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llvm-mirror/lib/Analysis/ScalarEvolution.cpp
Chris Lattner cb6744360c Fix a bug Brian found. 
llvm-svn: 12754
2004-04-07 16:16:11 +00:00

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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!");
return false;
}
const Type *SCEVCouldNotCompute::getType() const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return 0;
}
bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return false;
}
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!");
if (Ops.size() == 1) return Ops[0];
// 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;
assert(Idx < Ops.size());
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:
#if 0
std::cerr << "ComputeIterationCount ";
if (ExitCond->getOperand(0)->getType()->isUnsigned())
std::cerr << "[unsigned] ";
std::cerr << *LHS << " "
<< Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
#endif
break;
}
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)sqrt(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) {
#if 0
std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
<< " sol#2: " << *R2 << "\n";
#endif
// 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;
if (InvokeInst *II = dyn_cast<InvokeInst>(I))
IP = II->getNormalDest()->begin();
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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