[llvm-commits] CVS: llvm/lib/Analysis/ScalarEvolution.cpp
Chris Lattner
lattner at cs.uiuc.edu
Fri Apr 2 14:45:12 PST 2004
Changes in directory llvm/lib/Analysis:
ScalarEvolution.cpp added (r1.1)
---
Log message:
Add a new analysis
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Diffs of the changes: (+2482 -0)
Index: llvm/lib/Analysis/ScalarEvolution.cpp
diff -c /dev/null llvm/lib/Analysis/ScalarEvolution.cpp:1.1
*** /dev/null Fri Apr 2 14:23:27 2004
--- llvm/lib/Analysis/ScalarEvolution.cpp Fri Apr 2 14:23:17 2004
***************
*** 0 ****
--- 1,2482 ----
+ //===- 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);
+ }
+ }
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