+ APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
+
+ if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
+ ConstantRange X = getSignedRange(Add->getOperand(0));
+ for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
+ X = X.add(getSignedRange(Add->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
+ ConstantRange X = getSignedRange(Mul->getOperand(0));
+ for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
+ X = X.multiply(getSignedRange(Mul->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
+ ConstantRange X = getSignedRange(SMax->getOperand(0));
+ for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
+ X = X.smax(getSignedRange(SMax->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
+ ConstantRange X = getSignedRange(UMax->getOperand(0));
+ for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
+ X = X.umax(getSignedRange(UMax->getOperand(i)));
+ return ConservativeResult.intersectWith(X);
+ }
+
+ if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
+ ConstantRange X = getSignedRange(UDiv->getLHS());
+ ConstantRange Y = getSignedRange(UDiv->getRHS());
+ return ConservativeResult.intersectWith(X.udiv(Y));
+ }
+
+ if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
+ ConstantRange X = getSignedRange(ZExt->getOperand());
+ return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
+ }
+
+ if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
+ ConstantRange X = getSignedRange(SExt->getOperand());
+ return ConservativeResult.intersectWith(X.signExtend(BitWidth));
+ }
+
+ if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
+ ConstantRange X = getSignedRange(Trunc->getOperand());
+ return ConservativeResult.intersectWith(X.truncate(BitWidth));
+ }
+
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
+ // If there's no signed wrap, and all the operands have the same sign or
+ // zero, the value won't ever change sign.
+ if (AddRec->hasNoSignedWrap()) {
+ bool AllNonNeg = true;
+ bool AllNonPos = true;
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
+ if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
+ if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
+ }
+ if (AllNonNeg)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange(APInt(BitWidth, 0),
+ APInt::getSignedMinValue(BitWidth)));
+ else if (AllNonPos)
+ ConservativeResult = ConservativeResult.intersectWith(
+ ConstantRange(APInt::getSignedMinValue(BitWidth),
+ APInt(BitWidth, 1)));
+ }
+
+ // TODO: non-affine addrec
+ if (AddRec->isAffine()) {
+ const Type *Ty = AddRec->getType();
+ const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
+ if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
+ getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
+ MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
+
+ const SCEV *Start = AddRec->getStart();
+ const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
+
+ // Check for overflow.
+ if (!AddRec->hasNoSignedWrap())
+ return ConservativeResult;
+
+ ConstantRange StartRange = getSignedRange(Start);
+ ConstantRange EndRange = getSignedRange(End);
+ APInt Min = APIntOps::smin(StartRange.getSignedMin(),
+ EndRange.getSignedMin());
+ APInt Max = APIntOps::smax(StartRange.getSignedMax(),
+ EndRange.getSignedMax());
+ if (Min.isMinSignedValue() && Max.isMaxSignedValue())
+ return ConservativeResult;
+ return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
+ }
+ }
+
+ return ConservativeResult;
+ }
+
+ if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
+ // For a SCEVUnknown, ask ValueTracking.
+ if (!U->getValue()->getType()->isInteger() && !TD)
+ return ConservativeResult;
+ unsigned NS = ComputeNumSignBits(U->getValue(), TD);
+ if (NS == 1)
+ return ConservativeResult;
+ return ConservativeResult.intersectWith(
+ ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
+ APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
+ }
+
+ return ConservativeResult;
+}
+
+/// createSCEV - We know that there is no SCEV for the specified value.
+/// Analyze the expression.
+///
+const SCEV *ScalarEvolution::createSCEV(Value *V) {
+ if (!isSCEVable(V->getType()))
+ return getUnknown(V);
+
+ unsigned Opcode = Instruction::UserOp1;
+ if (Instruction *I = dyn_cast<Instruction>(V))
+ Opcode = I->getOpcode();
+ else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
+ Opcode = CE->getOpcode();
+ else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
+ return getConstant(CI);
+ else if (isa<ConstantPointerNull>(V))
+ return getIntegerSCEV(0, V->getType());
+ else if (isa<UndefValue>(V))
+ return getIntegerSCEV(0, V->getType());
+ else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
+ return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
+ else
+ return getUnknown(V);
+
+ Operator *U = cast<Operator>(V);
+ switch (Opcode) {
+ case Instruction::Add:
+ // Don't transfer the NSW and NUW bits from the Add instruction to the
+ // Add expression, because the Instruction may be guarded by control
+ // flow and the no-overflow bits may not be valid for the expression in
+ // any context.
+ return getAddExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::Mul:
+ // Don't transfer the NSW and NUW bits from the Mul instruction to the
+ // Mul expression, as with Add.
+ return getMulExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::UDiv:
+ return getUDivExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::Sub:
+ return getMinusSCEV(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::And:
+ // For an expression like x&255 that merely masks off the high bits,
+ // use zext(trunc(x)) as the SCEV expression.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
+ if (CI->isNullValue())
+ return getSCEV(U->getOperand(1));
+ if (CI->isAllOnesValue())
+ return getSCEV(U->getOperand(0));
+ const APInt &A = CI->getValue();
+
+ // Instcombine's ShrinkDemandedConstant may strip bits out of
+ // constants, obscuring what would otherwise be a low-bits mask.
+ // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
+ // knew about to reconstruct a low-bits mask value.
+ unsigned LZ = A.countLeadingZeros();
+ unsigned BitWidth = A.getBitWidth();
+ APInt AllOnes = APInt::getAllOnesValue(BitWidth);
+ APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
+ ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
+
+ APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
+
+ if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
+ return
+ getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
+ IntegerType::get(getContext(), BitWidth - LZ)),
+ U->getType());
+ }
+ break;
+
+ case Instruction::Or:
+ // If the RHS of the Or is a constant, we may have something like:
+ // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
+ // optimizations will transparently handle this case.
+ //
+ // In order for this transformation to be safe, the LHS must be of the
+ // form X*(2^n) and the Or constant must be less than 2^n.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
+ const SCEV *LHS = getSCEV(U->getOperand(0));
+ const APInt &CIVal = CI->getValue();
+ if (GetMinTrailingZeros(LHS) >=
+ (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
+ // Build a plain add SCEV.
+ const SCEV *S = getAddExpr(LHS, getSCEV(CI));
+ // If the LHS of the add was an addrec and it has no-wrap flags,
+ // transfer the no-wrap flags, since an or won't introduce a wrap.
+ if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
+ const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
+ if (OldAR->hasNoUnsignedWrap())
+ const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
+ if (OldAR->hasNoSignedWrap())
+ const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
+ }
+ return S;
+ }
+ }
+ break;
+ case Instruction::Xor:
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
+ // If the RHS of the xor is a signbit, then this is just an add.
+ // Instcombine turns add of signbit into xor as a strength reduction step.
+ if (CI->getValue().isSignBit())
+ return getAddExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+
+ // If the RHS of xor is -1, then this is a not operation.
+ if (CI->isAllOnesValue())
+ return getNotSCEV(getSCEV(U->getOperand(0)));
+
+ // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
+ // This is a variant of the check for xor with -1, and it handles
+ // the case where instcombine has trimmed non-demanded bits out
+ // of an xor with -1.
+ if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
+ if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
+ if (BO->getOpcode() == Instruction::And &&
+ LCI->getValue() == CI->getValue())
+ if (const SCEVZeroExtendExpr *Z =
+ dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
+ const Type *UTy = U->getType();
+ const SCEV *Z0 = Z->getOperand();
+ const Type *Z0Ty = Z0->getType();
+ unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
+
+ // If C is a low-bits mask, the zero extend is zerving to
+ // mask off the high bits. Complement the operand and
+ // re-apply the zext.
+ if (APIntOps::isMask(Z0TySize, CI->getValue()))
+ return getZeroExtendExpr(getNotSCEV(Z0), UTy);
+
+ // If C is a single bit, it may be in the sign-bit position
+ // before the zero-extend. In this case, represent the xor
+ // using an add, which is equivalent, and re-apply the zext.
+ APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
+ if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
+ Trunc.isSignBit())
+ return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
+ UTy);
+ }
+ }
+ break;
+
+ case Instruction::Shl:
+ // Turn shift left of a constant amount into a multiply.
+ if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
+ uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
+ Constant *X = ConstantInt::get(getContext(),
+ APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
+ return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
+ }
+ break;
+
+ case Instruction::LShr:
+ // Turn logical shift right of a constant into a unsigned divide.
+ if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
+ uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
+ Constant *X = ConstantInt::get(getContext(),
+ APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
+ return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
+ }
+ break;
+
+ case Instruction::AShr:
+ // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
+ if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
+ if (L->getOpcode() == Instruction::Shl &&
+ L->getOperand(1) == U->getOperand(1)) {
+ unsigned BitWidth = getTypeSizeInBits(U->getType());
+ uint64_t Amt = BitWidth - CI->getZExtValue();
+ if (Amt == BitWidth)
+ return getSCEV(L->getOperand(0)); // shift by zero --> noop
+ if (Amt > BitWidth)
+ return getIntegerSCEV(0, U->getType()); // value is undefined
+ return
+ getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
+ IntegerType::get(getContext(), Amt)),
+ U->getType());
+ }
+ break;
+
+ case Instruction::Trunc:
+ return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::ZExt:
+ return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::SExt:
+ return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
+
+ case Instruction::BitCast:
+ // BitCasts are no-op casts so we just eliminate the cast.
+ if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
+ return getSCEV(U->getOperand(0));
+ break;
+
+ // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
+ // lead to pointer expressions which cannot safely be expanded to GEPs,
+ // because ScalarEvolution doesn't respect the GEP aliasing rules when
+ // simplifying integer expressions.
+
+ case Instruction::GetElementPtr:
+ return createNodeForGEP(cast<GEPOperator>(U));
+
+ case Instruction::PHI:
+ return createNodeForPHI(cast<PHINode>(U));
+
+ case Instruction::Select:
+ // This could be a smax or umax that was lowered earlier.
+ // Try to recover it.
+ if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
+ Value *LHS = ICI->getOperand(0);
+ Value *RHS = ICI->getOperand(1);
+ switch (ICI->getPredicate()) {
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_SLE:
+ std::swap(LHS, RHS);
+ // fall through
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_SGE:
+ if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
+ return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
+ else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
+ return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
+ break;
+ case ICmpInst::ICMP_ULT:
+ case ICmpInst::ICMP_ULE:
+ std::swap(LHS, RHS);
+ // fall through
+ case ICmpInst::ICMP_UGT:
+ case ICmpInst::ICMP_UGE:
+ if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
+ return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
+ else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
+ return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
+ break;
+ case ICmpInst::ICMP_NE:
+ // n != 0 ? n : 1 -> umax(n, 1)
+ if (LHS == U->getOperand(1) &&
+ isa<ConstantInt>(U->getOperand(2)) &&
+ cast<ConstantInt>(U->getOperand(2))->isOne() &&
+ isa<ConstantInt>(RHS) &&
+ cast<ConstantInt>(RHS)->isZero())
+ return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
+ break;
+ case ICmpInst::ICMP_EQ:
+ // n == 0 ? 1 : n -> umax(n, 1)
+ if (LHS == U->getOperand(2) &&
+ isa<ConstantInt>(U->getOperand(1)) &&
+ cast<ConstantInt>(U->getOperand(1))->isOne() &&
+ isa<ConstantInt>(RHS) &&
+ cast<ConstantInt>(RHS)->isZero())
+ return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
+ break;
+ default:
+ break;
+ }
+ }
+
+ default: // We cannot analyze this expression.
+ break;
+ }
+
+ return getUnknown(V);
+}
+
+
+
+//===----------------------------------------------------------------------===//
+// Iteration Count Computation Code
+//
+
+/// getBackedgeTakenCount - If the specified loop has a predictable
+/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
+/// object. The backedge-taken count is the number of times the loop header
+/// will be branched to from within the loop. This is one less than the
+/// trip count of the loop, since it doesn't count the first iteration,
+/// when the header is branched to from outside the loop.
+///
+/// Note that it is not valid to call this method on a loop without a
+/// loop-invariant backedge-taken count (see
+/// hasLoopInvariantBackedgeTakenCount).
+///
+const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
+ return getBackedgeTakenInfo(L).Exact;
+}
+
+/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
+/// return the least SCEV value that is known never to be less than the
+/// actual backedge taken count.
+const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
+ return getBackedgeTakenInfo(L).Max;
+}
+
+/// PushLoopPHIs - Push PHI nodes in the header of the given loop
+/// onto the given Worklist.
+static void
+PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
+ BasicBlock *Header = L->getHeader();
+
+ // Push all Loop-header PHIs onto the Worklist stack.
+ for (BasicBlock::iterator I = Header->begin();
+ PHINode *PN = dyn_cast<PHINode>(I); ++I)
+ Worklist.push_back(PN);
+}
+
+const ScalarEvolution::BackedgeTakenInfo &
+ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
+ // Initially insert a CouldNotCompute for this loop. If the insertion
+ // succeeds, procede to actually compute a backedge-taken count and
+ // update the value. The temporary CouldNotCompute value tells SCEV
+ // code elsewhere that it shouldn't attempt to request a new
+ // backedge-taken count, which could result in infinite recursion.
+ std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
+ BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
+ if (Pair.second) {
+ BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
+ if (BECount.Exact != getCouldNotCompute()) {
+ assert(BECount.Exact->isLoopInvariant(L) &&
+ BECount.Max->isLoopInvariant(L) &&
+ "Computed backedge-taken count isn't loop invariant for loop!");
+ ++NumTripCountsComputed;
+
+ // Update the value in the map.
+ Pair.first->second = BECount;
+ } else {
+ if (BECount.Max != getCouldNotCompute())
+ // Update the value in the map.
+ Pair.first->second = BECount;
+ if (isa<PHINode>(L->getHeader()->begin()))
+ // Only count loops that have phi nodes as not being computable.
+ ++NumTripCountsNotComputed;
+ }
+
+ // Now that we know more about the trip count for this loop, forget any
+ // existing SCEV values for PHI nodes in this loop since they are only
+ // conservative estimates made without the benefit of trip count
+ // information. This is similar to the code in forgetLoop, except that
+ // it handles SCEVUnknown PHI nodes specially.
+ if (BECount.hasAnyInfo()) {
+ SmallVector<Instruction *, 16> Worklist;
+ PushLoopPHIs(L, Worklist);
+
+ SmallPtrSet<Instruction *, 8> Visited;
+ while (!Worklist.empty()) {
+ Instruction *I = Worklist.pop_back_val();
+ if (!Visited.insert(I)) continue;
+
+ std::map<SCEVCallbackVH, const SCEV *>::iterator It =
+ Scalars.find(static_cast<Value *>(I));
+ if (It != Scalars.end()) {
+ // SCEVUnknown for a PHI either means that it has an unrecognized
+ // structure, or it's a PHI that's in the progress of being computed
+ // by createNodeForPHI. In the former case, additional loop trip
+ // count information isn't going to change anything. In the later
+ // case, createNodeForPHI will perform the necessary updates on its
+ // own when it gets to that point.
+ if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
+ ValuesAtScopes.erase(It->second);
+ Scalars.erase(It);
+ }
+ if (PHINode *PN = dyn_cast<PHINode>(I))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ }
+
+ PushDefUseChildren(I, Worklist);
+ }
+ }
+ }
+ return Pair.first->second;
+}
+
+/// forgetLoop - This method should be called by the client when it has
+/// changed a loop in a way that may effect ScalarEvolution's ability to
+/// compute a trip count, or if the loop is deleted.
+void ScalarEvolution::forgetLoop(const Loop *L) {
+ // Drop any stored trip count value.
+ BackedgeTakenCounts.erase(L);
+
+ // Drop information about expressions based on loop-header PHIs.
+ SmallVector<Instruction *, 16> Worklist;
+ PushLoopPHIs(L, Worklist);
+
+ SmallPtrSet<Instruction *, 8> Visited;
+ while (!Worklist.empty()) {
+ Instruction *I = Worklist.pop_back_val();
+ if (!Visited.insert(I)) continue;
+
+ std::map<SCEVCallbackVH, const SCEV *>::iterator It =
+ Scalars.find(static_cast<Value *>(I));
+ if (It != Scalars.end()) {
+ ValuesAtScopes.erase(It->second);
+ Scalars.erase(It);
+ if (PHINode *PN = dyn_cast<PHINode>(I))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ }
+
+ PushDefUseChildren(I, Worklist);
+ }
+}
+
+/// ComputeBackedgeTakenCount - Compute the number of times the backedge
+/// of the specified loop will execute.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
+ SmallVector<BasicBlock *, 8> ExitingBlocks;
+ L->getExitingBlocks(ExitingBlocks);
+
+ // Examine all exits and pick the most conservative values.
+ const SCEV *BECount = getCouldNotCompute();
+ const SCEV *MaxBECount = getCouldNotCompute();
+ bool CouldNotComputeBECount = false;
+ for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
+ BackedgeTakenInfo NewBTI =
+ ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
+
+ if (NewBTI.Exact == getCouldNotCompute()) {
+ // We couldn't compute an exact value for this exit, so
+ // we won't be able to compute an exact value for the loop.
+ CouldNotComputeBECount = true;
+ BECount = getCouldNotCompute();
+ } else if (!CouldNotComputeBECount) {
+ if (BECount == getCouldNotCompute())
+ BECount = NewBTI.Exact;
+ else
+ BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
+ }
+ if (MaxBECount == getCouldNotCompute())
+ MaxBECount = NewBTI.Max;
+ else if (NewBTI.Max != getCouldNotCompute())
+ MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
+ }
+
+ return BackedgeTakenInfo(BECount, MaxBECount);
+}
+
+/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
+/// of the specified loop will execute if it exits via the specified block.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
+ BasicBlock *ExitingBlock) {
+
+ // Okay, we've chosen an exiting block. See what condition causes us to
+ // exit at this block.
+ //
+ // FIXME: we should be able to handle switch instructions (with a single exit)
+ BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
+ if (ExitBr == 0) return getCouldNotCompute();
+ assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
+
+ // At this point, we know we have a conditional branch that determines whether
+ // the loop is exited. However, we don't know if the branch is executed each
+ // time through the loop. If not, then the execution count of the branch will
+ // not be equal to the trip count of the loop.
+ //
+ // Currently we check for this by checking to see if the Exit branch goes to
+ // the loop header. If so, we know it will always execute the same number of
+ // times as the loop. We also handle the case where the exit block *is* the
+ // loop header. This is common for un-rotated loops.
+ //
+ // If both of those tests fail, walk up the unique predecessor chain to the
+ // header, stopping if there is an edge that doesn't exit the loop. If the
+ // header is reached, the execution count of the branch will be equal to the
+ // trip count of the loop.
+ //
+ // More extensive analysis could be done to handle more cases here.
+ //
+ if (ExitBr->getSuccessor(0) != L->getHeader() &&
+ ExitBr->getSuccessor(1) != L->getHeader() &&
+ ExitBr->getParent() != L->getHeader()) {
+ // The simple checks failed, try climbing the unique predecessor chain
+ // up to the header.
+ bool Ok = false;
+ for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
+ BasicBlock *Pred = BB->getUniquePredecessor();
+ if (!Pred)
+ return getCouldNotCompute();
+ TerminatorInst *PredTerm = Pred->getTerminator();
+ for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
+ BasicBlock *PredSucc = PredTerm->getSuccessor(i);
+ if (PredSucc == BB)
+ continue;
+ // If the predecessor has a successor that isn't BB and isn't
+ // outside the loop, assume the worst.
+ if (L->contains(PredSucc))
+ return getCouldNotCompute();
+ }
+ if (Pred == L->getHeader()) {
+ Ok = true;
+ break;
+ }
+ BB = Pred;
+ }
+ if (!Ok)
+ return getCouldNotCompute();
+ }
+
+ // Procede to the next level to examine the exit condition expression.
+ return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
+ ExitBr->getSuccessor(0),
+ ExitBr->getSuccessor(1));
+}
+
+/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
+/// backedge of the specified loop will execute if its exit condition
+/// were a conditional branch of ExitCond, TBB, and FBB.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
+ Value *ExitCond,
+ BasicBlock *TBB,
+ BasicBlock *FBB) {
+ // Check if the controlling expression for this loop is an And or Or.
+ if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
+ if (BO->getOpcode() == Instruction::And) {
+ // Recurse on the operands of the and.
+ BackedgeTakenInfo BTI0 =
+ ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
+ BackedgeTakenInfo BTI1 =
+ ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
+ const SCEV *BECount = getCouldNotCompute();
+ const SCEV *MaxBECount = getCouldNotCompute();
+ if (L->contains(TBB)) {
+ // Both conditions must be true for the loop to continue executing.
+ // Choose the less conservative count.
+ if (BTI0.Exact == getCouldNotCompute() ||
+ BTI1.Exact == getCouldNotCompute())
+ BECount = getCouldNotCompute();
+ else
+ BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
+ if (BTI0.Max == getCouldNotCompute())
+ MaxBECount = BTI1.Max;
+ else if (BTI1.Max == getCouldNotCompute())
+ MaxBECount = BTI0.Max;
+ else
+ MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
+ } else {
+ // Both conditions must be true for the loop to exit.
+ assert(L->contains(FBB) && "Loop block has no successor in loop!");
+ if (BTI0.Exact != getCouldNotCompute() &&
+ BTI1.Exact != getCouldNotCompute())
+ BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
+ if (BTI0.Max != getCouldNotCompute() &&
+ BTI1.Max != getCouldNotCompute())
+ MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
+ }
+
+ return BackedgeTakenInfo(BECount, MaxBECount);
+ }
+ if (BO->getOpcode() == Instruction::Or) {
+ // Recurse on the operands of the or.
+ BackedgeTakenInfo BTI0 =
+ ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
+ BackedgeTakenInfo BTI1 =
+ ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
+ const SCEV *BECount = getCouldNotCompute();
+ const SCEV *MaxBECount = getCouldNotCompute();
+ if (L->contains(FBB)) {
+ // Both conditions must be false for the loop to continue executing.
+ // Choose the less conservative count.
+ if (BTI0.Exact == getCouldNotCompute() ||
+ BTI1.Exact == getCouldNotCompute())
+ BECount = getCouldNotCompute();
+ else
+ BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
+ if (BTI0.Max == getCouldNotCompute())
+ MaxBECount = BTI1.Max;
+ else if (BTI1.Max == getCouldNotCompute())
+ MaxBECount = BTI0.Max;
+ else
+ MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
+ } else {
+ // Both conditions must be false for the loop to exit.
+ assert(L->contains(TBB) && "Loop block has no successor in loop!");
+ if (BTI0.Exact != getCouldNotCompute() &&
+ BTI1.Exact != getCouldNotCompute())
+ BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
+ if (BTI0.Max != getCouldNotCompute() &&
+ BTI1.Max != getCouldNotCompute())
+ MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
+ }
+
+ return BackedgeTakenInfo(BECount, MaxBECount);
+ }
+ }
+
+ // With an icmp, it may be feasible to compute an exact backedge-taken count.
+ // Procede to the next level to examine the icmp.
+ if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
+ return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
+
+ // If it's not an integer or pointer comparison then compute it the hard way.
+ return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
+}
+
+/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
+/// backedge of the specified loop will execute if its exit condition
+/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
+ ICmpInst *ExitCond,
+ BasicBlock *TBB,
+ BasicBlock *FBB) {
+
+ // If the condition was exit on true, convert the condition to exit on false
+ ICmpInst::Predicate Cond;
+ if (!L->contains(FBB))
+ Cond = ExitCond->getPredicate();
+ else
+ Cond = ExitCond->getInversePredicate();
+
+ // Handle common loops like: for (X = "string"; *X; ++X)
+ if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
+ if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
+ const SCEV *ItCnt =
+ ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
+ if (!isa<SCEVCouldNotCompute>(ItCnt)) {
+ unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
+ return BackedgeTakenInfo(ItCnt,
+ isa<SCEVConstant>(ItCnt) ? ItCnt :
+ getConstant(APInt::getMaxValue(BitWidth)-1));
+ }
+ }
+
+ const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
+ const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
+
+ // Try to evaluate any dependencies out of the loop.
+ LHS = getSCEVAtScope(LHS, L);
+ RHS = getSCEVAtScope(RHS, L);
+
+ // At this point, we would like to compute how many iterations of the
+ // loop the predicate will return true for these inputs.
+ if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
+ // If there is a loop-invariant, force it into the RHS.
+ std::swap(LHS, RHS);
+ Cond = ICmpInst::getSwappedPredicate(Cond);
+ }
+
+ // If we have a comparison of a chrec against a constant, try to use value
+ // ranges to answer this query.
+ if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
+ if (AddRec->getLoop() == L) {
+ // Form the constant range.
+ ConstantRange CompRange(
+ ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
+
+ const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
+ if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
+ }
+
+ switch (Cond) {
+ case ICmpInst::ICMP_NE: { // while (X != Y)
+ // Convert to: while (X-Y != 0)
+ const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_EQ: { // while (X == Y)
+ // Convert to: while (X-Y == 0)
+ const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_SLT: {
+ BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
+ if (BTI.hasAnyInfo()) return BTI;
+ break;
+ }
+ case ICmpInst::ICMP_SGT: {
+ BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
+ getNotSCEV(RHS), L, true);
+ if (BTI.hasAnyInfo()) return BTI;
+ break;
+ }
+ case ICmpInst::ICMP_ULT: {
+ BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
+ if (BTI.hasAnyInfo()) return BTI;
+ break;
+ }
+ case ICmpInst::ICMP_UGT: {
+ BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
+ getNotSCEV(RHS), L, false);
+ if (BTI.hasAnyInfo()) return BTI;
+ break;
+ }
+ default:
+#if 0
+ dbgs() << "ComputeBackedgeTakenCount ";
+ if (ExitCond->getOperand(0)->getType()->isUnsigned())
+ dbgs() << "[unsigned] ";
+ dbgs() << *LHS << " "
+ << Instruction::getOpcodeName(Instruction::ICmp)
+ << " " << *RHS << "\n";
+#endif
+ break;
+ }
+ return
+ ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
+}
+
+static ConstantInt *
+EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
+ ScalarEvolution &SE) {
+ const SCEV *InVal = SE.getConstant(C);
+ const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
+ assert(isa<SCEVConstant>(Val) &&
+ "Evaluation of SCEV at constant didn't fold correctly?");
+ return cast<SCEVConstant>(Val)->getValue();
+}
+
+/// GetAddressedElementFromGlobal - Given a global variable with an initializer
+/// and a GEP expression (missing the pointer index) indexing into it, return
+/// the addressed element of the initializer or null if the index expression is
+/// invalid.
+static Constant *
+GetAddressedElementFromGlobal(GlobalVariable *GV,
+ const std::vector<ConstantInt*> &Indices) {
+ Constant *Init = GV->getInitializer();
+ for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
+ uint64_t Idx = Indices[i]->getZExtValue();
+ if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
+ assert(Idx < CS->getNumOperands() && "Bad struct index!");
+ Init = cast<Constant>(CS->getOperand(Idx));
+ } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
+ if (Idx >= CA->getNumOperands()) return 0; // Bogus program
+ Init = cast<Constant>(CA->getOperand(Idx));
+ } else if (isa<ConstantAggregateZero>(Init)) {
+ if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
+ assert(Idx < STy->getNumElements() && "Bad struct index!");
+ Init = Constant::getNullValue(STy->getElementType(Idx));
+ } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
+ if (Idx >= ATy->getNumElements()) return 0; // Bogus program
+ Init = Constant::getNullValue(ATy->getElementType());
+ } else {
+ llvm_unreachable("Unknown constant aggregate type!");
+ }
+ return 0;
+ } else {
+ return 0; // Unknown initializer type
+ }
+ }
+ return Init;
+}
+
+/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
+/// 'icmp op load X, cst', try to see if we can compute the backedge
+/// execution count.
+const SCEV *
+ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
+ LoadInst *LI,
+ Constant *RHS,
+ const Loop *L,
+ ICmpInst::Predicate predicate) {
+ if (LI->isVolatile()) return getCouldNotCompute();
+
+ // Check to see if the loaded pointer is a getelementptr of a global.
+ GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
+ if (!GEP) return getCouldNotCompute();
+
+ // Make sure that it is really a constant global we are gepping, with an
+ // initializer, and make sure the first IDX is really 0.
+ GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
+ if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
+ GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
+ !cast<Constant>(GEP->getOperand(1))->isNullValue())
+ return getCouldNotCompute();
+
+ // Okay, we allow one non-constant index into the GEP instruction.
+ Value *VarIdx = 0;
+ std::vector<ConstantInt*> Indexes;
+ unsigned VarIdxNum = 0;
+ for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
+ Indexes.push_back(CI);
+ } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
+ if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
+ VarIdx = GEP->getOperand(i);
+ VarIdxNum = i-2;
+ Indexes.push_back(0);
+ }
+
+ // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
+ // Check to see if X is a loop variant variable value now.
+ const SCEV *Idx = getSCEV(VarIdx);
+ Idx = getSCEVAtScope(Idx, L);
+
+ // We can only recognize very limited forms of loop index expressions, in
+ // particular, only affine AddRec's like {C1,+,C2}.
+ const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
+ if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
+ !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
+ !isa<SCEVConstant>(IdxExpr->getOperand(1)))
+ return getCouldNotCompute();
+
+ unsigned MaxSteps = MaxBruteForceIterations;
+ for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
+ ConstantInt *ItCst = ConstantInt::get(
+ cast<IntegerType>(IdxExpr->getType()), IterationNum);
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
+
+ // Form the GEP offset.
+ Indexes[VarIdxNum] = Val;
+
+ Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
+ if (Result == 0) break; // Cannot compute!
+
+ // Evaluate the condition for this iteration.
+ Result = ConstantExpr::getICmp(predicate, Result, RHS);
+ if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
+ if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
+#if 0
+ dbgs() << "\n***\n*** Computed loop count " << *ItCst
+ << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
+ << "***\n";
+#endif
+ ++NumArrayLenItCounts;
+ return getConstant(ItCst); // Found terminating iteration!
+ }
+ }
+ return getCouldNotCompute();
+}
+
+
+/// CanConstantFold - Return true if we can constant fold an instruction of the
+/// specified type, assuming that all operands were constants.
+static bool CanConstantFold(const Instruction *I) {
+ if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
+ isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
+ return true;
+
+ if (const CallInst *CI = dyn_cast<CallInst>(I))
+ if (const Function *F = CI->getCalledFunction())
+ return canConstantFoldCallTo(F);
+ return false;
+}
+
+/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
+/// in the loop that V is derived from. We allow arbitrary operations along the
+/// way, but the operands of an operation must either be constants or a value
+/// derived from a constant PHI. If this expression does not fit with these
+/// constraints, return null.
+static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
+ // If this is not an instruction, or if this is an instruction outside of the
+ // loop, it can't be derived from a loop PHI.
+ Instruction *I = dyn_cast<Instruction>(V);
+ if (I == 0 || !L->contains(I)) return 0;
+
+ if (PHINode *PN = dyn_cast<PHINode>(I)) {
+ if (L->getHeader() == I->getParent())
+ return PN;
+ else
+ // We don't currently keep track of the control flow needed to evaluate
+ // PHIs, so we cannot handle PHIs inside of loops.
+ return 0;
+ }
+
+ // If we won't be able to constant fold this expression even if the operands
+ // are constants, return early.
+ if (!CanConstantFold(I)) return 0;
+
+ // Otherwise, we can evaluate this instruction if all of its operands are
+ // constant or derived from a PHI node themselves.
+ PHINode *PHI = 0;
+ for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
+ if (!(isa<Constant>(I->getOperand(Op)) ||
+ isa<GlobalValue>(I->getOperand(Op)))) {
+ PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
+ if (P == 0) return 0; // Not evolving from PHI
+ if (PHI == 0)
+ PHI = P;
+ else if (PHI != P)
+ return 0; // Evolving from multiple different PHIs.
+ }
+
+ // This is a expression evolving from a constant PHI!
+ return PHI;
+}
+
+/// EvaluateExpression - Given an expression that passes the
+/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
+/// in the loop has the value PHIVal. If we can't fold this expression for some
+/// reason, return null.
+static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
+ const TargetData *TD) {
+ if (isa<PHINode>(V)) return PHIVal;
+ if (Constant *C = dyn_cast<Constant>(V)) return C;
+ if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
+ Instruction *I = cast<Instruction>(V);
+
+ std::vector<Constant*> Operands;
+ Operands.resize(I->getNumOperands());
+
+ for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
+ Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
+ if (Operands[i] == 0) return 0;
+ }
+
+ if (const CmpInst *CI = dyn_cast<CmpInst>(I))
+ return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
+ Operands[1], TD);
+ return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
+ &Operands[0], Operands.size(), TD);
+}
+
+/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
+/// in the header of its containing loop, we know the loop executes a
+/// constant number of times, and the PHI node is just a recurrence
+/// involving constants, fold it.
+Constant *
+ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
+ const APInt &BEs,
+ const Loop *L) {
+ std::map<PHINode*, Constant*>::iterator I =
+ ConstantEvolutionLoopExitValue.find(PN);
+ if (I != ConstantEvolutionLoopExitValue.end())
+ return I->second;
+
+ if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
+ return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
+
+ Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
+
+ // Since the loop is canonicalized, the PHI node must have two entries. One
+ // entry must be a constant (coming in from outside of the loop), and the
+ // second must be derived from the same PHI.
+ bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
+ Constant *StartCST =
+ dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
+ if (StartCST == 0)
+ return RetVal = 0; // Must be a constant.
+
+ Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
+ PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
+ if (PN2 != PN)
+ return RetVal = 0; // Not derived from same PHI.
+
+ // Execute the loop symbolically to determine the exit value.
+ if (BEs.getActiveBits() >= 32)
+ return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
+
+ unsigned NumIterations = BEs.getZExtValue(); // must be in range
+ unsigned IterationNum = 0;
+ for (Constant *PHIVal = StartCST; ; ++IterationNum) {
+ if (IterationNum == NumIterations)
+ return RetVal = PHIVal; // Got exit value!
+
+ // Compute the value of the PHI node for the next iteration.
+ Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
+ if (NextPHI == PHIVal)
+ return RetVal = NextPHI; // Stopped evolving!
+ if (NextPHI == 0)
+ return 0; // Couldn't evaluate!
+ PHIVal = NextPHI;
+ }
+}
+
+/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
+/// constant number of times (the condition evolves only from constants),
+/// try to evaluate a few iterations of the loop until we get the exit
+/// condition gets a value of ExitWhen (true or false). If we cannot
+/// evaluate the trip count of the loop, return getCouldNotCompute().
+const SCEV *
+ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
+ Value *Cond,
+ bool ExitWhen) {
+ PHINode *PN = getConstantEvolvingPHI(Cond, L);
+ if (PN == 0) return getCouldNotCompute();
+
+ // Since the loop is canonicalized, the PHI node must have two entries. One
+ // entry must be a constant (coming in from outside of the loop), and the
+ // second must be derived from the same PHI.
+ bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
+ Constant *StartCST =
+ dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
+ if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
+
+ Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
+ PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
+ if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
+
+ // Okay, we find a PHI node that defines the trip count of this loop. Execute
+ // the loop symbolically to determine when the condition gets a value of
+ // "ExitWhen".
+ unsigned IterationNum = 0;
+ unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
+ for (Constant *PHIVal = StartCST;
+ IterationNum != MaxIterations; ++IterationNum) {
+ ConstantInt *CondVal =
+ dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
+
+ // Couldn't symbolically evaluate.
+ if (!CondVal) return getCouldNotCompute();
+
+ if (CondVal->getValue() == uint64_t(ExitWhen)) {
+ ++NumBruteForceTripCountsComputed;
+ return getConstant(Type::getInt32Ty(getContext()), IterationNum);
+ }
+
+ // Compute the value of the PHI node for the next iteration.
+ Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
+ if (NextPHI == 0 || NextPHI == PHIVal)
+ return getCouldNotCompute();// Couldn't evaluate or not making progress...
+ PHIVal = NextPHI;
+ }
+
+ // Too many iterations were needed to evaluate.
+ return getCouldNotCompute();
+}
+
+/// getSCEVAtScope - Return a SCEV expression for the specified value
+/// at the specified scope in the program. The L value specifies a loop
+/// nest to evaluate the expression at, where null is the top-level or a
+/// specified loop is immediately inside of the loop.
+///
+/// This method can be used to compute the exit value for a variable defined
+/// in a loop by querying what the value will hold in the parent loop.
+///
+/// In the case that a relevant loop exit value cannot be computed, the
+/// original value V is returned.
+const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
+ // Check to see if we've folded this expression at this loop before.
+ std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
+ std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
+ Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
+ if (!Pair.second)
+ return Pair.first->second ? Pair.first->second : V;
+
+ // Otherwise compute it.
+ const SCEV *C = computeSCEVAtScope(V, L);
+ ValuesAtScopes[V][L] = C;
+ return C;
+}
+
+const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
+ if (isa<SCEVConstant>(V)) return V;
+
+ // If this instruction is evolved from a constant-evolving PHI, compute the
+ // exit value from the loop without using SCEVs.
+ if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
+ if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
+ const Loop *LI = (*this->LI)[I->getParent()];
+ if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
+ if (PHINode *PN = dyn_cast<PHINode>(I))
+ if (PN->getParent() == LI->getHeader()) {
+ // Okay, there is no closed form solution for the PHI node. Check
+ // to see if the loop that contains it has a known backedge-taken
+ // count. If so, we may be able to force computation of the exit
+ // value.
+ const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
+ if (const SCEVConstant *BTCC =
+ dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
+ // Okay, we know how many times the containing loop executes. If
+ // this is a constant evolving PHI node, get the final value at
+ // the specified iteration number.
+ Constant *RV = getConstantEvolutionLoopExitValue(PN,
+ BTCC->getValue()->getValue(),
+ LI);
+ if (RV) return getSCEV(RV);
+ }
+ }
+
+ // Okay, this is an expression that we cannot symbolically evaluate
+ // into a SCEV. Check to see if it's possible to symbolically evaluate
+ // the arguments into constants, and if so, try to constant propagate the
+ // result. This is particularly useful for computing loop exit values.
+ if (CanConstantFold(I)) {
+ std::vector<Constant*> Operands;
+ Operands.reserve(I->getNumOperands());
+ for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
+ Value *Op = I->getOperand(i);
+ if (Constant *C = dyn_cast<Constant>(Op)) {
+ Operands.push_back(C);
+ } else {
+ // If any of the operands is non-constant and if they are
+ // non-integer and non-pointer, don't even try to analyze them
+ // with scev techniques.
+ if (!isSCEVable(Op->getType()))
+ return V;
+
+ const SCEV *OpV = getSCEVAtScope(Op, L);
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
+ Constant *C = SC->getValue();
+ if (C->getType() != Op->getType())
+ C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
+ Op->getType(),
+ false),
+ C, Op->getType());
+ Operands.push_back(C);
+ } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
+ if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
+ if (C->getType() != Op->getType())
+ C =
+ ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
+ Op->getType(),
+ false),
+ C, Op->getType());
+ Operands.push_back(C);
+ } else
+ return V;
+ } else {
+ return V;
+ }
+ }
+ }
+
+ Constant *C;
+ if (const CmpInst *CI = dyn_cast<CmpInst>(I))
+ C = ConstantFoldCompareInstOperands(CI->getPredicate(),
+ Operands[0], Operands[1], TD);
+ else
+ C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
+ &Operands[0], Operands.size(), TD);
+ return getSCEV(C);
+ }
+ }
+
+ // This is some other type of SCEVUnknown, just return it.
+ return V;
+ }
+
+ if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
+ // Avoid performing the look-up in the common case where the specified
+ // expression has no loop-variant portions.
+ for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
+ const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
+ if (OpAtScope != Comm->getOperand(i)) {
+ // Okay, at least one of these operands is loop variant but might be
+ // foldable. Build a new instance of the folded commutative expression.
+ SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
+ Comm->op_begin()+i);
+ NewOps.push_back(OpAtScope);
+
+ for (++i; i != e; ++i) {
+ OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
+ NewOps.push_back(OpAtScope);
+ }
+ if (isa<SCEVAddExpr>(Comm))
+ return getAddExpr(NewOps);
+ if (isa<SCEVMulExpr>(Comm))
+ return getMulExpr(NewOps);
+ if (isa<SCEVSMaxExpr>(Comm))
+ return getSMaxExpr(NewOps);
+ if (isa<SCEVUMaxExpr>(Comm))
+ return getUMaxExpr(NewOps);
+ llvm_unreachable("Unknown commutative SCEV type!");
+ }
+ }
+ // If we got here, all operands are loop invariant.
+ return Comm;
+ }
+
+ if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
+ const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
+ const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
+ if (LHS == Div->getLHS() && RHS == Div->getRHS())
+ return Div; // must be loop invariant
+ return getUDivExpr(LHS, RHS);
+ }
+
+ // If this is a loop recurrence for a loop that does not contain L, then we
+ // are dealing with the final value computed by the loop.
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
+ if (!L || !AddRec->getLoop()->contains(L)) {
+ // To evaluate this recurrence, we need to know how many times the AddRec
+ // loop iterates. Compute this now.
+ const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
+ if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
+
+ // Then, evaluate the AddRec.
+ return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
+ }
+ return AddRec;
+ }
+
+ if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
+ const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
+ if (Op == Cast->getOperand())
+ return Cast; // must be loop invariant
+ return getZeroExtendExpr(Op, Cast->getType());
+ }
+
+ if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
+ const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
+ if (Op == Cast->getOperand())
+ return Cast; // must be loop invariant
+ return getSignExtendExpr(Op, Cast->getType());
+ }
+
+ if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
+ const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
+ if (Op == Cast->getOperand())
+ return Cast; // must be loop invariant
+ return getTruncateExpr(Op, Cast->getType());
+ }
+
+ llvm_unreachable("Unknown SCEV type!");
+ return 0;
+}
+
+/// getSCEVAtScope - This is a convenience function which does
+/// getSCEVAtScope(getSCEV(V), L).
+const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
+ return getSCEVAtScope(getSCEV(V), L);
+}
+
+/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
+/// following equation:
+///
+/// A * X = B (mod N)
+///
+/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
+/// A and B isn't important.
+///
+/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
+static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
+ ScalarEvolution &SE) {
+ uint32_t BW = A.getBitWidth();
+ assert(BW == B.getBitWidth() && "Bit widths must be the same.");
+ assert(A != 0 && "A must be non-zero.");
+
+ // 1. D = gcd(A, N)
+ //
+ // The gcd of A and N may have only one prime factor: 2. The number of
+ // trailing zeros in A is its multiplicity
+ uint32_t Mult2 = A.countTrailingZeros();
+ // D = 2^Mult2
+
+ // 2. Check if B is divisible by D.
+ //
+ // B is divisible by D if and only if the multiplicity of prime factor 2 for B
+ // is not less than multiplicity of this prime factor for D.
+ if (B.countTrailingZeros() < Mult2)
+ return SE.getCouldNotCompute();
+
+ // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
+ // modulo (N / D).
+ //
+ // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
+ // bit width during computations.
+ APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
+ APInt Mod(BW + 1, 0);
+ Mod.set(BW - Mult2); // Mod = N / D
+ APInt I = AD.multiplicativeInverse(Mod);
+
+ // 4. Compute the minimum unsigned root of the equation:
+ // I * (B / D) mod (N / D)
+ APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
+
+ // The result is guaranteed to be less than 2^BW so we may truncate it to BW
+ // bits.
+ return SE.getConstant(Result.trunc(BW));
+}
+
+/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
+/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
+/// might be the same) or two SCEVCouldNotCompute objects.
+///
+static std::pair<const SCEV *,const SCEV *>
+SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
+ assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
+ const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
+ const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
+ const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
+
+ // We currently can only solve this if the coefficients are constants.
+ if (!LC || !MC || !NC) {
+ const SCEV *CNC = SE.getCouldNotCompute();
+ return std::make_pair(CNC, CNC);
+ }
+
+ uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
+ const APInt &L = LC->getValue()->getValue();
+ const APInt &M = MC->getValue()->getValue();
+ const APInt &N = NC->getValue()->getValue();
+ APInt Two(BitWidth, 2);
+ APInt Four(BitWidth, 4);
+
+ {
+ using namespace APIntOps;
+ const APInt& C = L;
+ // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
+ // The B coefficient is M-N/2
+ APInt B(M);
+ B -= sdiv(N,Two);
+
+ // The A coefficient is N/2
+ APInt A(N.sdiv(Two));
+
+ // Compute the B^2-4ac term.
+ APInt SqrtTerm(B);
+ SqrtTerm *= B;
+ SqrtTerm -= Four * (A * C);
+
+ // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
+ // integer value or else APInt::sqrt() will assert.
+ APInt SqrtVal(SqrtTerm.sqrt());
+
+ // Compute the two solutions for the quadratic formula.
+ // The divisions must be performed as signed divisions.
+ APInt NegB(-B);
+ APInt TwoA( A << 1 );
+ if (TwoA.isMinValue()) {
+ const SCEV *CNC = SE.getCouldNotCompute();
+ return std::make_pair(CNC, CNC);
+ }
+
+ LLVMContext &Context = SE.getContext();
+
+ ConstantInt *Solution1 =
+ ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
+ ConstantInt *Solution2 =
+ ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
+
+ return std::make_pair(SE.getConstant(Solution1),
+ SE.getConstant(Solution2));
+ } // end APIntOps namespace
+}
+
+/// HowFarToZero - Return the number of times a backedge comparing the specified
+/// value to zero will execute. If not computable, return CouldNotCompute.
+const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
+ // If the value is a constant
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
+ // If the value is already zero, the branch will execute zero times.
+ if (C->getValue()->isZero()) return C;
+ return getCouldNotCompute(); // Otherwise it will loop infinitely.
+ }
+
+ const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
+ if (!AddRec || AddRec->getLoop() != L)
+ return getCouldNotCompute();
+
+ if (AddRec->isAffine()) {
+ // If this is an affine expression, the execution count of this branch is
+ // the minimum unsigned root of the following equation:
+ //
+ // Start + Step*N = 0 (mod 2^BW)
+ //
+ // equivalent to:
+ //
+ // Step*N = -Start (mod 2^BW)
+ //
+ // where BW is the common bit width of Start and Step.
+
+ // Get the initial value for the loop.
+ const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
+ L->getParentLoop());
+ const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
+ L->getParentLoop());
+
+ if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
+ // For now we handle only constant steps.
+
+ // First, handle unitary steps.
+ if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
+ return getNegativeSCEV(Start); // N = -Start (as unsigned)
+ if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
+ return Start; // N = Start (as unsigned)
+
+ // Then, try to solve the above equation provided that Start is constant.
+ if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
+ return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
+ -StartC->getValue()->getValue(),
+ *this);
+ }
+ } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
+ // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
+ // the quadratic equation to solve it.
+ std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
+ *this);
+ const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
+ const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
+ if (R1) {
+#if 0
+ dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
+ << " sol#2: " << *R2 << "\n";
+#endif
+ // Pick the smallest positive root value.
+ if (ConstantInt *CB =
+ dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
+ R1->getValue(), R2->getValue()))) {
+ if (CB->getZExtValue() == false)
+ std::swap(R1, R2); // R1 is the minimum root now.
+
+ // We can only use this value if the chrec ends up with an exact zero
+ // value at this index. When solving for "X*X != 5", for example, we
+ // should not accept a root of 2.
+ const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
+ if (Val->isZero())
+ return R1; // We found a quadratic root!
+ }
+ }
+ }
+
+ return getCouldNotCompute();
+}
+
+/// HowFarToNonZero - Return the number of times a backedge checking the
+/// specified value for nonzero will execute. If not computable, return
+/// CouldNotCompute
+const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
+ // Loops that look like: while (X == 0) are very strange indeed. We don't
+ // handle them yet except for the trivial case. This could be expanded in the
+ // future as needed.
+
+ // If the value is a constant, check to see if it is known to be non-zero
+ // already. If so, the backedge will execute zero times.
+ if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
+ if (!C->getValue()->isNullValue())
+ return getIntegerSCEV(0, C->getType());
+ return getCouldNotCompute(); // Otherwise it will loop infinitely.
+ }
+
+ // We could implement others, but I really doubt anyone writes loops like
+ // this, and if they did, they would already be constant folded.
+ return getCouldNotCompute();
+}
+
+/// getLoopPredecessor - If the given loop's header has exactly one unique
+/// predecessor outside the loop, return it. Otherwise return null.
+///
+BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
+ BasicBlock *Header = L->getHeader();
+ BasicBlock *Pred = 0;
+ for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
+ PI != E; ++PI)
+ if (!L->contains(*PI)) {
+ if (Pred && Pred != *PI) return 0; // Multiple predecessors.
+ Pred = *PI;
+ }
+ return Pred;
+}
+
+/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
+/// (which may not be an immediate predecessor) which has exactly one
+/// successor from which BB is reachable, or null if no such block is
+/// found.
+///
+BasicBlock *
+ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
+ // If the block has a unique predecessor, then there is no path from the
+ // predecessor to the block that does not go through the direct edge
+ // from the predecessor to the block.
+ if (BasicBlock *Pred = BB->getSinglePredecessor())
+ return Pred;
+
+ // A loop's header is defined to be a block that dominates the loop.
+ // If the header has a unique predecessor outside the loop, it must be
+ // a block that has exactly one successor that can reach the loop.
+ if (Loop *L = LI->getLoopFor(BB))
+ return getLoopPredecessor(L);
+
+ return 0;
+}
+
+/// HasSameValue - SCEV structural equivalence is usually sufficient for
+/// testing whether two expressions are equal, however for the purposes of
+/// looking for a condition guarding a loop, it can be useful to be a little
+/// more general, since a front-end may have replicated the controlling
+/// expression.
+///
+static bool HasSameValue(const SCEV *A, const SCEV *B) {
+ // Quick check to see if they are the same SCEV.
+ if (A == B) return true;
+
+ // Otherwise, if they're both SCEVUnknown, it's possible that they hold
+ // two different instructions with the same value. Check for this case.
+ if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
+ if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
+ if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
+ if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
+ if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
+ return true;
+
+ // Otherwise assume they may have a different value.
+ return false;
+}
+
+bool ScalarEvolution::isKnownNegative(const SCEV *S) {
+ return getSignedRange(S).getSignedMax().isNegative();
+}
+
+bool ScalarEvolution::isKnownPositive(const SCEV *S) {
+ return getSignedRange(S).getSignedMin().isStrictlyPositive();
+}
+
+bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
+ return !getSignedRange(S).getSignedMin().isNegative();
+}
+
+bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
+ return !getSignedRange(S).getSignedMax().isStrictlyPositive();
+}
+
+bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
+ return isKnownNegative(S) || isKnownPositive(S);
+}
+
+bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+
+ if (HasSameValue(LHS, RHS))
+ return ICmpInst::isTrueWhenEqual(Pred);
+
+ switch (Pred) {
+ default:
+ llvm_unreachable("Unexpected ICmpInst::Predicate value!");
+ break;
+ case ICmpInst::ICMP_SGT:
+ Pred = ICmpInst::ICMP_SLT;
+ std::swap(LHS, RHS);
+ case ICmpInst::ICMP_SLT: {
+ ConstantRange LHSRange = getSignedRange(LHS);
+ ConstantRange RHSRange = getSignedRange(RHS);
+ if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
+ return true;
+ if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
+ return false;
+ break;
+ }
+ case ICmpInst::ICMP_SGE:
+ Pred = ICmpInst::ICMP_SLE;
+ std::swap(LHS, RHS);
+ case ICmpInst::ICMP_SLE: {
+ ConstantRange LHSRange = getSignedRange(LHS);
+ ConstantRange RHSRange = getSignedRange(RHS);
+ if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
+ return true;
+ if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
+ return false;
+ break;
+ }
+ case ICmpInst::ICMP_UGT:
+ Pred = ICmpInst::ICMP_ULT;
+ std::swap(LHS, RHS);
+ case ICmpInst::ICMP_ULT: {
+ ConstantRange LHSRange = getUnsignedRange(LHS);
+ ConstantRange RHSRange = getUnsignedRange(RHS);
+ if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
+ return true;
+ if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
+ return false;
+ break;
+ }
+ case ICmpInst::ICMP_UGE:
+ Pred = ICmpInst::ICMP_ULE;
+ std::swap(LHS, RHS);
+ case ICmpInst::ICMP_ULE: {
+ ConstantRange LHSRange = getUnsignedRange(LHS);
+ ConstantRange RHSRange = getUnsignedRange(RHS);
+ if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
+ return true;
+ if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
+ return false;
+ break;
+ }
+ case ICmpInst::ICMP_NE: {
+ if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
+ return true;
+ if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
+ return true;
+
+ const SCEV *Diff = getMinusSCEV(LHS, RHS);
+ if (isKnownNonZero(Diff))
+ return true;
+ break;
+ }
+ case ICmpInst::ICMP_EQ:
+ // The check at the top of the function catches the case where
+ // the values are known to be equal.
+ break;
+ }
+ return false;
+}
+
+/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
+/// protected by a conditional between LHS and RHS. This is used to
+/// to eliminate casts.
+bool
+ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
+ ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+ // Interpret a null as meaning no loop, where there is obviously no guard
+ // (interprocedural conditions notwithstanding).
+ if (!L) return true;
+
+ BasicBlock *Latch = L->getLoopLatch();
+ if (!Latch)
+ return false;
+
+ BranchInst *LoopContinuePredicate =
+ dyn_cast<BranchInst>(Latch->getTerminator());
+ if (!LoopContinuePredicate ||
+ LoopContinuePredicate->isUnconditional())
+ return false;
+
+ return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
+ LoopContinuePredicate->getSuccessor(0) != L->getHeader());
+}
+
+/// isLoopGuardedByCond - Test whether entry to the loop is protected
+/// by a conditional between LHS and RHS. This is used to help avoid max
+/// expressions in loop trip counts, and to eliminate casts.
+bool
+ScalarEvolution::isLoopGuardedByCond(const Loop *L,
+ ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS) {
+ // Interpret a null as meaning no loop, where there is obviously no guard
+ // (interprocedural conditions notwithstanding).
+ if (!L) return false;
+
+ BasicBlock *Predecessor = getLoopPredecessor(L);
+ BasicBlock *PredecessorDest = L->getHeader();
+
+ // Starting at the loop predecessor, climb up the predecessor chain, as long
+ // as there are predecessors that can be found that have unique successors
+ // leading to the original header.
+ for (; Predecessor;
+ PredecessorDest = Predecessor,
+ Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
+
+ BranchInst *LoopEntryPredicate =
+ dyn_cast<BranchInst>(Predecessor->getTerminator());
+ if (!LoopEntryPredicate ||
+ LoopEntryPredicate->isUnconditional())
+ continue;
+
+ if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
+ LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
+ return true;
+ }
+
+ return false;
+}
+
+/// isImpliedCond - Test whether the condition described by Pred, LHS,
+/// and RHS is true whenever the given Cond value evaluates to true.
+bool ScalarEvolution::isImpliedCond(Value *CondValue,
+ ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS,
+ bool Inverse) {
+ // Recursivly handle And and Or conditions.
+ if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
+ if (BO->getOpcode() == Instruction::And) {
+ if (!Inverse)
+ return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
+ isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
+ } else if (BO->getOpcode() == Instruction::Or) {
+ if (Inverse)
+ return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
+ isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
+ }
+ }
+
+ ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
+ if (!ICI) return false;
+
+ // Bail if the ICmp's operands' types are wider than the needed type
+ // before attempting to call getSCEV on them. This avoids infinite
+ // recursion, since the analysis of widening casts can require loop
+ // exit condition information for overflow checking, which would
+ // lead back here.
+ if (getTypeSizeInBits(LHS->getType()) <
+ getTypeSizeInBits(ICI->getOperand(0)->getType()))
+ return false;
+
+ // Now that we found a conditional branch that dominates the loop, check to
+ // see if it is the comparison we are looking for.
+ ICmpInst::Predicate FoundPred;
+ if (Inverse)
+ FoundPred = ICI->getInversePredicate();
+ else
+ FoundPred = ICI->getPredicate();
+
+ const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
+ const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
+
+ // Balance the types. The case where FoundLHS' type is wider than
+ // LHS' type is checked for above.
+ if (getTypeSizeInBits(LHS->getType()) >
+ getTypeSizeInBits(FoundLHS->getType())) {
+ if (CmpInst::isSigned(Pred)) {
+ FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
+ FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
+ } else {
+ FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
+ FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
+ }
+ }
+
+ // Canonicalize the query to match the way instcombine will have
+ // canonicalized the comparison.
+ // First, put a constant operand on the right.
+ if (isa<SCEVConstant>(LHS)) {
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedPredicate(Pred);
+ }
+ // Then, canonicalize comparisons with boundary cases.
+ if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
+ const APInt &RA = RC->getValue()->getValue();
+ switch (Pred) {
+ default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
+ case ICmpInst::ICMP_EQ:
+ case ICmpInst::ICMP_NE:
+ break;
+ case ICmpInst::ICMP_UGE:
+ if ((RA - 1).isMinValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ RHS = getConstant(RA - 1);
+ break;
+ }
+ if (RA.isMaxValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ break;
+ }
+ if (RA.isMinValue()) return true;
+ break;
+ case ICmpInst::ICMP_ULE:
+ if ((RA + 1).isMaxValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ RHS = getConstant(RA + 1);
+ break;
+ }
+ if (RA.isMinValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ break;
+ }
+ if (RA.isMaxValue()) return true;
+ break;
+ case ICmpInst::ICMP_SGE:
+ if ((RA - 1).isMinSignedValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ RHS = getConstant(RA - 1);
+ break;
+ }
+ if (RA.isMaxSignedValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ break;
+ }
+ if (RA.isMinSignedValue()) return true;
+ break;
+ case ICmpInst::ICMP_SLE:
+ if ((RA + 1).isMaxSignedValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ RHS = getConstant(RA + 1);
+ break;
+ }
+ if (RA.isMinSignedValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ break;
+ }
+ if (RA.isMaxSignedValue()) return true;
+ break;
+ case ICmpInst::ICMP_UGT:
+ if (RA.isMinValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ break;
+ }
+ if ((RA + 1).isMaxValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ RHS = getConstant(RA + 1);
+ break;
+ }
+ if (RA.isMaxValue()) return false;
+ break;
+ case ICmpInst::ICMP_ULT:
+ if (RA.isMaxValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ break;
+ }
+ if ((RA - 1).isMinValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ RHS = getConstant(RA - 1);
+ break;
+ }
+ if (RA.isMinValue()) return false;
+ break;
+ case ICmpInst::ICMP_SGT:
+ if (RA.isMinSignedValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ break;
+ }
+ if ((RA + 1).isMaxSignedValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ RHS = getConstant(RA + 1);
+ break;
+ }
+ if (RA.isMaxSignedValue()) return false;
+ break;
+ case ICmpInst::ICMP_SLT:
+ if (RA.isMaxSignedValue()) {
+ Pred = ICmpInst::ICMP_NE;
+ break;
+ }
+ if ((RA - 1).isMinSignedValue()) {
+ Pred = ICmpInst::ICMP_EQ;
+ RHS = getConstant(RA - 1);
+ break;
+ }
+ if (RA.isMinSignedValue()) return false;
+ break;
+ }
+ }
+
+ // Check to see if we can make the LHS or RHS match.
+ if (LHS == FoundRHS || RHS == FoundLHS) {
+ if (isa<SCEVConstant>(RHS)) {
+ std::swap(FoundLHS, FoundRHS);
+ FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
+ } else {
+ std::swap(LHS, RHS);
+ Pred = ICmpInst::getSwappedPredicate(Pred);
+ }
+ }
+
+ // Check whether the found predicate is the same as the desired predicate.
+ if (FoundPred == Pred)
+ return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
+
+ // Check whether swapping the found predicate makes it the same as the
+ // desired predicate.
+ if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
+ if (isa<SCEVConstant>(RHS))
+ return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
+ else
+ return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
+ RHS, LHS, FoundLHS, FoundRHS);
+ }
+
+ // Check whether the actual condition is beyond sufficient.
+ if (FoundPred == ICmpInst::ICMP_EQ)
+ if (ICmpInst::isTrueWhenEqual(Pred))
+ if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
+ return true;
+ if (Pred == ICmpInst::ICMP_NE)
+ if (!ICmpInst::isTrueWhenEqual(FoundPred))
+ if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
+ return true;
+
+ // Otherwise assume the worst.
+ return false;
+}
+
+/// isImpliedCondOperands - Test whether the condition described by Pred,
+/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
+/// and FoundRHS is true.
+bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ return isImpliedCondOperandsHelper(Pred, LHS, RHS,
+ FoundLHS, FoundRHS) ||
+ // ~x < ~y --> x > y
+ isImpliedCondOperandsHelper(Pred, LHS, RHS,
+ getNotSCEV(FoundRHS),
+ getNotSCEV(FoundLHS));
+}
+
+/// isImpliedCondOperandsHelper - Test whether the condition described by
+/// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
+/// FoundLHS, and FoundRHS is true.
+bool
+ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
+ const SCEV *LHS, const SCEV *RHS,
+ const SCEV *FoundLHS,
+ const SCEV *FoundRHS) {
+ switch (Pred) {
+ default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
+ case ICmpInst::ICMP_EQ:
+ case ICmpInst::ICMP_NE:
+ if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_SLT:
+ case ICmpInst::ICMP_SLE:
+ if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
+ isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_SGT:
+ case ICmpInst::ICMP_SGE:
+ if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
+ isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_ULT:
+ case ICmpInst::ICMP_ULE:
+ if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
+ isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
+ return true;
+ break;
+ case ICmpInst::ICMP_UGT:
+ case ICmpInst::ICMP_UGE:
+ if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
+ isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
+ return true;
+ break;
+ }
+
+ return false;
+}
+
+/// getBECount - Subtract the end and start values and divide by the step,
+/// rounding up, to get the number of times the backedge is executed. Return
+/// CouldNotCompute if an intermediate computation overflows.
+const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
+ const SCEV *End,
+ const SCEV *Step,
+ bool NoWrap) {
+ assert(!isKnownNegative(Step) &&
+ "This code doesn't handle negative strides yet!");
+
+ const Type *Ty = Start->getType();
+ const SCEV *NegOne = getIntegerSCEV(-1, Ty);
+ const SCEV *Diff = getMinusSCEV(End, Start);
+ const SCEV *RoundUp = getAddExpr(Step, NegOne);
+
+ // Add an adjustment to the difference between End and Start so that
+ // the division will effectively round up.
+ const SCEV *Add = getAddExpr(Diff, RoundUp);
+
+ if (!NoWrap) {
+ // Check Add for unsigned overflow.
+ // TODO: More sophisticated things could be done here.
+ const Type *WideTy = IntegerType::get(getContext(),
+ getTypeSizeInBits(Ty) + 1);
+ const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
+ const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
+ const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
+ if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
+ return getCouldNotCompute();
+ }
+
+ return getUDivExpr(Add, Step);
+}
+
+/// HowManyLessThans - Return the number of times a backedge containing the
+/// specified less-than comparison will execute. If not computable, return
+/// CouldNotCompute.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
+ const Loop *L, bool isSigned) {
+ // Only handle: "ADDREC < LoopInvariant".
+ if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
+
+ const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!AddRec || AddRec->getLoop() != L)
+ return getCouldNotCompute();
+
+ // Check to see if we have a flag which makes analysis easy.
+ bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
+ AddRec->hasNoUnsignedWrap();
+
+ if (AddRec->isAffine()) {
+ unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
+ const SCEV *Step = AddRec->getStepRecurrence(*this);
+
+ if (Step->isZero())
+ return getCouldNotCompute();
+ if (Step->isOne()) {
+ // With unit stride, the iteration never steps past the limit value.
+ } else if (isKnownPositive(Step)) {
+ // Test whether a positive iteration can step past the limit
+ // value and past the maximum value for its type in a single step.
+ // Note that it's not sufficient to check NoWrap here, because even
+ // though the value after a wrap is undefined, it's not undefined
+ // behavior, so if wrap does occur, the loop could either terminate or
+ // loop infinitely, but in either case, the loop is guaranteed to
+ // iterate at least until the iteration where the wrapping occurs.
+ const SCEV *One = getIntegerSCEV(1, Step->getType());
+ if (isSigned) {
+ APInt Max = APInt::getSignedMaxValue(BitWidth);
+ if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
+ .slt(getSignedRange(RHS).getSignedMax()))
+ return getCouldNotCompute();
+ } else {
+ APInt Max = APInt::getMaxValue(BitWidth);
+ if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
+ .ult(getUnsignedRange(RHS).getUnsignedMax()))
+ return getCouldNotCompute();
+ }
+ } else
+ // TODO: Handle negative strides here and below.
+ return getCouldNotCompute();
+
+ // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
+ // m. So, we count the number of iterations in which {n,+,s} < m is true.
+ // Note that we cannot simply return max(m-n,0)/s because it's not safe to
+ // treat m-n as signed nor unsigned due to overflow possibility.
+
+ // First, we get the value of the LHS in the first iteration: n
+ const SCEV *Start = AddRec->getOperand(0);
+
+ // Determine the minimum constant start value.
+ const SCEV *MinStart = getConstant(isSigned ?
+ getSignedRange(Start).getSignedMin() :
+ getUnsignedRange(Start).getUnsignedMin());
+
+ // If we know that the condition is true in order to enter the loop,
+ // then we know that it will run exactly (m-n)/s times. Otherwise, we
+ // only know that it will execute (max(m,n)-n)/s times. In both cases,
+ // the division must round up.
+ const SCEV *End = RHS;
+ if (!isLoopGuardedByCond(L,
+ isSigned ? ICmpInst::ICMP_SLT :
+ ICmpInst::ICMP_ULT,
+ getMinusSCEV(Start, Step), RHS))
+ End = isSigned ? getSMaxExpr(RHS, Start)
+ : getUMaxExpr(RHS, Start);
+
+ // Determine the maximum constant end value.
+ const SCEV *MaxEnd = getConstant(isSigned ?
+ getSignedRange(End).getSignedMax() :
+ getUnsignedRange(End).getUnsignedMax());
+
+ // If MaxEnd is within a step of the maximum integer value in its type,
+ // adjust it down to the minimum value which would produce the same effect.
+ // This allows the subsequent ceiling divison of (N+(step-1))/step to
+ // compute the correct value.
+ const SCEV *StepMinusOne = getMinusSCEV(Step,
+ getIntegerSCEV(1, Step->getType()));
+ MaxEnd = isSigned ?
+ getSMinExpr(MaxEnd,
+ getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
+ StepMinusOne)) :
+ getUMinExpr(MaxEnd,
+ getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
+ StepMinusOne));
+
+ // Finally, we subtract these two values and divide, rounding up, to get
+ // the number of times the backedge is executed.
+ const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
+
+ // The maximum backedge count is similar, except using the minimum start
+ // value and the maximum end value.
+ const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
+
+ return BackedgeTakenInfo(BECount, MaxBECount);
+ }
+
+ return getCouldNotCompute();
+}
+
+/// getNumIterationsInRange - Return the number of iterations of this loop that
+/// produce values in the specified constant range. Another way of looking at
+/// this is that it returns the first iteration number where the value is not in
+/// the condition, thus computing the exit count. If the iteration count can't
+/// be computed, an instance of SCEVCouldNotCompute is returned.
+const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
+ ScalarEvolution &SE) const {
+ if (Range.isFullSet()) // Infinite loop.
+ return SE.getCouldNotCompute();
+
+ // If the start is a non-zero constant, shift the range to simplify things.
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
+ if (!SC->getValue()->isZero()) {
+ SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
+ Operands[0] = SE.getIntegerSCEV(0, SC->getType());
+ const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
+ if (const SCEVAddRecExpr *ShiftedAddRec =
+ dyn_cast<SCEVAddRecExpr>(Shifted))
+ return ShiftedAddRec->getNumIterationsInRange(
+ Range.subtract(SC->getValue()->getValue()), SE);
+ // This is strange and shouldn't happen.
+ return SE.getCouldNotCompute();
+ }
+
+ // The only time we can solve this is when we have all constant indices.
+ // Otherwise, we cannot determine the overflow conditions.
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
+ if (!isa<SCEVConstant>(getOperand(i)))
+ return SE.getCouldNotCompute();
+
+
+ // Okay at this point we know that all elements of the chrec are constants and
+ // that the start element is zero.
+
+ // First check to see if the range contains zero. If not, the first
+ // iteration exits.
+ unsigned BitWidth = SE.getTypeSizeInBits(getType());
+ if (!Range.contains(APInt(BitWidth, 0)))
+ return SE.getIntegerSCEV(0, getType());
+
+ if (isAffine()) {
+ // If this is an affine expression then we have this situation:
+ // Solve {0,+,A} in Range === Ax in Range
+
+ // We know that zero is in the range. If A is positive then we know that
+ // the upper value of the range must be the first possible exit value.
+ // If A is negative then the lower of the range is the last possible loop
+ // value. Also note that we already checked for a full range.
+ APInt One(BitWidth,1);
+ APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
+ APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
+
+ // The exit value should be (End+A)/A.
+ APInt ExitVal = (End + A).udiv(A);
+ ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
+
+ // Evaluate at the exit value. If we really did fall out of the valid
+ // range, then we computed our trip count, otherwise wrap around or other
+ // things must have happened.
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
+ if (Range.contains(Val->getValue()))
+ return SE.getCouldNotCompute(); // Something strange happened
+
+ // Ensure that the previous value is in the range. This is a sanity check.
+ assert(Range.contains(
+ EvaluateConstantChrecAtConstant(this,
+ ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
+ "Linear scev computation is off in a bad way!");
+ return SE.getConstant(ExitValue);
+ } else if (isQuadratic()) {
+ // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
+ // quadratic equation to solve it. To do this, we must frame our problem in
+ // terms of figuring out when zero is crossed, instead of when
+ // Range.getUpper() is crossed.
+ SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
+ NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
+ const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
+
+ // Next, solve the constructed addrec
+ std::pair<const SCEV *,const SCEV *> Roots =
+ SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
+ const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
+ const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
+ if (R1) {
+ // Pick the smallest positive root value.
+ if (ConstantInt *CB =
+ dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
+ R1->getValue(), R2->getValue()))) {
+ if (CB->getZExtValue() == false)
+ std::swap(R1, R2); // R1 is the minimum root now.
+
+ // Make sure the root is not off by one. The returned iteration should
+ // not be in the range, but the previous one should be. When solving
+ // for "X*X < 5", for example, we should not return a root of 2.
+ ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
+ R1->getValue(),
+ SE);
+ if (Range.contains(R1Val->getValue())) {
+ // The next iteration must be out of the range...
+ ConstantInt *NextVal =
+ ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
+
+ R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
+ if (!Range.contains(R1Val->getValue()))
+ return SE.getConstant(NextVal);
+ return SE.getCouldNotCompute(); // Something strange happened
+ }
+
+ // If R1 was not in the range, then it is a good return value. Make
+ // sure that R1-1 WAS in the range though, just in case.
+ ConstantInt *NextVal =
+ ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
+ R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
+ if (Range.contains(R1Val->getValue()))
+ return R1;
+ return SE.getCouldNotCompute(); // Something strange happened
+ }
+ }
+ }
+
+ return SE.getCouldNotCompute();
+}
+
+
+
+//===----------------------------------------------------------------------===//
+// SCEVCallbackVH Class Implementation
+//===----------------------------------------------------------------------===//
+
+void ScalarEvolution::SCEVCallbackVH::deleted() {
+ assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
+ if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ SE->Scalars.erase(getValPtr());
+ // this now dangles!
+}
+
+void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
+ assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
+
+ // Forget all the expressions associated with users of the old value,
+ // so that future queries will recompute the expressions using the new
+ // value.
+ SmallVector<User *, 16> Worklist;
+ SmallPtrSet<User *, 8> Visited;
+ Value *Old = getValPtr();
+ bool DeleteOld = false;
+ for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
+ UI != UE; ++UI)
+ Worklist.push_back(*UI);
+ while (!Worklist.empty()) {
+ User *U = Worklist.pop_back_val();
+ // Deleting the Old value will cause this to dangle. Postpone
+ // that until everything else is done.
+ if (U == Old) {
+ DeleteOld = true;
+ continue;
+ }
+ if (!Visited.insert(U))
+ continue;
+ if (PHINode *PN = dyn_cast<PHINode>(U))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ SE->Scalars.erase(U);
+ for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
+ UI != UE; ++UI)
+ Worklist.push_back(*UI);
+ }
+ // Delete the Old value if it (indirectly) references itself.
+ if (DeleteOld) {
+ if (PHINode *PN = dyn_cast<PHINode>(Old))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ SE->Scalars.erase(Old);
+ // this now dangles!
+ }
+ // this may dangle!
+}
+
+ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
+ : CallbackVH(V), SE(se) {}
+
+//===----------------------------------------------------------------------===//
+// ScalarEvolution Class Implementation
+//===----------------------------------------------------------------------===//
+
+ScalarEvolution::ScalarEvolution()
+ : FunctionPass(&ID) {
+}
+
+bool ScalarEvolution::runOnFunction(Function &F) {
+ this->F = &F;
+ LI = &getAnalysis<LoopInfo>();
+ DT = &getAnalysis<DominatorTree>();
+ TD = getAnalysisIfAvailable<TargetData>();
+ return false;
+}
+
+void ScalarEvolution::releaseMemory() {
+ Scalars.clear();
+ BackedgeTakenCounts.clear();
+ ConstantEvolutionLoopExitValue.clear();
+ ValuesAtScopes.clear();
+ UniqueSCEVs.clear();
+ SCEVAllocator.Reset();
+}
+
+void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
+ AU.setPreservesAll();
+ AU.addRequiredTransitive<LoopInfo>();
+ AU.addRequiredTransitive<DominatorTree>();
+}
+
+bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
+ return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
+}
+
+static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
+ const Loop *L) {
+ // Print all inner loops first
+ for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
+ PrintLoopInfo(OS, SE, *I);
+
+ OS << "Loop ";
+ WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
+ OS << ": ";
+
+ SmallVector<BasicBlock *, 8> ExitBlocks;
+ L->getExitBlocks(ExitBlocks);
+ if (ExitBlocks.size() != 1)
+ OS << "<multiple exits> ";
+
+ if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
+ OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
+ } else {
+ OS << "Unpredictable backedge-taken count. ";
+ }
+
+ OS << "\n"
+ "Loop ";
+ WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
+ OS << ": ";
+
+ if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
+ OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
+ } else {
+ OS << "Unpredictable max backedge-taken count. ";
+ }
+
+ OS << "\n";
+}
+
+void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
+ // ScalarEvolution's implementaiton of the print method is to print
+ // out SCEV values of all instructions that are interesting. Doing
+ // this potentially causes it to create new SCEV objects though,
+ // which technically conflicts with the const qualifier. This isn't
+ // observable from outside the class though, so casting away the
+ // const isn't dangerous.
+ ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
+
+ OS << "Classifying expressions for: ";
+ WriteAsOperand(OS, F, /*PrintType=*/false);
+ OS << "\n";
+ for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
+ if (isSCEVable(I->getType())) {
+ OS << *I << '\n';
+ OS << " --> ";
+ const SCEV *SV = SE.getSCEV(&*I);
+ SV->print(OS);
+
+ const Loop *L = LI->getLoopFor((*I).getParent());
+
+ const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
+ if (AtUse != SV) {
+ OS << " --> ";
+ AtUse->print(OS);
+ }
+
+ if (L) {
+ OS << "\t\t" "Exits: ";
+ const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
+ if (!ExitValue->isLoopInvariant(L)) {
+ OS << "<<Unknown>>";
+ } else {
+ OS << *ExitValue;
+ }
+ }
+
+ OS << "\n";
+ }
+
+ OS << "Determining loop execution counts for: ";
+ WriteAsOperand(OS, F, /*PrintType=*/false);
+ OS << "\n";
+ for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
+ PrintLoopInfo(OS, &SE, *I);
+}
+