1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the const SCEV *
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Analysis/ConstantFolding.h"
70 #include "llvm/Analysis/Dominators.h"
71 #include "llvm/Analysis/LoopInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/Assembly/Writer.h"
74 #include "llvm/Target/TargetData.h"
75 #include "llvm/Support/CommandLine.h"
76 #include "llvm/Support/Compiler.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/ErrorHandling.h"
79 #include "llvm/Support/GetElementPtrTypeIterator.h"
80 #include "llvm/Support/InstIterator.h"
81 #include "llvm/Support/MathExtras.h"
82 #include "llvm/Support/raw_ostream.h"
83 #include "llvm/ADT/Statistic.h"
84 #include "llvm/ADT/STLExtras.h"
85 #include "llvm/ADT/SmallPtrSet.h"
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
98 static cl::opt<unsigned>
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant "
105 static RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
107 char ScalarEvolution::ID = 0;
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
119 void SCEV::dump() const {
124 void SCEV::print(std::ostream &o) const {
125 raw_os_ostream OS(o);
129 bool SCEV::isZero() const {
130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
131 return SC->getValue()->isZero();
135 bool SCEV::isOne() const {
136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
137 return SC->getValue()->isOne();
141 bool SCEV::isAllOnesValue() const {
142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
143 return SC->getValue()->isAllOnesValue();
147 SCEVCouldNotCompute::SCEVCouldNotCompute() :
148 SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
150 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
151 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
155 const Type *SCEVCouldNotCompute::getType() const {
156 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
160 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
161 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
166 SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete(
169 ScalarEvolution &SE) const {
173 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
174 OS << "***COULDNOTCOMPUTE***";
177 bool SCEVCouldNotCompute::classof(const SCEV *S) {
178 return S->getSCEVType() == scCouldNotCompute;
181 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
183 ID.AddInteger(scConstant);
186 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
187 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
188 new (S) SCEVConstant(ID, V);
189 UniqueSCEVs.InsertNode(S, IP);
193 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
194 return getConstant(ConstantInt::get(Val));
198 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
200 Context->getConstantInt(cast<IntegerType>(Ty), V, isSigned));
203 const Type *SCEVConstant::getType() const { return V->getType(); }
205 void SCEVConstant::print(raw_ostream &OS) const {
206 WriteAsOperand(OS, V, false);
209 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
210 unsigned SCEVTy, const SCEV *op, const Type *ty)
211 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
213 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
214 return Op->dominates(BB, DT);
217 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
218 const SCEV *op, const Type *ty)
219 : SCEVCastExpr(ID, scTruncate, op, ty) {
220 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
221 (Ty->isInteger() || isa<PointerType>(Ty)) &&
222 "Cannot truncate non-integer value!");
225 void SCEVTruncateExpr::print(raw_ostream &OS) const {
226 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
229 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
230 const SCEV *op, const Type *ty)
231 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
232 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
233 (Ty->isInteger() || isa<PointerType>(Ty)) &&
234 "Cannot zero extend non-integer value!");
237 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
238 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
241 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
242 const SCEV *op, const Type *ty)
243 : SCEVCastExpr(ID, scSignExtend, op, ty) {
244 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
245 (Ty->isInteger() || isa<PointerType>(Ty)) &&
246 "Cannot sign extend non-integer value!");
249 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
250 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
253 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
254 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
255 const char *OpStr = getOperationStr();
256 OS << "(" << *Operands[0];
257 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
258 OS << OpStr << *Operands[i];
263 SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete(
266 ScalarEvolution &SE) const {
267 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
269 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
270 if (H != getOperand(i)) {
271 SmallVector<const SCEV *, 8> NewOps;
272 NewOps.reserve(getNumOperands());
273 for (unsigned j = 0; j != i; ++j)
274 NewOps.push_back(getOperand(j));
276 for (++i; i != e; ++i)
277 NewOps.push_back(getOperand(i)->
278 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
280 if (isa<SCEVAddExpr>(this))
281 return SE.getAddExpr(NewOps);
282 else if (isa<SCEVMulExpr>(this))
283 return SE.getMulExpr(NewOps);
284 else if (isa<SCEVSMaxExpr>(this))
285 return SE.getSMaxExpr(NewOps);
286 else if (isa<SCEVUMaxExpr>(this))
287 return SE.getUMaxExpr(NewOps);
289 llvm_unreachable("Unknown commutative expr!");
295 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
296 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
297 if (!getOperand(i)->dominates(BB, DT))
303 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
304 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
307 void SCEVUDivExpr::print(raw_ostream &OS) const {
308 OS << "(" << *LHS << " /u " << *RHS << ")";
311 const Type *SCEVUDivExpr::getType() const {
312 // In most cases the types of LHS and RHS will be the same, but in some
313 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
314 // depend on the type for correctness, but handling types carefully can
315 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
316 // a pointer type than the RHS, so use the RHS' type here.
317 return RHS->getType();
321 SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym,
323 ScalarEvolution &SE) const {
324 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
326 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
327 if (H != getOperand(i)) {
328 SmallVector<const SCEV *, 8> NewOps;
329 NewOps.reserve(getNumOperands());
330 for (unsigned j = 0; j != i; ++j)
331 NewOps.push_back(getOperand(j));
333 for (++i; i != e; ++i)
334 NewOps.push_back(getOperand(i)->
335 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
337 return SE.getAddRecExpr(NewOps, L);
344 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
345 // Add recurrences are never invariant in the function-body (null loop).
349 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
350 if (QueryLoop->contains(L->getHeader()))
353 // This recurrence is variant w.r.t. QueryLoop if any of its operands
355 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
356 if (!getOperand(i)->isLoopInvariant(QueryLoop))
359 // Otherwise it's loop-invariant.
363 void SCEVAddRecExpr::print(raw_ostream &OS) const {
364 OS << "{" << *Operands[0];
365 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
366 OS << ",+," << *Operands[i];
367 OS << "}<" << L->getHeader()->getName() + ">";
370 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
371 // All non-instruction values are loop invariant. All instructions are loop
372 // invariant if they are not contained in the specified loop.
373 // Instructions are never considered invariant in the function body
374 // (null loop) because they are defined within the "loop".
375 if (Instruction *I = dyn_cast<Instruction>(V))
376 return L && !L->contains(I->getParent());
380 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
381 if (Instruction *I = dyn_cast<Instruction>(getValue()))
382 return DT->dominates(I->getParent(), BB);
386 const Type *SCEVUnknown::getType() const {
390 void SCEVUnknown::print(raw_ostream &OS) const {
391 WriteAsOperand(OS, V, false);
394 //===----------------------------------------------------------------------===//
396 //===----------------------------------------------------------------------===//
399 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
400 /// than the complexity of the RHS. This comparator is used to canonicalize
402 class VISIBILITY_HIDDEN SCEVComplexityCompare {
405 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
407 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
408 // Primarily, sort the SCEVs by their getSCEVType().
409 if (LHS->getSCEVType() != RHS->getSCEVType())
410 return LHS->getSCEVType() < RHS->getSCEVType();
412 // Aside from the getSCEVType() ordering, the particular ordering
413 // isn't very important except that it's beneficial to be consistent,
414 // so that (a + b) and (b + a) don't end up as different expressions.
416 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
417 // not as complete as it could be.
418 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
419 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
421 // Order pointer values after integer values. This helps SCEVExpander
423 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
425 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
428 // Compare getValueID values.
429 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
430 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
432 // Sort arguments by their position.
433 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
434 const Argument *RA = cast<Argument>(RU->getValue());
435 return LA->getArgNo() < RA->getArgNo();
438 // For instructions, compare their loop depth, and their opcode.
439 // This is pretty loose.
440 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
441 Instruction *RV = cast<Instruction>(RU->getValue());
443 // Compare loop depths.
444 if (LI->getLoopDepth(LV->getParent()) !=
445 LI->getLoopDepth(RV->getParent()))
446 return LI->getLoopDepth(LV->getParent()) <
447 LI->getLoopDepth(RV->getParent());
450 if (LV->getOpcode() != RV->getOpcode())
451 return LV->getOpcode() < RV->getOpcode();
453 // Compare the number of operands.
454 if (LV->getNumOperands() != RV->getNumOperands())
455 return LV->getNumOperands() < RV->getNumOperands();
461 // Compare constant values.
462 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
463 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
464 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
465 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
466 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
469 // Compare addrec loop depths.
470 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
471 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
472 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
473 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
476 // Lexicographically compare n-ary expressions.
477 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
478 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
479 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
480 if (i >= RC->getNumOperands())
482 if (operator()(LC->getOperand(i), RC->getOperand(i)))
484 if (operator()(RC->getOperand(i), LC->getOperand(i)))
487 return LC->getNumOperands() < RC->getNumOperands();
490 // Lexicographically compare udiv expressions.
491 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
492 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
493 if (operator()(LC->getLHS(), RC->getLHS()))
495 if (operator()(RC->getLHS(), LC->getLHS()))
497 if (operator()(LC->getRHS(), RC->getRHS()))
499 if (operator()(RC->getRHS(), LC->getRHS()))
504 // Compare cast expressions by operand.
505 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
506 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
507 return operator()(LC->getOperand(), RC->getOperand());
510 llvm_unreachable("Unknown SCEV kind!");
516 /// GroupByComplexity - Given a list of SCEV objects, order them by their
517 /// complexity, and group objects of the same complexity together by value.
518 /// When this routine is finished, we know that any duplicates in the vector are
519 /// consecutive and that complexity is monotonically increasing.
521 /// Note that we go take special precautions to ensure that we get determinstic
522 /// results from this routine. In other words, we don't want the results of
523 /// this to depend on where the addresses of various SCEV objects happened to
526 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
528 if (Ops.size() < 2) return; // Noop
529 if (Ops.size() == 2) {
530 // This is the common case, which also happens to be trivially simple.
532 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
533 std::swap(Ops[0], Ops[1]);
537 // Do the rough sort by complexity.
538 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
540 // Now that we are sorted by complexity, group elements of the same
541 // complexity. Note that this is, at worst, N^2, but the vector is likely to
542 // be extremely short in practice. Note that we take this approach because we
543 // do not want to depend on the addresses of the objects we are grouping.
544 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
545 const SCEV *S = Ops[i];
546 unsigned Complexity = S->getSCEVType();
548 // If there are any objects of the same complexity and same value as this
550 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
551 if (Ops[j] == S) { // Found a duplicate.
552 // Move it to immediately after i'th element.
553 std::swap(Ops[i+1], Ops[j]);
554 ++i; // no need to rescan it.
555 if (i == e-2) return; // Done!
563 //===----------------------------------------------------------------------===//
564 // Simple SCEV method implementations
565 //===----------------------------------------------------------------------===//
567 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
569 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
571 const Type* ResultTy) {
572 // Handle the simplest case efficiently.
574 return SE.getTruncateOrZeroExtend(It, ResultTy);
576 // We are using the following formula for BC(It, K):
578 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
580 // Suppose, W is the bitwidth of the return value. We must be prepared for
581 // overflow. Hence, we must assure that the result of our computation is
582 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
583 // safe in modular arithmetic.
585 // However, this code doesn't use exactly that formula; the formula it uses
586 // is something like the following, where T is the number of factors of 2 in
587 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
590 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
592 // This formula is trivially equivalent to the previous formula. However,
593 // this formula can be implemented much more efficiently. The trick is that
594 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
595 // arithmetic. To do exact division in modular arithmetic, all we have
596 // to do is multiply by the inverse. Therefore, this step can be done at
599 // The next issue is how to safely do the division by 2^T. The way this
600 // is done is by doing the multiplication step at a width of at least W + T
601 // bits. This way, the bottom W+T bits of the product are accurate. Then,
602 // when we perform the division by 2^T (which is equivalent to a right shift
603 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
604 // truncated out after the division by 2^T.
606 // In comparison to just directly using the first formula, this technique
607 // is much more efficient; using the first formula requires W * K bits,
608 // but this formula less than W + K bits. Also, the first formula requires
609 // a division step, whereas this formula only requires multiplies and shifts.
611 // It doesn't matter whether the subtraction step is done in the calculation
612 // width or the input iteration count's width; if the subtraction overflows,
613 // the result must be zero anyway. We prefer here to do it in the width of
614 // the induction variable because it helps a lot for certain cases; CodeGen
615 // isn't smart enough to ignore the overflow, which leads to much less
616 // efficient code if the width of the subtraction is wider than the native
619 // (It's possible to not widen at all by pulling out factors of 2 before
620 // the multiplication; for example, K=2 can be calculated as
621 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
622 // extra arithmetic, so it's not an obvious win, and it gets
623 // much more complicated for K > 3.)
625 // Protection from insane SCEVs; this bound is conservative,
626 // but it probably doesn't matter.
628 return SE.getCouldNotCompute();
630 unsigned W = SE.getTypeSizeInBits(ResultTy);
632 // Calculate K! / 2^T and T; we divide out the factors of two before
633 // multiplying for calculating K! / 2^T to avoid overflow.
634 // Other overflow doesn't matter because we only care about the bottom
635 // W bits of the result.
636 APInt OddFactorial(W, 1);
638 for (unsigned i = 3; i <= K; ++i) {
640 unsigned TwoFactors = Mult.countTrailingZeros();
642 Mult = Mult.lshr(TwoFactors);
643 OddFactorial *= Mult;
646 // We need at least W + T bits for the multiplication step
647 unsigned CalculationBits = W + T;
649 // Calcuate 2^T, at width T+W.
650 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
652 // Calculate the multiplicative inverse of K! / 2^T;
653 // this multiplication factor will perform the exact division by
655 APInt Mod = APInt::getSignedMinValue(W+1);
656 APInt MultiplyFactor = OddFactorial.zext(W+1);
657 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
658 MultiplyFactor = MultiplyFactor.trunc(W);
660 // Calculate the product, at width T+W
661 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
662 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
663 for (unsigned i = 1; i != K; ++i) {
664 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
665 Dividend = SE.getMulExpr(Dividend,
666 SE.getTruncateOrZeroExtend(S, CalculationTy));
670 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
672 // Truncate the result, and divide by K! / 2^T.
674 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
675 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
678 /// evaluateAtIteration - Return the value of this chain of recurrences at
679 /// the specified iteration number. We can evaluate this recurrence by
680 /// multiplying each element in the chain by the binomial coefficient
681 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
683 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
685 /// where BC(It, k) stands for binomial coefficient.
687 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
688 ScalarEvolution &SE) const {
689 const SCEV *Result = getStart();
690 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
691 // The computation is correct in the face of overflow provided that the
692 // multiplication is performed _after_ the evaluation of the binomial
694 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
695 if (isa<SCEVCouldNotCompute>(Coeff))
698 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
703 //===----------------------------------------------------------------------===//
704 // SCEV Expression folder implementations
705 //===----------------------------------------------------------------------===//
707 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
709 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
710 "This is not a truncating conversion!");
711 assert(isSCEVable(Ty) &&
712 "This is not a conversion to a SCEVable type!");
713 Ty = getEffectiveSCEVType(Ty);
716 ID.AddInteger(scTruncate);
720 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
722 // Fold if the operand is constant.
723 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
725 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
727 // trunc(trunc(x)) --> trunc(x)
728 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
729 return getTruncateExpr(ST->getOperand(), Ty);
731 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
732 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
733 return getTruncateOrSignExtend(SS->getOperand(), Ty);
735 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
736 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
737 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
739 // If the input value is a chrec scev, truncate the chrec's operands.
740 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
741 SmallVector<const SCEV *, 4> Operands;
742 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
743 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
744 return getAddRecExpr(Operands, AddRec->getLoop());
747 // The cast wasn't folded; create an explicit cast node.
748 // Recompute the insert position, as it may have been invalidated.
749 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
750 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
751 new (S) SCEVTruncateExpr(ID, Op, Ty);
752 UniqueSCEVs.InsertNode(S, IP);
756 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
758 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
759 "This is not an extending conversion!");
760 assert(isSCEVable(Ty) &&
761 "This is not a conversion to a SCEVable type!");
762 Ty = getEffectiveSCEVType(Ty);
764 // Fold if the operand is constant.
765 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
766 const Type *IntTy = getEffectiveSCEVType(Ty);
767 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
768 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
769 return getConstant(cast<ConstantInt>(C));
772 // zext(zext(x)) --> zext(x)
773 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
774 return getZeroExtendExpr(SZ->getOperand(), Ty);
776 // Before doing any expensive analysis, check to see if we've already
777 // computed a SCEV for this Op and Ty.
779 ID.AddInteger(scZeroExtend);
783 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
785 // If the input value is a chrec scev, and we can prove that the value
786 // did not overflow the old, smaller, value, we can zero extend all of the
787 // operands (often constants). This allows analysis of something like
788 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
789 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
790 if (AR->isAffine()) {
791 const SCEV *Start = AR->getStart();
792 const SCEV *Step = AR->getStepRecurrence(*this);
793 unsigned BitWidth = getTypeSizeInBits(AR->getType());
794 const Loop *L = AR->getLoop();
796 // Check whether the backedge-taken count is SCEVCouldNotCompute.
797 // Note that this serves two purposes: It filters out loops that are
798 // simply not analyzable, and it covers the case where this code is
799 // being called from within backedge-taken count analysis, such that
800 // attempting to ask for the backedge-taken count would likely result
801 // in infinite recursion. In the later case, the analysis code will
802 // cope with a conservative value, and it will take care to purge
803 // that value once it has finished.
804 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
805 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
806 // Manually compute the final value for AR, checking for
809 // Check whether the backedge-taken count can be losslessly casted to
810 // the addrec's type. The count is always unsigned.
811 const SCEV *CastedMaxBECount =
812 getTruncateOrZeroExtend(MaxBECount, Start->getType());
813 const SCEV *RecastedMaxBECount =
814 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
815 if (MaxBECount == RecastedMaxBECount) {
816 const Type *WideTy = IntegerType::get(BitWidth * 2);
817 // Check whether Start+Step*MaxBECount has no unsigned overflow.
819 getMulExpr(CastedMaxBECount,
820 getTruncateOrZeroExtend(Step, Start->getType()));
821 const SCEV *Add = getAddExpr(Start, ZMul);
822 const SCEV *OperandExtendedAdd =
823 getAddExpr(getZeroExtendExpr(Start, WideTy),
824 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
825 getZeroExtendExpr(Step, WideTy)));
826 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
827 // Return the expression with the addrec on the outside.
828 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
829 getZeroExtendExpr(Step, Ty),
832 // Similar to above, only this time treat the step value as signed.
833 // This covers loops that count down.
835 getMulExpr(CastedMaxBECount,
836 getTruncateOrSignExtend(Step, Start->getType()));
837 Add = getAddExpr(Start, SMul);
839 getAddExpr(getZeroExtendExpr(Start, WideTy),
840 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
841 getSignExtendExpr(Step, WideTy)));
842 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
843 // Return the expression with the addrec on the outside.
844 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
845 getSignExtendExpr(Step, Ty),
849 // If the backedge is guarded by a comparison with the pre-inc value
850 // the addrec is safe. Also, if the entry is guarded by a comparison
851 // with the start value and the backedge is guarded by a comparison
852 // with the post-inc value, the addrec is safe.
853 if (isKnownPositive(Step)) {
854 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
855 getUnsignedRange(Step).getUnsignedMax());
856 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
857 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
858 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
859 AR->getPostIncExpr(*this), N)))
860 // Return the expression with the addrec on the outside.
861 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
862 getZeroExtendExpr(Step, Ty),
864 } else if (isKnownNegative(Step)) {
865 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
866 getSignedRange(Step).getSignedMin());
867 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
868 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
869 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
870 AR->getPostIncExpr(*this), N)))
871 // Return the expression with the addrec on the outside.
872 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
873 getSignExtendExpr(Step, Ty),
879 // The cast wasn't folded; create an explicit cast node.
880 // Recompute the insert position, as it may have been invalidated.
881 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
882 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
883 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
884 UniqueSCEVs.InsertNode(S, IP);
888 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
890 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
891 "This is not an extending conversion!");
892 assert(isSCEVable(Ty) &&
893 "This is not a conversion to a SCEVable type!");
894 Ty = getEffectiveSCEVType(Ty);
896 // Fold if the operand is constant.
897 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
898 const Type *IntTy = getEffectiveSCEVType(Ty);
899 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
900 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
901 return getConstant(cast<ConstantInt>(C));
904 // sext(sext(x)) --> sext(x)
905 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
906 return getSignExtendExpr(SS->getOperand(), Ty);
908 // Before doing any expensive analysis, check to see if we've already
909 // computed a SCEV for this Op and Ty.
911 ID.AddInteger(scSignExtend);
915 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
917 // If the input value is a chrec scev, and we can prove that the value
918 // did not overflow the old, smaller, value, we can sign extend all of the
919 // operands (often constants). This allows analysis of something like
920 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
921 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
922 if (AR->isAffine()) {
923 const SCEV *Start = AR->getStart();
924 const SCEV *Step = AR->getStepRecurrence(*this);
925 unsigned BitWidth = getTypeSizeInBits(AR->getType());
926 const Loop *L = AR->getLoop();
928 // Check whether the backedge-taken count is SCEVCouldNotCompute.
929 // Note that this serves two purposes: It filters out loops that are
930 // simply not analyzable, and it covers the case where this code is
931 // being called from within backedge-taken count analysis, such that
932 // attempting to ask for the backedge-taken count would likely result
933 // in infinite recursion. In the later case, the analysis code will
934 // cope with a conservative value, and it will take care to purge
935 // that value once it has finished.
936 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
937 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
938 // Manually compute the final value for AR, checking for
941 // Check whether the backedge-taken count can be losslessly casted to
942 // the addrec's type. The count is always unsigned.
943 const SCEV *CastedMaxBECount =
944 getTruncateOrZeroExtend(MaxBECount, Start->getType());
945 const SCEV *RecastedMaxBECount =
946 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
947 if (MaxBECount == RecastedMaxBECount) {
948 const Type *WideTy = IntegerType::get(BitWidth * 2);
949 // Check whether Start+Step*MaxBECount has no signed overflow.
951 getMulExpr(CastedMaxBECount,
952 getTruncateOrSignExtend(Step, Start->getType()));
953 const SCEV *Add = getAddExpr(Start, SMul);
954 const SCEV *OperandExtendedAdd =
955 getAddExpr(getSignExtendExpr(Start, WideTy),
956 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
957 getSignExtendExpr(Step, WideTy)));
958 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
959 // Return the expression with the addrec on the outside.
960 return getAddRecExpr(getSignExtendExpr(Start, Ty),
961 getSignExtendExpr(Step, Ty),
965 // If the backedge is guarded by a comparison with the pre-inc value
966 // the addrec is safe. Also, if the entry is guarded by a comparison
967 // with the start value and the backedge is guarded by a comparison
968 // with the post-inc value, the addrec is safe.
969 if (isKnownPositive(Step)) {
970 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
971 getSignedRange(Step).getSignedMax());
972 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
973 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
974 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
975 AR->getPostIncExpr(*this), N)))
976 // Return the expression with the addrec on the outside.
977 return getAddRecExpr(getSignExtendExpr(Start, Ty),
978 getSignExtendExpr(Step, Ty),
980 } else if (isKnownNegative(Step)) {
981 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
982 getSignedRange(Step).getSignedMin());
983 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
984 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
985 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
986 AR->getPostIncExpr(*this), N)))
987 // Return the expression with the addrec on the outside.
988 return getAddRecExpr(getSignExtendExpr(Start, Ty),
989 getSignExtendExpr(Step, Ty),
995 // The cast wasn't folded; create an explicit cast node.
996 // Recompute the insert position, as it may have been invalidated.
997 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
998 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
999 new (S) SCEVSignExtendExpr(ID, Op, Ty);
1000 UniqueSCEVs.InsertNode(S, IP);
1004 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1005 /// unspecified bits out to the given type.
1007 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1009 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1010 "This is not an extending conversion!");
1011 assert(isSCEVable(Ty) &&
1012 "This is not a conversion to a SCEVable type!");
1013 Ty = getEffectiveSCEVType(Ty);
1015 // Sign-extend negative constants.
1016 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1017 if (SC->getValue()->getValue().isNegative())
1018 return getSignExtendExpr(Op, Ty);
1020 // Peel off a truncate cast.
1021 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1022 const SCEV *NewOp = T->getOperand();
1023 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1024 return getAnyExtendExpr(NewOp, Ty);
1025 return getTruncateOrNoop(NewOp, Ty);
1028 // Next try a zext cast. If the cast is folded, use it.
1029 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1030 if (!isa<SCEVZeroExtendExpr>(ZExt))
1033 // Next try a sext cast. If the cast is folded, use it.
1034 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1035 if (!isa<SCEVSignExtendExpr>(SExt))
1038 // If the expression is obviously signed, use the sext cast value.
1039 if (isa<SCEVSMaxExpr>(Op))
1042 // Absent any other information, use the zext cast value.
1046 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1047 /// a list of operands to be added under the given scale, update the given
1048 /// map. This is a helper function for getAddRecExpr. As an example of
1049 /// what it does, given a sequence of operands that would form an add
1050 /// expression like this:
1052 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1054 /// where A and B are constants, update the map with these values:
1056 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1058 /// and add 13 + A*B*29 to AccumulatedConstant.
1059 /// This will allow getAddRecExpr to produce this:
1061 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1063 /// This form often exposes folding opportunities that are hidden in
1064 /// the original operand list.
1066 /// Return true iff it appears that any interesting folding opportunities
1067 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1068 /// the common case where no interesting opportunities are present, and
1069 /// is also used as a check to avoid infinite recursion.
1072 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1073 SmallVector<const SCEV *, 8> &NewOps,
1074 APInt &AccumulatedConstant,
1075 const SmallVectorImpl<const SCEV *> &Ops,
1077 ScalarEvolution &SE) {
1078 bool Interesting = false;
1080 // Iterate over the add operands.
1081 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1082 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1083 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1085 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1086 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1087 // A multiplication of a constant with another add; recurse.
1089 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1090 cast<SCEVAddExpr>(Mul->getOperand(1))
1094 // A multiplication of a constant with some other value. Update
1096 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1097 const SCEV *Key = SE.getMulExpr(MulOps);
1098 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1099 M.insert(std::make_pair(Key, NewScale));
1101 NewOps.push_back(Pair.first->first);
1103 Pair.first->second += NewScale;
1104 // The map already had an entry for this value, which may indicate
1105 // a folding opportunity.
1109 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1110 // Pull a buried constant out to the outside.
1111 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1113 AccumulatedConstant += Scale * C->getValue()->getValue();
1115 // An ordinary operand. Update the map.
1116 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1117 M.insert(std::make_pair(Ops[i], Scale));
1119 NewOps.push_back(Pair.first->first);
1121 Pair.first->second += Scale;
1122 // The map already had an entry for this value, which may indicate
1123 // a folding opportunity.
1133 struct APIntCompare {
1134 bool operator()(const APInt &LHS, const APInt &RHS) const {
1135 return LHS.ult(RHS);
1140 /// getAddExpr - Get a canonical add expression, or something simpler if
1142 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) {
1143 assert(!Ops.empty() && "Cannot get empty add!");
1144 if (Ops.size() == 1) return Ops[0];
1146 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1147 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1148 getEffectiveSCEVType(Ops[0]->getType()) &&
1149 "SCEVAddExpr operand types don't match!");
1152 // Sort by complexity, this groups all similar expression types together.
1153 GroupByComplexity(Ops, LI);
1155 // If there are any constants, fold them together.
1157 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1159 assert(Idx < Ops.size());
1160 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1161 // We found two constants, fold them together!
1162 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1163 RHSC->getValue()->getValue());
1164 if (Ops.size() == 2) return Ops[0];
1165 Ops.erase(Ops.begin()+1); // Erase the folded element
1166 LHSC = cast<SCEVConstant>(Ops[0]);
1169 // If we are left with a constant zero being added, strip it off.
1170 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1171 Ops.erase(Ops.begin());
1176 if (Ops.size() == 1) return Ops[0];
1178 // Okay, check to see if the same value occurs in the operand list twice. If
1179 // so, merge them together into an multiply expression. Since we sorted the
1180 // list, these values are required to be adjacent.
1181 const Type *Ty = Ops[0]->getType();
1182 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1183 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1184 // Found a match, merge the two values into a multiply, and add any
1185 // remaining values to the result.
1186 const SCEV *Two = getIntegerSCEV(2, Ty);
1187 const SCEV *Mul = getMulExpr(Ops[i], Two);
1188 if (Ops.size() == 2)
1190 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1192 return getAddExpr(Ops);
1195 // Check for truncates. If all the operands are truncated from the same
1196 // type, see if factoring out the truncate would permit the result to be
1197 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1198 // if the contents of the resulting outer trunc fold to something simple.
1199 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1200 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1201 const Type *DstType = Trunc->getType();
1202 const Type *SrcType = Trunc->getOperand()->getType();
1203 SmallVector<const SCEV *, 8> LargeOps;
1205 // Check all the operands to see if they can be represented in the
1206 // source type of the truncate.
1207 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1208 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1209 if (T->getOperand()->getType() != SrcType) {
1213 LargeOps.push_back(T->getOperand());
1214 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1215 // This could be either sign or zero extension, but sign extension
1216 // is much more likely to be foldable here.
1217 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1218 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1219 SmallVector<const SCEV *, 8> LargeMulOps;
1220 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1221 if (const SCEVTruncateExpr *T =
1222 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1223 if (T->getOperand()->getType() != SrcType) {
1227 LargeMulOps.push_back(T->getOperand());
1228 } else if (const SCEVConstant *C =
1229 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1230 // This could be either sign or zero extension, but sign extension
1231 // is much more likely to be foldable here.
1232 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1239 LargeOps.push_back(getMulExpr(LargeMulOps));
1246 // Evaluate the expression in the larger type.
1247 const SCEV *Fold = getAddExpr(LargeOps);
1248 // If it folds to something simple, use it. Otherwise, don't.
1249 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1250 return getTruncateExpr(Fold, DstType);
1254 // Skip past any other cast SCEVs.
1255 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1258 // If there are add operands they would be next.
1259 if (Idx < Ops.size()) {
1260 bool DeletedAdd = false;
1261 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1262 // If we have an add, expand the add operands onto the end of the operands
1264 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1265 Ops.erase(Ops.begin()+Idx);
1269 // If we deleted at least one add, we added operands to the end of the list,
1270 // and they are not necessarily sorted. Recurse to resort and resimplify
1271 // any operands we just aquired.
1273 return getAddExpr(Ops);
1276 // Skip over the add expression until we get to a multiply.
1277 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1280 // Check to see if there are any folding opportunities present with
1281 // operands multiplied by constant values.
1282 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1283 uint64_t BitWidth = getTypeSizeInBits(Ty);
1284 DenseMap<const SCEV *, APInt> M;
1285 SmallVector<const SCEV *, 8> NewOps;
1286 APInt AccumulatedConstant(BitWidth, 0);
1287 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1288 Ops, APInt(BitWidth, 1), *this)) {
1289 // Some interesting folding opportunity is present, so its worthwhile to
1290 // re-generate the operands list. Group the operands by constant scale,
1291 // to avoid multiplying by the same constant scale multiple times.
1292 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1293 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1294 E = NewOps.end(); I != E; ++I)
1295 MulOpLists[M.find(*I)->second].push_back(*I);
1296 // Re-generate the operands list.
1298 if (AccumulatedConstant != 0)
1299 Ops.push_back(getConstant(AccumulatedConstant));
1300 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1301 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1303 Ops.push_back(getMulExpr(getConstant(I->first),
1304 getAddExpr(I->second)));
1306 return getIntegerSCEV(0, Ty);
1307 if (Ops.size() == 1)
1309 return getAddExpr(Ops);
1313 // If we are adding something to a multiply expression, make sure the
1314 // something is not already an operand of the multiply. If so, merge it into
1316 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1317 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1318 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1319 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1320 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1321 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1322 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1323 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1324 if (Mul->getNumOperands() != 2) {
1325 // If the multiply has more than two operands, we must get the
1327 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1328 MulOps.erase(MulOps.begin()+MulOp);
1329 InnerMul = getMulExpr(MulOps);
1331 const SCEV *One = getIntegerSCEV(1, Ty);
1332 const SCEV *AddOne = getAddExpr(InnerMul, One);
1333 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1334 if (Ops.size() == 2) return OuterMul;
1336 Ops.erase(Ops.begin()+AddOp);
1337 Ops.erase(Ops.begin()+Idx-1);
1339 Ops.erase(Ops.begin()+Idx);
1340 Ops.erase(Ops.begin()+AddOp-1);
1342 Ops.push_back(OuterMul);
1343 return getAddExpr(Ops);
1346 // Check this multiply against other multiplies being added together.
1347 for (unsigned OtherMulIdx = Idx+1;
1348 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1350 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1351 // If MulOp occurs in OtherMul, we can fold the two multiplies
1353 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1354 OMulOp != e; ++OMulOp)
1355 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1356 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1357 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1358 if (Mul->getNumOperands() != 2) {
1359 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1361 MulOps.erase(MulOps.begin()+MulOp);
1362 InnerMul1 = getMulExpr(MulOps);
1364 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1365 if (OtherMul->getNumOperands() != 2) {
1366 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1367 OtherMul->op_end());
1368 MulOps.erase(MulOps.begin()+OMulOp);
1369 InnerMul2 = getMulExpr(MulOps);
1371 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1372 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1373 if (Ops.size() == 2) return OuterMul;
1374 Ops.erase(Ops.begin()+Idx);
1375 Ops.erase(Ops.begin()+OtherMulIdx-1);
1376 Ops.push_back(OuterMul);
1377 return getAddExpr(Ops);
1383 // If there are any add recurrences in the operands list, see if any other
1384 // added values are loop invariant. If so, we can fold them into the
1386 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1389 // Scan over all recurrences, trying to fold loop invariants into them.
1390 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1391 // Scan all of the other operands to this add and add them to the vector if
1392 // they are loop invariant w.r.t. the recurrence.
1393 SmallVector<const SCEV *, 8> LIOps;
1394 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1395 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1396 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1397 LIOps.push_back(Ops[i]);
1398 Ops.erase(Ops.begin()+i);
1402 // If we found some loop invariants, fold them into the recurrence.
1403 if (!LIOps.empty()) {
1404 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1405 LIOps.push_back(AddRec->getStart());
1407 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1409 AddRecOps[0] = getAddExpr(LIOps);
1411 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1412 // If all of the other operands were loop invariant, we are done.
1413 if (Ops.size() == 1) return NewRec;
1415 // Otherwise, add the folded AddRec by the non-liv parts.
1416 for (unsigned i = 0;; ++i)
1417 if (Ops[i] == AddRec) {
1421 return getAddExpr(Ops);
1424 // Okay, if there weren't any loop invariants to be folded, check to see if
1425 // there are multiple AddRec's with the same loop induction variable being
1426 // added together. If so, we can fold them.
1427 for (unsigned OtherIdx = Idx+1;
1428 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1429 if (OtherIdx != Idx) {
1430 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1431 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1432 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1433 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1435 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1436 if (i >= NewOps.size()) {
1437 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1438 OtherAddRec->op_end());
1441 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1443 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1445 if (Ops.size() == 2) return NewAddRec;
1447 Ops.erase(Ops.begin()+Idx);
1448 Ops.erase(Ops.begin()+OtherIdx-1);
1449 Ops.push_back(NewAddRec);
1450 return getAddExpr(Ops);
1454 // Otherwise couldn't fold anything into this recurrence. Move onto the
1458 // Okay, it looks like we really DO need an add expr. Check to see if we
1459 // already have one, otherwise create a new one.
1460 FoldingSetNodeID ID;
1461 ID.AddInteger(scAddExpr);
1462 ID.AddInteger(Ops.size());
1463 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1464 ID.AddPointer(Ops[i]);
1466 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1467 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1468 new (S) SCEVAddExpr(ID, Ops);
1469 UniqueSCEVs.InsertNode(S, IP);
1474 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1476 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) {
1477 assert(!Ops.empty() && "Cannot get empty mul!");
1479 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1480 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1481 getEffectiveSCEVType(Ops[0]->getType()) &&
1482 "SCEVMulExpr operand types don't match!");
1485 // Sort by complexity, this groups all similar expression types together.
1486 GroupByComplexity(Ops, LI);
1488 // If there are any constants, fold them together.
1490 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1492 // C1*(C2+V) -> C1*C2 + C1*V
1493 if (Ops.size() == 2)
1494 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1495 if (Add->getNumOperands() == 2 &&
1496 isa<SCEVConstant>(Add->getOperand(0)))
1497 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1498 getMulExpr(LHSC, Add->getOperand(1)));
1502 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1503 // We found two constants, fold them together!
1504 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1505 RHSC->getValue()->getValue());
1506 Ops[0] = getConstant(Fold);
1507 Ops.erase(Ops.begin()+1); // Erase the folded element
1508 if (Ops.size() == 1) return Ops[0];
1509 LHSC = cast<SCEVConstant>(Ops[0]);
1512 // If we are left with a constant one being multiplied, strip it off.
1513 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1514 Ops.erase(Ops.begin());
1516 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1517 // If we have a multiply of zero, it will always be zero.
1522 // Skip over the add expression until we get to a multiply.
1523 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1526 if (Ops.size() == 1)
1529 // If there are mul operands inline them all into this expression.
1530 if (Idx < Ops.size()) {
1531 bool DeletedMul = false;
1532 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1533 // If we have an mul, expand the mul operands onto the end of the operands
1535 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1536 Ops.erase(Ops.begin()+Idx);
1540 // If we deleted at least one mul, we added operands to the end of the list,
1541 // and they are not necessarily sorted. Recurse to resort and resimplify
1542 // any operands we just aquired.
1544 return getMulExpr(Ops);
1547 // If there are any add recurrences in the operands list, see if any other
1548 // added values are loop invariant. If so, we can fold them into the
1550 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1553 // Scan over all recurrences, trying to fold loop invariants into them.
1554 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1555 // Scan all of the other operands to this mul and add them to the vector if
1556 // they are loop invariant w.r.t. the recurrence.
1557 SmallVector<const SCEV *, 8> LIOps;
1558 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1559 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1560 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1561 LIOps.push_back(Ops[i]);
1562 Ops.erase(Ops.begin()+i);
1566 // If we found some loop invariants, fold them into the recurrence.
1567 if (!LIOps.empty()) {
1568 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1569 SmallVector<const SCEV *, 4> NewOps;
1570 NewOps.reserve(AddRec->getNumOperands());
1571 if (LIOps.size() == 1) {
1572 const SCEV *Scale = LIOps[0];
1573 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1574 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1576 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1577 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1578 MulOps.push_back(AddRec->getOperand(i));
1579 NewOps.push_back(getMulExpr(MulOps));
1583 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1585 // If all of the other operands were loop invariant, we are done.
1586 if (Ops.size() == 1) return NewRec;
1588 // Otherwise, multiply the folded AddRec by the non-liv parts.
1589 for (unsigned i = 0;; ++i)
1590 if (Ops[i] == AddRec) {
1594 return getMulExpr(Ops);
1597 // Okay, if there weren't any loop invariants to be folded, check to see if
1598 // there are multiple AddRec's with the same loop induction variable being
1599 // multiplied together. If so, we can fold them.
1600 for (unsigned OtherIdx = Idx+1;
1601 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1602 if (OtherIdx != Idx) {
1603 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1604 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1605 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1606 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1607 const SCEV *NewStart = getMulExpr(F->getStart(),
1609 const SCEV *B = F->getStepRecurrence(*this);
1610 const SCEV *D = G->getStepRecurrence(*this);
1611 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1614 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1616 if (Ops.size() == 2) return NewAddRec;
1618 Ops.erase(Ops.begin()+Idx);
1619 Ops.erase(Ops.begin()+OtherIdx-1);
1620 Ops.push_back(NewAddRec);
1621 return getMulExpr(Ops);
1625 // Otherwise couldn't fold anything into this recurrence. Move onto the
1629 // Okay, it looks like we really DO need an mul expr. Check to see if we
1630 // already have one, otherwise create a new one.
1631 FoldingSetNodeID ID;
1632 ID.AddInteger(scMulExpr);
1633 ID.AddInteger(Ops.size());
1634 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1635 ID.AddPointer(Ops[i]);
1637 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1638 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1639 new (S) SCEVMulExpr(ID, Ops);
1640 UniqueSCEVs.InsertNode(S, IP);
1644 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1646 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1648 assert(getEffectiveSCEVType(LHS->getType()) ==
1649 getEffectiveSCEVType(RHS->getType()) &&
1650 "SCEVUDivExpr operand types don't match!");
1652 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1653 if (RHSC->getValue()->equalsInt(1))
1654 return LHS; // X udiv 1 --> x
1656 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1658 // Determine if the division can be folded into the operands of
1660 // TODO: Generalize this to non-constants by using known-bits information.
1661 const Type *Ty = LHS->getType();
1662 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1663 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1664 // For non-power-of-two values, effectively round the value up to the
1665 // nearest power of two.
1666 if (!RHSC->getValue()->getValue().isPowerOf2())
1668 const IntegerType *ExtTy =
1669 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1670 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1671 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1672 if (const SCEVConstant *Step =
1673 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1674 if (!Step->getValue()->getValue()
1675 .urem(RHSC->getValue()->getValue()) &&
1676 getZeroExtendExpr(AR, ExtTy) ==
1677 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1678 getZeroExtendExpr(Step, ExtTy),
1680 SmallVector<const SCEV *, 4> Operands;
1681 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1682 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1683 return getAddRecExpr(Operands, AR->getLoop());
1685 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1686 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1687 SmallVector<const SCEV *, 4> Operands;
1688 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1689 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1690 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1691 // Find an operand that's safely divisible.
1692 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1693 const SCEV *Op = M->getOperand(i);
1694 const SCEV *Div = getUDivExpr(Op, RHSC);
1695 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1696 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1697 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1700 return getMulExpr(Operands);
1704 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1705 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1706 SmallVector<const SCEV *, 4> Operands;
1707 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1708 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1709 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1711 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1712 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1713 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1715 Operands.push_back(Op);
1717 if (Operands.size() == A->getNumOperands())
1718 return getAddExpr(Operands);
1722 // Fold if both operands are constant.
1723 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1724 Constant *LHSCV = LHSC->getValue();
1725 Constant *RHSCV = RHSC->getValue();
1726 return getConstant(cast<ConstantInt>(Context->getConstantExprUDiv(LHSCV,
1731 FoldingSetNodeID ID;
1732 ID.AddInteger(scUDivExpr);
1736 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1737 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1738 new (S) SCEVUDivExpr(ID, LHS, RHS);
1739 UniqueSCEVs.InsertNode(S, IP);
1744 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1745 /// Simplify the expression as much as possible.
1746 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1747 const SCEV *Step, const Loop *L) {
1748 SmallVector<const SCEV *, 4> Operands;
1749 Operands.push_back(Start);
1750 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1751 if (StepChrec->getLoop() == L) {
1752 Operands.insert(Operands.end(), StepChrec->op_begin(),
1753 StepChrec->op_end());
1754 return getAddRecExpr(Operands, L);
1757 Operands.push_back(Step);
1758 return getAddRecExpr(Operands, L);
1761 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1762 /// Simplify the expression as much as possible.
1764 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1766 if (Operands.size() == 1) return Operands[0];
1768 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1769 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1770 getEffectiveSCEVType(Operands[0]->getType()) &&
1771 "SCEVAddRecExpr operand types don't match!");
1774 if (Operands.back()->isZero()) {
1775 Operands.pop_back();
1776 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1779 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1780 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1781 const Loop* NestedLoop = NestedAR->getLoop();
1782 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1783 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1784 NestedAR->op_end());
1785 Operands[0] = NestedAR->getStart();
1786 // AddRecs require their operands be loop-invariant with respect to their
1787 // loops. Don't perform this transformation if it would break this
1789 bool AllInvariant = true;
1790 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1791 if (!Operands[i]->isLoopInvariant(L)) {
1792 AllInvariant = false;
1796 NestedOperands[0] = getAddRecExpr(Operands, L);
1797 AllInvariant = true;
1798 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1799 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1800 AllInvariant = false;
1804 // Ok, both add recurrences are valid after the transformation.
1805 return getAddRecExpr(NestedOperands, NestedLoop);
1807 // Reset Operands to its original state.
1808 Operands[0] = NestedAR;
1812 FoldingSetNodeID ID;
1813 ID.AddInteger(scAddRecExpr);
1814 ID.AddInteger(Operands.size());
1815 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1816 ID.AddPointer(Operands[i]);
1819 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1820 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1821 new (S) SCEVAddRecExpr(ID, Operands, L);
1822 UniqueSCEVs.InsertNode(S, IP);
1826 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1828 SmallVector<const SCEV *, 2> Ops;
1831 return getSMaxExpr(Ops);
1835 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1836 assert(!Ops.empty() && "Cannot get empty smax!");
1837 if (Ops.size() == 1) return Ops[0];
1839 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1840 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1841 getEffectiveSCEVType(Ops[0]->getType()) &&
1842 "SCEVSMaxExpr operand types don't match!");
1845 // Sort by complexity, this groups all similar expression types together.
1846 GroupByComplexity(Ops, LI);
1848 // If there are any constants, fold them together.
1850 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1852 assert(Idx < Ops.size());
1853 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1854 // We found two constants, fold them together!
1855 ConstantInt *Fold = ConstantInt::get(
1856 APIntOps::smax(LHSC->getValue()->getValue(),
1857 RHSC->getValue()->getValue()));
1858 Ops[0] = getConstant(Fold);
1859 Ops.erase(Ops.begin()+1); // Erase the folded element
1860 if (Ops.size() == 1) return Ops[0];
1861 LHSC = cast<SCEVConstant>(Ops[0]);
1864 // If we are left with a constant minimum-int, strip it off.
1865 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1866 Ops.erase(Ops.begin());
1868 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1869 // If we have an smax with a constant maximum-int, it will always be
1875 if (Ops.size() == 1) return Ops[0];
1877 // Find the first SMax
1878 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1881 // Check to see if one of the operands is an SMax. If so, expand its operands
1882 // onto our operand list, and recurse to simplify.
1883 if (Idx < Ops.size()) {
1884 bool DeletedSMax = false;
1885 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1886 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1887 Ops.erase(Ops.begin()+Idx);
1892 return getSMaxExpr(Ops);
1895 // Okay, check to see if the same value occurs in the operand list twice. If
1896 // so, delete one. Since we sorted the list, these values are required to
1898 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1899 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1900 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1904 if (Ops.size() == 1) return Ops[0];
1906 assert(!Ops.empty() && "Reduced smax down to nothing!");
1908 // Okay, it looks like we really DO need an smax expr. Check to see if we
1909 // already have one, otherwise create a new one.
1910 FoldingSetNodeID ID;
1911 ID.AddInteger(scSMaxExpr);
1912 ID.AddInteger(Ops.size());
1913 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1914 ID.AddPointer(Ops[i]);
1916 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1917 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1918 new (S) SCEVSMaxExpr(ID, Ops);
1919 UniqueSCEVs.InsertNode(S, IP);
1923 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1925 SmallVector<const SCEV *, 2> Ops;
1928 return getUMaxExpr(Ops);
1932 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1933 assert(!Ops.empty() && "Cannot get empty umax!");
1934 if (Ops.size() == 1) return Ops[0];
1936 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1937 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1938 getEffectiveSCEVType(Ops[0]->getType()) &&
1939 "SCEVUMaxExpr operand types don't match!");
1942 // Sort by complexity, this groups all similar expression types together.
1943 GroupByComplexity(Ops, LI);
1945 // If there are any constants, fold them together.
1947 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1949 assert(Idx < Ops.size());
1950 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1951 // We found two constants, fold them together!
1952 ConstantInt *Fold = ConstantInt::get(
1953 APIntOps::umax(LHSC->getValue()->getValue(),
1954 RHSC->getValue()->getValue()));
1955 Ops[0] = getConstant(Fold);
1956 Ops.erase(Ops.begin()+1); // Erase the folded element
1957 if (Ops.size() == 1) return Ops[0];
1958 LHSC = cast<SCEVConstant>(Ops[0]);
1961 // If we are left with a constant minimum-int, strip it off.
1962 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1963 Ops.erase(Ops.begin());
1965 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
1966 // If we have an umax with a constant maximum-int, it will always be
1972 if (Ops.size() == 1) return Ops[0];
1974 // Find the first UMax
1975 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1978 // Check to see if one of the operands is a UMax. If so, expand its operands
1979 // onto our operand list, and recurse to simplify.
1980 if (Idx < Ops.size()) {
1981 bool DeletedUMax = false;
1982 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1983 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1984 Ops.erase(Ops.begin()+Idx);
1989 return getUMaxExpr(Ops);
1992 // Okay, check to see if the same value occurs in the operand list twice. If
1993 // so, delete one. Since we sorted the list, these values are required to
1995 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1996 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1997 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2001 if (Ops.size() == 1) return Ops[0];
2003 assert(!Ops.empty() && "Reduced umax down to nothing!");
2005 // Okay, it looks like we really DO need a umax expr. Check to see if we
2006 // already have one, otherwise create a new one.
2007 FoldingSetNodeID ID;
2008 ID.AddInteger(scUMaxExpr);
2009 ID.AddInteger(Ops.size());
2010 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2011 ID.AddPointer(Ops[i]);
2013 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2014 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2015 new (S) SCEVUMaxExpr(ID, Ops);
2016 UniqueSCEVs.InsertNode(S, IP);
2020 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2022 // ~smax(~x, ~y) == smin(x, y).
2023 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2026 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2028 // ~umax(~x, ~y) == umin(x, y)
2029 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2032 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2033 // Don't attempt to do anything other than create a SCEVUnknown object
2034 // here. createSCEV only calls getUnknown after checking for all other
2035 // interesting possibilities, and any other code that calls getUnknown
2036 // is doing so in order to hide a value from SCEV canonicalization.
2038 FoldingSetNodeID ID;
2039 ID.AddInteger(scUnknown);
2042 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2043 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2044 new (S) SCEVUnknown(ID, V);
2045 UniqueSCEVs.InsertNode(S, IP);
2049 //===----------------------------------------------------------------------===//
2050 // Basic SCEV Analysis and PHI Idiom Recognition Code
2053 /// isSCEVable - Test if values of the given type are analyzable within
2054 /// the SCEV framework. This primarily includes integer types, and it
2055 /// can optionally include pointer types if the ScalarEvolution class
2056 /// has access to target-specific information.
2057 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2058 // Integers are always SCEVable.
2059 if (Ty->isInteger())
2062 // Pointers are SCEVable if TargetData information is available
2063 // to provide pointer size information.
2064 if (isa<PointerType>(Ty))
2067 // Otherwise it's not SCEVable.
2071 /// getTypeSizeInBits - Return the size in bits of the specified type,
2072 /// for which isSCEVable must return true.
2073 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2074 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2076 // If we have a TargetData, use it!
2078 return TD->getTypeSizeInBits(Ty);
2080 // Otherwise, we support only integer types.
2081 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
2082 return Ty->getPrimitiveSizeInBits();
2085 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2086 /// the given type and which represents how SCEV will treat the given
2087 /// type, for which isSCEVable must return true. For pointer types,
2088 /// this is the pointer-sized integer type.
2089 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2090 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2092 if (Ty->isInteger())
2095 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2096 return TD->getIntPtrType();
2099 const SCEV *ScalarEvolution::getCouldNotCompute() {
2100 return &CouldNotCompute;
2103 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2104 /// expression and create a new one.
2105 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2106 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2108 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2109 if (I != Scalars.end()) return I->second;
2110 const SCEV *S = createSCEV(V);
2111 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2115 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2116 /// specified signed integer value and return a SCEV for the constant.
2117 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2118 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2119 return getConstant(Context->getConstantInt(ITy, Val));
2122 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2124 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2125 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2127 cast<ConstantInt>(Context->getConstantExprNeg(VC->getValue())));
2129 const Type *Ty = V->getType();
2130 Ty = getEffectiveSCEVType(Ty);
2131 return getMulExpr(V,
2132 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty))));
2135 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2136 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2137 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2139 cast<ConstantInt>(Context->getConstantExprNot(VC->getValue())));
2141 const Type *Ty = V->getType();
2142 Ty = getEffectiveSCEVType(Ty);
2143 const SCEV *AllOnes =
2144 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty)));
2145 return getMinusSCEV(AllOnes, V);
2148 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2150 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2153 return getAddExpr(LHS, getNegativeSCEV(RHS));
2156 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2157 /// input value to the specified type. If the type must be extended, it is zero
2160 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2162 const Type *SrcTy = V->getType();
2163 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2164 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2165 "Cannot truncate or zero extend with non-integer arguments!");
2166 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2167 return V; // No conversion
2168 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2169 return getTruncateExpr(V, Ty);
2170 return getZeroExtendExpr(V, Ty);
2173 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2174 /// input value to the specified type. If the type must be extended, it is sign
2177 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2179 const Type *SrcTy = V->getType();
2180 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2181 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2182 "Cannot truncate or zero extend with non-integer arguments!");
2183 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2184 return V; // No conversion
2185 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2186 return getTruncateExpr(V, Ty);
2187 return getSignExtendExpr(V, Ty);
2190 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2191 /// input value to the specified type. If the type must be extended, it is zero
2192 /// extended. The conversion must not be narrowing.
2194 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2195 const Type *SrcTy = V->getType();
2196 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2197 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2198 "Cannot noop or zero extend with non-integer arguments!");
2199 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2200 "getNoopOrZeroExtend cannot truncate!");
2201 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2202 return V; // No conversion
2203 return getZeroExtendExpr(V, Ty);
2206 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2207 /// input value to the specified type. If the type must be extended, it is sign
2208 /// extended. The conversion must not be narrowing.
2210 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2211 const Type *SrcTy = V->getType();
2212 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2213 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2214 "Cannot noop or sign extend with non-integer arguments!");
2215 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2216 "getNoopOrSignExtend cannot truncate!");
2217 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2218 return V; // No conversion
2219 return getSignExtendExpr(V, Ty);
2222 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2223 /// the input value to the specified type. If the type must be extended,
2224 /// it is extended with unspecified bits. The conversion must not be
2227 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2228 const Type *SrcTy = V->getType();
2229 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2230 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2231 "Cannot noop or any extend with non-integer arguments!");
2232 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2233 "getNoopOrAnyExtend cannot truncate!");
2234 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2235 return V; // No conversion
2236 return getAnyExtendExpr(V, Ty);
2239 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2240 /// input value to the specified type. The conversion must not be widening.
2242 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2243 const Type *SrcTy = V->getType();
2244 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2245 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2246 "Cannot truncate or noop with non-integer arguments!");
2247 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2248 "getTruncateOrNoop cannot extend!");
2249 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2250 return V; // No conversion
2251 return getTruncateExpr(V, Ty);
2254 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2255 /// the types using zero-extension, and then perform a umax operation
2257 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2259 const SCEV *PromotedLHS = LHS;
2260 const SCEV *PromotedRHS = RHS;
2262 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2263 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2265 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2267 return getUMaxExpr(PromotedLHS, PromotedRHS);
2270 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2271 /// the types using zero-extension, and then perform a umin operation
2273 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2275 const SCEV *PromotedLHS = LHS;
2276 const SCEV *PromotedRHS = RHS;
2278 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2279 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2281 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2283 return getUMinExpr(PromotedLHS, PromotedRHS);
2286 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
2287 /// the specified instruction and replaces any references to the symbolic value
2288 /// SymName with the specified value. This is used during PHI resolution.
2290 ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I,
2291 const SCEV *SymName,
2292 const SCEV *NewVal) {
2293 std::map<SCEVCallbackVH, const SCEV *>::iterator SI =
2294 Scalars.find(SCEVCallbackVH(I, this));
2295 if (SI == Scalars.end()) return;
2298 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2299 if (NV == SI->second) return; // No change.
2301 SI->second = NV; // Update the scalars map!
2303 // Any instruction values that use this instruction might also need to be
2305 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2307 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2310 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2311 /// a loop header, making it a potential recurrence, or it doesn't.
2313 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2314 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2315 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2316 if (L->getHeader() == PN->getParent()) {
2317 // If it lives in the loop header, it has two incoming values, one
2318 // from outside the loop, and one from inside.
2319 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2320 unsigned BackEdge = IncomingEdge^1;
2322 // While we are analyzing this PHI node, handle its value symbolically.
2323 const SCEV *SymbolicName = getUnknown(PN);
2324 assert(Scalars.find(PN) == Scalars.end() &&
2325 "PHI node already processed?");
2326 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2328 // Using this symbolic name for the PHI, analyze the value coming around
2330 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2332 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2333 // has a special value for the first iteration of the loop.
2335 // If the value coming around the backedge is an add with the symbolic
2336 // value we just inserted, then we found a simple induction variable!
2337 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2338 // If there is a single occurrence of the symbolic value, replace it
2339 // with a recurrence.
2340 unsigned FoundIndex = Add->getNumOperands();
2341 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2342 if (Add->getOperand(i) == SymbolicName)
2343 if (FoundIndex == e) {
2348 if (FoundIndex != Add->getNumOperands()) {
2349 // Create an add with everything but the specified operand.
2350 SmallVector<const SCEV *, 8> Ops;
2351 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2352 if (i != FoundIndex)
2353 Ops.push_back(Add->getOperand(i));
2354 const SCEV *Accum = getAddExpr(Ops);
2356 // This is not a valid addrec if the step amount is varying each
2357 // loop iteration, but is not itself an addrec in this loop.
2358 if (Accum->isLoopInvariant(L) ||
2359 (isa<SCEVAddRecExpr>(Accum) &&
2360 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2361 const SCEV *StartVal =
2362 getSCEV(PN->getIncomingValue(IncomingEdge));
2363 const SCEV *PHISCEV =
2364 getAddRecExpr(StartVal, Accum, L);
2366 // Okay, for the entire analysis of this edge we assumed the PHI
2367 // to be symbolic. We now need to go back and update all of the
2368 // entries for the scalars that use the PHI (except for the PHI
2369 // itself) to use the new analyzed value instead of the "symbolic"
2371 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2375 } else if (const SCEVAddRecExpr *AddRec =
2376 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2377 // Otherwise, this could be a loop like this:
2378 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2379 // In this case, j = {1,+,1} and BEValue is j.
2380 // Because the other in-value of i (0) fits the evolution of BEValue
2381 // i really is an addrec evolution.
2382 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2383 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2385 // If StartVal = j.start - j.stride, we can use StartVal as the
2386 // initial step of the addrec evolution.
2387 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2388 AddRec->getOperand(1))) {
2389 const SCEV *PHISCEV =
2390 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2392 // Okay, for the entire analysis of this edge we assumed the PHI
2393 // to be symbolic. We now need to go back and update all of the
2394 // entries for the scalars that use the PHI (except for the PHI
2395 // itself) to use the new analyzed value instead of the "symbolic"
2397 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2403 return SymbolicName;
2406 // It's tempting to recognize PHIs with a unique incoming value, however
2407 // this leads passes like indvars to break LCSSA form. Fortunately, such
2408 // PHIs are rare, as instcombine zaps them.
2410 // If it's not a loop phi, we can't handle it yet.
2411 return getUnknown(PN);
2414 /// createNodeForGEP - Expand GEP instructions into add and multiply
2415 /// operations. This allows them to be analyzed by regular SCEV code.
2417 const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) {
2419 const Type *IntPtrTy = TD->getIntPtrType();
2420 Value *Base = GEP->getOperand(0);
2421 // Don't attempt to analyze GEPs over unsized objects.
2422 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2423 return getUnknown(GEP);
2424 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2425 gep_type_iterator GTI = gep_type_begin(GEP);
2426 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2430 // Compute the (potentially symbolic) offset in bytes for this index.
2431 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2432 // For a struct, add the member offset.
2433 const StructLayout &SL = *TD->getStructLayout(STy);
2434 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2435 uint64_t Offset = SL.getElementOffset(FieldNo);
2436 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy));
2438 // For an array, add the element offset, explicitly scaled.
2439 const SCEV *LocalOffset = getSCEV(Index);
2440 if (!isa<PointerType>(LocalOffset->getType()))
2441 // Getelementptr indicies are signed.
2442 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2444 getMulExpr(LocalOffset,
2445 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy));
2446 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2449 return getAddExpr(getSCEV(Base), TotalOffset);
2452 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2453 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2454 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2455 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2457 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2458 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2459 return C->getValue()->getValue().countTrailingZeros();
2461 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2462 return std::min(GetMinTrailingZeros(T->getOperand()),
2463 (uint32_t)getTypeSizeInBits(T->getType()));
2465 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2466 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2467 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2468 getTypeSizeInBits(E->getType()) : OpRes;
2471 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2472 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2473 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2474 getTypeSizeInBits(E->getType()) : OpRes;
2477 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2478 // The result is the min of all operands results.
2479 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2480 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2481 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2485 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2486 // The result is the sum of all operands results.
2487 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2488 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2489 for (unsigned i = 1, e = M->getNumOperands();
2490 SumOpRes != BitWidth && i != e; ++i)
2491 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2496 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2497 // The result is the min of all operands results.
2498 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2499 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2500 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2504 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2505 // The result is the min of all operands results.
2506 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2507 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2508 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2512 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2513 // The result is the min of all operands results.
2514 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2515 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2516 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2520 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2521 // For a SCEVUnknown, ask ValueTracking.
2522 unsigned BitWidth = getTypeSizeInBits(U->getType());
2523 APInt Mask = APInt::getAllOnesValue(BitWidth);
2524 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2525 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2526 return Zeros.countTrailingOnes();
2533 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2536 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2538 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2539 return ConstantRange(C->getValue()->getValue());
2541 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2542 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2543 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2544 X = X.add(getUnsignedRange(Add->getOperand(i)));
2548 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2549 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2550 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2551 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2555 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2556 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2557 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2558 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2562 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2563 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2564 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2565 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2569 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2570 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2571 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2575 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2576 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2577 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2580 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2581 ConstantRange X = getUnsignedRange(SExt->getOperand());
2582 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2585 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2586 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2587 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2590 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2592 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2593 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2594 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2595 if (!Trip) return FullSet;
2597 // TODO: non-affine addrec
2598 if (AddRec->isAffine()) {
2599 const Type *Ty = AddRec->getType();
2600 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2601 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2602 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2604 const SCEV *Start = AddRec->getStart();
2605 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2607 // Check for overflow.
2608 if (!isKnownPredicate(ICmpInst::ICMP_ULE, Start, End))
2611 ConstantRange StartRange = getUnsignedRange(Start);
2612 ConstantRange EndRange = getUnsignedRange(End);
2613 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2614 EndRange.getUnsignedMin());
2615 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2616 EndRange.getUnsignedMax());
2617 if (Min.isMinValue() && Max.isMaxValue())
2618 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true);
2619 return ConstantRange(Min, Max+1);
2624 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2625 // For a SCEVUnknown, ask ValueTracking.
2626 unsigned BitWidth = getTypeSizeInBits(U->getType());
2627 APInt Mask = APInt::getAllOnesValue(BitWidth);
2628 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2629 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2630 return ConstantRange(Ones, ~Zeros);
2636 /// getSignedRange - Determine the signed range for a particular SCEV.
2639 ScalarEvolution::getSignedRange(const SCEV *S) {
2641 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2642 return ConstantRange(C->getValue()->getValue());
2644 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2645 ConstantRange X = getSignedRange(Add->getOperand(0));
2646 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2647 X = X.add(getSignedRange(Add->getOperand(i)));
2651 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2652 ConstantRange X = getSignedRange(Mul->getOperand(0));
2653 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2654 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2658 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2659 ConstantRange X = getSignedRange(SMax->getOperand(0));
2660 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2661 X = X.smax(getSignedRange(SMax->getOperand(i)));
2665 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2666 ConstantRange X = getSignedRange(UMax->getOperand(0));
2667 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2668 X = X.umax(getSignedRange(UMax->getOperand(i)));
2672 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2673 ConstantRange X = getSignedRange(UDiv->getLHS());
2674 ConstantRange Y = getSignedRange(UDiv->getRHS());
2678 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2679 ConstantRange X = getSignedRange(ZExt->getOperand());
2680 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2683 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2684 ConstantRange X = getSignedRange(SExt->getOperand());
2685 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2688 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2689 ConstantRange X = getSignedRange(Trunc->getOperand());
2690 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2693 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2695 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2696 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2697 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2698 if (!Trip) return FullSet;
2700 // TODO: non-affine addrec
2701 if (AddRec->isAffine()) {
2702 const Type *Ty = AddRec->getType();
2703 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2704 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2705 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2707 const SCEV *Start = AddRec->getStart();
2708 const SCEV *Step = AddRec->getStepRecurrence(*this);
2709 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2711 // Check for overflow.
2712 if (!(isKnownPositive(Step) &&
2713 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
2714 !(isKnownNegative(Step) &&
2715 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
2718 ConstantRange StartRange = getSignedRange(Start);
2719 ConstantRange EndRange = getSignedRange(End);
2720 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
2721 EndRange.getSignedMin());
2722 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
2723 EndRange.getSignedMax());
2724 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
2725 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true);
2726 return ConstantRange(Min, Max+1);
2731 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2732 // For a SCEVUnknown, ask ValueTracking.
2733 unsigned BitWidth = getTypeSizeInBits(U->getType());
2734 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
2738 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
2739 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
2745 /// createSCEV - We know that there is no SCEV for the specified value.
2746 /// Analyze the expression.
2748 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2749 if (!isSCEVable(V->getType()))
2750 return getUnknown(V);
2752 unsigned Opcode = Instruction::UserOp1;
2753 if (Instruction *I = dyn_cast<Instruction>(V))
2754 Opcode = I->getOpcode();
2755 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2756 Opcode = CE->getOpcode();
2757 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2758 return getConstant(CI);
2759 else if (isa<ConstantPointerNull>(V))
2760 return getIntegerSCEV(0, V->getType());
2761 else if (isa<UndefValue>(V))
2762 return getIntegerSCEV(0, V->getType());
2764 return getUnknown(V);
2766 User *U = cast<User>(V);
2768 case Instruction::Add:
2769 return getAddExpr(getSCEV(U->getOperand(0)),
2770 getSCEV(U->getOperand(1)));
2771 case Instruction::Mul:
2772 return getMulExpr(getSCEV(U->getOperand(0)),
2773 getSCEV(U->getOperand(1)));
2774 case Instruction::UDiv:
2775 return getUDivExpr(getSCEV(U->getOperand(0)),
2776 getSCEV(U->getOperand(1)));
2777 case Instruction::Sub:
2778 return getMinusSCEV(getSCEV(U->getOperand(0)),
2779 getSCEV(U->getOperand(1)));
2780 case Instruction::And:
2781 // For an expression like x&255 that merely masks off the high bits,
2782 // use zext(trunc(x)) as the SCEV expression.
2783 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2784 if (CI->isNullValue())
2785 return getSCEV(U->getOperand(1));
2786 if (CI->isAllOnesValue())
2787 return getSCEV(U->getOperand(0));
2788 const APInt &A = CI->getValue();
2790 // Instcombine's ShrinkDemandedConstant may strip bits out of
2791 // constants, obscuring what would otherwise be a low-bits mask.
2792 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2793 // knew about to reconstruct a low-bits mask value.
2794 unsigned LZ = A.countLeadingZeros();
2795 unsigned BitWidth = A.getBitWidth();
2796 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2797 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2798 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2800 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2802 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2804 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2805 IntegerType::get(BitWidth - LZ)),
2810 case Instruction::Or:
2811 // If the RHS of the Or is a constant, we may have something like:
2812 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2813 // optimizations will transparently handle this case.
2815 // In order for this transformation to be safe, the LHS must be of the
2816 // form X*(2^n) and the Or constant must be less than 2^n.
2817 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2818 const SCEV *LHS = getSCEV(U->getOperand(0));
2819 const APInt &CIVal = CI->getValue();
2820 if (GetMinTrailingZeros(LHS) >=
2821 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2822 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2825 case Instruction::Xor:
2826 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2827 // If the RHS of the xor is a signbit, then this is just an add.
2828 // Instcombine turns add of signbit into xor as a strength reduction step.
2829 if (CI->getValue().isSignBit())
2830 return getAddExpr(getSCEV(U->getOperand(0)),
2831 getSCEV(U->getOperand(1)));
2833 // If the RHS of xor is -1, then this is a not operation.
2834 if (CI->isAllOnesValue())
2835 return getNotSCEV(getSCEV(U->getOperand(0)));
2837 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2838 // This is a variant of the check for xor with -1, and it handles
2839 // the case where instcombine has trimmed non-demanded bits out
2840 // of an xor with -1.
2841 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2842 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2843 if (BO->getOpcode() == Instruction::And &&
2844 LCI->getValue() == CI->getValue())
2845 if (const SCEVZeroExtendExpr *Z =
2846 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2847 const Type *UTy = U->getType();
2848 const SCEV *Z0 = Z->getOperand();
2849 const Type *Z0Ty = Z0->getType();
2850 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2852 // If C is a low-bits mask, the zero extend is zerving to
2853 // mask off the high bits. Complement the operand and
2854 // re-apply the zext.
2855 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2856 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2858 // If C is a single bit, it may be in the sign-bit position
2859 // before the zero-extend. In this case, represent the xor
2860 // using an add, which is equivalent, and re-apply the zext.
2861 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2862 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2864 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2870 case Instruction::Shl:
2871 // Turn shift left of a constant amount into a multiply.
2872 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2873 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2874 Constant *X = ConstantInt::get(
2875 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2876 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2880 case Instruction::LShr:
2881 // Turn logical shift right of a constant into a unsigned divide.
2882 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2883 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2884 Constant *X = ConstantInt::get(
2885 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2886 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2890 case Instruction::AShr:
2891 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2892 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2893 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2894 if (L->getOpcode() == Instruction::Shl &&
2895 L->getOperand(1) == U->getOperand(1)) {
2896 unsigned BitWidth = getTypeSizeInBits(U->getType());
2897 uint64_t Amt = BitWidth - CI->getZExtValue();
2898 if (Amt == BitWidth)
2899 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2901 return getIntegerSCEV(0, U->getType()); // value is undefined
2903 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2904 IntegerType::get(Amt)),
2909 case Instruction::Trunc:
2910 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2912 case Instruction::ZExt:
2913 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2915 case Instruction::SExt:
2916 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2918 case Instruction::BitCast:
2919 // BitCasts are no-op casts so we just eliminate the cast.
2920 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2921 return getSCEV(U->getOperand(0));
2924 case Instruction::IntToPtr:
2925 if (!TD) break; // Without TD we can't analyze pointers.
2926 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2927 TD->getIntPtrType());
2929 case Instruction::PtrToInt:
2930 if (!TD) break; // Without TD we can't analyze pointers.
2931 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2934 case Instruction::GetElementPtr:
2935 if (!TD) break; // Without TD we can't analyze pointers.
2936 return createNodeForGEP(U);
2938 case Instruction::PHI:
2939 return createNodeForPHI(cast<PHINode>(U));
2941 case Instruction::Select:
2942 // This could be a smax or umax that was lowered earlier.
2943 // Try to recover it.
2944 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2945 Value *LHS = ICI->getOperand(0);
2946 Value *RHS = ICI->getOperand(1);
2947 switch (ICI->getPredicate()) {
2948 case ICmpInst::ICMP_SLT:
2949 case ICmpInst::ICMP_SLE:
2950 std::swap(LHS, RHS);
2952 case ICmpInst::ICMP_SGT:
2953 case ICmpInst::ICMP_SGE:
2954 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2955 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2956 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2957 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2959 case ICmpInst::ICMP_ULT:
2960 case ICmpInst::ICMP_ULE:
2961 std::swap(LHS, RHS);
2963 case ICmpInst::ICMP_UGT:
2964 case ICmpInst::ICMP_UGE:
2965 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2966 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2967 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2968 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2970 case ICmpInst::ICMP_NE:
2971 // n != 0 ? n : 1 -> umax(n, 1)
2972 if (LHS == U->getOperand(1) &&
2973 isa<ConstantInt>(U->getOperand(2)) &&
2974 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2975 isa<ConstantInt>(RHS) &&
2976 cast<ConstantInt>(RHS)->isZero())
2977 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2979 case ICmpInst::ICMP_EQ:
2980 // n == 0 ? 1 : n -> umax(n, 1)
2981 if (LHS == U->getOperand(2) &&
2982 isa<ConstantInt>(U->getOperand(1)) &&
2983 cast<ConstantInt>(U->getOperand(1))->isOne() &&
2984 isa<ConstantInt>(RHS) &&
2985 cast<ConstantInt>(RHS)->isZero())
2986 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
2993 default: // We cannot analyze this expression.
2997 return getUnknown(V);
3002 //===----------------------------------------------------------------------===//
3003 // Iteration Count Computation Code
3006 /// getBackedgeTakenCount - If the specified loop has a predictable
3007 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3008 /// object. The backedge-taken count is the number of times the loop header
3009 /// will be branched to from within the loop. This is one less than the
3010 /// trip count of the loop, since it doesn't count the first iteration,
3011 /// when the header is branched to from outside the loop.
3013 /// Note that it is not valid to call this method on a loop without a
3014 /// loop-invariant backedge-taken count (see
3015 /// hasLoopInvariantBackedgeTakenCount).
3017 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3018 return getBackedgeTakenInfo(L).Exact;
3021 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3022 /// return the least SCEV value that is known never to be less than the
3023 /// actual backedge taken count.
3024 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3025 return getBackedgeTakenInfo(L).Max;
3028 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3029 /// onto the given Worklist.
3031 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3032 BasicBlock *Header = L->getHeader();
3034 // Push all Loop-header PHIs onto the Worklist stack.
3035 for (BasicBlock::iterator I = Header->begin();
3036 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3037 Worklist.push_back(PN);
3040 /// PushDefUseChildren - Push users of the given Instruction
3041 /// onto the given Worklist.
3043 PushDefUseChildren(Instruction *I,
3044 SmallVectorImpl<Instruction *> &Worklist) {
3045 // Push the def-use children onto the Worklist stack.
3046 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
3048 Worklist.push_back(cast<Instruction>(UI));
3051 const ScalarEvolution::BackedgeTakenInfo &
3052 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3053 // Initially insert a CouldNotCompute for this loop. If the insertion
3054 // succeeds, procede to actually compute a backedge-taken count and
3055 // update the value. The temporary CouldNotCompute value tells SCEV
3056 // code elsewhere that it shouldn't attempt to request a new
3057 // backedge-taken count, which could result in infinite recursion.
3058 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
3059 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3061 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
3062 if (ItCount.Exact != getCouldNotCompute()) {
3063 assert(ItCount.Exact->isLoopInvariant(L) &&
3064 ItCount.Max->isLoopInvariant(L) &&
3065 "Computed trip count isn't loop invariant for loop!");
3066 ++NumTripCountsComputed;
3068 // Update the value in the map.
3069 Pair.first->second = ItCount;
3071 if (ItCount.Max != getCouldNotCompute())
3072 // Update the value in the map.
3073 Pair.first->second = ItCount;
3074 if (isa<PHINode>(L->getHeader()->begin()))
3075 // Only count loops that have phi nodes as not being computable.
3076 ++NumTripCountsNotComputed;
3079 // Now that we know more about the trip count for this loop, forget any
3080 // existing SCEV values for PHI nodes in this loop since they are only
3081 // conservative estimates made without the benefit of trip count
3082 // information. This is similar to the code in
3083 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
3085 if (ItCount.hasAnyInfo()) {
3086 SmallVector<Instruction *, 16> Worklist;
3087 PushLoopPHIs(L, Worklist);
3089 SmallPtrSet<Instruction *, 8> Visited;
3090 while (!Worklist.empty()) {
3091 Instruction *I = Worklist.pop_back_val();
3092 if (!Visited.insert(I)) continue;
3094 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3095 Scalars.find(static_cast<Value *>(I));
3096 if (It != Scalars.end()) {
3097 // SCEVUnknown for a PHI either means that it has an unrecognized
3098 // structure, or it's a PHI that's in the progress of being computed
3099 // by createNodeForPHI. In the former case, additional loop trip
3100 // count information isn't going to change anything. In the later
3101 // case, createNodeForPHI will perform the necessary updates on its
3102 // own when it gets to that point.
3103 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second))
3105 ValuesAtScopes.erase(I);
3106 if (PHINode *PN = dyn_cast<PHINode>(I))
3107 ConstantEvolutionLoopExitValue.erase(PN);
3110 PushDefUseChildren(I, Worklist);
3114 return Pair.first->second;
3117 /// forgetLoopBackedgeTakenCount - This method should be called by the
3118 /// client when it has changed a loop in a way that may effect
3119 /// ScalarEvolution's ability to compute a trip count, or if the loop
3121 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3122 BackedgeTakenCounts.erase(L);
3124 SmallVector<Instruction *, 16> Worklist;
3125 PushLoopPHIs(L, Worklist);
3127 SmallPtrSet<Instruction *, 8> Visited;
3128 while (!Worklist.empty()) {
3129 Instruction *I = Worklist.pop_back_val();
3130 if (!Visited.insert(I)) continue;
3132 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3133 Scalars.find(static_cast<Value *>(I));
3134 if (It != Scalars.end()) {
3136 ValuesAtScopes.erase(I);
3137 if (PHINode *PN = dyn_cast<PHINode>(I))
3138 ConstantEvolutionLoopExitValue.erase(PN);
3141 PushDefUseChildren(I, Worklist);
3145 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3146 /// of the specified loop will execute.
3147 ScalarEvolution::BackedgeTakenInfo
3148 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3149 SmallVector<BasicBlock*, 8> ExitingBlocks;
3150 L->getExitingBlocks(ExitingBlocks);
3152 // Examine all exits and pick the most conservative values.
3153 const SCEV *BECount = getCouldNotCompute();
3154 const SCEV *MaxBECount = getCouldNotCompute();
3155 bool CouldNotComputeBECount = false;
3156 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3157 BackedgeTakenInfo NewBTI =
3158 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3160 if (NewBTI.Exact == getCouldNotCompute()) {
3161 // We couldn't compute an exact value for this exit, so
3162 // we won't be able to compute an exact value for the loop.
3163 CouldNotComputeBECount = true;
3164 BECount = getCouldNotCompute();
3165 } else if (!CouldNotComputeBECount) {
3166 if (BECount == getCouldNotCompute())
3167 BECount = NewBTI.Exact;
3169 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3171 if (MaxBECount == getCouldNotCompute())
3172 MaxBECount = NewBTI.Max;
3173 else if (NewBTI.Max != getCouldNotCompute())
3174 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3177 return BackedgeTakenInfo(BECount, MaxBECount);
3180 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3181 /// of the specified loop will execute if it exits via the specified block.
3182 ScalarEvolution::BackedgeTakenInfo
3183 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3184 BasicBlock *ExitingBlock) {
3186 // Okay, we've chosen an exiting block. See what condition causes us to
3187 // exit at this block.
3189 // FIXME: we should be able to handle switch instructions (with a single exit)
3190 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3191 if (ExitBr == 0) return getCouldNotCompute();
3192 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3194 // At this point, we know we have a conditional branch that determines whether
3195 // the loop is exited. However, we don't know if the branch is executed each
3196 // time through the loop. If not, then the execution count of the branch will
3197 // not be equal to the trip count of the loop.
3199 // Currently we check for this by checking to see if the Exit branch goes to
3200 // the loop header. If so, we know it will always execute the same number of
3201 // times as the loop. We also handle the case where the exit block *is* the
3202 // loop header. This is common for un-rotated loops.
3204 // If both of those tests fail, walk up the unique predecessor chain to the
3205 // header, stopping if there is an edge that doesn't exit the loop. If the
3206 // header is reached, the execution count of the branch will be equal to the
3207 // trip count of the loop.
3209 // More extensive analysis could be done to handle more cases here.
3211 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3212 ExitBr->getSuccessor(1) != L->getHeader() &&
3213 ExitBr->getParent() != L->getHeader()) {
3214 // The simple checks failed, try climbing the unique predecessor chain
3215 // up to the header.
3217 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3218 BasicBlock *Pred = BB->getUniquePredecessor();
3220 return getCouldNotCompute();
3221 TerminatorInst *PredTerm = Pred->getTerminator();
3222 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3223 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3226 // If the predecessor has a successor that isn't BB and isn't
3227 // outside the loop, assume the worst.
3228 if (L->contains(PredSucc))
3229 return getCouldNotCompute();
3231 if (Pred == L->getHeader()) {
3238 return getCouldNotCompute();
3241 // Procede to the next level to examine the exit condition expression.
3242 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3243 ExitBr->getSuccessor(0),
3244 ExitBr->getSuccessor(1));
3247 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3248 /// backedge of the specified loop will execute if its exit condition
3249 /// were a conditional branch of ExitCond, TBB, and FBB.
3250 ScalarEvolution::BackedgeTakenInfo
3251 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3255 // Check if the controlling expression for this loop is an And or Or.
3256 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3257 if (BO->getOpcode() == Instruction::And) {
3258 // Recurse on the operands of the and.
3259 BackedgeTakenInfo BTI0 =
3260 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3261 BackedgeTakenInfo BTI1 =
3262 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3263 const SCEV *BECount = getCouldNotCompute();
3264 const SCEV *MaxBECount = getCouldNotCompute();
3265 if (L->contains(TBB)) {
3266 // Both conditions must be true for the loop to continue executing.
3267 // Choose the less conservative count.
3268 if (BTI0.Exact == getCouldNotCompute() ||
3269 BTI1.Exact == getCouldNotCompute())
3270 BECount = getCouldNotCompute();
3272 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3273 if (BTI0.Max == getCouldNotCompute())
3274 MaxBECount = BTI1.Max;
3275 else if (BTI1.Max == getCouldNotCompute())
3276 MaxBECount = BTI0.Max;
3278 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3280 // Both conditions must be true for the loop to exit.
3281 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3282 if (BTI0.Exact != getCouldNotCompute() &&
3283 BTI1.Exact != getCouldNotCompute())
3284 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3285 if (BTI0.Max != getCouldNotCompute() &&
3286 BTI1.Max != getCouldNotCompute())
3287 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3290 return BackedgeTakenInfo(BECount, MaxBECount);
3292 if (BO->getOpcode() == Instruction::Or) {
3293 // Recurse on the operands of the or.
3294 BackedgeTakenInfo BTI0 =
3295 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3296 BackedgeTakenInfo BTI1 =
3297 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3298 const SCEV *BECount = getCouldNotCompute();
3299 const SCEV *MaxBECount = getCouldNotCompute();
3300 if (L->contains(FBB)) {
3301 // Both conditions must be false for the loop to continue executing.
3302 // Choose the less conservative count.
3303 if (BTI0.Exact == getCouldNotCompute() ||
3304 BTI1.Exact == getCouldNotCompute())
3305 BECount = getCouldNotCompute();
3307 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3308 if (BTI0.Max == getCouldNotCompute())
3309 MaxBECount = BTI1.Max;
3310 else if (BTI1.Max == getCouldNotCompute())
3311 MaxBECount = BTI0.Max;
3313 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3315 // Both conditions must be false for the loop to exit.
3316 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3317 if (BTI0.Exact != getCouldNotCompute() &&
3318 BTI1.Exact != getCouldNotCompute())
3319 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3320 if (BTI0.Max != getCouldNotCompute() &&
3321 BTI1.Max != getCouldNotCompute())
3322 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3325 return BackedgeTakenInfo(BECount, MaxBECount);
3329 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3330 // Procede to the next level to examine the icmp.
3331 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3332 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3334 // If it's not an integer or pointer comparison then compute it the hard way.
3335 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3338 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3339 /// backedge of the specified loop will execute if its exit condition
3340 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3341 ScalarEvolution::BackedgeTakenInfo
3342 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3347 // If the condition was exit on true, convert the condition to exit on false
3348 ICmpInst::Predicate Cond;
3349 if (!L->contains(FBB))
3350 Cond = ExitCond->getPredicate();
3352 Cond = ExitCond->getInversePredicate();
3354 // Handle common loops like: for (X = "string"; *X; ++X)
3355 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3356 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3358 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3359 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3360 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3361 return BackedgeTakenInfo(ItCnt,
3362 isa<SCEVConstant>(ItCnt) ? ItCnt :
3363 getConstant(APInt::getMaxValue(BitWidth)-1));
3367 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3368 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3370 // Try to evaluate any dependencies out of the loop.
3371 LHS = getSCEVAtScope(LHS, L);
3372 RHS = getSCEVAtScope(RHS, L);
3374 // At this point, we would like to compute how many iterations of the
3375 // loop the predicate will return true for these inputs.
3376 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3377 // If there is a loop-invariant, force it into the RHS.
3378 std::swap(LHS, RHS);
3379 Cond = ICmpInst::getSwappedPredicate(Cond);
3382 // If we have a comparison of a chrec against a constant, try to use value
3383 // ranges to answer this query.
3384 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3385 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3386 if (AddRec->getLoop() == L) {
3387 // Form the constant range.
3388 ConstantRange CompRange(
3389 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3391 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3392 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3396 case ICmpInst::ICMP_NE: { // while (X != Y)
3397 // Convert to: while (X-Y != 0)
3398 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3399 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3402 case ICmpInst::ICMP_EQ: {
3403 // Convert to: while (X-Y == 0) // while (X == Y)
3404 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3405 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3408 case ICmpInst::ICMP_SLT: {
3409 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3410 if (BTI.hasAnyInfo()) return BTI;
3413 case ICmpInst::ICMP_SGT: {
3414 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3415 getNotSCEV(RHS), L, true);
3416 if (BTI.hasAnyInfo()) return BTI;
3419 case ICmpInst::ICMP_ULT: {
3420 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3421 if (BTI.hasAnyInfo()) return BTI;
3424 case ICmpInst::ICMP_UGT: {
3425 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3426 getNotSCEV(RHS), L, false);
3427 if (BTI.hasAnyInfo()) return BTI;
3432 errs() << "ComputeBackedgeTakenCount ";
3433 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3434 errs() << "[unsigned] ";
3435 errs() << *LHS << " "
3436 << Instruction::getOpcodeName(Instruction::ICmp)
3437 << " " << *RHS << "\n";
3442 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3445 static ConstantInt *
3446 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3447 ScalarEvolution &SE) {
3448 const SCEV *InVal = SE.getConstant(C);
3449 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3450 assert(isa<SCEVConstant>(Val) &&
3451 "Evaluation of SCEV at constant didn't fold correctly?");
3452 return cast<SCEVConstant>(Val)->getValue();
3455 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3456 /// and a GEP expression (missing the pointer index) indexing into it, return
3457 /// the addressed element of the initializer or null if the index expression is
3460 GetAddressedElementFromGlobal(LLVMContext *Context, GlobalVariable *GV,
3461 const std::vector<ConstantInt*> &Indices) {
3462 Constant *Init = GV->getInitializer();
3463 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3464 uint64_t Idx = Indices[i]->getZExtValue();
3465 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3466 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3467 Init = cast<Constant>(CS->getOperand(Idx));
3468 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3469 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3470 Init = cast<Constant>(CA->getOperand(Idx));
3471 } else if (isa<ConstantAggregateZero>(Init)) {
3472 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3473 assert(Idx < STy->getNumElements() && "Bad struct index!");
3474 Init = Context->getNullValue(STy->getElementType(Idx));
3475 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3476 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3477 Init = Context->getNullValue(ATy->getElementType());
3479 llvm_unreachable("Unknown constant aggregate type!");
3483 return 0; // Unknown initializer type
3489 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3490 /// 'icmp op load X, cst', try to see if we can compute the backedge
3491 /// execution count.
3493 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3497 ICmpInst::Predicate predicate) {
3498 if (LI->isVolatile()) return getCouldNotCompute();
3500 // Check to see if the loaded pointer is a getelementptr of a global.
3501 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3502 if (!GEP) return getCouldNotCompute();
3504 // Make sure that it is really a constant global we are gepping, with an
3505 // initializer, and make sure the first IDX is really 0.
3506 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3507 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3508 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3509 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3510 return getCouldNotCompute();
3512 // Okay, we allow one non-constant index into the GEP instruction.
3514 std::vector<ConstantInt*> Indexes;
3515 unsigned VarIdxNum = 0;
3516 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3517 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3518 Indexes.push_back(CI);
3519 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3520 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3521 VarIdx = GEP->getOperand(i);
3523 Indexes.push_back(0);
3526 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3527 // Check to see if X is a loop variant variable value now.
3528 const SCEV *Idx = getSCEV(VarIdx);
3529 Idx = getSCEVAtScope(Idx, L);
3531 // We can only recognize very limited forms of loop index expressions, in
3532 // particular, only affine AddRec's like {C1,+,C2}.
3533 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3534 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3535 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3536 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3537 return getCouldNotCompute();
3539 unsigned MaxSteps = MaxBruteForceIterations;
3540 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3541 ConstantInt *ItCst = Context->getConstantInt(
3542 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3543 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3545 // Form the GEP offset.
3546 Indexes[VarIdxNum] = Val;
3548 Constant *Result = GetAddressedElementFromGlobal(Context, GV, Indexes);
3549 if (Result == 0) break; // Cannot compute!
3551 // Evaluate the condition for this iteration.
3552 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3553 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3554 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3556 errs() << "\n***\n*** Computed loop count " << *ItCst
3557 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3560 ++NumArrayLenItCounts;
3561 return getConstant(ItCst); // Found terminating iteration!
3564 return getCouldNotCompute();
3568 /// CanConstantFold - Return true if we can constant fold an instruction of the
3569 /// specified type, assuming that all operands were constants.
3570 static bool CanConstantFold(const Instruction *I) {
3571 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3572 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3575 if (const CallInst *CI = dyn_cast<CallInst>(I))
3576 if (const Function *F = CI->getCalledFunction())
3577 return canConstantFoldCallTo(F);
3581 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3582 /// in the loop that V is derived from. We allow arbitrary operations along the
3583 /// way, but the operands of an operation must either be constants or a value
3584 /// derived from a constant PHI. If this expression does not fit with these
3585 /// constraints, return null.
3586 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3587 // If this is not an instruction, or if this is an instruction outside of the
3588 // loop, it can't be derived from a loop PHI.
3589 Instruction *I = dyn_cast<Instruction>(V);
3590 if (I == 0 || !L->contains(I->getParent())) return 0;
3592 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3593 if (L->getHeader() == I->getParent())
3596 // We don't currently keep track of the control flow needed to evaluate
3597 // PHIs, so we cannot handle PHIs inside of loops.
3601 // If we won't be able to constant fold this expression even if the operands
3602 // are constants, return early.
3603 if (!CanConstantFold(I)) return 0;
3605 // Otherwise, we can evaluate this instruction if all of its operands are
3606 // constant or derived from a PHI node themselves.
3608 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3609 if (!(isa<Constant>(I->getOperand(Op)) ||
3610 isa<GlobalValue>(I->getOperand(Op)))) {
3611 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3612 if (P == 0) return 0; // Not evolving from PHI
3616 return 0; // Evolving from multiple different PHIs.
3619 // This is a expression evolving from a constant PHI!
3623 /// EvaluateExpression - Given an expression that passes the
3624 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3625 /// in the loop has the value PHIVal. If we can't fold this expression for some
3626 /// reason, return null.
3627 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3628 if (isa<PHINode>(V)) return PHIVal;
3629 if (Constant *C = dyn_cast<Constant>(V)) return C;
3630 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3631 Instruction *I = cast<Instruction>(V);
3632 LLVMContext *Context = I->getParent()->getContext();
3634 std::vector<Constant*> Operands;
3635 Operands.resize(I->getNumOperands());
3637 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3638 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3639 if (Operands[i] == 0) return 0;
3642 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3643 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3644 &Operands[0], Operands.size(),
3647 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3648 &Operands[0], Operands.size(),
3652 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3653 /// in the header of its containing loop, we know the loop executes a
3654 /// constant number of times, and the PHI node is just a recurrence
3655 /// involving constants, fold it.
3657 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3660 std::map<PHINode*, Constant*>::iterator I =
3661 ConstantEvolutionLoopExitValue.find(PN);
3662 if (I != ConstantEvolutionLoopExitValue.end())
3665 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3666 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3668 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3670 // Since the loop is canonicalized, the PHI node must have two entries. One
3671 // entry must be a constant (coming in from outside of the loop), and the
3672 // second must be derived from the same PHI.
3673 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3674 Constant *StartCST =
3675 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3677 return RetVal = 0; // Must be a constant.
3679 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3680 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3682 return RetVal = 0; // Not derived from same PHI.
3684 // Execute the loop symbolically to determine the exit value.
3685 if (BEs.getActiveBits() >= 32)
3686 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3688 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3689 unsigned IterationNum = 0;
3690 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3691 if (IterationNum == NumIterations)
3692 return RetVal = PHIVal; // Got exit value!
3694 // Compute the value of the PHI node for the next iteration.
3695 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3696 if (NextPHI == PHIVal)
3697 return RetVal = NextPHI; // Stopped evolving!
3699 return 0; // Couldn't evaluate!
3704 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
3705 /// constant number of times (the condition evolves only from constants),
3706 /// try to evaluate a few iterations of the loop until we get the exit
3707 /// condition gets a value of ExitWhen (true or false). If we cannot
3708 /// evaluate the trip count of the loop, return getCouldNotCompute().
3710 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3713 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3714 if (PN == 0) return getCouldNotCompute();
3716 // Since the loop is canonicalized, the PHI node must have two entries. One
3717 // entry must be a constant (coming in from outside of the loop), and the
3718 // second must be derived from the same PHI.
3719 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3720 Constant *StartCST =
3721 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3722 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3724 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3725 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3726 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3728 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3729 // the loop symbolically to determine when the condition gets a value of
3731 unsigned IterationNum = 0;
3732 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3733 for (Constant *PHIVal = StartCST;
3734 IterationNum != MaxIterations; ++IterationNum) {
3735 ConstantInt *CondVal =
3736 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3738 // Couldn't symbolically evaluate.
3739 if (!CondVal) return getCouldNotCompute();
3741 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3742 ++NumBruteForceTripCountsComputed;
3743 return getConstant(Type::Int32Ty, IterationNum);
3746 // Compute the value of the PHI node for the next iteration.
3747 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3748 if (NextPHI == 0 || NextPHI == PHIVal)
3749 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3753 // Too many iterations were needed to evaluate.
3754 return getCouldNotCompute();
3757 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
3758 /// at the specified scope in the program. The L value specifies a loop
3759 /// nest to evaluate the expression at, where null is the top-level or a
3760 /// specified loop is immediately inside of the loop.
3762 /// This method can be used to compute the exit value for a variable defined
3763 /// in a loop by querying what the value will hold in the parent loop.
3765 /// In the case that a relevant loop exit value cannot be computed, the
3766 /// original value V is returned.
3767 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3768 // FIXME: this should be turned into a virtual method on SCEV!
3770 if (isa<SCEVConstant>(V)) return V;
3772 // If this instruction is evolved from a constant-evolving PHI, compute the
3773 // exit value from the loop without using SCEVs.
3774 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3775 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3776 const Loop *LI = (*this->LI)[I->getParent()];
3777 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3778 if (PHINode *PN = dyn_cast<PHINode>(I))
3779 if (PN->getParent() == LI->getHeader()) {
3780 // Okay, there is no closed form solution for the PHI node. Check
3781 // to see if the loop that contains it has a known backedge-taken
3782 // count. If so, we may be able to force computation of the exit
3784 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3785 if (const SCEVConstant *BTCC =
3786 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3787 // Okay, we know how many times the containing loop executes. If
3788 // this is a constant evolving PHI node, get the final value at
3789 // the specified iteration number.
3790 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3791 BTCC->getValue()->getValue(),
3793 if (RV) return getSCEV(RV);
3797 // Okay, this is an expression that we cannot symbolically evaluate
3798 // into a SCEV. Check to see if it's possible to symbolically evaluate
3799 // the arguments into constants, and if so, try to constant propagate the
3800 // result. This is particularly useful for computing loop exit values.
3801 if (CanConstantFold(I)) {
3802 // Check to see if we've folded this instruction at this loop before.
3803 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3804 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3805 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3807 return Pair.first->second ? &*getSCEV(Pair.first->second) : V;
3809 std::vector<Constant*> Operands;
3810 Operands.reserve(I->getNumOperands());
3811 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3812 Value *Op = I->getOperand(i);
3813 if (Constant *C = dyn_cast<Constant>(Op)) {
3814 Operands.push_back(C);
3816 // If any of the operands is non-constant and if they are
3817 // non-integer and non-pointer, don't even try to analyze them
3818 // with scev techniques.
3819 if (!isSCEVable(Op->getType()))
3822 const SCEV* OpV = getSCEVAtScope(Op, L);
3823 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3824 Constant *C = SC->getValue();
3825 if (C->getType() != Op->getType())
3826 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3830 Operands.push_back(C);
3831 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3832 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3833 if (C->getType() != Op->getType())
3835 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3839 Operands.push_back(C);
3849 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3850 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3851 &Operands[0], Operands.size(),
3854 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3855 &Operands[0], Operands.size(), Context);
3856 Pair.first->second = C;
3861 // This is some other type of SCEVUnknown, just return it.
3865 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3866 // Avoid performing the look-up in the common case where the specified
3867 // expression has no loop-variant portions.
3868 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3869 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3870 if (OpAtScope != Comm->getOperand(i)) {
3871 // Okay, at least one of these operands is loop variant but might be
3872 // foldable. Build a new instance of the folded commutative expression.
3873 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
3874 Comm->op_begin()+i);
3875 NewOps.push_back(OpAtScope);
3877 for (++i; i != e; ++i) {
3878 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3879 NewOps.push_back(OpAtScope);
3881 if (isa<SCEVAddExpr>(Comm))
3882 return getAddExpr(NewOps);
3883 if (isa<SCEVMulExpr>(Comm))
3884 return getMulExpr(NewOps);
3885 if (isa<SCEVSMaxExpr>(Comm))
3886 return getSMaxExpr(NewOps);
3887 if (isa<SCEVUMaxExpr>(Comm))
3888 return getUMaxExpr(NewOps);
3889 llvm_unreachable("Unknown commutative SCEV type!");
3892 // If we got here, all operands are loop invariant.
3896 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3897 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
3898 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
3899 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3900 return Div; // must be loop invariant
3901 return getUDivExpr(LHS, RHS);
3904 // If this is a loop recurrence for a loop that does not contain L, then we
3905 // are dealing with the final value computed by the loop.
3906 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3907 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3908 // To evaluate this recurrence, we need to know how many times the AddRec
3909 // loop iterates. Compute this now.
3910 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3911 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
3913 // Then, evaluate the AddRec.
3914 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3919 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3920 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3921 if (Op == Cast->getOperand())
3922 return Cast; // must be loop invariant
3923 return getZeroExtendExpr(Op, Cast->getType());
3926 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3927 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3928 if (Op == Cast->getOperand())
3929 return Cast; // must be loop invariant
3930 return getSignExtendExpr(Op, Cast->getType());
3933 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3934 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3935 if (Op == Cast->getOperand())
3936 return Cast; // must be loop invariant
3937 return getTruncateExpr(Op, Cast->getType());
3940 llvm_unreachable("Unknown SCEV type!");
3944 /// getSCEVAtScope - This is a convenience function which does
3945 /// getSCEVAtScope(getSCEV(V), L).
3946 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3947 return getSCEVAtScope(getSCEV(V), L);
3950 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3951 /// following equation:
3953 /// A * X = B (mod N)
3955 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3956 /// A and B isn't important.
3958 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3959 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3960 ScalarEvolution &SE) {
3961 uint32_t BW = A.getBitWidth();
3962 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3963 assert(A != 0 && "A must be non-zero.");
3967 // The gcd of A and N may have only one prime factor: 2. The number of
3968 // trailing zeros in A is its multiplicity
3969 uint32_t Mult2 = A.countTrailingZeros();
3972 // 2. Check if B is divisible by D.
3974 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3975 // is not less than multiplicity of this prime factor for D.
3976 if (B.countTrailingZeros() < Mult2)
3977 return SE.getCouldNotCompute();
3979 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3982 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3983 // bit width during computations.
3984 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3985 APInt Mod(BW + 1, 0);
3986 Mod.set(BW - Mult2); // Mod = N / D
3987 APInt I = AD.multiplicativeInverse(Mod);
3989 // 4. Compute the minimum unsigned root of the equation:
3990 // I * (B / D) mod (N / D)
3991 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3993 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3995 return SE.getConstant(Result.trunc(BW));
3998 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3999 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4000 /// might be the same) or two SCEVCouldNotCompute objects.
4002 static std::pair<const SCEV *,const SCEV *>
4003 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4004 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4005 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4006 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4007 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4009 // We currently can only solve this if the coefficients are constants.
4010 if (!LC || !MC || !NC) {
4011 const SCEV *CNC = SE.getCouldNotCompute();
4012 return std::make_pair(CNC, CNC);
4015 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4016 const APInt &L = LC->getValue()->getValue();
4017 const APInt &M = MC->getValue()->getValue();
4018 const APInt &N = NC->getValue()->getValue();
4019 APInt Two(BitWidth, 2);
4020 APInt Four(BitWidth, 4);
4023 using namespace APIntOps;
4025 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4026 // The B coefficient is M-N/2
4030 // The A coefficient is N/2
4031 APInt A(N.sdiv(Two));
4033 // Compute the B^2-4ac term.
4036 SqrtTerm -= Four * (A * C);
4038 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4039 // integer value or else APInt::sqrt() will assert.
4040 APInt SqrtVal(SqrtTerm.sqrt());
4042 // Compute the two solutions for the quadratic formula.
4043 // The divisions must be performed as signed divisions.
4045 APInt TwoA( A << 1 );
4046 if (TwoA.isMinValue()) {
4047 const SCEV *CNC = SE.getCouldNotCompute();
4048 return std::make_pair(CNC, CNC);
4051 LLVMContext *Context = SE.getContext();
4053 ConstantInt *Solution1 =
4054 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA));
4055 ConstantInt *Solution2 =
4056 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA));
4058 return std::make_pair(SE.getConstant(Solution1),
4059 SE.getConstant(Solution2));
4060 } // end APIntOps namespace
4063 /// HowFarToZero - Return the number of times a backedge comparing the specified
4064 /// value to zero will execute. If not computable, return CouldNotCompute.
4065 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4066 // If the value is a constant
4067 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4068 // If the value is already zero, the branch will execute zero times.
4069 if (C->getValue()->isZero()) return C;
4070 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4073 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4074 if (!AddRec || AddRec->getLoop() != L)
4075 return getCouldNotCompute();
4077 if (AddRec->isAffine()) {
4078 // If this is an affine expression, the execution count of this branch is
4079 // the minimum unsigned root of the following equation:
4081 // Start + Step*N = 0 (mod 2^BW)
4085 // Step*N = -Start (mod 2^BW)
4087 // where BW is the common bit width of Start and Step.
4089 // Get the initial value for the loop.
4090 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4091 L->getParentLoop());
4092 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4093 L->getParentLoop());
4095 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4096 // For now we handle only constant steps.
4098 // First, handle unitary steps.
4099 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4100 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4101 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4102 return Start; // N = Start (as unsigned)
4104 // Then, try to solve the above equation provided that Start is constant.
4105 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4106 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4107 -StartC->getValue()->getValue(),
4110 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4111 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4112 // the quadratic equation to solve it.
4113 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4115 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4116 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4119 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
4120 << " sol#2: " << *R2 << "\n";
4122 // Pick the smallest positive root value.
4123 if (ConstantInt *CB =
4124 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT,
4125 R1->getValue(), R2->getValue()))) {
4126 if (CB->getZExtValue() == false)
4127 std::swap(R1, R2); // R1 is the minimum root now.
4129 // We can only use this value if the chrec ends up with an exact zero
4130 // value at this index. When solving for "X*X != 5", for example, we
4131 // should not accept a root of 2.
4132 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4134 return R1; // We found a quadratic root!
4139 return getCouldNotCompute();
4142 /// HowFarToNonZero - Return the number of times a backedge checking the
4143 /// specified value for nonzero will execute. If not computable, return
4145 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4146 // Loops that look like: while (X == 0) are very strange indeed. We don't
4147 // handle them yet except for the trivial case. This could be expanded in the
4148 // future as needed.
4150 // If the value is a constant, check to see if it is known to be non-zero
4151 // already. If so, the backedge will execute zero times.
4152 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4153 if (!C->getValue()->isNullValue())
4154 return getIntegerSCEV(0, C->getType());
4155 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4158 // We could implement others, but I really doubt anyone writes loops like
4159 // this, and if they did, they would already be constant folded.
4160 return getCouldNotCompute();
4163 /// getLoopPredecessor - If the given loop's header has exactly one unique
4164 /// predecessor outside the loop, return it. Otherwise return null.
4166 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4167 BasicBlock *Header = L->getHeader();
4168 BasicBlock *Pred = 0;
4169 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4171 if (!L->contains(*PI)) {
4172 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4178 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4179 /// (which may not be an immediate predecessor) which has exactly one
4180 /// successor from which BB is reachable, or null if no such block is
4184 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4185 // If the block has a unique predecessor, then there is no path from the
4186 // predecessor to the block that does not go through the direct edge
4187 // from the predecessor to the block.
4188 if (BasicBlock *Pred = BB->getSinglePredecessor())
4191 // A loop's header is defined to be a block that dominates the loop.
4192 // If the header has a unique predecessor outside the loop, it must be
4193 // a block that has exactly one successor that can reach the loop.
4194 if (Loop *L = LI->getLoopFor(BB))
4195 return getLoopPredecessor(L);
4200 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4201 /// testing whether two expressions are equal, however for the purposes of
4202 /// looking for a condition guarding a loop, it can be useful to be a little
4203 /// more general, since a front-end may have replicated the controlling
4206 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4207 // Quick check to see if they are the same SCEV.
4208 if (A == B) return true;
4210 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4211 // two different instructions with the same value. Check for this case.
4212 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4213 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4214 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4215 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4216 if (AI->isIdenticalTo(BI))
4219 // Otherwise assume they may have a different value.
4223 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4224 return getSignedRange(S).getSignedMax().isNegative();
4227 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4228 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4231 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4232 return !getSignedRange(S).getSignedMin().isNegative();
4235 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4236 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4239 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4240 return isKnownNegative(S) || isKnownPositive(S);
4243 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4244 const SCEV *LHS, const SCEV *RHS) {
4246 if (HasSameValue(LHS, RHS))
4247 return ICmpInst::isTrueWhenEqual(Pred);
4251 assert(0 && "Unexpected ICmpInst::Predicate value!");
4253 case ICmpInst::ICMP_SGT:
4254 Pred = ICmpInst::ICMP_SLT;
4255 std::swap(LHS, RHS);
4256 case ICmpInst::ICMP_SLT: {
4257 ConstantRange LHSRange = getSignedRange(LHS);
4258 ConstantRange RHSRange = getSignedRange(RHS);
4259 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4261 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4264 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4265 ConstantRange DiffRange = getUnsignedRange(Diff);
4266 if (isKnownNegative(Diff)) {
4267 if (DiffRange.getUnsignedMax().ult(LHSRange.getUnsignedMin()))
4269 if (DiffRange.getUnsignedMin().uge(LHSRange.getUnsignedMax()))
4271 } else if (isKnownPositive(Diff)) {
4272 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin()))
4274 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax()))
4279 case ICmpInst::ICMP_SGE:
4280 Pred = ICmpInst::ICMP_SLE;
4281 std::swap(LHS, RHS);
4282 case ICmpInst::ICMP_SLE: {
4283 ConstantRange LHSRange = getSignedRange(LHS);
4284 ConstantRange RHSRange = getSignedRange(RHS);
4285 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4287 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4290 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4291 ConstantRange DiffRange = getUnsignedRange(Diff);
4292 if (isKnownNonPositive(Diff)) {
4293 if (DiffRange.getUnsignedMax().ule(LHSRange.getUnsignedMin()))
4295 if (DiffRange.getUnsignedMin().ugt(LHSRange.getUnsignedMax()))
4297 } else if (isKnownNonNegative(Diff)) {
4298 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin()))
4300 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax()))
4305 case ICmpInst::ICMP_UGT:
4306 Pred = ICmpInst::ICMP_ULT;
4307 std::swap(LHS, RHS);
4308 case ICmpInst::ICMP_ULT: {
4309 ConstantRange LHSRange = getUnsignedRange(LHS);
4310 ConstantRange RHSRange = getUnsignedRange(RHS);
4311 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4313 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4316 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4317 ConstantRange DiffRange = getUnsignedRange(Diff);
4318 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin()))
4320 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax()))
4324 case ICmpInst::ICMP_UGE:
4325 Pred = ICmpInst::ICMP_ULE;
4326 std::swap(LHS, RHS);
4327 case ICmpInst::ICMP_ULE: {
4328 ConstantRange LHSRange = getUnsignedRange(LHS);
4329 ConstantRange RHSRange = getUnsignedRange(RHS);
4330 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4332 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4335 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4336 ConstantRange DiffRange = getUnsignedRange(Diff);
4337 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin()))
4339 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax()))
4343 case ICmpInst::ICMP_NE: {
4344 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4346 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4349 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4350 if (isKnownNonZero(Diff))
4354 case ICmpInst::ICMP_EQ:
4360 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4361 /// protected by a conditional between LHS and RHS. This is used to
4362 /// to eliminate casts.
4364 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4365 ICmpInst::Predicate Pred,
4366 const SCEV *LHS, const SCEV *RHS) {
4367 // Interpret a null as meaning no loop, where there is obviously no guard
4368 // (interprocedural conditions notwithstanding).
4369 if (!L) return true;
4371 BasicBlock *Latch = L->getLoopLatch();
4375 BranchInst *LoopContinuePredicate =
4376 dyn_cast<BranchInst>(Latch->getTerminator());
4377 if (!LoopContinuePredicate ||
4378 LoopContinuePredicate->isUnconditional())
4382 isNecessaryCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4383 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4386 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4387 /// by a conditional between LHS and RHS. This is used to help avoid max
4388 /// expressions in loop trip counts, and to eliminate casts.
4390 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4391 ICmpInst::Predicate Pred,
4392 const SCEV *LHS, const SCEV *RHS) {
4393 // Interpret a null as meaning no loop, where there is obviously no guard
4394 // (interprocedural conditions notwithstanding).
4395 if (!L) return false;
4397 BasicBlock *Predecessor = getLoopPredecessor(L);
4398 BasicBlock *PredecessorDest = L->getHeader();
4400 // Starting at the loop predecessor, climb up the predecessor chain, as long
4401 // as there are predecessors that can be found that have unique successors
4402 // leading to the original header.
4404 PredecessorDest = Predecessor,
4405 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4407 BranchInst *LoopEntryPredicate =
4408 dyn_cast<BranchInst>(Predecessor->getTerminator());
4409 if (!LoopEntryPredicate ||
4410 LoopEntryPredicate->isUnconditional())
4413 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4414 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4421 /// isNecessaryCond - Test whether the condition described by Pred, LHS,
4422 /// and RHS is a necessary condition for the given Cond value to evaluate
4424 bool ScalarEvolution::isNecessaryCond(Value *CondValue,
4425 ICmpInst::Predicate Pred,
4426 const SCEV *LHS, const SCEV *RHS,
4428 // Recursivly handle And and Or conditions.
4429 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4430 if (BO->getOpcode() == Instruction::And) {
4432 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4433 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4434 } else if (BO->getOpcode() == Instruction::Or) {
4436 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4437 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4441 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4442 if (!ICI) return false;
4444 // Now that we found a conditional branch that dominates the loop, check to
4445 // see if it is the comparison we are looking for.
4446 Value *PreCondLHS = ICI->getOperand(0);
4447 Value *PreCondRHS = ICI->getOperand(1);
4448 ICmpInst::Predicate FoundPred;
4450 FoundPred = ICI->getInversePredicate();
4452 FoundPred = ICI->getPredicate();
4454 if (FoundPred == Pred)
4455 ; // An exact match.
4456 else if (!ICmpInst::isTrueWhenEqual(FoundPred) && Pred == ICmpInst::ICMP_NE) {
4457 // The actual condition is beyond sufficient.
4458 FoundPred = ICmpInst::ICMP_NE;
4459 // NE is symmetric but the original comparison may not be. Swap
4460 // the operands if necessary so that they match below.
4461 if (isa<SCEVConstant>(LHS))
4462 std::swap(PreCondLHS, PreCondRHS);
4464 // Check a few special cases.
4465 switch (FoundPred) {
4466 case ICmpInst::ICMP_UGT:
4467 if (Pred == ICmpInst::ICMP_ULT) {
4468 std::swap(PreCondLHS, PreCondRHS);
4469 FoundPred = ICmpInst::ICMP_ULT;
4473 case ICmpInst::ICMP_SGT:
4474 if (Pred == ICmpInst::ICMP_SLT) {
4475 std::swap(PreCondLHS, PreCondRHS);
4476 FoundPred = ICmpInst::ICMP_SLT;
4480 case ICmpInst::ICMP_NE:
4481 // Expressions like (x >u 0) are often canonicalized to (x != 0),
4482 // so check for this case by checking if the NE is comparing against
4483 // a minimum or maximum constant.
4484 if (!ICmpInst::isTrueWhenEqual(Pred))
4485 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(RHS)) {
4486 const APInt &A = C->getValue()->getValue();
4488 case ICmpInst::ICMP_SLT:
4489 if (A.isMaxSignedValue()) break;
4491 case ICmpInst::ICMP_SGT:
4492 if (A.isMinSignedValue()) break;
4494 case ICmpInst::ICMP_ULT:
4495 if (A.isMaxValue()) break;
4497 case ICmpInst::ICMP_UGT:
4498 if (A.isMinValue()) break;
4504 // NE is symmetric but the original comparison may not be. Swap
4505 // the operands if necessary so that they match below.
4506 if (isa<SCEVConstant>(LHS))
4507 std::swap(PreCondLHS, PreCondRHS);
4512 // We weren't able to reconcile the condition.
4516 assert(Pred == FoundPred && "Conditions were not reconciled!");
4518 // Bail if the ICmp's operands' types are wider than the needed type
4519 // before attempting to call getSCEV on them. This avoids infinite
4520 // recursion, since the analysis of widening casts can require loop
4521 // exit condition information for overflow checking, which would
4523 if (getTypeSizeInBits(LHS->getType()) <
4524 getTypeSizeInBits(PreCondLHS->getType()))
4527 const SCEV *FoundLHS = getSCEV(PreCondLHS);
4528 const SCEV *FoundRHS = getSCEV(PreCondRHS);
4530 // Balance the types. The case where FoundLHS' type is wider than
4531 // LHS' type is checked for above.
4532 if (getTypeSizeInBits(LHS->getType()) >
4533 getTypeSizeInBits(FoundLHS->getType())) {
4534 if (CmpInst::isSigned(Pred)) {
4535 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4536 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4538 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4539 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4543 return isNecessaryCondOperands(Pred, LHS, RHS,
4544 FoundLHS, FoundRHS) ||
4545 // ~x < ~y --> x > y
4546 isNecessaryCondOperands(Pred, LHS, RHS,
4547 getNotSCEV(FoundRHS), getNotSCEV(FoundLHS));
4550 /// isNecessaryCondOperands - Test whether the condition described by Pred,
4551 /// LHS, and RHS is a necessary condition for the condition described by
4552 /// Pred, FoundLHS, and FoundRHS to evaluate to true.
4554 ScalarEvolution::isNecessaryCondOperands(ICmpInst::Predicate Pred,
4555 const SCEV *LHS, const SCEV *RHS,
4556 const SCEV *FoundLHS,
4557 const SCEV *FoundRHS) {
4560 case ICmpInst::ICMP_SLT:
4561 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4562 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4565 case ICmpInst::ICMP_SGT:
4566 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4567 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4570 case ICmpInst::ICMP_ULT:
4571 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4572 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4575 case ICmpInst::ICMP_UGT:
4576 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4577 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4585 /// getBECount - Subtract the end and start values and divide by the step,
4586 /// rounding up, to get the number of times the backedge is executed. Return
4587 /// CouldNotCompute if an intermediate computation overflows.
4588 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4591 const Type *Ty = Start->getType();
4592 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4593 const SCEV *Diff = getMinusSCEV(End, Start);
4594 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4596 // Add an adjustment to the difference between End and Start so that
4597 // the division will effectively round up.
4598 const SCEV *Add = getAddExpr(Diff, RoundUp);
4600 // Check Add for unsigned overflow.
4601 // TODO: More sophisticated things could be done here.
4602 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1);
4603 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4604 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4605 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4606 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4607 return getCouldNotCompute();
4609 return getUDivExpr(Add, Step);
4612 /// HowManyLessThans - Return the number of times a backedge containing the
4613 /// specified less-than comparison will execute. If not computable, return
4614 /// CouldNotCompute.
4615 ScalarEvolution::BackedgeTakenInfo
4616 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4617 const Loop *L, bool isSigned) {
4618 // Only handle: "ADDREC < LoopInvariant".
4619 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4621 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4622 if (!AddRec || AddRec->getLoop() != L)
4623 return getCouldNotCompute();
4625 if (AddRec->isAffine()) {
4626 // FORNOW: We only support unit strides.
4627 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4628 const SCEV *Step = AddRec->getStepRecurrence(*this);
4630 // TODO: handle non-constant strides.
4631 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4632 if (!CStep || CStep->isZero())
4633 return getCouldNotCompute();
4634 if (CStep->isOne()) {
4635 // With unit stride, the iteration never steps past the limit value.
4636 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4637 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4638 // Test whether a positive iteration iteration can step past the limit
4639 // value and past the maximum value for its type in a single step.
4641 APInt Max = APInt::getSignedMaxValue(BitWidth);
4642 if ((Max - CStep->getValue()->getValue())
4643 .slt(CLimit->getValue()->getValue()))
4644 return getCouldNotCompute();
4646 APInt Max = APInt::getMaxValue(BitWidth);
4647 if ((Max - CStep->getValue()->getValue())
4648 .ult(CLimit->getValue()->getValue()))
4649 return getCouldNotCompute();
4652 // TODO: handle non-constant limit values below.
4653 return getCouldNotCompute();
4655 // TODO: handle negative strides below.
4656 return getCouldNotCompute();
4658 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4659 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4660 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4661 // treat m-n as signed nor unsigned due to overflow possibility.
4663 // First, we get the value of the LHS in the first iteration: n
4664 const SCEV *Start = AddRec->getOperand(0);
4666 // Determine the minimum constant start value.
4667 const SCEV *MinStart = getConstant(isSigned ?
4668 getSignedRange(Start).getSignedMin() :
4669 getUnsignedRange(Start).getUnsignedMin());
4671 // If we know that the condition is true in order to enter the loop,
4672 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4673 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4674 // the division must round up.
4675 const SCEV *End = RHS;
4676 if (!isLoopGuardedByCond(L,
4677 isSigned ? ICmpInst::ICMP_SLT :
4679 getMinusSCEV(Start, Step), RHS))
4680 End = isSigned ? getSMaxExpr(RHS, Start)
4681 : getUMaxExpr(RHS, Start);
4683 // Determine the maximum constant end value.
4684 const SCEV *MaxEnd = getConstant(isSigned ?
4685 getSignedRange(End).getSignedMax() :
4686 getUnsignedRange(End).getUnsignedMax());
4688 // Finally, we subtract these two values and divide, rounding up, to get
4689 // the number of times the backedge is executed.
4690 const SCEV *BECount = getBECount(Start, End, Step);
4692 // The maximum backedge count is similar, except using the minimum start
4693 // value and the maximum end value.
4694 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
4696 return BackedgeTakenInfo(BECount, MaxBECount);
4699 return getCouldNotCompute();
4702 /// getNumIterationsInRange - Return the number of iterations of this loop that
4703 /// produce values in the specified constant range. Another way of looking at
4704 /// this is that it returns the first iteration number where the value is not in
4705 /// the condition, thus computing the exit count. If the iteration count can't
4706 /// be computed, an instance of SCEVCouldNotCompute is returned.
4707 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4708 ScalarEvolution &SE) const {
4709 if (Range.isFullSet()) // Infinite loop.
4710 return SE.getCouldNotCompute();
4712 // If the start is a non-zero constant, shift the range to simplify things.
4713 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4714 if (!SC->getValue()->isZero()) {
4715 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4716 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4717 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4718 if (const SCEVAddRecExpr *ShiftedAddRec =
4719 dyn_cast<SCEVAddRecExpr>(Shifted))
4720 return ShiftedAddRec->getNumIterationsInRange(
4721 Range.subtract(SC->getValue()->getValue()), SE);
4722 // This is strange and shouldn't happen.
4723 return SE.getCouldNotCompute();
4726 // The only time we can solve this is when we have all constant indices.
4727 // Otherwise, we cannot determine the overflow conditions.
4728 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4729 if (!isa<SCEVConstant>(getOperand(i)))
4730 return SE.getCouldNotCompute();
4733 // Okay at this point we know that all elements of the chrec are constants and
4734 // that the start element is zero.
4736 // First check to see if the range contains zero. If not, the first
4738 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4739 if (!Range.contains(APInt(BitWidth, 0)))
4740 return SE.getIntegerSCEV(0, getType());
4743 // If this is an affine expression then we have this situation:
4744 // Solve {0,+,A} in Range === Ax in Range
4746 // We know that zero is in the range. If A is positive then we know that
4747 // the upper value of the range must be the first possible exit value.
4748 // If A is negative then the lower of the range is the last possible loop
4749 // value. Also note that we already checked for a full range.
4750 APInt One(BitWidth,1);
4751 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4752 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4754 // The exit value should be (End+A)/A.
4755 APInt ExitVal = (End + A).udiv(A);
4756 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal);
4758 // Evaluate at the exit value. If we really did fall out of the valid
4759 // range, then we computed our trip count, otherwise wrap around or other
4760 // things must have happened.
4761 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4762 if (Range.contains(Val->getValue()))
4763 return SE.getCouldNotCompute(); // Something strange happened
4765 // Ensure that the previous value is in the range. This is a sanity check.
4766 assert(Range.contains(
4767 EvaluateConstantChrecAtConstant(this,
4768 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) &&
4769 "Linear scev computation is off in a bad way!");
4770 return SE.getConstant(ExitValue);
4771 } else if (isQuadratic()) {
4772 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4773 // quadratic equation to solve it. To do this, we must frame our problem in
4774 // terms of figuring out when zero is crossed, instead of when
4775 // Range.getUpper() is crossed.
4776 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
4777 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4778 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4780 // Next, solve the constructed addrec
4781 std::pair<const SCEV *,const SCEV *> Roots =
4782 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4783 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4784 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4786 // Pick the smallest positive root value.
4787 if (ConstantInt *CB =
4788 dyn_cast<ConstantInt>(
4789 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT,
4790 R1->getValue(), R2->getValue()))) {
4791 if (CB->getZExtValue() == false)
4792 std::swap(R1, R2); // R1 is the minimum root now.
4794 // Make sure the root is not off by one. The returned iteration should
4795 // not be in the range, but the previous one should be. When solving
4796 // for "X*X < 5", for example, we should not return a root of 2.
4797 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4800 if (Range.contains(R1Val->getValue())) {
4801 // The next iteration must be out of the range...
4802 ConstantInt *NextVal =
4803 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1);
4805 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4806 if (!Range.contains(R1Val->getValue()))
4807 return SE.getConstant(NextVal);
4808 return SE.getCouldNotCompute(); // Something strange happened
4811 // If R1 was not in the range, then it is a good return value. Make
4812 // sure that R1-1 WAS in the range though, just in case.
4813 ConstantInt *NextVal =
4814 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1);
4815 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4816 if (Range.contains(R1Val->getValue()))
4818 return SE.getCouldNotCompute(); // Something strange happened
4823 return SE.getCouldNotCompute();
4828 //===----------------------------------------------------------------------===//
4829 // SCEVCallbackVH Class Implementation
4830 //===----------------------------------------------------------------------===//
4832 void ScalarEvolution::SCEVCallbackVH::deleted() {
4833 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4834 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4835 SE->ConstantEvolutionLoopExitValue.erase(PN);
4836 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4837 SE->ValuesAtScopes.erase(I);
4838 SE->Scalars.erase(getValPtr());
4839 // this now dangles!
4842 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4843 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4845 // Forget all the expressions associated with users of the old value,
4846 // so that future queries will recompute the expressions using the new
4848 SmallVector<User *, 16> Worklist;
4849 SmallPtrSet<User *, 8> Visited;
4850 Value *Old = getValPtr();
4851 bool DeleteOld = false;
4852 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4854 Worklist.push_back(*UI);
4855 while (!Worklist.empty()) {
4856 User *U = Worklist.pop_back_val();
4857 // Deleting the Old value will cause this to dangle. Postpone
4858 // that until everything else is done.
4863 if (!Visited.insert(U))
4865 if (PHINode *PN = dyn_cast<PHINode>(U))
4866 SE->ConstantEvolutionLoopExitValue.erase(PN);
4867 if (Instruction *I = dyn_cast<Instruction>(U))
4868 SE->ValuesAtScopes.erase(I);
4869 SE->Scalars.erase(U);
4870 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4872 Worklist.push_back(*UI);
4874 // Delete the Old value if it (indirectly) references itself.
4876 if (PHINode *PN = dyn_cast<PHINode>(Old))
4877 SE->ConstantEvolutionLoopExitValue.erase(PN);
4878 if (Instruction *I = dyn_cast<Instruction>(Old))
4879 SE->ValuesAtScopes.erase(I);
4880 SE->Scalars.erase(Old);
4881 // this now dangles!
4886 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4887 : CallbackVH(V), SE(se) {}
4889 //===----------------------------------------------------------------------===//
4890 // ScalarEvolution Class Implementation
4891 //===----------------------------------------------------------------------===//
4893 ScalarEvolution::ScalarEvolution()
4894 : FunctionPass(&ID) {
4897 bool ScalarEvolution::runOnFunction(Function &F) {
4899 LI = &getAnalysis<LoopInfo>();
4900 TD = getAnalysisIfAvailable<TargetData>();
4904 void ScalarEvolution::releaseMemory() {
4906 BackedgeTakenCounts.clear();
4907 ConstantEvolutionLoopExitValue.clear();
4908 ValuesAtScopes.clear();
4909 UniqueSCEVs.clear();
4910 SCEVAllocator.Reset();
4913 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4914 AU.setPreservesAll();
4915 AU.addRequiredTransitive<LoopInfo>();
4918 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4919 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4922 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4924 // Print all inner loops first
4925 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4926 PrintLoopInfo(OS, SE, *I);
4928 OS << "Loop " << L->getHeader()->getName() << ": ";
4930 SmallVector<BasicBlock*, 8> ExitBlocks;
4931 L->getExitBlocks(ExitBlocks);
4932 if (ExitBlocks.size() != 1)
4933 OS << "<multiple exits> ";
4935 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
4936 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
4938 OS << "Unpredictable backedge-taken count. ";
4942 OS << "Loop " << L->getHeader()->getName() << ": ";
4944 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
4945 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
4947 OS << "Unpredictable max backedge-taken count. ";
4953 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
4954 // ScalarEvolution's implementaiton of the print method is to print
4955 // out SCEV values of all instructions that are interesting. Doing
4956 // this potentially causes it to create new SCEV objects though,
4957 // which technically conflicts with the const qualifier. This isn't
4958 // observable from outside the class though, so casting away the
4959 // const isn't dangerous.
4960 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
4962 OS << "Classifying expressions for: " << F->getName() << "\n";
4963 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
4964 if (isSCEVable(I->getType())) {
4967 const SCEV *SV = SE.getSCEV(&*I);
4970 const Loop *L = LI->getLoopFor((*I).getParent());
4972 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
4979 OS << "\t\t" "Exits: ";
4980 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
4981 if (!ExitValue->isLoopInvariant(L)) {
4982 OS << "<<Unknown>>";
4991 OS << "Determining loop execution counts for: " << F->getName() << "\n";
4992 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
4993 PrintLoopInfo(OS, &SE, *I);
4996 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
4997 raw_os_ostream OS(o);