It's not necessary to do rounding for alloca operations when the requested
alignment is equal to the stack alignment.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@40004 91177308-0d34-0410-b5e6-96231b3b80d8
diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
new file mode 100644
index 0000000..0039144
--- /dev/null
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -0,0 +1,2656 @@
+//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file was developed by the LLVM research group and 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/LoopInfo.h"
+#include "llvm/Assembly/Writer.h"
+#include "llvm/Transforms/Scalar.h"
+#include "llvm/Support/CFG.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/Compiler.h"
+#include "llvm/Support/ConstantRange.h"
+#include "llvm/Support/InstIterator.h"
+#include "llvm/Support/ManagedStatic.h"
+#include "llvm/Support/MathExtras.h"
+#include "llvm/Support/Streams.h"
+#include "llvm/ADT/Statistic.h"
+#include <ostream>
+#include <algorithm>
+#include <cmath>
+using namespace llvm;
+
+STATISTIC(NumBruteForceEvaluations,
+ "Number of brute force evaluations needed to "
+ "calculate high-order polynomial exit values");
+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");
+
+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));
+
+namespace {
+ RegisterPass<ScalarEvolution>
+ R("scalar-evolution", "Scalar Evolution Analysis");
+}
+char ScalarEvolution::ID = 0;
+
+//===----------------------------------------------------------------------===//
+// SCEV class definitions
+//===----------------------------------------------------------------------===//
+
+//===----------------------------------------------------------------------===//
+// Implementation of the SCEV class.
+//
+SCEV::~SCEV() {}
+void SCEV::dump() const {
+ print(cerr);
+}
+
+/// getValueRange - Return the tightest constant bounds that this value is
+/// known to have. This method is only valid on integer SCEV objects.
+ConstantRange SCEV::getValueRange() const {
+ const Type *Ty = getType();
+ assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
+ // Default to a full range if no better information is available.
+ return ConstantRange(getBitWidth());
+}
+
+uint32_t SCEV::getBitWidth() const {
+ if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
+ return ITy->getBitWidth();
+ return 0;
+}
+
+
+SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
+
+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) const {
+ return this;
+}
+
+void SCEVCouldNotCompute::print(std::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 SCEVConstant::get(ConstantInt *V) {
+ SCEVConstant *&R = (*SCEVConstants)[V];
+ if (R == 0) R = new SCEVConstant(V);
+ return R;
+}
+
+SCEVHandle SCEVConstant::get(const APInt& Val) {
+ return get(ConstantInt::get(Val));
+}
+
+ConstantRange SCEVConstant::getValueRange() const {
+ return ConstantRange(V->getValue());
+}
+
+const Type *SCEVConstant::getType() const { return V->getType(); }
+
+void SCEVConstant::print(std::ostream &OS) const {
+ WriteAsOperand(OS, V, false);
+}
+
+// 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<SCEV*, const Type*>,
+ SCEVTruncateExpr*> > SCEVTruncates;
+
+SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
+ : SCEV(scTruncate), Op(op), Ty(ty) {
+ assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ "Cannot truncate non-integer value!");
+ assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
+ && "This is not a truncating conversion!");
+}
+
+SCEVTruncateExpr::~SCEVTruncateExpr() {
+ SCEVTruncates->erase(std::make_pair(Op, Ty));
+}
+
+ConstantRange SCEVTruncateExpr::getValueRange() const {
+ return getOperand()->getValueRange().truncate(getBitWidth());
+}
+
+void SCEVTruncateExpr::print(std::ostream &OS) const {
+ OS << "(truncate " << *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<SCEV*, const Type*>,
+ SCEVZeroExtendExpr*> > SCEVZeroExtends;
+
+SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
+ : SCEV(scZeroExtend), Op(op), Ty(ty) {
+ assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ "Cannot zero extend non-integer value!");
+ assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
+ && "This is not an extending conversion!");
+}
+
+SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
+ SCEVZeroExtends->erase(std::make_pair(Op, Ty));
+}
+
+ConstantRange SCEVZeroExtendExpr::getValueRange() const {
+ return getOperand()->getValueRange().zeroExtend(getBitWidth());
+}
+
+void SCEVZeroExtendExpr::print(std::ostream &OS) const {
+ OS << "(zeroextend " << *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<SCEV*, const Type*>,
+ SCEVSignExtendExpr*> > SCEVSignExtends;
+
+SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
+ : SCEV(scSignExtend), Op(op), Ty(ty) {
+ assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ "Cannot sign extend non-integer value!");
+ assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
+ && "This is not an extending conversion!");
+}
+
+SCEVSignExtendExpr::~SCEVSignExtendExpr() {
+ SCEVSignExtends->erase(std::make_pair(Op, Ty));
+}
+
+ConstantRange SCEVSignExtendExpr::getValueRange() const {
+ return getOperand()->getValueRange().signExtend(getBitWidth());
+}
+
+void SCEVSignExtendExpr::print(std::ostream &OS) const {
+ OS << "(signextend " << *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<SCEV*> >,
+ SCEVCommutativeExpr*> > SCEVCommExprs;
+
+SCEVCommutativeExpr::~SCEVCommutativeExpr() {
+ SCEVCommExprs->erase(std::make_pair(getSCEVType(),
+ std::vector<SCEV*>(Operands.begin(),
+ Operands.end())));
+}
+
+void SCEVCommutativeExpr::print(std::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) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
+ 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));
+
+ if (isa<SCEVAddExpr>(this))
+ return SCEVAddExpr::get(NewOps);
+ else if (isa<SCEVMulExpr>(this))
+ return SCEVMulExpr::get(NewOps);
+ else
+ assert(0 && "Unknown commutative expr!");
+ }
+ }
+ return this;
+}
+
+
+// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
+// input. Don't use a SCEVHandle here, or else the object will never be
+// deleted!
+static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
+ SCEVSDivExpr*> > SCEVSDivs;
+
+SCEVSDivExpr::~SCEVSDivExpr() {
+ SCEVSDivs->erase(std::make_pair(LHS, RHS));
+}
+
+void SCEVSDivExpr::print(std::ostream &OS) const {
+ OS << "(" << *LHS << " /s " << *RHS << ")";
+}
+
+const Type *SCEVSDivExpr::getType() const {
+ return LHS->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<SCEV*> >,
+ SCEVAddRecExpr*> > SCEVAddRecExprs;
+
+SCEVAddRecExpr::~SCEVAddRecExpr() {
+ SCEVAddRecExprs->erase(std::make_pair(L,
+ std::vector<SCEV*>(Operands.begin(),
+ Operands.end())));
+}
+
+SCEVHandle SCEVAddRecExpr::
+replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
+ const SCEVHandle &Conc) const {
+ for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
+ SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
+ 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));
+
+ return get(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.
+ return !QueryLoop->contains(L->getHeader()) &&
+ getOperand(0)->isLoopInvariant(QueryLoop);
+}
+
+
+void SCEVAddRecExpr::print(std::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.
+ if (Instruction *I = dyn_cast<Instruction>(V))
+ return !L->contains(I->getParent());
+ return true;
+}
+
+const Type *SCEVUnknown::getType() const {
+ return V->getType();
+}
+
+void SCEVUnknown::print(std::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.
+ struct VISIBILITY_HIDDEN SCEVComplexityCompare {
+ bool operator()(SCEV *LHS, SCEV *RHS) {
+ return LHS->getSCEVType() < RHS->getSCEVType();
+ }
+ };
+}
+
+/// 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) {
+ 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 (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
+ std::swap(Ops[0], Ops[1]);
+ return;
+ }
+
+ // Do the rough sort by complexity.
+ std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
+
+ // 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) {
+ 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
+//===----------------------------------------------------------------------===//
+
+/// getIntegerSCEV - Given an integer or FP type, create a constant for the
+/// specified signed integer value and return a SCEV for the constant.
+SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
+ Constant *C;
+ if (Val == 0)
+ C = Constant::getNullValue(Ty);
+ else if (Ty->isFloatingPoint())
+ C = ConstantFP::get(Ty, Val);
+ else
+ C = ConstantInt::get(Ty, Val);
+ return SCEVUnknown::get(C);
+}
+
+/// 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.
+static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert(SrcTy->isInteger() && Ty->isInteger() &&
+ "Cannot truncate or zero extend with non-integer arguments!");
+ if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
+ return V; // No conversion
+ if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
+ return SCEVTruncateExpr::get(V, Ty);
+ return SCEVZeroExtendExpr::get(V, Ty);
+}
+
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
+ if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
+
+ return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+ // X - Y --> X + -Y
+ return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
+}
+
+
+/// PartialFact - Compute V!/(V-NumSteps)!
+static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
+ // Handle this case efficiently, it is common to have constant iteration
+ // counts while computing loop exit values.
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
+ const APInt& Val = SC->getValue()->getValue();
+ APInt Result(Val.getBitWidth(), 1);
+ for (; NumSteps; --NumSteps)
+ Result *= Val-(NumSteps-1);
+ return SCEVConstant::get(Result);
+ }
+
+ const Type *Ty = V->getType();
+ if (NumSteps == 0)
+ return SCEVUnknown::getIntegerSCEV(1, Ty);
+
+ SCEVHandle Result = V;
+ for (unsigned i = 1; i != NumSteps; ++i)
+ Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
+ SCEVUnknown::getIntegerSCEV(i, Ty)));
+ return Result;
+}
+
+
+/// 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*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
+///
+/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
+/// Is the binomial equation safe using modular arithmetic??
+///
+SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
+ SCEVHandle Result = getStart();
+ int Divisor = 1;
+ const Type *Ty = It->getType();
+ for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
+ SCEVHandle BC = PartialFact(It, i);
+ Divisor *= i;
+ SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
+ SCEVUnknown::getIntegerSCEV(Divisor,Ty));
+ Result = SCEVAddExpr::get(Result, Val);
+ }
+ return Result;
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEV Expression folder implementations
+//===----------------------------------------------------------------------===//
+
+SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return SCEVUnknown::get(
+ ConstantExpr::getTrunc(SC->getValue(), Ty));
+
+ // If the input value is a chrec scev made out of constants, truncate
+ // all of the constants.
+ if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
+ std::vector<SCEVHandle> Operands;
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
+ // FIXME: This should allow truncation of other expression types!
+ if (isa<SCEVConstant>(AddRec->getOperand(i)))
+ Operands.push_back(get(AddRec->getOperand(i), Ty));
+ else
+ break;
+ if (Operands.size() == AddRec->getNumOperands())
+ return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
+ }
+
+ SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
+ return Result;
+}
+
+SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return SCEVUnknown::get(
+ ConstantExpr::getZExt(SC->getValue(), Ty));
+
+ // FIXME: 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 would allow analysis of something like
+ // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
+
+ SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
+ return Result;
+}
+
+SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return SCEVUnknown::get(
+ ConstantExpr::getSExt(SC->getValue(), Ty));
+
+ // FIXME: 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 would allow analysis of something like
+ // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
+
+ SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
+ return Result;
+}
+
+// get - Get a canonical add expression, or something simpler if possible.
+SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
+ assert(!Ops.empty() && "Cannot get empty add!");
+ if (Ops.size() == 1) return Ops[0];
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
+ RHSC->getValue()->getValue());
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
+ Ops[0] = SCEVConstant::get(CI);
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ if (Ops.size() == 1) return Ops[0];
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ } else {
+ // If we couldn't fold the expression, move to the next constant. Note
+ // that this is impossible to happen in practice because we always
+ // constant fold constant ints to constant ints.
+ ++Idx;
+ }
+ }
+
+ // 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 = SCEVUnknown::getIntegerSCEV(2, Ty);
+ SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
+ if (Ops.size() == 2)
+ return Mul;
+ Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
+ Ops.push_back(Mul);
+ return SCEVAddExpr::get(Ops);
+ }
+
+ // Now we know the first non-constant operand. Skip past any 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 (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 get(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) {
+ SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
+ for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
+ 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 = SCEVMulExpr::get(MulOps);
+ }
+ SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
+ SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
+ SCEVHandle OuterMul = SCEVMulExpr::get(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 SCEVAddExpr::get(Ops);
+ }
+
+ // Check this multiply against other multiplies being added together.
+ for (unsigned OtherMulIdx = Idx+1;
+ OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
+ ++OtherMulIdx) {
+ 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 = SCEVMulExpr::get(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 = SCEVMulExpr::get(MulOps);
+ }
+ SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
+ SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
+ if (Ops.size() == 2) return OuterMul;
+ Ops.erase(Ops.begin()+Idx);
+ Ops.erase(Ops.begin()+OtherMulIdx-1);
+ Ops.push_back(OuterMul);
+ return SCEVAddExpr::get(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;
+ 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] = SCEVAddExpr::get(LIOps);
+
+ SCEVHandle NewRec = SCEVAddRecExpr::get(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 SCEVAddExpr::get(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) {
+ 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] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
+ }
+ SCEVHandle NewAddRec = SCEVAddRecExpr::get(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 SCEVAddExpr::get(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<SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
+ SCEVOps)];
+ if (Result == 0) Result = new SCEVAddExpr(Ops);
+ return Result;
+}
+
+
+SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
+ assert(!Ops.empty() && "Cannot get empty mul!");
+
+ // Sort by complexity, this groups all similar expression types together.
+ GroupByComplexity(Ops);
+
+ // If there are any constants, fold them together.
+ unsigned Idx = 0;
+ if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+
+ // C1*(C2+V) -> C1*C2 + C1*V
+ if (Ops.size() == 2)
+ if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
+ if (Add->getNumOperands() == 2 &&
+ isa<SCEVConstant>(Add->getOperand(0)))
+ return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
+ SCEVMulExpr::get(LHSC, Add->getOperand(1)));
+
+
+ ++Idx;
+ while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
+ RHSC->getValue()->getValue());
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
+ Ops[0] = SCEVConstant::get(CI);
+ Ops.erase(Ops.begin()+1); // Erase the folded element
+ if (Ops.size() == 1) return Ops[0];
+ LHSC = cast<SCEVConstant>(Ops[0]);
+ } else {
+ // If we couldn't fold the expression, move to the next constant. Note
+ // that this is impossible to happen in practice because we always
+ // constant fold constant ints to constant ints.
+ ++Idx;
+ }
+ }
+
+ // 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 (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 get(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;
+ 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) {
+ SCEV *Scale = LIOps[0];
+ for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
+ NewOps.push_back(SCEVMulExpr::get(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(SCEVMulExpr::get(MulOps));
+ }
+ }
+
+ SCEVHandle NewRec = SCEVAddRecExpr::get(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 SCEVMulExpr::get(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) {
+ 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}
+ SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
+ SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
+ G->getStart());
+ SCEVHandle B = F->getStepRecurrence();
+ SCEVHandle D = G->getStepRecurrence();
+ SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
+ SCEVMulExpr::get(G, B),
+ SCEVMulExpr::get(B, D));
+ SCEVHandle NewAddRec = SCEVAddRecExpr::get(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 SCEVMulExpr::get(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<SCEV*> SCEVOps(Ops.begin(), Ops.end());
+ SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
+ SCEVOps)];
+ if (Result == 0)
+ Result = new SCEVMulExpr(Ops);
+ return Result;
+}
+
+SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+ if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+ if (RHSC->getValue()->equalsInt(1))
+ return LHS; // X sdiv 1 --> x
+ if (RHSC->getValue()->isAllOnesValue())
+ return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
+
+ if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
+ Constant *LHSCV = LHSC->getValue();
+ Constant *RHSCV = RHSC->getValue();
+ return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
+ }
+ }
+
+ // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
+
+ SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
+ if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
+ return Result;
+}
+
+
+/// SCEVAddRecExpr::get - Get a add recurrence expression for the
+/// specified loop. Simplify the expression as much as possible.
+SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
+ const SCEVHandle &Step, const Loop *L) {
+ std::vector<SCEVHandle> Operands;
+ Operands.push_back(Start);
+ if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
+ if (StepChrec->getLoop() == L) {
+ Operands.insert(Operands.end(), StepChrec->op_begin(),
+ StepChrec->op_end());
+ return get(Operands, L);
+ }
+
+ Operands.push_back(Step);
+ return get(Operands, L);
+}
+
+/// SCEVAddRecExpr::get - Get a add recurrence expression for the
+/// specified loop. Simplify the expression as much as possible.
+SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
+ const Loop *L) {
+ if (Operands.size() == 1) return Operands[0];
+
+ if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
+ if (StepC->getValue()->isZero()) {
+ Operands.pop_back();
+ return get(Operands, L); // { X,+,0 } --> X
+ }
+
+ SCEVAddRecExpr *&Result =
+ (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
+ Operands.end()))];
+ if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
+ return Result;
+}
+
+SCEVHandle SCEVUnknown::get(Value *V) {
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
+ return SCEVConstant::get(CI);
+ SCEVUnknown *&Result = (*SCEVUnknowns)[V];
+ if (Result == 0) Result = new SCEVUnknown(V);
+ return Result;
+}
+
+
+//===----------------------------------------------------------------------===//
+// ScalarEvolutionsImpl Definition and Implementation
+//===----------------------------------------------------------------------===//
+//
+/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
+/// evolution code.
+///
+namespace {
+ struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
+ /// F - The function we are analyzing.
+ ///
+ Function &F;
+
+ /// LI - The loop information for the function we are currently analyzing.
+ ///
+ LoopInfo &LI;
+
+ /// UnknownValue - This SCEV is used to represent unknown trip counts and
+ /// things.
+ SCEVHandle UnknownValue;
+
+ /// Scalars - This is a cache of the scalars we have analyzed so far.
+ ///
+ std::map<Value*, SCEVHandle> Scalars;
+
+ /// IterationCounts - Cache the iteration count of the loops for this
+ /// function as they are computed.
+ std::map<const Loop*, SCEVHandle> IterationCounts;
+
+ /// ConstantEvolutionLoopExitValue - This map contains entries for all of
+ /// the PHI instructions that we attempt to compute constant evolutions for.
+ /// This allows us to avoid potentially expensive recomputation of these
+ /// properties. An instruction maps to null if we are unable to compute its
+ /// exit value.
+ std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
+
+ public:
+ ScalarEvolutionsImpl(Function &f, LoopInfo &li)
+ : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
+
+ /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
+ /// expression and create a new one.
+ SCEVHandle getSCEV(Value *V);
+
+ /// hasSCEV - Return true if the SCEV for this value has already been
+ /// computed.
+ bool hasSCEV(Value *V) const {
+ return Scalars.count(V);
+ }
+
+ /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
+ /// the specified value.
+ void setSCEV(Value *V, const SCEVHandle &H) {
+ bool isNew = Scalars.insert(std::make_pair(V, H)).second;
+ assert(isNew && "This entry already existed!");
+ }
+
+
+ /// getSCEVAtScope - Compute the value of the specified expression within
+ /// the indicated loop (which may be null to indicate in no loop). If the
+ /// expression cannot be evaluated, return UnknownValue itself.
+ SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
+
+
+ /// hasLoopInvariantIterationCount - Return true if the specified loop has
+ /// an analyzable loop-invariant iteration count.
+ bool hasLoopInvariantIterationCount(const Loop *L);
+
+ /// getIterationCount - If the specified loop has a predictable iteration
+ /// count, return it. Note that it is not valid to call this method on a
+ /// loop without a loop-invariant iteration count.
+ SCEVHandle getIterationCount(const Loop *L);
+
+ /// deleteValueFromRecords - This method should be called by the
+ /// client before it removes a value from the program, to make sure
+ /// that no dangling references are left around.
+ void deleteValueFromRecords(Value *V);
+
+ private:
+ /// createSCEV - We know that there is no SCEV for the specified value.
+ /// Analyze the expression.
+ SCEVHandle createSCEV(Value *V);
+
+ /// createNodeForPHI - Provide the special handling we need to analyze PHI
+ /// SCEVs.
+ SCEVHandle createNodeForPHI(PHINode *PN);
+
+ /// 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 ReplaceSymbolicValueWithConcrete(Instruction *I,
+ const SCEVHandle &SymName,
+ const SCEVHandle &NewVal);
+
+ /// ComputeIterationCount - Compute the number of times the specified loop
+ /// will iterate.
+ SCEVHandle ComputeIterationCount(const Loop *L);
+
+ /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
+ /// 'setcc load X, cst', try to see if we can compute the trip count.
+ SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
+ Constant *RHS,
+ const Loop *L,
+ ICmpInst::Predicate p);
+
+ /// ComputeIterationCountExhaustively - 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 ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
+ bool ExitWhen);
+
+ /// HowFarToZero - Return the number of times a backedge comparing the
+ /// specified value to zero will execute. If not computable, return
+ /// UnknownValue.
+ SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
+
+ /// HowFarToNonZero - Return the number of times a backedge checking the
+ /// specified value for nonzero will execute. If not computable, return
+ /// UnknownValue.
+ SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
+
+ /// HowManyLessThans - Return the number of times a backedge containing the
+ /// specified less-than comparison will execute. If not computable, return
+ /// UnknownValue.
+ SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
+
+ /// 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 *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
+ const Loop *L);
+ };
+}
+
+//===----------------------------------------------------------------------===//
+// Basic SCEV Analysis and PHI Idiom Recognition Code
+//
+
+/// deleteValueFromRecords - This method should be called by the
+/// client before it removes an instruction from the program, to make sure
+/// that no dangling references are left around.
+void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
+ SmallVector<Value *, 16> Worklist;
+
+ if (Scalars.erase(V)) {
+ if (PHINode *PN = dyn_cast<PHINode>(V))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ Worklist.push_back(V);
+ }
+
+ while (!Worklist.empty()) {
+ Value *VV = Worklist.back();
+ Worklist.pop_back();
+
+ for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
+ UI != UE; ++UI) {
+ Instruction *Inst = cast<Instruction>(*UI);
+ if (Scalars.erase(Inst)) {
+ if (PHINode *PN = dyn_cast<PHINode>(VV))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ Worklist.push_back(Inst);
+ }
+ }
+ }
+}
+
+
+/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
+/// expression and create a new one.
+SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
+ assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
+
+ std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
+ if (I != Scalars.end()) return I->second;
+ SCEVHandle S = createSCEV(V);
+ Scalars.insert(std::make_pair(V, S));
+ return S;
+}
+
+/// 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 ScalarEvolutionsImpl::
+ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
+ const SCEVHandle &NewVal) {
+ std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
+ if (SI == Scalars.end()) return;
+
+ SCEVHandle NV =
+ SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
+ 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 ScalarEvolutionsImpl::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 = SCEVUnknown::get(PN);
+ assert(Scalars.find(PN) == Scalars.end() &&
+ "PHI node already processed?");
+ Scalars.insert(std::make_pair(PN, 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 (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 = SCEVAddExpr::get(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 = SCEVAddRecExpr::get(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 (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 == SCEV::getMinusSCEV(AddRec->getOperand(0),
+ AddRec->getOperand(1))) {
+ SCEVHandle PHISCEV =
+ SCEVAddRecExpr::get(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 SCEVUnknown::get(PN);
+}
+
+/// GetConstantFactor - Determine the largest constant factor that S has. For
+/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
+static APInt GetConstantFactor(SCEVHandle S) {
+ if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
+ const APInt& V = C->getValue()->getValue();
+ if (!V.isMinValue())
+ return V;
+ else // Zero is a multiple of everything.
+ return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
+ }
+
+ if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
+ return GetConstantFactor(T->getOperand()).trunc(
+ cast<IntegerType>(T->getType())->getBitWidth());
+ }
+ if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
+ return GetConstantFactor(E->getOperand()).zext(
+ cast<IntegerType>(E->getType())->getBitWidth());
+ if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S))
+ return GetConstantFactor(E->getOperand()).sext(
+ cast<IntegerType>(E->getType())->getBitWidth());
+
+ if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
+ // The result is the min of all operands.
+ APInt Res(GetConstantFactor(A->getOperand(0)));
+ for (unsigned i = 1, e = A->getNumOperands();
+ i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
+ APInt Tmp(GetConstantFactor(A->getOperand(i)));
+ Res = APIntOps::umin(Res, Tmp);
+ }
+ return Res;
+ }
+
+ if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
+ // The result is the product of all the operands.
+ APInt Res(GetConstantFactor(M->getOperand(0)));
+ for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
+ APInt Tmp(GetConstantFactor(M->getOperand(i)));
+ Res *= Tmp;
+ }
+ return Res;
+ }
+
+ if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
+ // For now, we just handle linear expressions.
+ if (A->getNumOperands() == 2) {
+ // We want the GCD between the start and the stride value.
+ APInt Start(GetConstantFactor(A->getOperand(0)));
+ if (Start == 1)
+ return Start;
+ APInt Stride(GetConstantFactor(A->getOperand(1)));
+ return APIntOps::GreatestCommonDivisor(Start, Stride);
+ }
+ }
+
+ // SCEVSDivExpr, SCEVUnknown.
+ return APInt(S->getBitWidth(), 1);
+}
+
+/// createSCEV - We know that there is no SCEV for the specified value.
+/// Analyze the expression.
+///
+SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
+ if (Instruction *I = dyn_cast<Instruction>(V)) {
+ switch (I->getOpcode()) {
+ case Instruction::Add:
+ return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
+ getSCEV(I->getOperand(1)));
+ case Instruction::Mul:
+ return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
+ getSCEV(I->getOperand(1)));
+ case Instruction::SDiv:
+ return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
+ getSCEV(I->getOperand(1)));
+ break;
+
+ case Instruction::Sub:
+ return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
+ getSCEV(I->getOperand(1)));
+ 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.
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
+ SCEVHandle LHS = getSCEV(I->getOperand(0));
+ APInt CommonFact(GetConstantFactor(LHS));
+ assert(!CommonFact.isMinValue() &&
+ "Common factor should at least be 1!");
+ if (CommonFact.ugt(CI->getValue())) {
+ // If the LHS is a multiple that is larger than the RHS, use +.
+ return SCEVAddExpr::get(LHS,
+ getSCEV(I->getOperand(1)));
+ }
+ }
+ break;
+ case Instruction::Xor:
+ // 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 (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
+ if (CI->getValue().isSignBit())
+ return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
+ getSCEV(I->getOperand(1)));
+ }
+ break;
+
+ case Instruction::Shl:
+ // Turn shift left of a constant amount into a multiply.
+ if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
+ uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
+ Constant *X = ConstantInt::get(
+ APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
+ return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
+ }
+ break;
+
+ case Instruction::Trunc:
+ return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
+
+ case Instruction::ZExt:
+ return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
+
+ case Instruction::SExt:
+ return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
+
+ case Instruction::BitCast:
+ // BitCasts are no-op casts so we just eliminate the cast.
+ if (I->getType()->isInteger() &&
+ I->getOperand(0)->getType()->isInteger())
+ return getSCEV(I->getOperand(0));
+ break;
+
+ case Instruction::PHI:
+ return createNodeForPHI(cast<PHINode>(I));
+
+ default: // We cannot analyze this expression.
+ break;
+ }
+ }
+
+ return SCEVUnknown::get(V);
+}
+
+
+
+//===----------------------------------------------------------------------===//
+// Iteration Count Computation Code
+//
+
+/// getIterationCount - If the specified loop has a predictable iteration
+/// count, return it. Note that it is not valid to call this method on a
+/// loop without a loop-invariant iteration count.
+SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
+ std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
+ if (I == IterationCounts.end()) {
+ SCEVHandle ItCount = ComputeIterationCount(L);
+ I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
+ if (ItCount != UnknownValue) {
+ assert(ItCount->isLoopInvariant(L) &&
+ "Computed trip count isn't loop invariant for loop!");
+ ++NumTripCountsComputed;
+ } else if (isa<PHINode>(L->getHeader()->begin())) {
+ // Only count loops that have phi nodes as not being computable.
+ ++NumTripCountsNotComputed;
+ }
+ }
+ return I->second;
+}
+
+/// ComputeIterationCount - Compute the number of times the specified loop
+/// will iterate.
+SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
+ // If the loop has a non-one exit block count, we can't analyze it.
+ std::vector<BasicBlock*> 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 its not an integer comparison then compute it the hard way.
+ // Note that ICmpInst deals with pointer comparisons too so we must check
+ // the type of the operand.
+ if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
+ return ComputeIterationCountExhaustively(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 =
+ ComputeLoadConstantCompareIterationCount(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.
+ SCEVHandle Tmp = getSCEVAtScope(LHS, L);
+ if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
+ Tmp = getSCEVAtScope(RHS, L);
+ if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
+
+ // At this point, we would like to compute how many iterations of the
+ // loop the predicate will return true for these inputs.
+ if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
+ // If there is a constant, force it into the RHS.
+ std::swap(LHS, RHS);
+ Cond = ICmpInst::getSwappedPredicate(Cond);
+ }
+
+ // FIXME: think about handling pointer comparisons! i.e.:
+ // while (P != P+100) ++P;
+
+ // If we have a comparison of a chrec against a constant, try to use value
+ // ranges to answer this query.
+ if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
+ if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
+ if (AddRec->getLoop() == L) {
+ // Form the comparison range using the constant of the correct type so
+ // that the ConstantRange class knows to do a signed or unsigned
+ // comparison.
+ ConstantInt *CompVal = RHSC->getValue();
+ const Type *RealTy = ExitCond->getOperand(0)->getType();
+ CompVal = dyn_cast<ConstantInt>(
+ ConstantExpr::getBitCast(CompVal, RealTy));
+ if (CompVal) {
+ // Form the constant range.
+ ConstantRange CompRange(
+ ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
+
+ SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
+ if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
+ }
+ }
+
+ switch (Cond) {
+ case ICmpInst::ICMP_NE: { // while (X != Y)
+ // Convert to: while (X-Y != 0)
+ SCEVHandle TC = HowFarToZero(SCEV::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(SCEV::getMinusSCEV(LHS, RHS), L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_SLT: {
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_SGT: {
+ SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS),
+ SCEV::getNegativeSCEV(RHS), L);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ default:
+#if 0
+ cerr << "ComputeIterationCount ";
+ if (ExitCond->getOperand(0)->getType()->isUnsigned())
+ cerr << "[unsigned] ";
+ cerr << *LHS << " "
+ << Instruction::getOpcodeName(Instruction::ICmp)
+ << " " << *RHS << "\n";
+#endif
+ break;
+ }
+ return ComputeIterationCountExhaustively(L, ExitCond,
+ ExitBr->getSuccessor(0) == ExitBlock);
+}
+
+static ConstantInt *
+EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C) {
+ SCEVHandle InVal = SCEVConstant::get(C);
+ SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
+ 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;
+}
+
+/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
+/// 'setcc load X, cst', try to se if we can compute the trip count.
+SCEVHandle ScalarEvolutionsImpl::
+ComputeLoadConstantCompareIterationCount(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);
+ SCEVHandle Tmp = getSCEVAtScope(Idx, L);
+ if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
+
+ // We can only recognize very limited forms of loop index expressions, in
+ // particular, only affine AddRec's like {C1,+,C2}.
+ 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);
+
+ // 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
+ cerr << "\n***\n*** Computed loop count " << *ItCst
+ << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
+ << "***\n";
+#endif
+ ++NumArrayLenItCounts;
+ return SCEVConstant::get(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((Function*)F); // FIXME: elim cast
+ 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 (GlobalValue *GV = dyn_cast<GlobalValue>(V))
+ return GV;
+ if (Constant *C = dyn_cast<Constant>(V)) return C;
+ 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;
+ }
+
+ return ConstantFoldInstOperands(I, &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 *ScalarEvolutionsImpl::
+getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
+ std::map<PHINode*, Constant*>::iterator I =
+ ConstantEvolutionLoopExitValue.find(PN);
+ if (I != ConstantEvolutionLoopExitValue.end())
+ return I->second;
+
+ if (Its.ugt(APInt(Its.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 (Its.getActiveBits() >= 32)
+ return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
+
+ unsigned NumIterations = Its.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;
+ }
+}
+
+/// ComputeIterationCountExhaustively - 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 ScalarEvolutionsImpl::
+ComputeIterationCountExhaustively(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 SCEVConstant::get(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 - Compute the value of the specified expression within the
+/// indicated loop (which may be null to indicate in no loop). If the
+/// expression cannot be evaluated, return UnknownValue.
+SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(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 evolves from a constant-evolving PHI, compute the
+ // exit value from the loop without using SCEVs.
+ if (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 iteration count.
+ // If so, we may be able to force computation of the exit value.
+ SCEVHandle IterationCount = getIterationCount(LI);
+ if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
+ // 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,
+ ICC->getValue()->getValue(),
+ LI);
+ if (RV) return SCEVUnknown::get(RV);
+ }
+ }
+
+ // Okay, this is an expression that we cannot symbolically evaluate
+ // into a SCEV. Check to see if it's possible to symbolically evaluate
+ // the arguments into constants, and if so, try to constant propagate the
+ // result. This is particularly useful for computing loop exit values.
+ if (CanConstantFold(I)) {
+ std::vector<Constant*> Operands;
+ Operands.reserve(I->getNumOperands());
+ for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
+ Value *Op = I->getOperand(i);
+ if (Constant *C = dyn_cast<Constant>(Op)) {
+ Operands.push_back(C);
+ } else {
+ SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
+ Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
+ Op->getType(),
+ false));
+ else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
+ if (Constant *C = dyn_cast<Constant>(SU->getValue()))
+ Operands.push_back(ConstantExpr::getIntegerCast(C,
+ Op->getType(),
+ false));
+ else
+ return V;
+ } else {
+ return V;
+ }
+ }
+ }
+ Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
+ return SCEVUnknown::get(C);
+ }
+ }
+
+ // This is some other type of SCEVUnknown, just return it.
+ return V;
+ }
+
+ if (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)) {
+ if (OpAtScope == UnknownValue) return UnknownValue;
+ // 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);
+ if (OpAtScope == UnknownValue) return UnknownValue;
+ NewOps.push_back(OpAtScope);
+ }
+ if (isa<SCEVAddExpr>(Comm))
+ return SCEVAddExpr::get(NewOps);
+ assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
+ return SCEVMulExpr::get(NewOps);
+ }
+ }
+ // If we got here, all operands are loop invariant.
+ return Comm;
+ }
+
+ if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
+ SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
+ if (LHS == UnknownValue) return LHS;
+ SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
+ if (RHS == UnknownValue) return RHS;
+ if (LHS == Div->getLHS() && RHS == Div->getRHS())
+ return Div; // must be loop invariant
+ return SCEVSDivExpr::get(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 (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 IterationCount = getIterationCount(AddRec->getLoop());
+ if (IterationCount == UnknownValue) return UnknownValue;
+ IterationCount = getTruncateOrZeroExtend(IterationCount,
+ AddRec->getType());
+
+ // If the value is affine, simplify the expression evaluation to just
+ // Start + Step*IterationCount.
+ if (AddRec->isAffine())
+ return SCEVAddExpr::get(AddRec->getStart(),
+ SCEVMulExpr::get(IterationCount,
+ AddRec->getOperand(1)));
+
+ // Otherwise, evaluate it the hard way.
+ return AddRec->evaluateAtIteration(IterationCount);
+ }
+ return UnknownValue;
+ }
+
+ //assert(0 && "Unknown SCEV type!");
+ return UnknownValue;
+}
+
+
+/// 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) {
+ assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
+ SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
+ SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
+ SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
+
+ // We currently can only solve this if the coefficients are constants.
+ if (!LC || !MC || !NC) {
+ SCEV *CNC = new SCEVCouldNotCompute();
+ 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 );
+ ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
+ ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
+
+ return std::make_pair(SCEVConstant::get(Solution1),
+ SCEVConstant::get(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 ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
+ // If the value is a constant
+ if (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.
+ }
+
+ 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
+ // equal to:
+ //
+ // (0 - Start/Step) iff Start % Step == 0
+ //
+ // Get the initial value for the loop.
+ SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
+ if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
+ SCEVHandle Step = AddRec->getOperand(1);
+
+ Step = getSCEVAtScope(Step, L->getParentLoop());
+
+ // Figure out if Start % Step == 0.
+ // FIXME: We should add DivExpr and RemExpr operations to our AST.
+ if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
+ if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
+ return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
+ if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
+ return Start; // 0 - Start/-1 == Start
+
+ // Check to see if Start is divisible by SC with no remainder.
+ if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
+ ConstantInt *StartCC = StartC->getValue();
+ Constant *StartNegC = ConstantExpr::getNeg(StartCC);
+ Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
+ if (Rem->isNullValue()) {
+ Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
+ return SCEVUnknown::get(Result);
+ }
+ }
+ }
+ } 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);
+ SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
+ SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
+ if (R1) {
+#if 0
+ cerr << "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);
+ if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
+ if (EvalVal->getValue()->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 ScalarEvolutionsImpl::HowFarToNonZero(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 (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
+ Constant *Zero = Constant::getNullValue(C->getValue()->getType());
+ Constant *NonZero =
+ ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
+ if (NonZero == ConstantInt::getTrue())
+ return getSCEV(Zero);
+ 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;
+}
+
+/// HowManyLessThans - Return the number of times a backedge containing the
+/// specified less-than comparison will execute. If not computable, return
+/// UnknownValue.
+SCEVHandle ScalarEvolutionsImpl::
+HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
+ // Only handle: "ADDREC < LoopInvariant".
+ if (!RHS->isLoopInvariant(L)) return UnknownValue;
+
+ SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
+ if (!AddRec || AddRec->getLoop() != L)
+ return UnknownValue;
+
+ if (AddRec->isAffine()) {
+ // FORNOW: We only support unit strides.
+ SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
+ if (AddRec->getOperand(1) != One)
+ return UnknownValue;
+
+ // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
+ // know that m is >= n on input to the loop. If it is, the condition return
+ // true zero times. What we really should return, for full generality, is
+ // SMAX(0, m-n). Since we cannot check this, we will instead check for a
+ // canonical loop form: most do-loops will have a check that dominates the
+ // loop, that only enters the loop if [n-1]<m. If we can find this check,
+ // we know that the SMAX will evaluate to m-n, because we know that m >= n.
+
+ // Search for the check.
+ BasicBlock *Preheader = L->getLoopPreheader();
+ BasicBlock *PreheaderDest = L->getHeader();
+ if (Preheader == 0) return UnknownValue;
+
+ BranchInst *LoopEntryPredicate =
+ dyn_cast<BranchInst>(Preheader->getTerminator());
+ if (!LoopEntryPredicate) return UnknownValue;
+
+ // This might be a critical edge broken out. If the loop preheader ends in
+ // an unconditional branch to the loop, check to see if the preheader has a
+ // single predecessor, and if so, look for its terminator.
+ while (LoopEntryPredicate->isUnconditional()) {
+ PreheaderDest = Preheader;
+ Preheader = Preheader->getSinglePredecessor();
+ if (!Preheader) return UnknownValue; // Multiple preds.
+
+ LoopEntryPredicate =
+ dyn_cast<BranchInst>(Preheader->getTerminator());
+ if (!LoopEntryPredicate) return UnknownValue;
+ }
+
+ // Now that we found a conditional branch that dominates the loop, check to
+ // see if it is the comparison we are looking for.
+ if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
+ Value *PreCondLHS = ICI->getOperand(0);
+ Value *PreCondRHS = ICI->getOperand(1);
+ ICmpInst::Predicate Cond;
+ if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
+ Cond = ICI->getPredicate();
+ else
+ Cond = ICI->getInversePredicate();
+
+ switch (Cond) {
+ case ICmpInst::ICMP_UGT:
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_ULT;
+ break;
+ case ICmpInst::ICMP_SGT:
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_SLT;
+ break;
+ default: break;
+ }
+
+ if (Cond == ICmpInst::ICMP_SLT) {
+ if (PreCondLHS->getType()->isInteger()) {
+ if (RHS != getSCEV(PreCondRHS))
+ return UnknownValue; // Not a comparison against 'm'.
+
+ if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
+ != getSCEV(PreCondLHS))
+ return UnknownValue; // Not a comparison against 'n-1'.
+ }
+ else return UnknownValue;
+ } else if (Cond == ICmpInst::ICMP_ULT)
+ return UnknownValue;
+
+ // cerr << "Computed Loop Trip Count as: "
+ // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
+ return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
+ }
+ else
+ return UnknownValue;
+ }
+
+ 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) const {
+ if (Range.isFullSet()) // Infinite loop.
+ return new SCEVCouldNotCompute();
+
+ // If the start is a non-zero constant, shift the range to simplify things.
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
+ if (!SC->getValue()->isZero()) {
+ std::vector<SCEVHandle> Operands(op_begin(), op_end());
+ Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
+ SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
+ if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
+ return ShiftedAddRec->getNumIterationsInRange(
+ Range.subtract(SC->getValue()->getValue()));
+ // This is strange and shouldn't happen.
+ return new SCEVCouldNotCompute();
+ }
+
+ // 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 new SCEVCouldNotCompute();
+
+
+ // 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.
+ if (!Range.contains(APInt(getBitWidth(),0)))
+ return SCEVConstant::get(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(getBitWidth(),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).sdiv(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);
+ if (Range.contains(Val->getValue()))
+ return new SCEVCouldNotCompute(); // 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))->getValue()) &&
+ "Linear scev computation is off in a bad way!");
+ return SCEVConstant::get(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] = SCEV::getNegativeSCEV(SCEVConstant::get(Range.getUpper()));
+ SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
+
+ // Next, solve the constructed addrec
+ std::pair<SCEVHandle,SCEVHandle> Roots =
+ SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
+ SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
+ 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());
+ 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);
+ if (!Range.contains(R1Val->getValue()))
+ return SCEVConstant::get(NextVal);
+ return new SCEVCouldNotCompute(); // 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);
+ if (Range.contains(R1Val->getValue()))
+ return R1;
+ return new SCEVCouldNotCompute(); // Something strange happened
+ }
+ }
+ }
+
+ // Fallback, if this is a general polynomial, figure out the progression
+ // through brute force: evaluate until we find an iteration that fails the
+ // test. This is likely to be slow, but getting an accurate trip count is
+ // incredibly important, we will be able to simplify the exit test a lot, and
+ // we are almost guaranteed to get a trip count in this case.
+ ConstantInt *TestVal = ConstantInt::get(getType(), 0);
+ ConstantInt *EndVal = TestVal; // Stop when we wrap around.
+ do {
+ ++NumBruteForceEvaluations;
+ SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
+ if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
+ return new SCEVCouldNotCompute();
+
+ // Check to see if we found the value!
+ if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
+ return SCEVConstant::get(TestVal);
+
+ // Increment to test the next index.
+ TestVal = ConstantInt::get(TestVal->getValue()+1);
+ } while (TestVal != EndVal);
+
+ return new SCEVCouldNotCompute();
+}
+
+
+
+//===----------------------------------------------------------------------===//
+// ScalarEvolution Class Implementation
+//===----------------------------------------------------------------------===//
+
+bool ScalarEvolution::runOnFunction(Function &F) {
+ Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
+ return false;
+}
+
+void ScalarEvolution::releaseMemory() {
+ delete (ScalarEvolutionsImpl*)Impl;
+ Impl = 0;
+}
+
+void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
+ AU.setPreservesAll();
+ AU.addRequiredTransitive<LoopInfo>();
+}
+
+SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
+}
+
+/// hasSCEV - Return true if the SCEV for this value has already been
+/// computed.
+bool ScalarEvolution::hasSCEV(Value *V) const {
+ return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
+}
+
+
+/// setSCEV - Insert the specified SCEV into the map of current SCEVs for
+/// the specified value.
+void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
+ ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
+}
+
+
+SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
+}
+
+bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
+ return !isa<SCEVCouldNotCompute>(getIterationCount(L));
+}
+
+SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
+}
+
+void ScalarEvolution::deleteValueFromRecords(Value *V) const {
+ return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
+}
+
+static void PrintLoopInfo(std::ostream &OS, const 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);
+
+ cerr << "Loop " << L->getHeader()->getName() << ": ";
+
+ std::vector<BasicBlock*> ExitBlocks;
+ L->getExitBlocks(ExitBlocks);
+ if (ExitBlocks.size() != 1)
+ cerr << "<multiple exits> ";
+
+ if (SE->hasLoopInvariantIterationCount(L)) {
+ cerr << *SE->getIterationCount(L) << " iterations! ";
+ } else {
+ cerr << "Unpredictable iteration count. ";
+ }
+
+ cerr << "\n";
+}
+
+void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
+ Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
+ LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
+
+ OS << "Classifying expressions for: " << F.getName() << "\n";
+ for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
+ if (I->getType()->isInteger()) {
+ OS << *I;
+ OS << " --> ";
+ SCEVHandle SV = getSCEV(&*I);
+ SV->print(OS);
+ OS << "\t\t";
+
+ if ((*I).getType()->isInteger()) {
+ ConstantRange Bounds = SV->getValueRange();
+ if (!Bounds.isFullSet())
+ OS << "Bounds: " << Bounds << " ";
+ }
+
+ if (const Loop *L = LI.getLoopFor((*I).getParent())) {
+ OS << "Exits: ";
+ SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
+ if (isa<SCEVCouldNotCompute>(ExitValue)) {
+ 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, this, *I);
+}
+