llvm-6502/include/llvm/Analysis/ScalarEvolutionExpressions.h
Wojciech Matyjewicz e3320a1bcc Fix PR1798 - an error in the evaluation of SCEVAddRecExpr at an
arbitrary iteration.

The patch:
1) changes SCEVSDivExpr into SCEVUDivExpr,
2) replaces PartialFact() function with BinomialCoefficient(); the 
computations (essentially, the division) in BinomialCoefficient() are 
performed with the apprioprate bitwidth necessary to avoid overflow; 
unsigned division is used instead of the signed one.

Computations in BinomialCoefficient() require support from the code 
generator for APInts. Currently, we use a hack rounding up the 
neccessary bitwidth to the nearest power of 2. The hack is easy to turn 
off in future.

One remaining issue: we assume the divisor of the binomial coefficient 
formula can be computed accurately using 16 bits. It means we can handle 
AddRecs of length up to 9. In future, we should use APInts to evaluate 
the divisor.

Thanks to Nicholas for cooperation!


git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@46955 91177308-0d34-0410-b5e6-96231b3b80d8
2008-02-11 11:03:14 +00:00

569 lines
20 KiB
C++

//===- llvm/Analysis/ScalarEvolutionExpressions.h - SCEV Exprs --*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines the classes used to represent and build scalar expressions.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_ANALYSIS_SCALAREVOLUTION_EXPRESSIONS_H
#define LLVM_ANALYSIS_SCALAREVOLUTION_EXPRESSIONS_H
#include "llvm/Analysis/ScalarEvolution.h"
namespace llvm {
class ConstantInt;
class ConstantRange;
class APInt;
enum SCEVTypes {
// These should be ordered in terms of increasing complexity to make the
// folders simpler.
scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
scUDivExpr, scAddRecExpr, scSMaxExpr, scUnknown, scCouldNotCompute
};
//===--------------------------------------------------------------------===//
/// SCEVConstant - This class represents a constant integer value.
///
class SCEVConstant : public SCEV {
friend class ScalarEvolution;
ConstantInt *V;
explicit SCEVConstant(ConstantInt *v) : SCEV(scConstant), V(v) {}
virtual ~SCEVConstant();
public:
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;
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;
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
return this;
}
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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.
///
class SCEVTruncateExpr : public SCEV {
friend class ScalarEvolution;
SCEVHandle Op;
const Type *Ty;
SCEVTruncateExpr(const SCEVHandle &op, const Type *ty);
virtual ~SCEVTruncateExpr();
public:
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);
}
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
SCEVHandle H = Op->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H == Op)
return this;
return SE.getTruncateExpr(H, Ty);
}
/// 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;
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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.
///
class SCEVZeroExtendExpr : public SCEV {
friend class ScalarEvolution;
SCEVHandle Op;
const Type *Ty;
SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty);
virtual ~SCEVZeroExtendExpr();
public:
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;
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
SCEVHandle H = Op->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H == Op)
return this;
return SE.getZeroExtendExpr(H, Ty);
}
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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;
}
};
//===--------------------------------------------------------------------===//
/// SCEVSignExtendExpr - This class represents a sign extension of a small
/// integer value to a larger integer value.
///
class SCEVSignExtendExpr : public SCEV {
friend class ScalarEvolution;
SCEVHandle Op;
const Type *Ty;
SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty);
virtual ~SCEVSignExtendExpr();
public:
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;
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
SCEVHandle H = Op->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H == Op)
return this;
return SE.getSignExtendExpr(H, Ty);
}
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// Methods for support type inquiry through isa, cast, and dyn_cast:
static inline bool classof(const SCEVSignExtendExpr *S) { return true; }
static inline bool classof(const SCEV *S) {
return S->getSCEVType() == scSignExtend;
}
};
//===--------------------------------------------------------------------===//
/// SCEVCommutativeExpr - This node is the base class for n'ary commutative
/// operators.
///
class SCEVCommutativeExpr : public SCEV {
friend class ScalarEvolution;
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();
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;
}
// hasComputableLoopEvolution - Commutative expressions have computable loop
// evolutions iff they have at least one operand that varies with the loop,
// but that all varying operands are computable.
virtual bool hasComputableLoopEvolution(const Loop *L) const {
bool HasVarying = false;
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
if (!getOperand(i)->isLoopInvariant(L))
if (getOperand(i)->hasComputableLoopEvolution(L))
HasVarying = true;
else
return false;
return HasVarying;
}
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const;
virtual const char *getOperationStr() const = 0;
virtual const Type *getType() const { return getOperand(0)->getType(); }
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*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 ||
S->getSCEVType() == scSMaxExpr;
}
};
//===--------------------------------------------------------------------===//
/// SCEVAddExpr - This node represents an addition of some number of SCEVs.
///
class SCEVAddExpr : public SCEVCommutativeExpr {
friend class ScalarEvolution;
explicit SCEVAddExpr(const std::vector<SCEVHandle> &ops)
: SCEVCommutativeExpr(scAddExpr, ops) {
}
public:
virtual const char *getOperationStr() const { return " + "; }
/// 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 SCEVs.
///
class SCEVMulExpr : public SCEVCommutativeExpr {
friend class ScalarEvolution;
explicit SCEVMulExpr(const std::vector<SCEVHandle> &ops)
: SCEVCommutativeExpr(scMulExpr, ops) {
}
public:
virtual const char *getOperationStr() const { return " * "; }
/// 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.
///
class SCEVUDivExpr : public SCEV {
friend class ScalarEvolution;
SCEVHandle LHS, RHS;
SCEVUDivExpr(const SCEVHandle &lhs, const SCEVHandle &rhs)
: SCEV(scUDivExpr), LHS(lhs), RHS(rhs) {}
virtual ~SCEVUDivExpr();
public:
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);
}
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
SCEVHandle L = LHS->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
SCEVHandle R = RHS->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (L == LHS && R == RHS)
return this;
else
return SE.getUDivExpr(L, R);
}
virtual const Type *getType() const;
void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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.
///
class SCEVAddRecExpr : public SCEV {
friend class ScalarEvolution;
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();
public:
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(ScalarEvolution &SE) const {
if (getNumOperands() == 2) return getOperand(1);
return SE.getAddRecExpr(std::vector<SCEVHandle>(op_begin()+1,op_end()),
getLoop());
}
virtual bool hasComputableLoopEvolution(const Loop *QL) const {
if (L == QL) return true;
return false;
}
virtual bool isLoopInvariant(const Loop *QueryLoop) const;
virtual const Type *getType() const { return Operands[0]->getType(); }
/// 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, ScalarEvolution &SE) 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,
ScalarEvolution &SE) const;
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const;
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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;
}
};
//===--------------------------------------------------------------------===//
/// SCEVSMaxExpr - This class represents a signed maximum selection.
///
class SCEVSMaxExpr : public SCEVCommutativeExpr {
friend class ScalarEvolution;
explicit SCEVSMaxExpr(const std::vector<SCEVHandle> &ops)
: SCEVCommutativeExpr(scSMaxExpr, ops) {
}
public:
virtual const char *getOperationStr() const { return " smax "; }
/// Methods for support type inquiry through isa, cast, and dyn_cast:
static inline bool classof(const SCEVSMaxExpr *S) { return true; }
static inline bool classof(const SCEV *S) {
return S->getSCEVType() == scSMaxExpr;
}
};
//===--------------------------------------------------------------------===//
/// 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.
///
class SCEVUnknown : public SCEV {
friend class ScalarEvolution;
Value *V;
explicit SCEVUnknown(Value *v) : SCEV(scUnknown), V(v) {}
protected:
~SCEVUnknown();
public:
Value *getValue() const { return V; }
virtual bool isLoopInvariant(const Loop *L) const;
virtual bool hasComputableLoopEvolution(const Loop *QL) const {
return false; // not computable
}
SCEVHandle replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
if (&*Sym == this) return Conc;
return this;
}
virtual const Type *getType() const;
virtual void print(std::ostream &OS) const;
void print(std::ostream *OS) const { if (OS) print(*OS); }
/// 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;
}
};
/// SCEVVisitor - This class defines a simple visitor class that may be used
/// for various SCEV analysis purposes.
template<typename SC, typename RetVal=void>
struct SCEVVisitor {
RetVal visit(SCEV *S) {
switch (S->getSCEVType()) {
case scConstant:
return ((SC*)this)->visitConstant((SCEVConstant*)S);
case scTruncate:
return ((SC*)this)->visitTruncateExpr((SCEVTruncateExpr*)S);
case scZeroExtend:
return ((SC*)this)->visitZeroExtendExpr((SCEVZeroExtendExpr*)S);
case scSignExtend:
return ((SC*)this)->visitSignExtendExpr((SCEVSignExtendExpr*)S);
case scAddExpr:
return ((SC*)this)->visitAddExpr((SCEVAddExpr*)S);
case scMulExpr:
return ((SC*)this)->visitMulExpr((SCEVMulExpr*)S);
case scUDivExpr:
return ((SC*)this)->visitUDivExpr((SCEVUDivExpr*)S);
case scAddRecExpr:
return ((SC*)this)->visitAddRecExpr((SCEVAddRecExpr*)S);
case scSMaxExpr:
return ((SC*)this)->visitSMaxExpr((SCEVSMaxExpr*)S);
case scUnknown:
return ((SC*)this)->visitUnknown((SCEVUnknown*)S);
case scCouldNotCompute:
return ((SC*)this)->visitCouldNotCompute((SCEVCouldNotCompute*)S);
default:
assert(0 && "Unknown SCEV type!");
abort();
}
}
RetVal visitCouldNotCompute(SCEVCouldNotCompute *S) {
assert(0 && "Invalid use of SCEVCouldNotCompute!");
abort();
return RetVal();
}
};
}
#endif