Add a new analysis

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@12619 91177308-0d34-0410-b5e6-96231b3b80d8

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diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
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+//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
+// 
+//                     The LLVM Compiler Infrastructure
+//
+// This file 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.
+//
+// Orthogonal to the analysis of code above, this file also implements the
+// ScalarEvolutionRewriter class, which is used to emit code that represents the
+// various recurrences present in a loop, in canonical forms.
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/Constants.h"
+#include "llvm/DerivedTypes.h"
+#include "llvm/Instructions.h"
+#include "llvm/Type.h"
+#include "llvm/Value.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Assembly/Writer.h"
+#include "llvm/Transforms/Scalar.h"
+#include "llvm/Support/CFG.h"
+#include "llvm/Support/ConstantRange.h"
+#include "llvm/Support/InstIterator.h"
+#include "Support/Statistic.h"
+using namespace llvm;
+
+namespace {
+  RegisterAnalysis<ScalarEvolution>
+  R("scalar-evolution", "Scalar Evolution Analysis Printer");
+
+  Statistic<>
+  NumBruteForceEvaluations("scalar-evolution",
+                           "Number of brute force evaluations needed to calculate high-order polynomial exit values");
+  Statistic<>
+  NumTripCountsComputed("scalar-evolution",
+                        "Number of loops with predictable loop counts");
+  Statistic<>
+  NumTripCountsNotComputed("scalar-evolution",
+                           "Number of loops without predictable loop counts");
+}
+
+//===----------------------------------------------------------------------===//
+//                           SCEV class definitions
+//===----------------------------------------------------------------------===//
+
+//===----------------------------------------------------------------------===//
+// Implementation of the SCEV class.
+//
+namespace {
+  enum SCEVTypes {
+    // These should be ordered in terms of increasing complexity to make the
+    // folders simpler.
+    scConstant, scTruncate, scZeroExtend, scAddExpr, scMulExpr, scUDivExpr,
+    scAddRecExpr, scUnknown, scCouldNotCompute
+  };
+
+  /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
+  /// than the complexity of the RHS.  If the SCEVs have identical complexity,
+  /// order them by their addresses.  This comparator is used to canonicalize
+  /// expressions.
+  struct SCEVComplexityCompare {
+    bool operator()(SCEV *LHS, SCEV *RHS) {
+      if (LHS->getSCEVType() < RHS->getSCEVType())
+        return true;
+      if (LHS->getSCEVType() == RHS->getSCEVType())
+        return LHS < RHS;
+      return false;
+    }
+  };
+}
+
+SCEV::~SCEV() {}
+void SCEV::dump() const {
+  print(std::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!");
+  Ty = Ty->getUnsignedVersion();
+  // Default to a full range if no better information is available.
+  return ConstantRange(getType());
+}
+
+
+SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
+
+bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
+  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+}
+
+const Type *SCEVCouldNotCompute::getType() const {
+  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+}
+
+bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
+  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+  return false;
+}
+
+Value *SCEVCouldNotCompute::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                          Instruction *InsertPt) {
+  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
+  return 0;
+}
+
+
+void SCEVCouldNotCompute::print(std::ostream &OS) const {
+  OS << "***COULDNOTCOMPUTE***";
+}
+
+bool SCEVCouldNotCompute::classof(const SCEV *S) {
+  return S->getSCEVType() == scCouldNotCompute;
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVConstant - This class represents a constant integer value.
+//
+namespace {
+  class SCEVConstant;
+  // 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!
+  std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
+
+  class SCEVConstant : public SCEV {
+    ConstantInt *V;
+    SCEVConstant(ConstantInt *v) : SCEV(scConstant), V(v) {}
+
+    virtual ~SCEVConstant() {
+      SCEVConstants.erase(V);
+    }
+  public:
+    /// get method - This just gets and returns a new SCEVConstant object.
+    ///
+    static SCEVHandle get(ConstantInt *V) {
+      // Make sure that SCEVConstant instances are all unsigned.
+      if (V->getType()->isSigned()) {
+        const Type *NewTy = V->getType()->getUnsignedVersion();
+        V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
+      }
+
+      SCEVConstant *&R = SCEVConstants[V];
+      if (R == 0) R = new SCEVConstant(V);
+      return R;
+    }
+
+    ConstantInt *getValue() const { return V; }
+
+    /// getValueRange - Return the tightest constant bounds that this value is
+    /// known to have.  This method is only valid on integer SCEV objects.
+    virtual ConstantRange getValueRange() const {
+      return ConstantRange(V);
+    }
+
+    virtual bool isLoopInvariant(const Loop *L) const {
+      return true;
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *L) const {
+      return false;  // Not loop variant
+    }
+
+    virtual const Type *getType() const { return V->getType(); }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt) {
+      return getValue();
+    }
+    
+    virtual void print(std::ostream &OS) const {
+      WriteAsOperand(OS, V, false);
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVConstant *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scConstant;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVTruncateExpr - This class represents a truncation of an integer value to
+// a smaller integer value.
+//
+namespace {
+  class SCEVTruncateExpr;
+  // 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!
+  std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
+
+  class SCEVTruncateExpr : public SCEV {
+    SCEVHandle Op;
+    const Type *Ty;
+    SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
+      : SCEV(scTruncate), Op(op), Ty(ty) {
+      assert(Op->getType()->isInteger() && Ty->isInteger() &&
+             Ty->isUnsigned() &&
+             "Cannot truncate non-integer value!");
+      assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
+             "This is not a truncating conversion!");
+    }
+
+    virtual ~SCEVTruncateExpr() {
+      SCEVTruncates.erase(std::make_pair(Op, Ty));
+    }
+  public:
+    /// get method - This just gets and returns a new SCEVTruncate object
+    ///
+    static SCEVHandle get(const SCEVHandle &Op, const Type *Ty);
+
+    const SCEVHandle &getOperand() const { return Op; }
+    virtual const Type *getType() const { return Ty; }
+    
+    virtual bool isLoopInvariant(const Loop *L) const {
+      return Op->isLoopInvariant(L);
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *L) const {
+      return Op->hasComputableLoopEvolution(L);
+    }
+
+    /// getValueRange - Return the tightest constant bounds that this value is
+    /// known to have.  This method is only valid on integer SCEV objects.
+    virtual ConstantRange getValueRange() const {
+      return getOperand()->getValueRange().truncate(getType());
+    }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+    
+    virtual void print(std::ostream &OS) const {
+      OS << "(truncate " << *Op << " to " << *Ty << ")";
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVTruncateExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scTruncate;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVZeroExtendExpr - This class represents a zero extension of a small
+// integer value to a larger integer value.
+//
+namespace {
+  class SCEVZeroExtendExpr;
+  // 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!
+  std::map<std::pair<SCEV*, const Type*>, SCEVZeroExtendExpr*> SCEVZeroExtends;
+
+  class SCEVZeroExtendExpr : public SCEV {
+    SCEVHandle Op;
+    const Type *Ty;
+    SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
+      : SCEV(scTruncate), Op(Op), Ty(ty) {
+      assert(Op->getType()->isInteger() && Ty->isInteger() &&
+             Ty->isUnsigned() &&
+             "Cannot zero extend non-integer value!");
+      assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
+             "This is not an extending conversion!");
+    }
+
+    virtual ~SCEVZeroExtendExpr() {
+      SCEVZeroExtends.erase(std::make_pair(Op, Ty));
+    }
+  public:
+    /// get method - This just gets and returns a new SCEVZeroExtend object
+    ///
+    static SCEVHandle get(const SCEVHandle &Op, const Type *Ty);
+
+    const SCEVHandle &getOperand() const { return Op; }
+    virtual const Type *getType() const { return Ty; }
+    
+    virtual bool isLoopInvariant(const Loop *L) const {
+      return Op->isLoopInvariant(L);
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *L) const {
+      return Op->hasComputableLoopEvolution(L);
+    }
+
+    /// getValueRange - Return the tightest constant bounds that this value is
+    /// known to have.  This method is only valid on integer SCEV objects.
+    virtual ConstantRange getValueRange() const {
+      return getOperand()->getValueRange().zeroExtend(getType());
+    }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+    
+    virtual void print(std::ostream &OS) const {
+      OS << "(zeroextend " << *Op << " to " << *Ty << ")";
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVZeroExtendExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scZeroExtend;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVCommutativeExpr - This node is the base class for n'ary commutative
+// operators.
+
+namespace {
+  class SCEVCommutativeExpr;
+  // 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!
+  std::map<std::pair<unsigned, std::vector<SCEV*> >,
+           SCEVCommutativeExpr*> SCEVCommExprs;
+
+  class SCEVCommutativeExpr : public SCEV {
+    std::vector<SCEVHandle> Operands;
+
+  protected:
+    SCEVCommutativeExpr(enum SCEVTypes T, const std::vector<SCEVHandle> &ops)
+      : SCEV(T) {
+      Operands.reserve(ops.size());
+      Operands.insert(Operands.end(), ops.begin(), ops.end());
+    }
+
+    ~SCEVCommutativeExpr() {
+      SCEVCommExprs.erase(std::make_pair(getSCEVType(),
+                                         std::vector<SCEV*>(Operands.begin(),
+                                                            Operands.end())));
+    }
+
+  public:
+    unsigned getNumOperands() const { return Operands.size(); }
+    const SCEVHandle &getOperand(unsigned i) const {
+      assert(i < Operands.size() && "Operand index out of range!");
+      return Operands[i];
+    }
+
+    const std::vector<SCEVHandle> &getOperands() const { return Operands; }
+    typedef std::vector<SCEVHandle>::const_iterator op_iterator;
+    op_iterator op_begin() const { return Operands.begin(); }
+    op_iterator op_end() const { return Operands.end(); }
+
+
+    virtual bool isLoopInvariant(const Loop *L) const {
+      for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
+        if (!getOperand(i)->isLoopInvariant(L)) return false;
+      return true;
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *L) const {
+      for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
+        if (getOperand(i)->hasComputableLoopEvolution(L)) return true;
+      return false;
+    }
+
+    virtual const Type *getType() const { return getOperand(0)->getType(); }
+
+    virtual const char *getOperationStr() const = 0;
+    
+    virtual void 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 << ")";
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVCommutativeExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scAddExpr ||
+             S->getSCEVType() == scMulExpr;
+    }
+  };
+}
+
+//===----------------------------------------------------------------------===//
+// SCEVAddExpr - This node represents an addition of some number of SCEV's.
+//
+namespace {
+  class SCEVAddExpr : public SCEVCommutativeExpr {
+    SCEVAddExpr(const std::vector<SCEVHandle> &ops)
+      : SCEVCommutativeExpr(scAddExpr, ops) {
+    }
+
+  public:
+    static SCEVHandle get(std::vector<SCEVHandle> &Ops);
+
+    static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+      std::vector<SCEVHandle> Ops;
+      Ops.push_back(LHS);
+      Ops.push_back(RHS);
+      return get(Ops);
+    }
+
+    static SCEVHandle get(const SCEVHandle &Op0, const SCEVHandle &Op1,
+                          const SCEVHandle &Op2) {
+      std::vector<SCEVHandle> Ops;
+      Ops.push_back(Op0);
+      Ops.push_back(Op1);
+      Ops.push_back(Op2);
+      return get(Ops);
+    }
+
+    virtual const char *getOperationStr() const { return " + "; }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVAddExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scAddExpr;
+    }
+  };
+}
+
+//===----------------------------------------------------------------------===//
+// SCEVMulExpr - This node represents multiplication of some number of SCEV's.
+//
+namespace {
+  class SCEVMulExpr : public SCEVCommutativeExpr {
+    SCEVMulExpr(const std::vector<SCEVHandle> &ops)
+      : SCEVCommutativeExpr(scMulExpr, ops) {
+    }
+
+  public:
+    static SCEVHandle get(std::vector<SCEVHandle> &Ops);
+
+    static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+      std::vector<SCEVHandle> Ops;
+      Ops.push_back(LHS);
+      Ops.push_back(RHS);
+      return get(Ops);
+    }
+
+    virtual const char *getOperationStr() const { return " * "; }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVMulExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scMulExpr;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVUDivExpr - This class represents a binary unsigned division operation.
+//
+namespace {
+  class SCEVUDivExpr;
+  // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
+  // input.  Don't use a SCEVHandle here, or else the object will never be
+  // deleted!
+  std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs;
+
+  class SCEVUDivExpr : public SCEV {
+    SCEVHandle LHS, RHS;
+    SCEVUDivExpr(const SCEVHandle &lhs, const SCEVHandle &rhs)
+      : SCEV(scUDivExpr), LHS(lhs), RHS(rhs) {}
+
+    virtual ~SCEVUDivExpr() {
+      SCEVUDivs.erase(std::make_pair(LHS, RHS));
+    }
+  public:
+    /// get method - This just gets and returns a new SCEVUDiv object.
+    ///
+    static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS);
+
+    const SCEVHandle &getLHS() const { return LHS; }
+    const SCEVHandle &getRHS() const { return RHS; }
+
+    virtual bool isLoopInvariant(const Loop *L) const {
+      return LHS->isLoopInvariant(L) && RHS->isLoopInvariant(L);
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *L) const {
+      return LHS->hasComputableLoopEvolution(L) &&
+             RHS->hasComputableLoopEvolution(L);
+    }
+
+    virtual const Type *getType() const {
+      const Type *Ty = LHS->getType();
+      if (Ty->isSigned()) Ty = Ty->getUnsignedVersion();
+      return Ty;
+    }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+    
+    virtual void print(std::ostream &OS) const {
+      OS << "(" << *LHS << " /u " << *RHS << ")";
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVUDivExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scUDivExpr;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+
+// SCEVAddRecExpr - This node represents a polynomial recurrence on the trip
+// count of the specified loop.
+//
+// All operands of an AddRec are required to be loop invariant.
+//
+namespace {
+  class SCEVAddRecExpr;
+  // 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!
+  std::map<std::pair<const Loop *, std::vector<SCEV*> >,
+           SCEVAddRecExpr*> SCEVAddRecExprs;
+
+  class SCEVAddRecExpr : public SCEV {
+    std::vector<SCEVHandle> Operands;
+    const Loop *L;
+
+    SCEVAddRecExpr(const std::vector<SCEVHandle> &ops, const Loop *l)
+      : SCEV(scAddRecExpr), Operands(ops), L(l) {
+      for (unsigned i = 0, e = Operands.size(); i != e; ++i)
+        assert(Operands[i]->isLoopInvariant(l) &&
+               "Operands of AddRec must be loop-invariant!");
+    }
+    ~SCEVAddRecExpr() {
+      SCEVAddRecExprs.erase(std::make_pair(L,
+                                           std::vector<SCEV*>(Operands.begin(),
+                                                              Operands.end())));
+    }
+  public:
+    static SCEVHandle get(const SCEVHandle &Start, const SCEVHandle &Step,
+                          const Loop *);
+    static SCEVHandle get(std::vector<SCEVHandle> &Operands,
+                          const Loop *);
+    static SCEVHandle get(const std::vector<SCEVHandle> &Operands,
+                          const Loop *L) {
+      std::vector<SCEVHandle> NewOp(Operands);
+      return get(NewOp, L);
+    }
+
+    typedef std::vector<SCEVHandle>::const_iterator op_iterator;
+    op_iterator op_begin() const { return Operands.begin(); }
+    op_iterator op_end() const { return Operands.end(); }
+
+    unsigned getNumOperands() const { return Operands.size(); }
+    const SCEVHandle &getOperand(unsigned i) const { return Operands[i]; }
+    const SCEVHandle &getStart() const { return Operands[0]; }
+    const Loop *getLoop() const { return L; }
+
+
+    /// getStepRecurrence - This method constructs and returns the recurrence
+    /// indicating how much this expression steps by.  If this is a polynomial
+    /// of degree N, it returns a chrec of degree N-1.
+    SCEVHandle getStepRecurrence() const {
+      if (getNumOperands() == 2) return getOperand(1);
+      return SCEVAddRecExpr::get(std::vector<SCEVHandle>(op_begin()+1,op_end()),
+                                 getLoop());
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *QL) const {
+      if (L == QL) return true;
+      /// FIXME: What if the start or step value a recurrence for the specified
+      /// loop?
+      return false;
+    }
+
+
+    virtual bool isLoopInvariant(const Loop *QueryLoop) const {
+      // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
+      // contain L.
+      return !QueryLoop->contains(L->getHeader());
+    }
+
+    virtual const Type *getType() const { return Operands[0]->getType(); }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt);
+
+
+    /// isAffine - Return true if this is an affine AddRec (i.e., it represents
+    /// an expressions A+B*x where A and B are loop invariant values.
+    bool isAffine() const {
+      // We know that the start value is invariant.  This expression is thus
+      // affine iff the step is also invariant.
+      return getNumOperands() == 2;
+    }
+
+    /// isQuadratic - Return true if this is an quadratic AddRec (i.e., it
+    /// represents an expressions A+B*x+C*x^2 where A, B and C are loop
+    /// invariant values.  This corresponds to an addrec of the form {L,+,M,+,N}
+    bool isQuadratic() const {
+      return getNumOperands() == 3;
+    }
+
+    /// evaluateAtIteration - Return the value of this chain of recurrences at
+    /// the specified iteration number.
+    SCEVHandle evaluateAtIteration(SCEVHandle It) const;
+
+    /// 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 getNumIterationsInRange(ConstantRange Range) const;
+
+
+    virtual void 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() + ">";
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVAddRecExpr *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scAddRecExpr;
+    }
+  };
+}
+
+
+//===----------------------------------------------------------------------===//
+// SCEVUnknown - This means that we are dealing with an entirely unknown SCEV
+// value, and only represent it as it's LLVM Value.  This is the "bottom" value
+// for the analysis.
+//
+namespace {
+  class SCEVUnknown;
+  // 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!
+  std::map<Value*, SCEVUnknown*> SCEVUnknowns;
+
+  class SCEVUnknown : public SCEV {
+    Value *V;
+    SCEVUnknown(Value *v) : SCEV(scUnknown), V(v) {}
+
+  protected:
+    ~SCEVUnknown() { SCEVUnknowns.erase(V); }
+  public:
+    /// get method - For SCEVUnknown, this just gets and returns a new
+    /// SCEVUnknown.
+    static SCEVHandle 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;
+    }
+
+    Value *getValue() const { return V; }
+
+    Value *expandCodeFor(ScalarEvolutionRewriter &SER,
+                         Instruction *InsertPt) {
+      return V;
+    }
+
+    virtual bool 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;
+    }
+
+    virtual bool hasComputableLoopEvolution(const Loop *QL) const {
+      return false; // not computable
+    }
+
+    virtual const Type *getType() const { return V->getType(); }
+
+    virtual void print(std::ostream &OS) const {
+      WriteAsOperand(OS, V, false);
+    }
+
+    /// Methods for support type inquiry through isa, cast, and dyn_cast:
+    static inline bool classof(const SCEVUnknown *S) { return true; }
+    static inline bool classof(const SCEV *S) {
+      return S->getSCEVType() == scUnknown;
+    }
+  };
+}
+
+//===----------------------------------------------------------------------===//
+//                      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.
+static SCEVHandle 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 if (Ty->isSigned())
+    C = ConstantSInt::get(Ty, Val);
+  else {
+    C = ConstantSInt::get(Ty->getSignedVersion(), Val);
+    C = ConstantExpr::getCast(C, Ty);
+  }
+  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->getPrimitiveSize() == Ty->getPrimitiveSize())
+    return V;  // No conversion
+  if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
+    return SCEVTruncateExpr::get(V, Ty);
+  return SCEVZeroExtendExpr::get(V, Ty);
+}
+
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+static SCEVHandle getNegativeSCEV(const SCEVHandle &V) {
+  if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+    return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
+  
+  return SCEVMulExpr::get(V, getIntegerSCEV(-1, V->getType()));
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+  // X - Y --> X + -Y
+  return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS));
+}
+
+
+/// Binomial - Evaluate N!/((N-M)!*M!)  .  Note that N is often large and M is
+/// often very small, so we try to reduce the number of N! terms we need to
+/// evaluate by evaluating this as  (N!/(N-M)!)/M!
+static ConstantInt *Binomial(ConstantInt *N, unsigned M) {
+  uint64_t NVal = N->getRawValue();
+  uint64_t FirstTerm = 1;
+  for (unsigned i = 0; i != M; ++i)
+    FirstTerm *= NVal-i;
+
+  unsigned MFactorial = 1;
+  for (; M; --M)
+    MFactorial *= M;
+
+  Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial);
+  Result = ConstantExpr::getCast(Result, N->getType());
+  assert(isa<ConstantInt>(Result) && "Cast of integer not folded??");
+  return cast<ConstantInt>(Result);
+}
+
+/// 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)) {
+    uint64_t Val = SC->getValue()->getRawValue();
+    uint64_t Result = 1;
+    for (; NumSteps; --NumSteps)
+      Result *= Val-(NumSteps-1);
+    Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
+    return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
+  }
+
+  const Type *Ty = V->getType();
+  if (NumSteps == 0)
+    return getIntegerSCEV(1, Ty);
+  
+  SCEVHandle Result = V;
+  for (unsigned i = 1; i != NumSteps; ++i)
+    Result = SCEVMulExpr::get(Result, getMinusSCEV(V, 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 = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
+                                       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::getCast(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::getCast(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;
+}
+
+// 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!");
+
+  // Sort by complexity, this groups all similar expression types together.
+  std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
+
+  // If there are any constants, fold them together.
+  unsigned Idx = 0;
+  if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+    ++Idx;
+    while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+      // We found two constants, fold them together!
+      Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->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];
+      } 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()->isNullValue()) {
+      Ops.erase(Ops.begin());
+      --Idx;
+    }
+  }
+
+  if (Ops.size() == 1)
+    return Ops[0];
+  
+  // Okay, check to see if the same value occurs in the operand list twice.  If
+  // so, merge them together into an multiply expression.  Since we sorted the
+  // list, these values are required to be adjacent.
+  const Type *Ty = Ops[0]->getType();
+  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
+    if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
+      // Found a match, merge the two values into a multiply, and add any
+      // remaining values to the result.
+      SCEVHandle Two = getIntegerSCEV(2, Ty);
+      SCEVHandle Mul = 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);
+    }
+
+  // Okay, now we know the first non-constant operand.  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] &&
+            (Mul->getNumOperands() != 2 || !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 = 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.
+  std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
+
+  // 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 = ConstantExpr::getMul(LHSC->getValue(), RHSC->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];
+      } 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()->isNullValue()) {
+      // 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 SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+  if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
+    if (RHSC->getValue()->equalsInt(1))
+      return LHS;                            // X /u 1 --> x
+    if (RHSC->getValue()->isAllOnesValue())
+      return getNegativeSCEV(LHS);           // X /u -1  -->  -x
+
+    if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
+      Constant *LHSCV = LHSC->getValue();
+      Constant *RHSCV = RHSC->getValue();
+      if (LHSCV->getType()->isSigned())
+        LHSCV = ConstantExpr::getCast(LHSCV,
+                                      LHSCV->getType()->getUnsignedVersion());
+      if (RHSCV->getType()->isSigned())
+        RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
+      return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
+    }
+  }
+
+  // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
+
+  SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
+  if (Result == 0) Result = new SCEVUDivExpr(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()->isNullValue()) {
+      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;
+}
+
+
+//===----------------------------------------------------------------------===//
+//                  Non-trivial closed-form SCEV Expanders
+//===----------------------------------------------------------------------===//
+
+Value *SCEVTruncateExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                       Instruction *InsertPt) {
+  Value *V = SER.ExpandCodeFor(getOperand(), InsertPt);
+  return new CastInst(V, getType(), "tmp.", InsertPt);
+}
+
+Value *SCEVZeroExtendExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                         Instruction *InsertPt) {
+  Value *V = SER.ExpandCodeFor(getOperand(), InsertPt,
+                               getOperand()->getType()->getUnsignedVersion());
+  return new CastInst(V, getType(), "tmp.", InsertPt);
+}
+
+Value *SCEVAddExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                  Instruction *InsertPt) {
+  const Type *Ty = getType();
+  Value *V = SER.ExpandCodeFor(getOperand(getNumOperands()-1), InsertPt, Ty);
+
+  // Emit a bunch of add instructions
+  for (int i = getNumOperands()-2; i >= 0; --i)
+    V = BinaryOperator::create(Instruction::Add, V,
+                               SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
+                               "tmp.", InsertPt);
+  return V;
+}
+
+Value *SCEVMulExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                  Instruction *InsertPt) {
+  const Type *Ty = getType();
+  int FirstOp = 0;  // Set if we should emit a subtract.
+  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getOperand(0)))
+    if (SC->getValue()->isAllOnesValue())
+      FirstOp = 1;
+
+  int i = getNumOperands()-2;
+  Value *V = SER.ExpandCodeFor(getOperand(i+1), InsertPt, Ty);
+
+  // Emit a bunch of multiply instructions
+  for (; i >= FirstOp; --i)
+    V = BinaryOperator::create(Instruction::Mul, V,
+                               SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
+                               "tmp.", InsertPt);
+  // -1 * ...  --->  0 - ...
+  if (FirstOp == 1)
+    V = BinaryOperator::create(Instruction::Sub, Constant::getNullValue(Ty), V,
+                               "tmp.", InsertPt);
+  return V;
+}
+
+Value *SCEVUDivExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                   Instruction *InsertPt) {
+  const Type *Ty = getType();
+  Value *LHS = SER.ExpandCodeFor(getLHS(), InsertPt, Ty);
+  Value *RHS = SER.ExpandCodeFor(getRHS(), InsertPt, Ty);
+  return BinaryOperator::create(Instruction::Div, LHS, RHS, "tmp.", InsertPt);
+}
+
+Value *SCEVAddRecExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
+                                     Instruction *InsertPt) {
+  const Type *Ty = getType();
+  // We cannot yet do fp recurrences, e.g. the xform of {X,+,F} --> X+{0,+,F}
+  assert(Ty->isIntegral() && "Cannot expand fp recurrences yet!");
+
+  // {X,+,F} --> X + {0,+,F}
+  if (!isa<SCEVConstant>(getStart()) ||
+      !cast<SCEVConstant>(getStart())->getValue()->isNullValue()) {
+    Value *Start = SER.ExpandCodeFor(getStart(), InsertPt, Ty);
+    std::vector<SCEVHandle> NewOps(op_begin(), op_end());
+    NewOps[0] = getIntegerSCEV(0, getType());
+    Value *Rest = SER.ExpandCodeFor(SCEVAddRecExpr::get(NewOps, getLoop()),
+                                    InsertPt, getType());
+
+    // FIXME: look for an existing add to use.
+    return BinaryOperator::create(Instruction::Add, Rest, Start, "tmp.",
+                                  InsertPt);
+  }
+
+  // {0,+,1} --> Insert a canonical induction variable into the loop!
+  if (getNumOperands() == 2 && getOperand(1) == getIntegerSCEV(1, getType())) {
+    // Create and insert the PHI node for the induction variable in the
+    // specified loop.
+    BasicBlock *Header = getLoop()->getHeader();
+    PHINode *PN = new PHINode(Ty, "indvar", Header->begin());
+    PN->addIncoming(Constant::getNullValue(Ty), L->getLoopPreheader());
+
+    // Insert a unit add instruction after the PHI nodes in the header block.
+    BasicBlock::iterator I = PN;
+    while (isa<PHINode>(I)) ++I;
+
+    Constant *One = Ty->isFloatingPoint() ?(Constant*)ConstantFP::get(Ty, 1.0)
+      :(Constant*)ConstantInt::get(Ty, 1);
+    Instruction *Add = BinaryOperator::create(Instruction::Add, PN, One,
+                                              "indvar.next", I);
+
+    pred_iterator PI = pred_begin(Header);
+    if (*PI == L->getLoopPreheader())
+      ++PI;
+    PN->addIncoming(Add, *PI);
+    return PN;
+  }
+
+  // Get the canonical induction variable I for this loop.
+  Value *I = SER.GetOrInsertCanonicalInductionVariable(getLoop(), Ty);
+
+  if (getNumOperands() == 2) {   // {0,+,F} --> i*F
+    Value *F = SER.ExpandCodeFor(getOperand(1), InsertPt, Ty);
+    return BinaryOperator::create(Instruction::Mul, I, F, "tmp.", InsertPt);
+  }
+
+  // If this is a chain of recurrences, turn it into a closed form, using the
+  // folders, then expandCodeFor the closed form.  This allows the folders to
+  // simplify the expression without having to build a bunch of special code
+  // into this folder.
+  SCEVHandle IH = SCEVUnknown::get(I);   // Get I as a "symbolic" SCEV.
+
+  SCEVHandle V = evaluateAtIteration(IH);
+  std::cerr << "Evaluated: " << *this << "\n     to: " << *V << "\n";
+
+  return SER.ExpandCodeFor(V, InsertPt, Ty);
+}
+
+
+//===----------------------------------------------------------------------===//
+//             ScalarEvolutionsImpl Definition and Implementation
+//===----------------------------------------------------------------------===//
+//
+/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
+/// evolution code.
+///
+namespace {
+  struct 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;
+
+  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);
+
+    /// 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);
+
+    /// deleteInstructionFromRecords - 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 deleteInstructionFromRecords(Instruction *I);
+
+  private:
+    /// createSCEV - We know that there is no SCEV for the specified value.
+    /// Analyze the expression.
+    SCEVHandle createSCEV(Value *V);
+    SCEVHandle createNodeForCast(CastInst *CI);
+
+    /// createNodeForPHI - Provide the special handling we need to analyze PHI
+    /// SCEVs.
+    SCEVHandle createNodeForPHI(PHINode *PN);
+    void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN,
+                                    std::set<Instruction*> &UpdatedInsts);
+
+    /// ComputeIterationCount - Compute the number of times the specified loop
+    /// will iterate.
+    SCEVHandle ComputeIterationCount(const Loop *L);
+
+    /// 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);
+  };
+}
+
+//===----------------------------------------------------------------------===//
+//            Basic SCEV Analysis and PHI Idiom Recognition Code
+//
+
+/// deleteInstructionFromRecords - 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::deleteInstructionFromRecords(Instruction *I) {
+  Scalars.erase(I);
+}
+
+
+/// 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;
+}
+
+
+/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of
+/// entries in the scalar map that refer to the "symbolic" PHI value instead of
+/// the recurrence value.  After we resolve the PHI we must loop over all of the
+/// using instructions that have scalar map entries and update them.
+void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I,
+                                                      PHINode *PN,
+                                        std::set<Instruction*> &UpdatedInsts) {
+  std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
+  if (SI == Scalars.end()) return;   // This scalar wasn't previous processed.
+  if (UpdatedInsts.insert(I).second) {
+    Scalars.erase(SI);                 // Remove the old entry
+    getSCEV(I);                        // Calculate the new entry
+    
+    for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
+         UI != E; ++UI)
+      UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts);
+  }
+}
+
+
+/// 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.
+              Scalars.find(PN)->second = PHISCEV;       // Update the PHI value
+              std::set<Instruction*> UpdatedInsts;
+              UpdatedInsts.insert(PN);
+              for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end();
+                   UI != E; ++UI)
+                UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN,
+                                           UpdatedInsts);
+              return PHISCEV;
+            }
+          }
+        }
+
+        return SymbolicName;
+      }
+  
+  // If it's not a loop phi, we can't handle it yet.
+  return SCEVUnknown::get(PN);
+}
+
+/// createNodeForCast - Handle the various forms of casts that we support.
+///
+SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
+  const Type *SrcTy = CI->getOperand(0)->getType();
+  const Type *DestTy = CI->getType();
+  
+  // If this is a noop cast (ie, conversion from int to uint), ignore it.
+  if (SrcTy->isLosslesslyConvertibleTo(DestTy))
+    return getSCEV(CI->getOperand(0));
+  
+  if (SrcTy->isInteger() && DestTy->isInteger()) {
+    // Otherwise, if this is a truncating integer cast, we can represent this
+    // cast.
+    if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
+      return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
+                                   CI->getType()->getUnsignedVersion());
+    if (SrcTy->isUnsigned() &&
+        SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
+      return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
+                                     CI->getType()->getUnsignedVersion());
+  }
+
+  // If this is an sign or zero extending cast and we can prove that the value
+  // will never overflow, we could do similar transformations.
+
+  // Otherwise, we can't handle this cast!
+  return SCEVUnknown::get(CI);
+}
+
+
+/// 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::Div:
+      if (V->getType()->isInteger() && V->getType()->isUnsigned())
+        return SCEVUDivExpr::get(getSCEV(I->getOperand(0)),
+                                 getSCEV(I->getOperand(1)));
+      break;
+
+    case Instruction::Sub:
+      return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1)));
+
+    case Instruction::Shl:
+      // Turn shift left of a constant amount into a multiply.
+      if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
+        Constant *X = ConstantInt::get(V->getType(), 1);
+        X = ConstantExpr::getShl(X, SA);
+        return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
+      }
+      break;
+
+    case Instruction::Shr:
+      if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1)))
+        if (V->getType()->isUnsigned()) {
+          Constant *X = ConstantInt::get(V->getType(), 1);
+          X = ConstantExpr::getShl(X, SA);
+          return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
+        }
+      break;
+
+    case Instruction::Cast:
+      return createNodeForCast(cast<CastInst>(I));
+
+    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.
+  if (L->getExitBlocks().size() != 1) return UnknownValue;
+
+  // Okay, there is one exit block.  Try to find the condition that causes the
+  // loop to be exited.
+  BasicBlock *ExitBlock = L->getExitBlocks()[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)
+  // FIXME: We should handle cast of int to bool as well
+  BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
+  if (ExitBr == 0) return UnknownValue;
+  assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
+  SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
+  if (ExitCond == 0) return UnknownValue;
+
+  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;
+
+  // If the condition was exit on true, convert the condition to exit on false.
+  Instruction::BinaryOps Cond;
+  if (ExitBr->getSuccessor(1) == ExitBlock)
+    Cond = ExitCond->getOpcode();
+  else
+    Cond = ExitCond->getInverseCondition();
+
+  // 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 = SetCondInst::getSwappedCondition(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::getCast(CompVal, RealTy));
+        if (CompVal) {
+          // Form the constant range.
+          ConstantRange CompRange(Cond, CompVal);
+          
+          // Now that we have it, if it's signed, convert it to an unsigned
+          // range.
+          if (CompRange.getLower()->getType()->isSigned()) {
+            const Type *NewTy = RHSC->getValue()->getType();
+            Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
+            Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
+            CompRange = ConstantRange(NewL, NewU);
+          }
+          
+          SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
+          if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
+        }
+      }
+  
+  switch (Cond) {
+  case Instruction::SetNE:                     // while (X != Y)
+    // Convert to: while (X-Y != 0)
+    if (LHS->getType()->isInteger())
+      return HowFarToZero(getMinusSCEV(LHS, RHS), L);
+    break;
+  case Instruction::SetEQ:
+    // Convert to: while (X-Y == 0)           // while (X == Y)
+    if (LHS->getType()->isInteger())
+      return HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
+    break;
+  default:
+    std::cerr << "ComputeIterationCount ";
+    if (ExitCond->getOperand(0)->getType()->isUnsigned())
+      std::cerr << "[unsigned] ";
+    std::cerr << *LHS << "   "
+              << Instruction::getOpcodeName(Cond) << "   " << *RHS << "\n";
+  }
+  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) || isa<SCEVUnknown>(V)) 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-1);
+        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 (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) {
+    SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L);
+    if (LHS == UnknownValue) return LHS;
+    SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L);
+    if (RHS == UnknownValue) return RHS;
+    if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS())
+      return UDiv;   // must be loop invariant
+    return SCEVUDivExpr::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 *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
+  SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
+  SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
+  
+  // We currently can only solve this if the coefficients are constants.
+  if (!L || !M || !N) {
+    SCEV *CNC = new SCEVCouldNotCompute();
+    return std::make_pair(CNC, CNC);
+  }
+
+  Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
+  
+  // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
+  Constant *C = L->getValue();
+  // The B coefficient is M-N/2
+  Constant *B = ConstantExpr::getSub(M->getValue(),
+                                     ConstantExpr::getDiv(N->getValue(),
+                                                          Two));
+  // The A coefficient is N/2
+  Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
+        
+  // Compute the B^2-4ac term.
+  Constant *SqrtTerm =
+    ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
+                         ConstantExpr::getMul(A, C));
+  SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
+
+  // Compute floor(sqrt(B^2-4ac))
+  ConstantUInt *SqrtVal =
+    cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
+                                   SqrtTerm->getType()->getUnsignedVersion()));
+  uint64_t SqrtValV = SqrtVal->getValue();
+  uint64_t SqrtValV2 = (uint64_t)sqrtl(SqrtValV);
+  // The square root might not be precise for arbitrary 64-bit integer
+  // values.  Do some sanity checks to ensure it's correct.
+  if (SqrtValV2*SqrtValV2 > SqrtValV ||
+      (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
+    SCEV *CNC = new SCEVCouldNotCompute();
+    return std::make_pair(CNC, CNC);
+  }
+
+  SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
+  SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
+  
+  Constant *NegB = ConstantExpr::getNeg(B);
+  Constant *TwoA = ConstantExpr::getMul(A, Two);
+  
+  // The divisions must be performed as signed divisions.
+  const Type *SignedTy = NegB->getType()->getSignedVersion();
+  NegB = ConstantExpr::getCast(NegB, SignedTy);
+  TwoA = ConstantExpr::getCast(TwoA, SignedTy);
+  SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
+  
+  Constant *Solution1 =
+    ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
+  Constant *Solution2 =
+    ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
+  return std::make_pair(SCEVUnknown::get(Solution1),
+                        SCEVUnknown::get(Solution2));
+}
+
+/// 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()->isNullValue()) 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());
+    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 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::getRem(StartNegC, StepC->getValue());
+        if (Rem->isNullValue()) {
+          Constant *Result =ConstantExpr::getDiv(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) {
+      std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
+                << "  sol#2: " << *R2 << "\n";
+      // Pick the smallest positive root value.
+      assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
+      if (ConstantBool *CB =
+          dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
+                                                        R2->getValue()))) {
+        if (CB != ConstantBool::True)
+          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()->isNullValue())
+            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::getSetNE(C->getValue(), Zero);
+    if (NonZero == ConstantBool::True)
+      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;
+}
+
+static ConstantInt *
+EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
+  SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
+  SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
+  assert(isa<SCEVConstant>(Val) &&
+         "Evaluation of SCEV at constant didn't fold correctly?");
+  return cast<SCEVConstant>(Val)->getValue();
+}
+
+
+/// 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()->isNullValue()) {
+      std::vector<SCEVHandle> Operands(op_begin(), op_end());
+      Operands[0] = getIntegerSCEV(0, SC->getType());
+      SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
+      if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
+        return ShiftedAddRec->getNumIterationsInRange(
+                                              Range.subtract(SC->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.
+  ConstantInt *Zero = ConstantInt::get(getType(), 0);
+  if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
+  
+  if (isAffine()) {
+    // If this is an affine expression then we have this situation:
+    //   Solve {0,+,A} in Range  ===  Ax in Range
+
+    // Since we know that zero is in the range, we know that the upper value of
+    // the range must be the first possible exit value.  Also note that we
+    // already checked for a full range.
+    ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
+    ConstantInt *A     = cast<SCEVConstant>(getOperand(1))->getValue();
+    ConstantInt *One   = ConstantInt::get(getType(), 1);
+
+    // The exit value should be (Upper+A-1)/A.
+    Constant *ExitValue = Upper;
+    if (A != One) {
+      ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
+      ExitValue = ConstantExpr::getDiv(ExitValue, A);
+    }
+    assert(isa<ConstantInt>(ExitValue) &&
+           "Constant folding of integers not implemented?");
+
+    // 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))
+      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,
+                              ConstantExpr::getSub(ExitValue, One))) &&
+           "Linear scev computation is off in a bad way!");
+    return SCEVConstant::get(cast<ConstantInt>(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] = getNegativeSCEV(SCEVUnknown::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.
+      assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
+      if (ConstantBool *CB =
+          dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
+                                                        R2->getValue()))) {
+        if (CB != ConstantBool::True)
+          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)) {
+          // The next iteration must be out of the range...
+          Constant *NextVal =
+            ConstantExpr::getAdd(R1->getValue(),
+                                 ConstantInt::get(R1->getType(), 1));
+          
+          R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
+          if (!Range.contains(R1Val))
+            return SCEVUnknown::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.
+        Constant *NextVal =
+          ConstantExpr::getSub(R1->getValue(),
+                               ConstantInt::get(R1->getType(), 1));
+        R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
+        if (Range.contains(R1Val))
+          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 *One     = ConstantInt::get(getType(), 1);
+  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()))
+      return SCEVConstant::get(TestVal);
+
+    // Increment to test the next index.
+    TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
+  } 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.addRequiredID(LoopSimplifyID);
+  AU.addRequiredTransitive<LoopInfo>();
+}
+
+SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
+  return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
+}
+
+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::deleteInstructionFromRecords(Instruction *I) const {
+  return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
+}
+
+
+/// shouldSubstituteIndVar - Return true if we should perform induction variable
+/// substitution for this variable.  This is a hack because we don't have a
+/// strength reduction pass yet.  When we do we will promote all vars, because
+/// we can strength reduce them later as desired.
+bool ScalarEvolution::shouldSubstituteIndVar(const SCEV *S) const {
+  // Don't substitute high degree polynomials.
+  if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S))
+    if (AddRec->getNumOperands() > 3) return false;
+  return true;
+}
+
+
+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);
+  
+  std::cerr << "Loop " << L->getHeader()->getName() << ": ";
+  if (L->getExitBlocks().size() != 1)
+    std::cerr << "<multiple exits> ";
+
+  if (SE->hasLoopInvariantIterationCount(L)) {
+    std::cerr << *SE->getIterationCount(L) << " iterations! ";
+  } else {
+    std::cerr << "Unpredictable iteration count. ";
+  }
+
+  std::cerr << "\n";
+}
+
+void ScalarEvolution::print(std::ostream &OS) 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()->isIntegral()) {
+        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);
+}
+
+//===----------------------------------------------------------------------===//
+//                ScalarEvolutionRewriter Class Implementation
+//===----------------------------------------------------------------------===//
+
+Value *ScalarEvolutionRewriter::
+GetOrInsertCanonicalInductionVariable(const Loop *L, const Type *Ty) {
+  assert((Ty->isInteger() || Ty->isFloatingPoint()) &&
+         "Can only insert integer or floating point induction variables!");
+
+  // Check to see if we already inserted one.
+  SCEVHandle H = SCEVAddRecExpr::get(getIntegerSCEV(0, Ty),
+                                     getIntegerSCEV(1, Ty), L);
+  return ExpandCodeFor(H, 0, Ty);
+}
+
+/// ExpandCodeFor - Insert code to directly compute the specified SCEV
+/// expression into the program.  The inserted code is inserted into the
+/// specified block.
+Value *ScalarEvolutionRewriter::ExpandCodeFor(SCEVHandle SH,
+                                              Instruction *InsertPt,
+                                              const Type *Ty) {
+  std::map<SCEVHandle, Value*>::iterator ExistVal =InsertedExpressions.find(SH);
+  Value *V;
+  if (ExistVal != InsertedExpressions.end()) {
+    V = ExistVal->second;
+  } else {
+    // Ask the recurrence object to expand the code for itself.
+    V = SH->expandCodeFor(*this, InsertPt);
+    // Cache the generated result.
+    InsertedExpressions.insert(std::make_pair(SH, V));
+  }
+
+  if (Ty == 0 || V->getType() == Ty)
+    return V;
+  if (Constant *C = dyn_cast<Constant>(V))
+    return ConstantExpr::getCast(C, Ty);
+  else if (Instruction *I = dyn_cast<Instruction>(V)) {
+    // FIXME: check to see if there is already a cast!
+    BasicBlock::iterator IP = I; ++IP;
+    while (isa<PHINode>(IP)) ++IP;
+    return new CastInst(V, Ty, V->getName(), IP);
+  } else {
+    // FIXME: check to see if there is already a cast!
+    return new CastInst(V, Ty, V->getName(), InsertPt);
+  }
+}