// These should be ordered in terms of increasing complexity to make the
// folders simpler.
scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
- scSDivExpr, scAddRecExpr, scSMaxExpr, scUnknown, scCouldNotCompute
+ scUDivExpr, scAddRecExpr, scSMaxExpr, scUnknown, scCouldNotCompute
};
//===--------------------------------------------------------------------===//
//===--------------------------------------------------------------------===//
- /// SCEVSDivExpr - This class represents a binary signed division operation.
+ /// SCEVUDivExpr - This class represents a binary unsigned division operation.
///
- class SCEVSDivExpr : public SCEV {
+ class SCEVUDivExpr : public SCEV {
friend class ScalarEvolution;
SCEVHandle LHS, RHS;
- SCEVSDivExpr(const SCEVHandle &lhs, const SCEVHandle &rhs)
- : SCEV(scSDivExpr), LHS(lhs), RHS(rhs) {}
+ SCEVUDivExpr(const SCEVHandle &lhs, const SCEVHandle &rhs)
+ : SCEV(scUDivExpr), LHS(lhs), RHS(rhs) {}
- virtual ~SCEVSDivExpr();
+ virtual ~SCEVUDivExpr();
public:
const SCEVHandle &getLHS() const { return LHS; }
const SCEVHandle &getRHS() const { return RHS; }
if (L == LHS && R == RHS)
return this;
else
- return SE.getSDivExpr(L, R);
+ return SE.getUDivExpr(L, R);
}
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 SCEVSDivExpr *S) { return true; }
+ static inline bool classof(const SCEVUDivExpr *S) { return true; }
static inline bool classof(const SCEV *S) {
- return S->getSCEVType() == scSDivExpr;
+ return S->getSCEVType() == scUDivExpr;
}
};
return ((SC*)this)->visitAddExpr((SCEVAddExpr*)S);
case scMulExpr:
return ((SC*)this)->visitMulExpr((SCEVMulExpr*)S);
- case scSDivExpr:
- return ((SC*)this)->visitSDivExpr((SCEVSDivExpr*)S);
+ case scUDivExpr:
+ return ((SC*)this)->visitUDivExpr((SCEVUDivExpr*)S);
case scAddRecExpr:
return ((SC*)this)->visitAddRecExpr((SCEVAddRecExpr*)S);
case scSMaxExpr:
}
-// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
+// 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!
static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
- SCEVSDivExpr*> > SCEVSDivs;
+ SCEVUDivExpr*> > SCEVUDivs;
-SCEVSDivExpr::~SCEVSDivExpr() {
- SCEVSDivs->erase(std::make_pair(LHS, RHS));
+SCEVUDivExpr::~SCEVUDivExpr() {
+ SCEVUDivs->erase(std::make_pair(LHS, RHS));
}
-void SCEVSDivExpr::print(std::ostream &OS) const {
- OS << "(" << *LHS << " /s " << *RHS << ")";
+void SCEVUDivExpr::print(std::ostream &OS) const {
+ OS << "(" << *LHS << " /u " << *RHS << ")";
}
-const Type *SCEVSDivExpr::getType() const {
+const Type *SCEVUDivExpr::getType() const {
return LHS->getType();
}
}
-/// PartialFact - Compute V!/(V-NumSteps)!
-static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps,
- ScalarEvolution &SE) {
+/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as
+/// It. Assume, K > 0.
+static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
+ ScalarEvolution &SE) {
+ // We are using the following formula for BC(It, K):
+ //
+ // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
+ //
+ // Suppose, W is the bitwidth of It (and of the return value as well). We
+ // must be prepared for overflow. Hence, we must assure that the result of
+ // our computation is equal to the accurate one modulo 2^W. Unfortunately,
+ // division isn't safe in modular arithmetic. This means we must perform the
+ // whole computation accurately and then truncate the result to W bits.
+ //
+ // The dividend of the formula is a multiplication of K integers of bitwidth
+ // W. K*W bits suffice to compute it accurately.
+ //
+ // FIXME: We assume the divisor can be accurately computed using 16-bit
+ // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In
+ // future we may use APInt to use the minimum number of bits necessary to
+ // compute it accurately.
+ //
+ // It is safe to use unsigned division here: the dividend is nonnegative and
+ // the divisor is positive.
+
+ // Handle the simplest case efficiently.
+ if (K == 1)
+ return It;
+
+ assert(K < 9 && "We cannot handle such long AddRecs yet.");
+
+ // FIXME: A temporary hack to remove in future. Arbitrary precision integers
+ // aren't supported by the code generator yet. For the dividend, the bitwidth
+ // we use is the smallest power of 2 greater or equal to K*W and less or equal
+ // to 64. Note that setting the upper bound for bitwidth may still lead to
+ // miscompilation in some cases.
+ unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth());
+ if (DividendBits > 64)
+ DividendBits = 64;
+#if 0 // Waiting for the APInt support in the code generator...
+ unsigned DividendBits = K * It->getBitWidth();
+#endif
+
+ const IntegerType *DividendTy = IntegerType::get(DividendBits);
+ const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy);
+
+ // The final number of bits we need to perform the division is the maximum of
+ // dividend and divisor bitwidths.
+ const IntegerType *DivisionTy =
+ IntegerType::get(std::max(DividendBits, 16U));
+
+ // Compute K! We know K >= 2 here.
+ unsigned F = 2;
+ for (unsigned i = 3; i <= K; ++i)
+ F *= i;
+ APInt Divisor(DivisionTy->getBitWidth(), F);
+
// Handle this case efficiently, it is common to have constant iteration
// counts while computing loop exit values.
- if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
- const APInt& Val = SC->getValue()->getValue();
- APInt Result(Val.getBitWidth(), 1);
- for (; NumSteps; --NumSteps)
- Result *= Val-(NumSteps-1);
- return SE.getConstant(Result);
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) {
+ const APInt& N = SC->getValue()->getValue();
+ APInt Dividend(N.getBitWidth(), 1);
+ for (; K; --K)
+ Dividend *= N-(K-1);
+ if (DividendTy != DivisionTy)
+ Dividend = Dividend.zext(DivisionTy->getBitWidth());
+ return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth()));
}
-
- const Type *Ty = V->getType();
- if (NumSteps == 0)
- return SE.getIntegerSCEV(1, Ty);
-
- SCEVHandle Result = V;
- for (unsigned i = 1; i != NumSteps; ++i)
- Result = SE.getMulExpr(Result, SE.getMinusSCEV(V,
- SE.getIntegerSCEV(i, Ty)));
- return Result;
+
+ SCEVHandle Dividend = ExIt;
+ for (unsigned i = 1; i != K; ++i)
+ Dividend =
+ SE.getMulExpr(Dividend,
+ SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy)));
+ if (DividendTy != DivisionTy)
+ Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy);
+ return
+ SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)),
+ It->getType());
}
-
/// 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)
+/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(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??
+/// where BC(It, k) stands for binomial coefficient.
///
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
ScalarEvolution &SE) 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, SE);
- Divisor *= i;
- SCEVHandle Val = SE.getSDivExpr(SE.getMulExpr(BC, getOperand(i)),
- SE.getIntegerSCEV(Divisor,Ty));
+ // The computation is correct in the face of overflow provided that the
+ // multiplication is performed _after_ the evaluation of the binomial
+ // coefficient.
+ SCEVHandle Val = SE.getMulExpr(getOperand(i),
+ BinomialCoefficient(It, i, SE));
Result = SE.getAddExpr(Result, Val);
}
return Result;
}
-
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
return Result;
}
-SCEVHandle ScalarEvolution::getSDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->equalsInt(1))
- return LHS; // X sdiv 1 --> x
- if (RHSC->getValue()->isAllOnesValue())
- return getNegativeSCEV(LHS); // X sdiv -1 --> -x
+ return LHS; // X udiv 1 --> x
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
- return getUnknown(ConstantExpr::getSDiv(LHSCV, RHSCV));
+ return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
}
}
// FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
- SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
- if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
+ SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
+ if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
return Result;
}
return MinOpRes;
}
- // SCEVSDivExpr, SCEVUnknown
+ // SCEVUDivExpr, SCEVUnknown
return 0;
}
case Instruction::Mul:
return SE.getMulExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
- case Instruction::SDiv:
- return SE.getSDivExpr(getSCEV(I->getOperand(0)),
+ case Instruction::UDiv:
+ return SE.getUDivExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Sub:
return SE.getMinusSCEV(getSCEV(I->getOperand(0)),
return Comm;
}
- if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
+ if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
if (LHS == UnknownValue) return LHS;
SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
if (RHS == UnknownValue) return RHS;
if (LHS == Div->getLHS() && RHS == Div->getRHS())
return Div; // must be loop invariant
- return SE.getSDivExpr(LHS, RHS);
+ return SE.getUDivExpr(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
projects / oota-llvm.git / commitdiff