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authored <ed@FreeBSD.org>2009-06-02 17:52:33 +0000
committered <ed@FreeBSD.org>2009-06-02 17:52:33 +0000
commit3277b69d734b9c90b44ebde4ede005717e2c3b2e (patch)
tree64ba909838c23261cace781ece27d106134ea451 /lib/Analysis/ScalarEvolution.cpp
downloadFreeBSD-src-3277b69d734b9c90b44ebde4ede005717e2c3b2e.zip
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Import LLVM, at r72732.
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diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
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+//===- 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. These classes are reference counted, managed by the SCEVHandle
+// class. 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/Instructions.h"
+#include "llvm/Analysis/ConstantFolding.h"
+#include "llvm/Analysis/Dominators.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Assembly/Writer.h"
+#include "llvm/Target/TargetData.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/Compiler.h"
+#include "llvm/Support/ConstantRange.h"
+#include "llvm/Support/GetElementPtrTypeIterator.h"
+#include "llvm/Support/InstIterator.h"
+#include "llvm/Support/ManagedStatic.h"
+#include "llvm/Support/MathExtras.h"
+#include "llvm/Support/raw_ostream.h"
+#include "llvm/ADT/Statistic.h"
+#include "llvm/ADT/STLExtras.h"
+#include <ostream>
+#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(errs());
+ errs() << '\n';
+}
+
+void SCEV::print(std::ostream &o) const {
+ raw_os_ostream OS(o);
+ print(OS);
+}
+
+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;
+}
+
+SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
+SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
+
+bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
+ assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+ return false;
+}
+
+const Type *SCEVCouldNotCompute::getType() const {
+ assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+ return 0;
+}
+
+bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
+ assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+ return false;
+}
+
+SCEVHandle SCEVCouldNotCompute::
+replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
+ return this;
+}
+
+void SCEVCouldNotCompute::print(raw_ostream &OS) const {
+ OS << "***COULDNOTCOMPUTE***";
+}
+
+bool SCEVCouldNotCompute::classof(const SCEV *S) {
+ return S->getSCEVType() == scCouldNotCompute;
+}
+
+
+// SCEVConstants - Only allow the creation of one SCEVConstant for any
+// particular value. Don't use a SCEVHandle here, or else the object will
+// never be deleted!
+static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
+
+
+SCEVConstant::~SCEVConstant() {
+ SCEVConstants->erase(V);
+}
+
+SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
+ SCEVConstant *&R = (*SCEVConstants)[V];
+ if (R == 0) R = new SCEVConstant(V);
+ return R;
+}
+
+SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
+ return getConstant(ConstantInt::get(Val));
+}
+
+const Type *SCEVConstant::getType() const { return V->getType(); }
+
+void SCEVConstant::print(raw_ostream &OS) const {
+ WriteAsOperand(OS, V, false);
+}
+
+SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
+ const SCEVHandle &op, const Type *ty)
+ : SCEV(SCEVTy), Op(op), Ty(ty) {}
+
+SCEVCastExpr::~SCEVCastExpr() {}
+
+bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ return Op->dominates(BB, DT);
+}
+
+// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will
+// never be deleted!
+static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
+ SCEVTruncateExpr*> > SCEVTruncates;
+
+SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
+ : SCEVCastExpr(scTruncate, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot truncate non-integer value!");
+}
+
+SCEVTruncateExpr::~SCEVTruncateExpr() {
+ SCEVTruncates->erase(std::make_pair(Op, Ty));
+}
+
+void SCEVTruncateExpr::print(raw_ostream &OS) const {
+ OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will never
+// be deleted!
+static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
+ SCEVZeroExtendExpr*> > SCEVZeroExtends;
+
+SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
+ : SCEVCastExpr(scZeroExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot zero extend non-integer value!");
+}
+
+SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
+ SCEVZeroExtends->erase(std::make_pair(Op, Ty));
+}
+
+void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
+ OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will never
+// be deleted!
+static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
+ SCEVSignExtendExpr*> > SCEVSignExtends;
+
+SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
+ : SCEVCastExpr(scSignExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
+ "Cannot sign extend non-integer value!");
+}
+
+SCEVSignExtendExpr::~SCEVSignExtendExpr() {
+ SCEVSignExtends->erase(std::make_pair(Op, Ty));
+}
+
+void SCEVSignExtendExpr::print(raw_ostream &OS) const {
+ OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
+}
+
+// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will never
+// be deleted!
+static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
+ SCEVCommutativeExpr*> > SCEVCommExprs;
+
+SCEVCommutativeExpr::~SCEVCommutativeExpr() {
+ std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
+ SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
+}
+
+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 << ")";
+}
+
+SCEVHandle SCEVCommutativeExpr::
+replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ SCEVHandle H =
+ getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
+ if (H != getOperand(i)) {
+ std::vector<SCEVHandle> NewOps;
+ NewOps.reserve(getNumOperands());
+ for (unsigned j = 0; j != i; ++j)
+ NewOps.push_back(getOperand(j));
+ NewOps.push_back(H);
+ for (++i; i != e; ++i)
+ NewOps.push_back(getOperand(i)->
+ replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
+
+ if (isa<SCEVAddExpr>(this))
+ return SE.getAddExpr(NewOps);
+ else if (isa<SCEVMulExpr>(this))
+ return SE.getMulExpr(NewOps);
+ else if (isa<SCEVSMaxExpr>(this))
+ return SE.getSMaxExpr(NewOps);
+ else if (isa<SCEVUMaxExpr>(this))
+ return SE.getUMaxExpr(NewOps);
+ else
+ assert(0 && "Unknown commutative expr!");
+ }
+ }
+ return this;
+}
+
+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;
+}
+
+
+// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
+// input. Don't use a SCEVHandle here, or else the object will never be
+// deleted!
+static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
+ SCEVUDivExpr*> > SCEVUDivs;
+
+SCEVUDivExpr::~SCEVUDivExpr() {
+ SCEVUDivs->erase(std::make_pair(LHS, RHS));
+}
+
+bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ return LHS->dominates(BB, DT) && RHS->dominates(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();
+}
+
+// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will never
+// be deleted!
+static ManagedStatic<std::map<std::pair<const Loop *,
+ std::vector<const SCEV*> >,
+ SCEVAddRecExpr*> > SCEVAddRecExprs;
+
+SCEVAddRecExpr::~SCEVAddRecExpr() {
+ std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
+ SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
+}
+
+SCEVHandle SCEVAddRecExpr::
+replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ SCEVHandle H =
+ getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
+ if (H != getOperand(i)) {
+ std::vector<SCEVHandle> NewOps;
+ NewOps.reserve(getNumOperands());
+ for (unsigned j = 0; j != i; ++j)
+ NewOps.push_back(getOperand(j));
+ NewOps.push_back(H);
+ for (++i; i != e; ++i)
+ NewOps.push_back(getOperand(i)->
+ replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
+
+ return SE.getAddRecExpr(NewOps, L);
+ }
+ }
+ return this;
+}
+
+
+bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
+ // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
+ // contain L and if the start is invariant.
+ // Add recurrences are never invariant in the function-body (null loop).
+ return QueryLoop &&
+ !QueryLoop->contains(L->getHeader()) &&
+ getOperand(0)->isLoopInvariant(QueryLoop);
+}
+
+
+void SCEVAddRecExpr::print(raw_ostream &OS) const {
+ OS << "{" << *Operands[0];
+ for (unsigned i = 1, e = Operands.size(); i != e; ++i)
+ OS << ",+," << *Operands[i];
+ OS << "}<" << L->getHeader()->getName() + ">";
+}
+
+// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
+// value. Don't use a SCEVHandle here, or else the object will never be
+// deleted!
+static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
+
+SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
+
+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->getParent());
+ 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;
+}
+
+const Type *SCEVUnknown::getType() const {
+ return V->getType();
+}
+
+void SCEVUnknown::print(raw_ostream &OS) const {
+ WriteAsOperand(OS, V, false);
+}
+
+//===----------------------------------------------------------------------===//
+// SCEV Utilities
+//===----------------------------------------------------------------------===//
+
+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 VISIBILITY_HIDDEN SCEVComplexityCompare {
+ LoopInfo *LI;
+ public:
+ explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
+
+ bool operator()(const SCEV *LHS, const SCEV *RHS) const {
+ // 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;
+ }
+
+ // Constant sorting doesn't matter since they'll be folded.
+ if (isa<SCEVConstant>(LHS))
+ return false;
+
+ // 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());
+ }
+
+ assert(0 && "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(std::vector<SCEVHandle> &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 SCEVHandle BinomialCoefficient(SCEVHandle 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(CalculationBits);
+ SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
+ for (unsigned i = 1; i != K; ++i) {
+ SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
+ Dividend = SE.getMulExpr(Dividend,
+ SE.getTruncateOrZeroExtend(S, CalculationTy));
+ }
+
+ // Divide by 2^T
+ SCEVHandle 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.
+///
+SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
+ ScalarEvolution &SE) const {
+ SCEVHandle 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.
+ SCEVHandle 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
+//===----------------------------------------------------------------------===//
+
+SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &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);
+
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getUnknown(
+ 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 made out of constants, truncate
+ // all of the constants.
+ if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
+ std::vector<SCEVHandle> Operands;
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
+ Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
+ return getAddRecExpr(Operands, AddRec->getLoop());
+ }
+
+ SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
+ return Result;
+}
+
+SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &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);
+
+ 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 getUnknown(C);
+ }
+
+ // zext(zext(x)) --> zext(x)
+ if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
+ return getZeroExtendExpr(SZ->getOperand(), Ty);
+
+ // 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()) {
+ // 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.
+ SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for
+ // overflow.
+ SCEVHandle Start = AR->getStart();
+ SCEVHandle Step = AR->getStepRecurrence(*this);
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ SCEVHandle CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType());
+ SCEVHandle RecastedMaxBECount =
+ getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
+ if (MaxBECount == RecastedMaxBECount) {
+ const Type *WideTy =
+ IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
+ // Check whether Start+Step*MaxBECount has no unsigned overflow.
+ SCEVHandle ZMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrZeroExtend(Step, Start->getType()));
+ SCEVHandle Add = getAddExpr(Start, ZMul);
+ SCEVHandle 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),
+ AR->getLoop());
+
+ // Similar to above, only this time treat the step value as signed.
+ // This covers loops that count down.
+ SCEVHandle 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),
+ AR->getLoop());
+ }
+ }
+ }
+
+ SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
+ return Result;
+}
+
+SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &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);
+
+ 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 getUnknown(C);
+ }
+
+ // sext(sext(x)) --> sext(x)
+ if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
+ return getSignExtendExpr(SS->getOperand(), Ty);
+
+ // 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()) {
+ // 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.
+ SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
+ if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
+ // Manually compute the final value for AR, checking for
+ // overflow.
+ SCEVHandle Start = AR->getStart();
+ SCEVHandle Step = AR->getStepRecurrence(*this);
+
+ // Check whether the backedge-taken count can be losslessly casted to
+ // the addrec's type. The count is always unsigned.
+ SCEVHandle CastedMaxBECount =
+ getTruncateOrZeroExtend(MaxBECount, Start->getType());
+ SCEVHandle RecastedMaxBECount =
+ getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
+ if (MaxBECount == RecastedMaxBECount) {
+ const Type *WideTy =
+ IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
+ // Check whether Start+Step*MaxBECount has no signed overflow.
+ SCEVHandle SMul =
+ getMulExpr(CastedMaxBECount,
+ getTruncateOrSignExtend(Step, Start->getType()));
+ SCEVHandle Add = getAddExpr(Start, SMul);
+ SCEVHandle 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),
+ AR->getLoop());
+ }
+ }
+ }
+
+ SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
+ return Result;
+}
+
+/// getAddExpr - Get a canonical add expression, or something simpler if
+/// possible.
+SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
+ 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
+
+ // 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(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 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.
+ SCEVHandle Two = getIntegerSCEV(2, Ty);
+ SCEVHandle 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);
+ }
+
+ // 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();
+ std::vector<SCEVHandle> 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])) {
+ std::vector<SCEVHandle> 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.
+ SCEVHandle Fold = getAddExpr(LargeOps);
+ // 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;
+
+ // 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>(MulOpSCEV)) {
+ // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
+ SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
+ if (Mul->getNumOperands() != 2) {
+ // If the multiply has more than two operands, we must get the
+ // Y*Z term.
+ std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
+ MulOps.erase(MulOps.begin()+MulOp);
+ InnerMul = getMulExpr(MulOps);
+ }
+ SCEVHandle One = getIntegerSCEV(1, Ty);
+ SCEVHandle AddOne = getAddExpr(InnerMul, One);
+ SCEVHandle 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))
+ SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
+ if (Mul->getNumOperands() != 2) {
+ std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
+ MulOps.erase(MulOps.begin()+MulOp);
+ InnerMul1 = getMulExpr(MulOps);
+ }
+ SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
+ if (OtherMul->getNumOperands() != 2) {
+ std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
+ OtherMul->op_end());
+ MulOps.erase(MulOps.begin()+OMulOp);
+ InnerMul2 = getMulExpr(MulOps);
+ }
+ SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
+ SCEVHandle 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.
+ std::vector<SCEVHandle> 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());
+
+ std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
+ AddRecOps[0] = getAddExpr(LIOps);
+
+ SCEVHandle 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}
+ std::vector<SCEVHandle> 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));
+ }
+ SCEVHandle 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.
+ std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
+ SCEVOps)];
+ if (Result == 0) Result = new SCEVAddExpr(Ops);
+ return Result;
+}
+
+
+/// getMulExpr - Get a canonical multiply expression, or something simpler if
+/// possible.
+SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
+ assert(!Ops.empty() && "Cannot get empty mul!");
+#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
+
+ // 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(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];
+ }
+ }
+
+ // 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.
+ std::vector<SCEVHandle> 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}
+ std::vector<SCEVHandle> 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) {
+ std::vector<SCEVHandle> MulOps(LIOps);
+ MulOps.push_back(AddRec->getOperand(i));
+ NewOps.push_back(getMulExpr(MulOps));
+ }
+ }
+
+ SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
+
+ // 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;
+ SCEVHandle NewStart = getMulExpr(F->getStart(),
+ G->getStart());
+ SCEVHandle B = F->getStepRecurrence(*this);
+ SCEVHandle D = G->getStepRecurrence(*this);
+ SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
+ getMulExpr(G, B),
+ getMulExpr(B, D));
+ SCEVHandle 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.
+ std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
+ SCEVOps)];
+ if (Result == 0)
+ Result = new SCEVMulExpr(Ops);
+ return Result;
+}
+
+/// getUDivExpr - Get a canonical multiply expression, or something simpler if
+/// possible.
+SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
+ const SCEVHandle &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(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())) {
+ std::vector<SCEVHandle> 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)) {
+ std::vector<SCEVHandle> 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) {
+ SCEVHandle Op = M->getOperand(i);
+ SCEVHandle Div = getUDivExpr(Op, RHSC);
+ if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
+ Operands = M->getOperands();
+ 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)) {
+ std::vector<SCEVHandle> 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) {
+ SCEVHandle 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 getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
+ }
+ }
+
+ SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
+ if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
+ return Result;
+}
+
+
+/// getAddRecExpr - Get an add recurrence expression for the specified loop.
+/// Simplify the expression as much as possible.
+SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
+ const SCEVHandle &Step, const Loop *L) {
+ std::vector<SCEVHandle> 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);
+}
+
+/// getAddRecExpr - Get an add recurrence expression for the specified loop.
+/// Simplify the expression as much as possible.
+SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
+ const Loop *L) {
+ 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); // {X,+,0} --> X
+ }
+
+ // 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->getLoopDepth() < NestedLoop->getLoopDepth()) {
+ std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
+ NestedAR->op_end());
+ SCEVHandle NestedARHandle(NestedAR);
+ Operands[0] = NestedAR->getStart();
+ NestedOperands[0] = getAddRecExpr(Operands, L);
+ return getAddRecExpr(NestedOperands, NestedLoop);
+ }
+ }
+
+ std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
+ SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
+ if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
+ return Result;
+}
+
+SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
+ const SCEVHandle &RHS) {
+ std::vector<SCEVHandle> Ops;
+ Ops.push_back(LHS);
+ Ops.push_back(RHS);
+ return getSMaxExpr(Ops);
+}
+
+SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> 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(
+ 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 -inf, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ }
+ }
+
+ 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.
+ std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
+ SCEVOps)];
+ if (Result == 0) Result = new SCEVSMaxExpr(Ops);
+ return Result;
+}
+
+SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
+ const SCEVHandle &RHS) {
+ std::vector<SCEVHandle> Ops;
+ Ops.push_back(LHS);
+ Ops.push_back(RHS);
+ return getUMaxExpr(Ops);
+}
+
+SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> 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(
+ 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 zero, strip it off.
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
+ Ops.erase(Ops.begin());
+ --Idx;
+ }
+ }
+
+ 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.
+ std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
+ SCEVOps)];
+ if (Result == 0) Result = new SCEVUMaxExpr(Ops);
+ return Result;
+}
+
+SCEVHandle ScalarEvolution::getUnknown(Value *V) {
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
+ return getConstant(CI);
+ if (isa<ConstantPointerNull>(V))
+ return getIntegerSCEV(0, V->getType());
+ SCEVUnknown *&Result = (*SCEVUnknowns)[V];
+ if (Result == 0) Result = new SCEVUnknown(V);
+ return Result;
+}
+
+//===----------------------------------------------------------------------===//
+// 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 are always SCEVable.
+ if (Ty->isInteger())
+ return true;
+
+ // Pointers are SCEVable if TargetData information is available
+ // to provide pointer size information.
+ if (isa<PointerType>(Ty))
+ return TD != NULL;
+
+ // Otherwise it's not SCEVable.
+ return false;
+}
+
+/// 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);
+
+ // Otherwise, we support only integer types.
+ assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
+ return Ty->getPrimitiveSizeInBits();
+}
+
+/// 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;
+
+ assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
+ return TD->getIntPtrType();
+}
+
+SCEVHandle ScalarEvolution::getCouldNotCompute() {
+ return UnknownValue;
+}
+
+/// hasSCEV - Return true if the SCEV for this value has already been
+/// computed.
+bool ScalarEvolution::hasSCEV(Value *V) const {
+ return Scalars.count(V);
+}
+
+/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
+/// expression and create a new one.
+SCEVHandle ScalarEvolution::getSCEV(Value *V) {
+ assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
+
+ std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
+ if (I != Scalars.end()) return I->second;
+ SCEVHandle S = createSCEV(V);
+ Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
+ return S;
+}
+
+/// getIntegerSCEV - Given an integer or FP type, create a constant for the
+/// specified signed integer value and return a SCEV for the constant.
+SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
+ Ty = getEffectiveSCEVType(Ty);
+ Constant *C;
+ if (Val == 0)
+ C = Constant::getNullValue(Ty);
+ else if (Ty->isFloatingPoint())
+ C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
+ APFloat::IEEEdouble, Val));
+ else
+ C = ConstantInt::get(Ty, Val);
+ return getUnknown(C);
+}
+
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getUnknown(ConstantExpr::getNeg(VC->getValue()));
+
+ const Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
+}
+
+/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
+ if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getUnknown(ConstantExpr::getNot(VC->getValue()));
+
+ const Type *Ty = V->getType();
+ Ty = getEffectiveSCEVType(Ty);
+ SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
+ return getMinusSCEV(AllOnes, V);
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
+ const SCEVHandle &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.
+SCEVHandle
+ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
+ const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
+ (Ty->isInteger() || (TD && 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.
+SCEVHandle
+ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
+ const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
+ (Ty->isInteger() || (TD && 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.
+SCEVHandle
+ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
+ (Ty->isInteger() || (TD && 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.
+SCEVHandle
+ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
+ (Ty->isInteger() || (TD && 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);
+}
+
+/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
+/// input value to the specified type. The conversion must not be widening.
+SCEVHandle
+ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
+ (Ty->isInteger() || (TD && 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);
+}
+
+/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
+/// the specified instruction and replaces any references to the symbolic value
+/// SymName with the specified value. This is used during PHI resolution.
+void ScalarEvolution::
+ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
+ const SCEVHandle &NewVal) {
+ std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
+ Scalars.find(SCEVCallbackVH(I, this));
+ if (SI == Scalars.end()) return;
+
+ SCEVHandle NV =
+ SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
+ if (NV == SI->second) return; // No change.
+
+ SI->second = NV; // Update the scalars map!
+
+ // Any instruction values that use this instruction might also need to be
+ // updated!
+ for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
+ UI != E; ++UI)
+ ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
+}
+
+/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
+/// a loop header, making it a potential recurrence, or it doesn't.
+///
+SCEVHandle 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.
+ SCEVHandle 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.
+ SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
+
+ // 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.
+ std::vector<SCEVHandle> Ops;
+ for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
+ if (i != FoundIndex)
+ Ops.push_back(Add->getOperand(i));
+ SCEVHandle 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)) {
+ SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
+ SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
+
+ // Okay, for the entire analysis of this edge we assumed the PHI
+ // to be symbolic. We now need to go back and update all of the
+ // entries for the scalars that use the PHI (except for the PHI
+ // itself) to use the new analyzed value instead of the "symbolic"
+ // value.
+ ReplaceSymbolicValueWithConcrete(PN, SymbolicName, 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()) {
+ SCEVHandle 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))) {
+ SCEVHandle 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 update all of the
+ // entries for the scalars that use the PHI (except for the PHI
+ // itself) to use the new analyzed value instead of the "symbolic"
+ // value.
+ ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
+ return PHISCEV;
+ }
+ }
+ }
+
+ return SymbolicName;
+ }
+
+ // 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.
+///
+SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
+
+ const Type *IntPtrTy = TD->getIntPtrType();
+ Value *Base = GEP->getOperand(0);
+ // Don't attempt to analyze GEPs over unsized objects.
+ if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
+ return getUnknown(GEP);
+ SCEVHandle 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.
+ const StructLayout &SL = *TD->getStructLayout(STy);
+ unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
+ uint64_t Offset = SL.getElementOffset(FieldNo);
+ TotalOffset = getAddExpr(TotalOffset,
+ getIntegerSCEV(Offset, IntPtrTy));
+ } else {
+ // For an array, add the element offset, explicitly scaled.
+ SCEVHandle LocalOffset = getSCEV(Index);
+ if (!isa<PointerType>(LocalOffset->getType()))
+ // Getelementptr indicies are signed.
+ LocalOffset = getTruncateOrSignExtend(LocalOffset,
+ IntPtrTy);
+ LocalOffset =
+ getMulExpr(LocalOffset,
+ getIntegerSCEV(TD->getTypeAllocSize(*GTI),
+ IntPtrTy));
+ TotalOffset = getAddExpr(TotalOffset, LocalOffset);
+ }
+ }
+ return getAddExpr(getSCEV(Base), TotalOffset);
+}
+
+/// 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.
+static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
+ 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(), SE),
+ (uint32_t)SE.getTypeSizeInBits(T->getType()));
+
+ if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
+ return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
+ SE.getTypeSizeInBits(E->getType()) : OpRes;
+ }
+
+ if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
+ return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
+ SE.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), SE);
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
+ 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), SE);
+ uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
+ for (unsigned i = 1, e = M->getNumOperands();
+ SumOpRes != BitWidth && i != e; ++i)
+ SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
+ 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), SE);
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
+ 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), SE);
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
+ 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), SE);
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
+ return MinOpRes;
+ }
+
+ // SCEVUDivExpr, SCEVUnknown
+ return 0;
+}
+
+/// createSCEV - We know that there is no SCEV for the specified value.
+/// Analyze the expression.
+///
+SCEVHandle 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
+ return getUnknown(V);
+
+ User *U = cast<User>(V);
+ switch (Opcode) {
+ case Instruction::Add:
+ return getAddExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::Mul:
+ 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();
+ unsigned Ones = A.countTrailingOnes();
+ if (APIntOps::isMask(Ones, A))
+ return
+ getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
+ IntegerType::get(Ones)),
+ 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))) {
+ SCEVHandle LHS = getSCEV(U->getOperand(0));
+ const APInt &CIVal = CI->getValue();
+ if (GetMinTrailingZeros(LHS, *this) >=
+ (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
+ return getAddExpr(LHS, getSCEV(U->getOperand(1)));
+ }
+ 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))))
+ return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
+ U->getType());
+ }
+ 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>(V->getType())->getBitWidth();
+ Constant *X = ConstantInt::get(
+ 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>(V->getType())->getBitWidth();
+ Constant *X = ConstantInt::get(
+ 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(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;
+
+ case Instruction::IntToPtr:
+ if (!TD) break; // Without TD we can't analyze pointers.
+ return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
+ TD->getIntPtrType());
+
+ case Instruction::PtrToInt:
+ if (!TD) break; // Without TD we can't analyze pointers.
+ return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
+ U->getType());
+
+ case Instruction::GetElementPtr:
+ if (!TD) break; // Without TD we can't analyze pointers.
+ return createNodeForGEP(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))
+ // ~smax(~x, ~y) == smin(x, y).
+ return getNotSCEV(getSMaxExpr(
+ getNotSCEV(getSCEV(LHS)),
+ getNotSCEV(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))
+ // ~umax(~x, ~y) == umin(x, y)
+ return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
+ getNotSCEV(getSCEV(RHS))));
+ 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).
+///
+SCEVHandle 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.
+SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
+ return getBackedgeTakenInfo(L).Max;
+}
+
+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 ItCount = ComputeBackedgeTakenCount(L);
+ if (ItCount.Exact != UnknownValue) {
+ assert(ItCount.Exact->isLoopInvariant(L) &&
+ ItCount.Max->isLoopInvariant(L) &&
+ "Computed trip count isn't loop invariant for loop!");
+ ++NumTripCountsComputed;
+
+ // Update the value in the map.
+ Pair.first->second = ItCount;
+ } else 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.
+ if (ItCount.hasAnyInfo())
+ forgetLoopPHIs(L);
+ }
+ return Pair.first->second;
+}
+
+/// forgetLoopBackedgeTakenCount - 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::forgetLoopBackedgeTakenCount(const Loop *L) {
+ BackedgeTakenCounts.erase(L);
+ forgetLoopPHIs(L);
+}
+
+/// forgetLoopPHIs - Delete the memoized SCEVs associated with the
+/// PHI nodes in the given loop. This is used when the trip count of
+/// the loop may have changed.
+void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
+ BasicBlock *Header = L->getHeader();
+
+ // Push all Loop-header PHIs onto the Worklist stack, except those
+ // that are presently represented via a SCEVUnknown. 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.
+ SmallVector<Instruction *, 16> Worklist;
+ for (BasicBlock::iterator I = Header->begin();
+ PHINode *PN = dyn_cast<PHINode>(I); ++I) {
+ std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
+ if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
+ Worklist.push_back(PN);
+ }
+
+ while (!Worklist.empty()) {
+ Instruction *I = Worklist.pop_back_val();
+ if (Scalars.erase(I))
+ for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
+ UI != UE; ++UI)
+ Worklist.push_back(cast<Instruction>(UI));
+ }
+}
+
+/// ComputeBackedgeTakenCount - Compute the number of times the backedge
+/// of the specified loop will execute.
+ScalarEvolution::BackedgeTakenInfo
+ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
+ // If the loop has a non-one exit block count, we can't analyze it.
+ SmallVector<BasicBlock*, 8> ExitBlocks;
+ L->getExitBlocks(ExitBlocks);
+ if (ExitBlocks.size() != 1) return UnknownValue;
+
+ // Okay, there is one exit block. Try to find the condition that causes the
+ // loop to be exited.
+ BasicBlock *ExitBlock = ExitBlocks[0];
+
+ BasicBlock *ExitingBlock = 0;
+ for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
+ PI != E; ++PI)
+ if (L->contains(*PI)) {
+ if (ExitingBlock == 0)
+ ExitingBlock = *PI;
+ else
+ return UnknownValue; // More than one block exiting!
+ }
+ assert(ExitingBlock && "No exits from loop, something is broken!");
+
+ // Okay, we've computed the exiting block. See what condition causes us to
+ // exit.
+ //
+ // FIXME: we should be able to handle switch instructions (with a single exit)
+ BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
+ if (ExitBr == 0) return UnknownValue;
+ 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. 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())
+ return UnknownValue;
+
+ ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
+
+ // If it's not an integer or pointer comparison then compute it the hard way.
+ if (ExitCond == 0)
+ return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
+ ExitBr->getSuccessor(0) == ExitBlock);
+
+ // If the condition was exit on true, convert the condition to exit on false
+ ICmpInst::Predicate Cond;
+ if (ExitBr->getSuccessor(1) == ExitBlock)
+ 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))) {
+ SCEVHandle ItCnt =
+ ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
+ if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
+ }
+
+ SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
+ SCEVHandle 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()));
+
+ SCEVHandle 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)
+ SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_EQ: {
+ // Convert to: while (X-Y == 0) // while (X == Y)
+ SCEVHandle 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
+ errs() << "ComputeBackedgeTakenCount ";
+ if (ExitCond->getOperand(0)->getType()->isUnsigned())
+ errs() << "[unsigned] ";
+ errs() << *LHS << " "
+ << Instruction::getOpcodeName(Instruction::ICmp)
+ << " " << *RHS << "\n";
+#endif
+ break;
+ }
+ return
+ ComputeBackedgeTakenCountExhaustively(L, ExitCond,
+ ExitBr->getSuccessor(0) == ExitBlock);
+}
+
+static ConstantInt *
+EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
+ ScalarEvolution &SE) {
+ SCEVHandle InVal = SE.getConstant(C);
+ SCEVHandle 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 {
+ assert(0 && "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.
+SCEVHandle ScalarEvolution::
+ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
+ const Loop *L,
+ ICmpInst::Predicate predicate) {
+ if (LI->isVolatile()) return UnknownValue;
+
+ // Check to see if the loaded pointer is a getelementptr of a global.
+ GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
+ if (!GEP) return UnknownValue;
+
+ // 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->hasInitializer() ||
+ GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
+ !cast<Constant>(GEP->getOperand(1))->isNullValue())
+ return UnknownValue;
+
+ // 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 UnknownValue; // 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.
+ SCEVHandle 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 UnknownValue;
+
+ unsigned MaxSteps = MaxBruteForceIterations;
+ for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
+ ConstantInt *ItCst =
+ ConstantInt::get(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
+ errs() << "\n***\n*** Computed loop count " << *ItCst
+ << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
+ << "***\n";
+#endif
+ ++NumArrayLenItCounts;
+ return getConstant(ItCst); // Found terminating iteration!
+ }
+ }
+ return UnknownValue;
+}
+
+
+/// 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->getParent())) 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) {
+ 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);
+ if (Operands[i] == 0) return 0;
+ }
+
+ if (const CmpInst *CI = dyn_cast<CmpInst>(I))
+ return ConstantFoldCompareInstOperands(CI->getPredicate(),
+ &Operands[0], Operands.size());
+ else
+ return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
+ &Operands[0], Operands.size());
+}
+
+/// 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);
+ if (NextPHI == PHIVal)
+ return RetVal = NextPHI; // Stopped evolving!
+ if (NextPHI == 0)
+ return 0; // Couldn't evaluate!
+ PHIVal = NextPHI;
+ }
+}
+
+/// ComputeBackedgeTakenCountExhaustively - If the trip 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 UnknownValue.
+SCEVHandle ScalarEvolution::
+ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
+ PHINode *PN = getConstantEvolvingPHI(Cond, L);
+ if (PN == 0) return UnknownValue;
+
+ // 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 UnknownValue; // Must be a constant.
+
+ Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
+ PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
+ if (PN2 != PN) return UnknownValue; // 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));
+
+ // Couldn't symbolically evaluate.
+ if (!CondVal) return UnknownValue;
+
+ if (CondVal->getValue() == uint64_t(ExitWhen)) {
+ ConstantEvolutionLoopExitValue[PN] = PHIVal;
+ ++NumBruteForceTripCountsComputed;
+ return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
+ }
+
+ // Compute the value of the PHI node for the next iteration.
+ Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
+ if (NextPHI == 0 || NextPHI == PHIVal)
+ return UnknownValue; // Couldn't evaluate or not making progress...
+ PHIVal = NextPHI;
+ }
+
+ // Too many iterations were needed to evaluate.
+ return UnknownValue;
+}
+
+/// getSCEVAtScope - Return a SCEV expression handle 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.
+SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
+ // FIXME: this should be turned into a virtual method on SCEV!
+
+ 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.
+ SCEVHandle 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 getUnknown(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)) {
+ // Check to see if we've folded this instruction at this loop before.
+ std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
+ std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
+ Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
+ if (!Pair.second)
+ return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
+
+ 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;
+
+ SCEVHandle OpV = getSCEVAtScope(getSCEV(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.size());
+ else
+ C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
+ &Operands[0], Operands.size());
+ Pair.first->second = C;
+ return getUnknown(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) {
+ SCEVHandle 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.
+ std::vector<SCEVHandle> 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);
+ assert(0 && "Unknown commutative SCEV type!");
+ }
+ }
+ // If we got here, all operands are loop invariant.
+ return Comm;
+ }
+
+ if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
+ SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
+ SCEVHandle 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->getHeader())) {
+ // To evaluate this recurrence, we need to know how many times the AddRec
+ // loop iterates. Compute this now.
+ SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
+ if (BackedgeTakenCount == UnknownValue) return AddRec;
+
+ // Then, evaluate the AddRec.
+ return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
+ }
+ return AddRec;
+ }
+
+ if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
+ SCEVHandle 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)) {
+ SCEVHandle 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)) {
+ SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
+ if (Op == Cast->getOperand())
+ return Cast; // must be loop invariant
+ return getTruncateExpr(Op, Cast->getType());
+ }
+
+ assert(0 && "Unknown SCEV type!");
+ return 0;
+}
+
+/// getSCEVAtScope - This is a convenience function which does
+/// getSCEVAtScope(getSCEV(V), L).
+SCEVHandle 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 SCEVHandle 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<SCEVHandle,SCEVHandle>
+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);
+ }
+
+ ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
+ ConstantInt *Solution2 = ConstantInt::get((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 UnknownValue.
+SCEVHandle 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 UnknownValue; // Otherwise it will loop infinitely.
+ }
+
+ const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
+ if (!AddRec || AddRec->getLoop() != L)
+ return UnknownValue;
+
+ 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.
+ SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
+ SCEVHandle 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<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
+ *this);
+ const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
+ const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
+ if (R1) {
+#if 0
+ errs() << "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.
+ SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
+ if (Val->isZero())
+ return R1; // We found a quadratic root!
+ }
+ }
+ }
+
+ return UnknownValue;
+}
+
+/// HowFarToNonZero - Return the number of times a backedge checking the
+/// specified value for nonzero will execute. If not computable, return
+/// UnknownValue
+SCEVHandle 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 UnknownValue; // 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 UnknownValue;
+}
+
+/// 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;
+}
+
+/// 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.
+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;
+
+ ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
+ if (!ICI) continue;
+
+ // Now that we found a conditional branch that dominates the loop, check to
+ // see if it is the comparison we are looking for.
+ Value *PreCondLHS = ICI->getOperand(0);
+ Value *PreCondRHS = ICI->getOperand(1);
+ ICmpInst::Predicate Cond;
+ if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
+ Cond = ICI->getPredicate();
+ else
+ Cond = ICI->getInversePredicate();
+
+ if (Cond == Pred)
+ ; // An exact match.
+ else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
+ ; // The actual condition is beyond sufficient.
+ else
+ // Check a few special cases.
+ switch (Cond) {
+ case ICmpInst::ICMP_UGT:
+ if (Pred == ICmpInst::ICMP_ULT) {
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_ULT;
+ break;
+ }
+ continue;
+ case ICmpInst::ICMP_SGT:
+ if (Pred == ICmpInst::ICMP_SLT) {
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_SLT;
+ break;
+ }
+ continue;
+ case ICmpInst::ICMP_NE:
+ // Expressions like (x >u 0) are often canonicalized to (x != 0),
+ // so check for this case by checking if the NE is comparing against
+ // a minimum or maximum constant.
+ if (!ICmpInst::isTrueWhenEqual(Pred))
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
+ const APInt &A = CI->getValue();
+ switch (Pred) {
+ case ICmpInst::ICMP_SLT:
+ if (A.isMaxSignedValue()) break;
+ continue;
+ case ICmpInst::ICMP_SGT:
+ if (A.isMinSignedValue()) break;
+ continue;
+ case ICmpInst::ICMP_ULT:
+ if (A.isMaxValue()) break;
+ continue;
+ case ICmpInst::ICMP_UGT:
+ if (A.isMinValue()) break;
+ continue;
+ default:
+ continue;
+ }
+ Cond = ICmpInst::ICMP_NE;
+ // NE is symmetric but the original comparison may not be. Swap
+ // the operands if necessary so that they match below.
+ if (isa<SCEVConstant>(LHS))
+ std::swap(PreCondLHS, PreCondRHS);
+ break;
+ }
+ continue;
+ default:
+ // We weren't able to reconcile the condition.
+ continue;
+ }
+
+ if (!PreCondLHS->getType()->isInteger()) continue;
+
+ SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
+ SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
+ if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
+ (LHS == getNotSCEV(PreCondRHSSCEV) &&
+ RHS == getNotSCEV(PreCondLHSSCEV)))
+ return true;
+ }
+
+ return false;
+}
+
+/// HowManyLessThans - Return the number of times a backedge containing the
+/// specified less-than comparison will execute. If not computable, return
+/// UnknownValue.
+ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
+HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
+ const Loop *L, bool isSigned) {
+ // Only handle: "ADDREC < LoopInvariant".
+ if (!RHS->isLoopInvariant(L)) return UnknownValue;
+
+ const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!AddRec || AddRec->getLoop() != L)
+ return UnknownValue;
+
+ if (AddRec->isAffine()) {
+ // FORNOW: We only support unit strides.
+ unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
+ SCEVHandle Step = AddRec->getStepRecurrence(*this);
+ SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
+
+ // TODO: handle non-constant strides.
+ const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
+ if (!CStep || CStep->isZero())
+ return UnknownValue;
+ if (CStep->isOne()) {
+ // With unit stride, the iteration never steps past the limit value.
+ } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
+ if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
+ // Test whether a positive iteration iteration can step past the limit
+ // value and past the maximum value for its type in a single step.
+ if (isSigned) {
+ APInt Max = APInt::getSignedMaxValue(BitWidth);
+ if ((Max - CStep->getValue()->getValue())
+ .slt(CLimit->getValue()->getValue()))
+ return UnknownValue;
+ } else {
+ APInt Max = APInt::getMaxValue(BitWidth);
+ if ((Max - CStep->getValue()->getValue())
+ .ult(CLimit->getValue()->getValue()))
+ return UnknownValue;
+ }
+ } else
+ // TODO: handle non-constant limit values below.
+ return UnknownValue;
+ } else
+ // TODO: handle negative strides below.
+ return UnknownValue;
+
+ // 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
+ SCEVHandle Start = AddRec->getOperand(0);
+
+ // Determine the minimum constant start value.
+ SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
+ getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
+ APInt::getMinValue(BitWidth));
+
+ // 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.
+ SCEVHandle 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.
+ SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
+ getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
+ APInt::getMaxValue(BitWidth));
+
+ // Finally, we subtract these two values and divide, rounding up, to get
+ // the number of times the backedge is executed.
+ SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
+ getAddExpr(Step, NegOne)),
+ Step);
+
+ // The maximum backedge count is similar, except using the minimum start
+ // value and the maximum end value.
+ SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
+ MinStart),
+ getAddExpr(Step, NegOne)),
+ Step);
+
+ return BackedgeTakenInfo(BECount, MaxBECount);
+ }
+
+ return UnknownValue;
+}
+
+/// 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.
+SCEVHandle 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()) {
+ std::vector<SCEVHandle> Operands(op_begin(), op_end());
+ Operands[0] = SE.getIntegerSCEV(0, SC->getType());
+ SCEVHandle 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.getConstant(ConstantInt::get(getType(),0));
+
+ 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(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(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.
+ std::vector<SCEVHandle> NewOps(op_begin(), op_end());
+ NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
+ SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
+
+ // Next, solve the constructed addrec
+ std::pair<SCEVHandle,SCEVHandle> 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(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(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 non-null ScalarEvolution!");
+ if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
+ SE->ValuesAtScopes.erase(I);
+ SE->Scalars.erase(getValPtr());
+ // this now dangles!
+}
+
+void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
+ assert(SE && "SCEVCallbackVH called with a non-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;
+ 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 (PHINode *PN = dyn_cast<PHINode>(U))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ if (Instruction *I = dyn_cast<Instruction>(U))
+ SE->ValuesAtScopes.erase(I);
+ if (SE->Scalars.erase(U))
+ for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
+ UI != UE; ++UI)
+ Worklist.push_back(*UI);
+ }
+ if (DeleteOld) {
+ if (PHINode *PN = dyn_cast<PHINode>(Old))
+ SE->ConstantEvolutionLoopExitValue.erase(PN);
+ if (Instruction *I = dyn_cast<Instruction>(Old))
+ SE->ValuesAtScopes.erase(I);
+ 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), UnknownValue(new SCEVCouldNotCompute()) {
+}
+
+bool ScalarEvolution::runOnFunction(Function &F) {
+ this->F = &F;
+ LI = &getAnalysis<LoopInfo>();
+ TD = getAnalysisIfAvailable<TargetData>();
+ return false;
+}
+
+void ScalarEvolution::releaseMemory() {
+ Scalars.clear();
+ BackedgeTakenCounts.clear();
+ ConstantEvolutionLoopExitValue.clear();
+ ValuesAtScopes.clear();
+}
+
+void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
+ AU.setPreservesAll();
+ AU.addRequiredTransitive<LoopInfo>();
+}
+
+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 " << L->getHeader()->getName() << ": ";
+
+ 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";
+}
+
+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 (the hasSCEV function
+ // notwithstanding), so casting away the const isn't dangerous.
+ ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
+
+ OS << "Classifying expressions for: " << F->getName() << "\n";
+ for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
+ if (isSCEVable(I->getType())) {
+ OS << *I;
+ OS << " --> ";
+ SCEVHandle SV = SE.getSCEV(&*I);
+ SV->print(OS);
+ OS << "\t\t";
+
+ if (const Loop *L = LI->getLoopFor((*I).getParent())) {
+ OS << "Exits: ";
+ SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
+ if (!ExitValue->isLoopInvariant(L)) {
+ OS << "<<Unknown>>";
+ } else {
+ OS << *ExitValue;
+ }
+ }
+
+ OS << "\n";
+ }
+
+ OS << "Determining loop execution counts for: " << F->getName() << "\n";
+ for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
+ PrintLoopInfo(OS, &SE, *I);
+}
+
+void ScalarEvolution::print(std::ostream &o, const Module *M) const {
+ raw_os_ostream OS(o);
+ print(OS, M);
+}
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